NeuroImage 56 (2011) 1316–1328

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Quantification of light reflectance spectroscopy and its application: Determination ofhemodynamics on the rat spinal cord and brain induced by electrical stimulation

Vikrant Sharma a,1, Ji-Wei He b,1, Sweta Narvenkar a,1, Yuan Bo Peng b,1, Hanli Liu a,⁎,1

a Department of Bioengineering, the University of Texas at Arlington, Arlington, TX, 76010, USAb Department of Psychology, the University of Texas at Arlington, Arlington, TX, 76010, USA

Abbreviations: LRS, Light Reflectance Spectroscopymodified Beer-Lambert law.⁎ Corresponding author at: P.O. Box 19138, 501 Wes

USA. Fax: +1 817 272 2251.E-mail address: hanli@uta.edu (H. Liu).

1 Groups a and b contribute equally to this project.

1053-8119/$ – see front matter © 2011 Elsevier Inc. Aldoi:10.1016/j.neuroimage.2011.01.020

a b s t r a c t

a r t i c l e i n f o

Article history:Received 31 May 2010Revised 6 January 2011Accepted 8 January 2011Available online 19 January 2011

Keywords:Light reflectance spectroscopyOptical propertiesHemodynamicsQuantification

Two quantification methods for light reflectance spectroscopy (LRS) were developed and validated todetermine absolute and relative values of hemodynamic parameters and light scattering, followed by aspecific application using in vivo animal experiments. A single-channel LRS system consisted of a light source,CCD-array detector, and a computer along with a bifurcated, 2-mm-diameter optical probe; this system wasutilized to perform laboratory tissue phantoms for validation of the algorithms. In the animal study, a multi-channel, multisite approach was used to measure several reflectance spectra from rat brain and spinal cord onboth the ipsi-lateral and contra-lateral sides, using thin 800-μm-diameter optic probes. The neuro-hemodynamic changes were induced by 10-V electrical stimulation in rat hind paw. The LRS data of theanimals were analyzed using both absolute and relative methods. The results show that the relative method iscomputation-efficient and offers a quick estimation of changes in oxy-hemoglobin concentration for real-timemonitoring. The absolute quantification method, on the other hand, provides us with an accuratecomputational tool to calculate absolute values of oxy-, deoxy-, total hemoglobin concentrations, and lightscattering coefficients. We also observe that the hemodynamic responses in rat spinal cord were delayed witha few seconds and have an overall broader full width at half maximum, as compared to those from ratsomatosensory cortex. LRS as a measurement system provides a robust method for studying localhemodynamic changes and a potential technique to investigate hemo-neural mechanisms in pain processing.

; S-D, source-detector; MBLL,

t First St, Arlington, TX 76010,

l rights reserved.

© 2011 Elsevier Inc. All rights reserved.

Introduction

Light reflectance spectroscopy (LRS) with a small source-detector(S-D) separation is based on spectral characteristics of light thattravels through tissue. Light absorption and scattering are two majoroptical parameters of the tissue and depend highly on structural aswell as functional properties of the tissue. Characterization of theseparameters may allow distinguishing tissue types, enabling LRS to beused for various clinical and preclinical applications. Previously, LRShas been applied to many areas such as cancer diagnosis (Backmanet al., 2000; Bigio et al., 2000; Utzinger et al., 2001; Zonios and Dimou,2009a), neurosurgery guidance, (Giller et al., 2009) , disease models(Radhakrishnan et al., 2005) and neural activities (Liu et al., 2008).Due to its potential to be used in clinical and preclinical applications,researchers have continuously made efforts to quantify hemodynamicparameters and reduced scattering coefficients using LRS. While

theoretical derivations are technically challenging (Zonios and Dimou,2006), semi-empirical (Graaff et al., 1992; Johns and Liu, 2003)models have also been developed for quantifying these parameters.

Theoretically, a widely used mathematical model to understand thepropagation of light, including near infrared (NIR) light, in biologicaltissues is the diffusion approximation. However, such an approximationhas its limitations for LRS with short S-D separation, as the diffusionmodel is not valid when light travels within a few millimeters or less.Also, thediffusionapproximation requires that the absorption coefficient,μa, bemuch smaller inmagnitude than the reduced scattering coefficient,μs′. Such disparity ofmagnitudes holdswell for larger S-D separations andin region of NIR wavelengths; but in the visible range, μa and μs′ can havecomparable magnitudes. It is conspicuous that conventional diffusiontheory (without inclusionof empirical parameters) is not a correctmodelfor probe geometry with small (b1 mm) S-D separation. A recentapproach to solve this problem was proposed by (Zonios and Dimou,2006) and provided a simple expression associating the measuredreflectance to light scattering and absorption. This model has been usedsuccessfully for measurement of optical properties of skin (Zonios andDimou, 2009a). Themodel, although simple, requires a careful calibrationfor system parameters, which needs to be performed only once for eachexperimental set-up or probe. The advantage of using this method oversemi-empirical techniques is that it canprovide staticmeasurements and

Fig. 1. (a) A block diagram illustrating our LRS system: A broadband light sourcedelivers light through a multiplexer to four source fibers, and four respective detectionfibers return the reflected light to a multi-channel, CCD-array spectrometer. Theacquisition and multiplexing is controlled by the CPU, where the data is stored afteracquisition. (b) Diagram for the experimental set-up used in tissue phantommeasurements: the ISS oximeter probe is used simultaneously with the LRS system(for either single-channel or multi-channel) to acquire spectral data from a laboratoryphantom. Homogeneity of liquid phantoms is maintained by using a magnetic stirrer atthe bottom (not shown).

1317V. Sharma et al. / NeuroImage 56 (2011) 1316–1328

is able to separate the effects of scattering from absorption. As will beseen in Analytical model for absolute calculation of hemodynamicparameters section, however, it requires multiple computational itera-tions for optimum determination of fitted parameters, making it lesssuitable for real-time monitoring in certain biomedical applications,particularly for time-dependent measurements.

In the field of neuroscience, real-time monitoring of brain and/orspinal cord hemodynamic responses to given functional stimulationsmay provide researchers with valuable information on neurovascularactivities and activation mechanism as well as help them understandpossible neurovascular pathways that may be associated with certainneurological diseases and dysfunctions. Thus, it would be highlydesirable if LRS can become a minimally-invasive, real-time, moni-toring tool even with a semi-quantitative approach. This desireinspired us to develop a simpler and faster algorithm, based on themodified Beer-Lambert law (MBLL), so as to estimate hemodynamicchanges in real-time for neurological measurements.

In this study, we wish to demonstrate the usefulness of LRS to beutilized for one specific neurological application with two indepen-dent quantification methods: (1) model-based, absolute quantifica-tion and (2) MBLL-based, relative approximation for hemodynamicparameters in response to 10-V electrical stimulation given in rat hindpaw. The motivation to investigate the response to electricalstimulation is driven by our research interest in better understandingof neuro-hemodynamic mechanism of pain, which may lead to theadvancement of more successful and specific therapies for pain in thenear future.

The novelty of this study includes (a) implementation andevaluation of a quantitative method, based on Zonios' model (Zoniosand Dimou, 2006), that can determine absolute concentrations ofoxygenated hemoglobin [HbO], deoxygenated hemoglobin [Hb], totalhemoglobin [HbT], and reduced light scattering coefficients (between500 and 850 nm), (b) development and evaluation of a simpler andfaster algorithm to estimate relative changes in [HbO], (c) simulta-neous monitoring of hemodynamic responses in the spinal cord andbrain when 10-V electrical stimulation was applied on rat hind paw ofthe studied animals. By the end of this paper, we will present ourfindings for hemodynamic signatures in the rat brain and spinal cord,and discuss the results obtained by the two methods.

Materials and methods

Instrumentation and experimental set-up

The essential components of LRS set-up are a light source, aspectrometer, a bifurcated optical fiber probe, and a computer forcontrol and data acquisition. This study was conducted in twosequences: the first one focused on the method development,calibration and algorithm testing; the second one was performedwith the in vivo animal study involving electrical stimulation. The LRSexperimental set-up for both sequences was essentially the same,except that the former employed only a single-channel system andthe latter involved the use of multi-channel system. The single-channel system comprised of a tungsten–halogen light source(HL2000HP, Ocean Optics Inc., Dunedin, FL, USA), a single-channelCCD (charge-coupled device) array spectrometer (USB 2000, OceanOptics, Dunedin, FL USA) in the spectral range of ~350–1000 nm, anda laptop computer. The system was interfaced with the computerusing OOIBase32 software provided by the manufacturer.

Fig. 1(a) shows a schematic diagram for the multi-channel LRS set-up utilized for our animal study. In this case, light illumination wasprovided by a tungsten–halogen light source (3900 Smart-Lite,Illumination Technologies, Inc., Elbridge, NY, USA). Four independentsource channels were obtained using four independent fibers throughan optical switch (Avantes, Inc., Broomfield, CO, USA), and theswitching of the source was timed using a code written in LabVIEW

(National Instruments, Inc., Austin, TX, USA) and data acquisition card(National Instruments, USA). A multi-channel, CCD-array spectrom-eter (Ocean Optics, Inc., USA) was set up along with ADC1000-USBinterface, and four spectrometer channels were used to collect thebroadband reflectance spectra ranging from ~350 to 1000 nm, with aspectral resolution of approximately 0.3 nm. There were four needle-like fiber probes which were bifurcated. Each probe contained a pairof fibers serving as a source and detector fiber. One branch of abifurcated probe was connected to one channel of the multi-channelspectrometer, and the other branch was connected to the optical lightswitch for light source. The data was acquired in sequence from eachof the four needle-like probes. The switching time between two lightsource channels depended on the integration time as well as theswitching time of the switch, which was within a few hundredmilliseconds. After data acquisition, similar to our previous study (Liuet al., 2008), the measured spectra in the wavelength range of500–850 nm were selected for data analysis.

We used 2 different types of needle-like fiber probes: Type-A andType-B in this study. Type-A fiber probes (TechEn, Inc., Milford, MA,USA) were bifurcated with two multi-mode fibers: one fiber for lightdelivery and the other for light detection. Each fiber had a single-fiber

1318 V. Sharma et al. / NeuroImage 56 (2011) 1316–1328

diameter of 400 μm for both the source and detector, an average S-Dseparation of 800 μm, and an outer diameter of 2 mm at the probe tip.Type-B fibers (Fiberguide Industries, Stirling, NJ, USA) were alsobifurcated; each of the two fibers had a diameter of 100 μm, anaverage S-D separation of 100 μm, and an outer diameter of 800 μm.Type-A fibers were utilized for algorithm development and modelvalidation with the single-channel set-up, while four Type-B fiberswere used in the animal measurements with the multi-channel set-up.

Phantom measurements

Phantommeasurements were carried out for calibration as well asfor validation of the methods. Each measurement was performedsimultaneously using our LRS system and a gold standard, dual-channel, tissue oximeter (ISS, Inc., IL, USA), as shown in Fig. 1(b). TheISS oximeter could provide absolute values of μa and μs′ for themeasured sample under light interrogation, thus providing a similarmeasure to our method. The difference between the two instrumentswas that the ISS oximeter sensed the optical properties over a muchlarger volume than LRS did at the probe tip. To create a homogenousphantom, a blood-intralipid solution was made by diluting a stockintralipid solution (concentration=20%, Baxter Healthcare Corpora-tion, Deerfield, IL) with phosphate buffered saline (PBS) and de-fibrinated horse blood (Hemostat Laboratories, Dixon, CA). We variedthe concentrations of intralipid and blood to obtain various combina-tions of scattering and absorption properties. To simulate hemody-namic changes in the phantom, 4 mg of yeast was added into a 3-literliquid phantom to deoxygenate the blood-containing phantom.Whenthe phantom was fully deoxygenated, 100% oxygen was slowlybubbled into the solution to re-oxygenate it. Overall, we couldsimulate changes in μs′ by alternating intralipid concentrations andmimic changes in μa by modifying either the blood volume oroxygenation state.

Animal preparation

The experimental procedures for animal study were approved bythe Institutional Animal Care and Use Committee (IACUC) at theUniversity of Texas at Arlington and performed under the guidelinesfor treatment of animals of the International Association for the study ofpain. For the methodology development and validation, 5 adult maleSprague–Dawley rats were used for this preliminary (Senapati et al.,2005) study. The rat was initially anesthetized using pentobarbital

Fig. 2. Experimental set-up and probe placement in animal study: (a) shows a rat was held inon the spinal cord (the two parallel lines underneath the spinal cord are a reflection of the psomatosensory cortex.

(50 mg/kg, i.p.). During the length of experiment, anesthesia wasmaintained by injecting pentobarbital (5 mg/ml) at 0.02 ml perminute, intravenously, through a catheter placed in jugular vein.After the animal was anesthetized, laminectomy was performed onthe rat in order to expose the spinal cord in the lower thoracic andlumbar regions. An incision was also made on the scalp to expose theskull over the somatosensory area of the brain. Two holes were drilledthrough the skull to expose the somatosensory cortex bilaterally(Paxinos and Watson, 1998) after the animal was fixed on astereotactic frame, as shown in Fig. 2. Mineral oil was applied overthe spinal cord and the brain to prevent drying of the tissue and toimprove optical coupling between the probes and tissue.

Four probes were utilized for this study: two on the left and rightsomatosensory cortex, and two on the left and right lumbar region ofthe spinal cord. To achieve muscular paralysis and minimize motionartifacts, the rat was administered with an intravenous injection of1-ml pancuronium delivered over a period of 1 min. The set-up forLRS shown in Fig. 1(a) was utilized for the rat measurements. Fig. 2(a)shows a picture of LRS set-up along with an experimental rat placedwithin a stereotactic frame; Figs. 2(b) and (c) illustrate a close-up ofprobe locations on both ipsi-lateral and contra-lateral sides. The LRSmeasurements were usually performed in a dark room, to minimizethe background noise.

Once the animal preparationwas complete, baseline data of LRSwasacquired for initial 2 min. A blocked design was used in functional dataacquisition during 10-V electrical stimulation (pulse width=1 ms,frequency=10 Hz) by two needles piercing through the ankle thatwere connected to the Grass stimulator. Five blocks were acquired witha stimulus period of 10 s, followed by a resting period of approximately2 min between each block. The data acquisition frequency was set to be0.5 Hz.

Post data processing was done in a similar manner in order tocompare both absolute and relative quantification techniques. First, toremove systemic and random noise, a sixth order Butterworth bandpass filter between 0.005 Hz and 0.06 Hz was applied. The filtereddata were then block averaged to obtain the overall response to thestimulus. For block-averaging, the data were visually inspected; someof the blocks where the signal was inadequate due to motion artifactsor other unknown reasons were excluded from the analysis.

Analytical model for absolute calculation of hemodynamic parameters

A recent approach by Zonios and Dimou (2006) establishes arelation between the optical reflectance, Rp(λ), measured with a

a stereotactic frame during the experiment; (b) shows a closer view at probe placementrobes by the mineral oil); (c) a closer view showing the placement of optical probes on

0 2 4 6

10

15

20

25(a)

500 600 700 800 9000.2

0.4

0.6

0.8

1

Nor

mal

ized

Ref

lect

ance

(A

.U.)

Measured DataFitted Data

(b)

µa (cm-1)

Wavelength (nm)

µ s’/

Rp

(cm

-1)

Fig. 3. Linear fit with a least-squares regression line to determine values of k1 and k2.The measurements were made with Type-A probe. (a) A linear fit to the measured datausing a phantom of total hemoglobin ([HbT])=45 μM and μs′(750 nm)=11.2 cm−1,giving rise to k1=9.89 cm−1 and k2=2.81. (b) Spectra predicted (red) by the modelandmeasured (blue) with Type-A probe using a tissue phantom of [HbT]=34 μMand μs′(750 nm)=8.31 cm−1.

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short-distance optical probe, the reduced scattering coefficient, μs′(λ),and absorption coefficient, μa(λ), of the medium, as given below:

Rp λð Þ =μ 0s λð Þ

k1 + k2μa λð Þ : ð1Þ

All measured spectra, Rp(λ), are referenced to a calibration standard(OceanOptics, Dunedin, FL, USA),whichwill be referred to as “thewhitesample” in the rest of this paper. Specifically, Rp(λ) represents thespectrum obtained by dividing the measured reflectance, R, by thereference reflectance taken from the white sample. This white samplereference is used to eliminate the spectral effect of the probe, lightsource, and detector on themeasured reflectance data. In Eq. (1), k1 andk2 are two calibration parameters depending only on the geometricalcharacteristics of the optical probes and the optical spectroscopicsystem, i.e., the light source and detector. In principle, k1 and k2 of aselected LRS system can be calibrated experimentally using tissuephantoms. Then, Eq. (1) is utilized to quantify both μa(λ) and μs′(λ) foran unknown tissue sample based on its LRS measurements.

It is well known that μa(λ) is a function of concentrations ofdeoxygenated hemoglobin, [Hb], oxygenated hemoglobin, [HbO], andwater, H2O. The spectral dependence of μa on [HbO], [Hb], and H2O forblood-perfused tissues can be written as

μa λð Þ = HbO½ � εHbO λð Þ + Hb½ �εHb λð Þ + %H2O½ �εH2Oλð Þ; ð2Þ

where ‘λ’ is the wavelength in nm, εHbO (λ), εHb (λ) and εH2O (λ) arethe wavelength dependent extinction coefficients of [HbO], [Hb], andwater, respectively (Zijlstra et al., 2000). [%H2O] represents thepercentage of water in the medium. Other chromophores, such asfat and melanin, may be added to this equation, depending on thewavelength range of interest and tissue type under investigation. Thespectral dependence of μ s′ can be approximated as given by Mietheory (van Staveren et al., 1991):

g = 1:1− 0:58 × 10−3� �

λ; ð3Þ

μ 0s = μ s 1−gð Þ; ð4Þ

μs = aλ−b; ð5Þ

where μs is the effective scattering coefficient, μs′ is the reduced scatteringcoefficient, and g is the anisotropy factor. In Eq. (5), parameters of a and bare constants and depend on scatterer sizes and types. For 10% intralipidsolution, the calculated values are a=2.54×109 cm−1 and b=2.4 (vanStaveren et al., 1991).

Calculation and calibration of k1 and k2In this study, we determined the values of k1 and k2 using the least-

squares regression approach. By rearranging Eq. (1), we obtain

μ′s λð ÞRp λð Þ = k1 + k2μa λð Þ: ð6Þ

This equation shows that k1 and k2 can be determined by obtaininga linear regression line that best fits μs′(λ)/Rp(λ) versus μa (λ). Inprinciple, we can obtain the measured spectra of Rp(λ) from the LRSsystem within 500–850 nm and also achieve quantification of μa andμs′ at 750 nm and 830 nm from ISS oximeter if the measurements byboth LRS and ISS oximeter are taken simultaneously. Besides μa values,ISS oximeter is also able to provide derived values of [Hb], [HbO], andμs′ at two wavelengths (OxiplexTS). Then, wavelength dependentabsorption spectra, μa(λ), can be quantified using Eq. (2) if themeasured [Hb] and [HbO] as well as the hemoglobin extinctioncoefficients (Matcher et al., 1994) are available. Moreover, given two

μs′ values at two measured wavelengths (750 nm and 830 nm), it isreasonable to interpolate and extrapolate μs′(λ) over the desiredwavelength range using Eqs. (3)–(5) based on Mie theory.

During the system calibration phase in our study, we followedthe exact principle or procedures given above to acquire Rp(λ), μa (λ), andμs′(λ) from a set of blood-containing tissue phantoms. A correspondingset of k1 and k2 at various total hemoglobin concentrations and reducedscattering coefficients were obtained, averaged, and calculated for theirmeans and standard deviations. If the relative errors for both k1 and k2were less than 10%, then the corresponding set of k1 and k2were finalizedas the system calibration parameters for the specific LRS system (i.e., thelight source, fiber probe, and spectrometer) chosen for this study.

As an example, Fig. 3(a) shows a set of measured Rp(λ), μa (λ), andμs′(λ) and the linear regression line for Type-A probe with k1 being they-intercept and k2 being the slope. While the inverse calculations foran unknown sample will be described in the next sub-section, anillustration of the measured and fitted reflectance is shown in Fig. 3(b).The accuracyof parameters k1 and k2 critically affects the ‘goodnessoffit’in the inverse calculations, and thus influences theaccuracy ofmeasuredoptical properties of tissues under interrogation. It is noteworthy topoint out that k1 and k2 depend highly on the white samplemeasurement for eliminating instrumentation effects on the measuredspectrum of the sample under examination. Incorrect measurement ofthewhite samplewill lead to serious errors for thefitted parameters, i.e.,[Hb], [HbO], a and b in Eq. (5).

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White sample measurement can vary with the following para-meters: distance between the fiber tip and sample surface, integrationtime, light source intensity. Measuring different types of tissue requiresa different integration time for the detector. Fig. 4 shows themeasurement geometry from the white sample. Since the reflectancecurve needs to be dividedby the reference curve from thewhite sample,care should be taken to standardize the procedure. This can be doneeither by fixing the distance and collecting white sample at variousintegration times to create a look-up table, or by scaling the whitesample reflectance curve based on one single measurement. The lattermethod is based on our observation that the relationship betweenreflectance spectra and integration times is approximately linear.

Inverse calculationThe inverse calculation of Eq. (1) deals with determination of

tissue chromophore concentrations and effective scattering coeffi-cients from the measurements of LRS taken on the tissue surface. Themathematical problem of inversion can be practically solved by anapproach of function minimization using an optimization algorithm.The algorithm searches for an optimal set of values, as represented byx=([Hb], [HbO], a, b), from the givenmulti-parameter space that bestmatch the measured Rp(λ) using the least-squares analysis. It can bemathematically expressed as follows:

f xð Þ = ∑M

i=1Rp λið Þ measuredð Þ−Rp λið Þ predictedð Þh i2

; ð7Þ

where f(x) represents an objective function and needs to be minimizedby finding an optimal set of the parameters, xopt, M is the number ofwavelengths, Rp (λi)(measured) and Rp (λi)(predicted) are the reflectancevalues (at wavelength λi) measured by the optical probe and predictedby Eqs. (1)–(5), respectively, with the parameter set, x, to be optimized.

Evolutionaryalgorithmsarewidelyutilized in thefieldof optimization(Angeline et al., 1999; Ashlock and SpringerLink (Online service), 2006;Eiben and Smith, 2003). The algorithms work on a population of valuesrather an initial guess,making the solution independentof an initial guess.Their inherent characteristics make them suitable to search for a globalminimum, rather than being stuck in local minima. The ant colonyoptimization (ACO) algorithm, introduced by M. Dorigo (Dorigo et al.,1996), is a probabilistic evolutionary technique for solving computationalproblems. This basic techniquewasmodified in this study to suit functionminimization (Kashyap, 2007). Since ACO requires the bounds to be setfor the fitting parameters, it allows the algorithm to search for the globalminimum only within the bounds. It is important to make sure that theglobalminimum iswithin these bounds. Appendix A provides test resultsof several fitting routines with different bounds, showing that the globalminimum is still in agreement regardless of different bounds chosen.

Fig. 4. Illustration of geometry for white sample measurement: the optical fiber isplaced on top of the pure reflectance sample (white sample), and the distance fromsurface is adjusted based on the integration time of the spectrometer.

Eq. (1) is very non-linear and spanned from 500 nm to 850 nm. Inorder to obtain optimal fit between the measured and calculatedreflectance curve, we had to incorporate a multiple-step sequence;within each step the objective function for minimization, Eq. (7), wasselected somewhat differently. First, the entire spectrum (500 nm–

850 nm) was utilized for fitting, and the fitted values of [Hb], [HbO], aand b in Eq. (5) were obtained. Second, the μs(λ) values (or a and b)were further re-fitted with ±15% bounds around the values found instep one; in the meantime, a smaller spectral region of 520–590 nmthat has a strong hemoglobin absorption band was selected for re-fitting to improve ‘goodness of fit’ for [Hb] and [HbO]. Third, afterrefining the fitted parameters of [Hb] and [HbO], they were re-fittedwithin ±20% bounds around the values found in step two while μs(λ)values (or a and b) were also re-fitted without the ±15% boundsconfinement. In the last step, the entire spectrum (500–850 nm) wasutilized, leading to the finally optimized values of xopt ([Hb]opt,[HbO]opt, aopt and bopt). More details are given in Appendix A2 todemonstrate the necessity, importance, and efficiency of this three-step fitting approach by comparing the “goodness of fit” using one-step versus three-step fitting sequence. Overall, three fitting stepswith changing parameter bounds and spectral regions were utilized inour animal study in order to obtain an optimal fit for scattering andabsorption parameters. An example to show comparison between themeasured and fitted reflectance is already given in Fig. 3(b).

Approximated method to determine changes in [HbO] in real-time

While the analytical reflectance model (Zonios and Dimou, 2006)provides accurate, absolute quantifications of [HbO], [Hb], and lightscattering parameters, it requires rigorous least-squares regression(Eq. (7)). As described above, such optimal fitting takes time and amulti-step sequenceand thus limits its use in real-time, time-dependentmeasurements, especially for long-term monitoring. To speed up theprocess of data quantification, we were motivated to explore a simplerand faster algorithmthatmay allowus to estimate changes in [HbO] and[Hb]with a relative error of 10–15%with respect to the expected values.To do so, modified Beer-Lambert law (MBLL) (Delpy et al., 1988) wasconsidered sinceMBLL has beenwidely used (Boas et al., 2004; Huppertet al., 2009) tomeasure changes in [HbO] and [Hb] for probe geometrieswith S-D separations larger than 1 cm, typically for functional brainimaging applications. We applied the same principle to LRS where amuch smaller S-D separation was utilized in the probe geometry. Herewe briefly review the mathematical basis for MBLL, given by Eq. (8),which associates the changes in light intensity, ΔOD(λ), to the changesin chromophore concentrations, such as Δ[HbO] and Δ[Hb]. Here weassume that water and chromophores other than hemoglobin deriva-tives are time invariant. A detailed explanation of this equation can befound elsewhere (Kim and Liu, 2007).

ΔOD λ1ð ÞΔOD λ2ð Þ⋮ΔOD λnð Þ

2664

3775 =

ελ1Hb ελ1

HbO

ελ2Hb ελ2HbO⋮ ⋮ελnHb ελn

HbO

2666664

3777775� Δ Hb½ �

Δ HbO½ �� �

� d � DPF: ð8Þ

In Eq. (8), ΔOD(λn) represents the change in optical density atwavelength λn, εcλn represents extinction coefficient of chromophore cat wavelength λn, DPF is the differential path-length factor, and d isthe S-D separation. DPF depends on tissue optical properties and alsois known to be slightly wavelength dependent (Kohl et al., 1998). Asan approximation, we assume a constant DPF (DPF=20, which givesresults of Δ[HbO] and Δ[Hb] similar to the expected changes), andthus assign arbitrary units to the calculated Δ[HbO] and Δ[Hb].

In principle, two wavelengths should be enough to calculate twounknowns (Δ[HbO] and Δ[Hb]). To increase the ‘goodness of fit’ and to

1321V. Sharma et al. / NeuroImage 56 (2011) 1316–1328

smooth the noise induced by a variety of experimental parameters, wedecided to use multiple wavelengths to over-determine the values ofΔ[HbO] andΔ[Hb] in the500–600 nmrange,where the absorptionbandsof [HbO] and [Hb] are characteristic and highly distinct fromone another.Themeasured spectra were down-sampled by a factor of three, to obtaina spectral resolution of ~1 nm from the original spectral resolution of~0.3 nm, thus giving us 94wavelength points in the desired range (500–600 nm). Note that the extinction coefficients available from theliterature were sampled at a spectral interval of 2 nm. The missingvalues were obtained by linear interpolation. Eq. (8) above was solvedusing the function of ‘mldivide’ inMATLAB (TheMathworks, Inc.), whichsolves an over-determined system using the least-squares approach.

Since MBLL does not take light scattering into consideration, weexpected to have errors for the fitted Δ[HbO] and Δ[Hb] and thushypothesized that such errors could be small enough to ignore. If ourhypothesis was proven to be correct, then we would have a fast,simple algorithm that led to real-time, accurate estimates of Δ[HbO]and Δ[Hb] measured by LRS for blood-perfused tissues or samples. Totest this hypothesis, we utilized liquid-tissue phantoms, as describedearlier, varied the phantom conditions with and without scatteringchanges, and then evaluated the effect of light scattering on thecalculated Δ[HbO] and Δ[Hb].

Results

Algorithm validation for absolute quantification

In order to validate the algorithm for absolute quantification, wecreated tissue phantoms and performed the measurements with bothour single-channel system and a tissue oximeter (ISS Oximeter),

Fig. 5. Comparison of parameters quantified from the LRS system and ISS oximeter: (a) oxygenabsolute errors in three calculated parameters of O2 Sat (3.0±0.7%), [Hb] (0.9±0.2 μM) and [standard error of mean. (c) Changes in [HbT] and μs′ (at 750 nm and 830 nm) observed during tusing ISS oximeter (black) and LRS system (red).

which was used as a gold standard device for comparison. Fig. 5(a)shows comparisons between the values obtained from ISS tissueoximeter and those quantified with our method when a change inoxygen saturation(O2 Sat) was achieved by adding yeast to the liquidphantom. Themeasurements weremade at 12 different time points inthe O2 Sat range of ~20%–80% during the oxygenation and de-oxygenation process, as described in the Materials and methodssection. It is clear from Fig. 5(a) that oxygen saturation(O2 Sat) valuesmeasured by bothmodalities are very consistant in the O2 Sat range of20%–80%. The absolute errors were also calculated at each data point(n=12) and are plotted in Fig. 5(b): average absolute errors for O2

Sat, [Hb] and [HbO], along with standard error of mean (SEM), were3.0±0.7%, 0.9±0.2 μM, and 0.9±0.2 μM, respectively. Similar experi-ments were repeated several times, and the results were very similarto those seen in Figs. 5(a) and (b).

The reason for limiting our comparison in the O2 Sat range of 20%–80% is as follows: (1) The ISS oximeter being used as a gold standarddevice in this study is a tissue oxygen saturation monitoringapparatus that is known to work well in the chosen physiologicalrange (Franceschini et al., 1999; Hueber et al., 2001). The errors inmeasurement beyond this range tend to increase, contingent uponone of the parameters (either [HbO] or [Hb]) approaching zero undereither 100% or 0% hemogobin oxygen saturation. (2) Opticalmeasurements through fiber probes interrogate a 3-dimensionalvolume with a banana pattern. The interrogated tissue volume ingeneral includes both blood-perfused vessels and bloodless tissuebackground. Themixture of these two compounds will create a partialvolume effect, leading to an averaged O2 Sat value lower than aregular arterial O2 Sat, and most likely to be in the region around 80%or lower. (3) It is almost physiologically impossible to have any value

saturation values obtained from ISS oximeter (black) and LRS system (red). (b) AverageHbO] (0.9±0.2 μM), with respect to those given by ISS oximeter. The error bars indicatehe cycle of oxygen saturation, as shown in (a). (d) Comparison of μs′ calculated at 830 nm

1322 V. Sharma et al. / NeuroImage 56 (2011) 1316–1328

of O2 Sat lower than 20%. Therefore, it is reasonable to select the rangeof vascular O2 Sat to be 20–80% used for algorithm validation.

The reliability of the algorithm was also evaluated by comparingthe changes in total hemoglobin concentration, [HbT], and μs′ for eachset of the above measurement. Since yeast did not induce muchchange in either [HbT] or μs′, these two parameters should ideallyremain constant when the oxygenation state was altered. Fig. 5(c)shows the measured values of [HbT] and μs′ ( at 750 nm and 830 nm)with changing O2 Sat. As expected, those values are found to beconstant across the saturation range of 20–80% with small SEMs as[HbT]=28.0±0.4 μM, μs′ (750 nm)=10.46±0.05 cm−1, and μs′(830 nm)=9.34±0.04 cm−1. Another set of experiments wereconducted to test the consistancy of μs′ when Intralipid volume wasvaried from 75 ml to 170 ml within the given liquid phantom volume.Fig. 5(d) shows a comparison of values obtained by the ISS oximeterand LRS system at 830 nm. The mean difference (with standarddeviation) between the scattering values obtained by two methodswas calculated to be 0.02±0.13 cm−1, demonstrating almost perfectmatch between the two methods.

Fig. 6. Comparison of the relative and absolute methods: (a) represents absolute valuesof [Hb] and [HbO] calculated utilizing the reflectance model and optimizationalgorithm; (b) represents calculated Δ[Hb] and Δ[HbO] values using modified Beer-Lambert law (MBLL), considering the first data point as baseline and sharing the samedata as those used in (a); (c) Normalized relative and absolute values of [Hb] and [HbO]plotted together, demonstrating the good consistency between the data derived fromthe two methods.

Algorithm validation for the relative method

In order to validate the relativemethod based onMBLL,we comparedit with the absolute value model that is already validated in the sectionabove. Figs. 6(a) and (b) show temporal profiles of [HbO] and [Hb]derived from the absolute and relative quantification, respectively, usingthe same data set taken from a dynamic phantom that contained anamount of oxygen-consuming yeast. For both figures, the first data pointwas taken as baseline, and the changes were calculated relative to thebaseline. Also, the baseline was acquired before adding the yeast. Thenthe data points were continuously acquired until the blood was fullydeoxygenated (sample number=10), followed by re-oxygenation withthe help of compressed-air bubbling. Note that the unit of x-axis in thosefigures is not time, rather sample numbers. Since the data points wereacquired at non-uniform intervals, the shapes of the curves do notnecessarily represent the time course of de-oxygenation-re-oxygenationcycle.

In order to compare the data shown in Figs. 6(a) and (b), wenormalized them between 0 and 1 (Fig. 6(c)). As clearly observed,changes in both [Hb] and [HbO] calculated using the two methods arewell overlapped. A quantitative comparison was performed bycalculating the correlation coefficient between two Δ[HbO] curves,rHbO, obtained by the absolute and relative methods. The data shownin Fig. 6(c) give rise to rHbO=0.99 and rHb=0.99; the latter one wasquantified between the two Δ[Hb] traces in a similar way used forrHbO.

As mentioned earlier, two wavelengths could be sufficient enoughto evaluate a relative change in [Hb] and [HbO] using MBLL. Inprinciple, however, more wavelengths should provide us with moreaccurate quantifications of [Hb] and [HbO] by using least-squaresregression fitting. In the meantime, it is desirable to utilize areasonable number of wavelengths to keep the accuracy high whilereducing the computation burden. It is expected that there must existan optimal set of wavelengths (Eames et al., 2008), with which theaccuracy of determined Δ[Hb] and Δ[HbO] values will be comparableto those determined by using the entire wavelength range. Asmentioned in Approximated method to determine changes in [HbO]in real-time section, the extinction coefficients available from theliterature were sampled at a spectral interval of 2 nm. As a match, it isreasonable in this study to select a comparable spectral resolution of1 nm for the least-squares fitting, i.e., to utilize 94 wavelengths forleast square estimation of Δ[Hb] and Δ[HbO] (see Approximatedmethod to determine changes in [HbO] in real-time section). We didnot notice any significant difference in data processing time betweenemploying 94 versus 2 wavelengths.

The results given above confirm the consistency and feasibility ofusing the relative method as compared with the absolute quantifica-tion method. Since MBLL does not account for light scattering,however, we need to further investigate the errors caused by ignoringlight scattering. Specifically, we created a set of phantom experimentsto vary light scattering properties while keeping the total bloodconcentration (~30 μM) and its oxygen saturation level (~100%)constant. In this case, the expected values of Δ[Hb], Δ[HbO], andΔ[HbT] should be all ‘zero’ since changes in light scattering would notlead to any changes in all three parameters. The actual calculatedvalues ofΔ[Hb],Δ[HbO], andΔ[HbT] by Eq. (8) are shown in Fig. 7. It is

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observed that the scattering change causes a significant error in bothΔ[Hb] and Δ[HbT], but leads to a much smaller error in Δ[HbO]comparatively. We repeated this experiment using 2 different Type-Bprobes and found similar results. All of these findings suggest that theMBLL-based relative method be able to estimate Δ[HbO] with apossible deviation of ~6 units (with a chosen DPF=20) even if achange in light scattering occurs with a span of 6–8 cm−1, namely, achange in μs′ of 1 cm−1 leads to a change inΔ[HbO] of 0.8–1 units. Thisestimation error may be insignificant in cases where large changes inlight absorption occur due to changes in blood concentration. So, inour in vivo animal studies, we will quantify only Δ[HbO] using therelative method, followed by comparison of the results obtained bythe absolute and relative methods.

Empirical in vivo evaluation in rats

In this sub-section, we present the results obtained from 10-Velectrical stimulation in rat hind paw. The LRS data were analyzed forall four channels using both the absolute and relative methods. Asmentioned in the previous section, the relative method was used toquantify only Δ[HbO] since the errors for Δ[Hb] were too large toignore.

As mentioned earlier, the block-averaged data were obtained fromfour measurement locations (contra-lateral and ipsi-lateral somato-sensory cortex, and contra-lateral and ipsi-lateral spinal cord). To berelevant to the signaling pathway, we focused on ipsi-lateral spinalcord, and contra-lateral somatosensory cortex for further analysis. Ingeneral, it was found that the signals taken from contra-lateral spinalcord and ipsi-lateral somatosensory cortex were often low inamplitude or at the noise level. The responses of Δ[HbO] and [HbO]

Fig. 7. Changes in [Hb] and [HbO] recorded as a function of light scattering coefficient, μs′, intissue phantoms for two Type-B probes (a) and (b), which were used in the rat study. Forthis set ofphantomexperiments, intralipid concentrationswerevaried from0.5% to1.5% tocreate a range of μs′.

obtained from the spinal cord were often much bigger in amplitudethan the brain responses. Consequently, spine signals hadmuch betterSNR (signal-to-noise ratio) as compared to the brain signals. Also,there was high variability in amplitudes of activation among the 5animals. To compare the temporal characteristics of Δ[HbO] and[HbO] obtained using the two methods, the block-averaged data fromeach rat was normalized between 0 and 1. Further averages ofnormalized Δ[HbO] by the relative method and [HbO] by the absolutemethod across 5 rats were calculated and shown in Figs. 8(a) and (b),respectively. The shaded grey bars in the figures represent theduration and temporal location (4–14 s) of the electrical stimulation,from the beginning of each block. It is observed that both Δ[HbO] and[HbO] rise during the stimulus period, followed by a gradual return tothe baseline after the stimulus stops.

Fig. 8(c) presents a more direct comparison between thenormalized Δ[HbO] values processed using the absolute and relativemethods in response to a single block stimulation, i.e., one 10-Vstimulus, on the spinal cord followed by its recovery period. As seenfrom the overlap, the results shown demonstrate a strong agreementwith one another (with a correlation coefficient of r=0.99).Furthermore, the absolute method was also used to calculate theabsolute values of [Hb] and [HbO] as well as the scattering coefficients.The data were block averaged in each animal, followed by a groupaverage over all 5 rats. The results are shown in Fig. 8(d), clearlyexhibiting a gradual decrease in [Hb] during the spine stimulation andgradual return during the recovery phase. It is noted that the fallingand rising rates in [Hb] are similar to those of [HbO], except in theopposite direction. Scattering changes in μs′ induced by the stimula-tion were often small and did not exhibit a consistent pattern amongthe study population.

Discussion

Discussion on quantification of light reflectance spectroscopy

In this study, we have developed and evaluated two quantificationmethods that can be used to determine tissue hemodynamics basedon LRS with the use of small S-D separation fiber probes. The twoquantification approaches result from (1) Zonio's reflectance model(Zonios and Dimou, 2006) for absolute calculation of [Hb], [HbO], andμs′, and (2) MBLL for relative calculation of changes in [HbO]. Theabsolute method utilizes the wavelength range of 500–850 nm andobtains the calculation of [Hb], [HbO], and μs′ by least-squaresregression using a multi-step sequence, optimization approach. Thismethod was evaluated by comparison with a commercial oximeter(ISS, Inc.) by performing laboratory experiments on homogenousliquid-tissue phantoms, and the results were found to be in closeagreement with each other. The calibration procedure for finding thesystem parameters, k1 and k2, was also described.

Previously published studies (Zonios and Dimou, 2008, 2009a,b)utilized the same reflectance model but a different mathematicalexpression (i.e., a linear function) for the spectral dependence of lightscattering (Zonios and Dimou, 2006) when investigating skinproperties. Our observation is that if adequate bounds are appliedfor the optimization function, similar results of fitted [Hb], [HbO], andμs′ could be obtained using either a linear or Mie function for lightscattering pattern.

The absolute calculationmethod provides insight into structural andfunctional changes happening inside the tissue and can be applied toclinical applications, such as for cancer diagnosis (Sharma et al., 2009)and neurosurgery guidance (Giller et al., 2009), as well as perhaps forneuro-functional monitoring, as demonstrated in our animal studies.Since the optimization routine requires multi-step sequence anditerativefitting, however, the processing time for continuously acquireddata can be an obstacle for real-time monitoring. While using otherfitting or minimization algorithms may help improve the processing

Fig. 8. Mean values (n=5) of normalized, block-averaged [HbO] responses induced by 10-V electrical stimulation quantified using (a) the relative method and (b) the absolutemethod. The brain response was taken from the contra-lateral side and spinal response was taken from the ipsi-lateral side; (c) comparison of normalized, spinal [HbO] response to asingle block (10-V stimulus for 10 s followed by a recovery period of 70 s) in a rat; the data were processed using both absolute and relative methods. (d) Absolute values of spinal[Hb] and [HbO] determined by the absolute method and averaged over all blocks for all rats. The shaded grey bars in all four graphs represent the duration and temporal location ofthe electrical stimulation, i.e., 4–14 s from the beginning of each block. The error bars seen in all four panels represent standard error of mean.

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time, we introduced a faster solution by using MBLL with multiplewavelengths to estimate changes in [HbO] with a reasonable accuracy.This “relative method” was compared with the above mentioned“absolute method” through laboratory phantommeasurements as wellas in vivo animal experiments. The phantom results suggest that whenthere is no change in light scattering, the values ofΔ[HbO] andΔ[Hb] arehighly reliable; but in the presence of changes in light scattering, Δ[Hb]signals are not reliable due to the contamination from μs′. The values ofΔ[HbO], on the other hand, exhibitmuch less variation and dependenceon changes in μs′. Therefore, the relative method can be utilized well toestimate temporal profiles of Δ[HbO] for real-time monitoring inappropriate clinical and neurological applications.

In general, the volumesmeasured by ISS and LRS are not necessarilycomparable, depending on the places where the probes are placed. TheISS probemeasures the optical properties of themedium 1–2 cm belowthe sources and detectors which are usually separated ranging from2.0 cmto 3.5 cm. The LRSprobes usually have a S-D separation of severalhundredmicronsand thus sense theoptical properties0.5–1.5 mmrightbeneath the probe tip. Since the tissue phantom was constructed usinghomogenous intralipid solutionmixedwith liquid blood, thematerial tobe measured by both ISS and LRS was completely uniform throughoutthe container. Thus, the optical properties of the phantom do not varywhen being measured in different interrogation volumes; the resultsobtained from both modalities are comparable and appropriate, asshown in Fig. 5(a).

It seems intuitive that standard deviation would be a valuableparameter to compare the results from both modalities, i.e., ISS andLRS. In the case for Fig. 5, however, standard deviation could not beobtained for Figs. 5(a) and (c) because these readings were singlepoint measurements as explained below. The blood de-oxygenation(controlled by yeast) and re-oxygenation (controlled by oxygenbubbling) processes were dynamically varied, i.e., the values of opticalproperties under study were changing as a function of time. Only onesimultaneous reading could be taken at one specific oxygenation levelduring de-oxygenation or re-oxygenation process. Similar experi-ments were repeated several times, but each time it was impossible totake the readings at the exact oxygen saturation level, O2 Sat (%).Instead, the average errors between the two modalities could bequantified by collectively taking into account all the readings atdifferent levels of O2 Sat (%), along with the standard error of mean(SEM) plotted for each parameter in Fig. 5(b).

Discussion on LRS-derived hemodynamics on the rat spinal cord andbrain

Feasibility of using bothmethods in a neuro-stimulation study wastested by performing a 10-V electrical stimulation given in rat hindpaw. It was observed that LRSwith small S-D separation probes can beeffectively used to study functional changes in tissues of centralnervous system. The response in both brain and spinal cord was

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measured; an increase in oxy-hemoglobin levels was observed duringthe 10-V electrical stimulation. Figs. 8(a) to (d) intriguingly revealseveral important features learned from this study, as stated below:

(a) The spinal response in Δ[HbO] or [HbO] continues to rise afterthe stimulation, having a delayed arrival of its peak ascompared to the stimulation. For a quantitative comparison,time to peak (Tp) and full width half maximum (FWHM) werecalculated for each case and are tabulated in Table 1. One of therelative brain responses was excluded for FWHM as it was aclear outlier. This table illustrates that the peaks of the spineresponses delay about 4.8–6 s with respect to those of the brainresponses. This table also confirms a good agreement betweenthe twomethods. The observation of delayed spinal response in[HbO] is consistent with a thermal stimulation study conductedusing fMRI (Brown et al., 2007). Moreover, Table 1 illustratesthat the spine responses are ~5.5 s broader in their FWHM thanthe brain responses, indicating that the return to hemodynamicbaseline in the cortex is faster than in the spinal cord. Themechanism of slower return to the baseline in the spineremains to be explored and understood better. A possiblespeculation is that the neuronal signals have to pass the spinalcord twice due to the given stimulation: the 1st pass is from thestimulation site to the brain, followed by the 2nd pass from theactivated cortical area to the stimulation location, prolongingthe activation time in the spinal cord with respect to theactivation time in the brain.

(b) In general, we have frequently observed that the amplitudes ofactivation ([HbO] and Δ[HbO]) in the rat brain were muchsmaller than those in the spinal cord, with a reduced signal-to-noise ratio (SNR) in the rat brain. We had to exclude severalblocks when analyzing the signals taken from the brain due toinconsistent peaks and large deviation from the expectedcharacteristics. To demonstrate our points, two specific figuresare given as supplementary data to show individual Δ[HbO]readings from each of the 25 experimental blocks (5 rats, 5blocks each). Specifically, 2 out of total 25 blockswere excludedwhen block-averaging the spinal responses, whereas 10 blockswere excluded for brain response analysis. The noisier featureof the brain responses could be due to either a smalleractivation in the detected brain region or an imperfectlymatched location of the fiber probe with respect to a relativelysmall target on the somatosensory cortex.

(c) An undershoot is observed in the brain response during therecovery phase of [HbO] (Fig. 8(b)) or Δ[HbO] (Fig. 8(a)), andwas absent in the spine response. The overall hemodynamicbehaviors, i.e., temporal profiles of [HbO] or Δ[HbO], observedin the rat brain are quite consistent with those seen in non-invasive functional brain studies using functional diffuseoptical tomography (fDOT) and functional magnetic resonanceimaging (fMRI) (Huppert et al., 2006a; Huppert et al., 2006b). Itis remarkable that the overall temporal feature of [HbO]resembles much the so called canonical hemodynamic re-sponse function (cHRF) commonly used to process humanBOLD signals in fMRI (Lu et al., 2006). If the cHRF is convolvedwith a 10-s stimulus, the resulting predicted response has a

Table 1Comparison of temporal behavior of [HbO] data for brain and spine. Full width at halfmaximum and time to peak response are the chosen statistical parameters.

Method Parameter FWHM (s) Tp (s)

Absolute Brain [HbO] 15.3±2.1 (n=5) 13.6±2.2 (n=5)Spine [HbO] 21.0±6.0 (n=5) 18.4±2.6 (n=5)

Relative Brain [HbO] 16.5±1.8 (n=4) 12.4±2.6 (n=5)Spine [HbO] 21.9±6.7 (n=5) 18.4±2.6 (n=5)

somewhat expanded plateau compared to the results seen inFig. 8(b). The close similarity between the two modalities (LRSversus fMRI) results from the fact that they are both sensitive tothe similar origin of signals, i.e., hemoglobin concentration inthe blood. On the other hand, the signals seen in this study andin conventional fMRI do not have to be exactly identical in theirhemodynamic shapes because (i) LRS senses more towardcapillaries and small vessels, while fMRI is more biased by largeveins; (ii) LRS can separate changes in oxy-hemoglobinconcentration from those in deoxy-hemoglobin concentration,whereas fMRI is sensitive only to changes in deoxy-hemoglobinconcentration; (iii) the “canonical” form of the HRFmight differbetween rats and humans.

Although the aforementioned differences between LRS and fMRIexist, we believe that LRS may still be feasibly utilized in humanmeasurements to refine current models of hemodynamics in thehuman brain after meeting additional requirements and challenges.One possible approach is to conduct LRS during human neurosurgerywith a neurosurgery-compatible optical fiber probe by inserting theprobe into a specific cortical or sub-cortical region. Such clinicalprocedures in the human brain have been performed over more than150 human patients (Giller et al., 2000; Giller et al., 2009) to locatesub-cortical lesions/targets for deep brain stimulation; the furtherstep is to include the LRSmeasurement while functional stimulation isgiven. The challenge for the next step is to accurately identify andlocate functional targets that can be both clinically relevant to theneurosurgery so that only minimal risk is added to the patient undersurgery and scientifically meaningful for improvement of currenthemodynamicmodels. Indeed, we are currently undertaking the stepsand processes for realizing this plan in clinical settings.

While optical imaging was used about 15 years ago to observechanges in [Hb] and [HbO] and to validate BOLD signals in fMRI(Malonek and Grinvald, 1996), the previous optical approach gave anarbitrary unit without absolute values of hemoglobin concentrations.

Onemajor novel aspect in our study includes the ability to quantifyhemodynamic responses with an absolute unit, namely [Hb] and[HbO] in μM, along with light scattering parameter right at the site ofactivity. Such quantification may enhance or lead to better under-standing of neurovascular coupling. However, it should be noted thatthe design of optical probe is critical to control the field of view/volume (FOV) of measurement, as FOV reflects essentially theinterrogated volume and is a function of source and detector (S-D)separation. Although lateral resolution is directly controlled byselecting S-D separation, the penetration depth of a 100-μm probecould be 1 mm or up to 2 mm into the biological tissue (Qian et al.,2003), depending on the light scattering and absorption properties ofthe underlying tissue. In light of aforementioned, two dimensionalscanning of such a probe over a selected surface area may have apotential to provide a 2D surface map for certain preclinical andresearch applications.

(d) It was found that the SEMs in spine responses (mean ~0.06) areoften lower than those in brain responses (mean ~0.08),especially during the recovery period after 30 s. Quantitatively,it is confirmed that the two means of SEMs (one for brainresponses and one for spine responses) are significantlydifferent across the entire temporal block by Student t-testwith a p valueb0.001. Note that the SEMs given here arecalculated for normalized responses (Figs. 8(a) and (b)); largerSEMs in brain responses imply higher variability in collectedsignals from the brain than from the spine. This implication issupported by experimental observations across multipleanimals (see supplementary data in Figs. S1 and S2).

(e) Furthermore, using the absolute method, the quantity of [Hb]was also analyzed for the brain response, which exhibits asimilar hemodynamic behavior but in the opposite direction as

Table A1Three sets of parameter bounds that are chosen to study their effects on theperformance of fitting routine.

[Hb], [HbO](mM)

a⁎ (cm) b μs′=aλ−b (cm−1)(λ=750 nm)

Upperbound

Lowerbound

Upperbound

Lowerbound

Upperbound

Lowerbound

Upperbound

Lowerbound

Original 0.9 0.0001 1000 0.01 2.6 2.3 1.8×104 2.5×10−2

Modified 3 0.0001 1000 0.1 3.0 1.7 9.8×104 1.8×10−3

Infinite 20 0.0001 100,000 0.01 10 0.1 3.9×1010 1.3×10−25

Where a⁎=2.54×109/a.

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compared to the hemodynamic profile of [HbO], as shown inFig. 8(d). Through the same process, light scattering coefficient,μs′(λ), was obtained, demonstrating that electrical stimulationdid not induce any consistent changes in light scattering ineither the brain or spinal cord (data not shown).

It is noted that in the animal studies, the rats were administeredwith 1-ml pancuronium since it could serve as an acetylcholineantagonist to relax muscle, and thus to minimize motion artifacts forthe optical measurements. Since little analgesic effect induced by thisdrug has been reported, we do not expect that the pancuronium willinfluence the neural network that is associated with pain perception.However, it is possible that the blood distribution or perfusion patternin the animal might be altered as the muscle stops working and cutsits energy or oxygen consumption. In our study, the signals weretaken from the somatosensory cortex and dorsal part of the spinalcord, which are minimally associated with the motor system.Therefore, it is less likely that pancuronium would cause sufficienteffect on either site. In spite of our speculation, we cannot completelyexclude the possibility that the pancuronium would reduce the painor sensing perception to certain extents such that the [HbO] changeswere less pronounced in the somatosensory area than in the spinalcord. To prove or disprove this possibility requires different animalprotocols and is beyond the scope of this study. Further investigationon this issue might lead to better understanding of the difference insignal intensity between [HbO] changes seen from the brain andspinal cord.

In summary, we have introduced two quantification methods tostudy changes in hemodynamic signals taken by LRS simultaneously atmulti-sites of the rat brain and spinal cord during 10-V electricalstimulation. The MBLL-based, relative method is computation-efficientand offers a quick estimation of changes in oxy-hemoglobin concentra-tion for real-time monitoring. The absolute quantification method, onthe other hand, provides us with an accurate computational tool tocalculate absolute values of oxy-, deoxy-, total hemoglobin concentra-tions, and light scattering coefficients using a multi-step, least-squaresregressionfitting. Amulti-channel LRS systemalongwith thedevelopedquantification methods opens a possibility to study neural pathways inanimals and to understand the relationship between neural activationand hemodynamic response at a sub-millimeter resolution. Anapplication of interest is to understand mechanism of pain bymeasurements at multiple sites along the pathway and will be furthercarried out in our future studies.

Acknowledgments

We would like to thank Dheerendra Kashyap, Ph.D. and Bo PingWang, Ph.D. (Professor, Mechanical and Aerospace Engineering, UTArlington), for their contribution in developing ant colony otimizationalgorithm.

Appendix A

A1. The effects of different bounds on optimization outcome

As stated in Inverse calculation section, ant colony optimization(ACO) requires upper and lower bounds to be given for each variableimplicitly used in Eq. (7) when we search for the optimal set ofabsolute values of [HbO], [Hb], a, and b, where a, and b account for μs′seen in Eqs. (4) and (5). ACO allows the algorithm to arrive at theglobal minimum only within the given bounds. While the bounds thatwe used in our data analysis were reasonable based on the tissue ofinterest, the final outcome of fitted parameters of [HbO], [Hb], a, and bare in theory affected by the selected bounds. It is important toexamine whether the global minimum for Eq. (7) exists outside theselected bounds or how much our fitted results depend on the

selection of different bounds. To answer these questions, weinvestigated if expanding the bounds would affect our results.Specifically, we chose three different ranges of bounds for all fourparameters of [HbO], [Hb], a, and b: (1) the original set of bounds thatare used in our current data analysis, (2) a modified set of boundsbroader than the original set, (3) and an infinite set of bounds thatrepresent the values much beyond their physiologically possiblelimits.

The normal levels of hemoglobin concentrations in pure blood areup to 10.7 mM in human adults (Dugdale, 2010); in general NIRSmeasures vascular hemoglobin concentrations in tissue vasculature,which are much lower than those in pure blood (Mitsuharu et al.,1995). For comparison, the three regions of bounds for both [HbO] and[Hb] are tabulated in Table A1. It is alsowell known that the range of μs′values for biological tissues is from1–40 cm−1, andmight extendup to200 cm−1 under extreme conditions in a highly light scatteringmedium, such as white matter in brain tissues. We also included threeregions of bounds for μs′ (through a and b) in Table A1, where a and bare associated with μs′ through Eqs. (3)–(5), to be used in our testingruns.

As seen in Inverse calculation section, Eq. (1) is coupled withEqs. (2)–(5) and is very non-linear with a broad spectral span from500 nm to 850 nm. In order to obtain an optimal fit between themeasured and calculated reflectance curve, we have incorporated athree-step fitting sequence. Each of the three bounds (for all fittingparameters) listed in Table A1 was initially set as broad bounds forstep-1 fitting routine; the fitting bounds for step-2 and step-3sequence were determined according to the fitting outputs in step-1,as explained in Inverse calculation section. The criteria to stop thefitting iterations at each step were defined either by a chosen numberfor maximum iterations or when a desired value of the objectivefunction (i.e., Eq. (7))was achieved.We evaluated thefitting efficiencyby comparing three output parameters by the end of fitting routine:(1) the number of total iterations (niteration), (2) the actual value of theobjective function (vobj), and (3) final fitted [HbO] values. Thenumbers of minimum and maximum iterations were chosen to be20 and 50 during step-1 fitting, 20 and 300 for step-2 and step-3. Thecriterion value of vobj to end the iterationswas chosen to be 2, 0.01, and0.05 during the three steps of fitting, respectively.

It was found that by increasing the bounds, the number of iterationsincreased significantly, as illustrated in Table A2, which was createdusing one of the data points shown in Fig. 5(a) as an example. Fivemoredata points with different O2 Sat values were also utilized for fittingroutine testing; the results were obtained and similar to the results aslisted in Table A2. It is clear from this table that the number of iterationsincreases significantly when the bounds become broader, from theoriginal bounds to themodified bounds and then to the infinite bounds.The actual objective function values obtained when the fitting was

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complete were often correspondingly higher in most cases using eithermodified or infinite bounds than the original bounds.

Table A2A comparison of number of iterations, niteration, and value of the objective function, vobj,for a specific O2 Sat data point using three different bounds.

Fitting step 1 Fitting step 2 Fitting step 3

niteration vobj niteration vobj niteration vobj

Original bound set 21 0.11 21 0.001 21 0.046Modified bound set 86 0.94 300 0.015 22 0.050Infinite bound set 300 8.01 300 0.147 300 0.153

Furthermore, to directly compare the resultswith different bounds,a set of fitted [HbO] values are shown in Fig. A1 using 6 different O2 Satvalues. This figure shows [HbO] values obtained using all three fittingbounds, plotted along with the expected values determined by thestandard ISS oximeter. Thefitted resultsmay vary somewhat each timewhen the fitting routine runs due to the nature of least-squares fitting.We also executed the 3-step fitting routine 15 times using the originalbounds to create amean fitted value of [HbO]with standard deviation,as represented by the black vertical lines in Fig. A1. The results shownin this figure confirm that the fitted [HbO] values are in goodagreement with the expected ones when either original or modifiedbounds were used. The infinite bounds are still able to provide us withreasonable fitted parameters with a certain degree of under-estimation, as seen in the figure, where the fitted results lie slightlybelow the range of mean fitted [HbO] values obtained by either theoriginal or modified bounds.

Fig. A1. Comparison of fitted [HbO] values obtained using three different bounds withthe expected values (solid circles) given by ISS oximeter. The six data points were takenfrom the phantom study presented in Fig. 5(a). Here, ‘Mod’ represents the case withmodified bounds, ‘Inf’ represents the case with infinite bounds, ‘ISS’ represents theexpected values determined by ISS oximeter, and ‘Mean Org’ represents mean valuesobtained after 15 of fitting routine runs with original bounds; error bars mark therespective standard deviations.

Overall, this part of study demonstrates that the 3-step fittingsequence based on ACO in our earlier fitting routine should be robustto create reliable results. Selections of different upper and lowerbounds have insignificant effects on the final output of fittedparameters.

A2. Comparison between three-step fitting versus single-step fitting

Our optimization algorithm varied wavelength ranges whenexecuting the 3-step fitting sequence: in step 1, 500–850 nm wasused with bounds as given in Table A1; in step 2, the wavelength

range was narrowed down to 520–590 nm with restricted scatteringbounds (±15% variation around the fitted a and b parameters); instep 3, the spectral range returned to 500–850 nm with restriction in[Hb] and [HbO] bounds (±20% variation around the fitted values of[Hb] and [HbO] given in step 2) but without restriction in scatteringbounds (i.e., having the same bounds for a and b as the ones used instep 1). Next, we compare and evaluate the difference in optimizationoutcome between 3-step fitting and 1-step fitting in the wavelengthrange of 500–850 nm.

Single-step fitting routine was utilized to fit the same data set asthose in Section A1, with the same bounds listed in Table A1. Themaximum number of iterations was set to 600, and the minimumobjective function value, vobj, was set to be 0.05, as in case of 3-stepfitting. It was found that the objective function could not converge tothe preset vobj within 600 iterations for all three kinds of bounds. Inthe case of using infinite bounds, the results were not usable since theoutput values of objective function were up to 7. When the originaland modified bounds were employed, the objective function valueswere around 0.1, but the [HbO] values were overestimated in mostcases. Careful inspection on the fitted curves in the wavelength regionof 500–600 nm revealed that the fitting was not adequate in thatrange, although the overall objective function values were relativelylow.

To summarize, 1-step fitting is not satisfactory or adequate,particularly with infinite bounds. The accuracies of fitting parametersare improved gradually as 3-step fittings are performed: step-1 fittingroutine results in a set of parameters close to the expected set in theoverall spectral range, but not good enough as the final output. Step-2fitting provides us with more accurate values of [HbO] and [Hb] basedon 500–600 nm spectra. Step-3 refines the fitting in the overallwavelength region again (500–850 nm) and outputs the best set offitting parameters.

Another way to improve the accuracy of 1-step fitting may beweighted-fitting with more weight in the 500–600 nm range. Ourresults indicate that with the current fitting method, a good set offitting parameters can be more accurately and quickly achieved withprior knowledge on the physiological bounds of the measurement.With tighter and narrower bounds, the speed and accuracy of thefitting algorithm increases. Also, it will help to increase the fittingspeed if parameter b is assumed to be constant (b=2.4), as previouslydetermined for intralipid by van Staveren et al. (1991).

Appendix B. Supplementary data

Supplementary data to this article can be found online atdoi:10.1016/j.neuroimage.2011.01.020.

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