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Sharifi Kia D, Fortunato R, Maiti S, Simon MA, Kim K. An exploratory assessment of stretch-induced transmural myocardial fiber kinematics in right ventricular pressure overload. Sci Rep 2021; 11:3587. [PMID: 33574400 PMCID: PMC7878470 DOI: 10.1038/s41598-021-83154-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 01/22/2021] [Indexed: 01/30/2023] Open
Abstract
Right ventricular (RV) remodeling and longitudinal fiber reorientation in the setting of pulmonary hypertension (PH) affects ventricular structure and function, eventually leading to RV failure. Characterizing the kinematics of myocardial fibers helps better understanding the underlying mechanisms of fiber realignment in PH. In the current work, high-frequency ultrasound imaging and structurally-informed finite element (FE) models were employed for an exploratory evaluation of the stretch-induced kinematics of RV fibers. Image-based experimental evaluation of fiber kinematics in porcine myocardium revealed the capability of affine assumptions to effectively approximate myofiber realignment in the RV free wall. The developed imaging framework provides a noninvasive modality to quantify transmural RV myofiber kinematics in large animal models. FE modeling results demonstrated that chronic pressure overload, but not solely an acute rise in pressures, results in kinematic shift of RV fibers towards the longitudinal direction. Additionally, FE simulations suggest a potential protective role for concentric hypertrophy (increased wall thickness) against fiber reorientation, while eccentric hypertrophy (RV dilation) resulted in longitudinal fiber realignment. Our study improves the current understanding of the role of different remodeling events involved in transmural myofiber reorientation in PH. Future experimentations are warranted to test the model-generated hypotheses.
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Affiliation(s)
- Danial Sharifi Kia
- grid.21925.3d0000 0004 1936 9000Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA USA
| | - Ronald Fortunato
- grid.21925.3d0000 0004 1936 9000Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA USA
| | - Spandan Maiti
- grid.21925.3d0000 0004 1936 9000Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA USA
| | - Marc A. Simon
- grid.21925.3d0000 0004 1936 9000Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000Division of Cardiology, Department of Medicine, University of Pittsburgh School of Medicine, 623A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA 15213 USA ,grid.412689.00000 0001 0650 7433Heart and Vascular Institute, University of Pittsburgh Medical Center (UPMC), Pittsburgh, PA USA ,grid.412689.00000 0001 0650 7433Pittsburgh Heart, Lung, Blood and Vascular Medicine Institute, University of Pittsburgh and University of Pittsburgh Medical Center (UPMC), Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA USA
| | - Kang Kim
- grid.21925.3d0000 0004 1936 9000Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000Division of Cardiology, Department of Medicine, University of Pittsburgh School of Medicine, 623A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA 15213 USA ,grid.412689.00000 0001 0650 7433Heart and Vascular Institute, University of Pittsburgh Medical Center (UPMC), Pittsburgh, PA USA ,grid.412689.00000 0001 0650 7433Pittsburgh Heart, Lung, Blood and Vascular Medicine Institute, University of Pittsburgh and University of Pittsburgh Medical Center (UPMC), Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA USA ,grid.21925.3d0000 0004 1936 9000Center for Ultrasound Molecular Imaging and Therapeutics, University of Pittsburgh, Pittsburgh, PA USA
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2
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Avazmohammadi R, Soares JS, Li DS, Eperjesi T, Pilla J, Gorman RC, Sacks MS. On the in vivo systolic compressibility of left ventricular free wall myocardium in the normal and infarcted heart. J Biomech 2020; 107:109767. [PMID: 32386714 PMCID: PMC7433024 DOI: 10.1016/j.jbiomech.2020.109767] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 03/26/2020] [Indexed: 01/01/2023]
Abstract
Although studied for many years, there remain continued gaps in our fundamental understanding of cardiac kinematics, such as the nature and extent of heart wall volumetric changes that occur over the cardiac cycle. Such knowledge is especially important for accurate in silico simulations of cardiac pathologies and in the development of novel therapies for their treatment. A prime example is myocardial infarction (MI), which induces profound, regionally variant maladaptive remodeling of the left ventricle (LV) wall. To address this problem, we conducted an in vivo fiduciary marker-based study in an established ovine model of MI to generate detailed, time-evolving transmural in vivo volumetric measurements of LV free wall deformations in the normal state, as well as up to 12 h post-MI. This was accomplished using a transmural array of sonomicrometry crystals that acquired fiducial positions at ∼250 Hz with a positional accuracy of ∼0.1 mm, covering the entire infarct, border, and remote zones. A convex-hull method was used to directly calculate the Jacobian J(t)=Δv(t)/ΔVED from sonocrystal positions over the entire cardiac cycle, where ΔV is the volume of each convex polyhedral at end diastole (ED) (typically ∼1 cc). We demonstrated significant in vivo compressibility in normal functioning LV free wall myocardium, with JES=0.85±0.07 at end systole (ES). We also observed substantial regional variations, with the largest reduction in local myocardial tissue volume during systole in the base region accompanied by substantial transmural gradients. These patterns changed profoundly following loss of perfusion post-MI, with the apical region showing the greatest loss of volume reduction at ES. To verify that the sonocrystals did not affect local volumetric measurements, JES measures were also verified by non-invasive magnetic resonance imaging, exhibiting very similar changes in regional volume. We note that while our estimates of regional compressibility were in close agreement with the values previously reported for large animals, ranging from 5% to 20%, the direct, comprehensive measurements of wall compressibility presented herein improved on the limitations of previous reports. These limitations included dependency on the small local volumes used for analysis and often indirect measurement of compressibility. Our novel findings suggest that proper accounting for the myocardial effective compressibility at the ∼1 cc volume scale can improve the accuracy of existing kinematic indices, such as wall thickening and axial shortening, and simulations of LV remodeling following MI.
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Affiliation(s)
- Reza Avazmohammadi
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA; Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA
| | - Joao S Soares
- Department of Mechanical and Nuclear Engineering, Virginia Commonweath University, Richmond VA 23284, USA
| | - David S Li
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
| | - Thomas Eperjesi
- Gorman Cardiovascular Research Group, Perelman School of Medicine, Department of Surgery, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - James Pilla
- Gorman Cardiovascular Research Group, Perelman School of Medicine, Department of Surgery, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Robert C Gorman
- Gorman Cardiovascular Research Group, Perelman School of Medicine, Department of Surgery, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Michael S Sacks
- James T. Willerson Center for Cardiovascular Modeling and Simulation, Oden Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA.
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Costabal FS, Concha FA, Hurtado DE, Kuhl E. The importance of mechano-electrical feedback and inertia in cardiac electromechanics. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2017; 320:352-368. [PMID: 29056782 PMCID: PMC5646712 DOI: 10.1016/j.cma.2017.03.015] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.
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Affiliation(s)
| | - Felipe A Concha
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Daniel E Hurtado
- Department of Structural and Geotechnical Engineering, School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
- Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Catoólica de Chile, Santiago, Chile
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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Shen N, Knopf A, Westendorf C, Kraushaar U, Riedl J, Bauer H, Pöschel S, Layland SL, Holeiter M, Knolle S, Brauchle E, Nsair A, Hinderer S, Schenke-Layland K. Steps toward Maturation of Embryonic Stem Cell-Derived Cardiomyocytes by Defined Physical Signals. Stem Cell Reports 2017; 9:122-135. [PMID: 28528699 PMCID: PMC5511039 DOI: 10.1016/j.stemcr.2017.04.021] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2016] [Revised: 04/19/2017] [Accepted: 04/20/2017] [Indexed: 01/18/2023] Open
Abstract
Cardiovascular disease remains a leading cause of mortality and morbidity worldwide. Embryonic stem cell-derived cardiomyocytes (ESC-CMs) may offer significant advances in creating in vitro cardiac tissues for disease modeling, drug testing, and elucidating developmental processes; however, the induction of ESCs to a more adult-like CM phenotype remains challenging. In this study, we developed a bioreactor system to employ pulsatile flow (1.48 mL/min), cyclic strain (5%), and extended culture time to improve the maturation of murine and human ESC-CMs. Dynamically-cultured ESC-CMs showed an increased expression of cardiac-associated proteins and genes, cardiac ion channel genes, as well as increased SERCA activity and a Raman fingerprint with the presence of maturation-associated peaks similar to primary CMs. We present a bioreactor platform that can serve as a foundation for the development of human-based cardiac in vitro models to verify drug candidates, and facilitates the study of cardiovascular development and disease. Custom-made bioreactor exposes ESC-CMs to defined shear stress and cyclic stretch Physical signals and extended culture significantly improve maturation of ESC-CMs Biochemical fingerprint of dynamically cultured ESC-CMs is similar to primary CMs
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Affiliation(s)
- Nian Shen
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Anne Knopf
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Claas Westendorf
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany
| | - Udo Kraushaar
- Department of Cell Biology, Electrophysiology, Natural and Medical Sciences Institute, University of Tübingen, Reutlingen 72770, Germany
| | - Julia Riedl
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Hannah Bauer
- Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Simone Pöschel
- Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Shannon Lee Layland
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Monika Holeiter
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Stefan Knolle
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Cell Biology, Electrophysiology, Natural and Medical Sciences Institute, University of Tübingen, Reutlingen 72770, Germany
| | - Eva Brauchle
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Ali Nsair
- Department of Medicine/Cardiology, Cardiovascular Research Laboratories (CVRL), David Geffen School of Medicine, University of California Los Angeles (UCLA), Los Angeles, CA 90095, USA; Broad Stem Cell Research Center, David School of Medicine at UCLA, Los Angeles, CA 90095, USA
| | - Svenja Hinderer
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany
| | - Katja Schenke-Layland
- Department of Cell and Tissue Engineering, Fraunhofer Institute for Interfacial Engineering and Biotechnology IGB, Stuttgart 70569, Germany; Department of Women's Health, Research Institute of Women's Health, University Hospital of the Eberhard Karls University Tübingen, Tübingen 72076, Germany; Department of Medicine/Cardiology, Cardiovascular Research Laboratories (CVRL), David Geffen School of Medicine, University of California Los Angeles (UCLA), Los Angeles, CA 90095, USA.
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5
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Stacey RB, Caine AJ, Hundley WG. Evaluation and management of left ventricular noncompaction cardiomyopathy. Curr Heart Fail Rep 2015; 12:61-7. [PMID: 25399629 DOI: 10.1007/s11897-014-0237-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Left ventricular (LV) noncompaction cardiomyopathy (LVNC) is a form of cardiomyopathy in which trabeculations fail to "compact" with the left ventricular endocardium during fetal cardiac development and is classically associated with subsequent impairment of LV function, significant mortality, ventricular dysrhythmias, and embolic phenomena. As awareness and medical imaging quality have improved, it is becoming easier to identify trabeculations that traverse the LV cavity and serve as a distinguishing feature of this disorder. Differentiating true noncompaction from mild increases in trabeculations requires prudent imaging and clinical correlation. This review seeks to discuss the potential methods of evaluating left ventricular trabeculations, the role of increased trabeculations in cardiovascular disease, and how their presence may affect clinical management.
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Affiliation(s)
- R Brandon Stacey
- Department of Internal Medicine Section on Cardiology, Wake Forest University School of Medicine, Winston-Salem, NC, 27157, USA,
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6
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Kim SA, Kim MN, Shim WJ, Park SM. Layer-specific dyssynchrony and its relationship to the change of left ventricular function in hypertensive patients. Heart Vessels 2015; 31:528-34. [PMID: 25573260 DOI: 10.1007/s00380-014-0626-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/29/2014] [Accepted: 12/26/2014] [Indexed: 10/24/2022]
Abstract
Left ventricular (LV) remodeling in systemic arterial hypertension causes electrical conduction delay and impairs synchronous contraction, which may contribute to the development of heart failure. This study aimed to assess the change of LV mechanics in hypertension by layer-specific dyssynchrony. One hundred and twenty-one patients with primary hypertension and LV ejection fraction >50 % (mean age, 62 ± 10 years) and 31 normotensive controls (mean age, 63 ± 9 years) were prospectively included. Layer-specific dyssynchrony index (DI) was defined as standard deviation of time interval (TI) from the onset of Q wave to peak longitudinal strain obtained from 18 segments in each endocardial, myocardial, and epicardial layer. The global TI between the onset of Q wave to peak global longitudinal strain in each layer was obtained and the time difference (TD) of global TI between layers was calculated. DIs were significantly different in three layers (P < 0.001 in both groups), and were significantly greater in hypertensive patients than in controls except epicardial DI. End diastolic filling pressure and LV global longitudinal strain were related with endocardial DI. TD between endocardium and myocardium was greater in hypertensive patients than in controls (P = 0.001). Layer-specific DI revealed delayed contraction in each layer and between layers in hypertensive patients, which were apparent in endocardium and between endocardium and myocardium. Increased layer-specific DIs were associated with subclinical LV dysfunction, although LV ejection fraction was preserved. These may be helpful to understand layer-specific mechanical property of LV myocardium and for early detection of subclinical impairment of myocardial function.
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Affiliation(s)
- Su-A Kim
- Division of Cardiology, Department of Internal Medicine, Korea University Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5 ga, Seongbuk-gu, Seoul, 136-705, Republic of Korea
| | - Mi-Na Kim
- Division of Cardiology, Department of Internal Medicine, Korea University Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5 ga, Seongbuk-gu, Seoul, 136-705, Republic of Korea
| | - Wan-Joo Shim
- Division of Cardiology, Department of Internal Medicine, Korea University Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5 ga, Seongbuk-gu, Seoul, 136-705, Republic of Korea
| | - Seong-Mi Park
- Division of Cardiology, Department of Internal Medicine, Korea University Anam Hospital, Korea University College of Medicine, 126-1, Anam-dong 5 ga, Seongbuk-gu, Seoul, 136-705, Republic of Korea.
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7
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Baillargeon B, Rebelo N, Fox DD, Taylor RL, Kuhl E. The Living Heart Project: A robust and integrative simulator for human heart function. EUROPEAN JOURNAL OF MECHANICS. A, SOLIDS 2014; 48:38-47. [PMID: 25267880 PMCID: PMC4175454 DOI: 10.1016/j.euromechsol.2014.04.001] [Citation(s) in RCA: 179] [Impact Index Per Article: 17.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The heart is not only our most vital, but also our most complex organ: Precisely controlled by the interplay of electrical and mechanical fields, it consists of four chambers and four valves, which act in concert to regulate its filling, ejection, and overall pump function. While numerous computational models exist to study either the electrical or the mechanical response of its individual chambers, the integrative electro-mechanical response of the whole heart remains poorly understood. Here we present a proof-of-concept simulator for a four-chamber human heart model created from computer topography and magnetic resonance images. We illustrate the governing equations of excitation-contraction coupling and discretize them using a single, unified finite element environment. To illustrate the basic features of our model, we visualize the electrical potential and the mechanical deformation across the human heart throughout its cardiac cycle. To compare our simulation against common metrics of cardiac function, we extract the pressure-volume relationship and show that it agrees well with clinical observations. Our prototype model allows us to explore and understand the key features, physics, and technologies to create an integrative, predictive model of the living human heart. Ultimately, our simulator will open opportunities to probe landscapes of clinical parameters, and guide device design and treatment planning in cardiac diseases such as stenosis, regurgitation, or prolapse of the aortic, pulmonary, tricuspid, or mitral valve.
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Affiliation(s)
| | - Nuno Rebelo
- Dassault Systèmes Simulia Corporation, Fremont, CA 94538, USA
| | - David D Fox
- Dassault Systèmes Simulia Corporation, Providence, RI 02909, USA
| | - Robert L Taylor
- Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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8
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Butters TD, Aslanidi OV, Zhao J, Smaill B, Zhang H. A novel computational sheep atria model for the study of atrial fibrillation. Interface Focus 2014; 3:20120067. [PMID: 24427521 DOI: 10.1098/rsfs.2012.0067] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2012] [Accepted: 12/21/2012] [Indexed: 11/12/2022] Open
Abstract
Sheep are often used as animal models for experimental studies into the underlying mechanisms of cardiac arrhythmias. Previous studies have shown that biophysically detailed computer models of the heart provide a powerful alternative to experimental animal models for underpinning such mechanisms. In this study, we have developed a family of mathematical models for the electrical action potentials of various sheep atrial cell types. The developed cell models were then incorporated into a three-dimensional anatomical model of the sheep atria, which was recently reconstructed and segmented based on anatomical features within different regions. This created a novel biophysically detailed computational model of the three-dimensional sheep atria. Using the model, we then investigated the mechanisms by which paroxysmal rapid focal activity in the pulmonary veins can transit to sustained atrial fibrillation. It was found that the anisotropic property of the atria arising from the fibre structure plays an important role in facilitating the development of fibrillatory atrial excitation waves, and the electrical heterogeneity plays an important role in its initiation.
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Affiliation(s)
- Timothy D Butters
- School of Physics and Astronomy , University of Manchester , Manchester , UK
| | - Oleg V Aslanidi
- School of Physics and Astronomy , University of Manchester , Manchester , UK ; Division of Imaging Sciences and Biomedical Engineering , King's College London , London , UK
| | - Jichao Zhao
- Auckland Bioengineering Institute , University of Auckland , Auckland , New Zealand
| | - Bruce Smaill
- Auckland Bioengineering Institute , University of Auckland , Auckland , New Zealand
| | - Henggui Zhang
- School of Physics and Astronomy , University of Manchester , Manchester , UK
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Wong J, Göktepe S, Kuhl E. Computational modeling of chemo-electro-mechanical coupling: a novel implicit monolithic finite element approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2013; 29:1104-33. [PMID: 23798328 PMCID: PMC4567385 DOI: 10.1002/cnm.2565] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2012] [Revised: 02/07/2013] [Accepted: 04/12/2013] [Indexed: 05/05/2023]
Abstract
Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.
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Affiliation(s)
- J Wong
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A
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10
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Dal H, Göktepe S, Kaliske M, Kuhl E. A fully implicit finite element method for bidomain models of cardiac electromechanics. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2013; 253:323-336. [PMID: 23175588 PMCID: PMC3501134 DOI: 10.1016/j.cma.2012.07.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.
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Affiliation(s)
- Hüsnü Dal
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland
- Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany
- Institut für Mechanik, (Bauwesen), Lehrstuhl I, Universität Stuttgart, Germany
| | - Serdar Göktepe
- Department of Civil Engineering, Middle East Technical University, Ankara, Turkey
| | - Michael Kaliske
- Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany
| | - Ellen Kuhl
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland
- Department of Mechanical Engineering, Stanford University, Stanford, USA
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11
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Wong J, Kuhl E. Generating fibre orientation maps in human heart models using Poisson interpolation. Comput Methods Biomech Biomed Engin 2012; 17:1217-26. [PMID: 23210529 DOI: 10.1080/10255842.2012.739167] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately -70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.
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Affiliation(s)
- Jonathan Wong
- a Department of Mechanical Engineering , Stanford University , Stanford , CA 94305 , USA
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Hurtado DE, Kuhl E. Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart. Comput Methods Biomech Biomed Engin 2012; 17:986-96. [PMID: 23113842 PMCID: PMC3574176 DOI: 10.1080/10255842.2012.729582] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
For more than a century, electrophysiologists, cardiologists and engineers have studied the electrical activity of the human heart to better understand rhythm disorders and possible treatment options. Although the depolarisation sequence of the heart is relatively well characterised, the repolarisation sequence remains a subject of great controversy. Here, we study regional and temporal variations in both depolarisation and repolarisation using a finite element approach. We discretise the governing equations in time using an unconditionally stable implicit Euler backward scheme and in space using a consistently linearised Newton-Raphson-based finite element solver. Through systematic parameter-sensitivity studies, we establish a direct relation between a normal positive T-wave and the non-uniform distribution of the controlling parameter, which we have termed refractoriness. To establish a healthy baseline model, we calibrate the refractoriness using clinically measured action potential durations at different locations in the human heart. We demonstrate the potential of our model by comparing the computationally predicted and clinically measured depolarisation and repolarisation profiles across the left ventricle. The proposed framework allows us to explore how local action potential durations on the microscopic scale translate into global repolarisation sequences on the macroscopic scale. We anticipate that our calibrated human heart model can be widely used to explore cardiac excitation in health and disease. For example, our model can serve to identify optimal pacing sites in patients with heart failure and to localise optimal ablation sites in patients with cardiac fibrillation.
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Affiliation(s)
- Daniel E. Hurtado
- Department of Structural and Geotechnical Engineering and Biomedical Engineering Group, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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Rausch MK, Tibayan FA, Miller DC, Kuhl E. Evidence of adaptive mitral leaflet growth. J Mech Behav Biomed Mater 2012; 15:208-17. [PMID: 23159489 DOI: 10.1016/j.jmbbm.2012.07.001] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2012] [Revised: 06/30/2012] [Accepted: 07/02/2012] [Indexed: 01/09/2023]
Abstract
Ischemic mitral regurgitation is mitral insufficiency caused by myocardial infarction. Recent studies suggest that mitral leaflets have the potential to grow and reduce the degree of regurgitation. Leaflet growth has been associated with papillary muscle displacement, but role of annular dilation in leaflet growth is unclear. We tested the hypothesis that chronic leaflet stretch, induced by papillary muscle tethering and annular dilation, triggers chronic leaflet growth. To decipher the mechanisms that drive the growth process, we further quantified regional and directional variations of growth. Five adult sheep underwent coronary snare and marker placement on the left ventricle, papillary muscles, mitral annulus, and mitral leaflet. After eight days, we tightened the snares to create inferior myocardial infarction. We recorded marker coordinates at baseline, acutely (immediately post-infarction), and chronically (five weeks post-infarction). From these coordinates, we calculated acute and chronic changes in ventricular, papillary muscle, and annular geometry along with acute and chronic leaflet strains. Chronic left ventricular dilation of 17.15% (p<0.001) induced chronic posterior papillary muscle displacement of 13.49 mm (p=0.07). Chronic mitral annular area, commissural and septal-lateral distances increased by 32.50% (p=0.010), 14.11% (p=0.007), and 10.84% (p=0.010). Chronic area, circumferential, and radial growth were 15.57%, 5.91%, and 3.58%, with non-significant regional variations (p=0.868). Our study demonstrates that mechanical stretch, induced by annular dilation and papillary muscle tethering, triggers mitral leaflet growth. Understanding the mechanisms of leaflet adaptation may open new avenues to pharmacologically or surgically manipulate mechanotransduction pathways to augment mitral leaflet area and reduce the degree of regurgitation.
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Klepach D, Lee LC, Wenk JF, Ratcliffe MB, Zohdi TI, Navia JA, Kassab GS, Kuhl E, Guccione JM. Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration. MECHANICS RESEARCH COMMUNICATIONS 2012; 42:134-141. [PMID: 22778489 PMCID: PMC3390946 DOI: 10.1016/j.mechrescom.2012.03.005] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations.
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Affiliation(s)
- Doron Klepach
- Department of Surgery, Division of Adult Cardiothoracic Surgery, UC San Francisco, San Francisco, CA 94121, USA
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Wong J, Abilez OJ, Kuhl E. Computational Optogenetics: A Novel Continuum Framework for the Photoelectrochemistry of Living Systems. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2012; 60:1158-1178. [PMID: 22773861 PMCID: PMC3388516 DOI: 10.1016/j.jmps.2012.02.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to virtually probe landscapes of process parameters, and to identify optimal photostimulation sequences with the goal to pace human hearts with light and, ultimately, to restore mechanical function.
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Affiliation(s)
- Jonathan Wong
- Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA,
| | - Oscar J. Abilez
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA,
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA
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Tsamis A, Cheng A, Nguyen TC, Langer F, Miller DC, Kuhl E. Kinematics of cardiac growth: in vivo characterization of growth tensors and strains. J Mech Behav Biomed Mater 2012; 8:165-77. [PMID: 22402163 PMCID: PMC3298662 DOI: 10.1016/j.jmbbm.2011.12.006] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2011] [Revised: 11/29/2011] [Accepted: 12/16/2011] [Indexed: 12/22/2022]
Abstract
Progressive growth and remodeling of the left ventricle are part of the natural history of chronic heart failure and strong clinical indicators for survival. Accompanied by changes in cardiac form and function, they manifest themselves in alterations of cardiac strains, fiber stretches, and muscle volume. Recent attempts to shed light on the mechanistic origin of heart failure utilize continuum theories of growth to predict the maladaptation of the heart in response to pressure or volume overload. However, despite a general consensus on the representation of growth through a second order tensor, the precise format of this growth tensor remains unknown. Here we show that infarct-induced cardiac dilation is associated with a chronic longitudinal growth, accompanied by a chronic thinning of the ventricular wall. In controlled in vivo experiments throughout a period of seven weeks, we found that the lateral left ventricular wall adjacent to the infarct grows longitudinally by more than 10%, thins by more than 25%, lengthens in fiber direction by more than 5%, and decreases its volume by more than 15%. Our results illustrate how a local loss of blood supply induces chronic alterations in structure and function in adjacent regions of the ventricular wall. We anticipate our findings to be the starting point for a series of in vivo studies to calibrate and validate constitutive models for cardiac growth. Ultimately, these models could be useful to guide the design of novel therapies, which allow us to control the progression of heart failure.
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Famaey N, Vander Sloten J, Kuhl E. A three-constituent damage model for arterial clamping in computer-assisted surgery. Biomech Model Mechanobiol 2012; 12:123-36. [DOI: 10.1007/s10237-012-0386-7] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Accepted: 02/24/2012] [Indexed: 10/28/2022]
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Choi HF, Rademakers FE, Claus P. Left-ventricular shape determines intramyocardial mechanical heterogeneity. Am J Physiol Heart Circ Physiol 2011; 301:H2351-61. [DOI: 10.1152/ajpheart.00568.2011] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.
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Affiliation(s)
- Hon Fai Choi
- Division Imaging and Cardiovascular Dynamics, Department of Cardiovascular Diseases, Katholieke Universiteit Leuven, University Hospitals–Campus Gasthuisberg, Leuven, Belgium
| | - Frank E. Rademakers
- Division Imaging and Cardiovascular Dynamics, Department of Cardiovascular Diseases, Katholieke Universiteit Leuven, University Hospitals–Campus Gasthuisberg, Leuven, Belgium
| | - Piet Claus
- Division Imaging and Cardiovascular Dynamics, Department of Cardiovascular Diseases, Katholieke Universiteit Leuven, University Hospitals–Campus Gasthuisberg, Leuven, Belgium
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