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Comsol multiphysics 4.4 tutorial1/1/2024 ![]() Using these equations and various parameters, users can visualize a reentrant wave that moves around the tissue without damping, which results in a characteristic spiral pattern. Using 2 Different PDEs to Analyze Electrical Signal Propagation in Cardiac Tissueīy using the FitzHugh-Nagumo equations to simulate excitable media, it is possible to create a simple physiological heart model with two variables: an activator (corresponding to the electric potential) and inhibitor (the voltage-dependent probability that the membrane’s pores are open and can transmit ionic current). The equations used in this model, FitzHugh-Nagumo and complex Ginzburg-Landau, are included in the PDE interfaces available in COMSOL Multiphysics. Simonetta Filippi from the Campus Bio-Medico University of Rome in Italy. One such example is the Electrical Signals in a Heart model, provided through the courtesy of Dr. To address this challenge, users can implement two sets of equations to describe various aspects of the electrical signal propagation. Studying the electrical signals in a heart is not a simple process and involves modeling excitable media. As such, to gain a better understanding of heart patterns, the electrical activity in cardiac tissue needs to be examined. During this process, ions flow through small pores that exist in an excitation (open) or rest (closed) state within the cellular membrane. The rhythmic contractions are triggered when the heart passes an ionic current through the muscle. ![]() Moving on to a medical example, let’s see how simulation can be used to understand the rhythmic patterns of contractions and dilations in a heart. ![]() Simulation showing how solitons maintain an intact shape when colliding and reappearing. If you want to learn more about this example, see the KdV equation model in the Application Gallery. This counterintuitive finding would be challenging to observe without simulation. In addition, the simulation reveals that, just like with linear waves, solitons can collide and reappear while maintaining their shape. According to the KdV equation, the speed of the pulse should determine both its amplitude and width, which can be observed via simulation. With this setup, users are able to model an initial pulse in an optical fiber and the resulting waves or solitons. It’s also possible to easily define dependent variables and identify coefficients via the General Form PDE interface. To solve the KdV equation in COMSOL Multiphysics, users can add PDEs and ODEs into the software interface via mathematical expressions and coefficient matching. Simulating the KdV Equations with Equation-Based Modeling As a result, one of the main modern applications of solitons is in optical fibers. Today, engineers use the KdV equation to understand light waves. These waves are now called solitons, which are seen as single “humps” that can travel over long distances without altering their shape or speed. Since the equation doesn’t introduce dissipation, the waves travel seemingly forever. In 1895, the Korteweg-de Vries (KdV) equation was created as a means to model water waves. To show this functionality in action, let’s take a look at three examples… Example 1: The KdV Equations and Solitons There is no limit to how creative you can be when setting up and solving your models with equation-based modeling, which expands what you can achieve with simulation.
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