Single cell models

The most prominent expression of cardiac activity is the rhythmical contraction of the heart - its pumping action. Less well known is the fact, that this mechanical activity is tightly controlled by an electrical process called 'excitation'.

In the normal heart, electrical excitation originates in specialised pacemaker cells and spreads as an electrical wave throughout the whole organ. This electrical signal determines the timing and, to a degree, the force of cardiac contraction. Thus, the heartbeat is a consequence of an electrical process (which does, however, go completely unnoticed in day-to-day life). Modelling of the heart's electrical activity has a long history. In 1928, two Dutch engineers, van der Pol and van der Mark, described the heartbeat by comparing it to a simple oscillator. This approach, which was revolutionary at the time, gave rise to a whole family of models of the heartbeat and of the operation of other periodically active, electrically excitable cells (like neurones or skeletal muscle cells).

A common denominator of these models is the attempt to represent cellular electrical activity by describing, with a very small number of equations, the time-course of changes in the electrical potential in the cells (Figure 8.1(a)), but not of the ionic currents that gave rise to it.

This approach is, at the same time, the great advantage and a major limitation of membrane potential models. As they are rather compact, models of this type were the first to be used in investigations of the spread of excitation in multi-dimensional 'tissue' representations consisting of relatively large numbers of interconnected excitable elements; their role in assessing biophysical behaviour like cardiac impulse propagation is undiminished.

The major drawback of these models, however, is their lack of a clear reference between model components and constituent parts of the biological system (e.g. structures like ion channels, transporter proteins, receptors, etc.). These models, therefore, do not permit the simulation of patho-physiological detail, such as the series of events that follows a reduction in oxygen supply to the cardiac muscle and, ultimately, causes serious disturbances in heart rhythm.

A breakthrough in cell modelling occurred with the work of the British scientists, Sir Alan L. Hodgkin and Sir Andrew F. Huxley, for which they were in 1963 (jointly with Sir John C. Eccles) awarded the Nobel prize. Their new electrical models calculated the changes in membrane potential on the basis of the underlying ionic currents.

In contrast to the pre-existing models that merely portrayed membrane potentials, the new generation of models calculated the ion fluxes that give rise to the changes in cell electrical potential. Thus, the new models provided the core foundation for a mechanistic description of cell function. Their concept was applied to cardiac cells by Denis Noble in 1960.

Since then, the study of cardiac cellular behaviour has made immense progress, as have the related 'ionic' mathematical models. There are various representations of all major cell types in the heart, descriptions of their metabolic activity, its relation to cell electrical and mechanical behaviour, etc. Drug-receptor interactions and even the effects of modifications in the genetic information on cardiac ion channel-forming proteins have begun to be computed. Principal components of cell models of this type are illustrated in Figure 8.1(b) on the example of work by the Oxford Cardiac Electrophysiology Group. As one can see, great attention is paid to the implementation of vital (sub)cellular mechanisms that determine function.

These detailed cell models can be used to study the development in time of processes like myocardial ischaemia (a reduction in coronary blood flow that causes under-supply of oxygen to the cardiac muscle), or effects of genetic mutations on cellular electrophysiology. They allow to predict the outcome of changes in the cell's environment, and may even be used to assess drug actions.

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