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Wu W, Daneker M, Turner KT, Jolley MA, Lu L. Identifying Heterogeneous Micromechanical Properties of Biological Tissues via Physics-Informed Neural Networks. SMALL METHODS 2024:e2400620. [PMID: 39091065 DOI: 10.1002/smtd.202400620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Revised: 07/19/2024] [Indexed: 08/04/2024]
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 data-driven models for learning 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, a physics-informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. The improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the training data.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
- Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
| | - Mitchell Daneker
- Department of Statistics and Data Science, Yale University, New Haven, CT, 06511, USA
- Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Kevin T Turner
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Matthew A Jolley
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
- Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
| | - Lu Lu
- Department of Statistics and Data Science, Yale University, New Haven, CT, 06511, USA
- Wu Tsai Institute, Yale University, New Haven, CT, 06510, USA
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Gallagher S, Josyula K, Rahul, Kruger U, Gong A, Song A, Eschelbach E, Crawford D, Pham T, Sweet R, Parsey C, Norfleet J, De S. Mechanical behavior of full-thickness burn human skin is rate-independent. Sci Rep 2024; 14:11096. [PMID: 38750077 PMCID: PMC11096406 DOI: 10.1038/s41598-024-61556-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 05/07/2024] [Indexed: 05/18/2024] Open
Abstract
Skin tissue is recognized to exhibit rate-dependent mechanical behavior under various loading conditions. Here, we report that the full-thickness burn human skin exhibits rate-independent behavior under uniaxial tensile loading conditions. Mechanical properties, namely, ultimate tensile stress, ultimate tensile strain, and toughness, and parameters of Veronda-Westmann hyperelastic material law were assessed via uniaxial tensile tests. Univariate hypothesis testing yielded no significant difference (p > 0.01) in the distributions of these properties for skin samples loaded at three different rates of 0.3 mm/s, 2 mm/s, and 8 mm/s. Multivariate multiclass classification, employing a logistic regression model, failed to effectively discriminate samples loaded at the aforementioned rates, with a classification accuracy of only 40%. The median values for ultimate tensile stress, ultimate tensile strain, and toughness are computed as 1.73 MPa, 1.69, and 1.38 MPa, respectively. The findings of this study hold considerable significance for the refinement of burn care training protocols and treatment planning, shedding new light on the unique, rate-independent behavior of burn skin.
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Grants
- W911NF-17-2-0022 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W911NF-17-2-0022 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W911NF-17-2-0022 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W911NF-17-2-0022 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W912CG-20-2-0004 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
- W911NF-17-2-0022 U.S. Army Futures Command, Combat Capabilities Development Command Soldier Center STTC
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Affiliation(s)
- Samara Gallagher
- Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Kartik Josyula
- Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Rahul
- Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA.
| | - Uwe Kruger
- Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA
- Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
| | - Alex Gong
- Center for Research in Education and Simulation Technologies, University of Washington, Seattle, WA, USA
| | - Agnes Song
- Center for Research in Education and Simulation Technologies, University of Washington, Seattle, WA, USA
| | - Emily Eschelbach
- UW Medicine Regional Burn Center at Harborview Medical Center, University of Washington, Seattle, WA, USA
| | - David Crawford
- UW Medicine Regional Burn Center at Harborview Medical Center, University of Washington, Seattle, WA, USA
| | - Tam Pham
- UW Medicine Regional Burn Center at Harborview Medical Center, University of Washington, Seattle, WA, USA
| | - Robert Sweet
- Center for Research in Education and Simulation Technologies, University of Washington, Seattle, WA, USA
| | - Conner Parsey
- U.S. Army Combat Capabilities Development Command - Soldier Center, Simulation and Training Technology Center, Orlando, FL, USA
| | - Jack Norfleet
- U.S. Army Combat Capabilities Development Command - Soldier Center, Simulation and Training Technology Center, Orlando, FL, USA
| | - Suvranu De
- Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
- Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA
- Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA
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Lin CY, Sugerman GP, Kakaletsis S, Meador WD, Buganza AT, Rausch MK. Sex- and age-dependent skin mechanics-A detailed look in mice. Acta Biomater 2024; 175:106-113. [PMID: 38042263 DOI: 10.1016/j.actbio.2023.11.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Revised: 10/28/2023] [Accepted: 11/21/2023] [Indexed: 12/04/2023]
Abstract
Skin aging is of immense societal and, thus, scientific interest. Because mechanics play a critical role in skin's function, a plethora of studies have investigated age-induced changes in skin mechanics. Nonetheless, much remains to be learned about the mechanics of aging skin. This is especially true when considering sex as a biological variable. In our work, we set out to answer some of these questions using mice as a model system. Specifically, we combined mechanical testing, histology, collagen assays, and two-photon microscopy to identify age- and sex-dependent changes in skin mechanics and to relate them to structural, microstructural, and compositional factors. Our work revealed that skin stiffness, thickness, and collagen content all decreased with age and were sex dependent. Interestingly, sex differences in stiffness were age induced. We hope our findings not only further our fundamental understanding of skin aging but also highlight both age and sex as important variables when conducting studies on skin mechanics. STATEMENT OF SIGNIFICANCE: Our work addresses the question, "How do sex and age affect the mechanics of skin?" Answering this question is of both scientific and societal importance. We do so in mice as a model system. Thereby, we hope to add clarity to a body of literature that appears divided on the effect of both factors. Our findings have important implications for those studying age and sex differences, especially in mice as a model system.
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Affiliation(s)
- Chien-Yu Lin
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA
| | - Gabriella P Sugerman
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA
| | - Sotirios Kakaletsis
- Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, Austin, TX, USA
| | - William D Meador
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA
| | - Adrian T Buganza
- Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
| | - Manuel K Rausch
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA; Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, Austin, TX, USA; Oden Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX, USA.
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Lin CY, Sugerman GP, Kakaletsis S, Meador WD, Buganza AT, Rausch MK. Sex- and Age-dependent Skin Mechanics - A Detailed Look in Mice. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.03.08.531781. [PMID: 36945509 PMCID: PMC10028869 DOI: 10.1101/2023.03.08.531781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2023]
Abstract
Skin aging is of immense societal and, thus, scientific interest. Because mechanics play a critical role in skin's function, a plethora of studies have investigated age-induced changes in skin mechanics. Nonetheless, much remains to be learned about the mechanics of aging skin. This is especially true when considering sex as a biological variable. In our work, we set out to answer some of these questions using mice as a model system. Specifically, we combined mechanical testing, histology, collagen assays, and two-photon microscopy to identify age- and sex-dependent changes in skin mechanics and to relate them to structural, microstructural, and compositional factors. Our work revealed that skin stiffness, thickness, and collagen content all decreased with age and were sex dependent. Interestingly, sex differences in stiffness were age induced. We hope our findings not only further our fundamental understanding of skin aging but also highlight both age and sex as important variables when conducting studies on skin mechanics.
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Affiliation(s)
- Chien-Yu Lin
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, USA
| | - Gabriella P Sugerman
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, USA
| | - Sotirios Kakaletsis
- Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, Austin, Texas, USA
| | - William D Meador
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, USA
| | - Adrian T Buganza
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA
| | - Manuel K Rausch
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, USA
- Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, Austin, Texas, USA
- Oden Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, Texas, USA
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Biaxial mechanical properties of the bronchial tree: Characterization of elasticity, extensibility, and energetics, including the effect of strain rate and preconditioning. Acta Biomater 2023; 155:410-422. [PMID: 36328122 DOI: 10.1016/j.actbio.2022.10.047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 10/18/2022] [Accepted: 10/21/2022] [Indexed: 11/05/2022]
Abstract
Distal airways commonly obstruct in lung disease and despite their importance, their mechanical properties are vastly underexplored. The lack of bronchial experiments restricts current airway models to either assume rigid structures, or extrapolate the material properties of the trachea to represent the small airways. Furthermore, past works are exclusively limited to uniaxial testing; investigating the multidirectional tensile loads of both the proximal and distal pulmonary airways is long overdue. Here we present comprehensive mechanical and viscoelastic properties of the porcine airway tree, including the trachea, trachealis muscle, large bronchi, and small bronchi, via measures of elasticity, extensibility, and energetics to explore regional and directional dependencies, cross-examining strain rate and preconditioning effects using planar equibiaxial tensile tests for the first time. We find bronchial regions are notably heterogeneous, where the trachea exhibits greater stiffness, energy loss, and preconditioning sensitivity than the smaller airways. Interestingly, the trachealis muscle is similar to the distal bronchi, despite being anatomically located adjacent to the proximal ring. Tissues are anisotropic and axially stiffer under initial loading, losing more energy with greater stress relaxation circumferentially. Strain rate dependency is also noted, where tissues are more energetically efficient at the faster strain rate, likely attributable to the microstructure. Findings highlight assumptions of homogeneity and isotropy are inadequate, and enable the improvement of aerosol flow and dynamic airway deformation computational predictive models. These results provide much needed fundamental material properties for future explorations contrasting healthy versus diseased pulmonary airway mechanics to better understand the relationship between structure and lung function. STATEMENT OF SIGNIFICANCE: We present comprehensive multiaxial mechanical tensile experiments of the proximal and distal airways via measures of maximum stress, initial and ultimate moduli, strain and stress transitions, hysteresis, energy loss, and stress relaxation, and further assess preconditioning and strain rate dependencies to examine the relationship between lung function and structure. The mechanical response of the bronchial tree demonstrates significant anisotropy and heterogeneity, even within the tracheal ring, and emphasizes that contrary to past studies, the behavior of the proximal airways cannot be extended to distal bronchial tree analyses. Establishing these material properties is critical to advancing our understanding of airway function and in developing accurate computational simulations to help diagnose and monitor pulmonary diseases.
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