Biomedical Engineering Reference
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in rat mesenteric arterioles via mathematical modeling [
35
]. This ODE model
predicted that in the rat mesenteric arterioles, ECs exert a stabilizing effect on
intracellular vascular SMC Ca
2+
oscillations, which synchronize with oscillations
in vessel tone to cause vasomotion. This stabilization allows Ca
2+
oscillations to be
maintained over a wider range of agonist concentrations. Models related to
intracellular signaling include those that simulate the dynamics of ionic flows
across the membrane. One group modeled the dynamics of the Na
+
/Ca
2+
exchanger (NCX) in vascular SMCs; this exchanger regulates the reloading of the
sarcoplasmic reticulum and the maintenance of Ca
2+
oscillations in activated
SMCs [
23
]. Although this model is not of an actual signaling network, it gives
insights into the mechanism of the coupling between Na
+
entry via TRPC6 (a non-
specific cation channel) and the NCX. This implicates the concentration of Ca
2+
in
the vascular SMC, which affects the signaling pathways involving Ca
2+
. The
model incorporates a stochastic element to simulate the movement of single Na
+
ions in the nanospace between the plasma membrane and the sarcoplasmic retic-
ulum. This model predicted that in order to have a Na
+
concentration transiently
elevated in the plasma membrane/sarcoplasmic reticulum nanospace, there must
be physical obstructions to Na
+
motion, which form a relatively impermeable
barrier around the TRPC6 channel. NCX must also be localized near TRPC6
within such barrier in order to sense the high Na
+
concentration, reverse, and allow
Ca
2+
into the sarcoplasmic reticulum. As the details of individual intracellular
signaling pathways become better understood, models can be evolved to incor-
porate additional pathways such that they combine to form an interconnected
signaling network that increasingly describes the physiological system with more
accuracy.
3.4 Limitations of Singular Modeling Approaches
3.4.1 CMM Limitations
Continuum models have proved very useful in vascular research, including helping
to reveal the existence of residual stresses and their effects on the transmural
distribution of stress that led to a fundamental mechanobiological hypothesis [
32
].
Continuum models also continue to be very successful in explaining and predicting
a wide variety of nontrivial aspects of vascular physiology and pathophysiology,
including the adaptation of arteries to sustained changes in blood pressure or flow
as well as the rupture of aneurysms. Nevertheless, limitations remain. For exam-
ple, the continuum approach assumes material is distributed continuously over
particular length scales, which can mask specific mechanisms of mechanotrans-
duction that result from cell-matrix interactions at discrete sites (e.g., focal
adhesions) but otherwise help to drive overall tissue-level adaptations. Current
models also do not account for the details of particular matrix-matrix interactions,
including interactions between collagen fibers and proteoglycans. Perhaps most
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