Chapter 33: Near-Infrared Fluorescence Imaging and ...huynhqlinh/qpys/seminar/Seminar... · 33.2.2...

33Near-Infrared

Fluorescence Imagingand Spectroscopy in

Random Mediaand Tissues

33.1 Introduction33.2 Background: Probing Random Media with Multiply

Scattered LightBeer–Lambert Relation for Absorption and Turbidity Spectroscopy • Fluorescence Spectroscopy and Fluorescence-Lifetime Spectroscopy • Measurement Approaches for Quantitative Spectroscopy and Imaging in Random Media

33.3 Frequency-Domain Photon Migration (FDPM) Measurement ApproachesHeterodyne Mixing for Frequency-Domain Photon Migration • Homodyne Mixing for Frequency-Domain Photon Migration • Homodyne I and Q • Excitation-Light- Rejection Considerations

33.4 Fluorescence Spectroscopy in Random MediaSingle-Exponential-Decay Spectroscopy • Multiexponential-Decay Kinetics

33.5 Fluorescence FDPM for Optical TomographyApproaches to the Inverse-Imaging Problem • Integral Formulation of the Inverse Problem • Differential Formulation of the Inverse Problem • Regularization and Other Approaches to Parameter Updating

33.6 Fluorescent Contrast Agents for Optical TomographyPhotodynamic Therapy Agents • Nontargeting Blood-Pooling Agents • Nontargeting Contrast Agents That “Report” or Sense Environment • Targeting Contrast Agents: Immunophotodiagnosis • Targeting Contrast Agents: Small-Peptide Conjugations • Reporting or Sensing Contrast Agents • Combined Targeting and Reporting Dyes • Summary

33.7 Challenges for NIR Fluorescence-Enhanced Imaging and Tomography

AcknowledgmentsReferences

Eva M. Sevick-MuracaTexas A&M UniversityCollege Station, Texas

Eddy KuwanaTexas A&M UniversityCollege Station, Texas

Anuradha GodavartyTexas A&M UniversityCollege Station, Texas

Jessica P. HoustonTexas A&M UniversityCollege Station, Texas

Alan B. ThompsonTexas A&M UniversityCollege Station, Texas

Ranadhir RoyTexas A&M UniversityCollege Station, Texas

©2003 CRC Press LLC

33.1 Introduction

Most radiation-based spectroscopic and imaging techniques typically depend on evaluation of a non-scattered or singly scattered signal for retrieval of quantitative information. For example, absorptionspectroscopy depends on the survival of unscattered light across a known pathlength, L; dynamic-lightscattering or photon-correlation spectroscopy, because of its scatter by Brownian motion out of theoptical path, requires the fluctuation of light intensity; x-ray and computed x-ray tomography dependon the straight-line path of nonabsorbed x-rays; and so forth. Yet most systems of interest multiply scatterradiation of low energy and require diluted suspensions or nonscattering media when dealing with opticalinterrogation. Hence, optical techniques developed for imaging and spectroscopy are usually plagued byscatter influence. To expand the quantitative applicability of optical techniques to these real systems newtechniques have been developed that focus on coherence properties, temporal and spatial correlation,and other properties; these allow for the extraction of nonscattered or singly scattered light from amultiply scattered signal. Yet these approaches neglect the scattered signal, which is the largest portionof the signal, in favor of that portion that possesses the smallest signal-to-noise ratio (SNR).

In this chapter, we first review continuous-wave and time-resolved techniques along with the associateddiffusion equation for quantitative absorption, scattering, and fluorescence spectroscopy using multiplyscattered light. In addition, since in the wavelength window of 600 to 900 nm light is multiply scatteredby most biological tissues, we then focus on the development of these optical techniques for biomedicalspectroscopy and imaging, i.e., optical tomography. Because of the limitations imposed by endogenouschromophores on tissues in this wavelength regime, we provide a comprehensive review of fluorescence-enhanced optical spectroscopy and imaging methods including measurement methods, solutions toforward- and inverse-imaging problems, and attributes of clinical and sensing fluorophore development.

33.2 Background: Probing Random Media with Multiply Scattered Light

Before presenting the measurement methods and analysis for probing random media with multiplyscattered light, we will first consider traditional light-spectroscopy techniques that depend on monitoringlight transmitted across a known pathlength, L.

33.2.1 Beer–Lambert Relation for Absorption and Turbidity Spectroscopy

Absorption and turbidity measurements consist of monitoring the attenuation of light intensity I(λ) atwavelength λ, given incident-light intensity Io (λ), to determine the absorption or scattering coefficients(µa [cm–1] or µs [cm–1], respectively):

(33.1)

where the absorption coefficient is provided by the product of the concentration of light-absorbingspecies, [Ci] [mM], and its extinction coefficient at wavelength λ, ελ

i [cm–1 mM–1]:

(33.2)

and the scattering coefficient can be predicted from:

(33.3)

log( )

( )( ) ( )

I

IL L

oa s

λλ

µ λ µ λ= − −or

µ λ ελa i

i

N

iC( ) . [ ]==

∑2 3031

µ λ φ λ θ φ θ θπ

si

i

j

ji j i j i j i j j ik

f x

x

f x

xF n x x S x x q dx dx d( )

( ) ( )( , , , , ) ( , , , )sin, ,= ⋅∫ ∫∫

∞∞122

03 3

00


where Fi,j is the binary form factor between the particles with different sizes xi and xj; Si,j is the corre-sponding partial structure factor, which describes the correction factor of coherent scattering due toparticle interactions of particles i and j; n is the relative refractive index of the particles to the medium;λ is wavelength; θ is the scattering angle; φ is the volume fraction of particles in the suspension; f(x) isthe particle-size distribution; and q is the magnitude of the wave vector, q = 2k sin(θ/2), where k is givenby 2πm/λ and m is the refractive index of the medium. The structure factor is a direct measure of thelocal ordering of colloidal particles, and the values of Si,j are equal to unity in the absence of particleinteractions (e.g., in a dilute suspension).

Determination of absorption and scattering coefficients through the Beer–Lambert relationship inEquation 33.1 assumes that light is absorbed or scattered out of the path and that no light scattered isback into the path. Absorption and scattering mechanisms can be considered simultaneously in dilutesuspensions as an effective absorption cross section:

(33.4)

33.2.2 Fluorescence Spectroscopy and Fluorescence-Lifetime Spectroscopy

Fluorescence spectroscopy, whether measured using time-resolved or continuous-wave (CW) techniques,is based on the absorption of excitation light at λx across path length L by fluorophores of concentration[Ci]. Quantum efficiency, α, describes the fraction number of emission photons at fluorescence wavelength λm emitted for each excitation photon absorbed by the fluorophore; it is typically described as therate of radiative decay, Γ, relative to the sum of radiative and nonradiative decay rates (Γ + knr). In otherwords, α = Γ/(Γ + knr). The intensity of detected fluorescence light, Im, in response to a constant intensityof incident excitation light, , can be expressed as:1

(33.5)

Here g(t) represents the time-dependent fluorescence decay that describes the process of radiative andnonradiative relaxation of the activated fluorophore elevated to an excited state by absorption of excitationlight. For most laser dyes the relaxation is a first-order process described by a mean lifetime, τ, of theactivated state. Consequently, the time-invariant emission intensity predicted by Equation 33.5 can berewritten as:

(33.6)

where the fluorescence lifetime, τ, is influenced by the relative rates of radiative and nonradiative decay[i.e., τ = 1/(Γ + knr)].

Ratiometric fluorescent probes, in which re-emission is monitored across two or more wavelengths(such as bis-carboxyethyl carboxyfluorescein [BCECF] or seminaphthofluorescein [SNAFL]), also providea means to monitor changes in decay kinetics using CW methods. The ratio of the emission intensitiesat λm1 and λm2 following excitation at a single excitation wavelength is independent of the concentrationof fluorophore available and depends only on the decay kinetics probed at the two emission wavelengths:

(33.7)

µ µ µeff a s= +

Ioxλ

I I C g t dtm o i ix x∝ [ ]⋅

∞

∫λ λα ε [ ] ( )

0

I I Ct

dt I Cm o i i o i ix x x x∝ [ ]⋅ −

∝ [ ]∞

∫λ λ λ λα ετ

α ε τ[ ] exp [ ]

0

I

I

I C

I Cm m

m m

o i i

o i i

x m x m

x m x m

m

m

m

m

( )

( )

[ ]

[ ]

λλ

α ε τ

α ε ταα

ττ

λ λ λ

λ λ λ

λ

λ

λ

λ

λ

λ

1

2

1 1

2 2

1

2

1

2= [ ]

[ ] = ⋅


In time-domain measurements, where an incident impulse of excitation light is used to excite thesample, the resulting time-dependent emission intensity can be predicted by:

(33.8)

Thus, when a dilute fluorescence sample is excited with an impulse of excitation light and the emissionintensity is monitored as a function of time, the lifetime or decay kinetics that govern the relaxation ofthe activated state to the ground state can be quantitated independently of the concentration of fluoro-phore present. The measurement of the time-dependent emission light following activation in a diluted,nonscattering suspension with an incident impulse of excitation light also serves as the basis of the time-domain measurements described below for random media.

Above, CW and time-domain analyses were presented for fluorophores exhibiting first-order decaykinetics in which the form of the decay kinetics, g(t), is given by:

(33.9)

However, most analyte fluorophores exhibit more complex decay kinetics such as multiexponentialdecays:

(33.10)

or stretched-exponential decay kinetics, which indicates collisional quenching among species j:

(33.11)

By monitoring the time dependence of the emitted fluorescence light as a function of time followingexcitation, the decay kinetics can best be ascertained and correlated with the local environment thatimpacts the relaxation process. For example, the Stern–Volmer equation relates the quencher concentra-tion, [Q], and fluorescence-intensity measurements made in the absence and presence of the quenchers

and Im, respectively:

(33.12)

where K is the Stern–Volmer constant, and kq and τo are the bimolecular quenching constant and thelifetime of the fluorophore in the absence of quencher.

The decay kinetics of many analyte-sensing fluorophores can be used to assess concentrations ofanalytes such as H+ and Ca2+, which may have no appreciable absorption cross section at the emissionand excitation wavelengths used. Consequently, fluorescence-lifetime spectroscopy broadens the appli-cability of absorption spectroscopy, provided a fluorophore with analyte-sensitive decay kinetics can beidentified.

While time-dependent techniques are the best way to assess fluorescence-decay kinetics, their need forDirac pulses of excitation light complicates instrumentation and limits quantitation. Frequency-domainapproaches provide an alternative approach to the impulse function by exciting with an intensity-modulatedexcitation light modulated at MHz–GHz modulation frequencies, ω. Activation of the fluorophore creates

I t I Ct

dtm o i i

t

x x( ) ( ) [ ] exp∝ [ ]⋅ − ′

′∫λ λδ α ετ

0

g tt

( ) exp( )= −τ

g t at

jjj

N

( ) exp= −

=

∑ τ1

g t a t tj j j

j

N

( ) exp= − ⋅ −[ ]=

∑ α β1

Imo

I

IK Q k Qm

o

mq o= + = + ( )1 1[ ] [ ]τ


isotropic, intensity-modulated fluorescent light that is both phase delayed and amplitude attenuatedrelative to the incident light owing to the kinetics of the relaxation process. For a simple, first-ordersystem the decay kinetics, the phase delay, θ(ω), and the modulation ratio, M(ω), at modulation frequencyω can be predicted from:

(33.13)

where the amplitude and average of the modulated emission light is given by IAC(ω) and IDC(ω). In dilute,nonscattering media, the fluorescent emission is collected at right angles to the excitation illuminationto avoid inadvertently collecting excitation light.

It has been proposed that absorption and scattering spectroscopy employing the Beer–Lambert rela-tionship as well as the CW, time-domain, and frequency-domain fluorescence-spectroscopy approachesfor quantitative spectroscopy when scattered back into the optical path do not corrupt attenuation orintensity measurements. However, most systems are comprised of random media, i.e., those that absorb,multiply scatter, and fluoresce. The techniques of CW, time and frequency domain, and associatedapproaches to performing quantitative spectroscopy and imaging in random media are outlined in thenext section.

33.2.3 Measurement Approaches for Quantitative Spectroscopy and Imaging in Random Media

Here we restrict our discussion to quantitative spectroscopy and imaging in random media in which thediffusion approximation to the radiative transport equation holds. The conditions are (1) the source ofincident (excitation) light is isotropic; (2) the scattering capacity of the tissue exceeds that of its absorptioncapacity, i.e., µa << (1 – g)µs, where g is the mean cosine of angular scatter of the medium; and (3) thelight that is collected has been multiply scattered. When referring to measurements of multiply scatteredlight, i.e., light that has traveled a distribution of pathlengths or “times of flight,” we term them photon-migration measurements.

33.2.3.1 CW and Time-Resolved-Measurement Approaches

CW measurements employ a light source whose intensity nominally does not vary with time. The constant-power, isotropic source illuminates the random medium with light whose intensity becomes exponentiallyattenuated with increasing distance from the tissue surface. Increased absorption or scattering propertiesof the medium result in increased light attenuation as the light propagates deeper into the random medium.In CW measurements, the time-invariant intensity is measured as a function of distance from the incidentsource and is primarily a function of the product µaµs′ or µaµs(1 – g). The amount of generated fluorescentlight at any position is proportional to the product of the concentration of fluorophore, [Ci], and thelocal excitation fluence, Φx(r), which is the concentration of excitation photons times the speed of lightwithin the medium. Thus, the origin of emission light predominates from the region in which the excitationfluence, Φx, is greatest. For time-invariant CW measurements, the region with the greatest excitation fluencealways remains close to the point of incident-excitation illumination. Consequently, the origin of fluores-cence is mainly from the surface or subsurface regions. For determination of fluorescent optical propertiesin a uniform medium with CW techniques, fluorescence spectroscopy may not be impacted by the con-finement of the origin of emission light if the random medium is indeed homogeneous. However, in imagingscenarios where concentration of fluorophore is nonuniform, CW techniques will undoubtedly emphasizesurface and subsurface regions. In imaging cases where the fluorescent dye acts as a contrast agent and has“perfect uptake,” (i.e., partitioning of the dye occurs exclusively in the tissue of interest without any residual

M i g t i t dtt

i t dt

MI

IAC

DC

a

( )exp( ( )) ( )exp exp exp

( )( )

( ) ( ); ( ) tan

ω θ ω ωτ

ω

ωωω

µ α

ωτθ ω ωτ

− = −[ ] = −

−[ ]

= =+

= [ ]

∞ ∞

−

∫ ∫0 0

2

1

1

r


dye in the intervening tissues between the target and the surface), then CW techniques may be appropriate.However, the elusive “holy grail” of contrast-based imaging for all medical-imaging modalities is to developagents that maximize their partitioning in the target region of interest. Near-infrared (NIR) techniquesinvolving fluorescent contrast agents for clinical imaging will likely not involve CW measurement despitethe simplicity of its instrumentation.

Time-domain photon-migration (TDPM) measurements employ a light source that delivers a pulseof excitation light that broadens and attenuates as it propagates through the random medium, as shownin Figure 33.1. TDPM techniques employ single-photon counting (sometimes called time-correlatedcounting) or gated integration measurements to acquire the emitted pulse broadened by as much as

FIGURE 33.1 Schematic of time-domain photon-migration (TDPM) measurement approach used in NIR opticalspectroscopy and tomography. TDPM imaging approaches use an incident impulse of light that results in thepropagation of the pulse, which attenuates as a function of distance from the source and time following its delivery.The detected pulse is measured as intensity vs. time, which represents the photon “time of flight.” Panel (A) illustratesthe light distribution in tissue from a pulse point source after 1 × 10–10 s, (B) 25 × 10–10 s, and (C) 150 × 10–10 sfollowing the incident impulse. The corresponding recorded data during the time intervals at the detector areillustrated in panels (D) through (F). A time-gated illumination measurement is shown in panel (F) in which theintegrated intensity measured within a specified window is measured. (From Hawrysz, D.J. and Sevick-Muraca, E.M.,Neoplasia, 2(5), 388, 2000. With permission.)

Pulsed SourceDetector

SourcePulse

Inte

nsity

DetectedLight

Inte

nsity


Inte

nsity

Time (10−10 s)

Time (10−10 s)

Time (10−10 s)

∆tTime-gated

Measurement


A

B

C

D

E

F


several nanoseconds of photon time of flight. As the absorption properties of the random media increase,the broadening of the excitation pulse lessens and greater attenuation occurs. In the case of increasedscattering properties, the excitation pulse increasingly broadens and attenuates during its propagationaway from the incident point source. Clearly the impact of absorption and scattering has differing effectson the photon time of flight: increased absorption decreases the path and travel time of migratingphotons, while increased scattering enhances it. When fluorophores are excited within the randommedium, a propagating excitation pulse generates a propagating emission pulse that is further broadenedowing to the decay kinetics of the dye.

Since the region of highest excitation fluence is not stationary and propagates away from its incidencewith time following delivery to the surface, the origin of fluorescent signals activated by the propagatingexcitation pulse may not be restricted to surface or subsurface tissues as in the case of CW measurements.If the time constant of the dye’s decay kinetics is less than or comparable to the detected excitation photontime of flight, then the fluorescence measured at a distance away from the incident excitation source mayoriginate deeply within the random medium. On the other hand, if the time constant of the dye’s decaykinetics is greater than the detected excitation photon times of flight, then the fluorescence will originatefrom shallow locations within the random medium.2

The phenomenon can be explained by the fact that at the medium surface, the position of maximumexcitation fluence travels from its point of incidence to deep within the medium and exponentiallyattenuates as it penetrates. Consider a fluorophore that has an instantaneous rate of radiative relaxation.The maximum emission fluence will likewise follow the trend of the propagating excitation pulse: at timet = 0 when the excitation pulse is launched, the emission fluence will be greatest at the point of incidence,and as time progresses the point of greatest emission fluence will propagate into the medium, attenuatingas it does so. The emission light that reaches the surface will initially originate from regions closest tothe incident source and then from deeper within the random medium with increased time after the initialimpulse of excitation light. However, in the case of a phosphorescent agent with a slow radiative relaxationrate and an effective lifetime on the order of milliseconds (much larger that the measured photon-migration times of flight), the greatest concentration of activated fluorophore will reside close to theincident point of excitation illumination; while the pulse of excitation fluence transits deeper within therandom medium, the slow decay of the activated fluorophore closest to the point of incident of excitationwill result in a pulse of emission fluence that does not propagate spatially with time into the randommedium and away from the point of the incident-excitation illumination. Consequently, for imaging andspectroscopic-imaging applications where information from within the random medium is desired, long-lived fluorophores cannot be employed.

The qualitative CW and TDPM measurements for fluorescence spectroscopy and imaging are describedabove. Quantitative prediction is also possible with the radiative transport equation, Monte Carlo, anddiffusion equations, provided the proper model for fluorescent decay is incorporated. Here we restrictour analysis to media in which the diffusion approximation to the radiative-transfer equation applies.The photon-diffusion equation may be written to predict CW and TDPM measurements of excitation(subscript x) and emission (subscript m) fluence, and , respectively:3,4

(33.14)

where Dx,m is the optical-diffusion coefficient at the excitation or emission wavelength in centimeters[cm] given by:

(33.15)

and is the isotroptic scattering coefficient given by (1 – g)µsx,m. The excitation or emission fluence,

[W/m2], is the angle-integrated scalar flux of photons and is defined as the power incident on an

Φx m r, ( )r

Φx m r t, ( , )r

r r r vv

v∇⋅ ∇( ) − =∂

∂−D r t r t

c

r t

tS r tx m x m a x m x m

x mx m, , , ,

,,( , ) ( , )

( , )( , )Φ Φ

Φµ 1

Dx ma sx m x m

, [ ], ,

=+ ′µ

1

3 µ

′µsx m,

Φx m r t, ( , )r


infinitesimally small sphere divided by its area. Again, it can also be thought of as the local concentration ofphotons times the speed of light, c, at a given position and (for time-dependent cases) at time t. Forcontinuous-wave spectroscopy or imaging there is no time dependence, and the source term, becomes time invariant. Assuming the source is isotropic, this term is equivalent to the power depositedover its area. For TDPM measurements the source, is assumed to be a Dirac delta function,assuming a finite value at time zero, but zero at all other times. For both CW and TDPM measurementsEquation 33.14 can be solved to predict the excitation fluence, , in response to the knownspatial distribution of absorption and scattering properties, , of the media volume atthe excitation wavelength. Here the absorption coefficient at the excitation wavelength is comprised ofcontributions from the endogenous chromophores ( ) as well as the exogenous fluorophores( ).

Since a closed-form solution for exists only for simple geometries such as infinite and semi-infinite media of uniform optical properties, the solutions are otherwise developed numerically usingfinite-difference or finite-element methods.

Of the three boundary conditions commonly used, the partial-current condition is the most rigorous.5,6

It states that a photon leaving a tissue never returns and uses a reflectance parameter to account forFresnel reflection at the tissue–air surface. If the boundary condition is perfectly transmitting (therebyexhibiting no Fresnel reflection), then the fluence evaluated at the boundary must fall to zero, creatinga discontinuity that violates the diffusion approximation that assumes isotropic radiance. When theFresnel reflection is considered at the boundary, this violation is eased by modeling a portion of thephotons to be reflected back into the medium. The partial-current-boundary condition can be expressedin terms of the fluence and its gradient normal to the boundary:

(33.16)

where Reff is the effective reflection coefficient whose quantity predicts the amount of light reflection anddegree of anisotropy at the boundary.

A slightly simpler condition, the extrapolated-boundary condition, is an approximation of the partial-current condition and yields solutions similar to those of the diffusion equation.7,8 In this case, the fluenceis set to zero at an extrapolated boundary located at a specified distance outside the medium to accountfor Fresnel reflection at the surface.

The third boundary condition, the zero condition, merely sets the fluence to zero on the boundaryand is used for its simplicity. In a homogeneous scattering medium, the zero-boundary condition resultsin an analytical solution to the diffusion equation in terms of the absorption and scattering coefficients.8,9

The measured flux or photon current in CW or TDPM measurements, or , is thendetermined by the gradient of fluence, and , at the surface (also known as Fick’s law):

(33.17)

As a result of combining Fick’s law and the partial-current- or extrapolated-boundary conditions, themeasured flux or photon density is simply proportional to the fluence at the surface.

Since red light multiply scatters as it transits tissues, it can excite exogenous fluorescent agents that,in turn, act as uniformly distributed sources of fluorescent light. The fluence at the emission wavelength,

or , is generated and propagates within the multiply scattering medium; it can also bedescribed by Equation 33.14, provided that its source-emission kinetics are properly modeled in thesource term, or The isotropic scattering coefficient at the emission wavelength, , maybe considered to be different than that at the excitation wavelength. The absorption coefficient at theemission wavelength, , is due to both endogenous chromophores and, if reabsorption of theemission light from the fluorophore occurs, the reabsorption of fluorescent light by the exogenous agent.While including secondary reabsorption and photobleaching effects is relatively straightforward, when

vr

S r tx( , ),r

S rx( , )v

0

Φ Φx xr r t( ) ( , )v v

orµa x sr r

x( ) ( )v v

and ′µ

µaxr

→( )r

µax mr

→( )r

Φx r t( , )r

Φ Φx m

eff

effx m n x mr t

R

RD r tx m

x m

, , ,( , ) ( , ),

,

r r r= ⋅

+

−⋅ ∇2

1

1

J rx m, ( )r

J r tx m, ( , )r

r r∇Φx m r, ( )

r r∇Φx m r t, ( , )

J r t D r tx m x m x m, , ,( , ) ( , )r v r

= − ∇Φ

Φm r( )r

Φm r t( , )r

S rm( )r

S r tm( , ).r

′µsm

µamr( )r


the excitation and emission spectra are well separated and the fluorophore is in dilute concentrations,we neglect this contribution to absorption at the emission wavelength. The general form for the emissionsource, , is:

(33.18)

where , α, and Ξm are, respectively, excitation photon density, quantum efficiency of the fluoro-phore, and the detection efficiency factor of the system at the emission wavelength (which contains thesystem-spectral response and the fluorophore spectral-emission efficiency10). The time-invariant sourceof CW measurements, , is described by Equation 33.18, with the upper limit of the time integralequal to infinity. The source of emission light from a mixture of fluorophores undergoing various decaykinetics is simply a combination of the above expressions.

If the solution for the excitation fluence, or , is first obtained, and the decay kineticsand optical properties at the emission wavelength are known, the emission fluence, or ,can then be solved using one of the three commonly used boundary conditions described above. Themeasured flux or photon current in CW or TDPM measurements is then determined from the gradientof the emission fluence.

While CW measurements can be limited in information content regarding decay kinetics and spatialdiscrimination, TDPM measurements are tedious in that they require an incident Dirac pulse or convo-lution/deconvolution of the pulse, suffer from low SNR, and mathematically require the solution of anintegral-differential equation for spectroscopy and imaging applications. Indeed, the large dynamic rangeof SNR over the entire distribution of photon times of flight in TDPM approaches can require significantdata-acquisition times to resolve or reduce uncertainty in the resulting images. However, some developersprefer to employ TDPM measurements to construct optical property maps since their information contentis the richest.11 Frequency-domain approaches sidestep these issues with the use of an easily achievablesinusoidally modulated light source, measurements possessing high SNR, and, as shown in the next section,a more tractable set of equations for solution of the spectroscopy and imaging-inverse problems.

33.2.3.2 Frequency-Domain Measurement Approaches

Frequency-domain measurements in random media are similar to those described in the previous section.An intensity-modulated point source of excitation light is launched into a scattering medium, and thepropagating “photon-density wave” is attenuated and phase delayed relative to the incident source as itpropagates through the random medium, as shown in Figure 33.2. The detected phase delay and ampli-tude attenuation measured at the excitation wavelength can be used to determine the optical propertiesof the random medium, whether they are uniform (for solution of the inverse-spectroscopy problem)or nonuniform (for solution of the inverse-imaging problem). The diffusion equation for solution of theforward problem of predicting measurements also applies, with the difference that the equation is castin the frequency domain rather than in the time domain:

(33.19)

Here the fluence, , is now a complex number describing the characteristics of the photon-density wave at position and modulated at angular frequency ω. Moreover, the fluence is comprisedof alternating, and nonalternating, components, of which the former providesan accurate description of the phase delay, and amplitude, , of the wave at position :

(33.20)

S r tm( , )r

S r t r r t g t dtm a m x

t

x m( , ) ( ) ( , ) ( )r r r

= µ ∫ ′ ⋅ ′ ′→

αΞ Φ0

Φx r t( , )r

S rm( )r

Φx r( )r

Φx r t( , )r

Φm r( )r

Φm r t( , )r

r r r r∇⋅ ∇( ) − +

+ =→D ri

cr S rx m x m a x m x m x m, , , ,( , ) ( , ) ( , )Φ Φω µ ω ω ω 0

Φx m r, ( , )v ωvr

ΦACx mr

,( , ),v ω ΦDCx m

r,

( , ),v

0θx m, , IACx m,

vr

Φ Φ Φx m ACx m DCx m

ACx m x m DCx m

r r r

I i I r

, , ,

, , ,

( , ) ( , ) ( , )

exp( ) ( , )

r r r

r

ω ω

θ

= +

= +

0

0


The nonalternating component of the fluence, is simply the fluence that is measuredwhen using a CW source (ω = 0). The pre-exponential factor, , is the amplitude of the photon-density wave, and θx,m, is the phase delay of the wave relative to the incident source. At larger modulationfrequencies the photon-density wave attenuates more rapidly during its propagation and experiencesgreater phase lag. Consequently, the amplitude decreases with increasing modulation frequency, whilethe phase delay increases with modulation frequency. Often the amplitude or modulation ratio is reportedas a measurement. The modulation ratio is simply the amplitude of the wave normalized by

For the solution of the excitation fluence via Equation 33.19 the source function is either a point source(as shown in Figure 33.2) or a plane source of modulated light:

(33.21)

FIGURE 33.2 Schematic of the frequency-domain photon-migration (FDPM) measurements used in NIR opticalspectroscopy and tomography. FDPM traditionally consists of an incident, intensity-modulated light source thatcreates a “photon-density wave” that spherically propagates continuously throughout the tissue. Panel (A) showslight distribution in tissue due to a modulated source (exaggerated for purposes of illustration), and panel (B)illustrates the detected signal (solid line) in response to the source illumination (dotted line). The typical frequencydomain data, where the measurable quantities are the phase shift θ, the amplitude of each wave IAC, and the averagevalue IDC of intensity. As shown in (B), the intensity wave that is detected some distance away from the source isamplitude-attenuated and phase-delayed relative to the source. (From Hawrysz, D.J. and Sevick-Muraca, E.M.,Neoplasia, 2(5), 388, 2000. With permission.)

0

0.5

1

1.5

2

2.5

0.E + 00

1.E − 06

2.E − 06

3.E − 06

4.E − 06

5.E − 06

6.E − 06

7.E − 06

8.E − 06

Sou

rce

Inte

nsity

Det

ecte

d In

tens

ity

Time (ns)

B

Detector

Modulated Source

A

Source

Detector

DCs DCd

PS

ACs

ACd

ΦDCx mr

,( , ),v

0IACx m,

I rDCx m,( , ).r

0

S r S r i rx s s s( , ) ( , )exp( ( , ))r r r

ω ω θ ω=


where the strength (or amplitude) of the excitation source at its position of incidence, , is , andits absolute phase is . Typically, frequency-domain photon-migration (FDPM) measurements areconducted between a point source of illumination, and the amplitude and the phase of the detected light(also collected at a point) is determined relative to the source. Consequently, in most cases in the literature,the source strength is designated as unity, and the phase of the incident source is taken as zero. Asdescribed in the next section, emission fluence in response to incident-planar-wave excitation can beemployed and predicted by the diffusion equation, provided that the spatial phase, , and ampli-tude, , of the source are properly accounted for.12

The boundary conditions for frequency-domain measurements in random media are identical to thosedescribed above for CW and TDPM techniques, and the partial-current-boundary condition is similarlywritten:

(33.22)

The measured flux or photon current in frequency-domain measurements, , is then deter-mined by Fick’s law:

(33.23)

The result of combining Fick’s law and the partial-current- or extrapolated-boundary conditions isthat the measured flux or photon density of the wave (now a complex number) is simply proportionalto the fluence at the surface. Consequently, the measured phase, , and amplitude, , are predictedfrom the fluence,

As with CW and TDPM methods, the radiative relaxation of the activated fluorophore serves as adistributed source of emission light within the random medium. The emission source, , forsingle-exponential-decay kinetics is:

(33.24)

and for any arbitrary-decay kinetics expressed by g(t), the source term can be generally derived from:

(33.25)

The solution of Equation 33.19 describes the propagation of excitation light; from this the excitationfluence, , can be directly obtained and used as input for the source term to solve Equation 33.19for the emission fluence, .13 Thus, the solution of the coupled equations with the specifiedboundary conditions, the phase and amplitude of the detected emission wave relative to the incidentexcitation source, can be directly determined.

As with TDPM measurements, the ability to use fluorescence to interrogate random media is affordedby FDPM measurements when the lifetime of the fluorescent agent is small when compared to the photontime-of-flights. As with TDPM approaches, effective contrasts for FDPM approaches are limited tofluorescence rather than phosphorescent or long-lived compounds. This was demonstrated in the Photon-Migration Laboratory (PML) by comparing FDPM contrast offered by tris (2,2′-bipyridyl) dichloro-ruthenium (II) Ru(bpy)3

2+ with a lifetime of 600 ns and ICG with a lifetime of 0.56 ns. In this case, theFDPM contrast was defined as the change in the phase and amplitude of the emission light as the positionof the target changed relative to the position of the point of excitation illumination and emission detection.Using a single target with 100-fold greater concentration than the background in a phantom (see Figure 33.3for measurement geometry of the phantom), the phase and amplitude modulation contrast at each of the

rrs S rs( , )

rω

θ ωs sr( , )r

θ ωs sr( , )r

S rs( , )r

ω

Φ Φx m

eff

effx m n x mr

R

RD rx m

x m

, , ,( , ) ( , ),

,

r r rω ω= ⋅

+

−⋅ ∇2

1

1

J rx m, ( , )r

ω

J r D rx m x m x m, , ,( , ) ( , )r v r

ω ω= − ∇Φ

θx m, IACx m,

ΦACx m ACx m x mI i, , ,exp( ).= θ

S rm( , )r

ω

S ri

rm a x mx m( , ) ( , )r r

ω µωτ

ω α=−

→

1

1Φ Ξ

S r r g t e dtm a x mi t

x m( , ) ( , ) ( ) ( )r r

ω µ ω α ω= ∫→

∞

Φ Ξ

0

Φx r( , )r

ωΦm r( , )

rω


detectors could be seen when ICG was used (Figure 33.4A); however, no contrast was measured whenruthenium dye, Ru(bpy)3

2+, was used as the contrast agent (Figure 33.4B). These results confirm compu-tational predictions that effective contrast agents must possess shorter lifetimes than the time of flightof photon propagation.14

Consequently, in order to develop fluorescence-lifetime spectroscopy and imaging techniques, the timedependence of the photon-migration process must be accounted for in order to obtain lifetime information.Whether imaging or spectroscopy is used, the inverse problem becomes one of separating photon migrationfrom fluorescence-decay kinetics. Some investigators have sought to avoid the problem by employing phos-phorescent dyes wherein the photon migration times of flight of picoseconds to nanoseconds are insignificantcompared to lifetimes on the order of micro- to milliseconds. Nonetheless, time-dependent emission mea-surements will be unable to interrogate beyond the surfaces or subsurfaces when long-lived dyes are employed.When used as contrast agents for imaging, these long-lived dyes do have utility, but only if their partitioningwithin the target is perfect and there is no residual dye in the background.

Finally, since the amplitude of the detected fluorescence, , is insensitive to the intensity due to theambient light, the frequency-domain approach has clear advantages for application in environments that arenot light tight. In addition, since frequency-domain approaches offer steady-state measurement of a time-dependent light-propagation process, they have comparatively high SNRs with respect to time-domainapproaches and retain lifetime-dependent signals, which is otherwise missing in CW measurements. Due tothe ease of instrumentation of frequency-domain over time-domain approaches, and due to the superiorinformation of time-dependent techniques over CW measurements, the remainder of this chapter will focuson FDPM measurements, but studies conducted using CW and TDPM techniques will be cited.

33.3 Frequency-Domain Photon Migration (FDPM) Measurement Approaches

Two approaches have been employed in spectroscopy and imaging of random media: (1) point detectionand point illumination and (2) area detection and area illumination. Point-detection schemes typicallyemploy heterodyne or I and Q mixing techniques, which employ signal mixing at the photodetectorfollowing point detection to extract signals of phase and amplitude modulation at a single point. Toconduct FDPM measurements among a number of sources and detectors, either scanning of the source/detector or transmitter/receiver pair or replication of the receiver/transmitter circuitry is required. Con-sequently, this restricts FDPM imaging and spectroscopy to sparse data sets for solving the inverse-spectroscopy and imaging problems. While sufficient for solving the problem of inverse spectroscopy (asdiscussed in Section 33.4), point illumination and point detection provide sparse sets for optical tomog-raphy or solution of the inverse-imaging problem (as discussed in Section 33.5). The use of an incidentpoint of excitation light delivered by a fiber optic requires a number of measurements as its position isscanned or replicated along the surface for imaging purposes (Figure 33.5).15 Since excitation fluence

FIGURE 33.3 Schematic of the phantom tests showing the change in emission-phase measurements as a fluorescentand phosphorescently tagged, 10-mm-diameter target was moved from the periphery toward the center of a 100-mm-diameter cylindrical vessel.

source1 12

6

34

5

2

78

910

11

pointdetectors

IACm


FIGURE 33.4 The phase contrast in degrees (determined from the phase measured in the presence and absence ofa target) measured at the emission light for a 100:1 target-to-background ratio for (A) phosphorescent dye withlifetime of 1 ms and (B) fluorescent dye with lifetime of 1 ns. The phase contrast is predicted from simulation of thetarget moving from the perimeter (10 mm) toward the center (50 mm) of a 10-cm-diameter cylinder under conditionsof maximum phase contrast, i.e., ωτ = 1 and uniform lifetime. The detectors are located around half of the perimeterof the cylinder, as described in Figure 33.3.

80

60

40

20

0

−200 2 4 6

Detector

A

8 10 12

10 mm20 mm30 mm40 mm50 mm

10

5

0

−5

−100 2 4 6

DetectorB

8 10 12

10 mm

20 mm30 mm

40 mm

50 mm


attenuates rapidly, each point-source illumination will not necessarily probe significant volumes and may“miss” the fluorescent target region of interest. Consequently, a high density of measurements is typicallyrequired for a relatively confined volume for imaging purposes, and area-illumination and area-detectionschemes may become pertinent for imaging. However, for optical-tomography work employing endog-enous contrast, measurement geometries are necessarily restricted to point illumination and point detec-tion. The general principles of frequency-domain measurements of fluorescence in random media usingheterodyne point measurements and homodyning area measurements, challenges for fluorescence spec-troscopy and imaging in random media, and, finally, measurements geometries are discussed below.

33.3.1 Heterodyne Mixing for Frequency-Domain Photon Migration

Point-illumination and point-detection measurements are most common because of their prevalence infrequency-domain spectrometers for measurement of decay kinetics in nonscattering diluted samples.For imaging systems the point-source and point-detection schemes and tomographic approaches aredeveloped exclusively for this geometry. The heterodyned point-illumination and point-detection mea-surements consist of three parts: (1) the modulated source; (2) the detector, which may also act as themixer; and (3) the electronics to accomplish mixing. A schematic of the system is illustrated in Figure 33.6.

The modulated source can be either a coherent light source that is externally modulated via an electro-optic modulator, a laser diode modulated by use of a radio frequency (RF) signal via a bias tee, or, whichis more complicated, a pulsed source with a constant and known pulse-repetition rate. A master oscillatordrives the source, which is focused to illuminate a point on the surface of the random medium or coupledto the surface through the use of fiber optics. Modulation frequencies are typically on the order of 30 to500 MHz. A fast detector — i.e., silicon photodiode, avalanche photodiode, or fast photomultiplier —is required to detect the amplitude and phase delay of the detected photon-density wave at excitationand emission wavelengths. To acquire the signal for standard data acquisition, the signal, L, of frequencyω is “mixed down” to a more manageable frequency, ∆ω, by mixing with another signal of frequency,ω + ∆ω. For example, the mixing can be accomplished through direct-gain modulation of the photo-multiplier tube or at a mixer, which receives the photomultiplier signal. (Figure 33.7). Consider the signal

FIGURE 33.5 Illustration of different geometries for illumination of deep tissues. (A) Single-point source of exci-tation-light delivery. (B) Multiple-point sources, which in the extreme of high density of simultaneous sources isrepresentative of (C). (C) Planar source of excitation light with illumination spread over an area of the tissue surface.

C Planar source

A

Single-point source

B Multiple-point sources

Tissue surface


representing the detected light, L, which has propagated to a position and experienced phase delay θ andhas amplitude LAC and average signal LDC.

(33.26)

Assume the signal G generated by a slave oscillator is in phase with the master oscillator (i.e., there isno phase delay relative to the incident light) and has amplitude GAC and average signal level GDC.

(33.27)

where θinst represents the phase delay introduced into the signal due to instrumentation rather than lightpropagation. Upon mixing the signals, one obtains S, which consists of high- (2ω + ∆ω, ω + ∆ω, ω) andlow-frequency (∆ω) components:

(33.28)

FIGURE 33.6 Schematic of heterodyned FDPM system that consists of three parts: (A) the modulated source (shownas laser diode), (B) the detector (PMT), which also acts as the mixer, and (C) the data-acquisition hardware andsoftware to accomplish mixing.

FIGURE 33.7 Schematic of mixer for heterodyne and homodyne detection of and θx,m for FDPM.

BeamSplitter

Laser diode SamplePMT

DataAcquisitionReference

PMT

ScatteringSolution

PhaseLock

A B C

FrequencySynthesizer

FrequencySynthesizer

G

SLmixer

IACx m,

L L L tDC AC= + ⋅ +[ ]cos ω θ

G G G tDC AC inst= + ⋅ +( ) +[ ]cos ω ω θ∆

S L G

S L G L G t

G L t

L Gt

L Gt

DC DC DC AC inst

DC AC

AC ACinst

AC ACinst

= ×

= ⋅ + ⋅ ⋅ +( ) +[ ]+ ⋅ ⋅ +[ ]

+⋅

⋅ − +[ ]

+⋅

⋅ +( ) + +[ ]

cos

cos

cos

cos

ω ω θ

ω θ

ω θ θ

ω ω θ θ

∆

∆

∆

2

22


When the mixed signal is filtered with a low-bandpass filter, the final detected signal is:

(33.29)

whereby the information of signal L is preserved in the low-frequency signal, where ∆ω is typically inthe hundreds of hertz or kilohertz. Following subtraction of the average of the signal, LDC ⋅ GDC, Fourieranalysis of the mixed signal at frequency ∆ω yields the phase information, [–θ + θinst], as well as theproduct of LAC · GAC. To solve the inverse spectroscopy or imaging problem, accurate assessment of LAC

and θ must be determined using a referencing approach to eliminate θinst, GAC, and GDC.When using external-cavity or laser-diode modulation, the modulation frequencies can be swept

continuously, providing a frequency spectrum of Φx,m(ω) or θx,m(ω) and However, in the caseof a pulsed light source, such as a Ti:sapphire picosecond or femtosecond laser, the master oscillator isset by the length of the laser cavity, which sets the laser repetition rate, 1/ω, and the signal G is sweptacross the harmonics of the laser-repetition frequency plus a small offset, nω + ∆ω, n = 1, 2, … . Thus,pulsed sources provide a frequency spectrum of Φx,m(nω) or θx,m(nω) and where n = 1, 2, … .See Reference 16 for more information about frequency-domain measurements with pulsed laser sources.

33.3.2 Homodyne Mixing for Frequency-Domain Photon Migration

The homodyne approach is similar to the heterodyne approach described above except that the signal,L, of frequency ω is mixed down to DC signal through mixing with another signal of identical frequency.Consider the signal G generated by the master oscillator with an introduced phase delay, η, with amplitudeGAC and average signal level GDC:

(33.30)

where θinst represents the phase delay introduced into the signal due to instrumentation rather than lightpropagation.

The mixing of signals L and G produces S, which consists of a high-frequency component (2ω, ω)and a DC component:

(33.31)

When the mixed signal is filtered with a low-bandpass filter, the final detected DC signal is:

(33.32)

When the phase delay η is changed by known values, it is possible to evaluate

and, by proper referencing, determine those quantities that define signal L and the light

propagation within the random medium.

S L GL G

tDC DCAC AC

inst= ⋅ +⋅

− +[ ]2

cos ∆ω θ θ

IACx m,( ).ω

I nACx m,( )ω

G G G tDC AC inst= + ⋅ ( ) + +[ ]cos ω θ η

S L G

S L G L G t

G L t

L G

L Gt

DC DC DC AC inst

DC AC

AC ACinst

AC ACinst

= ×

= ⋅ + ⋅ ⋅ ( ) + +[ ]+ ⋅ ⋅ +[ ]

+⋅

⋅ − + +[ ]

+⋅

⋅ ( ) + + +[ ]

cos

cos

cos

cos

ω θ η

ω θ

θ θ η

ω θ θ η

2

22

S L GL G

DC DCAC AC

inst= ⋅ +⋅

− + +[ ]2

cos θ θ η

L GL G

DC DCAC AC⋅

⋅, ,

2

− +[ ]θ θinst


Because image intensifiers used in area-detection schemes have slow response times, the homodyneapproach is typically used. Figure 33.8 illustrates the image-intensified charge-coupled device (ICCD)homodyne FDPM system consisting of three major components: (1) a CCD camera, which houses amultipixel array of photosensitive detectors; (2) a gain-modulated image intensifier, which acts as themixer (see below); and (3) oscillators that sinusoidally modulate the laser-diode light source and theimage intensifier’s photocathode gain at the same frequency, ω. A 10-MHz reference signal between theoscillators ensures that they operate at the same frequency with a constant phase difference. Emitted lightfrom the tissue or phantom surface is imaged via a lens onto the photocathode of the image intensifier.As before, the light (L) that reaches the photocathode of the image intensifier has a phase delay, θ(r),average intensity, LDC(r), and amplitude intensity, LAC(r), that may vary as a function of position on thesample and, consequently, across the photocathode face.

The gain of the image intensifier has an average, GDC, a possible phase delay due to the instrumentresponse time, θinst, and an amplitude, GAC, at the modulation frequency. The modulated gain is accom-plished by modulating the potential between the photocathode, which converts the NIR photons intoelectrons, and the multichannel plate (MCP), which multiplies the electrons before they are focused ontothe phosphor screen (Figure 33.9). The resulting signal at the phosphor screen is a mixed homodynesignal (S) containing all the amplitude, DC, and phase information of the optical signal collected by thedetector. Yet since the phosphor screen has response times on the order of submilliseconds, it acts as alow-pass filter so that the image transferred to the CCD camera is simply the homodyne signal representedin Equation 33.32. The time-invariant but phase-sensitive image on the phosphor screen is then imagedonto the CCD using a lens or fiber coupling.12,17–19

Rapid multipixel FDPM data acquisition proceeds as follows. The phase of the photocathode modu-lation is stepped, or delayed, at regular intervals between 0 and 360° relative to the phase of the laser-diode modulation. At each phase delay ηd, the CCD camera acquires a phase-sensitive image for a givenexposure time (see Figure 33.10), which is on the order of milliseconds. A computer program thenarranges the phase-sensitive images in the order acquired and performs a fast Fourier transform (FFT)to calculate modulation amplitude, IAC, and phase, θ, at each CCD pixel (i,j) using the following rela-tionships:

FIGURE 33.8 Schematic of ICCD homodyne FDPM system in the Photon-Migration Laboratory (PML).

laserDC bias

laser diode

oscillator

10 MHzfreq. ref.

oscillator

RFamplifier

intensifierDC bias

105 mmAF lens

CCD camera

50 mmAF lens

intensifier

sin[(2π · w)t ]

sin[(2π · ω)t + hd ]

introduce phase delay hd

tissuephantom


(33.33)

(33.34)

I(f) is the Fourier transform of the phase-sensitive intensity data and I(ηd). IMAG[I(fmax)] andREAL[I(fmax)] symbolize, respectively, the imaginary and real components in the digital-frequency spec-trum that best describe the sinusoidal data. N relates the number of phase delays between the gainmodulation of the image intensifier and the incident-light source.

Area illumination is accomplished simply by expanding a modulated laser-diode beam onto the surfaceof the phantom or tissue to be imaged. To date there has been no attempt to use area illumination andarea detection for tomographic reconstructions because all formulations are based on the propagationof light from a point-excitation source to a point on the medium’s surface. Yet despite its current lack ofacceptance by the tomographic community (see Section 33.5), planar-wave illumination is by far themost common means of illuminating photodynamic therapy (PDT) agents for assessing therapeutic drugdistribution and providing excitation for assessing diagnostic fluorochrome distribution in s.c. tumor-bearing rodents. Typically, CW light from a xenon or tungsten lamp, laser, or laser diode is expanded to

FIGURE 33.9 Schematic of the image-intensifier circuit and system used in the homodyne ICCD system. (FromThompson, A.B. and Sevick-Muraca, E.M., J. Biomed. Opt., 8, 111, 2003. With permission.)

−+ + +

RF in±22 V

50 Ω10 kΩ

0.0115 µF

0.0115 µF

65 V 1000 V

adjustable

4000 V

photocathodemulti-channel

platephosphor

screen

GBS Micro Power Supply

Image Intensifier

− −

I i jIMAG I f REAL I f

NACij ij( , )

[ [ ( ) ] [ ( ) ] ]

/max max

/

=+2 2 1 2

2

θ( , ) arctan[ ( ) ]

[ ( ) ]max

max

i jIMAG I f

REAL I fij

ij

=


illuminate an entire animal or portion of the animal. Incident powers range from µW/cm2 to mW/cm2,and area detection can be accomplished using a CCD with or without an image-intensifer coupling andwith or without a spectrograph for spectral discrimination. Typically, CW measurements are conductedin mice and rats of small tissue volumes, while the frequency-domain measurements of fluorescence-enhanced contrast have been performed in canines (see Section 33.5).

In addition to the area measurements, the ICCD can be employed to rapidly conduct single-pixelmeasurements for tomographic reconstructions by simply using the ICCD to simultaneously measurethe phase and amplitude of light collected by a number of fibers whose ends are affixed onto an interfacingplate focused on the photocathode of the image intensifier via a lens (Figure 33.11).

33.3.3 Homodyne I and Q

Another homodyning method for frequency-domain measurements that does not depend on conductingsuccessive measurements at varying phase delays, η, imposed on signal G employs I and Q demodula-tion.20 The technique depends on mixing signal L with two signals, G1 and G2, at the same frequency ω,but phase shifting it by 90° (Figure 33.12):

(33.35)

When L is mixed with G1, the signal output, S1, is given by:

(33.36)

When L is mixed with G2, the signal output, S2, is given by:

FIGURE 33.10 The process in which the phase delay between the image intensifier and laser-diode modulation isadjusted between 0 and 360° yielding phase-sensitive yet constant-intensity images at the phosphor screen. Whenthe intensities are compiled at each pixel, the sine wave is reconstructed and the phase and amplitude attenutationare obtained from simple FFT. (From Thompson, A.B. and Sevick-Muraca, E.M., J. Biomed. Opt., 8, 111, 2003. Withpermission.)

arrange phase-sensitive images inorder acquired at phase delay hd

phas

e-se

nsiti

ve in

tens

ity

hN

h

h1

G G t G G tAC AC1 2= =cos( ); sin( )ω ω

S L G tL G

tDC ACAC AC

inst inst1 22

2 2= ⋅ ⋅ +

⋅⋅ + + + + + +

cos( ) cos( ) cos( )ω ω θ θ π θ θ π


(33.37)

Upon passing through a low-pass filter, the high-frequency components at ω and 2ω can be eliminated,leaving two DC signals:

(33.38)

When the two signals are combined, the quantities of can be determined, and

by proper referencing the AC and phase delay associated with signal L and with the light propagationwithin the random medium can be determined.

FIGURE 33.11 The adaptation of a number of single fibers collecting detected light for imaging by the ICCD system,which is depicted in Figure 33.9.

FIGURE 33.12 Illustration of the homodyne FDPM detection employing the mixing of L, G1, and G2, where G2 isphase shifted by 90° relative to G1.

Detector fibers

NIR LightSource

Phantom

CCD camera

Interfacing plate

G

S1

S2

L

mixer

mixer

cos(ωt )GAC

sin(ωt )GAC

S L G tL G

tDC ACAC AC

inst inst2 22

2 2= ⋅ ⋅ +

⋅⋅ + + + − + +

sin( ) sin( ) sin( )ω ω θ θ π θ θ π

SL GAC AC

inst1 2 2=

⋅⋅ + +

cos( )θ θ π

SL GAC AC

inst2 2 2=

⋅⋅ − + +

sin( )θ θ π

L GAC ACinst

⋅− +[ ]

2, θ θ


33.3.4 Excitation-Light Rejection Considerations

Regardless of the measurement method (i.e., CW, time-domain, or frequency-domain), and regardlessof the measurement geometry (point or area illumination and detection), one of the greatest and largelyunrecognized challenges in fluorescence spectroscopy and imaging in random media is the importanceof excitation-light rejection. In fluorescence spectroscopy of dilute, nonscattering samples, the isotropicemission light is collected at right angles to the incident excitation light to avoid corruption of excitationlight in the fluorescence measurements (see Section 33.4). Yet in random media, the excitation light ispropagated isotropically, potentially corrupting measurements in random media. Generally, the Stoke’sshift associated with many fluorophores is small; in the case of indocyanine green (ICG), an FDA-approved agent, it is 50 nm. The wavelength sensitivity at the photocathode does not discriminate betweenexcitation and emission wavelengths requiring a mechanism for excitation-light rejection and passage ofemission light only for accurate spectroscopy and imaging data. The excitation light reaching a detectorat a location on the surface is the predominant signal and can be as little as 103 times greater than theemission fluence when the fluorophore concentration is high and significantly greater as the fluorophoreconcentration is reduced to nanomolar and femtomolar levels, as might be expected in fluorescentcontrast-agent identification of small cancer metastases. For planar-wave illumination, specularlyreflected excitation light would create an even greater portion of the signal, further compounding thediscrimination of the weak fluorescent signal emitted from the tissue surface (Figure 33.5). Generally,investigators employ interference filters with a rejection capability of OD 3 for excitation light, whichgenerally sets the noise floor of the fluorescent measurement and limits the smallest amount of detectablefluorophore. When interference and bandpass filters for emission-light passage and holographic filtersfor excitation-light rejection are stacked, the noise floor can be reduced as much as nine orders ofmagnitude.21 Clearly, the sensitivity of fluorescence spectroscopy and imaging in random media hingeson the success of excitation-light rejection.

The forward-spectroscopy and imaging problems consist of using the diffusion model to predict lightpropagation, fluorescence generation, and the resulting measurements at the medium–air interface giventhe spatial distribution of optical properties within the entire volume. To solve the inverse-spectroscopyproblem we assume a uniform distribution of optical properties with the unknowns being (1) the opticalproperties at the excitation and emission wavelengths, (i.e., and (2) the optical propertiesassociated with the fluorescent agent (i.e., , τ), which experiences first-order decay kinetics. Section33.4 further develops the inverse solution to the imaging problem for tomographic imaging.

33.4 Fluorescence Spectroscopy in Random Media

Fluorescence-lifetime spectroscopy is advantageous for quantitative spectroscopy of analytes and metab-olites because the measurement of fluorescence-decay kinetics (rather than fluorescence intensity) obvi-ates the need to know the concentration of the sensing fluorophore.1 As described in Section 33.1,frequency-domain techniques provide measurement of fluorescence lifetime (τ) using simple relation-ships of the phase delay (θ) and modulation ratio (M) of the re-emitted fluorescence as a function ofthe modulation frequency relative to the incident intensity-modulated excitation light. However, thedevelopment of fluorescence-lifetime spectroscopy for NIR biomedical tissue diagnostics for sensingthrough the use of systematically administered dyes22,23 or implantable devices24,25 requires deconvolvingthe influence of multiple scatter upon the measured emission phase delay and amplitude attenuation. Asshown below, the addition of scatter increases the sensitivity of fluorescence-lifetime spectroscopy overtraditional methods that focus on isotropic emission-light generation across a fixed path length, L.

Approaches to suitable modeling of multiply scattering of NIR excitation and fluorescence photonsand to the use of diffusion models for quantitative spectroscopy have been previously demonstrated10,26,27

for dyes exhibiting single-exponential-decay kinetics. Failure to properly account for multiply scatteredexcitation and emission-light propagation in random media can result in incorrect decay kinetics. Forexample, when conducting phase-modulation measurements on a solution of Intralipid® containing theNIR-excitable fluorophore ICG, Lakowicz et al.28 did not incorporate the propagation of light into their

µa sx m x m, ,, )′µ

αµax m→


calculations, yet they attribute multiexponential decay kinetics to this dye, which typically exhibits single-exponential decay kinetics.

33.4.1 Single-Exponential-Decay Spectroscopy

There are generally six unknowns to be solved for a uniform medium of unknown optical propertiescontaining a fluorophore exhibiting a first-order radiative relaxation process: with the subscripts altered slightly from the past nomenclature to emphasize the optical properties attwo separate wavelengths, λx and λm.

33.4.1.1 Optical Property Determination

For a uniform random medium, the optical properties can be accurately determined from multidistancefrequency-domain measurements.29,30 The analytical solution to the diffusion equation with point-sourceillumination at wavelength λ,

(33.39)

in an infinite medium provides three equations for , θλ, and as a function of modulationfrequency, ω, distance away from the source, r, in terms of the optical properties .

When FDPM measurements are conducted as a function of modulation frequency, nonlinear regressioncan be performed to arrive at the optical properties of the medium. Conversely, when referencing themeasurements of , θλ, and at position r to a “reference” position r0, linear regression of thefollowing equations:

(33.40)

(33.41)

(33.42)

enables accurate estimation of the optical properties at a single modulation frequency using a singledetector. Frequency-domain measurements must be referenced to eliminate contributions of GAC, GDC,and θinst, as denoted in Equation 33.29, before data are regressed to Equations 33.40 through 33.42.

An alternative referencing method was devised by Mayer et al.27 that involved measurement of mod-ulation and phase delay at two positions, r1 and r2, using two unmatched detectors. Unlike traditionalfluorescence-spectroscopy measurement across a known pathlength, L, the instrument-response functionfor frequency-domain measurements in scattering media can be corrected without the use of referencedyes. The correction can be obtained by multiplexing two unmatched detectors at two different positionsin the sample.27 The two fibers leading to the unmatched detectors shown in Figure 33.13 are of the samelength, which ensures equal optical pathlengths of the two received signals, L1,L2.

The measured relative phase shift between detector 1 and detector 2, θrel1,2, and measured modulation

ratio, Mrel1,2, between the two detectors reflect light propagation (and fluorescence generation, in the case

of fluorescence measurements) in the sample between the incident source and the two detectors, (i.e.,

) as well as the instrument function ( ):

µ µ αµ τλ λ λ λa a s s a

x m x m x m, , , , ,′µ ′µ

→

r r r r r∇⋅ ∇( ) − +

+ =D r

i

cr S raλ λ λ λ λω µ ω ω ωΦ Φ( , ) ( , ) ( , ) 0

IACλIDCλ

µλ λa s, ′µ

IACλIDCλ

DCDC r

DC r

r

rr r

Drela≡ = − −( )

( )exp[ ( )( ) ]

0

00

1 2µ

ACAC r

AC r

r

rr r

c

c D crela

a

≡ = − −+ −( )

( )exp ( )( ) cos[ tan ( )]

0

00

2 2 2

2 21 4 11

2

µ ω ωµ

θ θ θµ ω ω

µrela

a

r r r rc

c D c≡ − = −

+ −( ) ( ) ( )( ) sin[ tan ( )]0 0

2 2 2

2 21 4 11

2

θ θ1 21

1

2

2

, , ,L

L

L

LAC

DC

AC

DC

θ θinst inst

AC

DC

AC

DC

GG

GG1 2

1

1

2

2

, , ,


(33.43)

(33.44)

After multiplexing, the measured relative phase shift between detector 2 and detector 1, θrel2,1, and

measured modulation ratio, Mrel2,1, between the two detectors continue to reflect light propagation (and

fluorescence generation, in the case of fluorescence measurements) in the sample (

) as well as the instrument function ( ):

(33.45)

(33.46)

where subscript 12 denotes the relative value of the signal detected at detector 1 to the signal detectedat detector 2, and subscript 21 denotes the converse.

Combining Equations 33.43 and 33.45 and Equations 33.44 and 33.46 gives phase-shift and modula-tion ratios that are devoid of instrument function:

(33.47)

(33.48)

FIGURE 33.13 Schematic of fiber optically coupled source and detector placement for fluorescence measurementsin scattering media. The two detector fibers are of the same length to ensure equal optical pathlengths.

Sample

Modulated-lightfrom light source

Light toPMT1

Light toPMT2

r1

r2

θ θ θ θ θrel inst inst1 2 1 21 2,= − +( ) − − +( )

ML G

L G

L G

L Grel

AC AC

AC AC

DC DC

DC DC1 2

1 1

2 2

2 2

1 1

,= ⋅

θ θ1 21

1

, , ,L

LAC

DC

L

LAC

DC

2

2

θ θinst inst

AC

DC

AC

DC

GG

GG1 2

1

1

2

2

, , ,

θ θ θ θ θrel inst inst2 1 1 21 2,= − − +( ) + − +( )

ML G

L G

L G

L Grel

AC AC

AC AC

DC DC

DC DC2 1

2 2

1 1

1 1

2 2

,= ⋅

∆θ θ θ θ θ= − = −( )2 1

1

2 1 2 2 1rel rel

, ,

MM

M

L G

L G

L G

L G

L G

L G

L G

L G

L L

L L

G G

G

rel

rel

AC AC

AC AC

DC DC

DC DC

AC AC

AC AC

DC DC

DC DC

AC AC

DC DC

AC AC=

=

⋅

⋅

=

1 2

2 1

1 1

2 2

2 2

1 1

2 2

1 1

1 1

2 2

1 2

2 1

1 2

1 2

1 2

,

,

/

/

/

/

/

DCDC DCG2 1

/


For matched detectors, is unity. For unmatched detectors, the ratio must be experimentallydetermined.31

Figure 33.14 illustrates the multiplexing system for the conventional two-channel frequency-domainsystem developed for fluorescence-lifetime spectroscopy.

The multiplexing method described above can be used for measurements performed with sources atthe excitation and emission wavelengths, and hence single-distance (multifrequency) nonlinearregression29 can be performed to obtain optical properties of the medium without corruption from theinstrument functions. In a recent study, we showed that measurements made at multiple distances enablelinear regression of parameters29 and result in the most precise optical property estimation.30 Regardlessof whether from referenced or multiplexed frequency-domain measurements conducted with point-source illumination at wavelengths λx and λm, the optical properties of can beaccurately obtained.

33.4.1.2 Determination of Single-Exponential-Decay Lifetime

After the optical properties are estimated from frequency-domain measurements employing the twowavelength sources, the emission fluence is measured in response to point-source illumination at theexcitation wavelength using excitation-light-rejection filters to reduce the noise floor. From the referencedmeasurement used to arrive at , the fluorescent properties of and τ aredetermined from the solution to Equations 33.19 and 33.24 for an infinite medium:

(33.49)

where r is the distance to the excitation point source, SA is the complex fluence of the source describingits modulation depth and phase, and the terms ψ and κ are functions of optical properties (µa and ),c, and ω.10,27

(33.50)

(33.51)

(33.52)

FIGURE 33.14 Illustration of multiplexing system for the two-channel frequency-domain detection apparatus.

PMT1 PMT2

Sample system

Modulated-lightfrom light source system

(2 × 2)Multiplexer

G G

G GAC AC

DC DC

1 2

2 1

/

/

µ µλ λ λ λa a s s

x m x m, , ,′µ ′µ

Φm AC mr I im

( , ) exp( )r

ω θ= αµax m→

ΦΞ

m aca m

x m

rSA

cD D rix m( , )

( )

( )[ ] [ ]

rω

αµπ ωτ

ψ κωτ κ ψωτ=+[ ] − + + →

4

1

1 2

′µs

ψ ω δ ω ξ ζ ω ρ ωξ ρ ω

( , )( , ) ( , ) ( )

( )

rr r

rr r= +

+2 2

κ ω ζ ω ξ δ ω ρ ωξ ρ ω

( , )( , ) ( , ) ( )

( )

rr r

rr r= −

+2 2

δ ω β ω γ ω β ω γ ω( , ) exp ( ) ) cos ( ) exp ( ) ) cos ( )rr r r r rx x m m= −[ ] [ ]− −[ ] [ ]


(33.53)

(33.54)

(33.55)

Frequency-domain photon-migration measurements at both the excitation and emission wavelengthshave demonstrated experimentally the ability to measure the single exponential lifetimes of ICG and3,3′-diethylthiatricarbocyanine iodide (DTTCI),27 rhodamine B,10 and mixtures of ICG and DTTCI13 intissue-like scattering media of Intralipid.

Yet most analyte-sensing fluorphores exhibit multiexponential decays or stretched-exponential-decaykinetics, increasing the number of unknowns from two to 2j+1 for a fluorophore experiencingj-activated states (Equation 33.10): and to 3j+1 for a fluorophore undergoing collisionalquenching (Equation 33.11): .

33.4.2 Multiexponential-Decay Kinetics

In general, the solution for the emission fluence in an infinite medium of uniform optical properties isgiven by:

(33.56)

Generally, frequency-domain measurements are insensitive to the form of the decay kinetics used todescribe the relaxation process. As an example, Figure 33.15 illustrates the phase and modulation ratiomeasured in a dilute, nonscattering sample using traditional fluorescence-lifetime-spectroscopy tech-niques. The emitted fluorescence results from a combination of two dyes, ICG and DTTCI, that individ-ually exhibit first-order relaxation kinetics. The frequency-domain data are equally well fit using a single-exponential-decay (which represents the average of the decay times), a two-exponential-decay, and astretched-exponential-decay model, indicating that the data at these modulation frequencies are insuf-ficient to discern the relaxation processes. Typically, differences in decay kinetics are manifested at highermodulation frequencies, which unfortunately suffer from a small-instrument response function and lowSNR. However, when predicting the phase-delay and modulation ratio from the solution to the diffusionequation for infinite media employing the various kinetic models for radiative relaxation, significantdifferences in frequency-domain data taken at modulation frequencies below 150 MHz (Figure 33.16)become apparent. Figure 33.16 shows model predictions for the two dyes within a scattering mediumexperiencing different relaxation mechanisms along with the data, indicating the potential for enhancedsensitivity of fluorescence-lifetime spectroscopy in random or multiply scattering media. Note that thephase-delay and modulation ratios in Figures 33.15 and 33.16 span a larger range in scattering mediathan in nonscattering media.

In summary, challenges remain in connection with solving the inverse-fluorescence-spectroscopyproblem when it comes to extracting parameters that accurately predict changes in both decay kineticsand, therefore, analyte of metabolite concentrations. While a few studies in the literature indicate thatthe inverse-spectroscopy problem for fluorescence lifetime in random media can be solved, to date theinverse problem of multiexponential-decay functions that exist for analyte-sensing fluorophores has notbeen solved. However, as long as the number of unknown parameters remains smaller than the numberof measurements, the solution to the inverse-spectroscopy problem entails a straightforward least-squares-minimization problem. In contrast to the inverse-spectroscopy problem, the inverse-imaging

ζ ω β ω γ ω β ω γ ω( , ) exp ( ) ) sin ( ) exp ( ) ) sin ( )rr r r r rx x m m= −[ ] [ ]− −[ ] [ ]

ξµ µ

= −a

m

a

x

m x

D D

ρ ω ω( ) = −

c D Dx m

1 1

( , )αµ τax m→( , , )µ τa j jx m

a→

( , , , , )µ τ α βa j j j jx ma

→

ΦΞ

m

a m

x m

i trSA

cD D ri g t e dtx m( , )

( )( ) ( )

rω

αµπ

ψ κ ω= − ∫

→∞

4 0


problem entails a smaller number of measurements than unknown parameters, necessitating optimizationapproaches.

33.5 Fluorescence FDPM for Optical Tomography15

The solution to the inverse-imaging problem, known as optical tomography, has been motivated overthe past decade by optical mammography, i.e., the use of deeply penetrating NIR light for detecting breastcancer on the basis of endogenous optical property contrast between normal and diseased tissues. It hasbeen proposed that the optical property contrast in scattering and absorption is due to the increased sizeand density of neoplastic cells in a tumor region and the increased vascular blood supply (as a result ofangiogenesis) that locally increases hemoglobin, a primary chromophore in tissues. While optical mam-mography has seen many advances in recent years, most notably in the application of FDPM,32.33 TDPM,11

and continuous-wave34 measurements (see also Reference 22), the need for angiogenesis-mediated absorptioncontrast for diagnostic optical mammography limits the potential applications of optical mammography.Since the endogenous contrast from angiogenesis can be expected to be low in small lesions and non-specific to cancer, NIR detection of nonpalpable disease in dense breast tissue is limited without theaddition of contrast. Hence, moderately resolved, biochemical molecular imaging within tissues using

FIGURE 33.15 The plot of fluorescence phase shift (top) and modulation ratio (bottom) as a function of modulationfrequency on ICG–DTTCI mixture (ICG:DTTCI = 0.15 mM: 0.5 mM, in a dilute nonscattering medium) for correctedexperimental measurements (), and that predicted by incorporating two-exponential-decay kinetics or stretched-exponential-decay kinetics (bold line) and average of two-exponential-decay kinetics (thin gray line).

0 20 40 60 80 100 1200

20

40

60

80

100

120

Frequency (MHz)

Ph

ase

sh

ift (

de

gre

es)

datatwo or st-expavg of two-exp

0 20 40 60 80 100 1200.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (MHz)

Mo

du

latio

n r

atio

datatwo or st-expavg of two-exp


unassisted NIR optical techniques is somewhat limited in scope and can be expanded through the useof contrast-enhancing agents.

Fluorescent contrast agents have been proposed and independently confirmed as the most efficientmeans for inducing optical contrast when time-dependent measurements (i.e., TDPM or FDPM) areconducted.35,36 Furthermore, in the near future these agents may offer a host of opportunities for molec-ular imaging that are limited only by synthetic design. The basic principles behind fluorescence-enhancedNIR optical tomography stem first from the kinetics of fluorescence generation. It is the kinetics of thefluorescence-decay process that imparts the superior contrast of fluorescence over absorbance whenTDPM or FDPM measurements are made.

Figure 33.17 provides a simple schematic describing in physical terms why contrast by fluorescence isgreater than contrast by absorption for FDPM imaging. Consider a tissue volume illuminated by anintensity-modulated light source at source position rs. The propagating wave is denoted by dotted lines.As the propagating excitation wave transits through the tissue, it is attenuated and phase delayed due tothe tissue optical properties. If the wave encounters a light-absorbing heterogeneity, such as a highlyvascularized tumor, a portion of the intensity wave is reflected. The strength of the “reflected wave” (ordotted line) depends on the absorption contrast and the size and depth of the heterogeneity. This reflectedwave makes a small contribution to the wave that ultimately is detected at detector position rd. It is this

FIGURE 33.16 The plot of fluorescence phase shift (top) and modulation ratio as (bottom) a function of modulationfrequency on ICG–DTTCI mixture (ICG:DTTCI = 0.15 mM: 0.5 mM, in 2% Intralipid® solution) for correctedexperimental measurements () and that predicted by the propagation model incorporating two-exponential-decaykinetics (bold line), average of two-exponential-decay kinetics (thin gray line), and the stretched-exponential-decaykinetics (dashed line).

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Frequency (MHz)

Pha

se s

hift

(deg

ree)

data in 2% Intralipid

two-exp

avg of two-exp

st-exp

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120

Frequency (MHz)

Mod

ulat

ion

ratio

data in 2% Intralipid

two-exp

avg of two-exp

st-exp


small, added contribution that is used to detect the heterogeneity when endogenous contrast is employed.If the added contribution is not within the measurement noise, then it provides information for imagerecovery in one of the inversion strategies outlined below. However, if the heterogeneity is contrasted byfluorescence, then upon reaching the heterogeneity the excitation wave generates an emission wave (solidlines). The emission wave then acts as a beacon, and, when appropriate filters are used to reject theexcitation light, it can be measured to directly locate the heterogeneity. In small tissue volumes, such asthe mouse or rat, inversion algorithms may not be required to detect the fluorescent heterogeneity, asshown in the literature results summarized in Section 33.6. However, in larger tissue volumes, the forward-and inverse-imaging problems require solution for effective image recovery. Most importantly, since aphase delay and amplitude attenuation occur between the activating excitation wave and the re-emittedfluorescent wave associated with the fluorescence-decay kinetics, the fluorescence decay increases thecontrast or phase-delay and amplitude-attenuation change associated with the detected signal. Finally,since a fluorescent probe can be “tuned” to exhibit differing fluorescence-decay characteristics that dependon the probe’s local environment, the re-emitted signal can contain diagnostic information about thetissue of interest.

Few studies have successfully inverted NIR tissue optical measurements to render images of exoge-nously contrasted tissues or tissue-mimicking phantoms. Table 33.1 outlines several investigations thathave employed “synthetic” data sets and phantoms.37–57 The approaches are basically similar to thoseused in NIR optical-tomography work, with the following three exceptions: (1) because of the lowquantum yield of fluorescent dyes, the SNR for CW, TDPM, and FDPM measurements is inarguablylower, potentially making it more difficult to successfully reconstruct images; (2) due to the fluorescence-lifetime delay, both TDPM and FDPM approaches have additional contrast in the time-dependentphoton-migration characteristics; and, finally, (3) because the fluorescence-kinetic parameters of fluo-rescence lifetime and quantum efficiency can be directly inverted, the technique can be used to performquantitative imaging via dyes that report cancer.

FIGURE 33.17 Schematic detailing the propagation of excitation photon-density waves (solid lines) and theirperturbation by absorbing heterogeneities (dotted lines) and the generation of emission photon-density waves (solidgray lines) within the tissues. Fluorescence contrast-enhance optical tomography provides greater localization capa-bility because the detected emission waves act as “beacons” providing information regarding the tagged heterogeneity.(From Hawrysz, D.J. and Sevick-Muraca, E.M., Neoplasia, 2(5), 388, 2000. With permission.)

NIR Laser

Detector

FiberOptics

100 MHz

Incident PhotonDensity Waves

IntensityModulation

Air-TissueInterface

Scattered PhotonDensity Waves

Fluorescent PhotonDensity Waves


TABLE 33.1 Fluorescence-Enhanced Contrast Imaging: Literature of Image Reconstructions

Ref. Inversion Formulation Data Type Noise Two- or Three-Dimensional

Forward Method

Measurement Method Contrast Agent Uptake Ratio

O’Leary, M.A. et al., 199437 Localization Experimental phantom

Yes Two-dimensional None TDPM ICG Perfect uptake

Wu, J. et al., 199538 Localization Experimental phantom

Yes Three-dimensional None TDPM Diethylthiatricarbocyanine

Perfect uptake

Chang, J. et al., 199539 POCS, CGD, SART Experimental phantom

Yes Two-dimensional NS CW Rhodamine 6G dye

Perfect uptake and 1000:1

O’Leary, M.A. et al., 199640 Integral(SIRT) Synthetic data 0.1ο in phase, 1% in amplitude

Two-dimensional Analytical FDPM ICG Perfect uptake, 20:1

Paithankar, D.Y. et al., 199741 Differential (Newton-Raphson) Synthetic data 0.1ο–1ο in phase; 0.01 in log AC (Gaussian)

Two-dimensional MFD FDPM ICG 20:1

Wu, J. et al., 199742 Laplace transform Experimental phantom

Yes Two-dimensional NS TDPM HITCI iodide dye

Perfect uptake

Chang, J. et al., 199843 Differential (conjugate gradient) Synthetic data 1–10% white noise Two-dimensional or three-dimensional

NS CW/FDPM N/A 100:1 10:1

Jiang, H., 199844 Differential (Newton’s iterative method)

Synthetic data 0–5% Two-dimensional FEM FDPM N/A 2:1 contrast in φ, τ

Hull, E.L. et al., 199845 Localization Experimental phantom

Yes Two-dimensional Monte Carlo

CW Nile BlueA

Perfect uptake

Eppstein, M.J. et al., 199946,47 Differential Synthetic data 0.1ο in phase; 1% in log AC (Gaussian)

Two-dimensional, three-dimensional

MFD FDPM N/A Perfect uptake and 100:1 10:1

Chernomordik, V. et al., 199948

Random walk theory Experimental phantom

Yes Two-dimensional and three-dimensional

NS CCD Rhodamine Perfect uptake

Roy, R. and Sevick-Muraca, E.M., 1999, 200049,50

Differential (gradient-based and truncated Newton method)

Synthetic data 0.1ο in phase; 1% in log AC (Gaussian)

Two-dimensional FEM FDPM N/A 2.5:1 5:1 10:1

Yang, Y. et al., 200051 Marquardt and Tikhonov regularization

In vivo (rats) Yes Two-dimensional images

FEM FDPM ICG and DTTCI

Perfect and imperfect uptake

Eppstein, M.J. et al., 2001;52

Hawrysz, D.J. et al., 200153

Differential Experimental phantom

Yes Three-dimensional MFD FDPM ICG 50:1 100:1

Roy, R. and Sevick-Muraca, E.M., 200154,55

Differential (gradient-based optimization and truncated Newton’s method)

Synthetic data 55 dB in excitation; 35 dB in emission

Two-dimensional, three-dimensional

FEM FDPM N/A 10:1


Ntziachristos, V. et al., 200156 Integral (normalized Born expansion)

Experimental phantom

2% amplitude noise in source

Two-dimensional along z-planes

FD CW ICG in background; Cy5.5 as contrast tumor

Perfect uptake

Lee, J. and Sevick-Muraca, E.M., 200257

Integral (distorted BIM) Experimental phantom

Yes Three-dimensional MFD FDPM ICG 100:1

CCD = charge-coupled device; CGD = conjugate gradient descent; CW = continuous-wave imaging; FD = finite difference; FDPM = frequency-domain photon migration; FEM = finite-element method; MFD = multigrid finite difference; N/A = not applicable; NS = not specified; POCS = projection onto convex sets; SART/SIRT = simultaneous algebraic reconstructiontechniques; TDPM = time-domain photon migration; φ, τ = quantum efficiency and lifetime of contrast agent.

TABLE 33.1 Fluorescence-Enhanced Contrast Imaging: Literature of Image Reconstructions (continued)

Ref. Inversion Formulation Data Type Noise Two- or Three-Dimensional

Forward Method

Measurement Method Contrast Agent Uptake Ratio


The latter characteristic of fluorescence-lifetime imaging reveals its similarity to magnetic resonanceimaging (MRI). In MRI, imaging is accomplished by monitoring the RF signal arising from the relaxationof a magnetic dipole perturbed from its aligned state using a pulsed magnetic field. In fluorescence-contrast-enhanced optical tomography, imaging is accomplished by monitoring the emission signalarising from the electronic relaxation from an optically activated state to its ground state. Unfortunately,the emission light is multiply scattered; hence, the resolution afforded by MRI is unlikely to be matchedby contrast-enhanced optical tomography. Unlike contrast agents for conventional imaging modalities,optical contrast, due to fluorescent agents, may be achieved in two ways: (1) through increased tar-get:background concentration ratios and (2) through alteration in the fluorescence-decay kinetics uponpartitioning within tissue regions of interest.58 Section 33.6 summarizes the literature on fluorescentcontrast agents and their development over the past decade. The approaches for solving the inverse-imaging problem are presented in the next section.

33.5.1 Approaches to the Inverse-Imaging Problem

Attempts to solve the fluorescence-enhanced optical-imaging problem have been made both by solvinga formal inverse problem and by taking a less rigorous model-based approach. For example, localizationof a fluorescent target has been demonstrated using localization techniques in which the strength ofreradiating target is used to ascertain its central position within a background containing no fluorophore.Through the use of FDPM measurements between a point source and detector as the pair was scannedover the phantom surface, the center of a single fluorescent target could be accurately identified.37 In yetanother approach, an analytical solution to the spherical propagation of emission light in uniformscattering media was used to determine the x,y,z position of the point source of fluorescence in anotherwise nonfluorescent background probed by CW measurements.48 Using time-domain measure-ments, Wu et al.38,42 developed a system for assessing the position of a fluorescent target in turbid mediaby evaluating early-arriving photons to determine the origin of the fluorescence generation. Hull et al.similarly used spatially resolved CW measurements to determine the location of the fluorescent targetin scattering media.45 Unlike the studies described above, when there is presence of background signalor if the goal of reporting fluorescence-decay kinetics prevents a localization approach, then a solutionto the full inverse-imaging problem is required.

The solution of a formal inverse problem requires the use of the appropriate mathematical modelsdescribed above in Section 33.2. Specifically, a guess of the interior optical or fluorescence properties isiteratively updated until the predicted measurements given by the solution of the forward problem matchthe actual measurements. Since the number of unknowns (or optical and fluorescent contrast-agentproperties) is greater than the number of measurements, the problem is underdetermined and especiallydifficult. This inverse problem is unavoidably “ill-posed,” which generally means that the solutions arenonunique and unstable in the presence of measurement error. In addition, the optical-tomographyproblem is generally highly nonlinear, and attempts to linearize it result in solution instabilities and oftenintractably long computational times if the update step is to remain within the range of accuracy of thelinearization. The solution of the inverse problem is an intensive area of research in itself that is motivatedby several different research areas including biomedical NIR optical tomography based on endogenouscontrast.

To assess the performance of an inverse-problem algorithm, the achieved solution must be comparedto the known distribution of optical properties. As a consequence, studies investigating the inverse optical-tomography problem are performed using either (1) “synthetic” measurements, i.e., measurements thatare predicted by the forward problem to which artificial random “noise” is added to simulate measurementerror; or (2) phantom studies in which tissue-mimicking scattering media of known optical propertiesare used to collect experimental CW, time, or frequency-domain measurements that are used for theinverse solution. In the following sections, we briefly review the methods used to solve fluorescence-enhanced optical-tomography problems, broadly classified into categories of integral and differential


approaches and employing a number of parameter-updating schemes. Finally, sample reconstructionsfrom actual experimental data are presented.

33.5.2 Integral Formulation of the Inverse Problem

One of the more common methods of formulating the inverse problem is by integral treatment. Sincethe emission diffusion equation is in the form of an nonhomogeneous differential equation, Green’sfunction is used to obtain the analytical solution of the emission fluence . Equation 33.19 canbe rewritten to account for variation in the endogenous and exogenous optical properties including theabsorption due to fluorophore, , and the optical-diffusion coefficient, :

(33.57)

where the complex diffusion wave number can be expressed as:

(33.58)

The term in Equation 33.57 accounts for the discontinuity in . However,since there is little or no variation in the isotropic scattering coefficient (the component that constitutesthe overwhelming contribution to at the emission wavelength, λm) the above term is insignificant.The Green’s function corresponding to Equation 33.57 consequently satisfies

(33.59)

by manipulating Equations 33.57 and 33.19 (at the excitation wavelength), and with the use of Green’s

theorem, , one can obtain the expression of the emission fluence

measured at rd following point excitation at rs, Φm(rd, rs), which arises due to Sm(r′, rs), the emission generation

at point r′ following the incident illumination of excitation light at rs, and due to the propagation of the

emission light from position r′ to detector point rd as predicted from the Green’s solution, Gf(rd, rs):

(33.60)

where Ω is the volume of integration, is the point-detector location, and is the point-source location.To reconstruct the spatial map of detailing the heterogeneity, Equation 33.60 is discretized

into a series of equations in terms of Gf, , and the vector of measurements of . Weconsider the excitation source to be amplitude-modulated by a frequency of ω. Measurements of phaseshift, θm, and amplitude of AC component IAC (or ) are obtained at detector positions

in response to the excitation source at . [Note: It is assumed that the phase shift and the AC componentare predicted relative to the incident excitation light at . In addition, it is assumed that absolute measure-ments of and θm are used as inputs.] Discretizing Equation 33.60 yields:

(33.61)

Φm r( , )v ω

µax mr

→( )r

D rm( )r

r r r rr

r

r r r r

r∇ + = − −∇ ⋅∇2 2Φ Φ

Φm m m

m

m

m m

m

r k r rS r

D r

D r r

D r( , ) ( ) ( , )

( )

( )

( ) ( , )

( )ω ω

ω

k rD r

r icm

mam

2 1( )

( )( )

rr

r= − +

µ ω

r r r r r∇[ ]⋅∇D r D r rm m m( ) / ( ) ( )Φ D rm( )

r

D rm( )r

r r r r r r r r∇ ′( ) + ′( ) = − − ′2 2G r r k r G r r r rf m f, ( ) , ( )δ

U G G U d r U G G U dSSv

r r r r∇ − ∇( ) = ∇ − ∇( )⋅∫∫ 2 2 3

˜ , , ,Φ ΩΩ

m d s f d m sr r G r r S r r dr r r r r r( ) = ′( ) ′( )∫ = ′( ) ′( )

+( ) ′( )∫ →G r rr

D r ir r df d

a

m

x sx m

r rr

rr r

,( )

,Ω

Φ Ωαµ

ωτ1

rrd

rrs

µax mr

→ ( )r

Φx sr r′( )r r, ˜ ,Φm d sr r

r r( )Φm d s AC

ir r I em

mr r

,( ) = − θ

rrd

rrs r

rs

IACm

˜ , , ,( )

Φ Φ∆

m d s f j d x j s

a j

mj

N

r r G r r r rr

D r ix m

r r r r r rr

r( ) = ( ) ( ) ( )+( )

→

=∑ αµ

ωτ11


where N is the total number of cells in the domain, and ∆ is the area or volume of the pixel or voxel. Ifthere are K sources and L detectors, then can be denoted as:

(33.62)

(33.63)

(33.64)

where , and M = K*L.Equation 33.64 is also appropriate if imaging is performed on the basis of a fluorophore-absorption

cross section with a constant lifetime τ. The problem formulated in Equations 33.62 through 33.64 isnonlinear in since the excitation fluence, , is also a function of absorption.

However, if tomographic reconstruction on lifetime were pursued, the problem would become linear,and Equations 33.63 and 33.64 would be rewritten as:

(33.65)

(33.66)

where the vector X represents the sources of fluorescence within the random medium.The formulation of the inverse-lifetime problem is called fluorescence-lifetime imaging40,41,59 and has

been the subject of tomographic reconstructions from synthetic measurements. Fluorescence-lifetimeimaging is not possible for CW measurements (ω = 0). To date fluorescence-lifetime imaging has beenaccomplished using actual experimental measurements only in limited works,51 probably because fewcontrast agents exist that are designed with “tuneable” lifetimes.

Nonetheless, the opportunity for lifetime imaging is clearly evidenced by ICCD measurements usingthe instrumentation depicted in Figure 33.8. Two fluorescent targets were positioned 0.5 cm from theimaged surface of a tissue-simulating phantom and embedded in 10 × 10 × 10 cm3 of 0.5% Intralipid.The first target encapsulated a 1-µM solution of ICG, and the second encapsulated a 1.42-µM solutionof 3,3′-DTTCI. These solution concentrations were chosen to equilibrate the number of fluorescentphotons emitted from each target because an equivalent number of excitation photons encounter eachtarget. Figures 33.18A and 33.18B confirm this equilibration, as it is difficult to differentiate the targetsfrom the DC and AC measurements. However, Figures 33.18C and 33.18D plot the phase delay and themodulation ratio (IAC/IDC) and provide differentiation of the two volumes. The differentiation, whichresults from a disparity in lifetime (0.62 ns) between the two fluorescent agents, demonstrates thepotential of fluorescence-lifetime imaging. While these images present raw data, quantitative tomographicrecovery of fluorescence lifetime is possible with solution to the inverse-imaging problem.

The inverse-imaging problem can be approximated as a linear problem and iteratively solved usingthe Gauss–Newton method:

(33.67)

Φm FX=

˜ ,˜ ,

˜ ,

ΦΦ

Φ

m d s

m d s

m d s M

N

N

M MN N

r r

r r

r r

F F

F F

F F

X r

X r

X r

r r

r r

M

Mr r

L

L

M O M

M O M

L

r

r

M

Mr

( )( )

( )

=

( )( )

(

1

2

11 1

21 2

1

1

2

))

FG r r r r

D r iij

f di j x si j

m

=( ) ( )

+( )r r r r

r, ,

( )

Φ ∆α

ωτ1

X r rj a jx m

r r( ) = ( )→µ

F C X CM N Nm

M∈ ∈ℜ ∈× , , Φ

µax m→Φx r( )

r

FG r r r r

D ri jf di j x si j

m,

( , ) ( , )

( )=

r r r r

rΦ ∆

X rr

ij

a jx m( )( )

( )

rr

=+

→αµ

ωτ1

Φ Φ ∆mmeas

d s mcomp

d sr r r r r( , ) ( , ) ( )r r r r r

− = ⋅F X


Regardless of whether absorption or fluorescence-lifetime imaging is to be performed, parameterupdating can be accomplished by noting that F is simply the Jacobian, J, and the difference between themeasurement and the model-predicted fluence, Φmeas – Φcomp = ∆Φ, can be used to update the opticalproperty map, , by the relationship specified above, or alternatively by:

(33.68)

While a number of investigators report reconstructions based on the integral approaches using fre-quency-domain or CW (ω = 0) approaches, all assume that the measurements can be accurately measuredrelative to the incident light. Yet in practice, it is nearly impossible to perform such a measurement.Typically, a portion of the incident light is split for simultaneous measurement at a reference detectorthat cannot report the source strength or the phase delay of light that is incident on the medium surface.Calibration of the source via a “reference” phantom may also be conducted if a three-dimensional (3D)model can be used to predict the measurements and if the source strength can be accurately recoveredfrom the measurements and model. Yet such a procedure is cumbersome and susceptible to errors andincreases the challenges for incorporation into medical imaging in clinical situations. A method toeliminate “calibration” against an external standard would eliminate the number of measurements aswell as improve measurement accuracy. The following sections present three general approaches toreference measurements for the recovery of optical properties in light of image-reconstruction formal-isms: (1) emission measurements at detector position rd referenced to the background emission wave,

; (2) emission measurements at detector position rd referenced to the detected emission waveat a single reference position rr , ; and (3) emission measurements at detector position rd refer-enced to the detected excitation wave at a single reference position rr , .

33.5.2.1 Measurement Referenced to the Background Emission Wave

In this approach, calibration of the detection system is achieved by normalizing the measurement in thepresence of the heterogeneity with that measured or predicted in its absence. Typically, the “absence”case consists of a uniform medium with constant and known optical properties. In this case, the main

FIGURE 33.18 The (A) IDC, (B) IAC, (C) phase, and (D) IAC/IDC modulation ratio of two submerged targets of differingfluorescent lifetimes showing that IDC cannot distinguish the difference in fluorescence-decay kinetics.

DTTCI

ICG

120

0113-1 IDC (a.u.) IAC (a.u.)

IAC /IDC

100

80

60

40

200.5

1

1.56000

4000

2000

×104

120

−275

−280

−285

Pix

elP

ixel

Pixel

Phase (°)

100

80

60

40

20

12010080604020

Pixel

12010080604020

0.48

0.46

0.44

0.42

0.4

0.38

A B

C D

∆X r( )r

∆Φ ∆= ⋅J X

Φmb

s dr r( , )r r

Φm s rr r( , )r r

Φx s rr r( , )r r

Φmb

s rr r( , )r r


problem associated with matching experimental data to the solution of Equation 33.57 has been theunknown source strength, the unknown phase delay from the timing characteristics of various compo-nents of the detection system, and the amplitude gain or loss. The advantage of using background or awell-defined reference phantom is that it allows for the elimination of the most systematic errors commonto both background and actual measurement data sets. This approach has been widely employed in bothfrequency60,61 and time-domain62,63 photon-migration measurements. However, this is an unrealisticapproach in a clinical sense because, unlike phantom studies, the absence case and “background” fluencemeasurements are impossible in clinical applications. For contrast-enhanced imaging, “absence” may beachieved prior to the administration of a contrast agent or activation-induced contrast such as thatresulting from blood flow. Yet when the agent is fluorescent, there is no emission signal to measure theabsence scenario; hence, the “absence” scenario is unrealistic in fluorescence imaging.

For heterodyne FDPM measurements the referenced measurements enable elimination of instrumentresponses. For example, an emission measurement referenced to the background case in which the target,

successfully eliminates the instrument response, and the background optical properties are known.The mechanics of inverting data referenced to the background absence case may be illustrated by the

following equation, which shows the relationship between the measurement and the inversion algorithmfor a source–detector pair when a Born-type inversion scheme is used for fluorescent measurements,

where the referenced measurement is represented by :

(33.69)

Here, is the background emission wave detected at the same detector position, , as inthe presence of the heterogeneity case in response to excitation from the source position, . is computed from the known optical properties of the assumed uniform background case or measuredin the case of an absent heterogeneity.

In contrast to the absolute-measurement case, where the matrix, F, is itself the Jacobian matrix(Equation 33.63), relative-measurement schemes have the added complication of calculating the Jacobianmatrix by using the integral equation. However, in this case, the stays constant throughoutthe iteration due to its homogeneous nature, the inversion problem remains linear, and the calculationof the Jacobian matrix is straightforward. As a result, the reconstruction remains stable during the iterativeprocess, while the source strength dependency and other calibration problems are eliminated. Eventhough the reference to the background-emission-fluence approach is relatively easy to implement inphantom studies and is a good benchmark to test the inversion algorithms, it can be difficult in actualapplication to clinical trials where a true absence condition does not occur or where the spatiallydistributed optical properties are not known.

33.5.2.2 Measurement Referenced to the Emission Wave

Because of the unrealistic nature of referencing to the background emission wave, the inversion schemeuses the emission fluence at the reference point on the tissue surface. This approach involves the mea-surements of the emission fluence relative to one another, where the referenced measurement is repre-

sented by and

ΦΦ

AC d s

ACb

d s

AC AC m instr

ACb

AC mb

instr

ACm

ACb m

bm

m

m

m

m m

r r

r r

L G i

L G i

L

Li

( , )

( , )

exp( ( ))

exp( ( ))exp ( )=

− +− +

= −[ ]θ θθ θ

θ θ

Φ

ΦAC s d

ACb

s d

m

m

r r

r r

r r

r r,

exp,

( )( )

Φ

Φ ΦΦ Ω

Ω

AC s d

ACb

s d ACb

s d a priori m

f d x s am

m m

x m

r r

r r r r D iG r r r r r d

r r

r r r rr r r r r,

exp ,, ( )

, , ( )( )( )

= [ ] +( ) ( ) ( )∫ →

1

1

αωτ

µ

ΦACb

s da priorim

r r( , )r r[ ] r

rdrrs ΦAC

bs rm

r r( , )r r

ΦACb

s dmr r( , )r r

Φm s rr r( , )r r

Φ

Φm s d

m s r

r r

r r

r r

r r,

exp,

( )( )


and the Fredholm’s equation to be solved is written:

(33.70)

Here is the emission wave detected at the reference position, , in response to excitation fromthe source position, . This referencing approach is the most reasonable method for matching the actualmeasurement data with simulation data because it does not require the separate measurement of ahomogeneous background wave. Also, this referencing approach has merit in that, unlike the methoddescribed below, it uses the measurements at the same wavelength.

While referencing to the emission wave, , is more practical than referencing to the backgroundemission wave, , normalization by renders the inversion algorithm using the Born-type integral approach highly nonlinear. This nonlinearity is absent when referencing to the backgroundemission wave. Consequently, the calculation of the Jacobian matrix is not as straightforward as with thebackground emission wave (for details see Reference 57).

Hence, the formulated inverse-imaging problem is inherently unstable due to its nonlinear nature.Using the Marquardt-Levenberg regularization, Lee and Sevick-Muraca57 were unable to recover opticalproperty maps in two-dimensional (2D) or 3D synthetic data. In contrast, through the use of theapproximate extended Kalman filter for nonlinear systems,64–66 3D reconstructions from sparse experi-mental measurements were possible in a large 256-cm3 volume.53

33.5.2.3 Measurement Referenced to the Excitation Wave

Another practical referencing scheme utilizes measurements of excitation fluence at fixed referencepositions to be used as the normalization factors; these would, in turn, eliminate the source strengthdependency. This approach is more realistic than measurements referenced to the background-emissioncase because it does not require separate and impractical measurements with and without heterogeneity.

The relationship between the experimental measurements and the simulation for a given source anddetector pair is represented by:

and described by the following integral equation:

(33.71)

where the referenced measurement is represented by

Here , represents the excitation fluence detected at a fixed reference position, , in responseto excitation from the source position, .

Even though the excitation fluence, , is updated during the iteration, the Jacobian matrixcan be directly calculated from Equation 33.71, and the change in is small compared to thechange in . As the source term of the emission-diffusion equation is modified after each iteration

ΦΦ

AC d s

AC d r

AC d AC m instr

AC r AC m r instr

ACm d

AC rm r m d

m

m

m

m m

r r

r r

L r G i

L r G i r

L r

L ri r r

( , )

( , )

( ) exp( ( ))

( ) exp( ( ( ) ))

( )

( )exp ( ) ( )=

− +− +

= −( )[ ]θ θθ θ

θ θ

Φ

Φ ΦΦ Ω

Ω

m s d

m s r m s r m

f d x s a x m

r r


r r

r r r rr r r r r,

, ( , ), , ( )

( )( ) =

+( ) ( ) ( )∫ →1

1

αωτ

µ

Φm s rr r( , )r r r

rrrrs

Φm s rr r( , )r r

ΦACb

s dmr r( , )r r

Φm s rr r( , )r r

Φx s rr r( , )r r

ΦΦ

AC d s

ACb

d r

AC d AC m dm

instr

AC r ACx x rm

instr

ACm d

ACx rx r m d

m

x

m m

x

r r

r r

L r G i r

L r G i r

L r

L ri r r

( , )

( , )

( ) exp( ( ( ) ))

( ) exp( ( ( ) ))

( )

( )exp ( ( ) ( )=

− +− +

≈ −[ ]θ θθ θ

θ θ

Φ

Φ ΦΦ Ω

Ω

AC s d

AC s r AC s r m

f d x s am

x x

x m

r r


r r

r r r rr r r r r,

exp, ( , )

, , ( )( )( )

=+( ) ( ) ( )∫ →

1

1

αωτ

µ

ΦΦ

AC s d

AC s r

m

x

r r

r r

r r

r r,

exp,

( )( )

ΦAC s rxr r( , )r r r

rrrrs

ΦAC s rxr r( , )r r

Φx s rr r( , )r r

Φm s rr r( , )r r


(Equation 33.57), changes in the emission fluence are greater than those in the excitation fluence. Thesame consequence can be inferred from the integral equation (Equation 33.71). Moreover, the phase ofthe emission fluence is greater than that of the excitation fluence, and the normalized fluence, Φm/Φx,maintains a high phase contrast.

Due to noise and the ill condition of the Jacobian matrix for inverting systems of equations, updatingcan be accomplished using Newton’s method67 with Marquardt–Levenberg parameters λ:

(33.72)

Using excitation referencing at a single reference point, Lee and Sevick-Muraca57 reconstructed an 8× 4 × 8 cm3 phantom containing a 1 × 1 × 1 cm3 target with 100-fold greater ICG concentration by using8 excitation sources, 24 detection fibers for collecting excitation light, and 2 reference detection fibers(one on either side of the reflectance and transillumination measurements) for collecting excitation light.Figure 33.19A is the original map containing 2D slices that demark the heterogeneity placement, whileFigure 33.19B is the 3D reconstructed image.

While the results in Figure 33.19 represent reconstructions based on emission FDPM measurementsrelative to excitation FDPM measurements at a fixed reference position, Ntziachristos and Weissleder56

successfully reconstructed two fluorescent targets in a 2.5-cm-diameter, 2.5-cm-long cylindrical vesselcontaining ICG and Cy5.5 dyes. In addition, they used CW emission measurements referenced to exci-tation measurements at each of the 36 detector fibers as a result of point excitation at 24 source fibers.The high density of measurements for reconstruction of the small simulated tissue volume is troublesomefor validity of the diffusion equation used in the forward solver but is similar to that demonstrated byYang et al.,51 who reconstructed ICG and DTTCI in similarly sized phantoms and mice, presumably fromabsolute FDPM measurements at the emission wavelength alone.

The studies of the reconstruction presented above assumed that the absorption and scattering prop-erties were known a priori. However, using a differential approach coupled with Bayesian reconstructionapproaches (see below), Eppstein et al.68 were able to demonstrate the insensitivity of reconstructions tochanges in endogenous optical properties. Using a synthetic 256-cm3 volume containing 0.125-cm3 targetswith 10:1 contrast in absorption due to fluorophore and surrounded on four sides by 68 sources and408 detection fibers, Eppstein was able to show that when the absorption cross section at the excitationwavelength, , varied as much as 90% and was unmodeled, while the scattering coefficient, , varied10% or less and was also unmodeled, the impact on the reconstruction was minimal or negligible.Recently, Roy et al.69 produced similar results when they demonstrated unmodeled variations in allendogenous optical properties by as much as 50%, which did not impact reconstructions when emissionFDPM measurements were individually self-referenced to excitation FDPM measurements, as was donewith the CW measurements of Ntziachristos and Weissleder.56 While it appears promising that fluores-cence-enhanced optical tomography can be accomplished without much a priori information about theendogenous optical properties, these results nonetheless pertain to synthetic studies and must be con-ducted on actual tissues of substantive and clinically relevant volumes for validation.

33.5.3 Differential Formulation of the Inverse Problem

A second approach to the full-inverse-imaging problem may be the differential formulation, but thistime it is rewritten for measurement , whether absolute, relative to a reference measurement atthe emission or excitation wavelength, or self-referenced relative to the excitation wavelength at eachdetector position, . We term this approach the differential formulation because a small change in thepredicted measurements is directly expressed in terms of a small change in the optical properties, ∆X,using a Jacobian matrix, J , . Consider a number of detectors, M; the error function is then

( )( , )

( , )

( , )

( , )J J I JT T AC s d

AC s r

meas

AC s d

AC s r

comp

Xr r

r r

r r

r rm

x

m

x

+ =

−

λ ∆ΦΦ

ΦΦ

r r

r r

r r

r r

µaxiµsxi

Z r rd s( , )r r

rrd

∂ ∂( )∆Z Xi j


defined as the sum of the square of errors between the measured and calculated values at detector i =1…M:

(33.73)

We refer to each fi as a residual and the gradients of the error function with respect to the property, X:

(33.74)

FIGURE 33.19 The reconstruction of µa→m using the excitation wave as a reference using the integral approach andMarquardt–Levenberg reconstruction. The image was required after 27 iterations with regularization parameters forIAC ratio (ACR), λAC = 1.0, and for relative phase shift (RPS), λθ = 0.02. (A) Optical property maps of true µa→m

distribution and (B) reconstructed µa→m distribution. Peak values of µa→m reached 0.1205 cm–1. (C) Iteration vs. SSE.

4.5

4

3

2

1

3.5

2.5

0.5

1.5

4

4 6 82

20X [cm]

Y [cm]

Z [c

m]

A

4.5

4

3

2

1

3.5

2.5

0.5

1.5

4

4 6 82

20X [cm]

Y [cm]

B

0.55

0.45

0.35

0.25

0.15

0.05

0.5

0.4

0.3

0.2

0.1

80

70

60

50

40

30

20

10

00 5 10 15 20 25 30

SS

E

Iterations

0.14

0.12

0.1

0.08

0.06

0.04

0.02

C

F Z Z f Xi

m

i

c

i

M

i

i

M

( ) ( )( ) ( )

X = ( ) − ( )[ ] = [ ]= =

∑ ∑1

2

2

1

∇ =F f XT( ) ( )X J2


(33.75)

Consider the Taylor’s expansion of function F around a small perturbation of optical properties, ∆X:

(33.76)

which can be expressed as:

(33.77)

and the function to be minimized, Φ(∆X), can be explicitly written:

(33.78)

For first-order Newton’s methods, the term is neglected, and the Gauss–Newton method becomes one of minimizing:

(33.79)

(33.80)

The Levenberg–Marquardt method of optimization becomes49

(33.81)

The gradient-based truncated Newton’s method is based on retaining the second-order terms suchthat Equation 33.78 becomes49

(33.82)

or alternatively,

(33.83)

Typically, the first-order Newton’s methods were employed, with the exception of the work by Roy.70

In the Newton’s methods, it is assumed that ∆Φ = J ⋅ ∆ΧΧΧΧ, and the solution is found using one of theseveral optimization approaches. The Jacobian matrix can be computed either directly from the stiffnessmatrices of the finite element formulation or simply, but more computationally time-consuming, frombackward, forward, or central differencing approaches that compute the differences in the values of

, with small differences in the parameter to be updated, The Gauss–Newton and theLevenberg–Marquardt algorithms performed poorly in a large residual problem. Since the inverse ishighly nonlinear and ill conditioned due to the error in measurement data, the residual at the solutionwill be large. It seems reasonable, therefore, to consider the truncated Newton’s method.

∇ = + ∇

=

∑2 2

1

2F f X f XTi i

i

M

( ) ( ) ( )X J J

F F F FT( ) ( ) ( ) ( ) ( )X X X X X X X X+ = + ∇ ⋅ + ⋅∇ ⋅∆ ∆ ∆ ∆1

22

F F f f X f XT T Ti i

i

M

( ) ( ) ( ) ( ) ( )X X X J X X X J J X+ = + ⋅ + ⋅ + ∇

⋅=

∑∆ ∆ ∆ ∆2 2 2

1

Φ ∆ ∆ ∆ ∆ ∆( ) ( ) ( ) ( ) ( ) ( )X X X X J X X X J J X= + − = ⋅ + ⋅ + ∇

⋅=

∑F F f f X f XT T Ti i

i

M

2 2 2

1

2 2

1

⋅ ∇

⋅

=∑∆ ∆X XT

i i

i

M

f X f X( ) ( )

∇ ⇒ = ⋅ +Φ ∆ ∆( ) ( )X J J X J X0 T T f

J J X J XT T f⋅ = −∆ ( )

J J I X J XT T f+[ ]⋅ = −λ ∆ ( )

∇ ⇒ = + + ∇

⋅

=∑Φ ∆ ∆( ) ( ) ( ) ( )X J X J J X0 2

1

T Ti i

i

M

f f X f X

′ ⇒ = ∇ + ∇ ⋅Φ ∆ ∆( ) ( ) ( )X X X X0 2F F

Z r rd s( , )r r

X rj( ).r


For the truncated Newton’s method, the additional computational cost of computing the Hessian[associated with ∇2 F(X)] is assisted by reverse automatic differentiation.49,70 Using synthetic data, Royhas shown the feasibility of using the technique for 3D reconstruction of lifetime, τ, and absorption-coefficient changes in frustrum and slab geometries from synthetic data containing noise thatmimics experimental data.54

33.5.4 Regularization and Other Approaches to Parameter Updating

In both the integral and differential formulations of the inverse problem, the tissue to be imaged mustbe mathematically discretized into a series of nodes or volume elements (voxels) in order to solve theseinverse problems. The unknowns of the inverse problems are then comprised of the optical propertiesat each node or voxel. The final image resolution is naturally related to the density nodes or voxels.However, the dimensionality of the imaging problem is directly related to the number of nodes and caneasily exceed 10,000 unknowns for a 3D image. In a problem of this scale, the calculation of Jacobianmatrices and matrix inversions involved in updating the optical property map are computationallyintensive and contribute to the long computing times required to reconstruct the image. The instabilityarises because the measurement noise in the data or errors associated with the validity of the diffusionapproximation can result in large errors in the reconstructed image.

One of the greatest challenges associated with fluorescence-enhanced tomography is the propagationof error. In comparison with absorption imaging based on measurements of excitation light, fluorescencemeasurements have a reduced signal level and SNR. Lee and Sevick-Muraca71 measured the SNR forsingle-pixel excitation and the emission-frequency domain at 100 MHz and found them to be 55 and 35dB, respectively. In addition to the reduced signal, the noise floor of emission measurements can beexpected to be elevated when excitation-light leakage constitutes an increased proportion of the detectedsignal. Consequently, for emission-tomography measurements, excitation-light leakage is crucial, andinterference filters that attenuate excitation light four orders of magnitude (i.e., filters of OD 4) may beclearly insufficient. Excitation-light leakage will be a significant problem when emission measurementsare conducted in tissue regions where the target is absent and fluorescent contrast agents are not activated.Unfortunately, this type of error is not present in synthetic studies and is undoubtedly underestimatedin the vast proportion of tomography investigations to date.

33.5.4.1 Regularization

Regularization is a mathematical tool used to stabilize the solution of the Newton’s inverse problem andto make it more tolerant to measurement error. Regularization approaches will play an important rolein the development of suitable algorithms for actual clinical screening. For example, when discretized,the differential and integral general formulations result in a set of linear Newton’s equations generallydenoted by AY = Z, where Y is the unknown optical properties and Z is the measurements. This systemis commonly solved in the least-squares sense where the object function Q = AY – Z2 + λY2 is minimizedand λ is called the regularization parameter. The minimization of this function results in Y = (ATA+

–1ATZ. The regularization parameter is generally chosen either arbitrarily or by a Levenberg–Marquardt algorithm so that the object function is minimized.72 Thus, the choice of regularizationparameter is through a priori information and adds another degree of freedom to the inverse-problemsolution. Finally, in a recent work, Pogue et al.60 present a physically based rationale for empiricallychoosing a spatially varying regularization parameter to improve image reconstruction.

33.5.4.2 Bayesian Regularization

Eppstein et al.46,47,52,68 used actual measurement-error statistics to govern the choice of varying regular-ization parameters in their Kalman filter implementation in optical tomography. In their work, theydeveloped a novel Bayesian reconstruction technique, called APPRIZE (automatic progressive parameter-reducing inverse zonation and estimation), specifically for groundwater problems and adapted them tofluorescence-enhanced optical tomography.64–66 Unique components of the APPRIZE method are an approx-imate extended Kalman filter (AEKF), which employs measurement error and parameter uncertainty to

µax m→

λI)


regularize the inversion and compensate for spatial variability in SNR, and a unique approach to stabi-lizing and accelerating convergence called data-driven zonation (DDZ). Using the notation (∆X, f(X))as described in Section 33.5.3, the Newton’s solution is formulated here as:52

(33.84)

where Q is the system-noise covariance, which describes the inherent model mismatch between theforward model (the diffusion equation) and the actual physics of the problem; R is the covariance of themeasurement error that is actually acquired in the measurement set; and Pxx is the recursively updatederror covariance of the parameters, X, and is estimated from the measurement error, f(X). The use ofthis spatially and dynamically variant covariance matrix results in the minimization of the variance ofthe estimated parameters, taking into account the measurement and system error.

The novel Bayesian minimum-variance reconstruction algorithm compensates for the spatial variabil-ity in SNR that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging.Figure 33.20 illustrates the image reconstruction of 256-cm3 tissue-mimicking phantoms containingnone, one, or two 1-cm3 heterogeneities with 50- to 100-fold greater concentration of ICG dye overbackground levels. The spatial-parameter estimate of absorption from the dye was reconstructed fromonly 160 to 296 surface reference measurements of emission light at 830 nm in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emissionwavelengths is shown to be highly variable.

Another important feature of the Bayesian APPRIZE algorithm is the use of DZZ. With DDZ, spatiallyadjacent voxels with similarly updated estimates are identified through cluster analysis and merged into

FIGURE 33.20 Image reconstruction with APPRIZE. (A) The initial homogeneous estimate discretized onto the9 × 17 × 17 grid used for the initial inversion iteration and shown with the true locations of the 3 heterogeneitiesand 50 detectors (small dots). (B) Case 1: the reconstructed absorption due to the middle fluorescing heterogeneity,interpolated onto the 17 × 33 × 33 grid used for prediction and shown with the locations of the four sources used(open circles). (C) Case 2: the reconstructed absorption due to the top and bottom fluorescing heterogeneities shownwith the locations of the eight sources used (open circles). (D) Case 3: the reconstructed absorption of a homogeneousphantom shown with the locations of the four sources used (open circles). Although the phantoms and reconstruc-tions were actually 8 cm in the vertical dimension, only the center four vertical centimeters are shown here. (FromEppstein, M.J. et al., Proc. Natl. Acad. Sci. U.S.A., 99, 9619, 2002. With permission.)

6

4

2

4 2 0 2 4 6cmcm

8

cm

(A) (C) Case 2 (D) Case 3(B) Case 1cm−1

20 its 51 its 24 its

0.8

0.7

0.6

0.5

0.4

0.2

0.3

0.1

0

∆X J Q R J P J Q R X= + +[ ] ⋅ +

⋅− − − −T

xxT f( ) ( ) ( )1 1 1 1


larger stochastic parameter “zones” via random field union.73 Thus, as the iterative process proceeds, thenumber of unknown parameters, X, decreases dramatically, and the size, shape, value, and covariance ofthe different “parameter zones” are simultaneously determined in a data-driven fashion. Other approachesto reducing the dimensionality of the problems involve concurrent NIR optical imaging with MRI74–76

and ultrasound77 to compartmentalize tissue volumes and to reduce the number of parameters to berecovered in the optical-image reconstruction.

33.5.4.3 Simply Bounded Constrained Optimization

Imposing restrictions on the ill-posed problem can transform it to a well-posed problem, as discussedabove. Regularization is one method for reducing the ill-posedness of the problem.78 In the optical-tomography problem, its solution, i.e., the optical properties of tissue, must satisfy certain constraints,and imposing these conditions can in itself regularize or stabilize the problem. Imposing these constraintsalso explicitly restricts the solution sets and can restore uniqueness.

Provencher and Vogel78 have suggested two techniques, prior knowledge and parsimony, for makingthe problem well posed. The first condition requires that all prior physical knowledge about the solutionbe included in the model. The second condition protects against the introduction of nonphysical phe-nomena. Tikhonov and Arsenin79 also suggested that, to obtain a unique and stable solution from thedata, supplementary information should be used so that the inverse problem becomes well posed. Thebasic principle of using a priori knowledge of the properties of the inverse problem is to restrict the spaceof possible solutions so that the data uniquely determine a stable solution.

Roy and Sevick-Muraca showed that the constrained optimization technique, which places simplebounds on a physical parameter to be estimated, might be more appropriate for solving the fluorescence-enhanced optical-tomography problem.50 That is, a range of fluorescent optical properties is physicallydefined for the problem, and the recovered parameter, X, must always be positive. Specifically, Roydemonstrated the use of the bounding parameter, ε, both as a means of regularizing and acceleratingconvergence and as a means of setting the level of optical property contrast to be reconstructed usingreferenced emission measurements.69 Here, the possible values of parameter estimates are stated to liebetween an upper and lower bound. In the first pass of the iterative solution, the optical property mapis recovered, and parameter estimates that lie within the upper and lower bounds plus and minus a smallbounding parameter, ε, are recovered and held constant for the next iteration. Thus, the number ofunknowns decreases with each iteration. Indeed, the value of the bounding parameter can be used to setthe resolution and the performance of the tomographic image. For example, if the bounding parameteris large, then the tomographic image will “filter out” artifacts not associated with the target; but if thebounding parameter is small, the tomographic image may sensitively capture artifacts and heterogeneitythat are not necessarily associated with the target. Figure 33.21 illustrates the reconstruction using thesimply bounded truncated Newton’s method, which shows that as the bounding parameter is increased,the recovered image becomes less sensitive to the background “noise.” This approach may have significantapplication for increasing the target to background signals, an issue related to nuclear imaging thatimpairs tomographic reconstructions.

33.6 Fluorescent Contrast Agents for Optical Tomography15

Table 33.2 provides a chronological listing of studies reported in the literature over the past decade thatinvolve a number of different fluorescent-contrast agents.23,51,80–116 While the studies have progressed fromusing photodynamic agents; freely-diffusable agents, such as ICG; fluorochromes conjugated to mono-clonal antibodies (MAb) and their fragments; small-peptide targeting agents similar to those employedin nuclear imaging; and, finally, activatable and “reporting agents.” Unfortunately, the translation of theseagents to human clinical studies has been limited. Furthermore, investigations have been largely confinedto superficial or subcutaneous tumors, where the true advantages of NIR fluorescent agents, that is, deep-tissue penetration and optical tomography, cannot be aptly demonstrated. Nonetheless, the strategies for


NIR fluorescent-contrast agents have been impressive and have included using simple blood-poolingagents to highlight hypervascularity, employing contrast provided by pharmacokinetic model-parameterestimates of uptake, and designing agents that specifically target membrane receptors of cells lining

FIGURE 33.21 (Color figure follows p. 28-30.) Three-dimensional reconstruction from simply bound truncatedNewton’s method. (A) Actual distribution of fluorophore-absorption coefficient of background tissue variability ofendogenous (50%) and exogenous (500%) properties. (B) Reconstructed fluorophore-absorption coefficient of back-ground tissue variability of endogenous (50%) and exogenous (500%) properties using relative measurement of theemission fluence with respect to the excitation fluence at the same detector point, > = 0.0001. (C) Reconstructedfluorophore absorption coefficient of background tissue variability of endogenous (50%) and exogenous (500%) prop-erties using relative measurement of the emission fluence with respect to the excitation fluence at the same detector point.(From Roy, R., Godavarty, A., and Sevick-Muraca, E.M., IEEE Trans. Med. Imaging, in press. With permission.)


TABLE 33.2 Fluorescence-Enhanced Contrast Imaging: Literature of Agent Studies

Ref.Imaging System(incident fluence)

Animal Model Dose Contrast Agent λ Excitation/Emission Comments

Biolo et al., 199180 Spectrograph for point detection of fluorescence following surface illumination

Mouse 0.12mg/kg bw ~0.24 µmol/kg bw

ZnPc (phthalocyanine) in liposomes, spectral detection of fluorescence at λ

600 nm Provide measurements for assessing pharmacokinetics of PDT agent

Pelegrin et al., 199181 Area illumination with area (133 mW/cm2)detection using photography

Mouse, deceased

100 µg/animal~600 pmol/kg bw

Fluorescein isothiocyanate (FITC) coupled to MAb

488 nmKodak Wratten filter #12

for excitation light rejection

Study the localization of dye targeted to human colon carcinoma in mice after coupling to MAb

Straight et al., 199182 Interstitial illumination (20 mW) with area detection using CCD camera

Mouse 20 mg/kg bw ~70 µmol/kg bw

Photofrin II 514.5/spectral discrimination 585–730 nm

Validate CCD technology for imaging drug distribution in tumors

Folli et al., 199283 Fiber through endoscope illumination (10 mW/cm2) with area detection using photography

Human 0.1–0.28 mg/patient ~0.1 nmol to 0.28 nmol/patient

Fluorescein isothiocyanate (FITC) coupled to MAb



Study immunophotodiagnosis in colon carcinoma patients

Cubeddu et al., 1993, 199784–85

Area illumination (75 µW/cm2) with pulsed dye laser with gated CCD video camera

Mouse 5–25 mg/kg bw ~17–87 µmol/kg bw, 1993

0.1 mg/kg~0.35 µmol/kg bw, 1997

HpD (hematopor-phyrin derivative)

405 nm/>560 nm Demonstrate the use of time-dependent measurements to identify HpD distinct from native fluorescence based upon long fluorescent lifetimes

Kohl et al., 199386 Intensified CCD Mouse 0.2–1 mg/kg bw~0.7–3.5 µmol/kg bw

Porphyrin-based photosensitizers

Demonstrate the ability to image s.c. tumor

Folli et al., 199487 Area illumination with area (13 mW/cm2)detection using photography

Mouse, deceased

100 µg/animal~600 pmol/kg bwa

Indopentamethine-cyanine coupled to MAb directed against squamous cell carcinoma



Show the ability to detect indocyanine dye targeted to squamous cell carcinoma in the upper respiratory tract through MAb E48 without removing skin, as was necessary when fluorescein was employed

Haglund et al., 199488 Area illumination (100-W tungsten-halogen bulb) and area detection with CCD camera

Rat 1.0 mg/kg bw1.3 µmol/kg bw

ICG 780/830 Distinguish rat gliomas from normal brain tissue through free-agent fluorophore imaging with CCD camera


Mordon et al., 199489 Area illumination (150W Xenon lamp, 2.5 mW/cm2) with area detection using intensified CCD

Mouse 5 mg/kg bw(~13 µmol)

5,6-CF carboxyfluorescein(BCECF)

465 nm/490 and 515 nm Show the use of dual-wavelength measurements of a ratiometric dye to provide a 2D pH image of tumor tissues

Ballou et al., 199590 Area illumination with area detection using intensified video camera or cooled CCD

Mouse 10–100 µg/animal~40 pmol to 6 nmol/

animal

Cyanine fluorochromes coupled to MAb

550–674 nm/565–694 nm Demonstrate the use of tumor-targeting antibodies using Cy3.18, Cy5.18, and Cy5.5.18 cyanine fluorochromes

Devoisselle et al., 199591 Area (50 mm2)illumination (Xe lamp) with point detection using fiber optics and spectrograph

Mouse 7.5 mg/kg bw ~10 µmol/kg bw

ICG emulsion 720 nm/spectra discrimination of fluorescence

Demonstrate the use of emulsion preparation to alter the pharmacokinetics of ICG

Rokahr et al., 199592 N2 laser pulsed through fiber and detected with fiber to spectrometer

Human undergoingurinary-bladdercytoscopy

50 mg/patient (ALA induces fluorescence)

Protoporphyrin IX 337 and 405/380 through 685 spectral discrimination

Discriminate malignant and normal bladder tissue with ALA-induced protoporphyrin imaging

Haglund et al., 199693 Area illumination with photography lights and area detection with CCD camera

Human (open brain)

1 mg/kg bw ~1.3 mmol/kg bw

ICG 790/805 nm Study detection of human glioma with ICG imaging

Sakatani et al., 199794 Cooled CCD camera, 100-mW laser diode

Rat 554 pmol/rat ICG-lipoprotein 790 nm/840 nm Conduct cerebrospinal imaging with ICG bound to lipoprotein, injected intracranially

Neri, 199795 Method similar to Folli et al. (1994); 100-W tungsten lamp for area illumination with detection via an 8-bit CCD in a light-tight box

Mouse 100 µl/mouse of a concentrated antibody solution of 1 mg/ml with dye:MAb ratio of 1:1

Fragments of human antibodies directed against oncofetal fibronectin (B-FN) and labeled with Cy7

673–748 nm/765–855 nm Demonstrate the use of B-FN targeting for providing diagnostic imaging and therapy of cancer targeting angiogenic vessels

Ballou et al., 199896 Area illumination and area detection via CCD

Mouse 50 µg/animalMAb:dye (1:2)

~600pmol/animal

Cy3, Cy5, Cy5.5, and Cy7 labeled antibodies against human nucleolin and stage-specificembryonic antigen-1

Demonstrate the ability to penetrate more deeply with Cy7 dye

TABLE 33.2 Fluorescence-Enhanced Contrast Imaging: Literature of Agent Studies (continued)




Eker et al., 199997 Fiber for excitation and collection in a colonoscope for detection via a spectrometer

Human 5mg/kg bw ~30 nmol/kg bw

Protoporphyrin IX, as a metabolized product of ALA (photosensitizer)

337, 405, 436 nm excitation

Demonstrate the use of ALA as a contrast agent for detecting adenomatous polyps of the colon and showed promise for distinguishing adenomatous from hyperplastic polyps

Reynolds et al., 199998 Area illumination with laser diode (1 mW/cm2)and area detection using intensified FDPM CCD system

Canine 1.0 mg/kg bw ~1.3 µmol/kg bw

ICG 780 nm/830 nm Demonstrate the ability to detect spontaneous disease of the canine mammary chain as well as reactive lymph nodes

Becker et al.,199999

Area illumination and area detection with CCD and MRI

Mouse 2 µmol/kg bw(1:2.4 or 2 for transferrin

or HSA)

Indotricarbocyanine and ultrasmall superparamagnetic iron oxide particles coupled to transferrin or human serum albumin (HSA)

Demonstrate targeting of tumors that express the transferring receptor using an optical agent as well as an MRI agent

Weissleder et al., 1999;23

Mahmood et al.,1999100

Area illumination and area detection using CCD in a light-tight chamber; illumination with 150-W halogen lamp with interference filters, 10–100 µW/cm2

Mouse 10 µmol/animal(92 MEG, 11 dye

molecules);250 pmol/animal

Cy5.5. loaded onto a polylysine and methoxypolyethylene glycol polymer backbone with cathepsin B and H-cleavage sites

610–650 nm/>700 nm Demonstrate that tumor proteases can be used as molecular targets

SNR for 30-sec exposure 173 for 200 pmol in phantom

Becker et al., 2000101 Area illumination and area detection with CCD

Mouse 2 µmol/kg bw Transferrin and human serum albumin coupled with indotricarbocyanine dye

740 nm/780–900 nm Demonstrate targeting to the tumors expressing transferring receptor





Gurfinkel et al., 2000102 Area illumination (1.98 and 5.5 mW/cm2) and area detection using intensified FDPM CCD system

Canine 1.1 and 1.0 mg/kg bw~1.3 µmol/kg bw

ICG and carotene-modifiedPDT agent (HPPH) conjugated with carotene moiety for reduction of phototoxicity

780 nm/830 nm (ICG)660 nm/710 nm

(HPPH-car)

Demonstrate the use of temporal AC measurements to image pharmacokinetic parameters to discern diseased tissues

Licha et al.,2000103

Single-point detection and point illumination (5 mW) using FDPM

Rat 0.5 µmol/kg bw Derivatives of ICG(unclear whether

fluorescence was detected in vivo)

750 and 786 nm excitation

Provide measurements of absorption at the excitation wavelength as a function of time to provide pharmacokinetic evaluation of ICG and its hydrophilic derivatives

Yang et al., 2000;104

Hoffman et. al., 2001105

Area illumination and detection using CCD camera

Mouse GFP expressed in vivo Demonstrate visualization of tumors and tumor metastasis by whole-body fluorescence imaging

Ntziachristos et al., 200074

Fiber bundle to PMT using time-domain photon migration, point illumination and point detection

Breast 0.25 mg/kg bw~0.32 µmol/kg bw

ICG Fluorescence was not used, but absorption provided contrast that was validated by simultaneous MRI images obtained with gadolinium contrast

Bugaj et al., 2001;106

S. Achilefu et al., 2000, 2001107–109

Area illumination (40 mW) and area detection using CCD camera

Rat 5.2–6.0 mg/kg bw~6.7–7.7 µmol/kg bw

ICG, ICG small-peptide conjugates cytate and cybesin

780 nm/830 nm Targeting to rat tumor lines expressing the somatostatin and bombesin receptors

Becker et al., 2001110 Area illumination and detection using CCD camera

Mouse 0.02 µmol/kg bw Peptide-cyanine dye conjugate, indodicarbocyanine (IDCC), and indotricarbocyanine (ITCC) conjugated to octreotate, an analog of somatostatin

740 nm/780–900 nm Targeting to mouse tumor lines expressing the somatostatin receptors





Bremer et al., 2001111 Area illumination and area detection using CCD in a light-tight chamber; illumination with 150-W halogen lamp with interference filters, 10–100 µW/cm2

Mouse167 pmol/animal, i.v. Polylysine polymer coupled

with mMP-2 peptide substrates holding Cy5.5

610–650 nm/>700 nm Measure matrix metalloproteinase (MMP) activity in vivo for directing the therapeutic use of proteinase inhibitors

Ebert et al., 2001112 Area illumination with pulsed laser and detection using CCD camera (ambient light rejection)

Rat 2 µmol/kg bw, i.v. SIDAG (hydrophilic derivative of cyanine dye), 1–1′-bis-(4-sulfbutyl) indotricarbocyanine 5,5′-dicarboxylic acid diglucamide monosodium salt; Nd:YAG

740 nm, 3 ns FWHM, 50 Hz/750–800 nm

Demonstrated localization of tumor and presented phantom data using FDPM with contrast ratios of 6:1

Finlay et al., 2001113 Point illumination with fiber probe, point detection with fibers directed to a spectrograph and CCD

Rat 200 mg/kg bw (ALA injected)

ALA-induced porphyrin 514 nm/676 nm emission Photobleaching kinetics of ALA-induced protoporphyrin measured

Rice et al., 2001114 Area detection of light-emitting probes with CCD

Mouse Bioluminescence of fluorescent proteins

Firefly luciferase >600 nm emission Imaging light-emitting probes





Soukos et al., 2001115 Area illumination using pumped dye laser (15 mW/cm2) and detection using room temperature CCD camera

DMBA- induced tumor in hamster cheek pouch

670 µg/animal~3.3nmol/kg bwa

Anti-EGFR MAb (C225) coupled to Cy5.5 (1:2.1)

IgG-Cy5.5 (1:2.3)

670 nm/>700 nm Demonstrate that the targeted MAb–dye complex could be used to provide immunophotodiagnostic information, thereby guiding therapeutic intervention

Yang et al., 200151 Single-pixel FDPM using point source and point detector

Rat 1.5 mg/kg bw ~2 µmol/kg bw

ICG,DTTCI

Work toward demonstration of fluorescence imaging in vivo

Zaheer et al., 2001116 Area illumination (18 mW/cm2)

Mice (hairless)

100 nmol/kg (i.v) (Indocyanine) IR Dye 78 conjugated to pamidronate with hydroxyapatite binding properties

771 nm/796 nm Assess osteoblastic activity for skeletal development, osteoblastic metastasis, and coronary atherosclerosis

a Molecular weight of proteins are estimated on the order of 106 g/mol.





neovasculatures as well as the neoplastic cells that the vasculature feeds. Strategies that focus on lysosomalactivity and enzyme cleavage for fluorochrome activation and mediation of fluorescence decay as well asfor fluorochrome accumulation specific to cancer cells have also been demonstrated. Table 33.1 outlinesthese fluorochromes used in in vivo studies. When available, the chronological listing also notes theexcitation and emission wavelengths used, the incident illumination, the measurement geometry, andthe type as well as number of fluorochrome molecules used to detect a signal. The fluorophores arebroadly classified into PDT agents, nontargeting blood-pooling agents, agents that “report” or sense,targeting agents based on immunodiagnostics and small-peptide conjugation, and activatable agents.

33.6.1 Photodynamic Therapy Agents

Starting with the area of photodynamic imaging, the early studies relating to fluorescence-enhancedimaging date back to 1991 and focused on evaluating the spatial distribution as well as the pharmaco-kinetics of PDT agents for dosimetry purposes. Measurements were typically conducted in tumor-bearingmice with total agent administration between 0.1 and 90 µM/kg bw using area illumination and CCDcamera detection. PDT agents are likely candidates for fluorescent-enhanced imaging, more than likelydue to their existing Food and Drug Administration investigational-new-drug (IND) applications fortherapeutic use. The ability to obtain an IND for a diagnostic agent previously approved for therapeuticuse enhances the opportunity for fluorescence-enhanced optical imaging. Yet despite the attractivenessfor their current and pending INDs, photodynamic agents do not possess the excitation and emissionspectra favorable for fluorescent contrast agents for imaging deep tissues. First, to maximize penetrationdepth into tissues, excitation must be between 750 and 800 nm, and the Stokes shift must be significant(~50 nm) to enable discrimination of the small fluorescent component from the overwhelming largecomponent of excitation light. An insufficient Stokes shift of 10 nm or less complicates the process ofrejecting multiply scattered light as the efficiency of filters cannot be guaranteed. Next, the fluorochromefor systemic administration should not experience a net lifetime or long-lived decay kinetics that exceedthe photon time of flight, as described in Section 33.2.3. For these reasons, the usefulness of PDT agentsfor contrast (and for therapy) is largely limited to epithelial linings of accessible tissues and not for deeptissues. However, one notable use of a PDT agent for contrast-enhanced surface imaging involves the useof its metabolic by product. Using exogenous δ aminolevulinic acid (ALA) for natural production ofprotoporphryin IX, Ecker et al.97 showed the ability to detect adenomatous polyps of the colon in humansand provided evidence to suggest the ability to discriminate between hyperplastic and adenomatouspolyps. While excitation at 337, 405, and 436 nm does not classify this agent as an NIR probe for deep-tissue penetration, this study is nonetheless significant in that it employs a natural “reporting” mechanismin which the nonfluorescent ALA is hypermetabolized in diseased tissue to the fluorescent porphyrinform.

33.6.2 Nontargeting Blood-Pooling Agents

ICG, with its 778-/830-nm excitation/emission maxima was an early contrast agent choice used as ablood-pooling agent for assessing hypervascularity and “leaky” angiogenic vessels of high permeability.While many advances in dye development have accelerated within the past 2 years, the majority of studiesinvestigating NIR fluorescent-contrast agents have been limited to ICG, a compound with FDA approvalfor systemic administration for investigating hepatic function117 and retinal angiography.118 ICG is excitedat 780 nm and emits at 830 nm. It has an extinction coefficient of 130,000 M–1cm–1, a fluorescent lifetimeof 0.56 ns, and a quantum efficiency of 0.016 for the 780-/830-nm excitation/emission wavelengths inwater.35 These values are not necessarily what will be observed in vivo.

When dissolved in blood, ICG binds to proteins such as albumin and lipoproteins. The absorptionmaximum shifts up to 805 nm, but the wavelength of maximum fluorescence is stable near 830 nm, andthe fluorescent intensity depends on its concentration.119,120 ICG is a nonspecific agent and is clearedrapidly from the blood, but it tends to collect in regions of dense vascularity through extravasation.


Devoisselle et al.91 demonstrated the use of ICG in an emulsion preparation at an administration of 10µmol/kg bw in a tumor-bearing rat to measure its prolonged pharmacokinetics, while Reynolds et al.98

used free ICG (1.3 µmol/kg bw) as a fluorescent agent in canines to image spontaneous mammary diseaseon a veterinary-outpatient basis.

In a study by Reynolds et al.,98 frequency-domain approaches were employed whereby the caninemammary chain area was illuminated with intensity-modulated light, and the resulting amplitude of thegenerated fluorescent light that propagated to the surface was imaged by a gain-modulated image-intensified camera. The approach enabled rejection of room light and provided the first demonstrationof fluorescence-enhanced imaging in a spontaneous tumor as in a large animal (Figure 33.22). Since thecanine is the only species other than the human to naturally encounter mammary and prostate cancer,121

this is an excellent animal model in which to assess the potential of detecting diseased tissue via a contrastagent. However, penetration depths are nonetheless limited to 0.5 to 2 cm, still not meeting the deepimaging potential of fluorescence-enhanced optical imaging.

In measurements of the canine mammary chain, also by Reynolds et al., a homodyned, gain-modulatedimage intensifier was used as described in Section 33.3.2. Excitation was accomplished by illuminatingthe tissue surface with a 4-cm-diameter expanded beam of a 20-mW, 780-nm laser, which was modulatedat 100 MHz. Figure 33.23 shows the DC, amplitude, phase, and modulation ratio (IAC/IDC) of an 830-nm wavelength emitted from the left fourth mammary gland with a palpable 1.2-cm (longitudinal) by0.5-cm (axial) papillary adenoma located approximately 1 cm deep within the mammary tissue. Theimage was acquired 23 min following i.v. injection of l mg/kg ICG. The diseased region is clearly shownin the raw, unprocessed DC, amplitude, phase, and modulation images.

The use of ICG for optical tomography has already been identified by the Chance group at theUniversity of Pennsylvania. In a combined time-domain and MRI-imaging study of 11 patients, Ntzi-achristos et al.74 administered 0.2 mg/kg ICG i.v. and conducted measurements in response to pulsedexcitation at 780 nm. Their time-domain system involved pulsed laser diodes at 780 and 830 nmmultiplexed into 24 source fibers and collected at 8 detection points.122 Using the MRI images to validatetheir integral inversion results, they were able to reconstruct images of an infiltrating ductal carcinomadue to the enhanced signature from the vascular blood pooling of ICG. Unfortunately, fluorescencesignals were not acquired, possibly due to the low SNR available with TDPM measurements, and theimages were reconstructed from signals at the incident wavelength.

FIGURE 33.22 Use of an incident-expanded beam on the mammary chain of the canine to excite systemicallyadministered fluorophore and to collect the emission of generated light from the tissue surface. (From Hawrysz, D.J.and Sevick-Muraca, E.M., Neoplasia, 2(5), 388, 2000. With permission.)


Later, using the modulated ICCD system Gurfinkel et al.102 used FDPM measurements with ICG as ablood-pooling agent as well as with a photodynamic agent, carotene-conjugated 2-devinyl-2-(1-hexylox-yethyl) pyropheophorbide (HPPH-car), to provide the difference in pharmacokinetics. The time courseof images was clearly able to discriminate between the nonselective uptake of the ICG blood-poolingagent, whose contrast was due mainly to the density of the microvasculature associated with the disease,

FIGURE 33.23 (Color figure follows p. 28-30.) The 128 ? 128 pixel-based imaging of 830-nm fluorescence of(A) CW IDC , (B) amplitude IAC , (C) phase delay, and (D) modulation ratio of the detected fluorescence generatedfrom the area cranial of the left fourth mammary gland of a canine. Illumination was accomplished with an expanded780-nm laser diode. Modulation frequency was 100 MHz. (From Reynolds, J.S. et al., Photochem. Photobiol., 70, 87,1999. With permission.)

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and the specific uptake of the HPPH agent, whose uptake is hypothesized to be mediated with theenhanced overexpression of low-density lipoprotein (LDL) receptors on the surface of cancer cells andthe association of HPPH and LDL in the blood compartment. Figure 33.24 represents the values of theAC intensity as a function of time at a single point in the area detection corresponding to the s.c. tumorfollowing i.v. injection of ICG as well as HPPH-car. Upon fitting the time course of AC-intensitymeasurements with pharmacokinetic models, a map of uptake parameters shown in Figure 33.25 dem-onstrates the ability to enhance optical contrast based on pharmacokinetics, as is currently done in MRI.In an effort to tune the pharmacokinetics of cyanine dyes by changing the level of hydrophobicity/philicity,Licha et al.103 and Ebert et al.112 showed that a hydrophilic derivative of cyanine dyes could enhance

FIGURE 33.24 AC fluorescent intensity as a function of time illustrating typical curve fits using (A) the ICGpharmacokinetic model and (B) the HPPH-car pharmacokinetic model. The symbols denote actual measurements,while the solid curve denotes the model fit. (From Gurfinkel, M. et al., Photochem. Photobiol., 72, 94, 2000. Withpermission.)


uptake and be detected using single-point illumination and detection at the excitation wavelength(0.5 @mol/kg bw) and area illumination and detection at the emission wavelength (2 @mol/kg bw).

In addition to using ICG as a means for assessing hypervascularity associated with cancer, ICG mayalso be used to assess lymph flow. Figure 33.26 is an in vivo ICCD image of a canine made cranial to thenipple of the left fifth gland 30 min after ICG injection. While the imaged area was not associated witha palpable nodule, pathologic examination confirmed that the fluorescence was attributed to a bloodvessel that bifurcated approximately 1 cm below the tissue surface in an area cranial to a regional lymphnode. Figure 33.27 represents the in vivo FDPM images of the fluorescence generated from the area ofthe right fifth mammary gland 43 min after injection of the ICG. Pathologic examination showed thatthe fluorescent source in this image corresponded to the regional lymph node.

The ability to detect fluorescence signals originating from regional lymph nodes suggests that FDPMfluorescence imaging coupled with improved fluorescent dyes could provide a valuable diagnostic methodfor assessing regional lymph-node status in breast cancer patients. Lymph-node status in breast cancerpatients can be a powerful predictor of recurrence and survival, and the number of lymph nodes withmetastases provides crucial prognostic information regarding the choice of adjuvant therapy.123 Currently,lymph-node involvement is assessed by dissection and subsequent pathologic examination, but researchersare investigating the use of other diagnostic modalities including MRI, x-ray-computed tomography, andsonography.123 More recently, nuclear imaging of a technetium-99 sulfur colloid injected into the tissue areaof a known breast tumor has been used to identify the sentinel lymph nodes. With the simultaneous orsequential injection of a blue dye to visually aid in its location, the sentinel lymph node can then be surgicallyremoved.123,124 Moreover, with NIR fluorescent agents, sentinel-lymph-node mapping could possibly beachieved without the use of the radionucleotide or with the introduction of a second dye to aid in surgicalincision. Furthermore, the development of peptide-, protein-, or antibody-conjugated fluorescent dye (seebelow) makes possible nonsurgical, optical diagnosis of nodal involvement.

FIGURE 33.25 (Color figure follows p. 28-30.) (A) Fluorescence IAC intensity map from ICG delineating diseasedtissue and (B) map of pharmacokinetic uptake parameters obtained from fitting the time sequences of fluorescence-intensity images showing no specific uptake of ICG in diseased tissue. (C) Fluorescence AC intensity map fromHPPH-car delineating diseased tissue and (D) map of pharmacokinetic uptake parameters obtained from fitting thetime sequences of fluorescence-intensity images showing specific uptake of HPPH-car in diseased tissue. (FromGurfinkel, M. et al., Photochem. Photobiol., 72, 94, 2000. With permission.)

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Using intracranial injection of ICG bound to lipoprotein, Sakatani et al.94 also showed the use of ICGin mapping the cerebrospinal fluid pathways in rats. Area illumination using a 100-mW laser diode andarea detection with a cooled CCD camera was sufficient to detect meaningful images of fluid pathwaysfollowing injection of 554 pmol ICG.

FIGURE 33.26 (Color figure follows p. 28-30.) The 128 ? 128 pixel-based imaging of 830-nm fluorescence of(A) CW IDC , (B) amplitude IAC , (C) phase delay, and (D) modulatio0n ratio of the detected fluorescence generatedfrom the area cranial of the left fifth mammary gland of a canine. Illumination was accomplished with an expanded780-nm laser diode. Modulation frequency was 100 MHz. (From Reynolds, J.S. et al., Photochem. Photobiol., 70, 87,1999. With permission.)



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33.6.3 Nontargeting Contrast Agents That “Report” or Sense Environment

While not employing the favorable excitation/emission characteristics, the studies of Mordon et al.89 areespecially intriguing because they are the first studies to employ a “reporting” dye, or a dye whose emissioncharacteristics varied with tissue milieu. Specifically, they employed the pH-sensitive dye of 5,6 CF

FIGURE 33.27 (Color figure follows p. 28-30.) The 128 ? 128 pixel-based imaging of 830-nm fluorescence of(A) CW IDC , (B) amplitude IAC , (C) phase delay, and (D) modulation ratio of the detected fluorescence generatedfrom a lymph node in the area of the right fifth mammary gland of a canine. Illumination was accomplished withan expanded 780-nm laser diode. Modulation frequency was 100 MHz. (From Reynolds, J.S. et al., Photochem.Photobiol., 70, 87, 1999. With permission.)

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carboxyfluorescence (BCECF), which is a ratiometric dye sensitive to pH. Using CW, spectrally resolvedmeasurements of fluorescence resulting from area illumination with excitation light at 465 and 490 nm,they employed area detection using an intensified CCD camera to determine changes in fluorescencewith changes in wavelength of the excitation light. Using an in vitro calibration of the ratiomeric dye,Mordon et al. were able to correlate the 2D fluorescent images to provide 2D images of tumor pH in as.c. mouse model. While CW measurements are not time-dependent methods, this study did not directlymeasure changes in the fluorescence-decay kinetics but rather used spectral ratiometric changes to demarkthe change in the radiative relaxation rates that arose owing to acidotic tissue conditions.

33.6.4 Targeting, Contrast Agents: Immunophotodiagnosis

Folli et al.87 were the first to demonstrate the use of NIR targeting agents by coupling an indopentame-thinecyanine dye coupled to a MAb E48 for targeting squamous cell carcinoma in the upper respiratorytract in mice. Approximately 600 pmol conjugated dye molecules were injected into mice and imagedpostmortem using simple planar illumination and photography. This was the first demonstration of NIRimmunophotodiagnosis that followed prior work to employ non-NIR, fluorescein-labeled antibodiestargeted against carcinomembryonic antigen (CEA) in mouse81 and clinical studies.83 The study wasrepeated by Neri,95 who used generated antibodies targeted to oncofetal fibronectin (B-FN), which ispresent in the angiogenic vessels of neoplasms but not in mature vessels. Further emphasizing the useof NIR fluorochromes in deep-tissue penetration for photoimmunodiagnosis, Ballou et al.90,96 conjugatedthe cyanine dye class of Cy3, Cy5, Cy5.5, and Cy7 fluorochromes and not unsurprisingly found theycould probe more deeply with the Cy7-conjugated MAbs in living tumor-bearing mice. They were ableto image targeted delivery of fluorochromes of 40 pmol to 6 nmol/kg bw, and 600 pmol/animal usingarea illumination and an intensified or cooled CCD camera. More recently, Soukos et al.115 used a 7,12-dimethylbenz(a)anthracene (DMBA)-induced tumor in the hamster-cheek-pouch model and showedthe ability to target cyanine dye to express endothelial growth factor receptor using the antiendothelialgrowth factor receptor (EGFR) MAb (C225) in surface illumination and detection. Approximately 3.3nmol fluorochrome was used in each animal.

33.6.5 Targeting Contrast Agents: Small-Peptide Conjugations

A significant advancement in the design of optical contrast agents mimicked those used in other medicalimaging modalities. Achilefu et al.107–109 and Bugaj et al.106 used area illumination and area CCD detectionin tumor-bearing rats in order to detect ~6 to 7 µmol/kg bw of cyanine dye conjugated to small peptidesfor targeting somatostatin and bombesin receptors. One commercial nuclear diagnostic agent,Octreoscan®, is based on targeting the somatostatin receptor, which is overexpressed in neuroendocrinetumors. Bugaj et al. showed that the optical imaging using cytate, the derivatized and peptide-conjugatedICG, is similar to the radiolabeled peptide analog for somatostatin. Similar results were reported fromusing the peptide-conjugated derivative of ICG, cybesin, which is similar to the radiolabeled peptideanalog for bombesin. Becker et al.110 reported similar work in tumor-bearing mice with detection limitsreduced to 0.02 µmol/kg bw using a similar targeting construct. In their work, they conjugated theindodicarbocyanine dyes and the indotricarbocyanine (ITCC) dyes with analogs of somatostatin, soma-tostatin-14, and octreotate. In another approach, Becker et al.99,101 followed the targeting approachpreviously used for methotrexate and PDT therapies, MRI gadolinium and magnetic-particle contrast,with human serum albumin (HSA) and transferrin (Tf) coupled to indotricarbocyanine dyes. While Tfbinds to specific cell-surface receptors, HSA binds nonspecifically. Their studies show the contrastenhancement of targeting specificity using the Tf-ITCC.

In another study involving peptide conjugation, Zaheer et al.116 conjugated a bisphosphonate derivative,pamidronate, which exhibits specific binding to hydroxyapatite to an indocyanine dye to image bonestructure in hairless mouse. The system may be capable of NIR detection of osteoblastic activity, enablingNIR imaging of skeletal development, coronary atherosclerosis, and other diseases.


33.6.6 Reporting or Sensing Contrast Agents

A novel “reporting” optical-contrast design was reported by Weissleder et al.,23 who employed fluorophoreCy5.5 loaded onto a polylysine backbone with methoxypolyethylene glycol polymer. When conjugatedto the polymer backbone in high concentration, the fluorochrome tends to quench itself. However, whenthe polymer backbone is cleaved by cathespin B or H, lysosomal proteases whose activity may be enhancedin cancer cells, the fluorochromes become free and radiatively relax to produce fluorescence. In contrastto the small-peptide-conjugated dyes, this system requires fluorochrome internalization. The pioneeringwork enabled detection of 10 µmol of agent or 250 pmol of fluorochrome administered per tumor-bearing animal and represented the first time an optical-contrast agent based on an internalizationconstruct had been demonstrated. Along the same lines, another agent that reported on the basis of proteaseactivity was developed using the same design principles. Bremer et al.111 coupled matrix metalloproteinase-2 (MMP-2) peptide substrates onto a poly-L-lysine polymer backbone and onto the peptides further conju-gated with Cy5.5. The fluorochromes were sufficiently packed to be quenched upon activation. Upon actionof the proteinase on the peptide, the Cy5.5 was freed and able to radiatively relax, reporting proteinase activity.MMPs are overexpressed in cancers, and MMP-2 in particular has been identified as the cause of collagenIV degradation. (Collagen IV is the major component of basement membranes.) The MMP-2 activity isthought to be responsible for the pathogenesis of cancer, including spread, metastasis, and angiogenesis.Using area illumination and detection, as little as 167 pmol per animal resulted in detected fluorescence tomeasure MMP activity in vivo for directing the therapeutic use of proteinase activity.

33.6.7 Combined Targeting and Reporting Dyes

Finally, Licha et al.125 sought to combine fluorochrome targeting using membrane receptors, such astransferrin, or the somatostatin and bombesin receptors with acid-cleavable constructs that would enableinternalization of the fluorochromes in the lysosomal compartments and recycling of the receptors. Suchconstructs to augment the accumulation and, therefore, concentrate the signal from the targeting fluo-rochrome would be enhanced only if the contrast agent had a long half-life in the circulation. Couplingthese cyanine dyes to different acid-cleavable hydrazone links that were bound to peptides, proteins, andantibodies, Licha et al. furthermore sought to develop a pH-sensitive contrast agent whose fluorescenceis mediated by tumor acidosis.

In another innovative development, Huber et al.126 synthesized bifunctional contrast agents containinga metal chelator for binding of a paramagnetic ion such as gadolinium and a conjugated fluorescent dyesuch as tetramethylrhodamine to combine optical imaging and MRI of experimental animals. Whilerhodamine excites within the visible with maximum absorbance at 547 nm and emission at 572 nm, theapproach was successful for imaging of Xenopus laevis embryos. With the conjugation of an NIR-excitabledye, the potential to develop bifunctional contrast agents for deep-tissue medical imaging could also berealized. Again the reader is urged to be cautious in assessing contrast-agent studies conducted in miceand rats. These tissue volumes are not comparable to those in humans, and it is unlikely that emissionsignals at these wavelengths can be detected with sufficient SNR for image reconstruction in large volumes.

33.6.8 Summary

In summary, the approaches for fluorescent contrast-agent development have to date focused on:

• Blood-pooling agents specific to increased microvessel density in neovascularized tumors

• Targeting agents based on:

• Immunophotodiagnosis

• Small-peptide conjugations targeting overexpressed receptors whose location of action isdirected to:

• Membrane receptors of endothelial cells that line angiogenic vessels of tumors

• Membrane receptors of cancer cells


• Reporting agents that change their fluorescence-decay kinetics either through self-quenching orthrough environmental changes associated with:

• Interstitial pH

• Membrane associated proteases and receptors

• Lysosomal, enzymatic degradation

In addition, the summary of the literature reports presented in Table 33.1 leads to the followingconclusions:

• Fluorescence-enhanced optical imaging has not been demonstrated on large tissue volumes thatare scalable to the clinic.

• The minimum number of fluorochrome molecules reported detected in a mouse or rat is 167 pmol.

• Favorable excitation and emission spectra are currently achievable using only the cyanine dyefamily.

Table 33.2 also contains limited references to endogenous fluorescence-enhanced contrast owing togreen-fluorescence-protein-expressing tumors. In these systems, the green fluorescent protein has beentransduced into cancer-cell lines to “report” tumors and metastases as well as their response to therapy.While the approach uses similar detection technology, it is not subject to the excitation-light-rejectionissues that can plague fluorescence-enhanced contrast imaging. We present literature in this area forcompleteness.

In the following section, we summarize the theory and mathematics that enable us to predict thesuccess of optical imaging using CW and time- and frequency-domain approaches as well as to developthe tomographic algorithms for fluorescence-enhanced optical tomography.

33.7 Challenges for NIR Fluorescence-Enhanced Imaging and Tomography

The preceding discussion presented an overview of the status of fluorescence-enhanced optical imaging.The opportunity to develop an emission-based tomographic imaging modality similar to that providedby nuclear imaging but without the use of radionucleotides is offered by NIR fluorescent agents. Yet theadded challenge for NIR fluorescence-enhanced imaging over nuclear imaging is that, unlike nucleartechniques, an activating or excitation signal must first be delivered to the contrast agent before regis-tration of the emission signal from the tissue. Preliminary data from animals (Table 33.2) and phantoms(not presented here) suggests that penetration depth and sensitivity may be comparable to nucleartechniques. A side-by-side comparison of NIR fluorescence-enhanced imaging with nuclear imaging isneeded before the comparative performance can be ascertained.

Another opportunity for optical imaging is the ability for tomographic reconstruction and additionaldiagnostic information based on the fluorescence-decay kinetics of smartly designed probes. Tomographyof large tissue-simulating volume has been demonstrated from experimental data as well as syntheticdata (Table 33.1), albeit with the rather inconvenient point-source and point-detector geometries. Thesingle-point-source and detector geometry is a throwback to NIR optical tomography from endogenouscontrast studies and may not be the appropriate geometry for fluorescence-enhanced optical imaging,especially when transillumination through large tissues is required. Nonetheless, the tomographic algo-rithms as reviewed in Section 33.5 are already established for these systems. The challenge for the futureis to develop tomographic algorithms for illumination and detection that are clinically feasible andadaptable for hybrid nuclear imaging.

While the field of NIR fluorescence-enhanced optical imaging is less than a decade old, the comingdecade holds great promise for exciting new developments and, it is hoped, will result in an adjuvanttomographic imaging modality for nuclear imaging.


Acknowledgments

This review was supported in part by the National Institutes of Health grants R01CA67176 andR01CA88082 and the State of Texas Advanced Research/Advanced Technology Program.

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