55

The History of Bioelectromagnetism

   

Rudolf Höber (1873–1953), a German physician, investigator, examined the frequency dependence of the

conductivity of blood at low (100–200 Hz) and high (~MHz) frequencies. He presented that the interiors

of red blood cells and muscle cells contain conducting electrolytes, and that each conducting core is

contained within an insulating membrane (Pethig and Schmueser, 2012). He showed that the imped­

ance decreased with increasing frequency and estimated the resistivity of the interior of the erythrocyte

(Höber, 1910, 1912, 1913). He also developed the concept of β-dispersion in suspended red blood cells

which later generalized to muscle tissue. Höber with his Jewish wife had lef Germany before World

War II and got a position in the physiology department at the University of Pennsylvania.

Afer Höber’s investigation, Maurice Philippson (1877–1938), professor of zoology and physiology at

Brussels University, measured animal tissue impedance as a function of frequency (500 Hz–3 MHz) and

found that the capacitance of animal tissues varied roughly as the inverse square root of the frequency

(Philippson, 1920, 1921). Te capacity of vegetable tissues varied as the inverse fourth root of the fre­

quency. Te magnitude of the impedances decreased with frequency. Tis polarization capacitance was

similar to that found for the metal/electrolyte interphase (Grimnes and Martinse, 2000). He reported

the β-dispersion by red blood cells (Pethig and Schmueser, 2012). Historically, equivalent circuits have

been proposed by many scientists. Maurice Philippson presented an equivalent circuit of red blood cells

consisting of the protoplast resistance in series with a parallel combination of the membrane resistance

and capacitance.

Te next important step was made by Hugo Fricke (1892–1972), Cleveland Clinic Foundation,

Cleveland, and Sterne Morse, who proposed an equivalent circuit of red blood cell suspensions.

Assuming that the cell membrane is electrically as a thin dielectric layer, and analyzing the passive elec­

trical properties of canine red blood cells, they hypothesized that the reasonable thickness of the mem­

brane is around 3.3 nm and that the electrical capacity of the membrane is of 1 μF per square centimeter.

Teir equivalent circuit consisted of the resistance around the cell, resistance of the cytoplasm, and

the capacitances of the membranes (Fricke, 1925; Fricke and Morse, 1924, 1925a, b). In this circuit, the

membranes have a high reactance at low frequencies and a low reactance at high frequencies. Kenneth

Stewart Cole and Richard F. Baker, Columbia University, developed an equivalent circuit with the resis­

tance of the cytoplasm, the inductance of the membrane and in series with a parallel combination of

capacitance of the membrane afer discovering an inductive reactance within the membrane structure

(Cole and Baker, 1941: Pethig and Kell, 1987; Pethig and Schmueser, 2012). Tissue can be modeled as an

electric circuit with resistive and capacitive properties.

Kenneth Stewart Cole, American biophysicist, Columbia University, was trained as biophysicist

and spent time with Peter Debye (1884–1966) in Leipzig. In 1941, Cole and Robert H. Cole (1914–1990),

K. S. Cole brothers, chemist, the professor at Brown University, published a paper in which they intro­

duced the famous Cole-Cole equation (Cole, 1928a, b; Cole and Cole, 1941). Tey opened the way to

treat analytically and mathematically the tissue conductivity and permittivity. K. S. Cole frst derived

the electric impedance of a suspension of spheres each having a homogeneous non-reactive interior

and a thin surface layer with both resistance and reactance (Cole, 1928a). His discussion was that the

equivalent circuit has the form of a capacitor in parallel with resistors. Impedance is the ratio between

voltage and current. In a companion paper, he presented the results for the measurements of the elec­

trical impedance of suspensions of small arbacia eggs in sea water (Cole, 1928b). Te results were in

accordance with the theory presented in the previous paper. Teir introduced Cole-Cole plot is a useful

method which shows the behavior of tissue impedance as a function of frequency. Tis is a complex

plane locus of real components versus imaginary components with the frequency parameter (Cole and

Cole, 1941). Now, it is a simple presentation. It has been successfully applied to a wide variety of tissues.

Te Cole-Cole plot is an empirical model of measured data. However, it does not give any information

about the underlying electrical phenomena being measured.

During the 1920s and 1940s, great interest in the electric properties of cells and tissues increased rap­

idly among researchers. Cole, Curtis, and others applied the potential theory based on Maxwell’s work

to cell suspensions (Cole and Curtis, 1939). Tey also collected data of the electric properties of cells and