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 PhaseEmission 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
Convent
ional
DCA
GSD
1 dimension sensitivity profile
Anomaly position at 20mm from the center
Convent
ional
DCA
GSD
1 dimension sensitivity profile
Anomaly position at 25mm from the center
Convent
ional
DCA
GSD
1 dimension sensitivity profile
(B) Negative target single anomalyAnomaly position at 15.5mm from the center
Convent
ional
DCA
GSD
1 dimension sensitivity profile
Anomaly position at 20mm from the center
Convent
ional
DCA
GSD
1 dimension sensitivity profile
Convent
ional
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.
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