Mathematical modelling of the train station of the heart: the atrio-ventricular node

The cardiac conduction system produces and transmits electrical impulses that prompt myocardial contraction, ensuring efficient heart function. This intricate system ensures that the heart beats in a coordinated and efficient manner, beginning with the atria and then the ventricles. The conduction system optimizes cardiac output by maintaining this precise sequence, which is crucial for adequate blood circulation.
This system relies on the unique properties of nodal and Purkinje cells:...

Consider an angioplasty system featuring a catheter equipped with a turbine, a critical tool for removing plaque deposits from coronary arteries. This intricate medical device operates using a circuit model reminiscent of a dual-node RLC circuit powered by a current-controlled voltage source.
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...

The normal cardiac rhythm is a synchronized electrical activity that facilitates the regular and coordinated contraction of the heart muscle. This process is essential for efficient blood circulation throughout the body. The fundamental elements involved in establishing and maintaining this rhythm include the unique electrical properties of cardiac muscle cells, the sinoatrial (SA) node's pacemaker function, the specialized conducting system, and the ionic mechanisms underlying each phase...

The heart beats rhythmically in a sequence called the cardiac cycle—a rapid coordination of contraction (systole) and relaxation (diastole).
The Process
Electrical signals—sent from the sinoatrial (SA) node in the right atrial wall to the atrioventricular (AV) node between the right atrium and right ventricle—cause both atria to simultaneously contract. When the signal reaches the AV node, it pauses for approximately a tenth of a second, allowing the atria to contract and...

Nodal analysis is a fundamental method in electrical engineering used to simplify the process of circuit analysis. This method revolves around the concept of using node voltages as the primary variables for circuit analysis. The objective is to determine the voltage at each node in a circuit, which can then be used to find other quantities of interest, such as currents through specific components.
Consider, for instance, a simple circuit composed of three nodes and three resistors, as shown in...

Nodal analysis is a remarkably effective method used in electrical engineering to simplify the analysis of complex circuits, including those with dependent or independent voltage sources. Its strength lies in its systematic approach to breaking down circuits into manageable components, making it easier for engineers to understand and solve.
Consider a circuit that contains four resistors and two voltage sources, as shown in Figure 1. One of these voltage sources is connected between a...