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Krishna Teja Tokala, 1 Daqing Piao, 1 Gary Xu, 2

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

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Krishna Teja Tokala, 1 Daqing Piao, 1 Gary Xu, 2

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  1. 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 74075 2Department of Radiology, Medical School, University of Michigan, Ann Arbor, 48109

  2. 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

  3. Motivation • The prostate cancer is considered to be the most vexing problem in USA. 11% of the deaths caused by cancer are due to prostate cancer http://anthony.com/philosophy/fight-cancer

  4. 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).

  5. Principle Demonstration Fluorescence 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

  6. Conventional Reconstruction Set Image Reconstructed Image • Depth Localization problem.

  7. The new reconstruction method involves pairing of the source-detectors. Does this reconstruct correctly? Set Image Ref: Guan Xu,DaqingPiao, "A Geometric-Differential-Sensitivity Based Algorithm Improves Object-Depth Localization for Diffuse Optical Tomography circular array Outward-Imaging,“ 40(1) Med. Phys January2013

  8. 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

  9. Conventional Method GSD Method • 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 : 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.

  10. Conventional Method GSD Method • 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 New Jacobian

  11. The Jacobian w.r.t the <S1, Dm> where m=1:16 Conventional Method GSD Method • Jacobian now is w.r.t the relative sensitivity difference of <S1,D1,Dm > Conventional Jacobian (J): This is the [Diff] matrix. J

  12. Comparing GSD with another method Ref: H. Niu, F. Tian, Z.-J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography," Opt. Lett. 35, 429-431 (2010). • 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.

  13. 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: DCA Method GSD Method DCA: “Depth Compensation Algorithm” method

  14. (d) Conventional Mesh (b) (e) DCA weighting Mesh (g) Depth Sensitivity of the three methods. (c) (f) Sensitivity Difference 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.

  15. Materials and 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.

  16. 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.

  17. 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.

  18. (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.

  19. (A) Single positive target anomaly Anomaly position at 15.5mm from the center Conventional DCA GSD Simulation results 1 dimension sensitivity profile

  20. Anomaly position at 20mm from the center Conventional DCA GSD 1 dimension sensitivity profile

  21. Anomaly position at 25mm from the center Conventional DCA GSD 1 dimension sensitivity profile

  22. (B) Negative target single anomaly Anomaly position at 15.5mm from the center Conventional DCA GSD 1 dimension sensitivity profile

  23. Anomaly position at 20mm from the center Conventional DCA GSD 1 dimension sensitivity profile

  24. Anomaly position at 25mm from the center Conventional DCA GSD 1 dimension sensitivity profile

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

  26. Thank You

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