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Updated: Aug 25, 2025

Optocardiography and Electrophysiology Studies of Ex Vivo Langendorff-perfused Hearts

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Published on: November 7, 2019

Electrophysiology.

Boyce E Griffith¹, Charles S Peskin²

¹Leon H. Charney, Division of Cardiology, Department of Medicine, New York University, School of Medicine, 550 First Ave., New York, NY 10016, USA.

Communications on Pure and Applied Mathematics

|October 14, 2022

Summary

This summary is machine-generated.

Mathematical models describe electrical signaling in cells, building upon the Hodgkin-Huxley model. This review covers advancements like cardiac electrophysiology equations and multiscale models for action potential propagation.

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Area of Science:

* Physiology
* Mathematical Biology
* Computational Science

Background:

* Electrical signaling is a rapid intercellular communication mechanism essential for physiological processes.
* The Hodgkin-Huxley model, using partial differential equations, historically described action potential propagation.
* Mathematical models are crucial for understanding complex biological electrical activity.

Purpose of the Study:

* To review the foundational Hodgkin-Huxley model for electrical signaling.
* To present contemporary mathematical models of physiological electrical processes.
* To explore advanced models including cardiac electrophysiology and multiscale approaches.

Main Methods:

* Analysis of partial differential equations derived from the Hodgkin-Huxley framework.
* Review of established and novel mathematical modeling techniques.
* Examination of three-dimensional bidomain/monodomain equations and electrodiffusion models.

Main Results:

* The Hodgkin-Huxley model provides a basis for understanding action potential propagation.
* Advanced models offer greater spatial and temporal resolution for physiological systems.
* Cardiac electrophysiology is described using bidomain and monodomain equations.
* Multiscale models incorporate cellular structure for detailed wavefront analysis.

Conclusions:

* Mathematical modeling is indispensable for studying cellular electrical signaling.
* Recent advancements extend the Hodgkin-Huxley paradigm to complex systems like the heart.
* Electrodiffusion models offer a more detailed reformulation of physiological electrical processes.