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6 Applications and Methods in Biosignal Processing

Fig. 6.14: Influence of cardiac excitation on the

body surface by a central cardiac Vector PQ in

3D representation during a vector ECG. Here,

the change in the heart vector is described

by a brown or light brown locus curve, which

indicates the position of the vector peak as a

function of time.

course of which is called electrocardiogram (ECG). The aim is to be able to examine

the excitation of the heart muscles as precisely as possible so that the physician can

diagnose any heart disease that may be present. If, as already shown in section 3.2, the

excitation of the heart is represented by a single electrical heart vector PQ at a central

location Q in the heart, this changes its strength and direction during cardiac activity

as a function of time (see Figure 6.14).

The electromagnetic field generated by the cardiac vector influences the potential

at the body surface. The heart vector is a current vector that summarises all the cur-

rents of the heart cells generated by individual current dipoles (cf. subsection 3.2.2). If

this relationship is approximately linear and the superposition principle applies, the

potential ΦP at any point P on the body surface can be described as a scalar product of

the heart vector with a so-called lead vector CQ, which has its origin at the same place

as the heart-current-dipole [47], i.e. h.

ΦP = CQ ⋅PQ .

(6.4)

The difference between two potentials ΦPi = CQi ⋅PQi and ΦPj = CQj ⋅PQj on the body

surface is the voltage VPij measured between the recording points i and j, which can

also be expressed by a lead vector:

VPij = (CQi −CQj)

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

CQij

⋅PQ = CQij ⋅PQ .

The new Vector CQij now point not from the origin of the heart vector to the body sur-

face, but from one recording point on the body surface to another.

In order to assess the excitation of the heart muscle well, the potentials are meas-

ured at different locations on the surface of the body. Depending on the location, num-

ber and presentation of the recording points, a distinction is made between different

leads. The standard "12-channel" lead includes: