Abstract
Identifying the elastic parameters of a finite element model from a dynamically acquired set of observations is a fundamental challenge in many data-driven medical applications going from soft surgical robotics to image-guided per-operative simulations. While various strategies exist to tackle the parameter-identification inverse problem (Aster et al. 2013), the effect of sub-optimal discretization, as often required in real-time applications, is largely overlooked. Indeed, the need to tune the parameter values in order to account for discretization-induced stiffening in specific models is reported in different works (e.g. Chen et al. 2015; Mira et al. 2018). However, to the best of our knowledge, no systematic study of this phenomenon exists to date, nor has any strategy to select optimal effective values been developed. Our work addresses the issue of parameter identification in coarsened meshes with special attention to the dynamical nature of the identification. We focus on the estimation of Young’s moduli in simplified systems and show that the estimated stiffnesses are underestimated in a systematic manner when reducing the number of degrees of freedom. We also show that the effective stiffness of a given coarse mesh, when associated with an undersampled mesh discretization, is not constant but strongly depends on the prescribed deformations. These results show that the estimated parameters should not be considered as the true parameter value of the organ or tissue but instead are model-dependent values. We argue that Bayesian methods present a clear advantage w.r.t. classical minimization methods by their ability to efficiently adapt the local parameter values.
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Anna, M., Carton, A.-K., Muller, S., Payan, Y.: Breast biomechanical modeling for compression optimization in digital breast tomosynthesis. In: Gefen, A., Weihs, D., (eds.) Computer Methods in Biomechanics and Biomedical Engineering. Lecture Notes in Bioengineering, pp. 29–35. Springer (2018)
Aster, R.C., Borchers, B., Thurber, C.H.: Parameter Estimation and Inverse Problems, 2nd edn. Academic Press, Cambridge (2013)
Avril, S., Evans, S.: Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics, vol. 573. Springer, Heidelberg (2017)
Bialecki, R.A., Kassab, A.J., Fic, A.: Proper orthogonal decomposition and modal analysis for acceleration of transient fem thermal analysis. Int. J. Numer. Methods Eng. 62, 774–797 (2005)
Chen, D., Levin, D.I.W., Sueda, S., Matusik, W.: Data-driven finite elements for geometry and material design. ACM Trans. Graph. 34(4), 74:1–74:10 (2015)
Collins, J.A., Weis, J.A., Heiselman, J.S., Clements, L.W., Simpson, A.L., Jarnagin, W.R., Miga, M.I., et al.: Improving registration robustness for image-guided liver surgery in a novel human-to-phantom data framework. IEEE Trans. Med. Imaging 36(7), 1502–1510 (2017)
Han, L., Hipwell, J.H., Tanner, C., Taylor, Z., Mertzanidou, T., Cardoso, J., Ourselin, S., Hawkes, D.J.: Development of patient-specific biomechanical models for predicting large breast deformation. Phys. Med. Biol. 57(2), 455–472 (2011)
Haouchine, N., Cotin, S., Peterlik, I., Dequidt, J., Lopez, M.S., Kerrien, E., Berger, M.-O.: Impact of soft tissue heterogeneity on augmented reality for liver surgery. IEEE Trans. Visual. Comput. Graph. 21(5), 584–597 (2015)
Heiselman, J.S., Clements, L.W., Collins, J.A., Weis, J.A., Simpson, A.L., Geevarghese, S.K., Kingham, T.P., Jarnagin, W.R., Miga, M.I.: Characterization and correction of intraoperative soft tissue deformation in image-guided laparoscopic liver surgery. J. Med. Imaging 5(2), 021203 (2017)
Marchesseau, S., Heimann, T., Chatelin, S., Willinger, R., Delingette, H.: Multiplicative Jacobian energy decomposition method for fast porous visco-hyperelastic soft tissue model. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 235–242. Springer (2010)
Moireau, P., Chapelle, D.: Reduced-order unscented Kalman filtering with application to parameter identification in large-dimensional systems. Control Optim. Calc. Var. 17(2), 380–405 (2011)
Niroomandi, S., González, D., Alfaro, I., Bordeu, F., Leygue, A., Cueto, E., Chinesta, F.: Real-time simulation of biological soft tissues: a PGD approach. Int. J. Numer. Methods Biomed. Eng. 29(5), 586–600 (2013)
Ophir, J., Céspedes, I., Ponnekanti, H., Yazdi, Y., Li, X.: Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason. Imaging 13(2), 111–134 (1991)
Peters, T., Cleary, K.: Image-Guided Interventions: Technology and Applications. Springer, Heidelberg (2008)
Rifai, K., Cornberg, J., Mederacke, I., Bahr, M.J., Wedemeyer, H., Malinski, P., Bantel, H., Boozari, B., Potthoff, A., Manns, M.P., et al.: Clinical feasibility of liver elastography by acoustic radiation force impulse imaging (ARFI). Dig. Liver Dis. 43(6), 491–497 (2011)
Suwelack, S., Röhl, S., Bodenstedt, S., Reichard, D., Dillmann, R., dos Santos, T., Maier-Hein, L., Wagner, M., Wünscher, J., Kenngott, H., et al.: Physics-based shape matching for intraoperative image guidance. Med. phys. 41(11), 111901 (2014)
Wittek, A., Hawkins, T., Miller, K.: On the unimportance of constitutive models in computing brain deformation for image-guided surgery. Biomech. Model. Mechanobiol. 8(1), 77–84 (2009)
Zhang, J., Zhong, Y., Gu, C.: Deformable models for surgical simulation: a survey. IEEE Rev. Biomed. Eng. 11, 143–164 (2018)
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Schulmann, N., Cotin, S., Peterlik, I. (2020). The Effect of Discretization on Parameter Identification. Application to Patient-Specific Simulations. In: Ateshian, G., Myers, K., Tavares, J. (eds) Computer Methods, Imaging and Visualization in Biomechanics and Biomedical Engineering. CMBBE 2019. Lecture Notes in Computational Vision and Biomechanics, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-43195-2_19
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DOI: https://doi.org/10.1007/978-3-030-43195-2_19
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