Kenneth Stewart Cole

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Kenneth Stewart Cole
Kenneth Stewart Cole.gif
Born 10 July 1900
Ithaca, New York
Died 18 April 1984
La Jolla
Fields Biophysics
Alma mater Oberlin College
Cornell University
Notable awards National Medal of Science (1967)

Kenneth Stewart Cole (July 10, 1900 – April 18, 1984) was an American biophysicist described by his peers as "a pioneer in the application of physical science to biology".[1] Cole was awarded the National Medal of Science in 1967.[2][3]


Kenneth Cole was known to his wife as Ken but to all his friends as Kacy. His father, Charles Nelson Cole, was an instructor in Latin at Cornell University, and two years later the family moved to Oberlin, Ohio, when his father took a post at Oberlin College. His father would later become the Dean. Kenneth's mother was Mabel Stewart, and he had a younger brother, Robert H., with whom he remained very close throughout his life despite a large difference in age; they were joint authors of four papers published between 1936 and 1942.[4]

Cole graduated from Oberlin College in 1922 and received a Ph.D. in physics with Floyd K. Richtmyer from Cornell University in 1926. He spent summers working at the General Electric Laboratory in Schenectady, New York.

In 1932, Cole married Elizabeth Evans Roberts, an attorney. Later, her work was mostly concerned with civil rights and in 1956 she joined the staff of the new Civil Rights Commission [4]

Kenneth joined the staff of Columbia University in 1937 and remained there until 1946. He had also been associated with the Presbyterian Hospital, and the Guggenheim Foundation for Advanced Study at Princeton University and the University of Chicago. From 1949 to 1954 he was the technical director of the Naval Medicine Research Institute in Bethesda, Maryland. In 1954 he became chief of the laboratory of biophysics of the National Institute of Neurological Diseases and Blindness. He achieved advances that led to the "sodium theory" of nerve transmission that later won Nobel Prizes for Alan L. Hodgkin and Andrew F. Huxley in 1947. He was awarded the National Medal of Science in 1967, the award citation, read: "As a result, we know far more about how the nervous system functions." In 1972 he was made a member of the Royal Society of London. The Biophysical Society awards the Kenneth S. Cole medal to a scientist studying cell membranes. In 1980 he became an adjunct professor of the Department of Neurosciences at the Scripps Institute of Oceanography in San Diego. He had a son, Roger Braley Cole, and a daughter, Sarah Roberts Cole. He died on April 18, 1984.[2]

Electrical Model of Tissue

Tissue can be modeled as an electrical circuit with resistive and capacitive properties:

Equivalent Electrical Circuit

Its dispersion and absorption are represented by the empirical formula:

\epsilon^* - \epsilon_\infty  = \dfrac{\epsilon_0 - \epsilon_\infty}{1 + (i\omega\tau_0)^{1-\alpha}}

In this equation \epsilon^* is the complex dielectric constant,  {\epsilon_0 } and \epsilon_\infty are the "static" and "infinite frequency" dielectric constants, \omega = 2\pi times the frequency, and \tau_0 is a generalized relaxation time. The parameter \alpha can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. This expression requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below the axis.

It is worth emphasizing that the Cole–Cole model is an empirical model of the measured data. It has been successfully applied to a wide variety of tissues over the past 60 years, but it does not give any information about the underlying causes of the phenomena being measured.

Several references in the literature use a form of the Cole equation written in terms of impedance instead of a complex permittivity.[5] The impedance Z is given by:

Z = R_\infty\frac{R_0-R_\infty}{1+(\tfrac{jf}{f_c})^{1-\alpha}}

Where R_0 and R_\infty are the resistances at zero frequency (i.e. DC) and infinity, respectively. f_c is often referred to as the characteristic frequency. It should be emphasized that the characteristic frequency is not the same when the analysis is carried out in terms of the complex permittivity. A simple interpretation of the above equation is in terms of a circuit where a resistance S is in series with a capacitor C and this combination is placed in parallel with a resistance R. In this case R_0 = R and R_\infty\ = \tfrac{RS}{R+S}. It can be shown that f_c is given by f_c=\tfrac{1}{2\pi C(R+S)}


  1. Goldman, D.E. 1985. Kenneth S. Cole 1900-1984. Biophysical Journal 47:859-860
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  3. Schwan HP. 2001. The concept of bioimpedance from the start: evolution and personal historical reminiscences. Proc. IX Bioimpedance Conf., Oslo, Norway
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  • Cole, K.S. 1979. Mostly membranes. Annual Review of Physiology 41:1-23 PMID 373584
  • Cole, K. S., and R. H. Cole. 1941. Dispersion and absorption in dielectrics. J. Chem. Phys. 9:341-351 [1]
  • Cole, K.S., and Baker, R.F. 1941. Longitudial Impedance of the Squid Giant Axon. J. Gen. Physiol. 24:771-788 (Inductance of membrane)

External links