A single heartbeat's R-wave gives amplitudes and in an Einthoven ECG

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Muscle, heart and the fields outside the body

Problem

A single heartbeat's R-wave gives amplitudes

\mathrm{II} = 0.8\,\mathrm{mV}

and

\mathrm{III} = 0.3\,\mathrm{mV}

in an Einthoven ECG. In the standard frontal-plane diagram, lead I's axis points along

0^\circ

, lead II's axis along

60^\circ

and lead III's axis along

120^\circ

(angles measured clockwise from lead I, as seen facing the patient, so that positive angles point towards the feet), and each lead reads the projection of the heart's dipole vector onto its own axis. ((a)) Find lead I from Einthoven's law, without using the projection formulae. ((b)) Represent the heart's dipole as a single vector in this diagram: find its magnitude

p

(in mV) and its angle

\theta

from the lead I axis, using

\mathrm{I} = p\cos\theta

and

\mathrm{II} = p\cos(\theta-60^\circ)

. ((c)) Using your vector, predict the reading lead III should show, and confirm it against the given value of

0.3\,\mathrm{mV}

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