Biomedical Engineering Reference
In-Depth Information
where
v
(
t
) is membrane potential,
I
i
ion
[
v
(
t
)] is the current carried by the
i
th mem-
brane current, and
I
i
pump
[
v
(
t
),
c
(
t
)] is the current through the
i
th membrane
pump/exchanger, which can depend on both membrane potential
v
(
t
) and the
relevant ion concentration
c
(
t
). Figure 3 shows examples of simulated normal
APs (solid line, Figure 3C) and Ca
2+
transients (solid line, Figure 3D) compared
with those measured from isolated canine ventricular myocytes (AP = solid line,
Figure 3A; Ca
2+
transient = solid line, Figure 3B). These data demonstrate that
common pool models have been quite successful in reconstruction of the AP and
in reconstructing some aspects (the time-varying waveform) of the Ca
2+
tran-
sient. In the following section, we illustrate how such models may be used to
gain insight into cardiovascular disease mechanisms.
2.6. Application: Modeling the Molecular Basis of Heart Failure
Heart failure (HF), the most common cardiovascular disorder, is character-
ized by ventricular dilatation, and decreased myocardial contractility and cardiac
output. Prevalence in the general population is over 4.5 million, and increases
with age to levels as high as 10%. New cases number approximately 400,000
per year. Patient prognosis is poor, with mortality roughly 15% at one year, in-
creasing to 80% at six years subsequent to diagnosis. It is now the leading cause
of sudden cardiac death (SCD) in the United States. An increased understanding
of the molecular basis of this disease therefore offers the possibility of improved
treatments that can reduce the risk of SCD.
Experimental studies have now identified two major features of the cellular
phenotype of heart failure. First, ventricular myocytes isolated from failing hu-
man (35) and canine (36,37) hearts exhibit significant AP prolongation. An ex-
ample of this AP prolongation recorded from normal versus failing canine
ventricular myocytes is shown in Figure 3A (normal and failing APs shown in
solid and dashed lines, respectively). Duration of the failing AP (~660 msec) is
roughly twice that of the normal (~330 msec). AP duration is controlled by the
balance between inward and outward membrane currents during the plateau
phase of the AP. Possible explanations for this prolongation are therefore HF-
induced upregulation of inward currents, and/or downregulation of outward cur-
rents. Second, failing ventricular myocytes exhibit altered Ca
2+
transients. An
example of normal and failing Ca
2+
transients obtained simultaneously with the
AP recordings of Figure 3A is shown in Figure 3B. Differences between normal
(solid line) and failing (dotted line) Ca
2+
transients include: (a) reduced ampli-
tude; and (b) reduced rate of decline of the Ca
2+
transient subsequent to repolari-
zation of the AP.
There is little evidence to support the idea that upregulation of inward cur-
rents is responsible for prolongation of AP duration in HF, as the majority of
measurements of whole-cell Na
+
and Ca
2+
current density show no change in the
