ECG Signals Derived from Maxwell’s Equations
Scientists have been measuring the electrical activity in human organs for more than a hundred years. Today, electrocardiography, electroencephalography and electromyography give remarkable insight into diseases of the heart, brain and muscles respectively.
The trouble is that nobody really understands how these macroscopic signals are linked to the microscopic state of the body. That makes it hard to interpret the signals in any way other than trial and error. What’s needed is a good theoretical model of how the processes at work at the microscopic level lead to the measurements picked up by modern equipment. Such a description ought to lead to an entirely new understanding of the data and what it can be used to detect.
Now Gunter Scharf at the University of Zurich and a couple of buddies put forward just such a model. Their approach is to work out the kind of charge and current densities that cells produce and to average it over many cells in a specific organ. “In this way we get a description of the electrical activity of the organ from first principles,” they say.
The key insight which they derive is that the main source of any measured potential is caused by the separation of charge by the cells in question.
This insight embodies the crucial difference between dead and living matter. “In dead matter the polarization is generated by passive response to an applied external electric field; in living matter an electric dipole moment can be produced actively by chemical processes,” say Scharf and co.
For example, positively charged sodium ions are known to move in and out of cells while negatively charged proteins remain inside. The combined effect of all these dipole moments averaged throughout the organ is what determines the measured potential.
What seems to have confused people in the past is that the movement of ions also generates a current. Scharf and co say this current cannot be the origin of the measured potential because it would tend to diminish any potential measured outside the organ.
That ought to have some important implications for the way bioelectric measurements are made. Scharf and co calculate one example in which they determine that a measurement of the potential on the innermost layer of tissue in the heart is a direct measurement of the dipole density in the tissue. That makes it the best place to pick up arryhthmias in the heart, which is exactly what heart specialists have found using conventional trial and error approaches.
The question, of course, is what to do next with this model. If it allows more detailed theoretical studies indicating the best places to measure the behaviour of muscles and even the brain, then medical specialists could be in for a treat.
Ref: arxiv.org/abs/1006.3453: Electrophysiology Of Living Organs From First Principles
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