NIR three dimensional Imaging Of

breast model using f-DOT with target

specific contrast agent.

By

M.Nagendra Babu

(1227003)

Dr . Iven Jose, (Associate dean)-

CUFE

Under the

Guidance of

General Introduction

Picture Taken from YouTube video : cancer cell vs. normal cell

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.

Light projected on, has the tendency to spread

as it penetrate deep into tissue.

Propagation of light into tissue

Why NIR

Optical Properties of tissues

Absorption

Scattering

Propagation of light into tissue

[1]

Absorption at different wavelength[1]

DOT

DOT is a technique where NIR light is

projected on the surface of imaging volume

and the emergent light is measured at other

location of surface.

An equation for the radiant intensity is

obtained by balancing the absorption and

scatter mechanism by which the photons can

be gained or lost from arbitrary volume V

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.

The Radiative Transport Equation

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

The magnitude of the isotropic fluence within

tissue is significantly larger than the directional

flux magnitude, the light field is „diffuse‟.

This assumption allows a transition from the

radiative transport equation, which is used to

describe an anisotropic light field, to the

diffusion equation approximation

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 minimizationmin

22 2

0

1 1

( )

NM NN

M C

i i j

i j

X

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 x

c

x mD D D

ax am a

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

Three dimension Methodology

2D reconstruction from three dimensional data

yield better reconstruction results then absolute

reconstruction

“Problem” with this method is that light will be

scattered out of the imaging plane. (For our

experiment we are neglecting this scattered data)

Forward method and the reconstruction method

will be same as that of two dimension only

difference will be in mesh generation

In three dimensional we will consider the mesh

with tetrahedral prism for FEM with 6 basis

function.

Three dimensional Mesh Structure

Figure : Source and detector position of three dimensional mesh for forward model

Forward model of the three dimensional

mesh will yield 2256 output data

Ie

15*16 : 1st ring measurement

16*16 : 1st ring sources and 2nd ring detectors

16*16 : 1st ring sources and 3rd ring detectors

Total 3 ring detectors;

(((15*16)+(16*16)+(16*16))*3) = 2256

No we will map the required (15*16)= 240 data

for reconstruction and simple reconstruction

can be done

Figure : Reconstructed three dimensional image

A B

C

Figure Showing reconstructed image at fallowing ring position A-Top, B-

Bottom, C-Middle

Acceptance letter

References

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