Electrophysiology

Griffith, Boyce E.; Peskin, Charles S.

doi:10.1002/cpa.21484

Cited by 25 publications

(11 citation statements)

References 104 publications

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“…For a singular perturbation analysis of the steady-state PNP system, see e.g. [26,212,438,484] and the references therein. In addition to continuum PNP equations, more detailed approaches have been studied, such as all-atom Molecular Dynamics (MD), nonlinear Poisson-Boltzmann (PB) equation, Brownian Dynamics (BD), see Roux et al [437].…”

Section: Electrodiffusion Models: the Poisson-nernst-planck (Pnp) Equmentioning

confidence: 99%

Mathematical Cardiac Electrophysiology

Franzone

Pavarino

Scacchi

2014

MS&A

193

261

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Section: Electrodiffusion Models: the Poisson-nernst-planck (Pnp) Equmentioning

confidence: 99%

Mathematical Cardiac Electrophysiology

Franzone

Pavarino

Scacchi

2014

MS&A

193

261

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“…There are, however, qualitative differences between the two models. An important difference between the bidomain and monodomain models from a physiological standpoint is that the former can explain cardiac defibrillation whereas the latter cannot [15,18]. Despite its central importance in cardiac electrophysiology, there are few analytical studies of the bidomain model.…”

Section: Introductionmentioning

confidence: 97%

Stability of Front Solutions of the Bidomain Equation

Mori

Matano

2016

Comm Pure Appl Math

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The bidomain model is the standard model describing electrical activity of the heart. Here we study the stability of planar front solutions of the bidomain equation with a bistable nonlinearity (the bidomain Allen-Cahn equation) in two spatial dimensions. In the bidomain Allen-Cahn equation a Fourier multiplier operator whose symbol is a positive homogeneous rational function of degree two (the bidomain operator) takes the place of the Laplacian in the classical AllenCahn equation. Stability of the planar front may depend on the direction of propagation given the anisotropic nature of the bidomain operator. We establish various criteria for stability and instability of the planar front in each direction of propagation. Our analysis reveals that planar fronts can be unstable in the bidomain Allen-Cahn equation in striking contrast to the classical or anisotropic Allen-Cahn equations. We identify two types of instabilities, one with respect to long-wavelength perturbations, the other with respect to medium-wavelength perturbations. Interestingly, whether the front is stable or unstable under longwavelength perturbations does not depend on the bistable nonlinearity and is fully determined by the convexity properties of a suitably defined Frank diagram. On the other hand, stability under intermediate-wavelength perturbations does depend on the choice of bistable nonlinearity. Intermediate-wavelength instabilities can occur even when the Frank diagram is convex, so long as the bidomain operator does not reduce to the Laplacian. We shall also give a remarkable example in which the planar front is unstable in all directions.

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“…The electrophysiological properties of artificial heart muscle need to be comparable to that of mammalian tissue, prior to in vivo utilization of these tissue equivalents. Therefore, the evaluation of the electrophysiological properties of the fabricated myocardium is of utmost importance [16], [17]. This study addresses this need by developing a novel system to record the EKG properties of 3D-AHM.…”

mentioning

confidence: 99%

32-Channel System to Measure the Electrophysiological Properties of Bioengineered Cardiac Muscle

Salazar

Reddy

Zheng

et al. 2015

IEEE Trans. Biomed. Eng.

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The purpose of this study was to develop, assess, and validate a custom 32-channel system to analyze the electrical properties of 3-D artificial heart muscle (3D-AHM). In this study, neonatal rat cardiac cells were cultured in a fibrin gel to drive the formation of 3D-AHM. Once the tissues were fully formed, the customized electrocardiogram (EKG) sensing system was used to obtain the different electrophysiological characteristics of the muscle constructs. Additionally, this system was used to evaluate the electrical properties of native rat hearts, for comparison to the fabricated tissues and native values found in the literature. Histological evaluation showed extensive cellularization and cardiac tissue formation. EKG data analysis yielded time delays between the signals ranging from 0 to 7 ms. Optical maps exhibited slight trends in impulse propagation throughout the fabricated tissue. Conduction velocities were calculated longitudinally at 277.81 cm/s, transversely at 300.79 cm/s, and diagonally at 285.68 cm/s for 3D-AHM. The QRS complex exhibited an R-wave amplitude of 438.42 ± 36.96 μV and an average duration of 317.5 ± 16.5 ms for the tissue constructs. The data collected in this study provide a clearer picture about the intrinsic properties of the 3D-AHM while proving our system's efficacy for EKG data procurement. To achieve a viable and permanent solution, the bioengineered heart muscle must physiologically resemble native heart tissue as well as mimic its electrical properties for proper contractile function. This study allows us to monitor such properties and assess the necessary changes that will improve construct development and function.

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Electrophysiology

Cited by 25 publications

References 104 publications

Mathematical Cardiac Electrophysiology

Mathematical Cardiac Electrophysiology

Stability of Front Solutions of the Bidomain Equation

32-Channel System to Measure the Electrophysiological Properties of Bioengineered Cardiac Muscle

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