Biomedical Engineering Reference
In-Depth Information
Fig. 5.5.
Isochrones of activation time on the epicardial surface (left) and the two transmural diag-
onal sections (right) elicited by anode make stimulation in tissue with the unequal anisotropy ratios
(Fig. 5.3, right column). Below each panel the minimum, maximum and step of the displayed map
are reported
along fibres, and also across the slab thickness, and subsequently collide. These two
3D wavefronts are shaped as open surfaces, each having a closed curve as rim lying
on the epicardial surface. At about 12 ms, the central epicardial area of the virtual
anode is suddenly activated, since it becomes excitable only after the stimulus is
turned off. Subsequently, only a unique large wavefront remains.
The epicardial and intramural excitation pathways start from the virtual cathodes,
proceed turning around the boundary of the virtual anode volume and point toward
its epicardial center. These pairs of pathways, coming from the virtual cathodes,
cause the merging of the two wavefronts by forming an activated tissue volume
bounded by two intramural surfaces, one consisting of a wavefront by moving to-
ward the epicardial boundary and intramurally toward the endocardial face, and the
other being the conduction block surface surrounding the inexcitable region, which
is suddenly activated after the stimulus is turned off. From the inspection of the trans-
mural isochrones pattern displayed in Fig. 5.5, we observe that the major transmural
effect of the virtual electrode polarization is the propagation of two wavefronts, sep-
arated by the transmural part of the virtual anode region, that merge about 5 ms after
the beginning of epicardial excitation at a 1
mm
depth.
5.6 Conclusions
We have presented the main mathematical models used in computational electrocar-
diology to describe the complex multiscale structure of the bioelectrical activity of
the heart, from the microscopic activity of ion channels of the cellular membrane to
the macroscopic properties of the anisotropic propagation of excitation and recov-
ery fronts in the whole heart. We have described how reaction-diffusion systems can
be rigorously derived from microscopic models of cellular aggregates by homoge-
