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Campos T, Araújo R, Xavier J, Nguyễn Q, Dourado N, Morais J, Pereira F. Identification of Apple Fruit-Skin Constitutive Laws by Full-Field Methods Using Uniaxial Tensile Loading. MATERIALS (BASEL, SWITZERLAND) 2024; 17:700. [PMID: 38591566 PMCID: PMC10856416 DOI: 10.3390/ma17030700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2023] [Revised: 01/25/2024] [Accepted: 01/26/2024] [Indexed: 04/10/2024]
Abstract
The protective and preservative role of apple skin in maintaining the integrity of the fruit is well-known, with its mechanical behaviour playing a pivotal role in determining fruit storage capacity. This study employs a combination of experimental and numerical methodologies, specifically utilising the digital image correlation (DIC) technique. A specially devised inverse strategy is applied to evaluate the mechanical behaviour of apple skin under uniaxial tensile loading. Three apple cultivars were tested in this work: Malus domestica Starking Delicious, Malus pumila Rennet, and Malus domestica Golden Delicious. Stress-strain curves were reconstructed, revealing distinct variations in the mechanical responses among these cultivars. Yeoh's hyperelastic model was fitted to the experimental data to identify the coefficients capable of reproducing the non-linear deformation. The results suggest that apple skin varies significantly in composition and structure among the tested cultivars, as evidenced by differences in elastic properties and non-linear behaviour. These differences can significantly affect how fruit is handled, stored, and transported. Thus, the insights resulting from this research enable the development of mathematical models based on the mechanical behaviour of apple tissue, constituting important data for improvements in the economics of the agri-food industry.
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Affiliation(s)
- Teresa Campos
- CMEMS-UMINHO, Universidade do Minho, 4800-058 Guimarães, Portugal (N.D.)
- LABBELS–Associate Laboratory, 4800-058 Guimarães, Portugal
| | - Rafael Araújo
- CITAB/UTAD, Departamento de Engenharias, Quinta de Prados, 5001-801 Vila Real, Portugal (J.M.); (F.P.)
| | - José Xavier
- UNIDEMI, Department of Mechanical and Industrial Engineering, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal
- LASI, Intelligent Systems Associate Laboratory, 4800-058 Guimarães, Portugal
| | - Quyền Nguyễn
- 2C2T-Centro de Ciência e Tecnologia Têxtil, Universidade do Minho, 4800-058 Guimarães, Portugal
| | - Nuno Dourado
- CMEMS-UMINHO, Universidade do Minho, 4800-058 Guimarães, Portugal (N.D.)
- LABBELS–Associate Laboratory, 4800-058 Guimarães, Portugal
| | - José Morais
- CITAB/UTAD, Departamento de Engenharias, Quinta de Prados, 5001-801 Vila Real, Portugal (J.M.); (F.P.)
| | - Fábio Pereira
- CITAB/UTAD, Departamento de Engenharias, Quinta de Prados, 5001-801 Vila Real, Portugal (J.M.); (F.P.)
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2
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Weissmann J, Charles CJ, Richards AM, Yap CH, Marom G. Material property alterations for phenotypes of heart failure with preserved ejection fraction: A numerical study of subject-specific porcine models. Front Bioeng Biotechnol 2022; 10:1032034. [PMID: 36312535 PMCID: PMC9614036 DOI: 10.3389/fbioe.2022.1032034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 09/26/2022] [Indexed: 11/19/2022] Open
Abstract
A substantial proportion of heart failure patients have a preserved left ventricular (LV) ejection fraction (HFpEF). This condition carries a high burden of morbidity and mortality and has limited therapeutic options. left ventricular pressure overload leads to an increase in myocardial collagen content, causing left ventricular stiffening that contributes to the development of heart failure patients have a preserved left ventricular ejection fraction. Although several heart failure patients have a preserved left ventricular ejection fraction models have been developed in recent years to aid the investigation of mechanical alterations, none has investigated different phenotypes of the disease and evaluated the alterations in material properties. In this study, two similar healthy swine were subjected to progressive and prolonged pressure overload to induce diastolic heart failure characteristics, providing a preclinical model of heart failure patients have a preserved left ventricular ejection fraction. Cardiac magnetic resonance imaging (cMRI) scans and intracardiac pressures were recorded before and after induction. In both healthy and disease states, a corresponding finite element (FE) cardiac model was developed via mesh morphing of the Living Heart Porcine model. The material properties were derived by calibrating to its passive and active behavior. The change in the passive behavior was predominantly isotropic when comparing the geometries before and after induction. Myocardial thickening allowed for a steady transition in the passive properties while maintaining tissue incompressibility. This study highlights the importance of hypertrophy as an initial compensatory response and might also pave the way for assessing disease severity.
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Affiliation(s)
- Jonathan Weissmann
- Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Christopher J. Charles
- Department of Surgery, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
- Cardiovascular Research Institute, National University of Singapore, Singapore, Singapore
- Christchurch Heart Institute, Department of Medicine, University of Otago, Christchurch, New Zealand
| | - A. Mark Richards
- Cardiovascular Research Institute, National University of Singapore, Singapore, Singapore
- Christchurch Heart Institute, Department of Medicine, University of Otago, Christchurch, New Zealand
| | - Choon Hwai Yap
- Department of Bioengineering, Imperial College London, London, United Kingdom
| | - Gil Marom
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel
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3
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Marx L, Niestrawska JA, Gsell MA, Caforio F, Plank G, Augustin CM. Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration. JOURNAL OF COMPUTATIONAL PHYSICS 2022; 463:111266. [PMID: 35662800 PMCID: PMC7612790 DOI: 10.1016/j.jcp.2022.111266] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.
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Affiliation(s)
- Laura Marx
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
| | - Justyna A. Niestrawska
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
| | - Matthias A.F. Gsell
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
| | - Federica Caforio
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria
| | - Gernot Plank
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
| | - Christoph M. Augustin
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Biophysics, Medical University of Graz, Graz, Austria
- BioTechMed-Graz, Graz, Austria
- Corresponding author at: Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Neue Stiftingtalstrasse 6/D04, 8010 Graz, Austria. (C.M.Augustin)
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Xu J, Wong TC, Simon MA, Brigham JC. A clinically applicable strategy to estimate the in vivo distribution of mechanical material properties of the right ventricular wall. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3548. [PMID: 34724355 DOI: 10.1002/cnm.3548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 10/27/2021] [Indexed: 06/13/2023]
Abstract
A clinically applicable approach to estimate the in vivo mechanical material properties of the heart wall is presented. This optimization-based inverse estimation approach applies a shape-based objective functional combined with rigid body registration and incremental parameterization of heterogeneity to use standard clinical imaging data along with simplified representations of cardiac function to provide consistent and physically meaningful solution estimates. The capability of the inverse estimation algorithm is evaluated through application to two clinically obtained human datasets to estimate the passive elastic mechanical properties of the heart wall, with an emphasis on the right ventricle. One dataset corresponded to a subject with normal heart function, while the other corresponded to a subject with severe pulmonary hypertension, and therefore expected to have a substantially stiffer right ventricle. Patient-specific pressure-driven bi-ventricle finite element analysis was used as the forward model and the endocardial surface of the right ventricle was used as the target data for the inverse problem. By using the right ventricle alone as the target of the inverse problem the relative sensitivity of the objective function to the right ventricle properties is increased. The method was able to identify material properties to accurately match the corresponding shape of the simplified forward model to the clinically obtained target data, and the properties obtained for the example cases are consistent with the clinical expectation for the right ventricle. Additionally, the material property estimates indicate significant heterogeneity in the heart wall for both subjects, and more so for the subject with pulmonary hypertension.
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Affiliation(s)
- Jing Xu
- Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA
| | - Timothy C Wong
- UPMC Cardiovascular Magnetic Resonance Center, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, USA
| | - Marc A Simon
- Department of Medicine, Division of Cardiology, University of California, San Francisco, California, USA
| | - John C Brigham
- Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA
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5
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Cai L, Ren L, Wang Y, Xie W, Zhu G, Gao H. Surrogate models based on machine learning methods for parameter estimation of left ventricular myocardium. ROYAL SOCIETY OPEN SCIENCE 2021; 8:201121. [PMID: 33614068 PMCID: PMC7890479 DOI: 10.1098/rsos.201121] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 12/15/2020] [Indexed: 05/12/2023]
Abstract
A long-standing problem at the frontier of biomechanical studies is to develop fast methods capable of estimating material properties from clinical data. In this paper, we have studied three surrogate models based on machine learning (ML) methods for fast parameter estimation of left ventricular (LV) myocardium. We use three ML methods named K-nearest neighbour (KNN), XGBoost and multi-layer perceptron (MLP) to emulate the relationships between pressure and volume strains during the diastolic filling. Firstly, to train the surrogate models, a forward finite-element simulator of LV diastolic filling is used. Then the training data are projected in a low-dimensional parametrized space. Next, three ML models are trained to learn the relationships of pressure-volume and pressure-strain. Finally, an inverse parameter estimation problem is formulated by using those trained surrogate models. Our results show that the three ML models can learn the relationships of pressure-volume and pressure-strain very well, and the parameter inference using the surrogate models can be carried out in minutes. Estimated parameters from both the XGBoost and MLP models have much less uncertainties compared with the KNN model. Our results further suggest that the XGBoost model is better for predicting the LV diastolic dynamics and estimating passive parameters than other two surrogate models. Further studies are warranted to investigate how XGBoost can be used for emulating cardiac pump function in a multi-physics and multi-scale framework.
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Affiliation(s)
- Li Cai
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Lei Ren
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Yongheng Wang
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Wenxian Xie
- Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an 710129, China
- NPU-UoG International Cooperative Lab for Computation and Application in Cardiology, Northwestern Polytechnical University, Xi’an 710129, China
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
| | - Guangyu Zhu
- School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
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6
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Ficarella E, Lamberti L, Degertekin SO. Mechanical Identification of Materials and Structures with Optical Methods and Metaheuristic Optimization. MATERIALS (BASEL, SWITZERLAND) 2019; 12:ma12132133. [PMID: 31269761 PMCID: PMC6651162 DOI: 10.3390/ma12132133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/27/2019] [Revised: 06/22/2019] [Accepted: 06/24/2019] [Indexed: 06/09/2023]
Abstract
This study presents a hybrid framework for mechanical identification of materials and structures. The inverse problem is solved by combining experimental measurements performed by optical methods and non-linear optimization using metaheuristic algorithms. In particular, we develop three advanced formulations of Simulated Annealing (SA), Harmony Search (HS) and Big Bang-Big Crunch (BBBC) including enhanced approximate line search and computationally cheap gradient evaluation strategies. The rationale behind the new algorithms-denoted as Hybrid Fast Simulated Annealing (HFSA), Hybrid Fast Harmony Search (HFHS) and Hybrid Fast Big Bang-Big Crunch (HFBBBC)-is to generate high quality trial designs lying on a properly selected set of descent directions. Besides hybridizing SA/HS/BBBC metaheuristic search engines with gradient information and approximate line search, HS and BBBC are also hybridized with an enhanced 1-D probabilistic search derived from SA. The results obtained in three inverse problems regarding composite and transversely isotropic hyperelastic materials/structures with up to 17 unknown properties clearly demonstrate the validity of the proposed approach, which allows to significantly reduce the number of structural analyses with respect to previous SA/HS/BBBC formulations and improves robustness of metaheuristic search engines.
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Affiliation(s)
- Elisa Ficarella
- Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70126 Bari, Italy
| | - Luciano Lamberti
- Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70126 Bari, Italy.
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7
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Finsberg H, Xi C, Tan JL, Zhong L, Genet M, Sundnes J, Lee LC, Wall ST. Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2982. [PMID: 29521015 PMCID: PMC6043386 DOI: 10.1002/cnm.2982] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Revised: 02/16/2018] [Accepted: 03/03/2018] [Indexed: 05/26/2023]
Abstract
Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes.
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Affiliation(s)
- Henrik Finsberg
- Simula Research Laboratory1325LysakerNorway
- Center for Cardiological InnovationSongsvannsveien 90372OsloNorway
- Department of InformaticsUniversity of OsloP.O. Box 1080, Blindern0316 OsloNorway
| | - Ce Xi
- Department of Mechanical EngineeringMichigan State University220 Trowbridge RdEast Lansing48824MIUSA
| | - Ju Le Tan
- National Heart Center Singapore5 Hospital DrSingapore
| | - Liang Zhong
- National Heart Center Singapore5 Hospital DrSingapore
- Duke National University of Singapore8 College RoadSingapore
| | - Martin Genet
- Mechanics Department and Solid Mechanics LaboratoryÉcole Polytechnique (CNRS, Paris‐Saclay University)Route de Saclay91128PalaiseauFrance
- M3DISIM research teamINRIA (Paris‐Saclay University)91120PalaiseauFrance
| | - Joakim Sundnes
- Simula Research Laboratory1325LysakerNorway
- Center for Cardiological InnovationSongsvannsveien 90372OsloNorway
- Department of InformaticsUniversity of OsloP.O. Box 1080, Blindern0316 OsloNorway
| | - Lik Chuan Lee
- Department of Mechanical EngineeringMichigan State University220 Trowbridge RdEast Lansing48824MIUSA
| | - Samuel T. Wall
- Simula Research Laboratory1325LysakerNorway
- Center for Cardiological InnovationSongsvannsveien 90372OsloNorway
- Department of Mathematical Science and TechnologyNorwegian University of Life SciencesUniversitetstunet 3 1430 ÅsNorway
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8
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Abstract
Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments. Graphical abstract.
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9
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In vivo estimation of passive biomechanical properties of human myocardium. Med Biol Eng Comput 2018; 56:1615-1631. [PMID: 29479659 PMCID: PMC6096751 DOI: 10.1007/s11517-017-1768-x] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Accepted: 12/13/2017] [Indexed: 11/24/2022]
Abstract
Identification of in vivo passive biomechanical properties of healthy human myocardium from regular clinical data is essential for subject-specific modelling of left ventricle (LV). In this work, myocardium was defined by Holzapfel-Ogden constitutive law. Therefore, the objectives of the study were (a) to estimate the ranges of the constitutive parameters for healthy human myocardium using non-invasive routine clinical data, and (b) to investigate the effect of geometry, LV end-diastolic pressure (EDP) and fibre orientations on estimated values. In order to avoid invasive measurements and additional scans, LV cavity volume, measured from routine MRI, and empirical pressure-normalised-volume relation (Klotz-curve) were used as clinical data. Finite element modelling, response surface method and genetic algorithm were used to inversely estimate the constitutive parameters. Due to the ill-posed nature of the inverse optimisation problem, the myocardial properties was extracted by identifying the ranges of the parameters, instead of finding unique values. Additional sensitivity studies were carried out to identify the effect of LV EDP, fibre orientation and geometry on estimated parameters. Although uniqueness of the solution cannot be achieved, the normal ranges of the parameters produced similar mechanical responses within the physiological ranges. These information could be used in future computational studies for designing heart failure treatments. Graphical abstract ![]()
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10
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Nasopoulou A, Shetty A, Lee J, Nordsletten D, Rinaldi CA, Lamata P, Niederer S. Improved identifiability of myocardial material parameters by an energy-based cost function. Biomech Model Mechanobiol 2017. [PMID: 28188386 DOI: 10.1007/s10237‐016‐0865‐3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.
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Affiliation(s)
- Anastasia Nasopoulou
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - Anoop Shetty
- Cardiovascular Department, Guy's and St. Thomas' NHS Foundation Trust, London, UK
| | - Jack Lee
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - David Nordsletten
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - C Aldo Rinaldi
- Cardiovascular Department, Guy's and St. Thomas' NHS Foundation Trust, London, UK
| | - Pablo Lamata
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
| | - Steven Niederer
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
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11
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Nasopoulou A, Shetty A, Lee J, Nordsletten D, Rinaldi CA, Lamata P, Niederer S. Improved identifiability of myocardial material parameters by an energy-based cost function. Biomech Model Mechanobiol 2017; 16:971-988. [PMID: 28188386 PMCID: PMC5480093 DOI: 10.1007/s10237-016-0865-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2016] [Accepted: 12/09/2016] [Indexed: 12/16/2022]
Abstract
Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the HF cases and [Formula: see text] and [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]) for the healthy case.
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Affiliation(s)
- Anastasia Nasopoulou
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - Anoop Shetty
- Cardiovascular Department, Guy's and St. Thomas' NHS Foundation Trust, London, UK
| | - Jack Lee
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - David Nordsletten
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK
| | - C Aldo Rinaldi
- Cardiovascular Department, Guy's and St. Thomas' NHS Foundation Trust, London, UK
| | - Pablo Lamata
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
| | - Steven Niederer
- Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical Engineering, King's College London, London, UK.
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12
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Nikou A, Dorsey SM, McGarvey JR, Gorman JH, Burdick JA, Pilla JJ, Gorman RC, Wenk JF. Computational Modeling of Healthy Myocardium in Diastole. Ann Biomed Eng 2016; 44:980-92. [PMID: 26215308 PMCID: PMC4731326 DOI: 10.1007/s10439-015-1403-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2015] [Accepted: 07/18/2015] [Indexed: 11/28/2022]
Abstract
In order to better understand the mechanics of the heart and its disorders, engineers increasingly make use of the finite element method (FEM) to investigate healthy and diseased cardiac tissue. However, FEM is only as good as the underlying constitutive model, which remains a major challenge to the biomechanics community. In this study, a recently developed structurally based constitutive model was implemented to model healthy left ventricular myocardium during passive diastolic filling. This model takes into account the orthotropic response of the heart under loading. In-vivo strains were measured from magnetic resonance images (MRI) of porcine hearts, along with synchronous catheterization pressure data, and used for parameter identification of the passive constitutive model. Optimization was performed by minimizing the difference between MRI measured and FE predicted strains and cavity volumes. A similar approach was followed for the parameter identification of a widely used phenomenological constitutive law, which is based on a transversely isotropic material response. Results indicate that the parameter identification with the structurally based constitutive law is more sensitive to the assigned fiber architecture and the fit between the measured and predicted strains is improved with more realistic sheet angles. In addition, the structurally based model is capable of generating a more physiological end-diastolic pressure-volume relationship in the ventricle.
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Affiliation(s)
- Amir Nikou
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY, 40506-0503, USA
| | - Shauna M Dorsey
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA
| | - Jeremy R McGarvey
- Gorman Cardiovascular Research Group and Department of Surgery, University of Pennsylvania, Philadelphia, PA, USA
| | - Joseph H Gorman
- Gorman Cardiovascular Research Group and Department of Surgery, University of Pennsylvania, Philadelphia, PA, USA
| | - Jason A Burdick
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA
| | - James J Pilla
- Gorman Cardiovascular Research Group and Department of Surgery, University of Pennsylvania, Philadelphia, PA, USA
- Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA
| | - Robert C Gorman
- Gorman Cardiovascular Research Group and Department of Surgery, University of Pennsylvania, Philadelphia, PA, USA
| | - Jonathan F Wenk
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY, 40506-0503, USA.
- Department of Surgery, University of Kentucky, Lexington, KY, USA.
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13
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Lago MA, Rúperez MJ, Martínez-Martínez F, Martínez-Sanchis S, Bakic PR, Monserrat C. Methodology based on genetic heuristics for in-vivo characterizing the patient-specific biomechanical behavior of the breast tissues. EXPERT SYSTEMS WITH APPLICATIONS 2015; 42:7942-7950. [PMID: 27103760 PMCID: PMC4834716 DOI: 10.1016/j.eswa.2015.05.058] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper presents a novel methodology to in-vivo estimate the elastic constants of a constitutive model proposed to characterize the mechanical behavior of the breast tissues. An iterative search algorithm based on genetic heuristics was constructed to in-vivo estimate these parameters using only medical images, thus avoiding invasive measurements of the mechanical response of the breast tissues. For the first time, a combination of overlap and distance coefficients were used for the evaluation of the similarity between a deformed MRI of the breast and a simulation of that deformation. The methodology was validated using breast software phantoms for virtual clinical trials, compressed to mimic MRI-guided biopsies. The biomechanical model chosen to characterize the breast tissues was an anisotropic neo-Hookean hyperelastic model. Results from this analysis showed that the algorithm is able to find the elastic constants of the constitutive equations of the proposed model with a mean relative error of about 10%. Furthermore, the overlap between the reference deformation and the simulated deformation was of around 95% showing the good performance of the proposed methodology. This methodology can be easily extended to characterize the real biomechanical behavior of the breast tissues, which means a great novelty in the field of the simulation of the breast behavior for applications such as surgical planing, surgical guidance or cancer diagnosis. This reveals the impact and relevance of the presented work.
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Affiliation(s)
- M. A. Lago
- LabHuman, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain
| | - M. J. Rúperez
- Departamento de Ingeniería Mecánica Y Construcción, Universitat Jaume I, Av. de Vicent Sos Baynat, s/n 12071 Castelló de la Plana, Spain
| | - F. Martínez-Martínez
- LabHuman, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain
| | - S. Martínez-Sanchis
- LabHuman, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain
| | - P. R. Bakic
- Department of Radiology, University of Pennsylvania, 1 Silverstein Building, 3400 Spruce Street, Philadelphia, PA 19104, USA
| | - C. Monserrat
- LabHuman, Universitat Politècnica de València, Camino de Vera s/n, 46022, Valencia, Spain
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14
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Gao H, Li WG, Cai L, Berry C, Luo XY. Parameter estimation in a Holzapfel-Ogden law for healthy myocardium. JOURNAL OF ENGINEERING MATHEMATICS 2015; 95:231-248. [PMID: 26663931 PMCID: PMC4662962 DOI: 10.1007/s10665-014-9740-3] [Citation(s) in RCA: 59] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2014] [Accepted: 08/10/2014] [Indexed: 05/26/2023]
Abstract
A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is to estimate material properties from in vivo clinical measurements. In this work we evaluate the passive myocardial mechanical properties inversely from the in vivo LV chamber pressure-volume and strain data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law with eight parameters. In the first part of the paper we demonstrate how to use a multi-step non-linear least-squares optimization procedure to inversely estimate the parameters from the pressure-volume and strain data obtained from a synthetic LV model in diastole. In the second part, we show that to apply this procedure to clinical situations with limited in vivo data, additional constraints are required in the optimization procedure. Our study, based on three different healthy volunteers, demonstrates that the parameters of the Holzapfel-Ogden law could be extracted from pressure-volume and strain data with a suitable multi-step optimization procedure. Although the uniqueness of the solution cannot be addressed using our approaches, the material response is shown to be robustly determined.
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Affiliation(s)
- H. Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - W. G. Li
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - L. Cai
- School of Science, Northwestern Polytechnical University Xi’an, Xi’an, 710072 Shaanxi People’s Republic of China
| | - C. Berry
- Institute of Cardiovascular and Medical Sciences, University of Glasgow, Glasgow, UK
| | - X. Y. Luo
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
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15
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Estimating passive mechanical properties in a myocardial infarction using MRI and finite element simulations. Biomech Model Mechanobiol 2014. [PMID: 25315521 DOI: 10.1007/s10237‐014‐0627‐z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/29/2022]
Abstract
Myocardial infarction (MI) triggers a series of maladaptive events that lead to structural and functional changes in the left ventricle. It is crucial to better understand the progression of adverse remodeling, in order to develop effective treatment. In addition, being able to assess changes in vivo would be a powerful tool in the clinic. The goal of the current study is to quantify the in vivo material properties of infarcted and remote myocardium 1 week after MI, as well as the orientation of collagen fibers in the infarct. This will be accomplished by using a combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numerical optimization to analyze a porcine model ([Formula: see text]) of posterolateral myocardial infarction. Specifically, properties will be determined by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. The results indicate that the infarct region is stiffer than the remote region and that the infarct collagen fibers become more circumferentially oriented 1 week post-MI. These findings are consistent with previous studies, which employed ex vivo techniques. The proposed methodology will ultimately provide a means of predicting remote and infarct mechanical properties in vivo at any time point post-MI.
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16
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Estimating passive mechanical properties in a myocardial infarction using MRI and finite element simulations. Biomech Model Mechanobiol 2014; 14:633-47. [PMID: 25315521 DOI: 10.1007/s10237-014-0627-z] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2014] [Accepted: 10/06/2014] [Indexed: 10/24/2022]
Abstract
Myocardial infarction (MI) triggers a series of maladaptive events that lead to structural and functional changes in the left ventricle. It is crucial to better understand the progression of adverse remodeling, in order to develop effective treatment. In addition, being able to assess changes in vivo would be a powerful tool in the clinic. The goal of the current study is to quantify the in vivo material properties of infarcted and remote myocardium 1 week after MI, as well as the orientation of collagen fibers in the infarct. This will be accomplished by using a combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numerical optimization to analyze a porcine model ([Formula: see text]) of posterolateral myocardial infarction. Specifically, properties will be determined by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. The results indicate that the infarct region is stiffer than the remote region and that the infarct collagen fibers become more circumferentially oriented 1 week post-MI. These findings are consistent with previous studies, which employed ex vivo techniques. The proposed methodology will ultimately provide a means of predicting remote and infarct mechanical properties in vivo at any time point post-MI.
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17
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Sun K, Stander N, Jhun CS, Zhang Z, Suzuki T, Wang GY, Saeed M, Wallace AW, Tseng EE, Baker AJ, Saloner D, Einstein DR, Ratcliffe MB, Guccione JM. A computationally efficient formal optimization of regional myocardial contractility in a sheep with left ventricular aneurysm. J Biomech Eng 2010; 131:111001. [PMID: 20016753 DOI: 10.1115/1.3148464] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
A non-invasive method for estimating regional myocardial contractility in vivo would be of great value in the design and evaluation of new surgical and medical strategies to treat and/or prevent infarction-induced heart failure. As a first step towards developing such a method, an explicit finite element (FE) model-based formal optimization of regional myocardial contractility in a sheep with left ventricular (LV) aneurysm was performed using tagged magnetic resonance (MR) images and cardiac catheterization pressures. From the tagged MR images, 3-dimensional (3D) myocardial strains, LV volumes and geometry for the animal-specific 3D FE model of the LV were calculated, while the LV pressures provided physiological loading conditions. Active material parameters (T(max_B) and T(max_R)) in the non-infarcted myocardium adjacent to the aneurysm (borderzone) and in myocardium remote from the aneurysm were estimated by minimizing the errors between FE model-predicted and measured systolic strains and LV volumes using the successive response surface method for optimization. The significant depression in optimized T(max_B) relative to T(max_R) was confirmed by direct ex vivo force measurements from skinned fiber preparations. The optimized values of T(max_B) and T(max_R) were not overly sensitive to the passive material parameters specified. The computation time of less than 5 hours associated with our proposed method for estimating regional myocardial contractility in vivo makes it a potentially very useful clinical tool.
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Affiliation(s)
- Kay Sun
- Department of Surgery, University of California, San Francisco, USA
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18
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Bischoff JE, Drexler ES, Slifka AJ, McCowan CN. Quantifying nonlinear anisotropic elastic material properties of biological tissue by use of membrane inflation. Comput Methods Biomech Biomed Engin 2009; 12:353-69. [DOI: 10.1080/10255840802609420] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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