A Computationally Efficient Approach for Estimation of Tissue Material Parameters from Clinical Imaging Data Using a Level Set Method
Publication: Journal of Engineering Mechanics
Volume 150, Issue 10
Abstract
This study proposes a computational method for estimating in vivo mechanical properties of tissues using clinical imaging data. In particular, a new level-set-based objective functional to compare a target and estimated shape of a tissue structure is introduced, along with its integration into an optimization-based approach for inverse material parameter estimation. The approach employs a continuous shape comparison metric using signed distance functions and combines the adjoint method for efficient gradient-based optimization. Simulated inverse problems based upon estimating cardiac ventricular wall stiffness from untagged imaging and hemodynamic data are used to assess the capability of the proposed approach. The results show that the proposed method is able to consistently and effectively minimize the shape-based objective functional to estimate material parameters. The minimization of this shape difference is capable of providing relatively accurate estimates of material parameters, although naturally depending on the sensitivity of the shape change to the particular parameters, and the process is tolerant to the inclusion of model error. Thus, the approach has the potential capability to provide estimates of in vivo mechanical properties of tissues from the shape of the tissue structure as can be directly estimated from imaging data.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Alnæs, M. S., A. Logg, K. B. Ølgaard, M. E. Rognes, and G. N. Wells. 2014. “Unified form language: A domain-specific language for weak formulations of partial differential equations.” ACM Trans. Math. Software 40 (2): 1–37. https://doi.org/10.1145/2566630.
Asbach, P., D. Klatt, U. Hamhaber, J. Braun, R. Somasundaram, B. Hamm, and I. Sack. 2008. “Assessment of liver viscoelasticity using multifrequency MR elastography.” Magn. Reson. Med. 60 (2): 373–379. https://doi.org/10.1002/mrm.21636.
Brigham, J., W. Aquino, F. Mitri, J. F. Greenleaf, and M. Fatemi. 2007. “Inverse estimation of viscoelastic material properties for solids immersed in fluids using vibroacoustic techniques.” J. Appl. Phys. 101 (2): 23509. https://doi.org/10.1063/1.2423227.
Brigham, J. C., and W. Aquino. 2007. “Surrogate-model accelerated random search algorithm for global optimization with applications to inverse material identification.” Comput. Methods Appl. Mech. Eng. 196 (45–48): 4561–4576. https://doi.org/10.1016/j.cma.2007.05.013.
Dorn, O., H. Bertete-Aguirre, J. Berryman, and G. Papanicolaou. 1999. “A nonlinear inversion method for 3d electromagnetic imaging using adjoint fields.” Inverse Prob. 15 (6): 1523. https://doi.org/10.1088/0266-5611/15/6/309.
Feijoo, G. R., M. Malhotra, A. A. Oberai, and P. M. Pinsky. 2001. “Shape sensitivity calculations for exterior acoustics problems.” Eng. Comput. 18 (3/4): 376–393. https://doi.org/10.1108/02644400110387000.
Feng, Y., E. Clayton, R. Okamoto, J. Engelbach, P. Bayly, and J. Garbow. 2016. “A longitudinal magnetic resonance elastography study of murine brain tumors following radiation therapy.” Phys. Med. Biol. 61 (16): 6121. https://doi.org/10.1088/0031-9155/61/16/6121.
Hassouna, M. S., and A. A. Farag. 2007. “Multistencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains.” IEEE Trans. Pattern Anal. Mach. Intell. 29 (9): 1563–1574. https://doi.org/10.1109/TPAMI.2007.1154.
Jameson, A. 1988. “Aerodynamic design via control theory.” J. Sci. Comput. 3 (Jun): 233–260. https://doi.org/10.1007/BF01061285.
Korinek, J., J. Wang, P. P. Sengupta, C. Miyazaki, J. Kjaergaard, E. McMahon, T. P. Abraham, and M. Belohlavek. 2005. “Two-dimensional strain–a doppler-independent ultrasound method for quantitation of regional deformation: Validation in vitro and in vivo.” J. Am. Soc. Echocardiography 18 (12): 1247–1253. https://doi.org/10.1016/j.echo.2005.03.024.
Kroon, D. 2011. “Accurate fast marching, MATLAB central file exchange.” Accessed December 10, 2023. https://www.mathworks.com/matlabcentral/fileexchange/24531-accurate-fast-marching.
Krouskop, T. A., T. M. Wheeler, F. Kallel, B. S. Garra, and T. Hall. 1998. “Elastic moduli of breast and prostate tissues under compression.” Ultrason. Imaging 20 (4): 260–274. https://doi.org/10.1177/016173469802000403.
Li, C., G. Guan, Y. Ling, Y.-T. Hsu, S. Song, J. T. Huang, S. Lang, R. K. Wang, Z. Huang, and G. Nabi. 2015. “Detection and characterisation of biopsy tissue using quantitative optical coherence elastography (OCE) in men with suspected prostate cancer.” Cancer Lett. 357 (1): 121–128. https://doi.org/10.1016/j.canlet.2014.11.021.
Natterer, F., and F. Wubbeling. 1995. “A propagation-backpropagation method for ultrasound tomography.” Inverse Prob. 11 (6): 1225. https://doi.org/10.1088/0266-5611/11/6/007.
Nazari, S. S., and P. Mukherjee. 2018. “An overview of mammographic density and its association with breast cancer.” Breast Cancer 25 (3): 259–267. https://doi.org/10.1007/s12282-018-0857-5.
Oberai, A. A., N. H. Gokhale, M. M. Doyley, and J. C. Bamber. 2004. “Evaluation of the adjoint equation based algorithm for elasticity imaging.” Phys. Med. Biol. 49 (13): 2955. https://doi.org/10.1088/0031-9155/49/13/013.
Oberai, A. A., N. H. Gokhale, and G. R. Feijóo. 2003. “Solution of inverse problems in elasticity imaging using the adjoint method.” Inverse Prob. 19 (2): 297. https://doi.org/10.1088/0266-5611/19/2/304.
Phipps, S. 2006. “Prostate tissue stiffness as measured with a resonance sensor system: A study on silicone and human prostate tissue in vitro.” Med. Biol. Eng. Comput. 44 (11): 941–943. https://doi.org/10.1007/s11517-006-0110-9.
Phipps, S., T. H. Yang, F. K. Habib, R. L. Reuben, and S. A. McNeill. 2005. “Measurement of tissue mechanical characteristics to distinguish between benign and malignant prostatic disease.” Urology 66 (2): 447–450. https://doi.org/10.1016/j.urology.2005.03.017.
Riklin Raviv, T., Y. Gao, J. J. Levitt, and S. Bouix. 2014. “Statistical shape analysis of neuroanatomical structures via level-set–based shape morphing.” SIAM J. Imag. Sci. 7 (3): 1645–1668. https://doi.org/10.1137/13093978X.
Riklin Raviv, T., K. Van Leemput, B. H. Menze, W. M. Wells III, and P. Golland. 2010. “Segmentation of image ensembles via latent atlases.” Med. Image Anal. 14 (5): 654–665. https://doi.org/10.1016/j.media.2010.05.004.
Seidl, D. T., A. A. Oberai, and P. E. Barbone. 2019. “The coupled adjoint-state equation in forward and inverse linear elasticity: Incompressible plane stress.” Comput. Methods Appl. Mech. Eng. 357 (Mar): 112588. https://doi.org/10.1016/j.cma.2019.112588.
Sengupta, P. P., V. K. Krishnamoorthy, J. Korinek, J. Narula, M. A. Vannan, S. J. Lester, J. A. Tajik, J. B. Seward, B. K. Khandheria, and M. Belohlavek. 2007. “Left ventricular form and function revisited: Applied translational science to cardiovascular ultrasound imaging.” J. Am. Soc. Echocardiography 20 (5): 539–551. https://doi.org/10.1016/j.echo.2006.10.013.
Veress, A., J. Weiss, R. Rabbitt, J. Lee, and G. Gullberg. 2001. “Measurement of 3D left ventricular strains during diastole using image warping and untagged MRI images.” In Vol. 28 of Computers in cardiology 2001, 165–168. New York: IEEE.
Xu, J., E. L. Desmond, T. C. Wong, C. G. Neill, M. A. Simon, and J. C. Brigham. 2022a. “Right ventricular shape feature quantification for evaluation of pulmonary hypertension: Feasibility and preliminary associations with clinical outcome.” J. Biomech. Eng. 144 (4): 044502. https://doi.org/10.1115/1.4052495.
Xu, J., T. C. Wong, M. A. Simon, and J. C. Brigham. 2022b. “A clinically applicable strategy to estimate the in vivo distribution of mechanical material properties of the right ventricular wall.” Int. J. Numer. Methods Biomed. Eng. 38 (2): e3548. https://doi.org/10.1002/cnm.3548.
Xu, J., R. J. Zupan, M. A. Simon, T. C. Wong, and J. C. Brigham. 2021. “Shape-based strategy for inverse estimation of soft tissue mechanical material properties from untagged medical imaging data.” J. Eng. Mech. 147 (8): 04021046. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001955.
Zile, M. R., and D. L. Brutsaert. 2002. “New concepts in diastolic dysfunction and diastolic heart failure: Part I: Diagnosis, prognosis, and measurements of diastolic function.” Circulation 105 (11): 1387–1393. https://doi.org/10.1161/hc1102.105289.
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© 2024 American Society of Civil Engineers.
History
Received: Jan 29, 2024
Accepted: May 16, 2024
Published online: Jul 29, 2024
Published in print: Oct 1, 2024
Discussion open until: Dec 29, 2024
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