Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
158 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks (2402.10741v3)

Published 16 Feb 2024 in math.NA, cs.NA, and physics.bio-ph

Abstract: The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elasticity map in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) by inferring the heterogeneous elasticity maps across three materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. We further applied our improved architecture to three additional examples of breast cancer tissue and extended our analysis to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Our selected network architecture consistently produced highly accurate estimations of heterogeneous elasticity maps, even when there was up to 10% noise present in the training data.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (89)
  1. Wei, J. et al. Bioinspired additive manufacturing of hierarchical materials: From biostructures to functions. \JournalTitleResearch 6, 0164, DOI: https://doi.org/10.34133/research.0164 (2023).
  2. Data-driven design for metamaterials and multiscale systems: A review. \JournalTitleAdvanced Materials n/a, 2305254, DOI: https://doi.org/10.1002/adma.202305254 (2023).
  3. Xuan, Y. et al. Regional biomechanical and failure properties of healthy human ascending aorta and root. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 123, 104705, DOI: https://doi.org/10.1016/j.jmbbm.2021.104705 (2021).
  4. Burris, N. S. et al. Vascular deformation mapping for CT surveillance of thoracic aortic aneurysm growth. \JournalTitleRadiology 302, 218–225, DOI: https://doi.org/10.1148/radiol.2021210658 (2022). PMID: 34665030.
  5. Lin, S. et al. Aortic local biomechanical properties in ascending aortic aneurysms. \JournalTitleActa Biomaterialia 149, 40–50, DOI: https://doi.org/10.1016/j.actbio.2022.06.019 (2022).
  6. Vander Linden, K. et al. Stiffness matters: Improved failure risk assessment of ascending thoracic aortic aneurysms. \JournalTitleJTCVS Open 16, 66–83, DOI: https://doi.org/10.1016/j.xjon.2023.09.008 (2023). Precision Therapy in Lung Cancer.
  7. New mechanical markers for tracking the progression of myocardial infarction. \JournalTitleNano Letters 23, 7350–7357, DOI: https://doi.org/10.1021/acs.nanolett.3c01712 (2023).
  8. Sadeghinia, M. J. et al. Mechanical behavior and collagen structure of degenerative mitral valve leaflets and a finite element model of primary mitral regurgitation. \JournalTitleActa Biomaterialia 164, 269–281, DOI: https://doi.org/10.1016/j.actbio.2023.03.029 (2023).
  9. 3D in vitro models for investigating the role of stiffness in cancer invasion. \JournalTitleACS Biomaterials Science & Engineering 9, 3729–3741, DOI: https://doi.org/10.1021/acsbiomaterials.0c01530 (2023).
  10. Seifert, A. W. et al. Skin shedding and tissue regeneration in african spiny mice (Acomys). \JournalTitleNature 489, 561–565, DOI: https://doi.org/10.1038/nature11499 (2012).
  11. Maden, M. et al. Perfect chronic skeletal muscle regeneration in adult spiny mice, Acomys cahirinus. \JournalTitleScientific Reports 8, 8920, DOI: https://doi.org/10.1038/s41598-018-27178-7 (2018).
  12. Notari, M. et al. The local microenvironment limits the regenerative potential of the mouse neonatal heart. \JournalTitleScience Advances 4, eaao5553, DOI: https://doi.org/10.1126/sciadv.aao5553 (2018).
  13. Harn, H. I.-C. et al. Symmetry breaking of tissue mechanics in wound induced hair follicle regeneration of laboratory and spiny mice. \JournalTitleNature Communications 12, 2595, DOI: https://doi.org/10.1038/s41467-021-22822-9 (2021).
  14. Paszek, M. J. et al. Tensional homeostasis and the malignant phenotype. \JournalTitleCancer Cell 8, 241–254, DOI: https://doi.org/10.1016/j.ccr.2005.08.010 (2005).
  15. Matrix elasticity directs stem cell lineage specification. \JournalTitleCell 126, 677–689, DOI: https://doi.org/10.1016/j.cell.2006.06.044 (2006).
  16. Materials approaches for modulating neural tissue responses to implanted microelectrodes through mechanical and biochemical means. \JournalTitleCurrent Opinion in Solid State and Materials Science 18, 319–328, DOI: https://doi.org/10.1016/j.cossms.2014.07.005 (2014). Neuroengineering Materials.
  17. Wilson, H. M. Modulation of macrophages by biophysical cues in health and beyond. \JournalTitleDiscovery Immunology 2, kyad013, DOI: https://doi.org/10.1093/discim/kyad013 (2023).
  18. Wu, H. et al. Progressive pulmonary fibrosis is caused by elevated mechanical tension on alveolar stem cells. \JournalTitleCell 180, 107–121, DOI: https://doi.org/10.1016/j.cell.2019.11.027 (2020).
  19. Fibrosis: from mechanisms to medicines. \JournalTitleNature 587, 555–566, DOI: https://doi.org/10.1038/s41586-020-2938-9 (2020).
  20. Sommer, G. et al. Biomechanical properties and microstructure of human ventricular myocardium. \JournalTitleActa Biomaterialia 24, 172–192, DOI: https://doi.org/10.1016/j.actbio.2015.06.031 (2015).
  21. Materials and manufacturing perspectives in engineering heart valves: a review. \JournalTitleMaterials Today Bio 5, 100038, DOI: https://doi.org/10.1016/j.mtbio.2019.100038 (2020).
  22. Wu, W. et al. A computational framework for atrioventricular valve modeling using open-source software. \JournalTitleJournal of Biomechanical Engineering 144, 101012, DOI: https://doi.org/10.1115/1.4054485 (2022).
  23. Wu, W. et al. The effects of leaflet material properties on the simulated function of regurgitant mitral valves. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 142, 105858, DOI: https://doi.org/10.1016/j.jmbbm.2023.105858 (2023).
  24. Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 123, 104745, DOI: https://doi.org/10.1016/j.jmbbm.2021.104745 (2021).
  25. Finite element analysis of mitraclip procedure on a patient-specific model with functional mitral regurgitation. \JournalTitleJournal of Biomechanics 104, 109730, DOI: https://doi.org/10.1016/j.jbiomech.2020.109730 (2020).
  26. Additive manufacturing of multi-material structures. \JournalTitleMaterials Science and Engineering: R: Reports 129, 1–16, DOI: https://doi.org/10.1016/j.mser.2018.04.001 (2018).
  27. Design of mechanical heterogeneous specimens using topology optimization. \JournalTitleInternational Journal of Mechanical Sciences 181, 105764, DOI: https://doi.org/10.1016/j.ijmecsci.2020.105764 (2020).
  28. Mazza, G. et al. Decellularized human liver as a natural 3D-scaffold for liver bioengineering and transplantation. \JournalTitleScientific Reports 5, 13079, DOI: https://doi.org/10.1038/srep13079 (2015).
  29. Guyette, J. P. et al. Bioengineering human myocardium on native extracellular matrix. \JournalTitleCirculation Research 118, 56–72, DOI: https://doi.org/10.1161/CIRCRESAHA.115.306874 (2016).
  30. Human-scale lung regeneration based on decellularized matrix scaffolds as a biologic platform. \JournalTitleSurgery Today 50, 633–643, DOI: https://doi.org/10.1007/s00595-020-02000-y (2020).
  31. Li, G. et al. Bioinspired soft robots for deep-sea exploration. \JournalTitleNature Communications 14, 7097, DOI: https://doi.org/10.1038/s41467-023-42882-3 (2023).
  32. Yang, X. et al. Bioinspired soft robots based on organic polymer-crystal hybrid materials with response to temperature and humidity. \JournalTitleNature Communications 14, 2287, DOI: https://doi.org/10.1038/s41467-023-37964-1 (2023).
  33. Lim, C. et al. Tissue-like skin-device interface for wearable bioelectronics by using ultrasoft, mass-permeable, and low-impedance hydrogels. \JournalTitleScience Advances 7, eabd3716, DOI: https://doi.org/10.1126/sciadv.abd3716 (2021).
  34. Kok, Y. et al. Anisotropy and heterogeneity of microstructure and mechanical properties in metal additive manufacturing: A critical review. \JournalTitleMaterials & Design 139, 565–586, DOI: https://doi.org/10.1016/j.matdes.2017.11.021 (2018).
  35. Dufrêne, Y. F. et al. Imaging modes of atomic force microscopy for application in molecular and cell biology. \JournalTitleNature Nanotechnology 12, 295–307, DOI: https://doi.org/10.1038/nnano.2017.45 (2017).
  36. Mapping elastic properties of heterogeneous materials in liquid with angstrom-scale resolution. \JournalTitleACS Nano 11, 8650–8659, DOI: https://doi.org/10.1021/acsnano.7b04381 (2017). PMID: 28770996.
  37. A magnetically actuated, optically sensed tensile testing method for mechanical characterization of soft biological tissues. \JournalTitleScience Advances 9, eade2522, DOI: https://doi.org/10.1126/sciadv.ade2522 (2023).
  38. The stiffness of living tissues and its implications for tissue engineering. \JournalTitleNature Reviews Materials 5, 351–370, DOI: https://doi.org/10.1038/s41578-019-0169-1 (2020).
  39. Deplano, V. et al. Biaxial tensile tests of the porcine ascending aorta. \JournalTitleJournal of Biomechanics 49, 2031–2037, DOI: https://doi.org/10.1016/j.jbiomech.2016.05.005 (2016).
  40. Experimental investigation of the tensile test using digital image correlation (dic) method. \JournalTitleMaterials Today: Proceedings 27, 757–763, DOI: https://doi.org/10.1016/j.matpr.2019.12.072 (2020). First International conference on Advanced Lightweight Materials and Structures.
  41. Mechanical characterization and identification of material parameters of porcine aortic valve leaflets. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 112, 104036, DOI: https://doi.org/10.1016/j.jmbbm.2020.104036 (2020).
  42. Stress distribution retrieval in granular materials: A multi-scale model and digital image correlation measurements. \JournalTitleOptics and Lasers in Engineering 76, 17–26, DOI: https://doi.org/10.1016/j.optlaseng.2015.04.009 (2016). Special Issue: Optical Methods in Nanobiotechnology.
  43. An analysis of macro- and micro-scale residual stresses of Type I, II and III using FIB-DIC micro-ring-core milling and crystal plasticity FE modelling. \JournalTitleInternational Journal of Plasticity 98, 123–138, DOI: https://doi.org/10.1016/j.ijplas.2017.07.004 (2017).
  44. Integrated digital image correlation for micro-mechanical parameter identification in multiscale experiments. \JournalTitleInternational Journal of Solids and Structures 267, 112130, DOI: https://doi.org/10.1016/j.ijsolstr.2023.112130 (2023).
  45. Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling with applications to heterogeneous material modeling. \JournalTitleComputer Methods in Applied Mechanics and Engineering 398, 115296, DOI: https://doi.org/10.1016/j.cma.2022.115296 (2022).
  46. Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels. \JournalTitleExtreme Mechanics Letters 50, 101566, DOI: https://doi.org/10.1016/j.eml.2021.101566 (2022).
  47. Enhancing mechanical metamodels with a generative model-based augmented training dataset. \JournalTitleJournal of Biomechanical Engineering 144, 121002, DOI: https://doi.org/10.1115/1.4054898 (2022).
  48. Hoq, E. et al. Data-driven methods for stress field predictions in random heterogeneous materials. \JournalTitleEngineering Applications of Artificial Intelligence 123, 106267, DOI: https://doi.org/10.1016/j.engappai.2023.106267 (2023).
  49. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. \JournalTitleJournal of Computational Physics 378, 686–707, DOI: https://doi.org/10.1016/j.jcp.2018.10.045 (2019).
  50. Karniadakis, G. E. et al. Physics-informed machine learning. \JournalTitleNature Reviews Physics 3, 422–440 (2021).
  51. Reliable extrapolation of deep neural operators informed by physics or sparse observations. \JournalTitleComputer Methods in Applied Mechanics and Engineering 412, 116064, DOI: https://doi.org/10.1016/j.cma.2023.116064 (2023).
  52. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. \JournalTitleComputer Methods in Applied Mechanics and Engineering 393, 114823, DOI: https://doi.org/10.1016/j.cma.2022.114823 (2022).
  53. Lu, L. et al. Physics-informed neural networks with hard constraints for inverse design. \JournalTitleSIAM Journal on Scientific Computing 43, B1105–B1132, DOI: https://doi.org/10.1137/21M1397908 (2021).
  54. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. \JournalTitleComputer Methods in Applied Mechanics and Engineering 379, 113741, DOI: https://doi.org/10.1016/j.cma.2021.113741 (2021).
  55. Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics. \JournalTitleApplied Mathematics and Mechanics 44, 1039–1068, DOI: https://doi.org/10.1007/s10483-023-2995-8 (2023).
  56. Single-test evaluation of directional elastic properties of anisotropic structured materials. \JournalTitleJournal of the Mechanics and Physics of Solids 181, 105471, DOI: https://doi.org/10.1016/j.jmps.2023.105471 (2023).
  57. A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method. \JournalTitleComputer Methods in Applied Mechanics and Engineering 401, 115616, DOI: https://doi.org/10.1016/j.cma.2022.115616 (2022).
  58. Analyses of internal structures and defects in materials using physics-informed neural networks. \JournalTitleScience Advances 8, eabk0644, DOI: https://doi.org/10.1126/sciadv.abk0644 (2022).
  59. Physics informed neural networks for continuum micromechanics. \JournalTitleComputer Methods in Applied Mechanics and Engineering 393, 114790, DOI: https://doi.org/10.1016/j.cma.2022.114790 (2022).
  60. Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and poisson’s ratio. \JournalTitleActa Biomaterialia 155, 400–409, DOI: https://doi.org/10.1016/j.actbio.2022.11.024 (2023).
  61. Physics‐informed deep‐learning for elasticity: Forward, inverse, and mixed problems. \JournalTitleAdvanced Science 10, DOI: https://doi.org/10.1002/advs.202300439 (2023).
  62. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks feature networks. \JournalTitleComputer Methods in Applied Mechanics and Engineering 384, 113938, DOI: https://doi.org/10.1016/j.cma.2021.113938 (2021).
  63. Hao, Z. et al. PINNacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs. \JournalTitlearXiv preprint arXiv:2306.08827 DOI: https://doi.org/10.48550/arXiv.2306.08827 (2023).
  64. Challenges in training PINNs: A loss landscape perspective. \JournalTitlearXiv preprint arXiv:2402.01868 DOI: https://doi.org/10.48550/arXiv.2402.01868 (2024).
  65. Simulating seismic multifrequency wavefields with the Fourier feature physics-informed neural network. \JournalTitleGeophysical Journal International 232, 1503–1514, DOI: https://doi.org/10.1093/gji/ggac399 (2022).
  66. Physics-informed neural network with Fourier features for radiation transport in heterogeneous media. \JournalTitleNuclear Science and Engineering 197, 2484–2497, DOI: https://doi.org/10.1080/00295639.2023.2184194 (2023).
  67. Systems biology informed deep learning for inferring parameters and hidden dynamics. \JournalTitlePLoS Computational Biology 16, e1007575, DOI: https://doi.org/10.1371/journal.pcbi.1007575 (2020).
  68. Systems Biology: Identifiability Analysis and Parameter Identification via Systems-Biology-Informed Neural Networks, 87–105 (Springer US, New York, NY, 2023).
  69. Interstitial growth and remodeling of biological tissues: Tissue composition as state variables. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 29, 544–556, DOI: https://doi.org/10.1016/j.jmbbm.2013.03.003 (2014).
  70. Growth and remodeling play opposing roles during postnatal human heart valve development. \JournalTitleScientific Reports 8, 1235, DOI: https://doi.org/10.1038/s41598-018-19777-1 (2018).
  71. Modulation of tissue growth heterogeneity by responses to mechanical stress. \JournalTitleProc Natl Acad Sci U S A 116, 1940–1945, DOI: https://doi.org/10.1073/pnas.1815342116 (2019).
  72. Hormuth, D. A. et al. Mechanism-based modeling of tumor growth and treatment response constrained by multiparametric imaging data. \JournalTitleJCO Clinical Cancer Informatics 1–10, DOI: https://doi.org/10.1200/CCI.18.00055 (2019).
  73. The effects of heterogeneous mechanical properties on the response of a ductile material. \JournalTitleScientific Reports 11, 18170, DOI: https://doi.org/10.1038/s41598-021-97495-x (2021).
  74. Strength-ductility synergy in heterogeneous-structured metals and alloys. \JournalTitleMatter 5, 2430–2433, DOI: https://doi.org/10.1016/j.matt.2022.05.023 (2022).
  75. Investigation of microstructure, mechanical properties and cellular viability of poly(L-lactic acid) tissue engineering scaffolds prepared by different thermally induced phase separation protocols. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 17, 186–197, DOI: https://doi.org/10.1016/j.jmbbm.2012.08.021 (2013).
  76. Budday, S. et al. Towards microstructure-informed material models for human brain tissue. \JournalTitleActa Biomaterialia 104, 53–65, DOI: https://doi.org/10.1016/j.actbio.2019.12.030 (2020).
  77. Mechanical properties of brain tissue based on microstructure. \JournalTitleJournal of the Mechanical Behavior of Biomedical Materials 126, 104924, DOI: https://doi.org/10.1016/j.jmbbm.2021.104924 (2022).
  78. Gaussian process random fields. In Cortes, C., Lawrence, N., Lee, D., Sugiyama, M. & Garnett, R. (eds.) Advances in Neural Information Processing Systems, vol. 28 (Curran Associates, Inc., 2015).
  79. DIC image reconstruction using an energy minimization framework to visualize optical path length distribution. \JournalTitleScientific Reports 6, 30420, DOI: https://doi.org/10.1038/srep30420 (2016).
  80. On the constitutive models for heart valve leaflet mechanics. \JournalTitleCardiovascular Engineering 5, 37–43, DOI: https://doi.org/10.1007/s10558-005-3072-x (2005).
  81. Larkin, K. G. Reflections on shannon information: In search of a natural information-entropy for images. \JournalTitlearXiv preprint arXiv:1609.01117 DOI: https://doi.org/10.48550/arXiv.1609.01117 (2016).
  82. Leveraging image complexity in macro-level neural network design for medical image segmentation. \JournalTitleScientific Reports 12, 22286, DOI: https://doi.org/10.1038/s41598-022-26482-7 (2022).
  83. DOLFIN: Automated finite element computing. \JournalTitleACM Trans. Math. Softw. 37, DOI: https://doi.org/10.1145/1731022.1731030 (2010).
  84. Ryu JeongAh, J. W. K. Current status of musculoskeletal application of shear wave elastography. \JournalTitleUltrasonography 36, 185–197, DOI: https://doi.org/10.14366/usg.16053 (2017).
  85. DeepXDE: A deep learning library for solving differential equations. \JournalTitleSIAM Review 63 (2021).
  86. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. \JournalTitleComputer Methods in Applied Mechanics and Engineering 403, 115671, DOI: https://doi.org/10.1016/j.cma.2022.115671 (2023).
  87. On the limited memory BFGS method for large scale optimization. \JournalTitleMathematical Programming 45, 503–528, DOI: https://doi.org/10.1007/BF01589116 (1989).
  88. Speeding up and reducing memory usage for scientific machine learning via mixed precision. \JournalTitlearXiv preprint arXiv:2401.16645 DOI: https://doi.org/10.48550/arXiv.2401.16645 (2024).
  89. Nonlinear Continuum Mechanics for Finite Element Analysis (Cambridge University Press, 2008), 2 edn.
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now