Download PWE 3-2: At What Angle Is Your Heart?

 Example 3-2 At What Angle Is Your Heart?
Vertical
In your heart, pacemaker cells generate electrical signals that trigger a contraction of the heart as the signals spread from
the top of the heart to the bottom. The direction in which these signals travel is called the electrical axis of the heart,
which reflects the angle at which the heart is positioned in the chest cavity.
The direction of a person’s electrical axis is found using a technique called electrocardiography. In a simplified version of electrocardiography, electrodes are placed on the person’s left wrist, right wrist, and right ankle.The electrical
signal between the two wrist electrodes tells
(b)
us the horizontal, right-to-left component of (a)
the heart’s electrical activity. The signal beHorizontal
tween the right wrist and right ankle (which
1.00 mV
component
is recorded simultaneously with the signal
between the wrists) gives us the vertical,
top-to-bottom component. The vector found Electrode on
Vertical
Electrode on
1.40 mV
by combining these horizontal and vertical
component
right wrist
left wrist
components points in the direction of the
heart’s electrical axis (Figure 3-12a).
The graphs in Figure 3-12b show
0s
1.25 s
sample recordings of the electrical signal
Electrode on
versus time for these two pairs of electrodes.
right ankle
These graphs are called electrocardiograms,
abbreviated ECG or EKG (after their
Horizontal
German name Elektrokardiogramm). In this
particular example, the maximum ECG
signal between the wrists is 1.00 millivolt
(mV) and the maximum ECG signal
Figure 3-12 Electrocardiography
between the right wrist and right ankle is
and the electrical axis of the
1.40 mV. At what angle u does the electrical
heart (a) Locating the electrical
signal propagate across the heart?
axis. (b) Horizontal and vertical
electrocardiograms.
Set Up
Finding vector direction
from vector components:
tan u =
Solve
The angle u is measured from the positive
x axis toward the positive y axis, so we
can safely use Equation 3-2b. Using your
calculator, you’ll find that tan21 1.40 = 54.5°.
We saw in Example 3-1 that a second solution
is 180° plus the result from your calculator, or
180° + 54.5°, or 234.5°. However, the figure
above shows that u is between 0 and 90°, so
the ­correct answer is 54.5°.
Reflect
tan u =
=
Ay
Ax
(3-2b)
1.00 mV
θ
1.40 mV
Our goal is to find the angle u shown in
the figure, which is the direction of the
heart’s electrical axis measured relative
to the horizontal. We choose the x axis to
be horizontal and choose the y axis to be
vertically downward. (We can choose the
axes to be whatever we want, provided
they’re mutually perpendicular.) The sketch
shows the electrical axis as a green vector; it
has an x component of 1.00 mV (shown in
red) and a y component of 1.40 mV (shown
in purple). As in Example 3-1, we’ll use
Equation 3-2b to find this angle.
electrical
axis
y component
x component
1.40 mV
= 1.40
1.00 mV
u = tan21 1.40 = 54.5° or 234.5°
Correct answer: u = 54.5°
If the horizontal and vertical signals were equally strong, the electrical axis would be tilted at an angle of 45° from the
horizontal. In this example the vertical component is somewhat larger than the horizontal component, so the angle is
a bit more than 45°. Normal clinical values are between 230° (that is, pointing 30° above the horizontal) and +90°
(pointing straight down), so our result is reasonable.