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Giannakidis A, Gullberg GT. Transmural Remodeling of Cardiac Microstructure in Aged Spontaneously Hypertensive Rats by Diffusion Tensor MRI. Front Physiol 2020; 11:265. [PMID: 32296341 PMCID: PMC7136532 DOI: 10.3389/fphys.2020.00265] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 03/09/2020] [Indexed: 11/16/2022] Open
Abstract
The long-standing high blood pressure (also known as hypertension) overworks the heart. Microstructural remodeling is a key factor of hypertensive heart disease progression. Diffusion tensor magnetic resonance imaging (DT-MRI) is a powerful tool for the rapid noninvasive nondestructive delineation of the cardiomyocyte organization. The spontaneously hypertensive rat (SHR) is a well-established model of genetic hypertension. The goal of this study was to employ high-resolution DT-MRI and the SHR animal model to assess the transmural layer-specific remodeling of myocardial microstructure associated with hypertension. Ex vivo experiments were performed on excised formalin-fixed hearts of aged SHRs (n = 4) and age-matched controls (n = 4). The DT-MRI-derived fractional anisotropy (FA), longitudinal diffusivity (λL), transversal diffusivity (λT), and mean diffusivity (MD) served as the readout parameters investigated at three transmural zones (i.e., endocardium, mesocardium, and epicardium). The helix angles (HAs) of the aggregated cardiomyocytes and the orientation of laminar sheetlets were also studied. Compared with controls, the SHRs exhibited decreased epicardial FA, while FA changes in the other two transmural regions were insignificant. No substantial differences were observed in the diffusivity parameters and the transmural course of HAs between the two groups. A consistent distribution pattern of laminar sheetlet orientation was not identified for either group. Our findings are in line with the known cellular microstructure from early painstaking histological studies. Biophysical explanations of the study outcomes are provided. In conclusion, our experimental findings indicate that the epicardial microstructure is more vulnerable to high blood pressure leading to more pronounced changes in this region during remodeling. DT-MRI is well-suited for elucidating these alterations. The revealed transmural nonuniformity of myocardial reorganization may shed light on the mechanisms of the microstructure-function relationship in hypertension progression. Our results provide insights into the management of patients with systemic arterial hypertension, thus prevent the progression toward heart failure. The findings of this study should be acknowledged by electromechanical models of the heart that simulate the specific cardiac pathology.
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Affiliation(s)
- Archontis Giannakidis
- School of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom.,Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States.,National Heart & Lung Institute, Imperial College London, London, United Kingdom
| | - Grant T Gullberg
- Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States.,Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, CA, United States
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2
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Das PN, Kumar A, Bairagi N, Chatterjee S. Restoring calcium homeostasis in diabetic cardiomyocytes: an investigation through mathematical modelling. MOLECULAR BIOSYSTEMS 2017; 13:2056-2068. [PMID: 28795720 DOI: 10.1039/c7mb00264e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Regulated calcium flux from sarcoplasmic reticulum could be a possible therapeutic strategy in diabetic cardiomyocyte problem.
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Affiliation(s)
| | - Ajay Kumar
- Drug Discovery Research Center
- Translational Health Science and Technology Institute
- Faridabad-121001
- India
| | | | - Samrat Chatterjee
- Drug Discovery Research Center
- Translational Health Science and Technology Institute
- Faridabad-121001
- India
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3
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Das PN, Pedruzzi G, Bairagi N, Chatterjee S. Coupling calcium dynamics and mitochondrial bioenergetic: an in silico study to simulate cardiomyocyte dysfunction. MOLECULAR BIOSYSTEMS 2016; 12:806-17. [PMID: 26742687 DOI: 10.1039/c5mb00872g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
The coupling of intracellular Ca(2+) dynamics with mitochondrial bioenergetic is crucial for the functioning of cardiomyocytes both in healthy and disease conditions. The pathophysiological signature of the Cardiomyocyte Dysfunction (CD) is commonly related to decreased ATP production due to mitochondrial functional impairment and to an increased mitochondrial calcium content ([Ca(2+)]m). These features advanced the therapeutic approaches which aim to reduce [Ca(2+)]m. But whether [Ca(2+)]m overload is the pathological trigger for CD or a physiological consequence, remained controversial. We addressed this issue in silico and showed that [Ca(2+)]m might not directly cause CD. Through model parameter recalibration, we demonstrated how mitochondria cope up with functionally impaired processes and consequently accumulate calcium. A strong coupling of the [Ca(2+)]m oscillations with the ATP synthesis rate ensures robust calcium cycling and avoids CD. We suggested a cardioprotective role of the mitochondrial calcium uniporter and predicted that a mitochondrial sodium calcium exchanger could be a potential therapeutic target to restore the normal functioning of the cardiomyocyte.
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Affiliation(s)
- Phonindra Nath Das
- International Centre for Genetic Engineering and Biotechnology, Aruna Asaf Ali Marg, New Delhi-110067, India
| | - Gabriele Pedruzzi
- International Centre for Genetic Engineering and Biotechnology, Aruna Asaf Ali Marg, New Delhi-110067, India
| | - Nandadulal Bairagi
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata-700032, India
| | - Samrat Chatterjee
- Drug Discovery Research Centre, Translational Health Science and Technology Institute, Faridabad-121001, India.
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Gomez JF, Cardona K, Trenor B. Lessons learned from multi-scale modeling of the failing heart. J Mol Cell Cardiol 2015; 89:146-59. [PMID: 26476237 DOI: 10.1016/j.yjmcc.2015.10.016] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Revised: 10/07/2015] [Accepted: 10/14/2015] [Indexed: 12/26/2022]
Abstract
Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.
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Affiliation(s)
- Juan F Gomez
- Instituto de Investigación Interuniversitario en Bioingeniería y Tecnología Orientada, al Ser Humano (I3BH), Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
| | - Karen Cardona
- Instituto de Investigación Interuniversitario en Bioingeniería y Tecnología Orientada, al Ser Humano (I3BH), Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
| | - Beatriz Trenor
- Instituto de Investigación Interuniversitario en Bioingeniería y Tecnología Orientada, al Ser Humano (I3BH), Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
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Lopez-Perez A, Sebastian R, Ferrero JM. Three-dimensional cardiac computational modelling: methods, features and applications. Biomed Eng Online 2015; 14:35. [PMID: 25928297 PMCID: PMC4424572 DOI: 10.1186/s12938-015-0033-5] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2014] [Accepted: 04/02/2015] [Indexed: 01/19/2023] Open
Abstract
The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.
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Affiliation(s)
- Alejandro Lopez-Perez
- Centre for Research and Innovation in Bioengineering (Ci2B), Universitat Politècnica de València, València, Spain.
| | - Rafael Sebastian
- Computational Multiscale Physiology Lab (CoMMLab), Universitat de València, València, Spain.
| | - Jose M Ferrero
- Centre for Research and Innovation in Bioengineering (Ci2B), Universitat Politècnica de València, València, Spain.
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Jiang C, Liu GR, Han X, Zhang ZQ, Zeng W. A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2015; 31:e02697. [PMID: 25382158 DOI: 10.1002/cnm.2697] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2014] [Revised: 10/29/2014] [Accepted: 10/30/2014] [Indexed: 06/04/2023]
Abstract
The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics.
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Affiliation(s)
- Chen Jiang
- State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body, Hunan University, 410082, People's Republic of China
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Ghasemi O, Ma Y, Lindsey ML, Jin YF. Using systems biology approaches to understand cardiac inflammation and extracellular matrix remodeling in the setting of myocardial infarction. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2014; 6:77-91. [PMID: 24741709 DOI: 10.1002/wsbm.1248] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Inflammation and extracellular matrix (ECM) remodeling are important components regulating the response of the left ventricle to myocardial infarction (MI). Significant cellular- and molecular-level contributors can be identified by analyzing data acquired through high-throughput genomic and proteomic technologies that provide expression levels for thousands of genes and proteins. Large-scale data provide both temporal and spatial information that need to be analyzed and interpreted using systems biology approaches in order to integrate this information into dynamic models that predict and explain mechanisms of cardiac healing post-MI. In this review, we summarize the systems biology approaches needed to computationally simulate post-MI remodeling, including data acquisition, data analysis for biomarker classification and identification, data integration to build dynamic models, and data interpretation for biological functions. An example for applying a systems biology approach to ECM remodeling is presented as a reference illustration.
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EAD and DAD mechanisms analyzed by developing a new human ventricular cell model. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2014; 116:11-24. [PMID: 25192800 DOI: 10.1016/j.pbiomolbio.2014.08.008] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Accepted: 08/09/2014] [Indexed: 12/31/2022]
Abstract
It has long been suggested that the Ca(2+)-mechanisms are largely involved in generating the early afterdepolarization (EAD) as well as the delayed afterdepolarization (DAD). This view was examined in a quantitative manner by applying the lead potential analysis to a new human ventricular cell model. In this ventricular cell model, the tight coupled LCC-RyR model (CaRU) based on local control theory (Hinch et al. 2004) and ion channel models mostly based on human electrophysiological data were included to reproduce realistic Ca(2+) dynamics as well as the membrane excitation. Simultaneously, the Ca(2+) accumulation near the Ca(2+) releasing site was incorporated as observed in real cardiac myocytes. The maximum rate of ventricular repolarization (-1.02 mV/ms) is due to IK1 (-0.55 mV/ms) and the rest is provided nearly equally by INCX (-0.20 mV/ms), INaL (-0.16 mV/ms) and INaT (-0.13 mV/ms). These INaL and INaT components are due to closure of the voltage gate, which remains partially open during the plateau potential. DADs could be evoked by applying high-frequency stimulations supplemented by a partial Na(+)/K(+) pump inhibition, or by a microinjection of Ca(2+). EADs was evoked by retarding the inactivation of INaL. The lead potential (VL) analysis revealed that IK1 and IKr played the primary role to reverse the AP repolarization to depolarizing limb of EAD. ICaL and INCX amplified EAD, while the remaining currents partially antagonized dVL/dt. The maximum rate of rise of EAD was attributable to the rapid activation of both ICaL (45.5%) and INCX (54.5%).
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9
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Optimisation of a generic ionic model of cardiac myocyte electrical activity. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2013; 2013:706195. [PMID: 23710254 PMCID: PMC3659483 DOI: 10.1155/2013/706195] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2012] [Revised: 02/11/2013] [Accepted: 02/18/2013] [Indexed: 12/19/2022]
Abstract
A generic cardiomyocyte ionic model, whose complexity lies between a simple phenomenological formulation and a biophysically detailed ionic membrane current description, is presented. The model provides a user-defined number of ionic currents, employing two-gate Hodgkin-Huxley type kinetics. Its generic nature allows accurate reconstruction of action potential waveforms recorded experimentally from a range of cardiac myocytes. Using a multiobjective optimisation approach, the generic ionic model was optimised to accurately reproduce multiple action potential waveforms recorded from central and peripheral sinoatrial nodes and right atrial and left atrial myocytes from rabbit cardiac tissue preparations, under different electrical stimulus protocols and pharmacological conditions. When fitted simultaneously to multiple datasets, the time course of several physiologically realistic ionic currents could be reconstructed. Model behaviours tend to be well identified when extra experimental information is incorporated into the optimisation.
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10
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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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Kapela A, Nagaraja S, Parikh J, Tsoukias NM. Modeling Ca2+ signaling in the microcirculation: intercellular communication and vasoreactivity. Crit Rev Biomed Eng 2012; 39:435-60. [PMID: 22196162 DOI: 10.1615/critrevbiomedeng.v39.i5.50] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
A network of intracellular signaling pathways and complex intercellular interactions regulate calcium mobilization in vascular cells, arteriolar tone, and blood flow. Different endothelium-derived vasoreactive factors have been identified and the importance of myoendothelial communication in vasoreactivity is now well appreciated. The ability of many vascular networks to conduct signals upstream also is established. This phenomenon is critical for both short-term changes in blood perfusion as well as long-term adaptations of a vascular network. In addition, in a phenomenon termed vasomotion, arterioles often exhibit spontaneous oscillations in diameter. This is thought to improve tissue oxygenation and enhance blood flow. Experimentation has begun to reveal important aspects of the regulatory machinery and the significance of these phenomena for the regulation of local perfusion and oxygenation. Mathematical modeling can assist in elucidating the complex signaling mechanisms that participate in these phenomena. This review highlights some of the important experimental studies and relevant mathematical models that provide the current understanding of these mechanisms in vasoreactivity.
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Affiliation(s)
- Adam Kapela
- Department of Biomedical Engineering, Florida International University, Miami, FL, USA
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Abstract
Excitation-contraction coupling describes the processes relating to electrical excitation through force generation and contraction in the heart. It occurs at multiple levels from the whole heart, to single myocytes and down to the sarcomere. A central process that links electrical excitation to contraction is calcium mobilization. Computational models that are well grounded in experimental data have been an effective tool to understand the complex dynamics of the processes involved in excitation-contraction coupling. Presented here is a summary of some computational models that have added to the understanding of the cellular and subcellular mechanisms that control ventricular myocyte calcium dynamics. Models of cardiac ventricular myocytes that have given insight into termination of calcium release and interval-force relations are discussed in this manuscript. Computational modeling of calcium sparks, the elementary events in cardiac excitation-contraction coupling, has given insight into mechanism governing their dynamics and termination as well as their role in excitation-contraction coupling and is described herein.
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Affiliation(s)
- M Saleet Jafri
- School of Systems Biology, George Mason University, Manassas, VA, USA.
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Han C, Pogwizd SM, Killingsworth CR, He B. Noninvasive reconstruction of the three-dimensional ventricular activation sequence during pacing and ventricular tachycardia in the canine heart. Am J Physiol Heart Circ Physiol 2011; 302:H244-52. [PMID: 21984548 DOI: 10.1152/ajpheart.00618.2011] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Single-beat imaging of myocardial activation promises to aid in both cardiovascular research and clinical medicine. In the present study we validate a three-dimensional (3D) cardiac electrical imaging (3DCEI) technique with the aid of simultaneous 3D intracardiac mapping to assess its capability to localize endocardial and epicardial initiation sites and image global activation sequences during pacing and ventricular tachycardia (VT) in the canine heart. Body surface potentials were measured simultaneously with bipolar electrical recordings in a closed-chest condition in healthy canines. Computed tomography images were obtained after the mapping study to construct realistic geometry models. Data analysis was performed on paced rhythms and VTs induced by norepinephrine (NE). The noninvasively reconstructed activation sequence was in good agreement with the simultaneous measurements from 3D cardiac mapping with a correlation coefficient of 0.74 ± 0.06, a relative error of 0.29 ± 0.05, and a root mean square error of 9 ± 3 ms averaged over 460 paced beats and 96 ectopic beats including premature ventricular complexes, couplets, and nonsustained monomorphic VTs and polymorphic VTs. Endocardial and epicardial origins of paced beats were successfully predicted in 72% and 86% of cases, respectively, during left ventricular pacing. The NE-induced ectopic beats initiated in the subendocardium by a focal mechanism. Sites of initial activation were estimated to be ∼7 mm from the measured initiation sites for both the paced beats and ectopic beats. For the polymorphic VTs, beat-to-beat dynamic shifts of initiation site and activation pattern were characterized by the reconstruction. The present results suggest that 3DCEI can noninvasively image the 3D activation sequence and localize the origin of activation of paced beats and NE-induced VTs in the canine heart with good accuracy. This 3DCEI technique offers the potential to aid interventional therapeutic procedures for treating ventricular arrhythmias arising from epicardial or endocardial sites and to noninvasively assess the mechanisms of these arrhythmias.
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Affiliation(s)
- Chengzong Han
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, USA
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Majumder R, Nayak AR, Pandit R. Scroll-wave dynamics in human cardiac tissue: lessons from a mathematical model with inhomogeneities and fiber architecture. PLoS One 2011; 6:e18052. [PMID: 21483682 PMCID: PMC3071724 DOI: 10.1371/journal.pone.0018052] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2010] [Accepted: 02/21/2011] [Indexed: 12/03/2022] Open
Abstract
Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.
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Affiliation(s)
- Rupamanjari Majumder
- Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore, India.
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Tsoukias NM. Calcium dynamics and signaling in vascular regulation: computational models. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2011; 3:93-106. [PMID: 21061306 DOI: 10.1002/wsbm.97] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Calcium is a universal signaling molecule with a central role in a number of vascular functions including in the regulation of tone and blood flow. Experimentation has provided insights into signaling pathways that lead to or affected by Ca(2+) mobilization in the vasculature. Mathematical modeling offers a systematic approach to the analysis of these mechanisms and can serve as a tool for data interpretation and for guiding new experimental studies. Comprehensive models of calcium dynamics are well advanced for some systems such as the heart. This review summarizes the progress that has been made in modeling Ca(2+) dynamics and signaling in vascular cells. Model simulations show how Ca(2+) signaling emerges as a result of complex, nonlinear interactions that cannot be properly analyzed using only a reductionist's approach. A strategy of integrative modeling in the vasculature is outlined that will allow linking macroscale pathophysiological responses to the underlying cellular mechanisms.
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16
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Abstract
Excitation-contraction coupling in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²(+) transport. The complexity and integrative nature of heart cell electrophysiology and Ca²(+) cycling has led to an evolution of computational models that have played a crucial role in shaping our understanding of heart function. An important emerging theme in systems biology is that the detailed nature of local signaling events, such as those that occur in the cardiac dyad, have important consequences at higher biological scales. Multiscale modeling techniques have revealed many mechanistic links between microscale events, such as Ca²(+) binding to a channel protein, and macroscale phenomena, such as excitation-contraction coupling gain. Here, we review experimentally based multiscale computational models of excitation-contraction coupling and the insights that have been gained through their application.
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Affiliation(s)
- Joseph L Greenstein
- Center for Cardiovascular Bioinformatics and Modeling, Whitaker Biomedical Engineering Institute, The Johns Hopkins University, Baltimore, MD, USA
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Abstract
Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.
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Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218, USA.
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Szilágyi SM, Szilágyi L, Benyó Z. A patient specific electro-mechanical model of the heart. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2011; 101:183-200. [PMID: 20692715 DOI: 10.1016/j.cmpb.2010.06.006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2009] [Revised: 04/26/2010] [Accepted: 06/13/2010] [Indexed: 05/29/2023]
Abstract
This paper presents a patient specific deformable heart model that involves the known electrical and mechanical properties of the cardiac cells and tissue. The whole heart model comprises ten Tusscher's ventricular and Nygren's atrial cell models, the anatomical and electrophysiological model descriptions of the atria (introduced by Harrild et al.) and ventricle (given by Winslow et al.), and the mechanical model of the periodical cardiac contraction and resting phenomena proposed by Moireau et al. During the propagation of the depolarization wave, the kinetic, compositional and rotational anisotropy is handled by the tissue, organ and torso model. The applied patient specific parameters were determined by an evolutionary computation method. An intensive parameter reduction was performed using the abstract formulation of the searching space. This patient specific parameter representation enables the adjustment of deformable model parameters in real-time. The validation process was performed using simultaneously measured ECG and ultrasound image records that were compared with simulated signals and shapes using an abstract, parameterized evaluation criterion.
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Affiliation(s)
- Sándor M Szilágyi
- Sapientia University of Transylvania, Faculty of Technical and Human Sciences, Calea Sighişoarei 1/C, 547367 Corunca, Romania.
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Williams GSB, Smith GD, Sobie EA, Jafri MS. Models of cardiac excitation-contraction coupling in ventricular myocytes. Math Biosci 2010; 226:1-15. [PMID: 20346962 PMCID: PMC5499386 DOI: 10.1016/j.mbs.2010.03.005] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2009] [Revised: 03/09/2010] [Accepted: 03/12/2010] [Indexed: 01/27/2023]
Abstract
Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.
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Affiliation(s)
- George S B Williams
- The Department of Bionformatics and Computational Biology, George Mason University, VA, USA.
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20
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Surovyatkina E, Noble D, Gavaghan D, Sher A. Multistability property in cardiac ionic models of mammalian and human ventricular cells. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2010; 103:131-41. [PMID: 20153355 DOI: 10.1016/j.pbiomolbio.2010.01.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2009] [Accepted: 01/15/2010] [Indexed: 11/16/2022]
Abstract
The underlying mechanisms of irregular cardiac rhythms are still poorly understood. Many experimental and modeling studies are aimed at identifying factors which cause cardiac arrhythmias. However, a lack of understanding of heart rhythm dynamical properties makes it difficult to uncover precise mechanisms of electrical instabilities, and hence to predict the onset of heart rhythm disorders. We review and compare the existing methods of studying cardiac dynamics, including restitution protocol (S1-S2), dynamic restitution protocol and multistability test protocol (S1-CI-S2). We focus on cardiac cell dynamics to elucidate regularities of heart rhythm. We demonstrate the advantages of our newly proposed systematic approach of analysis of cardiac cell dynamics using mammalian Luo Rudy 1991 and human ventricular Ten Tusscher 2006 single cell models under healthy and diseased conditions such as altered K(+) or Ca(2+) related currents. We investigate the role of ionic properties and the shape of an action potential on the nonlinear dynamics of electrical processes in periodically stimulated cardiac cells. We show the existence of multistability property for human ventricular cells. Moreover, the multistability is proposed to be an intrinsic property of cardiac cells, and is also suggested to be one of the mechanisms which could underlie the sudden triggering of life-threatening ventricular arrhythmias in the human heart.
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Affiliation(s)
- Elena Surovyatkina
- Space Dynamics and Data Analysis Department, Space Research Institute, Russian Academy of Sciences, Moscow 117997, Russia.
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Erson E, Cavusoglu M. Design of a framework for modeling, integration and simulation of physiological models. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2010; 2010:1485-1489. [PMID: 21096363 DOI: 10.1109/iembs.2010.5626848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Modeling and simulation of physiological processes deal with the challenges of multiscale models in which coupling is very high within and among scales. Information technology approaches together with related analytical and computational tools will help to deal with these challenges. Physiological Model Simulation, Integration and Modeling Framework, Phy-SIM, provides the modeling environment which will help to cultivate various approaches to deal with the inherent problem of multiscale modeling of physiological systems. In this paper, we present the modular design of Phy-SIM. The proposed layered design of Phy-SIM, separates structure from function in physiological processes advocating modular thinking in developing and integrating physiological models. Moreover, the ontology based architecture will improve the modeling process by the mechanisms to attach anatomical and physiological ontological information to the models. The ultimate aim of the proposed approaches is to enhance the physiological model development and integration processes by providing the tools and mechanisms in Phy-SIM.
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Affiliation(s)
- E Erson
- Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH 44106, USA.
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22
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Bajaj C, Goswami S. Modeling Cardiovascular Anatomy from Patient-Specific Imaging Data. COMPUTATIONAL METHODS IN APPLIED SCIENCES (SPRINGER) 2009; 13:1-28. [PMID: 20871793 PMCID: PMC2943643 DOI: 10.1007/978-1-4020-9086-8_1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Chandrajit Bajaj
- Computational Visualization Center, Institute of Computational Engineering and Sciences, University of Texas, Austin Texas 78712
| | - Samrat Goswami
- Computational Visualization Center, Institute of Computational Engineering and Sciences, University of Texas, Austin Texas 78712
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Soubret A, Helmlinger G, Dumotier B, Bibas R, Georgieva A. Modeling and Simulation of Preclinical Cardiac Safety: Towards an Integrative Framework. Drug Metab Pharmacokinet 2009; 24:76-90. [DOI: 10.2133/dmpk.24.76] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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24
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25
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Bourgeois EB, Fast VG, Collins RL, Gladden JD, Rogers JM. Change in conduction velocity due to fiber curvature in cultured neonatal rat ventricular myocytes. IEEE Trans Biomed Eng 2008; 56:855-61. [PMID: 19272891 DOI: 10.1109/tbme.2008.2007501] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Computer modeling of cardiac propagation suggests that curvature of muscle fibers modulates conduction velocity (CV). The effect could be involved in arrhythmogenesis by altering the dynamics of reentrant wavefronts or by causing propagation block. To verify the existence of this effect experimentally, we measured CV in anisotropic neonatal rat ventricular myocyte monolayers. The orientation of the cells was directed by scratches machined into plastic coverslips. Each substrate contained a region in which scratch radius of curvature varied from 0.25 to 1.0 cm. The CV anisotropy ratio (longitudinal CV/transverse CV in straight fiber regions) was 2.3 +/- 0.3 (n = 38). We initiated wavefronts transverse to fibers with the fibers either curving toward or away from the wavefronts. Action potentials were recorded using a potentiometric dye and a video camera. Propagation was faster (p = 0.0003) when fibers curved toward wavefronts than when fibers curved in the opposite direction. The mean CV difference was 0.38 +/- 0.44 cm/s (n = 24), which is 3.5% of nominal straight fiber transverse CV (11.0 +/- 3.2 cm/s). The effect was also present (p = 0.07) when pacing was slowed from 350 to 500 ms (n = 6). In a control group (n = 8) with uncurved fibers, CV was the same in both directions (p = NS). We conclude that fiber curvature is a factor in modulating cardiac propagation.
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Affiliation(s)
- Elliot B Bourgeois
- Department of Biomedical Engineering, University of Alabama, Birmingham, AL 35294-0019, USA.
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26
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Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors. J Theor Biol 2008; 253:170-88. [DOI: 10.1016/j.jtbi.2008.02.040] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2007] [Revised: 02/29/2008] [Accepted: 02/29/2008] [Indexed: 11/23/2022]
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Southern J, Pitt-Francis J, Whiteley J, Stokeley D, Kobashi H, Nobes R, Kadooka Y, Gavaghan D. Multi-scale computational modelling in biology and physiology. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2008; 96:60-89. [PMID: 17888502 PMCID: PMC7112301 DOI: 10.1016/j.pbiomolbio.2007.07.019] [Citation(s) in RCA: 91] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.
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Affiliation(s)
- James Southern
- Fujitsu Laboratories of Europe Ltd, Hayes Park Central, Hayes End Road, Hayes, Middlesex UB4 8FE, UK.
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28
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Biktashev VN, Suckley R, Elkin YE, Simitev RD. Asymptotic analysis and analytical solutions of a model of cardiac excitation. Bull Math Biol 2007; 70:517-54. [PMID: 18060462 DOI: 10.1007/s11538-007-9267-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2007] [Accepted: 08/08/2007] [Indexed: 11/25/2022]
Abstract
We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble in J. Physiol. 160:317-352, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an "Archetypal Model" with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable "caricature" of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the "caricature" right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model.
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Affiliation(s)
- V N Biktashev
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
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29
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Ahlberg SE, Grenz NA, Ewert DL, Iaizzo PA, Mulligan LJ. Effect of pacing site on systolic mechanical restitution curves in the in vivo canine model. CARDIOVASCULAR ENGINEERING (DORDRECHT, NETHERLANDS) 2007; 7:89-96. [PMID: 17876706 DOI: 10.1007/s10558-007-9033-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
INTRODUCTION Pacing site is known to influence the contractile state of the ventricle. Non-physiologic pacing sites such as the right ventricular apex (RVA) or left ventricular freewall (LVFW) have been shown to decrease the contractile state of normal myocardium, due to abnormal electrical propagation. The impact of pacing at these sites may alter mechanical restitution (MR), a fundamental cardiac property involving the electro-mechanical regulation of contraction. This, in turn, may affect cardiac function. The present study was conducted to determine if pacing site alters the time constant of MR: tau. METHODS AND RESULTS Anesthetized canines (n = 6) were acutely paced at four sites: right atrium (RA), RVA, right ventricular septum (RVS), and LVFW. MR data was captured by the S1-S2 pacing protocol and used to create MR curves, generating a restitution time constant, tau, at each site. No significant difference in tau was found between pacing sites. A linear regression analysis of MR curves revealed that there was no significant difference in slope between pacing sites. CONCLUSION Although pacing site has been found to influence the contractile state of the ventricle, this is the first known study to demonstrate no change in tau in an in vivo preparation. This suggests that alteration of electro-mechanical coupling described by MR is not sufficiently robust to provide insight into pacing site and cardiac function in healthy hearts.
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Affiliation(s)
- Sarah E Ahlberg
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
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30
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Pásek M, Simurda J, Christé G, Orchard CH. Modelling the cardiac transverse-axial tubular system. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2007; 96:226-43. [PMID: 17868782 DOI: 10.1016/j.pbiomolbio.2007.07.021] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The transverse-axial tubular system (TATS) of cardiac ventricular myocytes is a complex network of tubules that arises as invaginations of the surface membrane; it appears to form a specialised region of cell membrane that is particularly important for excitation-contraction coupling. However, much remains unknown about the structure and role of the TATS. In this brief review we use experimental data and computer modelling to address the following key questions: (i) What fraction of the cell membrane is within the TATS? (ii) Is the composition of the TATS membrane the same as the surface membrane? (iii) How good is electrical coupling between the surface and TATS membranes? (iv) What fraction of each current is within the TATS? (v) How important is the complex structure of the TATS network? (vi) What is the effect of current inhomogeneity on lumenal ion concentrations? (vii) Does the TATS contribute to the functional changes observed in heart failure? Although there are many areas in which experimental evidence is lacking, computer models provide a method to assess and predict the possible function of the TATS; such models suggest that although the surface and TATS membranes are electrically well coupled, concentration of ion flux pathways within the TATS, coupled to restricted diffusion, may result in the ionic composition in the TATS lumen being different from that in the bulk extracellular space, and varying with activity and in pathological conditions.
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Affiliation(s)
- M Pásek
- Institute of Thermomechanics, Czech Academy of Science, Branch Brno, Brno, Czech Republic
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31
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Silva HS, Kapela A, Tsoukias NM. A mathematical model of plasma membrane electrophysiology and calcium dynamics in vascular endothelial cells. Am J Physiol Cell Physiol 2007; 293:C277-93. [PMID: 17459942 DOI: 10.1152/ajpcell.00542.2006] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Vascular endothelial cells (ECs) modulate smooth muscle cell (SMC) contractility, assisting in vascular tone regulation. Cytosolic Ca2+ concentration ([Ca2+]i) and membrane potential ( Vm) play important roles in this process by controlling EC-dependent vasoactive signals and intercellular communication. The present mathematical model integrates plasmalemma electrophysiology and Ca2+ dynamics to investigate EC responses to different stimuli and the controversial relationship between [Ca2+]i and Vm. The model contains descriptions for the intracellular balance of major ionic species and the release of Ca2+ from intracellular stores. It also expands previous formulations by including more detailed transmembrane current descriptions. The model reproduces Vm responses to volume-regulated anion channel (VRAC) blockers and extracellular K+ concentration ([K+]o) challenges, predicting 1) that Vm changes upon VRAC blockade are [K+]o dependent and 2) a biphasic response of Vm to increasing [K+]o. Simulations of agonist-induced Ca2+ mobilization replicate experiments under control and Vm hyperpolarization blockade conditions. They show that peak [Ca2+]i is governed by store Ca2+ release while Ca2+ influx (and consequently Vm) impacts more the resting and plateau [Ca2+]i. The Vm sensitivity of rest and plateau [Ca2+]i is dictated by a [Ca2+]i “buffering” system capable of masking the Vm-dependent transmembrane Ca2+ influx. The model predicts plasma membrane Ca2+-ATPase and Ca2+ permeability as main players in this process. The heterogeneous Vm impact on [Ca2+]i may elucidate conflicting reports on how Vm influences EC Ca2+. The present study forms the basis for the development of multicellular EC-SMC models that can assist in understanding vascular autoregulation in health and disease.
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Affiliation(s)
- Haroldo S Silva
- Dept. of Biomedical Engineering, Florida International University, 10555 W. Flagler St., TEC 2674, Miami, FL 33174, USA
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32
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Fraser JA, Huang CLH. Quantitative techniques for steady-state calculation and dynamic integrated modelling of membrane potential and intracellular ion concentrations. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2007; 94:336-72. [PMID: 17129600 DOI: 10.1016/j.pbiomolbio.2006.10.001] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
The membrane potential (E(m)) is a fundamental cellular parameter that is primarily determined by the transmembrane permeabilities and concentration gradients of various ions. However, ion gradients are themselves profoundly influenced by E(m) due to its influence upon transmembrane ion fluxes and cell volume (V(c)). These interrelationships between E(m), V(c) and intracellular ion concentrations make computational modelling useful or necessary in order to guide experimentation and to achieve an integrated understanding of experimental data, particularly in complex, dynamic, multi-compartment systems such as skeletal and cardiac myocytes. A variety of quantitative techniques exist that may assist such understanding, from classical approaches such as the Goldman-Hodgkin-Katz equation and the Gibbs-Donnan equilibrium, to more recent "current-summing" models as exemplified by cardiac myocyte models including those of DiFrancesco & Noble, Luo & Rudy and Puglisi & Bers, or the "charge-difference" modelling technique of Fraser & Huang so far applied to skeletal muscle. In general, the classical approaches provide useful and important insights into the relationships between E(m), V(c) and intracellular ion concentrations at steady state, providing their core assumptions are fully understood, while the more recent techniques permit the modelling of changing values of E(m), V(c) and intracellular ion concentrations. The present work therefore reviews the various approaches that may be used to calculate E(m), V(c) and intracellular ion concentrations with the aim of establishing the requirements for an integrated model that can both simulate dynamic systems and recapitulate the key findings of classical techniques regarding the cellular steady state. At a time when the number of cellular models is increasing at an unprecedented rate, it is hoped that this article will provide a useful and critical analysis of the mathematical techniques fundamental to each of them.
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Affiliation(s)
- James A Fraser
- Physiological Laboratory, Department of Physiology, Development and Neuroscience, University of Cambridge, Downing Street, Cambridge, UK.
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Parallel Solution in Simulation of Cardiac Excitation Anisotropic Propagation. FUNCTIONAL IMAGING AND MODELING OF THE HEART 2007. [DOI: 10.1007/978-3-540-72907-5_18] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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Abstract
Experimentally based models of the heart have been developed since 1960, starting with the discovery and modelling of potassium channels. The early models were based on extensions of the Hodgkin-Huxley nerve impulse equations. The first models including calcium balance and signalling were made in the 1980s and have now reached a high degree of physiological detail. During the 1990s these cell models have been incorporated into anatomically detailed tissue and organ models to create the first virtual organ, the Virtual Heart. With over 40 years of interaction between simulation and experiment, the models are now sufficiently refined to begin to be of use in drug development.
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Affiliation(s)
- Denis Noble
- Department of Physiology, Anatomy and Genetics, Parks Road, Oxford, OX1 3PT, UK.
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Affiliation(s)
- Trey Ideker
- Department of Bioengineering, University of California at San Diego, USA
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Lee J, Smaill B, Smith N. Hodgkin–Huxley type ion channel characterization: An improved method of voltage clamp experiment parameter estimation. J Theor Biol 2006; 242:123-34. [PMID: 16563440 DOI: 10.1016/j.jtbi.2006.02.006] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2005] [Revised: 02/07/2006] [Accepted: 02/10/2006] [Indexed: 11/16/2022]
Abstract
The Hodgkin-Huxley formalism for quantitative characterization of ionic channels is widely used in cellular electrophysiological models. Model parameters for these individual channels are determined from voltage clamp experiments and usually involve the assumption that inactivation process occurs on a time scale which is infinitely slow compared to the activation process. This work shows that such an assumption may lead to appreciable errors under certain physiological conditions and proposes a new numerical approach to interpret voltage clamp experiment results. In simulated experimental protocols the new method was shown to exhibit superior accuracy compared to the traditional least squares fitting methods. With noiseless input data the error in gating variables and time constants was less than 1%, whereas the traditional methods generated upwards of 10% error and predicted incorrect gating kinetics. A sensitivity analysis showed that the new method could tolerate up to approximately 15% perturbation in the input data without unstably amplifying error in the solution. This method could also assist in designing more efficient experimental protocols, since all channel parameters (gating variables, time constants and maximum conductance) could be determined from a single voltage step.
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Affiliation(s)
- Jack Lee
- Bioengineering Institute, Level 6, 70 Symonds Street, University of Auckland, Auckland, New Zealand.
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37
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Affiliation(s)
- Trey Ideker
- Department of Bioengineering, University of California at San Diego, San Diego, USA
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38
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Bayer JD, Beaumont J, Krol A. Laplace-Dirichlet energy field specification for deformable models. an FEM approach to active contour fitting. Ann Biomed Eng 2005; 33:1175-86. [PMID: 16133925 DOI: 10.1007/s10439-005-5624-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2004] [Accepted: 05/02/2005] [Indexed: 11/26/2022]
Abstract
The construction of large scale computer models for complex biological systems requires the fitting of curves or surfaces to anatomical data sets. Algorithms recently developed to perform this task are based on the displacement of an initial model contour. There are several problems associated with this approach. Here we present improvements which eliminate the (i) sensitivity to the initial model position and shape; (ii) existence of local minima or maxima in the field used to displace the model; and (iii) presence of multiple solutions in the rules governing model displacement. Key elements of our algorithm are first that both the energy field used to displace the model and the model displacement itself are governed by partial differential equations. Secondly, we approximate the model with a polygonal contour which facilitates accurate displacement. Tests performed against cases that are known to be problematic show that our algorithm can fit complex data sets entirely automatically.
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Affiliation(s)
- Jason D Bayer
- Department of Radiology, Upstate Medical University of SUNY, Syracuse, NY 13210, USA
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39
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Patel SP, Campbell DL. Transient outward potassium current, 'Ito', phenotypes in the mammalian left ventricle: underlying molecular, cellular and biophysical mechanisms. J Physiol 2005; 569:7-39. [PMID: 15831535 PMCID: PMC1464208 DOI: 10.1113/jphysiol.2005.086223] [Citation(s) in RCA: 147] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Revised: 03/07/2005] [Accepted: 04/13/2005] [Indexed: 11/08/2022] Open
Abstract
At least two functionally distinct transient outward K(+) current (I(to)) phenotypes can exist across the free wall of the left ventricle (LV). Based upon their voltage-dependent kinetics of recovery from inactivation, these two phenotypes are designated 'I(to,fast)' (recovery time constants on the order of tens of milliseconds) and 'I(to,slow)' (recovery time constants on the order of thousands of milliseconds). Depending upon species, either I(to,fast), I(to,slow) or both current phenotypes may be expressed in the LV free wall. The expression gradients of these two I(to) phenotypes across the LV free wall are typically heterogeneous and, depending upon species, may consist of functional phenotypic gradients of both I(to,fast) and I(to,slow) and/or density gradients of either phenotype. We review the present evidence (molecular, biophysical, electrophysiological and pharmacological) for Kv4.2/4.3 alpha subunits underlying LV I(to,fast) and Kv1.4 alpha subunits underlying LV I(to,slow) and speculate upon the potential roles of each of these currents in determining frequency-dependent action potential characteristics of LV subepicardial versus subendocardial myocytes in different species. We also review the possible functional implications of (i) ancillary subunits that regulate Kv1.4 and Kv4.2/4.3 (Kvbeta subunits, DPPs), (ii) KChIP2 isoforms, (iii) spider toxin-mediated block of Kv4.2/4.3 (Heteropoda toxins, phrixotoxins), and (iv) potential mechanisms of modulation of I(to,fast) and I(to,slow) by cellular redox state, [Ca(2)(+)](i) and kinase-mediated phosphorylation. I(to) phenotypic activation and state-dependent gating models and molecular structure-function relationships are also discussed.
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Affiliation(s)
- Sangita P Patel
- Department of Physiology and Biophysics, University at Buffalo, State University of New York, NY 14214-3078, USA.
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40
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Helm P, Beg MF, Miller MI, Winslow RL. Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging. Ann N Y Acad Sci 2005; 1047:296-307. [PMID: 16093505 DOI: 10.1196/annals.1341.026] [Citation(s) in RCA: 199] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
The ventricular myocardium is known to exhibit a complex spatial organization, with fiber orientation varying as a function of transmural location. It is now well established that diffusion tensor magnetic resonance imaging (DTMRI) may be used to measure this fiber orientation at high spatial resolution. Cardiac fibers are also known to be organized in sheets with surface orientation varying throughout the ventricles. This article reviews results on use of DTMRI for measuring ventricular fiber orientation, as well as presents new results providing strong evidence that the tertiary eigenvector of the diffusion tensor is aligned locally with the cardiac sheet surface normal. Considered together, these data indicate that DTMRI may be used to reconstruct both ventricular fiber and sheet organization. This article also presents the large deformation diffeomorphic metric mapping (LDDMM) algorithm and shows that this algorithm may be used to bring ensembles of imaged and reconstructed hearts into correspondence (e.g., registration) so that variability of ventricular geometry, fiber, and sheet orientation may be quantified. Ventricular geometry and fiber structure is known to be remodeled in a range of disease processes; however, descriptions of this remodeling have remained subjective and qualitative. We anticipate that use of DTMRI for reconstruction of ventricular anatomy coupled with application of the LDDMM method for image volume registration will enable the detection and quantification of changes in cardiac anatomy that are characteristic of specific disease processes in the heart. Finally, we show that epicardial electrical mapping and DTMRI imaging may be performed in the same hearts. The anatomic data may then be used to simulate electrical conduction in a computational model of the very same heart that was mapped electrically. This facilitates direct comparison and testing of model versus experimental results and opens the door to quantitative measurement, modeling, and analysis of the ways in which remodeling of ventricular microanatomy influences electrical conduction in the heart.
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Affiliation(s)
- Patrick Helm
- The Center for Cardiovascular Bioinformatics & Modeling, The Johns Hopkins University School of Medicine and Whiting School of Engineering, Baltimore, Maryland 21218, USA
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Demir SS. Computational modeling of cardiac ventricular action potentials in rat and mouse: review. ACTA ACUST UNITED AC 2005; 54:523-30. [PMID: 15760484 DOI: 10.2170/jjphysiol.54.523] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Little is known about the ionic mechanisms underlying the action potential heterogeneity in ventricle-associated healthy and disease conditions, even though five decades of histological, electrophysiological, pharmacological, and biochemical investigations exist. The computational modeling in murine ventricular myocytes can complement our knowledge of the experimental data and provide us with more quantitative descriptions in understanding different conditions related to normal and disease conditions. This paper initially reviews the theoretical modeling for cardiac ventricular action potentials of various species and the related experimental work. It then presents the progress of the computational modeling of cardiac ventricular cells for normal, diabetic, and spontaneously hypertensive rats. The paper also introduces recent modeling efforts for the action potential heterogeneity in mouse ventricular cells. The computational insights gained into the ionic mechanisms in rodents will continue to enhance our understanding of the heart and provide us with new knowledge for future studies to treat cardiac diseases in children and adults. Because the dissemination of computational models is very important, we continue to disseminate these models by iCell, the interactive cell modeling resource. iCell (http://ssd1.bme.memphis.edu/icell/) has been developed as a simulation-based teaching and learning tool for electrophysiology and contains JAVA applets that present models of various cardiac cells and neurons and simulation data of their bioelectric activities at cellular level.
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Affiliation(s)
- Semahat S Demir
- Biomedical Engineering & Research to Aid Persons with Disabilities Program, Division of Bioengineering and Environmental Systems, National Science Foundation, Arlington, VA, USA.
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Watanabe H, Sugiura S, Kafuku H, Hisada T. Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophys J 2005; 87:2074-85. [PMID: 15345582 PMCID: PMC1304609 DOI: 10.1529/biophysj.103.035840] [Citation(s) in RCA: 177] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
To relate the subcellular molecular events to organ level physiology in heart, we have developed a three-dimensional finite-element-based simulation program incorporating the cellular mechanisms of excitation-contraction coupling and its propagation, and simulated the fluid-structure interaction involved in the contraction and relaxation of the human left ventricle. The FitzHugh-Nagumo model and four-state model representing the cross-bridge kinetics were adopted for cellular model. Both ventricular wall and blood in the cavity were modeled by finite element mesh. An arbitrary Lagrangian Eulerian finite element method with automatic mesh updating has been formulated for large domain changes, and a strong coupling strategy has been taken. Using electrical analog of pulmonary circulation and left atrium as a preload and the windkessel model as an afterload, dynamics of ventricular filling as well as ejection was simulated. We successfully reproduced the biphasic filling flow consisting of early rapid filling and atrial contraction similar to that reported in clinical observation. Furthermore, fluid-structure analysis enabled us to analyze the wave propagation velocity of filling flow. This simulator can be a powerful tool for establishing a link between molecular abnormality and the clinical disorder at the macroscopic level.
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Affiliation(s)
- Hiroshi Watanabe
- Computational Biomechanics Division, Institute of Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
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Abstract
Models of the heart have been developed since 1960, starting with the discovery and modeling of potassium channels. The first models of calcium balance were made in the 1980s and have now reached a high degree of physiological detail. During the 1990s, these cell models were incorporated into anatomically detailed tissue and organ models.
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Affiliation(s)
- Denis Noble
- University Laboratory of Physiology Oxford OX1 3PT, UK.
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Pollard AE, Smith WM, Barr RC. Feasibility of cardiac microimpedance measurement using multisite interstitial stimulation. Am J Physiol Heart Circ Physiol 2004; 287:H2402-11. [PMID: 15284069 DOI: 10.1152/ajpheart.00289.2004] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
This study was designed to test the hypothesis that analyses of central interstitial potential differences recorded during multisite stimulation with a set of interstitial electrodes provide sufficient data for accurate measurement of cardiac microimpedances. On theoretical grounds, interstitial current injected and removed using electrodes in close proximity does not cross the membrane, whereas equilibration of intracellular and interstitial potentials occurs distant from electrodes widely separated. Multisite interstitial stimulation should therefore give rise to interstitial potential differences recorded centrally that depend on intracellular and interstitial microimpedances, allowing independent measurement. Simulations of multisite stimulation with fine (25 microm) and wide (400 microm) spacing in one-dimensional models that included Luo-Rudy dynamic membrane equations were performed. Constant interstitial and intracellular microimpedances were prescribed for initial analyses. Discrete myoplasmic and gap-junctional components were prescribed intracellularly in later simulations. With constant microimpedances, multisite stimulation using 29 total electrode combinations allowed interstitial and intracellular microimpedance measurements at errors of 0.30% and 0.34%, respectively, with errors of 0.05% and 0.40% achieved using 6 combinations and 10 total electrodes. With discrete myoplasmic and junctional components, comparable accuracy was maintained following adjustments to the junctions to reflect uncoupling. This allowed uncoupling to be quantified as relative increases in total junctional resistance. Our findings suggest development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.
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Affiliation(s)
- Andrew E Pollard
- Cardiac Rhythm Management Laboratory, Univ. of Alabama at Birmingham, Volker Hall B140, 1670 University Blvd., Birmingham, AL 35294, USA.
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Demir SS. The significance of computational modelling in murine cardiac ventricular cells. Appl Bionics Biomech 2004. [DOI: 10.1533/abib.2004.1.2.107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Belik ME, Usyk TP, McCulloch AD. Computational Methods for Cardiac Electrophysiology. HANDBOOK OF NUMERICAL ANALYSIS 2004. [DOI: 10.1016/s1570-8659(03)12002-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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Pandit SV, Giles WR, Demir SS. A mathematical model of the electrophysiological alterations in rat ventricular myocytes in type-I diabetes. Biophys J 2003; 84:832-41. [PMID: 12547767 PMCID: PMC1302663 DOI: 10.1016/s0006-3495(03)74902-9] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Our mathematical model of the rat ventricular myocyte (Pandit et al., 2001) was utilized to explore the ionic mechanism(s) that underlie the altered electrophysiological characteristics associated with the short-term model of streptozotocin-induced, type-I diabetes. The simulations show that the observed reductions in the Ca(2+)-independent transient outward K(+) current (I(t)) and the steady-state outward K(+) current (I(ss)), along with slowed inactivation of the L-type Ca(2+) current (I(CaL)), can result in the prolongation of the action potential duration, a well-known experimental finding. In addition, the model demonstrates that the slowed reactivation kinetics of I(t) in diabetic myocytes can account for the more pronounced rate-dependent action potential duration prolongation in diabetes, and that a decrease in the electrogenic Na(+)-K(+) pump current (I(NaK)) results in a small depolarization in the resting membrane potential (V(rest)). This depolarization reduces the availability of the Na(+) channels (I(Na)), thereby resulting in a slower upstroke (dV/dt(max)) of the diabetic action potential. Additional simulations suggest that a reduction in the magnitude of I(CaL), in combination with impaired sarcoplasmic reticulum uptake can lead to a decreased sarcoplasmic reticulum Ca(2+) load. These factors contribute to characteristic abnormal [Ca(2+)](i) homeostasis (reduced peak systolic value and rate of decay) in myocytes from diabetic animals. In combination, these simulation results provide novel information and integrative insights concerning plausible ionic mechanisms for the observed changes in cardiac repolarization and excitation-contraction coupling in rat ventricular myocytes in the setting of streptozotocin-induced, type-I diabetes.
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Affiliation(s)
- Sandeep V Pandit
- Joint Graduate Program in Biomedical Engineering, The University of Memphis, Memphis, Tennessee 38152-3210, USA
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Abstract
Mathematical models of the heart have developed over a period of about 40 years. Cell types in all regions of the heart have been modelled and they are now being incorporated into anatomically detailed models of the whole organ. This combination is leading to the creation of the first 'virtual organ,' which is being used in drug discovery and testing, and in simulating the action of devices, such as cardiac defibrillators. Simulation is a necessary tool of analysis in attempting to understand biological complexity. We often learn as much from the failures as from the successes of mathematical models. It is the iterative interaction between experiment and simulation that is important. Examples are given where this process has been instrumental in some of the major advances in the field.
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Affiliation(s)
- Denis Noble
- University Laboratory of Physiology, Parks Road, Oxford OX1 3PT, UK.
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Mazhari R, Nuss HB, Armoundas AA, Winslow RL, Marbán E. Ectopic expression of KCNE3 accelerates cardiac repolarization and abbreviates the QT interval. J Clin Invest 2002; 109:1083-90. [PMID: 11956246 PMCID: PMC150950 DOI: 10.1172/jci15062] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Regulatory subunit KCNE3 (E3) interacts with KCNQ1 (Q1) in epithelia, regulating its activation kinetics and augmenting current density. Since E3 is expressed weakly in the heart, we hypothesized that ectopic expression of E3 in cardiac myocytes might abbreviate action potential duration (APD) by interacting with Q1 and augmenting the delayed rectifier current (I(K)). Thus, we transiently coexpressed E3 with Q1 and KCNE1 (E1) in Chinese hamster ovary cells and found that E3 coexpression increased outward current at potentials by > or = -80 mV and accelerated activation. We then examined the changes in cardiac electrophysiology following injection of adenovirus-expressed E3 into the left ventricular cavity of guinea pigs. After 72 hours, the corrected QT interval of the electrocardiogram was reduced by approximately 10%. APD was reduced by >3-fold in E3-transduced cells relative to controls, while E-4031-insensitive I(K) and activation kinetics were significantly augmented. Based on quantitative modeling of a transmural cardiac segment, we demonstrate that the degree of QT interval abbreviation observed results from electrotonic interactions in the face of limited transduction efficiency and that heterogeneous transduction of E3 may actually potentiate arrhythmias. Provided that fairly homogeneous ectopic ventricular expression of regulatory subunits can be achieved, this approach may be useful in enhancing repolarization and in treating long QT syndrome.
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Affiliation(s)
- Reza Mazhari
- Department of Medicine, Institute of Molecular Cardiobiology, Johns Hopkins University, 720 Rutland Avenue, Baltimore, MD 21205, USA
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