Biomedical Engineering Reference
In-Depth Information
Figure 2
. Sample electrocardiograms. In all traces one large box represents 0.2 s. (
A
) The
normal electrocardiogram. The P wave, QRS complex, and T wave are labelled. (
B
) 3:2
Wenckebach rhythm, an example of second-degree heart block. There are three P waves for
each R wave in a repeating pattern. (
C
) Parasystole. The normal beats, labelled N, occur with a
period of about 790 ms, and the abnormal ectopic beats, labelled E, occur with a regular period
of 1300 ms. However, when ectopic beats fall too soon after the normal beats, they are
blocked. Normal beats that occur after an ectopic beat are also blocked. If a normal and ectopic
beat occur at the same time, the complex has a different geometry, labelled F for fusion. In this
record, the number of normal beats occurring between ectopic beats is either 4, 2, or 1, satisfy-
ing the rules given in the text. Panels
A
and
B
are adapted with permission from Goldberger
and Goldberger (1994) (1). Panel
C
is adapted with permission from Courtemanche et al.
(1989) (16).
2.
TWO ARRHYTHMIAS WITH A SIMPLE
MATHEMATICAL ANALYSIS
Even a cursory examination of electrocardiograms from some patients ex-
periencing a cardiac arrhythmia would convince a mathematician or a mathe-
matically oriented physician that there must be an underlying mathematical
theory. To illustrate this observation, I consider a class of cardiac arrhythmias
associated with conduction defects through the AV node. In Wenckebach
rhythms there is a normal sinus rhythm, but not all atrial activations propagate to
the ventricles, leading to rhythms in which there are more P waves than QRS
complexes. It is common to classify Wenckebach rhythms by a ratio giving the
number of P waves to the number of QRS complexes. For example, Figure 2B
shows a 3:2 Wenckebach rhythm. In the 1920s, van der Pol and van der Mark
developed a mathematical model of the heart as coupled nonlinear oscillators
that display striking similarities to the Wenckebach rhythms (2).
Subsequently, a number of studies have demonstrated striking mathematical
characteristics of Wenckebach rhythms (3-7). The basis of these formulations is
