3.2 Electrophysiology of the Heart

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In particular, the ECG can also provide information about whether, for example, a

heart attack or other heart diseases is present.

As an alternative to the determination of a single heart vector, whose projection

onto the body surface yields the respective potential differences, the effects of the elec-

trical potential distributed over the closed surface of the heart on the body surface can

also be investigated. The equivalent double layer model (EDL, see [8, 57]) used for this

purpose can be formulated as a matrix equation:

Φ = A ⋅S .

(3.22)

S here is a N × T potential matrix of the heart surface and Φ is the corresponding L

× T-potentiometer matrixL × T-potential matrix of the body surface for N or L meas-

urement locations and T time points. A is the so-called L × N transfer matrix. Thereby,

according to Equation 3.22, given the potential on the heart surface, the potential on

the body surface can be determined by matrix multiplication. This is called the for-

ward problem. Often, however, because of the non-invasive measurement on the body

surface, only the potential at this location is known. If one wants to determine from

this the potential at the heart surface, the so-called inverse problem has to be solved,

which presupposes an invertibility of the transfer matrix A:

S = A⁻¹ ⋅Φ .

(3.23)

3.2.3 Process of Excitation Propagation during a Heart Beat

As already described, the excitation of the heart muscle cells takes place through a

conduction system, whereby the pacemaker cells in the sinus node excite further pace-

maker cells in the AV node and these in turn excite pacemaker cells in the His bundle

and the Purkinje-fibres. The latter finally cause the heart muscle cells to periodically

contract and relax again. The sequential course of a heartbeat is shown by Figure 3.17

in eight phases A to H. The course of this excitation can be measured with the help of

electrodes on the surface of the body and is known as an electrocardiogram. For the

sections shown in Figure 3.17, the individual phases (A to H) can be assigned to a wave

or stretch of the ECG (P, Q, R, S or T).

Section A: The cardiac excitation cycle is initiated by an action potential from the

pacemaker cells in the sinus node.

Section B: The excitation spreads across both atria, and the cell membranes of the at-

rial cells become depolarised, which is evident on the ECG as a P wave. In this sec-

tion, the atria contract and fill the ventricles with blood, causing the leaflet valves

(mitral and tricuspid valves) to open between the atria and the main chamber and

the semilunar valve indexes (aortic and pulmonary valves) to open between the

atria and the main chamber; a (aortic and pulmonary) valves are closed.

Section C: The excitation through the sinus node spreads to the AV node. It can only

spread further into the wall between the left and right main chamber ("tawara" =