RESULTS & CONCLUSIONThe MFP on which photons will be found can be obtained from thepath of the net flux using the diffusion equation; Figure 2 illustratesexample phase lag & relative amplitude through layers of normal &tumour tissue. The diffusion equation is valid when studying diffuselight propagation, where photon scattering is much greater than theabsorption, or at a sufficient distance from the light sources. Thediffusion intensity and net flux through multiple layers of biologicaltissue were calculated using COMSOL. Variations in modelparameters such as source-detector separation, absorptioncoefficient, scattering coefficient & anisotropic properties wereassessed & compared with the theoretical predictions of MFP.

References:1. Zhou & Bai, Photon migration in turbid media: a finite-element solution for the most favorable path , Opt. Eng. 41(10) 2577–2581 (2002)2. Perelman et al., Photon migration in turbid media using path integrals,’ Phys. Rev. Lett. 72(9), 1341–1344 (1994)3. Perelman et al., Time-dependent photon migration using path integrals Phys. Rev. E, 51, 6134–41 (1995)4. Pham et al., Broad Bandwidth Frequency Domain Instrument for Quantitative Tissue Optical Spectroscopy, Rev. Sci. Instrum. 71 (6), (2000)5. Fishkin et al., Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject, Applied Optics 36(1), (1997)

METHODBy using the diffusion equation as described by Equation (5), making

& implementing this in to the Helmholtz Equation todescribe diffusion as described by Equation (6) & multiplying all termsby –D, one obtains Equation (7). For tissue without a fluorescentsource, = 0 in Equation (6).

INTRODUCTIONOptical tomography involves the non-invasive measurement ofphoton flight through soft tissue. Through the reconstruction ofimages made from the transmitted light & scatter, the study of photonpaths through soft tissue can be used to assess anatomicalstructures & tissue under investigation. High scatter-basedattenuation is frequently performed using intense, often pulsed ormodulated light sources & at frequencies where body tissues aremost transmissive. The optical properties of tissue vary considerablyover a range of wavelengths, soft tissues are highly scattering butinadequately absorb in the near-infrared range, thus this wavelengthis typically used. The separation of absorption from scatter is donewith either time-resolved or frequency domain data which is thenfitted with a diffusion theory of how light propagates through thetissue. The measurement of time of flight or frequency domain phaseshift is essential to allow separation of absorption from scatter withsufficient accuracy.

Photon Migration through Multiple Layers of Biological Tissue Mark S Yeoman1, Ebrahem Sultan2

1. Continuum Blue Ltd., Tredomen Innovation & Technology Park, CF82 7FQ, United Kingdom2. College of Technological Studies, PAAET, Kuwait.

OBSERVED COEFFICIENTSFishkin et al [97] obtained relationships for absorption coefficient (a)& scattering coefficient (s) with respect to wavelength () for bothtumor & non-tumor human tissue. Additionally, Pham et al. [2000]used reduced scattering values calculated from previously reportedintralipid optical properties, where Mie theory was used to relate s &the anisotropy factor (g) to the optical wavelength for 10% intralipid,as given by Equations (8) & (9):

Figure 2. Phase lag & relative amplitude plots through normal & tumourscattering & absorption coefficients obtained from Fishkin et al. [97]

AIMTo produce a multilayer photon migration model to predict the MFPon which photons will be found can be obtained from the path of thenet flux propagation using the diffusion equation. The diffusionequation is valid when studying diffuse light propagation. Themodelling of light propagation through multiple layers of biologicaltissue are assessed & compared to the theoretical predictions byPerelman at al. [94 & 95] for the most-favourable-path (MFP) asdescribed by Equation (1) & analytical solutions for light propagationphase (), lag (lag), amplitude of attenuation (Aatt) as described byEquations (2)-(4), & illustrated in Figure 1 below.

Figure 1. Schematic diagram of experimental geometry & coordinates

Laser Beam Collector

Extrapolated Boundary

Tissue Layer 1

Tissue Layer 2

Tissue Layer 3z

xrs

O Rzb

MFP

ltr

v0

r

vT

Equation 1. General form of MFP obtained from Perelman et al [95]

(1)

Equations 2. Analytical solutions obtained from Pham et al [2000]

⁄(2)

(3)

(4)

where:

(5)

(6)

(7)

Where for a layer of tissue:

. (8)

(9)

Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan