zbMATH — the first resource for mathematics

Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach. (English) Zbl 1440.74229
Summary: The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters is established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.

74L15 Biomechanical solid mechanics
65D17 Computer-aided design (modeling of curves and surfaces)
76Z05 Physiological flows
74S99 Numerical and other methods in solid mechanics
Adam; DeepFace; GNMT; LIBSVM
Full Text: DOI
[1] Taylor, C. A.; Figueroa, C. A., Patient-specific modeling of cardiovascular mechanics, Annu. Rev. Biomed. Eng., 11, 109-134 (2009)
[2] Liu, H.; Shi, P., Maximum a posteriori strategy for the simultaneous motion and material property estimation of the heart, IEEE Trans. Biomed. Eng., 56, 378-389 (2009)
[3] Zhang, F.; Kanik, J.; Mansi, T.; Voigt, I.; Sharma, P.; Ionasec, R. I.; Subrahmanyan, L.; Lin, B. A.; Sugeng, L.; Yuh, D.; Comaniciu, D.; Duncan, J., Towards patient-specific modeling of mitral valve repair: 3D transesophageal echocardiography-derived parameter estimation, Med. Image Anal., 35, 599-609 (2017)
[4] Franquet, A.; Avril, S.; Le Riche, R.; Badel, P.; Schneider, F. C.; Boissier, C.; Favre, J. P., Identification of the in vivo elastic properties of common carotid arteries from MRI: A study on subjects with and without atherosclerosis, J. Mech. Behav. Biomed. Mater., 27, 184-203 (2013)
[5] Schulze-Bauer, C. A.J.; Holzapfel, G. A., Determination of constitutive equations for human arteries from clinical data, J. Biomech., 36, 165-169 (2003)
[6] Stålhand, J., Determination of human arterial wall parameters from clinical data, Biomech. Model. Mechanobiol., 8, 141-148 (2009)
[7] Olsson, T.; Klarbring, J. S.A., Modeling initial strain distribution in soft tissues with application to arteries, Biomech. Model. Mechanobiol., 5, 27-38 (2006)
[8] Masson, I.; Boutouyrie, P.; Laurent, S.; Humphrey, J. D.; Zidi, M., Characterization of arterial wall mechanical behavior and stresses from human clinical data, J. Biomech., 41, 2618-2627 (2008)
[9] Masson, I.; Beaussier, H.; Boutouyrie, P.; Laurent, S.; Humphrey, J. D.; Zidi, M., Carotid artery mechanical properties and stresses quantified using in vivo data from normotensive and hypertensive humans, Biomech. Model. Mechanobiol., 10, 867-882 (2011)
[10] Holzapfel, G. A.; Gasser, T. C.; Ogden, R. W., A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elast. Phys. Sci. Solids, 61, 1-48 (2000) · Zbl 1023.74033
[11] Smoljkić, M.; Vander Sloten, J.; Segers, P.; Famaey, N., Non-invasive, energy-based assessment of patient-specific material properties of arterial tissue, Biomech. Model. Mechanobiol., 14, 1045-1056 (2015)
[12] Gasser, T. C.; Ogden, R. W.; Holzapfel, G. A., Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, J. R. Soc. Interface, 3, 15-35 (2006)
[13] Liu, H.; Canton, G.; Yuan, C.; Yang, C.; Billiar, K.; Teng, Z.; Hoffman, A. H.; Tang, D., Using in vivo cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions, J. Biomech. Eng., 134 (2012), 011008-011008-011009
[14] Wittek, A.; Karatolios, K.; Bihari, P.; Schmitz-Rixen, T.; Moosdorf, R.; Vogt, S.; Blase, C., In vivo determination of elastic properties of the human aorta based on 4D ultrasound data, J. Mech. Behav. Biomed. Mater., 27, 167-183 (2013)
[15] Wittek, A.; Derwich, W.; Karatolios, K.; Fritzen, C. P.; Vogt, S.; Schmitz-Rixen, T.; Blase, C., A finite element updating approach for identification of the anisotropic hyperelastic properties of normal and diseased aortic walls from 4D ultrasound strain imaging, J. Mech. Behav. Biomed. Mater., 58, 122-138 (2016)
[16] Wittek, A.; Karatolios, K.; Fritzen, C.-P.; Bereiter-Hahn, J.; Schieffer, B.; Moosdorf, R.; Vogt, S.; Blase, C., Cyclic three-dimensional wall motion of the human ascending and abdominal aorta characterized by time-resolved three-dimensional ultrasound speckle tracking, Biomech. Model. Mechanobiol., 15, 1375-1388 (2016)
[17] Liu, M.; Liang, L.; Sun, W., Estimation of in vivo mechanical properties of the aortic wall: A multi-resolution direct search approach, J. Mech. Behav. Biomed. Mater., 77, 649-659 (2018)
[18] Joldes, G. R.; Miller, K.; Wittek, A.; Doyle, B.; simple, A., effective and clinically applicable method to compute abdominal aortic aneurysm wall stress, J. Mech. Behav. Biomed. Mater., 58, 139-148 (2016)
[19] Miller, K.; Lu, J., On the prospect of patient-specific biomechanics without patient-specific properties of tissues, J. Mech. Behav. Biomed. Mater., 27, 154-166 (2013)
[20] Liu, M.; Liang, L.; Liu, H.; Zhang, M.; Martin, C.; Sun, W., On the computation of in vivo transmural mean stress of patient-specific aortic wall, Biomech. Model. Mechanobiol. (2018), (in press)
[21] Liu, M.; Liang, L.; Sun, W., A new inverse method for estimation of in vivo mechanical properties of the aortic wall, J. Mech. Behav. Biomed. Mater., 72, 148-158 (2017)
[22] LeCun, Y.; Bengio, Y.; Hinton, G. E., Deep Learning, Nature, 521, 436-444 (2015)
[24] Shen, D.; Wu, G.; Suk, H.-I., Deep learning in medical image analysis, Annu. Rev. Biomed. Eng., 19, 221-248 (2017)
[25] He, K.; Zhang, X.; Ren, S.; Sun, J., Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, (IEEE International Conference on Computer Vision (2015))
[26] Kokkinos, I., Pushing the boundaries of boundary detection using deep learning, (Int.l Conf. on Learning Representations (2016))
[27] Taigman, Y.; Yang, M.; Ranzato, M. A.; Wolf, L., DeepFace: Closing the gap to human-level performance in face verification, (IEEE Conference on Computer Vision and Pattern Recognition (2014))
[28] He, K.; Zhang, X.; Ren, S.; Sun, J., Deep residual learning for image recognition, (IEEE Conference on Computer Vision and Pattern Recognition (2016))
[29] Krizhevsky, A.; Sutskever, I.; Hinton, G. E., ImageNet classification with deep convolutional neural networks, (Neural Information Processing Systems (2012))
[30] Wu, Y.; Schuster, M.; Chen, Z., Google’s neural machine translation system: bridging the gap between human and machine translation, Comput. Res. Repository (2016), abs/160908144
[31] Hannun, A.; Case, C.; Casper, J., Deep Speech: Scaling up end-to-end speech recognition, Comput. Res. Repository (2014), abs/14125567
[32] Luo, Y.; Fan, Z.; Baek, S.; Lu, J., Machine learning – aided exploration of relationship between strength and elastic properties in ascending thoracic aneurysm, Int. J. Numer. Methods Biomed. Eng., 34, Article e2977 pp. (2018)
[33] Cilla, M.; Pérez-Rey, I.; Martínez, M. A.; Peña, E.; Martínez, J., On the use of machine learning techniques for the mechanical characterization of soft biological tissues, Int. J. Numer. Methods Biomed. Eng., 0, p. e3121 (2018)
[34] Pham, T.; Martin, C.; Elefteriades, J.; Sun, W., Biomechanical characterization of ascending aortic aneurysm with concomitant bicuspid aortic valve and bovine aortic arch, Acta Biomater., 9, 7927-7936 (2013)
[35] Martin, C.; Sun, W.; Pham, T.; Elefteriades, J., Predictive biomechanical analysis of ascending aortic aneurysm rupture potential, Acta Biomater., 9, 9392-9400 (2013)
[36] Geman, S.; Geman, D., Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., PAMI-6, 721-741 (1984) · Zbl 0573.62030
[37] Martin, C.; Sun, W.; Elefteriades, J., Patient-specific finite element analysis of ascending aorta aneurysms, Amer. J. Physiol. Heart Circ. Physiol., 308, H1306-H1316 (2015)
[38] Liang, L.; Liu, M.; Martin, C.; Elefteriades, J. A.; Sun, W., A machine learning approach to investigate the relationship between shape features and numerically predicted risk of ascending aortic aneurysm, Biomech. Model. Mechanobiol., 1-15 (2017)
[39] Weisbecker, H.; Pierce, D. M.; Holzapfel, G. A., A generalized prestressing algorithm for finite element simulations of preloaded geometries with application to the aorta, Int. J. Numer. Methods Biomed. Eng., 30, 857-872 (2014)
[40] Webb, A. R.; Copsey, K. D., Statistical Pattern Recognition (2011), in, Wiley · Zbl 1237.68006
[41] Dugas, C.; Bengio, Y., Fran, #231, o. B, #233, lisle, C. Nadeau, Ren, #233, Garcia, Incorporating second-order functional knowledge for better option pricing, (Proc. Proceedings of the 13th International Conference on Neural Information Processing Systems (2000), MIT Press: MIT Press Denver, CO), 451-457
[42] Glorot, X.; Bordes, A.; Bengio, Y., Deep sparse rectifier neural networks, (Proc. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR, Proceedings of Machine Learning Research (2011)), 315-323
[43] Hahnloser, R. H.R.; Sarpeshkar, R.; Mahowald, M. A.; Douglas, R. J.; Seung, H. S., Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit, Nature, 405, 947 (2000)
[45] Kingma, D. P.; Ba, J., Adam: A method for stochastic optimization, (The 3rd International Conference for Learning Representations (2015))
[46] Goodfellow, I.; Bengio, Y.; Courville, A., Deep Learning (2016), The MIT Press · Zbl 1373.68009
[47] Pierce, D. M.; Maier, F.; Weisbecker, H.; Viertler, C.; Verbrugghe, P.; Famaey, N.; Fourneau, I.; Herijgers, P.; Holzapfel, G. A., Human thoracic and abdominal aortic aneurysmal tissues: Damage experiments, statistical analysis and constitutive modeling, J. Mech. Behav. Biomed. Mater., 41, 92-107 (2015)
[48] Weisbecker, H.; Pierce, D. M.; Regitnig, P.; Holzapfel, G. A., Layer-specific damage experiments and modeling of human thoracic and abdominal aortas with non-atherosclerotic intimal thickening, J. Mech. Behav. Biomed. Mater., 12, 93-106 (2012)
[49] Chang, C.-C.; Lin, C.-J., LIBSVM: a library for support vector machines, ACM Trans. Intell. Syst. Technol. (TIST), 2, 27 (2011)
[50] Li, K.; Ogden, R. W.; Holzapfel, G. A., An exponential constitutive model excluding fibres under compression: Application to extension – inflation of a residually stressed carotid artery, Math. Mech. Solids, 23, 1206-1224 (2018) · Zbl 1401.74244
[51] Li, K.; Ogden, R. W.; Holzapfel, G. A., A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues, J. R. Soc. Interface, 15 (2018)
[52] Li, K.; Ogden, R. W.; Holzapfel, G. A., Modeling fibrous biological tissues with a general invariant that excludes compressed fibers, J. Mech. Phys. Solids, 110, 38-53 (2018)
[53] Yagawa, G.; Okuda, H., Neural networks in computational mechanics, Arch. Comput. Methods Eng., 3, 435 (1996)
[54] Ghaboussi, J.; Sidarta, D. E., New nested adaptive neural networks (NANN) for constitutive modeling, Comput. Geotech., 22, 29-52 (1998)
[55] Theocaris, P. S.; Panagiotopoulos, P. D., Neural networks for computing in fracture mechanics. Methods and prospects of applications, Comput. Methods Appl. Mech. Engrg., 106, 213-228 (1993) · Zbl 0782.73077
[56] Huber, N.; Tsakmakis, C., Determination of constitutive properties fromspherical indentation data using neural networks. Part i:the case of pure kinematic hardening in plasticity laws, J. Mech. Phys. Solids, 47, 1569-1588 (1999) · Zbl 0960.74015
[57] Huber, N.; Tsakmakis, C., Determination of constitutive properties fromspherical indentation data using neural networks. Part ii:plasticity with nonlinear isotropic and kinematichardening, J. Mech. Phys. Solids, 47, 1589-1607 (1999)
[58] Klambauer, G.; Unterthiner, T.; Mayr, A.; Hochreiter, S., Self-normalizing neural networks, (Advances in Neural Information Processing Systems (2017)), 972-981
[59] Barrett, J. F.; Keat, N., Artifacts in CT: Recognition and avoidance, RadioGraphics, 24, 1679-1691 (2004)
[60] Labrosse, M. R.; Beller, C. J.; Mesana, T.; Veinot, J. P., Mechanical behavior of human aortas: Experiments, material constants and 3-D finite element modeling including residual stress, J. Biomech., 42, 996-1004 (2009)
[61] Botsch, M.; Kobbelt, L.; Pauly, M.; Alliez, P.; Lévy, B., Polygon Mesh Processing (2010), CRC press
[62] Dieleman, N.; van der Kolk, A. G.; Zwanenburg, J. J.M.; Harteveld, A. A.; Biessels, G. J.; Luijten, P. R.; Hendrikse, J., Imaging intracranial vessel wall pathology with magnetic resonance imaging, Curr. Prospects Future Dir., 130, 192-201 (2014)
[63] Pierce, D. M.; Fastl, T. E.; Rodriguez-Vila, B.; Verbrugghe, P.; Fourneau, I.; Maleux, G.; Herijgers, P.; Gomez, E. J.; Holzapfel, G. A., A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries, J. Mech. Behav. Biomed. Mater., 47, 147-164 (2015)
[64] Bartlett, P. L.; Wegkamp, M. H., Classification with a reject option using a hinge loss, J. Mach. Learn. Res., 9, 1823-1840 (2008) · Zbl 1225.62080
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.