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Hinrichsen J, Ferlay C, Reiter N, Budday S. Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue. Front Physiol 2024; 15:1321298. [PMID: 38322614 PMCID: PMC10844559 DOI: 10.3389/fphys.2024.1321298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 01/08/2024] [Indexed: 02/08/2024] Open
Abstract
Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the "most rewarding" training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.
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Affiliation(s)
- Jan Hinrichsen
- Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Carl Ferlay
- Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
- Ecole Polytechnique, Palaiseau, France
| | - Nina Reiter
- Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Silvia Budday
- Institute of Continuum Mechanics and Biomechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
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2
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Oddes Z, Solav D. Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation. J Mech Behav Biomed Mater 2023; 140:105708. [PMID: 36801779 DOI: 10.1016/j.jmbbm.2023.105708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 01/27/2023] [Accepted: 02/02/2023] [Indexed: 02/05/2023]
Abstract
Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter's force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).
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Affiliation(s)
- Zohar Oddes
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel
| | - Dana Solav
- Faculty of Mechanical Engineering, Technion Institute of Technology, Haifa, Israel.
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3
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Kakaletsis S, Lejeune E, Rausch MK. Can machine learning accelerate soft material parameter identification from complex mechanical test data? Biomech Model Mechanobiol 2023; 22:57-70. [PMID: 36229697 PMCID: PMC11048729 DOI: 10.1007/s10237-022-01631-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Accepted: 08/23/2022] [Indexed: 11/28/2022]
Abstract
Identifying the constitutive parameters of soft materials often requires heterogeneous mechanical test modes, such as simple shear. In turn, interpreting the resulting complex deformations necessitates the use of inverse strategies that iteratively call forward finite element solutions. In the past, we have found that the cost of repeatedly solving non-trivial boundary value problems can be prohibitively expensive. In this current work, we leverage our prior experimentally derived mechanical test data to explore an alternative approach. Specifically, we investigate whether a machine learning-based approach can accelerate the process of identifying material parameters based on our mechanical test data. Toward this end, we pursue two different strategies. In the first strategy, we replace the forward finite element simulations within an iterative optimization framework with a machine learning-based metamodel. Here, we explore both Gaussian process regression and neural network metamodels. In the second strategy, we forgo the iterative optimization framework and use a stand alone neural network to predict the entire material parameter set directly from experimental results. We first evaluate both approaches with simple shear experiments on blood clot, an isotropic, homogeneous material. Next, we evaluate both approaches against simple shear and uniaxial loading experiments on right ventricular myocardium, an anisotropic, heterogeneous material. We find that replacing the forward finite element simulations with metamodels significantly accelerates the parameter identification process with excellent results in the case of blood clot, and with satisfying results in the case of right ventricular myocardium. On the other hand, we find that replacing the entire optimization framework with a neural network yielded unsatisfying results, especially for right ventricular myocardium. Overall, the importance of our work stems from providing a baseline example showing how machine learning can accelerate the process of material parameter identification for soft materials from complex mechanical data, and from providing an open access experimental and simulation dataset that may serve as a benchmark dataset for others interested in applying machine learning techniques to soft tissue biomechanics.
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Affiliation(s)
- Sotirios Kakaletsis
- Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX, 78712, USA
| | - Emma Lejeune
- Department of Mechanical Engineering, Boston University, Boston, MA, 02215, USA
| | - Manuel K Rausch
- Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX, 78712, USA.
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4
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Pourmodheji R, Jiang Z, Tossas-Betancourt C, Figueroa CA, Baek S, Lee LC. Inverse modeling framework for characterizing patient-specific microstructural changes in the pulmonary arteries. J Mech Behav Biomed Mater 2021; 119:104448. [PMID: 33836475 DOI: 10.1016/j.jmbbm.2021.104448] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 02/18/2021] [Accepted: 03/02/2021] [Indexed: 10/21/2022]
Abstract
Microstructural changes in the pulmonary arteries associated with pulmonary arterial hypertension (PAH) is not well understood and characterized in humans. To address this issue, we developed and applied a patient-specific inverse finite element (FE) modeling framework to characterize mechanical and structural changes of the micro-constituents in the proximal pulmonary arteries using in-vivo pressure measurements and magnetic resonance images. The framework was applied using data acquired from a pediatric PAH patient and a heart transplant patient with normal pulmonary arterial pressure, which serves as control. Parameters of a constrained mixture model that are associated with the structure and mechanical properties of elastin, collagen fibers and smooth muscle cells were optimized to fit the patient-specific pressure-diameter responses of the main pulmonary artery. Based on the optimized parameters, individual stress and linearized stiffness resultants of the three tissue constituents, as well as their aggregated values, were estimated in the pulmonary artery. Aggregated stress resultant and stiffness are, respectively, 4.6 and 3.4 times higher in the PAH patient than the control subject. Stress and stiffness resultants of each tissue constituent are also higher in the PAH patient. Specifically, the mean stress resultant is highest in elastin (PAH: 69.96, control: 14.42 kPa-mm), followed by those in smooth muscle cell (PAH: 13.95, control: 4.016 kPa-mm) and collagen fibers (PAH: 13.19, control: 2.908 kPa-mm) in both the PAH patient and the control subject. This result implies that elastin may be the key load-bearing constituent in the pulmonary arteries of the PAH patient and the control subject.
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Affiliation(s)
- Reza Pourmodheji
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA.
| | - Zhenxiang Jiang
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | | | - C Alberto Figueroa
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA; Department of Surgery, University of Michigan, Ann Arbor, MI, USA
| | - Seungik Baek
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - Lik-Chuan Lee
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
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5
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Safa BN, Santare MH, Ethier CR, Elliott DM. Identifiability of tissue material parameters from uniaxial tests using multi-start optimization. Acta Biomater 2021; 123:197-207. [PMID: 33444797 PMCID: PMC8518191 DOI: 10.1016/j.actbio.2021.01.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 01/06/2021] [Accepted: 01/07/2021] [Indexed: 02/05/2023]
Abstract
Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.
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Affiliation(s)
- Babak N Safa
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology/Emory University, Atlanta, GA, USA; Department of Biomedical Engineering, University of Delaware, Newark, DE, USA; Department of Mechanical Engineering, University of Delaware, Newark, DE, USA.
| | - Michael H Santare
- Department of Biomedical Engineering, University of Delaware, Newark, DE, USA; Department of Mechanical Engineering, University of Delaware, Newark, DE, USA
| | - C Ross Ethier
- Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology/Emory University, Atlanta, GA, USA
| | - Dawn M Elliott
- Department of Biomedical Engineering, University of Delaware, Newark, DE, USA
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Mineroff J, McCulloch AD, Krummen D, Ganapathysubramanian B, Krishnamurthy A. Optimization Framework for Patient-Specific Cardiac Modeling. Cardiovasc Eng Technol 2019; 10:553-567. [PMID: 31531820 PMCID: PMC6868335 DOI: 10.1007/s13239-019-00428-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 08/05/2019] [Indexed: 01/18/2023]
Abstract
PURPOSE Patient-specific models of the heart can be used to improve the diagnosis of cardiac diseases, but practical application of these models can be impeded by the computational costs and numerical uncertainties of fitting mechanistic models to clinical measurements from individual patients. Reliable and efficient tuning of these models within clinically appropriate error bounds is a requirement for practical deployment in the time-constrained environment of the clinic. METHODS We developed an optimization framework to tune parameters of patient-specific mechanistic models using routinely-acquired non-invasive patient data more efficiently than manual methods. We employ a hybrid particle swarm and pattern search optimization algorithm, but the framework can be readily adapted to use other optimization algorithms. RESULTS We apply the proposed framework to tune full-cycle lumped parameter circulatory models using clinical data. We show that our framework can be easily adapted to optimize cross-species models by tuning the parameters of the same circulation model to four canine subjects. CONCLUSIONS This work will facilitate the use of biomechanics and circulatory cardiac models in both clinical and research environments by ameliorating the tedious process of manually fitting the parameters.
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Affiliation(s)
- Joshua Mineroff
- Department of Mechanical Engineering, Iowa State University, Ames, IA, USA
| | - Andrew D McCulloch
- Bioengineering and Medicine, University of California, San Diego, La Jolla, CA, USA
| | - David Krummen
- Department of Medicine (Cardiology), University of California, San Diego, La Jolla, CA, USA
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7
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Avazmohammadi R, Soares JS, Li DS, Raut SS, Gorman RC, Sacks MS. A Contemporary Look at Biomechanical Models of Myocardium. Annu Rev Biomed Eng 2019; 21:417-442. [PMID: 31167105 PMCID: PMC6626320 DOI: 10.1146/annurev-bioeng-062117-121129] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.
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Affiliation(s)
- Reza Avazmohammadi
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, and Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA;
| | - João S Soares
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, and Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA;
- Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA
| | - David S Li
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, and Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA;
| | - Samarth S Raut
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, and Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA;
| | - Robert C Gorman
- Gorman Cardiovascular Research Group, Smilow Center for Translational Research, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Michael S Sacks
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, and Department of Biomedical Engineering, University of Texas, Austin, Texas 78712, USA;
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8
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Tobajas R, Elduque D, Ibarz E, Javierre C, Canteli AF, Gracia L. Visco-Hyperelastic Model with Damage for Simulating Cyclic Thermoplastic Elastomers Behavior Applied to an Industrial Component. Polymers (Basel) 2018; 10:E668. [PMID: 30966702 PMCID: PMC6404139 DOI: 10.3390/polym10060668] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Revised: 05/31/2018] [Accepted: 06/13/2018] [Indexed: 11/17/2022] Open
Abstract
In this work a nonlinear phenomenological visco-hyperelastic model including damage consideration is developed to simulate the behavior of Santoprene 101-73 material. This type of elastomeric material is widely used in the automotive and aeronautic sectors, as it has multiple advantages. However, there are still challenges in properly analyzing the mechanical phenomena that these materials exhibit. To simulate this kind of material a lot of theories have been exposed, but none of them have been endorsed unanimously. In this paper, a new model is presented based on the literature, and on experimental data. The test samples were extracted from an air intake duct component of an automotive engine. Inelastic phenomena such as hyperelasticity, viscoelasticity and damage are considered singularly in this model, thus modifying and improving some relevant models found in the literature. Optimization algorithms were used to find out the model parameter values that lead to the best fit of the experimental curves from the tests. An adequate fitting was obtained for the experimental results of a cyclic uniaxial loading of Santoprene 101-73.
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Affiliation(s)
- Rafael Tobajas
- Department of Mechanical Engineering, University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain.
| | - Daniel Elduque
- i+aitiip, Department of Mechanical Engineering, University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain.
| | - Elena Ibarz
- i3A, Department of Mechanical Engineering, University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain.
| | - Carlos Javierre
- i+aitiip, Department of Mechanical Engineering, University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain.
| | - Alfonso F Canteli
- Department of Construction and Manufacturing Engineering, University of Oviedo, C/Pedro Puig Adam, 33203 Gijón, Spain.
| | - Luis Gracia
- i3A, Department of Mechanical Engineering, University of Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain.
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9
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Balaban G, Finsberg H, Funke S, Håland TF, Hopp E, Sundnes J, Wall S, Rognes ME. In vivo estimation of elastic heterogeneity in an infarcted human heart. Biomech Model Mechanobiol 2018; 17:1317-1329. [PMID: 29774440 PMCID: PMC6154126 DOI: 10.1007/s10237-018-1028-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2017] [Accepted: 05/05/2018] [Indexed: 11/26/2022]
Abstract
In myocardial infarction, muscle tissue of the heart is damaged as a result of ceased or severely impaired blood flow. Survivors have an increased risk of further complications, possibly leading to heart failure. Material properties play an important role in determining post-infarction outcome. Due to spatial variation in scarring, material properties can be expected to vary throughout the tissue of a heart after an infarction. In this study we propose a data assimilation technique that can efficiently estimate heterogeneous elastic material properties in a personalized model of cardiac mechanics. The proposed data assimilation is tested on a clinical dataset consisting of regional left ventricular strains and in vivo pressures during atrial systole from a human with a myocardial infarction. Good matches to regional strains are obtained, and simulated equi-biaxial tests are carried out to demonstrate regional heterogeneities in stress–strain relationships. A synthetic data test shows a good match of estimated versus ground truth material parameter fields in the presence of no to low levels of noise. This study is the first to apply adjoint-based data assimilation to the important problem of estimating cardiac elastic heterogeneities in 3-D from medical images.
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Affiliation(s)
- Gabriel Balaban
- Division of Imaging Sciences and Biomedical Engineering, King's College London, St. Thomas Hospital, London, UK.
| | - Henrik Finsberg
- Simula Research Laboratory, Oslo, Norway
- Department of Informatics, University of Oslo, Oslo, Norway
| | | | - Trine F Håland
- Department of Cardiology, Center for Cardiological, Oslo University Hospital, Rikhospitalet, Oslo, Norway
| | - Einar Hopp
- Department of Radiology and Nuclear Medicine, Oslo University Hospital, Rikshospitalet, Oslo, Norway
| | - Joakim Sundnes
- Simula Research Laboratory, Oslo, Norway
- Department of Informatics, University of Oslo, Oslo, Norway
| | - Samuel Wall
- Simula Research Laboratory, Oslo, Norway
- Department of Mathematical Science and Technology, Norwegian University of Life Sciences, Ås, Norway
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10
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Balaban G, Finsberg H, Odland HH, Rognes ME, Ross S, Sundnes J, Wall S. High-resolution data assimilation of cardiac mechanics applied to a dyssynchronous ventricle. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:e2863. [PMID: 28039961 DOI: 10.1002/cnm.2863] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Revised: 10/31/2016] [Accepted: 12/28/2016] [Indexed: 06/06/2023]
Abstract
Computational models of cardiac mechanics, personalized to a patient, offer access to mechanical information above and beyond direct medical imaging. Additionally, such models can be used to optimize and plan therapies in-silico, thereby reducing risks and improving patient outcome. Model personalization has traditionally been achieved by data assimilation, which is the tuning or optimization of model parameters to match patient observations. Current data assimilation procedures for cardiac mechanics are limited in their ability to efficiently handle high-dimensional parameters. This restricts parameter spatial resolution, and thereby the ability of a personalized model to account for heterogeneities that are often present in a diseased or injured heart. In this paper, we address this limitation by proposing an adjoint gradient-based data assimilation method that can efficiently handle high-dimensional parameters. We test this procedure on a synthetic data set and provide a clinical example with a dyssynchronous left ventricle with highly irregular motion. Our results show that the method efficiently handles a high-dimensional optimization parameter and produces an excellent agreement for personalized models to both synthetic and clinical data.
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Affiliation(s)
- Gabriel Balaban
- Simula Research Laboratory, P.O. Box 134 1325 Lysaker, Norway
- Department of Informatics, University of Oslo, P.O. Box 1080, Blindern 0316 Oslo, Norway
- Center for Cardiological Innovation, Songsvannsveien 9, 0372 Oslo, Norway
| | - Henrik Finsberg
- Simula Research Laboratory, P.O. Box 134 1325 Lysaker, Norway
- Department of Informatics, University of Oslo, P.O. Box 1080, Blindern 0316 Oslo, Norway
- Center for Cardiological Innovation, Songsvannsveien 9, 0372 Oslo, Norway
| | - Hans Henrik Odland
- Faculty of Medicine, University of Oslo, P.O. Box 1078 Blindern, 0316 Oslo, Norway
- Department of Pediatrics, Oslo University Hospital, PO Nydalen, Oslo, Norway
| | - Marie E Rognes
- Simula Research Laboratory, P.O. Box 134 1325 Lysaker, Norway
- Department of Mathematics, University of Oslo, P.O Box 1053, Blindern 0316 Oslo, Norway
| | - Stian Ross
- Faculty of Medicine, University of Oslo, P.O. Box 1078 Blindern, 0316 Oslo, Norway
- Center for Cardiological Innovation, Songsvannsveien 9, 0372 Oslo, Norway
| | - Joakim Sundnes
- Simula Research Laboratory, P.O. Box 134 1325 Lysaker, Norway
- Department of Informatics, University of Oslo, P.O. Box 1080, Blindern 0316 Oslo, Norway
- Center for Cardiological Innovation, Songsvannsveien 9, 0372 Oslo, Norway
| | - Samuel Wall
- Simula Research Laboratory, P.O. Box 134 1325 Lysaker, Norway
- Center for Cardiological Innovation, Songsvannsveien 9, 0372 Oslo, Norway
- Department of Mathematical Science and Technology, Norwegian University of Life Sciences, Universitetstunet 3 1430 Ås, Norway
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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. [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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12
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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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