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136  P. KOHL ET AL.



                               cellular electrical activity by describing, with a very small number of equa-
                               tions, 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 bio-
                               logical 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 reduc-
                               tion 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 pro-
                               vided 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 beha-
                               viour, 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.
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