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Latorre ÁT, Martínez MA, Peña E. Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods. Front Bioeng Biotechnol 2023; 11:1304278. [PMID: 38152285 PMCID: PMC10751321 DOI: 10.3389/fbioe.2023.1304278] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Accepted: 11/27/2023] [Indexed: 12/29/2023] Open
Abstract
Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R 2 of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.
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Affiliation(s)
- Álvaro T. Latorre
- Aragón Institute for Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
| | - Miguel A. Martínez
- Aragón Institute for Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain
| | - Estefanía Peña
- Aragón Institute for Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain
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Dong H, Liu M, Woodall J, Leshnower BG, Gleason RL. Effect of Nonlinear Hyperelastic Property of Arterial Tissues on the Pulse Wave Velocity Based on the Unified-Fiber-Distribution (UFD) Model. Ann Biomed Eng 2023; 51:2441-2452. [PMID: 37326947 DOI: 10.1007/s10439-023-03275-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Accepted: 06/01/2023] [Indexed: 06/17/2023]
Abstract
Pulse wave velocity (PWV) is a key, independent risk factor for future cardiovascular events. The Moens-Korteweg equation describes the relation between PWV and the stiffness of arterial tissue with an assumption of isotopic linear elastic property of the arterial wall. However, the arterial tissue exhibits highly nonlinear and anisotropic mechanical behaviors. There is a limited study regarding the effect of arterial nonlinear and anisotropic properties on the PWV. In this study, we investigated the impact of the arterial nonlinear hyperelastic properties on the PWV, based on our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers (embedded in the matrix of the tissue) as a unified distribution, which expects to be more physically consistent with the real fiber distribution than existing models that separate the fiber distribution into two/several fiber families. With the UFD model, we fitted the measured relation between the PWV and blood pressure which obtained a good accuracy. We also modeled the aging effect on the PWV based on observations that the stiffening of arterial tissue increases with aging, and the results agree well with experimental data. In addition, we did parameter studies on the dependence of the PWV on the arterial properties of fiber initial stiffness, fiber distribution, and matrix stiffness. The results indicate the PWV increases with increasing overall fiber component in the circumferential direction. The dependences of the PWV on the fiber initial stiffness, and matrix stiffness are not monotonic and change with different blood pressure. The results of this study could provide new insights into arterial property changes and disease information from the clinical measured PWV data.
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Affiliation(s)
- Hai Dong
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Minliang Liu
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Julia Woodall
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - Bradley G Leshnower
- Division of Cardiothoracic Surgery, Department of Surgery, Emory University School of Medicine, Atlanta, GA, USA
| | - Rudolph L Gleason
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA.
- The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 204, 387 Technology Circle, Atlanta, GA, 30313-2412, USA.
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Liang L, Liu M, Elefteriades J, Sun W. PyTorch-FEA: Autograd-enabled finite element analysis methods with applications for biomechanical analysis of human aorta. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 238:107616. [PMID: 37230048 PMCID: PMC10330852 DOI: 10.1016/j.cmpb.2023.107616] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 05/15/2023] [Accepted: 05/16/2023] [Indexed: 05/27/2023]
Abstract
BACKGROUND AND OBJECTIVES Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. METHODS In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. RESULTS We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs. CONCLUSIONS We have presented PyTorch-FEA, a new library of FEA code and methods, representing a new approach to develop FEA methods to forward and inverse problems in solid mechanics. PyTorch-FEA eases the development of new inverse methods and enables a natural integration of FEA and DNNs, which will have numerous potential applications.
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Affiliation(s)
- Liang Liang
- Department of Computer Science, University of Miami, Coral Gables, FL, United States.
| | - Minliang Liu
- Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA, United States
| | - John Elefteriades
- Aortic Institute, School of Medicine, Yale University, New Haven, CT, United States
| | - Wei Sun
- Sutra Medical Inc, Lake Forest, CA, United States
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Wang X, Carpenter HJ, Ghayesh MH, Kotousov A, Zander AC, Amabili M, Psaltis PJ. A review on the biomechanical behaviour of the aorta. J Mech Behav Biomed Mater 2023; 144:105922. [PMID: 37320894 DOI: 10.1016/j.jmbbm.2023.105922] [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: 03/06/2023] [Revised: 05/14/2023] [Accepted: 05/20/2023] [Indexed: 06/17/2023]
Abstract
Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.
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Affiliation(s)
- Xiaochen Wang
- School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia.
| | - Harry J Carpenter
- School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia
| | - Mergen H Ghayesh
- School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia.
| | - Andrei Kotousov
- School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia
| | - Anthony C Zander
- School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia
| | - Marco Amabili
- Department of Mechanical Engineering, McGill University, Montreal H3A 0C3, Canada
| | - Peter J Psaltis
- Adelaide Medical School, The University of Adelaide, Adelaide, South Australia 5005, Australia; Department of Cardiology, Central Adelaide Local Health Network, Adelaide, South Australia 5000, Australia; Vascular Research Centre, Heart Health Theme, South Australian Health & Medical Research Institute (SAHMRI), Adelaide, South Australia 5000, Australia
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Liang L, Liu M, Elefteriades J, Sun W. PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.03.27.533816. [PMID: 37034587 PMCID: PMC10081215 DOI: 10.1101/2023.03.27.533816] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Motivation Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. Methods In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. Results We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.
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Li Z, Luo T, Wang S, Jia H, Gong Q, Liu X, Sutcliffe MPF, Zhu H, Liu Q, Chen D, Xiong J, Teng Z. Mechanical and histological characteristics of aortic dissection tissues. Acta Biomater 2022; 146:284-294. [PMID: 35367380 DOI: 10.1016/j.actbio.2022.03.042] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Revised: 03/23/2022] [Accepted: 03/24/2022] [Indexed: 12/14/2022]
Abstract
AIMS This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations. METHODS Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C1, D1, and D2) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness. RESULTS The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C1 and D2, respectively, while the elastin and collagen waviness were negatively correlated with C1 and D2, respectively. Elastin dispersion was negatively correlated to D2. Multivariate analysis showed that D2 was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip. CONCLUSION Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function. STATEMENT OF SIGNIFICANCE Aortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.
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Peng C, Zou L, Hou K, Liu Y, Jiang X, Fu W, Yang Y, Bou-Said B, Wang S, Dong Z. Material parameter identification of the proximal and distal segments of the porcine thoracic aorta based on ECG-gated CT angiography. J Biomech 2022; 138:111106. [DOI: 10.1016/j.jbiomech.2022.111106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/28/2022] [Accepted: 04/26/2022] [Indexed: 11/16/2022]
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Bracamonte JH, Saunders SK, Wilson JS, Truong UT, Soares JS. Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications. APPLIED SCIENCES-BASEL 2022; 12:3954. [PMID: 36911244 PMCID: PMC10004130 DOI: 10.3390/app12083954] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.
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Affiliation(s)
- Johane H. Bracamonte
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
| | - Sarah K. Saunders
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
| | - John S. Wilson
- Department of Biomedical Engineering and Pauley Heart Center, Virginia Commonwealth University, Richmond, VA 23219, USA
| | - Uyen T. Truong
- Department of Pediatrics, School of Medicine, Children’s Hospital of Richmond at Virginia Commonwealth University, Richmond, VA 23219, USA
| | - Joao S. Soares
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
- Correspondence:
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Dong H, Liu M, Qin T, Liang L, Ziganshin B, Ellauzi H, Zafar M, Jang S, Elefteriades J, Sun W, Gleason RL. A novel computational growth framework for biological tissues: Application to growth of aortic root aneurysm repaired by the V-shape surgery. J Mech Behav Biomed Mater 2022; 127:105081. [DOI: 10.1016/j.jmbbm.2022.105081] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 12/28/2021] [Accepted: 01/08/2022] [Indexed: 01/15/2023]
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Liu M, Liang L, Ismail Y, Dong H, Lou X, Iannucci G, Chen EP, Leshnower BG, Elefteriades JA, Sun W. Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model. Comput Biol Med 2021; 137:104794. [PMID: 34482196 DOI: 10.1016/j.compbiomed.2021.104794] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Revised: 08/20/2021] [Accepted: 08/21/2021] [Indexed: 01/15/2023]
Abstract
Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.
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Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Liang Liang
- Department of Computer Science, University of Miami, Coral Gables, FL, USA
| | - Yasmeen Ismail
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Hai Dong
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Xiaoying Lou
- Emory University School of Medicine, Atlanta, GA, USA
| | - Glen Iannucci
- Emory University School of Medicine, Atlanta, GA, USA
| | - Edward P Chen
- Emory University School of Medicine, Atlanta, GA, USA
| | | | | | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.
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Finite element analysis of transcatheter aortic valve implantation: Insights on the modelling of self-expandable devices. J Mech Behav Biomed Mater 2021; 123:104772. [PMID: 34481297 DOI: 10.1016/j.jmbbm.2021.104772] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Revised: 07/29/2021] [Accepted: 08/08/2021] [Indexed: 01/24/2023]
Abstract
Computational simulations of Transcatheter Aortic Valve Implantation (TAVI) have reached a high level of complexity and accuracy for the prediction of possible implantation scenarios during the decision-making process. However, when focusing on the prosthetic device, currently different devices are available on the market which not only have different geometries, but also different material properties. The present work focuses on the calibration of Nitinol constitutive parameters of four self-expandable devices starting from experimental radial force tests on the prosthetic samples. Beside providing optimal material properties for each specific device, we also perform a patient-specific simulation, comparing the results obtained using both "literature" and calibrated parameters with the aim of investigating the impact of metallic frame parameters choice on simulation results.
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Bracamonte JH, Wilson JS, Soares JS. Assessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures From In Vivo DENSE Magnetic Resonance Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions. J Biomech Eng 2020; 142:121011. [PMID: 32632452 DOI: 10.1115/1.4047721] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Indexed: 11/08/2022]
Abstract
The establishment of in vivo, noninvasive patient-specific, and regionally resolved techniques to quantify aortic properties is key to improving clinical risk assessment and scientific understanding of vascular growth and remodeling. A promising and novel technique to reach this goal is an inverse finite element method (FEM) approach that utilizes magnetic resonance imaging (MRI)-derived displacement fields from displacement encoding with stimulated echoes (DENSE). Previous studies using DENSE MRI suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously during the cardiac cycle. We hypothesize that this heterogeneity is driven in healthy aortas by regional adventitial tethering and interaction with perivascular tissues, which can be modeled with elastic foundation boundary conditions (EFBCs) using a collection of radially oriented springs with varying stiffness with circumferential distribution. Nine healthy IAAs were modeled using previously acquired patient-specific imaging and displacement fields from steady-state free procession (SSFP) and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse FEM. In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived heterogeneous strain distribution. Estimated aortic wall properties were in reasonable agreement with previously reported experimental biaxial testing data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features, suggesting that EFBC could be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for clinical research and future incorporation into cardiovascular fluid-structure analyses.
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Affiliation(s)
- Johane H Bracamonte
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, 401 West Main Street, Richmond, VA 23284
| | - John S Wilson
- Department of Biomedical Engineering and Pauley Heart Center, Virginia Commonwealth University, 601 West Main Street, Richmond, VA 23284
| | - Joao S Soares
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, 401 West Main Street, Richmond, VA 23284
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Liu M, Liang L, Sun W. A generic physics-informed neural network-based constitutive model for soft biological tissues. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020; 372:113402. [PMID: 34012180 PMCID: PMC8130895 DOI: 10.1016/j.cma.2020.113402] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser-Ogden-Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R2 value of 0.9632 vs 0.9019, p=0.0053) and testing (R2 value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel-Gasser-Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.
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Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, United States of America
| | - Liang Liang
- Department of Computer Science, University of Miami, Coral Gables, FL, United States of America
| | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, United States of America
- Correspondence to: The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta GA 30313-2412, United States of America. (W. Sun)
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Liu M, Dong H, Lou X, Iannucci G, Chen EP, Leshnower BG, Sun W. A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues. J Biomech Eng 2020; 142:111002. [PMID: 32766773 DOI: 10.1115/1.4048029] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2020] [Indexed: 12/14/2022]
Abstract
Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.
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Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30313
| | - Hai Dong
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA 30313
| | - Xiaoying Lou
- Emory University School of Medicine, Atlanta, GA 30332
| | - Glen Iannucci
- Emory University School of Medicine, Atlanta, GA 30332
| | - Edward P Chen
- Emory University School of Medicine, Atlanta, GA 30332
| | | | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta, GA 30313
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15
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Cebull HL, Rayz VL, Goergen CJ. Recent Advances in Biomechanical Characterization of Thoracic Aortic Aneurysms. Front Cardiovasc Med 2020; 7:75. [PMID: 32478096 PMCID: PMC7235347 DOI: 10.3389/fcvm.2020.00075] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 04/14/2020] [Indexed: 12/18/2022] Open
Abstract
Thoracic aortic aneurysm (TAA) is a focal enlargement of the thoracic aorta, but the etiology of this disease is not fully understood. Previous work suggests that various genetic syndromes, congenital defects such as bicuspid aortic valve, hypertension, and age are associated with TAA formation. Though occurrence of TAAs is rare, they can be life-threatening when dissection or rupture occurs. Prevention of these adverse events often requires surgical intervention through full aortic root replacement or implantation of endovascular stent grafts. Currently, aneurysm diameters and expansion rates are used to determine if intervention is warranted. Unfortunately, this approach oversimplifies the complex aortopathy. Improving treatment of TAAs will likely require an increased understanding of the biological and biomechanical factors contributing to the disease. Past studies have substantially contributed to our knowledge of TAAs using various ex vivo, in vivo, and computational methods to biomechanically characterize the thoracic aorta. However, any singular approach typically focuses on only material properties of the aortic wall, intra-aneurysmal hemodynamics, or in vivo vessel dynamics, neglecting combinatorial factors that influence aneurysm development and progression. In this review, we briefly summarize the current understanding of TAA causes, treatment, and progression, before discussing recent advances in biomechanical studies of TAAs and possible future directions. We identify the need for comprehensive approaches that combine multiple characterization methods to study the mechanisms contributing to focal weakening and rupture. We hope this summary and analysis will inspire future studies leading to improved prediction of thoracic aneurysm progression and rupture, improving patient diagnoses and outcomes.
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Affiliation(s)
- Hannah L Cebull
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Vitaliy L Rayz
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States
| | - Craig J Goergen
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States.,Purdue Center for Cancer Research, Purdue University, West Lafayette, IN, United States
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16
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Liu M, Liang L, Sulejmani F, Lou X, Iannucci G, Chen E, Leshnower B, Sun W. Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans. Sci Rep 2019; 9:12983. [PMID: 31506507 PMCID: PMC6737100 DOI: 10.1038/s41598-019-49438-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Accepted: 08/24/2019] [Indexed: 12/15/2022] Open
Abstract
Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.
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Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Liang Liang
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.,Department of Computer Science, University of Miami, Coral Gables, FL, USA
| | - Fatiesa Sulejmani
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Xiaoying Lou
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.,Emory University School of Medicine, Atlanta, GA, USA
| | - Glen Iannucci
- Emory University School of Medicine, Atlanta, GA, USA
| | - Edward Chen
- Emory University School of Medicine, Atlanta, GA, USA
| | | | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.
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17
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Liu M, Liang L, Sun W. Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019; 347:201-217. [PMID: 31160830 PMCID: PMC6544444 DOI: 10.1016/j.cma.2018.12.030] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
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 are 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.
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Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
| | - Liang Liang
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
| | - Wei Sun
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
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