Biomedical Engineering Reference
In-Depth Information
to assume that the conduction time of the
i
th beat through the AV node,
AV
i
, is a
function
F
of the recovery time since the passage of the last excitation through
the AV node, which is designated
VA
i
-1
. Assuming that there is a periodic atrial
stimulation, either from the sinus node or by an artificial pacemaker with a pe-
riod
AA
, we find (5) that
AV
i
=
F
(
VA
i
-1
) =
F
(
k
+
AA
-
AV
i
-1
),
[1]
where
k
is the smallest integer such that
k
+
AA
> R, Rbeing the refractory period
of the AV node. Typically, the recovery curve
F
is a monotonically decreasing
curve. In this case, it is possible to demonstrate mathematically that, if the prop-
erties of the AV node are fixed, as the frequency of atrial activation is increased,
different types of
N
:
M
heart block, where
N
is the number of sinus beats and
M
is the number of ventricular beats in a repeating sequence, can be observed. If
there is
N
:
M
heart block at one stimulation frequency and
N
':
M
' heart block at a
higher frequency, then
N
+
N
':
M
+
M
' heart block is expected at some intermediate
stimulation frequency (4-7). This result provides a mathematical classification
complementary to the cardiological classification, and can be confirmed in clini-
cal settings. Experimental and clinical studies have also demonstrated that these
basic properties of Wenckebach rhythms can be observed in normal mammalian
hearts as the atrial activation rate is increased (5-7). However, careful analysis
of data shows that the above generalizations need to be modified. For example,
if the atria are stimulated at a rapid rate so that 1:1 conduction is lost, there can
often be an evolution of rhythms over a course of several minutes so that fewer
atrial activations are conducted to the ventricles over time (8). In other circum-
stances, as the atria are stimulated at a rapid rate that still is associated with 1:1
conduction, there can be an alternation or other complex fluctuation of conduc-
tion time through the AV node (9,10). These effects are associated with changes
in the properties of the AV node during rapid activation.
A different type of rhythm that is appealing to mathematicians is called
parasystole. In the "pure" case, the normal sinus rhythm beats at a constant fre-
quency, and an abnormal (ectopic) pacemaker in the ventricles beats at a second
slower frequency (11). Figure 2C labels the normal (N) beats and the ectopic (E)
beats. If the ectopic pacemaker fires at a time outside the refractory period of the
ventricles, then there is an abnormal ectopic beat, identifiable on the electrocar-
diogram by a distinct morphology from the normal beat, and the following nor-
mal sinus beat is blocked. If the normal and abnormal beats occur at the same
time, this leads to a fusion (F) beat. This simple mechanism has amazing conse-
quences. These can be appreciated by forming a sequence of integers that counts
the number of sinus beats between two ectopic beats. In general, for fixed sinus
and ectopic frequencies and a fixed refractory period, in this sequence there are
at most three integers, where the sum of the two smaller integers is one less than
the largest integer. Moreover, given the values of the parameters, it is possible to
