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Information about NIR imaging

NIR 3D optical imaging of biological tissue using f-DOT with target specific contrast agent.

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INDEX Introduction DOT F-DOT Results Conclusion Future work to be done

Introduction Non-Invasive Imaging has become an indispensable tool in medical diagnosis. However most of these methods have intrinsic drawbacks. Diffuse Optical Tomography (DOT) is a relatively new medical imaging modality which promises to address some of these problems.

DOT basics Forward Model Reverse Model DOT

DOT Basics Propagation of light into tissue Why NIR Optical Properties of tissues Absorption Scattering Propagation of light into tissue [15] Absorption at different wavelength[15]

Forward model Aim of forward model is to find out of the path traveled by photon. If the magnitude of the isotropic fluence within tissue is significantly larger than the directional flux magnitude, the light field is ‘diffuse’

The Radiative Transport Equation Light propagation in tissue behaves more like erratically moving photons migrating on average through the medium than like a propagating wave or a ray. Thus we use linear transport theory to model the propagation of light. In this approach light is treated as composed of distinct photons, propagating through a medium modeled as a background which has constant scattering and absorption characteristics.

L(r, Ω, t) radiance at position ‘r’ in the direction ‘Ω’ at time ‘t’, F (Ω, Ω′) is the scattering phase function, Q(r, Ω, t) is the radiant source function, v- velocity in medium. The left-hand side of accounts for photons leaving the tissue, and the right-hand side accounts for photons entering it.

Time derivative of the radiance, which equals the net number of photons entering the tissue. accounts for the flux of photons along the direction Ω The scattering and absorption of photons within the phase element Photons scattered from an element in phase space are balanced by the scattering into another element in phase space. The balance is handled by the integral term which accounts for photons at position r being scattered from all directions' Ω into direction Ω. photon source.

Photon Diffusion Equation If the scattering probability is much larger than that of absorption within the medium we can use a simple approximation. The basic idea is that if the reduced scattering coefficient is much greater than the absorption coefficient, the radiance can be approximated as a weighted sum of the photon fluence rate and the photon flux.

This approximation is valid when the radiance is almost angularly uniform, having only a relatively small flux in any particular angular direction. Expressing the radiance in this form, allows for the simplification of the linear transport equation to the variable-scattering form of what is known as the photon diffusion equation:

FEM implementation When the RI is homogeneous, the finite element discretization of a volume, Ω, can be obtained by subdividing the domain into D elements joined at V vertex nodes. . In finite element formalism, the fluence at a given point, Φ(r) is approximated by the piecewise continuous polynomial function, where Ω, is a finite dimensional subspace spanned by basis functions {Ui,i=1…V} 1 (r) ( ) Vh h i iu r

The diffusion equation in the FEM framework can be expressed as system of linear algebraic equations: 0 1 (K(k) C( ) F) q 2 a m i c A (r) u (r). u (r)d n ij i jK k r ( (r) )u (r)u (r)d (r) n ij a i j m i C r c 1 (r) (r)dn ij i jF u u r 0 0(r)q (r)dn iq u r

Inverse model The goal of the inverse problem is the recovery of optical properties μ at each FEM node within the domain using measurements of light fluence from the tissue surface. This inversion can be achieved using a modified-Tikhonov minimization min 22 2 0 1 1 ( ) NM NN M C i i j i j X

We minimize this ‘objective’ function: 2 2 1 ( ) NM M C i i i X 2 2 2 0 0 0( ) ( ) ( ) .... X X d X d 1 1 T Tc c c c M i i

1 [J J I] ( )T T c M J c J This derivative is called Jacobian Here is the regularization parameter which helps in converging the solution. And will yield to better result, instead of this regularization parameter we can also use priori conditions, Which can be obtained from already performed medical operations.

Introduction Forward model Inversion scheme F-DOT

Introduction Fluorescence tomography methods aim at reconstructing the concentration of fluorophores within the imaged object Diffuse measurement of the fluorescence emissions are obtained on the boundary of the object Excitation is performed through external laser sources at various position Important terms to know Stoke shift Quantum yield Molar excitation

Forward model Fluorochrome within domain Ω increases the absorption at λ by C is the Spatially varying Concentration is the molar excitation of fluorochrome. • The fluorochrome will emit at a wavelength λ with the probability of • Assuming that only two distinct wavelength are present (r)c &x m

We can write the equations as Where 1st equation stands for excitation wavelength and 2nd equation for emission wavelength Under the assumption that stokes shift is small 0( (r) c(r)) (r) ( )x ax x x s sD r r ( D (r)) (r) (r) (r)m am f m x xc x mD D D ax am a

Solving the equations… The final equation is diffusion equation and hence both equations becomes independent and can be computed completely in parallel. 0 0(r) (r) (r r ) ( D (r)) (r)x s a xc 0 1 ( (r))( (r) (r)) (r r )a f x s sD 1 ( (r) (r))f x t 0( (r)) (r r )a t s sD

0 1 ( (r))( (r) (r)) (r r )a f x s sD The 1st Equation describes the propagation of excitation light with absorption of both tissue and the inside fluorophores. The Quantum yield is defined as the ratio between emitting fluorescence photon numbers and the number of excitation photon absorbed by fluorophore 1 (r)f It compensates the excitation photon density absorbed by fluorescent. Thus the 2nd Equation describes the transportation of excitation light in tissue with assumed no fluorophore inside. 0( (r) c(r)) (r) ( )x ax x x s sD r r

Parallel inversion scheme

SIMULATION RESULTS SIMULATION IN MATLAB Original Mesh Reconstructed image

Error vs. Iteration Graph

Reconstruction with priors Without Priori condition With priori condition

3 D Reconstructed image using nirfast

Conclusion In this presentation the work towards development and demonstration of DOT algorithms in two dimensions progress towards f-DOT which have certain advantages over the existing ones is presented . In the first set of simulations it is shown that recovery of optical properties and the location of the inhomogenities in two dimensions. And in three dimension the simulations is done using the NIRFAST.

Future Progress As the further work I will like to progress on with the image reconstruction of biological tissue with diffuse optical tomography and fluorescence diffuse optical tomography in three dimension with Matlab. I will also extend my work towards the software development for interfacing with instrumentation of diffuse optical tomography so that it can be implemented in real time.

References Kanmani Buddhi, “Studies on improvement of reconstruction methods in diffuse optical tomography”, Department of Instrumentation, Indian Institute of Science, April (2006). Tuchin V, ‘Tissue Optics Light scattering methods and instruments for medical diagnosis’, SPIE (2000). Hamid Dehghani, Matthew E. Eames, Phaneendra K. Yalavarthy, Scott C. Davis, Subhadra Srinivasan, Colin M. Carpenter, Brian W. Pogue and Keith D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction”, Wiley InterScience Publications, Commun. Numer. Meth. Engng(2008). Arridge SR, Schweiger M., “Direct calculation of the moments of the distribution of photon time-of-flight in tissue with a finite-element method.” Applied Optics (1995). Arridge SR., “Optical tomography in medical imaging. Inverse Problems”, (1999). Brooksby B, Jiang S, Kogel C, Doyley M, Dehghani H, Weaver JB, Poplack SP, Pogue BW, Paulsen KD., “Magnetic resonance-guided near-infrared tomography of the breast. Review of Scientific Instruments (2004).

Schweiger M, Arridge SR, Hiroaka M, Delpy DT. The finite element model for the propagation of light in scattering media: boundary and source conditions. Medical Physics (1995). Paulsen KD, Jiang H. “Spatially varying optical property reconstruction using a finite element diffusion equation approximation”. Medical Physics(1995). Ben A. Brooks. “Combining near infrared tomography and magnetic resonance imaging to improve breast tissue chromophore and scattering assessment”, “Thayer School of Engineering Dartmouth College Hanover, New Hampshire”- May 2005. Xiaolei Song, Ji Yi, and Jing Bai. “A Parallel Reconstruction Scheme in fluorescence Tomography Based on Contrast of Independent Inversed Absorption Properties”, Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China, Accepted 13 August (2006). R. B. Schulz, J. Peter, W. Semmler, and W. Bangerth, “Indepen-dent modeling of fluorescence excitation and emission with the finite element method,” inProceedings of OSA Biomedical Topic al Meeting s, Miami, Fla, USA, April 2004. David A. Boas, Dana H. Brooks, Eric L. Miller, Charles A. DiMarzio, Misha Kilmer, Richard J. Gaudette and Quan Zhang, ““Imaging the Body With Diffuse Optical Tomography” November 2001.

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