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Moulton MJ, Secomb TW. A fast computational model for circulatory dynamics: effects of left ventricle-aorta coupling. Biomech Model Mechanobiol 2023. [PMID: 36639560 DOI: 10.1007/s10237-023-01690-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 01/05/2023] [Indexed: 01/15/2023]
Abstract
The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure-volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.
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Hong BD, Moulton MJ, Secomb TW. Modeling left ventricular dynamics with characteristic deformation modes. Biomech Model Mechanobiol 2019; 18:1683-96. [PMID: 31129860 DOI: 10.1007/s10237-019-01168-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 05/12/2019] [Indexed: 01/07/2023]
Abstract
A computationally efficient method is described for simulating the dynamics of the left ventricle (LV) in three dimensions. LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions while conserving volume in the LV wall. The contribution of each mode to wall motion is determined by a corresponding time-dependent deformation variable. The principle of virtual work is applied to these deformation variables, yielding a system of ordinary differential equations for LV dynamics, including effects of muscle fiber orientations, active and passive stresses, and surface tractions. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length-tension and force-velocity properties of cardiac muscle. Preload and afterload are represented by lumped vascular models. The variational equations and their numerical solutions are verified by comparison to analytic solutions of the strong form equations. Deformation modes are constructed using Fourier series with an arbitrary number of terms. Greater numbers of deformation modes increase deformable model resolution but at increased computational cost. Simulations of normal LV motion throughout the cardiac cycle are presented using models with 8, 23, or 46 deformation modes. Aggregate quantities that describe LV function vary little as the number of deformation modes is increased. Spatial distributions of stress and strain change as more deformation modes are included, but overall patterns are conserved. This approach yields three-dimensional simulations of the cardiac cycle on a clinically relevant time-scale.
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Kallhovd S, Sundnes J, Wall ST. Sensitivity of stress and strain calculations to passive material parameters in cardiac mechanical models using unloaded geometries. Comput Methods Biomech Biomed Engin 2019; 22:664-675. [DOI: 10.1080/10255842.2019.1579312] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - J. Sundnes
- Simula Research Laboratory, Lysaker, Norway
| | - S. T. Wall
- Simula Research Laboratory, Lysaker, Norway
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Peirlinck M, Sack KL, De Backer P, Morais P, Segers P, Franz T, De Beule M. Kinematic boundary conditions substantially impact in silico ventricular function. Int J Numer Method Biomed Eng 2019; 35:e3151. [PMID: 30188608 DOI: 10.1002/cnm.3151] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Revised: 08/28/2018] [Accepted: 09/01/2018] [Indexed: 06/08/2023]
Abstract
Computational cardiac mechanical models, individualized to the patient, have the potential to elucidate the fundamentals of cardiac (patho-)physiology, enable non-invasive quantification of clinically significant metrics (eg, stiffness, active contraction, work), and anticipate the potential efficacy of therapeutic cardiovascular intervention. In a clinical setting, however, the available imaging resolution is often limited, which limits cardiac models to focus on the ventricles, without including the atria, valves, and proximal arteries and veins. In such models, the absence of surrounding structures needs to be accounted for by imposing realistic kinematic boundary conditions, which, for prognostic purposes, are preferably generic and thus non-image derived. Unfortunately, the literature on cardiac models shows no consistent approach to kinematically constrain the myocardium. The impact of different approaches (eg, fully constrained base, constrained epi-ring) on the predictive capacity of cardiac mechanical models has not been thoroughly studied. For that reason, this study first gives an overview of current approaches to kinematically constrain (bi) ventricular models. Next, we developed a patient-specific in silico biventricular model that compares well with literature and in vivo recorded strains. Alternative constraints were introduced to assess the influence of commonly used mechanical boundary conditions on both the predicted global functional behavior of the in-silico heart (cavity volumes, stroke volume, ejection fraction) and local strain distributions. Meaningful differences in global functioning were found between different kinematic anchoring strategies, which brought forward the importance of selecting appropriate boundary conditions for biventricular models that, in the near future, may inform clinical intervention. However, whilst statistically significant differences were also found in local strain distributions, these differences were minor and mostly confined to the region close to the applied boundary conditions.
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Affiliation(s)
- Mathias Peirlinck
- Biofluid, Tissue and Solid Mechanics for Medical Applications Lab (IBiTech, bioMMeda), Ghent University, Ghent, Belgium
| | - Kevin L Sack
- Department of Surgery, University of California at San Francisco, San Francisco, CA, USA
- Division of Biomedical Engineering, Department of Human Biology, Faculty of Health Sciences, University of Cape Town, Cape Town, Observatory, South Africa
| | | | - Pedro Morais
- Lab on Cardiovascular Imaging and Dynamics, Department of Cardiovascular Sciences, KULeuven-University of Leuven, Leuven, Belgium
| | - Patrick Segers
- Biofluid, Tissue and Solid Mechanics for Medical Applications Lab (IBiTech, bioMMeda), Ghent University, Ghent, Belgium
| | - Thomas Franz
- Division of Biomedical Engineering, Department of Human Biology, Faculty of Health Sciences, University of Cape Town, Cape Town, Observatory, South Africa
- Bioengineering Science Research Group, Engineering Sciences, Faculty of Engineering and the Environment, University of Southampton, Southampton, UK
| | - Matthieu De Beule
- Biofluid, Tissue and Solid Mechanics for Medical Applications Lab (IBiTech, bioMMeda), Ghent University, Ghent, Belgium
- FEops nv, Ghent, Belgium
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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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. Int J Numer Method Biomed Eng 2017; 33:e2863. [PMID: 28039961 DOI: 10.1002/cnm.2863] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [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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Teh I, McClymont D, Burton RAB, Maguire ML, Whittington HJ, Lygate CA, Kohl P, Schneider JE. Resolving Fine Cardiac Structures in Rats with High-Resolution Diffusion Tensor Imaging. Sci Rep 2016; 6:30573. [PMID: 27466029 PMCID: PMC4964346 DOI: 10.1038/srep30573] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2016] [Accepted: 07/04/2016] [Indexed: 02/03/2023] Open
Abstract
Cardiac architecture is fundamental to cardiac function and can be assessed non-invasively with diffusion tensor imaging (DTI). Here, we aimed to overcome technical challenges in ex vivo DTI in order to extract fine anatomical details and to provide novel insights in the 3D structure of the heart. An integrated set of methods was implemented in ex vivo rat hearts, including dynamic receiver gain adjustment, gradient system scaling calibration, prospective adjustment of diffusion gradients, and interleaving of diffusion-weighted and non-diffusion-weighted scans. Together, these methods enhanced SNR and spatial resolution, minimised orientation bias in diffusion-weighting, and reduced temperature variation, enabling detection of tissue structures such as cell alignment in atria, valves and vessels at an unprecedented level of detail. Improved confidence in eigenvector reproducibility enabled tracking of myolaminar structures as a basis for segmentation of functional groups of cardiomyocytes. Ex vivo DTI facilitates acquisition of high quality structural data that complements readily available in vivo cardiac functional and anatomical MRI. The improvements presented here will facilitate next generation virtual models integrating micro-structural and electro-mechanical properties of the heart.
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Affiliation(s)
- Irvin Teh
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
| | - Darryl McClymont
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
| | - Rebecca A. B. Burton
- Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, OX1 3PT, United Kingdom
| | - Mahon L. Maguire
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
| | - Hannah J. Whittington
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
| | - Craig A. Lygate
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
| | - Peter Kohl
- National Heart and Lung Institute, Imperial College London, London, SW3 6NP, United Kingdom
- Institute for Experimental Cardiovascular Medicine, University Heart Centre Freiburg · Bad Krozingen, Medical School of the University of Freiburg, Freiburg, 79110, Germany
| | - Jürgen E. Schneider
- Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 7BN, United Kingdom
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Affiliation(s)
- V.Y. Wang
- Auckland Bioengineering Institute and
| | - P.M.F. Nielsen
- Auckland Bioengineering Institute and
- Department of Engineering Science, Faculty of Engineering, University of Auckland, Auckland 1010, New Zealand; , ,
| | - M.P. Nash
- Auckland Bioengineering Institute and
- Department of Engineering Science, Faculty of Engineering, University of Auckland, Auckland 1010, New Zealand; , ,
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Nasopoulou A, Blazevic B, Crozier A, Shi W, Shetty A, Rinaldi CA, Lamata P, Niederer SA. Myocardial Stiffness Estimation: A Novel Cost Function for Unique Parameter Identification. In: van Assen H, Bovendeerd P, Delhaas T, editors. Functional Imaging and Modeling of the Heart. Cham: Springer International Publishing; 2015. pp. 355-63. [DOI: 10.1007/978-3-319-20309-6_41] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
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