Biomedical Engineering Reference
In-Depth Information
ments. Furthermore, it should be noted that FEM programs work best with a
small number of geometrical element types, making them at first glance incom-
patible with the Voronoi tessellation scheme suggested earlier. This problem can
be resolved either by giving up the advantages of the Voronoi approach and re-
verting to regular mesh elements, or else by first making the Voronoi tessella-
tion and then dividing each of the Voronoi polyhedra into smaller tetrahedra
(triangles in a two-dimensional model), an operation that is always guaranteed to
be possible. However, tetrahedra are intrinsically rigid unless special tricks are
applied and may not make the best elements for FEM of soft tissue.
A further necessity with FEM that needs to be kept in mind is that the calcu-
lations lose accuracy as the initial mesh elements become more and more dis-
torted during the course of the simulation. The software must therefore be
designed to suspend the calculations at certain intervals and remesh the model
volume to provide a new starting point with undistorted mesh elements.
An attractive feature of FEM is that the mesh elements do not need to be of
comparable size. Therefore, the level of detail can be varied from place to place
within a single model. This suggests that the transition from tissue-level to cell-
level modeling might initially be made by surrounding a small volume of de-
tailed cell-level mesh with a larger volume modeled on a cruder mesh scale. The
surround could provide a spatially nonuniform external pressure resisting
growth, a source for nutrients and oxygen, and a sink for waste products, while
the fine-meshed interior would allow one to explore the processes of interest in
greater detail. Initially, even this fine-meshed volume might not comprise indi-
vidual neurons, but eventually, one would want it to do so in order to permit the
study of the effects of pressure and distortion on the functioning of a working
neural network model. If the FEM neurons were modeled as cylindrical mesh
elements, these could be made to correspond with compartments in a multicom-
partment electrophysiological neural function model (77). One could then study,
for example, the effects on function of changes in membrane capacitance, ax-
onal resistivity, ionic equilibria, or channel dynamics caused by the pressure
resulting from normal development or from tumor growth. Similarly, neurite
bending or shear caused by the growth of a nearby tumor might lead to the chok-
ing off of conductance along a neural pathway with functional implications.
3.
CONCLUSIONS
The basic physiology of neuronal activation and discharge is reasonably
well understood, and a vast literature of modeling studies, using approaches
ranging from very abstract to very realistic, is available. While it is true that not
all aspects of single neuron function, not to mention network function, can yet
be routinely simulated, and certainly not with a single set of parameters applica-
ble to even one type of cell in all experimental situations, nonetheless, there is
