Related Experiment Video
Updated: Jul 16, 2026

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
An unconditionally stable numerical method for the Luo-Rudy 1 model used in simulations of defibrillation
Monica Hanslien1, Joakim Sundnes, Aslak Tveito
1Department of Scientific Computing, Simula Research Laboratory, P.O. Box 134, N-1325 Lysaker, Norway. monicaha@simula.no
Abstract:
Numerical simulations of defibrillation using the Bidomain model coupled to a model of membrane kinetics represent a serious numerical challenge. This is because very high voltages close to defibrillation electrodes demand that extreme time step restrictions be placed on standard numerical schemes, e.g. the forward Euler scheme. A common solution to this problem is to modify the cell model by simple if-tests applied to several equations and rate functions. These changes are motivated by numerical problems rather than physiology, and should therefore be avoided whenever possible. The purpose of this paper is to present a numerical scheme that handles the original model without modifications and which is unconditionally stable for the Luo-Rudy phase 1 model. This also shows that the cell model is mathematically well-behaved, even in the presence of very high voltages. Our theoretical results are illustrated by numerical computations.
Related Concept Videos
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Node Analysis for AC Circuits
To unravel the complexities of this system, nodal analysis is employed, a powerful technique founded on Kirchhoff's current law (KCL), which remains valid for phasors. AC circuits can effectively be...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

