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The electrical forces of cardiac depolarisation and repolarisation are vectors and as vectors
they obey certain mathematical principles. You need to have a basic knowledge of some
of these principles in order to understand the normal ECG / EKG and ECG / EKG abnormalities
discussed in the next section. Firstly, vectors have both magnitude and direction.
In mathematics a vector is drawn as an arrow indicating its direction while the length
of the arrow from the initial point to the terminal point is indicative of its magnitude.
If the vector shown here represents a depolarising voltage of one milivolt travelling in the
direction indicated, then a depolarising force of 2mV travelling in the same direction is
represented by an arrow twice its length. We've already seen that if this 1 mV depolarising
vector is moving directly towards an ecg lead, set at a standard sensitivity, it will produce
a positive deflection of 10 small squares on the readout from this lead. In contrast,
in a lead positioned such that the vector is heading directly away from the lead, it
will produce a negative deflection of the same magnitude. This is simple enough, however,
it is important to realise that vectors can be resolved into smaller components travelling
in different directions. Components are also vectors and may be drawn in many different
directions off the initial point of the parent vector in accordance with the so called 'parallelogram
rule'. As illustrated here, the magnitude of components are linked by the requirement
that they form the sides of a parallelogram touching the apex of the parent vector. For
our purposes, what this means is that a depolarising vector produces an effect in leads positioned
off its direct line of travel. Calculation of the magnitude of this effect in the direction
of any given lead is relatively straightforward. Look at this situation, a depolarising vector
of voltage v is travelling at an angle theta off the direct line to lead A. What is the
maximum voltage component of this vector travelling directly towards the lead? To calculate this,
we let the direct line to the lead define the x --axis. Using the parallelogram rule,
if we draw the parallelogram as a rectangle, this sets the component on the y axis at zero
relative to the lead (the reason for this will be obvious shortly) and gives us the
maximum possible length of the component vector travelling directly towards the lead. The
magnitude of this x-axial component can be calculated very simply. In a right angled
triangle the cosine of the angle theta is given by the length of the adjacent side divided
by the length of the hypotenuse. Remembering that length equates to magnitude, the magnitude
of the x axial component is, therefore, equal to the magnitude of the parent vector multiplied
by the cosine of the angle theta. In the example shown here, a depolarising force of 1 mV is
travelling at an angle of 40 degrees off the direct line to the lead. The component of
this depolarising vector travelling towards the lead is therefore 1 x cosine 40 degrees
or (1 x 0.766) mV. At standard ECG / EKG sensitivity, this gives a positive deflection of just under
8 small squares in the readout from the lead. Remember also that cosine declines as the
angle increases, therefore the larger the angle the parent vector makes with the direct
line to the lead, the smaller the component in its direction. Importantly, as the cosine
of 90 degrees is zero, when the parent vector reaches 90 degrees relative to the lead, the
component on the x axis will also be zero and no deflection is produced in the readout.
This is a very important principle in ECG / EKG analysis. A vector has no component
at right angles to itself. So no matter how large in voltage a depolarisation vector may
be, if it is moving at 90 degrees relative to an ECG lead, no net deflection is produced
in the readout from that lead. Once the vectors direction of travel moves beyond 90 degrees
relative to the lead, the signal produced is negative and the same simple maths we've
just employed can be used to calculate the magnitude of the negative signal generated.