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Reduced Models of Cardiomyocytes Excitability: Comparing Karma and FitzHugh-Nagumo. Bull Math Biol 2021; 83:88. [PMID: 34213628 PMCID: PMC8253715 DOI: 10.1007/s11538-021-00898-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Accepted: 03/29/2021] [Indexed: 10/27/2022]
Abstract
Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres, the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensional systems of coupled equations so that the possible mathematical analysis is quite limited, even numerically. This has inspired the development of reduced, phenomenological models that preserve qualitatively the main feature of cardiomyocyte's dynamics. In this paper, we present a systematic comparison of the dynamics between two notable low-dimensional models, the FitzHugh-Nagumo model (FitzHugh in Bull Math Biophys 17:257-269, 1955, J Gen Physiol 43:867-896, 1960, Biophys J 1:445-466, 1961) as a prototype of excitable behaviour and a polynomial version of the Karma model (Karma in Phys Rev Lett 71(7):16, 1993, Chaos 4:461, 1994) which is specifically developed to fit cardiomyocyte's behaviour well. We start by introducing the models and considering their pure ODE versions. We analyse the ODEs employing the main ideas and steps used in the setting of geometric singular perturbation theory. Next, we turn to the spatially extended models, where we focus on travelling wave solutions in 1D. Finally, we perform numerical simulations of the 1D PDE Karma model varying model parameters in order to systematically investigate the impact on wave propagation velocity and shape. In summary, our study provides a reference regarding key similarities as well as key differences of the two models.
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Liu H, Bolonduro OA, Hu N, Ju J, Rao AA, Duffy BM, Huang Z, Black LD, Timko BP. Heart-on-a-Chip Model with Integrated Extra- and Intracellular Bioelectronics for Monitoring Cardiac Electrophysiology under Acute Hypoxia. NANO LETTERS 2020; 20:2585-2593. [PMID: 32092276 DOI: 10.1021/acs.nanolett.0c00076] [Citation(s) in RCA: 101] [Impact Index Per Article: 25.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We demonstrated a bioelectronic heart-on-a-chip model for studying the effects of acute hypoxia on cardiac function. A microfluidic channel enabled rapid modulation of medium oxygenation, which mimicked the regimes induced by a temporary coronary occlusion and reversibly activated hypoxia-related transduction pathways in HL-1 cardiac model cells. Extracellular bioelectronics provided continuous readouts demonstrating that hypoxic cells experienced an initial period of tachycardia followed by a reduction in beat rate and eventually arrhythmia. Intracellular bioelectronics consisting of Pt nanopillars temporarily entered the cytosol following electroporation, yielding action potential (AP)-like readouts. We found that APs narrowed during hypoxia, consistent with proposed mechanisms by which oxygen deficits activate ATP-dependent K+ channels that promote membrane repolarization. Significantly, both extra- and intracellular devices could be multiplexed, enabling mapping capabilities unachievable by other electrophysiological tools. Our platform represents a significant advance toward understanding electrophysiological responses to hypoxia and could be applicable to disease modeling and drug development.
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Affiliation(s)
- Haitao Liu
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
- School of Materials Science and Technology, Beijing Key Laboratory of Materials Utilization of Nonmetallic Minerals and Solid Wastes, National Laboratory of Mineral Materials, China University of Geosciences, Beijing 100083, PR China
| | - Olurotimi A Bolonduro
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
| | - Ning Hu
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Guangdong Province Key Laboratory of Display Material and Technology, The First Affiliated Hospital of Sun Yat-Sen University, Sun Yat-Sen University, Guangzhou 510275, PR China
| | - Jie Ju
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
| | - Akshita A Rao
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
| | - Breanna M Duffy
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
| | - Zhaohui Huang
- School of Materials Science and Technology, Beijing Key Laboratory of Materials Utilization of Nonmetallic Minerals and Solid Wastes, National Laboratory of Mineral Materials, China University of Geosciences, Beijing 100083, PR China
| | - Lauren D Black
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
- Department of Cell, Molecular & Developmental Biology, School of Graduate Biomedical Sciences, Tufts University, Boston, Massachusetts 02111, United States
| | - Brian P Timko
- Department of Biomedical Engineering, Tufts University, Medford, Massachusetts 02155, United States
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