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The making of the virtual heart  135



                                      The extent and localisation of the area is investigated and confirmed, using
                                      catheter impedance tracking of ventricular wall tissue properties and non-
                                      invasive monitoring of cardiac dimensions and relative catheter location. A
                                      small area of increased fibrosis is diagnosed and mapped in real time to a
                                      patient-specific 3D virtual heart model. The model is then used to assess treat-
                                      ment strategies. A decision is taken by the surgeons to ablate the area. Using
                                      the virtual heart, optimal pattern and localisation for the tissue ablation are
                                      established with the aim of maximising the anti-arrhythmic effect while mini-
                                      mising the energy levels of the procedure. Using the same catheter, a minimal
                                      tissue area is ablated, obliterating the ectopic focus and terminating the
                                      arrhythmia. The whole, minimally-invasive procedure took only 12 minutes,
                                      and the patient made – as typical for 97 per cent of cases – a full recovery . . .
                                 Cardiac models are amongst the most advanced in silico tools for bio-med-
                                 icine, and the above scenario is bound to become reality rather sooner than
                                 later. Both cellular and whole organ models have already ‘matured’ to a
                                 level where they have started to possess predictive power. We will now
                                 address some aspects of single cell model development (the ‘cars’), and then
                                 look at how virtual cells interact to simulate the spreading wave of electri-
                                 cal excitation in anatomically representative, virtual hearts (the ‘traffic’).


                                 8.4.2 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 pace-
                                 maker 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 revolution-
                                 ary 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
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