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DHAWAN et al.: OPTICAL IMAGING MODALITIES FOR BIOMEDICAL APPLICATIONS71Fig. 3. Wavelength dependent absorption spectra of seven-layer model of skin and subcutaneous fat.simplicity, each layer is assigned average absorption and scattering coefficients, an anisotropy factor, and an index of refraction. It should be noted that these optical parameters for biological tissues are wavelength dependent and have been investigated by many researchers. For example, a seven-layer modelof skin with absorption and reflectance spectra in the visibleand near-infrared spectral regions is presented and analyzed byMeglinski et al. [9]. Fig. 3 shows the wavelength dependent absorption spectra for a seven-layer tissue model of skin and subcutaneous fat. Light transmission in a turbid heterogeneous biological medium, also called a random biological medium, isgoverned by radiative transport theory [10], [11] for which theGreen’s function is widely used to find a solution.Optical imaging through surface reflectance follows basicprinciples of reflection, refraction, and scalar wave theory.From the incident light, some photons are reflected by theair-tissue surface interface [for example, the stratum corneumof the skin, if a skin lesion is being imaged through epi-illumination light microscopy (ELM)] [12]. Remaining photonsenter the multilayered turbid tissue medium following thebasic laws of radiative transfer that can be represented byMaxwell’s equations. The radiative transfer theory in a randommedium is also called the transport theory of light propagation. Optical radiation diffuses in a large random medium bypropagating as planar and even spherical waves. Analyticalsolutions to the radiative transfer theory have been attemptedbut are quite difficult to compute due to the complex natureof the transport equation. As a result, approximations to thetransport equation have been used which are easier to solve,such as the Fokker–Planck equation as well as a modificationof that equation proposed by Leakeas and Larson [13], [14].Many investigators have used the Green’s function on theradiative transport and Fokker–Planck equations to computethe point spread function in a half-space composed of a uniformscattering and absorbing medium [2]. Diffusion theory hasalso been used as an approximation of the radiative transportequations to describe light propagation in a turbid medium[11], [15]. This alternative has been widely popular because ofits simplicity, specifically to model time-resolved light propagation with physical constraints. However, diffusion theoryassumes a constant scattering phase function, which is not necessarily accurate for a biological medium since it is typicallyanisotropic with a sharply forward peaked phase function buta directionally dependent point spread function. In addition tomultiple reflections and refractions in a multilayered biological medium, optical photons suffer from wavelength/energydependent absorption through elastic and inelastic scatteringevents that are isotropic as well as anisotropic in nature.Photon transport and propagation in an absorbing mediumcan be modeled analytically by the radiative transfer equation through total radiance defined as the spectral radianceintegrated over a narrow band of frequenciesas [2]–[4], [16](1)where is the position vector, is the unit direction vector, andrepresents time.is defined as the light enThe spectral radianceergy flow per unit normal area (perpendicular to the flow direction) per unit solid angle per unit time per unit frequency bandwidth., defined as the energy flow per unitThe fluence ratearea per unit time, can be expressed over the entire solid angleas(2)

72IEEE REVIEWS IN BIOMEDICAL ENGINEERING, VOL. 3, 2010Fig. 4. Photon energy distribution curves in biological medium that is illuminated through two point sources incident perpendicular to the tissue model with10- m cubical voxels: (a) and (b) for the second and seventh voxel layer parallel to the tissue surface, (c) for the Y -Z plane passing through the point of incidence,– m.and (d) for the X -Z plane passing through the point of incidence. Axis dimensions in all plots are in terms of voxel indices [36]. (a) XY plane at Z(b) XY plane at Z– m. (c) YZ plane at X. (d) XZ plane at Y. 70 80 0 0From the above, it can be shown that the specific absorptionin the light energy can be obtained as [2]–[4], [16](3)where the specific absorption rateis given as(4)whereis the absorption coefficient of the medium.It is usually difficult to analytically solve the radiativetransport equation due to a number of independent variables.The basic radiative transport equation is thus simplified usingthe diffusion approximation that the biological medium is notonly an absorbing medium, but it also contains heterogeneousmolecules which cause significant scattering. It is assumed that 10 20the absorption coefficient in a biological scattering medium ismuch smaller than the scattering coefficient, and the mediumis nearly isotropic after scattering events. Using an expansionof radiance in (1) and limiting the coefficients to first-orderspherical harmonics allowing only a fractional change in onetransport mean free path, it can be shown that fluence rate canbe expressed with much less complexity through the diffusionequation as [3], [16](5)where is an isotropic source distribution and is a diffusionconstant that can be described using the Fick’s law for diffusionof light photons in a scattering medium [16] as(6)

DHAWAN et al.: OPTICAL IMAGING MODALITIES FOR BIOMEDICAL APPLICATIONSwhereandare absorption and scattering coefficients andis the anisotropic factor of the medium.Maxwell’s equations, the transport equation, and the diffusion equation have been applied for biological imaging applications at the microscopic, mesoscopic, and macroscopic scales,respectively. For small volumes, analytical or numerical solutions of the Maxwell’s equations have been used to model thelight propagation in a random medium. For large volumes thediffusion equation can be solved, but for intermediate volumesthe transport theory has been applied using the Monte Carlo simulation method [17]–[20].As mentioned previously, visible and NIR optical wavelengths suffer from multiple reflections and scattering inaddition to absorption when propagated into random biological media. This causes uncertainty in the photon distributionpaths between the source and detector. Hence, the problem ofreconstructing the perturbation profile from scattered radiationis not simple. Usually, numerical and analytical solutionsare based on gross approximations that are inconsistent withphysical conditions and constraints. Therefore, to reconstructimages of a biological turbid medium, a forward model basedon the imaging geometry and pre-assumed approximations ofthe biological medium with distributions of optical photons inthe modeled medium is used to find the inverse solution (thereconstructed images of the known medium). Since feasiblesolutions are obtained by the basic theory of radiative transfer,propagation of light can be modeled using the Monte Carlosimulation method [17], [18], [20].A. Monte Carlo Simulation of Light Propagation in BiologicalMediumMonte Carlo simulation is a statistical technique for simulating random processes and has been applied to light-tissueinteractions under a wide variety of situations [15], [17]–[24].Photon interaction with matter via scattering and absorption isstochastic in nature and can be described using Monte Carlomethods by appropriately weighting absorption and scatteringevents [15]. Laser irradiation of skin using homogeneous [25]and layered geometries [21], [22] has been simulated usingMonte Carlo methods. In addition, for light propagation inhighly scattering tissue-like media, the results of the diffusionapproximation to the radiative transport equation have beencompared to Monte Carlo simulation results [17]. The MonteCarlo approach is in close agreement with the results of independent radiative transfer calculations [26], while the diffusionmodels examined [27], [28] were inaccurate for predictingsome of the characteristics of light fluence distributions.The most commonly simulated tissue models used in MonteCarlo simulations assume tissues to be layered structures withhomogeneous properties within each layer [18]–[21]. Althoughthese models are simple and easy to implement, real tissuesare more complex geometrically and consist of nonhomogeneous layers. Thus, a modular representation of the tissue architecture is a more appropriate method for capturing variationsin the tissue structure. Two primary methods, shape-based andvoxel-based, have been used to represent an object in a mathematical simulation. The shape-based approach [29] describesthe boundaries of each object using mathematical equations.73However, in these shape-based methods, irregular boundariesare difficult to describe mathematically. The voxel-based approach [24] represents an object as a set of voxels. The accuracy with which irregular boundaries can be described using thevoxel-based approach depends on the size of the voxels.Monte Carlo methods simulate the light propagation in aturbid multilayered medium with a photon step size which isdependent on the absorption and scattering coefficients withinthe tissue voxel and is calculated randomly from a logarithmicdistribution of path lengths. The step size is calculated as(7)whereis the local absorption coefficient,is the scatteringcoefficient, and is a random number uniformly distributed in.the intervalThe photon interacts with the tissue after propagating the pathlength equal to the step size. The tissue absorbs some part of thephoton weight during the interaction, which is given by(8)where the sum ofand is the tissue interaction or transportcoefficient in the tissue voxel.The new direction of the photon after interacting with thetissue is calculated by a random selection of the azimuthal anddeflection angles. The azimuthal angle is independent of thetissue properties and is uniformly distributed over the interval. The value of the azimuthal angle is based on selectionof another random number and is calculated as(9)The deflection angleis sampled statisticallyusing the probability distribution of the cosine of the deflec, described by the scattering function. Using thetion angle,scattering function proposed by Henyey and Greenstein [30],isthe probability distribution of(10)where the anisotropy factor , which is dependent on theandscattering characteristics of the tissue, is equal tohas a value between 1 and 1. For isotropic scattering, theanisotropy factor is equal to 0; for forward directed scatteringthe anisotropy factor is equal to 1. The cosine of the deflectionangle can be calculated by selecting another random numbergiven the following equations:(11)

74IEEE REVIEWS IN BIOMEDICAL ENGINEERING, VOL. 3, 2010where is a random number uniformly distributed in the interval[0,1].During its propagation, if the photon comes across a boundarywhere the refractive index changes, a decision about internalreflectance or transmittance is made based on the internal recalculated using Fresnel’s formulaflectance parameter[2], [31] as(12)whereis the angle of incidence of the photon with theis the angle of transmission. By generatingboundary anda random number uniformly distributed in the interval [0,1],and comparing it with the internal reflectance parameterwe determine whether the photon is internally reflected. If, the photon is internally reflected; ot

wavelengths for biomedical and clinical applications. Index Terms—Biomedical optical imaging, confocal microscopy, diffuse reflectance imaging, endoscopic imaging, fluorescence dif-fused optical tomography, microscopy, Monte Carlo simulation, multispectral imaging, optical coherence tomography, photoa-coustic imaging, transillumination. I.