Improving the object depth localization in fluorescence diffuse optical tomography in an axial

outward imaging geometry using a geometric sensitivity difference method.

Krishna Teja Tokala,1 Daqing Piao,1

Gary Xu,2

1School of Electrical and Computer Science Engineering, Oklahoma State University 740752Department of Radiology, Medical School, University of Michigan, Ann Arbor, 48109

Outline Motivation Improve decision making in prostate biopsy.

Principle Demonstration FDOT in an axial outward imaging geometry.

Analytical Representation The modification and enhancement.

Performance, Challenges and Future work Simulation Results

The prostate cancer is considered to be the most vexing problem in USA.

Motivation

11% of the deaths caused by cancer are due to prostate cancer

http://anthony.com/philosophy/fight-cancer

Zinc secretion from prostate cells is 10 times more than any soft tissue in the body.

Adenocarcinoma cells taken from prostate tumors have lost their ability to amass zinc.

Occurrence of this change is early in prostate malignancy.

Use of Zinc specific fluorophore.

Hence, we have a negative contrast target to be reconstructed and resolve the issues of depth localization while using FDOT.

Ref: V. Zaichick, T. Sviridova, and S. Zaichick, "Zinc concentration in human prostatic fluid: Normal, chronic prostatitis, adenoma and cancer," International Urology and Nephrology 28, 687-694 (1996).

Principle DemonstrationFluorescence Diffused Optical Tomography (FDOT) • The FDOT technique we are using is governed by 2 coupled equations.• 1st equation is related to the excitation phase.• 2nd equation is related to the emission phase.

Source Term

Fluorescence absorption

Quantum Yield

Excitation Phase

Emission Phase

Conventional Reconstruction

Depth Localization problem.

Set Image

Reconstructed Image

The new reconstruction method involves pairing of the source-detectors.

Set Image

Does this reconstruct correctly?

Ref: Guan Xu,Daqing Piao, "A Geometric-Differential-Sensitivity Based Algorithm Improves Object-Depth Localization for Diffuse Optical Tomography circular array Outward-Imaging,“ 40(1) Med. Phys January2013

Analytical Representation (Comparison)

Conventional Method GSD Method

• The conventional objective function to

be minimized during the FDOT

reconstruction is given by:

Where, denotes the measured and calculated fluence rate at a given

iteration and is the change in the optical properties of the

medium.

• The objective function to be minimized

during the FDOT reconstruction using

GSD is given by:

[Diff] matrix performing the forward-pairing differentiation of

the native sensitivity values is called the GSD operation matrix.

GSD : “ Geometry Sensitivity Difference“ method

Objective Function Change of optical properties

The change in the optical properties of the medium at each iteration is :

The change in the optical properties of the medium at each iteration is :

Conventional Method GSD Method

Where is the sensitivity matrix or the jacobian and n and n-1 are the iteration numbers is the change in the referred and the previous iteration.

Note that at each iteration the matrix is bigger compared to the conventional reconstruction and hence the computational time increases.

So for a conventional reconstruction the Jacobian matrix at each iteration for a source-detector pair is given by

i ={1,2,3…16} j = {1,2,3,…16} and <> = {1,2,3,….N} N is the number of nodes.

For the GSD method that we are implementing we perform the modification on this Jacobian matrix by forward pairing of the source or the detector measurements

Conventional Method GSD Method

New Jacobian

The Jacobian w.r.t the <S1, Dm> where m=1:16

Conventional Method GSD Method

Conventional Jacobian (J):

• Jacobian now is w.r.t the relative sensitivity difference of <S1,D1,Dm >

This is the [Diff] matrix. J

Comparing GSD with another method

The comparison of GSD to the conventional reconstruction method is well known.

We need to compare this GSD method with another methods which have active compensation of the depth variation of the update function.

In our study we compare the GSD method with DCA method which modifies the Jacobian by a weighting scheme.

Ref: H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm foraccurate depth localization in diffuse optical tomography," Opt. Lett. 35, 429-431 (2010).

Analytical Comparison

The change in the optical properties at each iteration is given by:

The change in the optical properties at each iteration is given by:

Where, Here M is the weighting matrix given by:

GSD MethodDCA Method

DCA: “Depth Compensation Algorithm” method

(g) Depth Sensitivity of the three methods.

(d) Conventional Mesh

(f) Sensitivity Difference

(e) DCA weighting Mesh(b)

(c)

Fig (a)-(c) shows how the methods were implemented. (d)-(f) shows the 2-D sensitivity mapping (g) shows the 1-D depth sensitivity plot of the 3 methods.

Circular Array of outward imaging geometry.

Inner radius of 10mm and outer radius of 50mm.

A FEM mesh with 7708 nodes and 15040 elements.

32 evenly distributed channels i.e 16 sources and 16 detectors.

Materials and methods

The sensitivity distributions, forward and inverse computations were realized based on NIRFAST with 16 source detector pairs on the inner boundary geometry.

Simulation studies were done on a single anomaly positive and negative contrast at 3 different depths and the 1-D reconstruction profile was extracted.

The figure shows the fem modeled outward imaging geometry for 3 depth positions we are simulating. o1 denotes the tissue region and o2 represents the anomaly.

Simulation parameters(A) Single positive target anomaly

The contrast of the anomaly is 3 times the background The anomaly at three depths was considered, 15.5mm, 20mm,

25mm from the center of the geometry was considered.

)

)

)

(B) Single negative target anomaly

The contrast of the anomaly is 1/3 times the background The anomaly at three depths was considered, 15.5mm, 20mm,

25mm from the center of the geometry was considered.

)

)

)

Simulation results(A) Single positive target anomalyAnomaly position at 15.5mm from the center

Conve

ntio

nal

DCA

GSD

1 dimension sensitivity profile

Anomaly position at 20mm from the center

Conve

ntio

nal

DCA

GSD

1 dimension sensitivity profile

Anomaly position at 25mm from the center

Conve

ntio

nal

DCA

GSD

1 dimension sensitivity profile

(B) Negative target single anomalyAnomaly position at 15.5mm from the center

Conve

ntio

nal

DCA

GSD

1 dimension sensitivity profile

Anomaly position at 20mm from the center

Conve

ntio

nal

DCA

GSD

1 dimension sensitivity profile

Conve

ntio

nal

DCA

GSD

Anomaly position at 25mm from the center

1 dimension sensitivity profile

The single anomaly target at different depths for both positive and negative contrast targets have clearly shows GSD outworks both the conventional and the DCA reconstruction methods.

Currently we are working on the dual anomaly targets at different azimuthal positions and at different depths.

Conclusion and ongoing work

This work was supported by DoD Prostate Cancer Research Program through a grant #W81XWH-10-1-0836.

THANK YOU