51
|
Weise LD, Panfilov AV. A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics. PLoS One 2013; 8:e59317. [PMID: 23527160 PMCID: PMC3602082 DOI: 10.1371/journal.pone.0059317] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2012] [Accepted: 02/13/2013] [Indexed: 11/24/2022] Open
Abstract
We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.
Collapse
Affiliation(s)
- Louis D Weise
- Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands.
| | | |
Collapse
|
52
|
OKADA JUNICHI, SASAKI TERUYOSHI, WASHIO TAKUMI, YAMASHITA HIROSHI, KARIYA TARO, IMAI YASUSHI, NAKAGAWA MACHIKO, KADOOKA YOSHIMASA, NAGAI RYOZO, HISADA TOSHIAKI, SUGIURA SEIRYO. Patient Specific Simulation of Body Surface ECG using the Finite Element Method. PACING AND CLINICAL ELECTROPHYSIOLOGY: PACE 2013; 36:309-21. [DOI: 10.1111/pace.12057] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2012] [Revised: 09/22/2012] [Accepted: 10/23/2012] [Indexed: 11/30/2022]
Affiliation(s)
- JUN-ICHI OKADA
- Department of Human and Engineered Environmental Studies; Graduate School of Frontier Sciences; The University of Tokyo; Kashiwanoha; Japan
| | - TERUYOSHI SASAKI
- Department of Human and Engineered Environmental Studies; Graduate School of Frontier Sciences; The University of Tokyo; Kashiwanoha; Japan
| | - TAKUMI WASHIO
- Department of Human and Engineered Environmental Studies; Graduate School of Frontier Sciences; The University of Tokyo; Kashiwanoha; Japan
| | - HIROSHI YAMASHITA
- Department of Cardiovascular Medicine; School of Medicine; The University of Tokyo; Bunkyo-ku; Tokyo; Japan
| | - TARO KARIYA
- Department of Cardiovascular Medicine; School of Medicine; The University of Tokyo; Bunkyo-ku; Tokyo; Japan
| | - YASUSHI IMAI
- Department of Cardiovascular Medicine; School of Medicine; The University of Tokyo; Bunkyo-ku; Tokyo; Japan
| | | | | | | | - TOSHIAKI HISADA
- Department of Human and Engineered Environmental Studies; Graduate School of Frontier Sciences; The University of Tokyo; Kashiwanoha; Japan
| | - SEIRYO SUGIURA
- Department of Human and Engineered Environmental Studies; Graduate School of Frontier Sciences; The University of Tokyo; Kashiwanoha; Japan
| |
Collapse
|
53
|
Barrabés JA, Figueras J, Candell-Riera J, Agulló L, Inserte J, Garcia-Dorado D. La distensión de la región isquémica predice una mayor inducibilidad de fibrilación ventricular tras la oclusión coronaria en el modelo porcino. Rev Esp Cardiol 2013. [DOI: 10.1016/j.recesp.2012.08.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
54
|
Takahashi K, Kakimoto Y, Toda K, Naruse K. Mechanobiology in cardiac physiology and diseases. J Cell Mol Med 2013; 17:225-32. [PMID: 23441631 PMCID: PMC3822585 DOI: 10.1111/jcmm.12027] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2012] [Accepted: 01/11/2013] [Indexed: 11/28/2022] Open
Abstract
Mechanosensitivity is essential for heart function just as for all other cells and organs in the body, and it is involved in both normal physiology and diseases processes of the cardiovascular system. In this review, we have outlined the relationship between mechanosensitivity and heart physiology, including the Frank-Starling law of the heart and mechanoelectric feedback. We then focused on molecules involved in mechanotransduction, particularly mechanosensitive ion channels. We have also discussed the involvement of mechanosensitivity in heart diseases, such as arrhythmias, hypertrophy and ischaemic heart disease. Finally, mechanobiology in cardiogenesis is described with regard to regenerative medicine.
Collapse
Affiliation(s)
- Ken Takahashi
- Department of Cardiovascular Physiology, Graduate School of Medicine Dentistry and Pharmaceutical Sciences, Okayama University, Okayama, Japan.
| | | | | | | |
Collapse
|
55
|
Simkó J, Szabó Z, Barta K, Ujvárosi D, Nánási P, Lőrincz I. [Molecular and genetic background of sudden cardiac death]. Orv Hetil 2012; 153:1967-83. [PMID: 23220363 DOI: 10.1556/oh.2012.29498] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Despite recent findings on the functional, structural and genetic background of sudden cardiac death, the incidence is still relatively high in the entire population. A thorough knowledge on susceptibility, as well as pathophysiology behind the development of malignant arrhythmias will help us to identify individuals at risk and prevent sudden cardiac death. This article presents a review of the current literature on the role of altered intracellular Ca2+ handling, acute myocardial ischaemia, cardiac autonomic innervation, renin-angiotensin-aldosterone system, monogenic and complex heritability in the pathogenesis of sudden cardiac death.
Collapse
Affiliation(s)
- József Simkó
- Miskolci Semmelweis Ignác Egészségügyi Központ és Egyetemi Oktatókórház Nonprofit Kft. Belgyógyászati Intézet, Kardiológiai Osztály Miskolc.
| | | | | | | | | | | |
Collapse
|
56
|
Trayanova NA. Computational cardiology: the heart of the matter. ISRN CARDIOLOGY 2012; 2012:269680. [PMID: 23213566 PMCID: PMC3505657 DOI: 10.5402/2012/269680] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/16/2012] [Accepted: 09/06/2012] [Indexed: 12/19/2022]
Abstract
This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.
Collapse
Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, 3400 North Charles Street, Hackerman Hall Room 216, Baltimore, MD 21218, USA
| |
Collapse
|
57
|
Distension of the ischemic region predicts increased ventricular fibrillation inducibility following coronary occlusion in swine. ACTA ACUST UNITED AC 2012; 66:171-6. [PMID: 24775450 DOI: 10.1016/j.rec.2012.08.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2012] [Accepted: 08/01/2012] [Indexed: 11/21/2022]
Abstract
INTRODUCTION AND OBJECTIVES Distension of the ischemic region has been related to an increased incidence of spontaneous ventricular arrhythmias following coronary occlusion. This study analyzed whether regional ischemic distension predicts increased ventricular fibrillation inducibility after coronary occlusion in swine. METHODS In 18 anesthetized, open-chest pigs, the left anterior descending coronary artery was ligated for 60 min. Myocardial segment length in the ischemic region was monitored by means of ultrasonic crystals. Programmed stimulation was applied at baseline and then continuously between 10 and 60 min after coronary occlusion. RESULTS Coronary occlusion induced a rapid increase in end-diastolic length in the ischemic region, which reached 109.4% (0.9%) of baseline values 10 min after occlusion (P<.001). On average, 6.6 (0.5) stimulation protocols were completed and 5.4 (0.6) ventricular fibrillation episodes induced between 10 and 60 min of coronary occlusion. Neither baseline serum potassium levels nor the size of the ischemic region were significantly related to ventricular fibrillation inducibility. In contrast, the increase in end-diastolic length 10 min after coronary occlusion was associated directly (r=0.67; P=.002) with the number of induced ventricular fibrillation episodes and inversely (r=-0.55; P=.018) with the number of extrastimuli needed for ventricular fibrillation induction. CONCLUSIONS Regional ischemic expansion predicts increased ventricular fibrillation inducibility following coronary occlusion. These results highlight the potential influence of mechanical factors, acting not only on the triggers but also on the substrate, in the genesis of malignant ventricular arrhythmias during acute ischemia.
Collapse
|
58
|
Increased mechanically-induced ectopy in the hypertrophied heart. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2012; 110:331-9. [DOI: 10.1016/j.pbiomolbio.2012.07.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2012] [Accepted: 07/11/2012] [Indexed: 02/04/2023]
|
59
|
Circulation Research
Thematic Synopsis. Circ Res 2012. [DOI: 10.1161/circresaha.112.280024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
60
|
Friedrich O, Wagner S, Battle AR, Schürmann S, Martinac B. Mechano-regulation of the beating heart at the cellular level--mechanosensitive channels in normal and diseased heart. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2012; 110:226-38. [PMID: 22959495 DOI: 10.1016/j.pbiomolbio.2012.08.009] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2012] [Accepted: 08/09/2012] [Indexed: 01/22/2023]
Abstract
The heart as a contractile hollow organ finely tunes mechanical parameters such as stroke volume, stroke pressure and cardiac output according to filling volumes, filling pressures via intrinsic and neuronal routes. At the cellular level, cardiomyocytes in beating hearts are exposed to large mechanical stress during successive heart beats. Although the mechanisms of excitation-contraction coupling are well established in mammalian heart cells, the putative contribution of mechanosensitive channels to Ca²⁺ homeostasis, Ca²⁺ signaling and force generation has been primarily investigated in relation to heart disease states. For instance, transient receptor potential channels (TRPs) are up-regulated in animal models of congestive heart failure or hypertension models and seem to play a vital role in pathological Ca²⁺ overload to cardiomyocytes, thus aggravating the pathology of disease at the cellular level. Apart from that, the contribution of mechanosensitive channels (MsC) in the normal beating heart to the downstream force activation cascade has not been addressed. We present an overview of the current literature and concepts of mechanosensitive channel involvement in failing hearts and cardiomyopathies and novel data showing a likely contribution of Ca²⁺ influx via mechanosensitive channels in beating normal cardiomyocytes during systolic shortening.
Collapse
Affiliation(s)
- Oliver Friedrich
- Institute of Medical Biotechnology, Friedrich-Alexander-University Erlangen-Nuremberg, Paul-Gordan-Str. 3, 91052 Erlangen, Germany
| | | | | | | | | |
Collapse
|
61
|
Roberts BN, Yang PC, Behrens SB, Moreno JD, Clancy CE. Computational approaches to understand cardiac electrophysiology and arrhythmias. Am J Physiol Heart Circ Physiol 2012; 303:H766-83. [PMID: 22886409 DOI: 10.1152/ajpheart.01081.2011] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.
Collapse
Affiliation(s)
- Byron N Roberts
- Tri-Institutional MD-PhD Program, Physiology, Biophysics and Systems Biology Graduate Program, Weill Cornell Medical College/The Rockefeller University/Sloan-Kettering Cancer Institute, Weill Medical College of Cornell University, New York, New York, USA
| | | | | | | | | |
Collapse
|
62
|
Gauthier LD, Greenstein JL, Winslow RL. Toward an integrative computational model of the Guinea pig cardiac myocyte. Front Physiol 2012; 3:244. [PMID: 22783206 PMCID: PMC3389778 DOI: 10.3389/fphys.2012.00244] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2012] [Accepted: 06/14/2012] [Indexed: 11/22/2022] Open
Abstract
The local control theory of excitation-contraction (EC) coupling asserts that regulation of calcium (Ca2+) release occurs at the nanodomain level, where openings of single L-type Ca2+ channels (LCCs) trigger openings of small clusters of ryanodine receptors (RyRs) co-localized within the dyad. A consequence of local control is that the whole-cell Ca2+ transient is a smooth continuous function of influx of Ca2+ through LCCs. While this so-called graded release property has been known for some time, its functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca2+ release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally observed causal relationship between action potential (AP) shape and timing of Ca2+ and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca2+ transients, thus influencing tissue level electromechanical function.
Collapse
Affiliation(s)
- Laura Doyle Gauthier
- Department of Biomedical Engineering, Institute for Computational Medicine, The Johns Hopkins University School of Medicine and Whiting School of Engineering Baltimore, MD, USA
| | | | | |
Collapse
|
63
|
Weise LD, Panfilov AV. Emergence of spiral wave activity in a mechanically heterogeneous reaction-diffusion-mechanics system. PHYSICAL REVIEW LETTERS 2012; 108:228104. [PMID: 23003658 DOI: 10.1103/physrevlett.108.228104] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2012] [Indexed: 06/01/2023]
Abstract
We perform a numerical study of emergent spiral wave activity in a two-dimensional reaction-diffusion-mechanics medium with a regional inhomogeneity in active and passive mechanical properties. We find that self-sustaining spiral wave activity emerges for a wide range of mechanical parameters of the inhomogeneity via five mechanisms. We classify these mechanisms, relate them to parameters of the inhomogeneity, and discuss how these results can be applied to understand the onset of cardiac arrhythmias due to regional mechanical heterogeneity.
Collapse
Affiliation(s)
- L D Weise
- Department of Theoretical Biology, Utrecht University, Padualaan 8, Utrecht, 3584 CH, The Netherlands
| | | |
Collapse
|
64
|
Kuijpers NHL, Hermeling E, Bovendeerd PHM, Delhaas T, Prinzen FW. Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts: insight from adaptive computer models. J Cardiovasc Transl Res 2012; 5:159-69. [PMID: 22271009 PMCID: PMC3294221 DOI: 10.1007/s12265-012-9346-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/13/2011] [Accepted: 01/04/2012] [Indexed: 12/13/2022]
Abstract
Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.
Collapse
Affiliation(s)
- Nico H. L. Kuijpers
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Evelien Hermeling
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Peter H. M. Bovendeerd
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Tammo Delhaas
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Frits W. Prinzen
- Department of Physiology, Maastricht University, Maastricht, The Netherlands
| |
Collapse
|
65
|
Miura M, Hattori T, Murai N, Nagano T, Nishio T, Boyden PA, Shindoh C. Regional increase in extracellular potassium can be arrhythmogenic due to nonuniform muscle contraction in rat ventricular muscle. Am J Physiol Heart Circ Physiol 2012; 302:H2301-9. [PMID: 22447939 DOI: 10.1152/ajpheart.01161.2011] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
In the ischemic myocardium, extracellular potassium ([K(+)](o)) increases to ≥20 mmol/l. To determine how lethal arrhythmias occur during ischemia, we investigated whether the increased spatial pattern of [K(+)](o), i.e., a regional or a global increase, affects the incidence of arrhythmias. Force, sarcomere length, membrane potential, and nonuniform intracellular Ca(2+) ([Ca(2+)](i)) were measured in rat ventricular trabeculae. A "regional" or "global" increase in [K(+)](o) was produced by exposing a restricted region of muscle to a jet of 30 mmol/l KCl or by superfusing trabeculae with a solution containing 30 mmol/l KCl, respectively. The increase in [Ca(2+)](i) (Ca(CW)) during Ca(2+) waves was measured (24°C, 3.0 mmol/l [Ca(2+)](o)). A regional increase in [K(+)](o) caused nonuniform [Ca(2+)](i) and contraction. In the presence of isoproterenol, the regional increase in [K(+)](o) induced sustained arrhythmias in 10 of 14 trabeculae, whereas the global increase did not induce such arrhythmias. During sustained arrhythmias, Ca(2+) surged within the jet-exposed region. In the absence of isoproterenol, the regional increase in [K(+)](o) increased Ca(CW), whereas the global increase decreased it. This increase in Ca(CW) with the regional increase in [K(+)](o) was not suppressed by 100 μmol/l streptomycin, whereas it was suppressed by 1) a combination of 10 μmol/l cilnidipine and 3 μmol/l SEA0400; 2) 20 mmol/l 2,3-butanedione monoxime; and 3) 10 μmol/l blebbistatin. A regional but not a global increase in [K(+)](o) induces sustained arrhythmias, probably due to nonuniform excitation-contraction coupling. The same mechanism may underlie arrhythmias during ischemia.
Collapse
Affiliation(s)
- Masahito Miura
- Department of Clinical Physiology, Health Science, Tohoku University Graduate School of Medicine, Sendai, Japan.
| | | | | | | | | | | | | |
Collapse
|
66
|
Electromechanical wave imaging for noninvasive mapping of the 3D electrical activation sequence in canines and humans in vivo. J Biomech 2012; 45:856-64. [PMID: 22284425 DOI: 10.1016/j.jbiomech.2011.11.027] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/02/2011] [Indexed: 11/22/2022]
Abstract
Cardiovascular diseases rank as America's primary killer, claiming the lives of over 41% of more than 2.4 million Americans. One of the main reasons for this high death toll is the severe lack of effective imaging techniques for screening, early detection and localization of an abnormality detected on the electrocardiogram (ECG). The two most widely used imaging techniques in the clinic are CT angiography and echocardiography with limitations in speed of application and reliability, respectively. It has been established that the mechanical and electrical properties of the myocardium change dramatically as a result of ischemia, infarction or arrhythmia; both at their onset and after survival. Despite these findings, no imaging technique currently exists that is routinely used in the clinic and can provide reliable, non-invasive, quantitative mapping of the regional, mechanical, and electrical function of the myocardium. Electromechanical Wave Imaging (EWI) is an ultrasound-based technique that utilizes the electromechanical coupling and its associated resulting strain to infer to the underlying electrical function of the myocardium. The methodology of EWI is first described and its fundamental performance is presented. Subsequent in vivo canine and human applications are provided that demonstrate the applicability of Electromechanical Wave Imaging in differentiating between sinus rhythm and induced pacing schemes as well as mapping arrhythmias. Preliminary validation with catheter mapping is also provided and transthoracic electromechanical mapping in all four chambers of the human heart is also presented demonstrating the potential of this novel methodology to noninvasively infer to both the normal and pathological electrical conduction of the heart.
Collapse
|
67
|
Abstract
The link between experimental data and biophysically based mathematical models is key to computational simulation meeting its potential to provide physiological insight. However, despite the importance of this link, scrutiny and analysis of the processes by which models are parameterised from data are currently lacking. While this situation is common to many areas of physiological modelling, to provide a concrete context, we use examples drawn from detailed models of cardiac electro-mechanics. Using this biophysically detailed cohort of models we highlight the specific issues of model parameterization and propose this process can be separated into three stages: observation, fitting and validation. Finally, future research challenges and directions in this area are discussed.
Collapse
Affiliation(s)
- S A Niederer
- Imaging Sciences & Biomedical Engineering Division, King's College London, London, UK
| | | |
Collapse
|
68
|
Lim KM, Constantino J, Gurev V, Zhu R, Shim EB, Trayanova NA. Comparison of the effects of continuous and pulsatile left ventricular-assist devices on ventricular unloading using a cardiac electromechanics model. J Physiol Sci 2012; 62:11-9. [PMID: 22076841 PMCID: PMC3313670 DOI: 10.1007/s12576-011-0180-9] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2011] [Accepted: 10/23/2011] [Indexed: 01/24/2023]
Abstract
Left ventricular-assist devices (LVADs) are used to supply blood to the body of patients with heart failure. Pressure unloading is greater for counter-pulsating LVADs than for continuous LVADs. However, several clinical trials have demonstrated that myocardial recovery is similar for both types of LVAD. This study examined the contractile energy consumption of the myocardium with continuous and counter-pulsating LVAD support to ascertain the effect of the different LVADs on myocardial recovery. We used a three-dimensional electromechanical model of canine ventricles, with models of the circulatory system and an LVAD. We compared the left ventricular peak pressure (LVPP) and contractile ATP consumption between pulsatile and continuous LVADs. With the continuous and counter-pulsating LVAD, the LVPP decreased to 46 and 10%, respectively, and contractile ATP consumption decreased to 60 and 50%. The small difference between the contractile ATP consumption of these two types of LVAD may explain the comparable effects of the two types on myocardial recovery.
Collapse
Affiliation(s)
- Ki Moo Lim
- Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Kangwon-do Republic of Korea
| | - Jason Constantino
- Institute for Computational Medicine and the Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
| | - Viatcheslav Gurev
- Institute for Computational Medicine and the Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
| | - Renjun Zhu
- Institute for Computational Medicine and the Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
| | - Eun Bo Shim
- Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Kangwon-do Republic of Korea
| | - Natalia A. Trayanova
- Institute for Computational Medicine and the Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
| |
Collapse
|
69
|
Wall ST, Guccione JM, Ratcliffe MB, Sundnes JS. Electromechanical feedback with reduced cellular connectivity alters electrical activity in an infarct injured left ventricle: a finite element model study. Am J Physiol Heart Circ Physiol 2011; 302:H206-14. [PMID: 22058157 DOI: 10.1152/ajpheart.00272.2011] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Myocardial infarction (MI) significantly alters the structure and function of the heart. As abnormal strain may drive heart failure and the generation of arrhythmias, we used computational methods to simulate a left ventricle with an MI over the course of a heartbeat to investigate strains and their potential implications to electrophysiology. We created a fully coupled finite element model of myocardial electromechanics consisting of a cellular physiological model, a bidomain electrical diffusion solver, and a nonlinear mechanics solver. A geometric mesh built from magnetic resonance imaging (MRI) measurements of an ovine left ventricle suffering from a surgically induced anteroapical infarct was used in the model, cycled through the cardiac loop of inflation, isovolumic contraction, ejection, and isovolumic relaxation. Stretch-activated currents were added as a mechanism of mechanoelectric feedback. Elevated fiber and cross fiber strains were observed in the area immediately adjacent to the aneurysm throughout the cardiac cycle, with a more dramatic increase in cross fiber strain than fiber strain. Stretch-activated channels decreased action potential (AP) dispersion in the remote myocardium while increasing it in the border zone. Decreases in electrical connectivity dramatically increased the changes in AP dispersion. The role of cross fiber strain in MI-injured hearts should be investigated more closely, since results indicate that these are more highly elevated than fiber strain in the border of the infarct. Decreases in connectivity may play an important role in the development of altered electrophysiology in the high-stretch regions of the heart.
Collapse
Affiliation(s)
- Samuel T Wall
- Center for Biomedical Computing, Simula Research Laboratory, Oslo, Norway.
| | | | | | | |
Collapse
|
70
|
Trayanova NA, Rice JJ. Cardiac electromechanical models: from cell to organ. Front Physiol 2011; 2:43. [PMID: 21886622 PMCID: PMC3154390 DOI: 10.3389/fphys.2011.00043] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2011] [Accepted: 07/12/2011] [Indexed: 11/13/2022] Open
Abstract
The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin–myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank–Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction–diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.
Collapse
Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University Baltimore, MD, USA
| | | |
Collapse
|
71
|
Abstract
Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.
Collapse
Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
| | | | | |
Collapse
|
72
|
Provost J, Gurev V, Trayanova N, Konofagou EE. Mapping of cardiac electrical activation with electromechanical wave imaging: an in silico-in vivo reciprocity study. Heart Rhythm 2011; 8:752-9. [PMID: 21185403 PMCID: PMC3100212 DOI: 10.1016/j.hrthm.2010.12.034] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/14/2010] [Accepted: 12/19/2010] [Indexed: 10/18/2022]
Abstract
BACKGROUND Electromechanical wave imaging (EWI) is an entirely noninvasive, ultrasound-based imaging method capable of mapping the electromechanical activation sequence of the ventricles in vivo. Given the broad accessibility of ultrasound scanners in the clinic, the application of EWI could constitute a flexible surrogate for the 3-dimensional electrical activation. OBJECTIVE The purpose of this report is to reproduce the electromechanical wave (EW) using an anatomically realistic electromechanical model, and establish the capability of EWI to map the electrical activation sequence in vivo when pacing from different locations. METHODS EWI was performed in 1 canine during pacing from 3 different sites. A high-resolution dynamic model of coupled cardiac electromechanics of the canine heart was used to predict the experimentally recorded electromechanical wave. The simulated 3-dimensional electrical activation sequence was then compared with the experimental EW. RESULTS The electrical activation sequence and the EW were highly correlated for all pacing sites. The relationship between the electrical activation and the EW onset was found to be linear, with a slope of 1.01 to 1.17 for different pacing schemes and imaging angles. CONCLUSION The accurate reproduction of the EW in simulations indicates that the model framework is capable of accurately representing the cardiac electromechanics and thus testing new hypotheses. The one-to-one correspondence between the electrical activation and the EW sequences indicates that EWI could be used to map the cardiac electrical activity. This opens the door for further exploration of the technique in assisting in the early detection, diagnosis, and treatment monitoring of rhythm dysfunction.
Collapse
Affiliation(s)
- Jean Provost
- Department of Biomedical Engineering, Columbia University, New York, NY, USA
| | - Viatcheslav Gurev
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Natalia Trayanova
- Department of Biomedical Engineering and Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, USA
| | - Elisa E. Konofagou
- Department of Biomedical Engineering, Columbia University, New York, NY, USA
- Department of Radiology, Columbia University, New York, NY, USA
| |
Collapse
|
73
|
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.
Collapse
Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering, Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD 21218, USA.
| |
Collapse
|
74
|
Fishman GI, Chugh SS, Dimarco JP, Albert CM, Anderson ME, Bonow RO, Buxton AE, Chen PS, Estes M, Jouven X, Kwong R, Lathrop DA, Mascette AM, Nerbonne JM, O'Rourke B, Page RL, Roden DM, Rosenbaum DS, Sotoodehnia N, Trayanova NA, Zheng ZJ. Sudden cardiac death prediction and prevention: report from a National Heart, Lung, and Blood Institute and Heart Rhythm Society Workshop. Circulation 2011; 122:2335-48. [PMID: 21147730 DOI: 10.1161/circulationaha.110.976092] [Citation(s) in RCA: 443] [Impact Index Per Article: 34.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Glenn I Fishman
- NYU School of Medicine, Division of Cardiology, 522 First Avenue, Smilow 801, New York, NY 10016, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
75
|
Benson AP, Bernus O, Dierckx H, Gilbert SH, Greenwood JP, Holden AV, Mohee K, Plein S, Radjenovic A, Ries ME, Smith GL, Sourbron S, Walton RD. Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology. Interface Focus 2010; 1:101-16. [PMID: 22419977 DOI: 10.1098/rsfs.2010.0005] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2010] [Accepted: 11/08/2010] [Indexed: 11/12/2022] Open
Abstract
Reaction-diffusion computational models of cardiac electrophysiology require both dynamic excitation models that reconstruct the action potentials of myocytes as well as datasets of cardiac geometry and architecture that provide the electrical diffusion tensor D, which determines how excitation spreads through the tissue. We illustrate an experimental pipeline we have developed in our laboratories for constructing and validating such datasets. The tensor D changes with location in the myocardium, and is determined by tissue architecture. Diffusion tensor magnetic resonance imaging (DT-MRI) provides three eigenvectors e(i) and eigenvalues λ(i) at each voxel throughout the tissue that can be used to reconstruct this architecture. The primary eigenvector e(1) is a histologically validated measure of myocyte orientation (responsible for anisotropic propagation). The secondary and tertiary eigenvectors (e(2) and e(3)) specify the directions of any orthotropic structure if λ(2) is significantly greater than λ(3)-this orthotropy has been identified with sheets or cleavage planes. For simulations, the components of D are scaled in the fibre and cross-fibre directions for anisotropic simulations (or fibre, sheet and sheet normal directions for orthotropic tissues) so that simulated conduction velocities match values from optical imaging or plunge electrode experiments. The simulated pattern of propagation of action potentials in the models is partially validated by optical recordings of spatio-temporal activity on the surfaces of hearts. We also describe several techniques that enhance components of the pipeline, or that allow the pipeline to be applied to different areas of research: Q ball imaging provides evidence for multi-modal orientation distributions within a fraction of voxels, infarcts can be identified by changes in the anisotropic structure-irregularity in myocyte orientation and a decrease in fractional anisotropy, clinical imaging provides human ventricular geometry and can identify ischaemic and infarcted regions, and simulations in human geometries examine the roles of anisotropic and orthotropic architecture in the initiation of arrhythmias.
Collapse
Affiliation(s)
- Alan P Benson
- Institute of Membrane and Systems Biology , University of Leeds , Leeds LS2 9JT , UK
| | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
76
|
Venable PW, Taylor TG, Shibayama J, Warren M, Zaitsev AV. Complex structure of electrophysiological gradients emerging during long-duration ventricular fibrillation in the canine heart. Am J Physiol Heart Circ Physiol 2010; 299:H1405-18. [PMID: 20802138 DOI: 10.1152/ajpheart.00419.2010] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Long-duration ventricular fibrillation (LDVF) in the globally ischemic heart is a common setting of cardiac arrest. Electrical heterogeneities during LDVF may affect outcomes of defibrillation and resuscitation. Previous studies in large mammalian hearts have investigated the role of Purkinje fibers and electrophysiological gradients between the endocardium (Endo) and epicardium (Epi). Much less is known about gradients between the right ventricle (RV) and left ventricle (LV) and within each chamber during LDVF. We studied the transmural distribution of the VF activation rate (VFR) in the RV and LV and at the junction of RV, LV, and septum (Sep) during LDVF using plunge needle electrodes in opened-chest dogs. We also used optical mapping to analyze the Epi distribution of VFR, action potential duration (APD), and diastolic interval (DI) during LDVF in the RV and LV of isolated hearts. Transmural VFR gradients developed in both the RV and LV, with a faster VFR in Endo. Concurrently, large VFR gradients developed in Epi, with the fastest VFR in the RV-Sep junction, intermediate in the RV, and slowest in the LV. Optical mapping revealed a progressively increasing VFR dispersion within both the LV and RV, with a mosaic presence of fully inexcitable areas after 4-8 min of LDVF. The transmural, interchamber, and intrachamber VFR heterogeneities were of similar magnitude. In both chambers, the inverse of VFR was highly correlated with DI, but not APD, at all time points of LDVF. We conclude that the complex VFR gradients during LDVF in the canine heart cannot be explained solely by the distribution of Purkinje fibers and are related to regional differences in the electrical depression secondary to LDVF.
Collapse
Affiliation(s)
- Paul W Venable
- Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, Utah 84112-5000, USA
| | | | | | | | | |
Collapse
|
77
|
Abstract
One of the most important components of mechanoelectric coupling is stretch-activated channels, sarcolemmal channels that open upon mechanical stimuli. Uncovering the mechanisms by which stretch-activated channels contribute to ventricular arrhythmogenesis under a variety of pathologic conditions is hampered by the lack of experimental methodologies that can record the 3-dimensional electromechanical activity simultaneously at high spatiotemporal resolution. Computer modeling provides such an opportunity. The goal of this review is to illustrate the utility of sophisticated, physiologically realistic, whole heart computer simulations in determining the role of mechanoelectric coupling in ventricular arrhythmogenesis. We first present the various ways by which stretch-activated channels have been modeled and demonstrate how these channels affect cardiac electrophysiologic properties. Next, we use an electrophysiologic model of the rabbit ventricles to understand how so-called commotio cordis, the mechanical impact to the precordial region of the heart, can initiate ventricular tachycardia via the recruitment of stretch-activated channels. Using the same model, we also provide mechanistic insight into the termination of arrhythmias by precordial thump under normal and globally ischemic conditions. Lastly, we use a novel anatomically realistic dynamic 3-dimensional coupled electromechanical model of the rabbit ventricles to gain insight into the role of electromechanical dysfunction in arrhythmogenesis during acute regional ischemia.
Collapse
|
78
|
Models of cardiac tissue electrophysiology: progress, challenges and open questions. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2010; 104:22-48. [PMID: 20553746 DOI: 10.1016/j.pbiomolbio.2010.05.008] [Citation(s) in RCA: 290] [Impact Index Per Article: 20.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2009] [Revised: 04/09/2010] [Accepted: 05/19/2010] [Indexed: 01/03/2023]
Abstract
Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
Collapse
|
79
|
Keldermann RH, Nash MP, Gelderblom H, Wang VY, Panfilov AV. Electromechanical wavebreak in a model of the human left ventricle. Am J Physiol Heart Circ Physiol 2010; 299:H134-43. [PMID: 20400690 DOI: 10.1152/ajpheart.00862.2009] [Citation(s) in RCA: 85] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.
Collapse
Affiliation(s)
- R H Keldermann
- Department of Theoretical Biology, Utrecht University, Padualaan 8, Utrecht, The Netherlands
| | | | | | | | | |
Collapse
|
80
|
Abstract
This paper discusses about the electromechanical effect of rabbit ventricals and abnormalities caused by asynchronous electrical activation in perfusion and pump function. These applications are of paramount importance to therapies that employ pacing of the heart, and particularly cardiac resynchronization therapy (CRT).
Collapse
Affiliation(s)
- Natalia Trayanova
- Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD 21224, USA.
| |
Collapse
|