Kenneth Stewart Cole

Kenneth Stewart Cole (July 10, 1900 – April 18, 1984) was an American

In 1932, Cole married Elizabeth Evans Roberts, an attorney. Later, her work was mostly concerned with civil rights and in 1957 she joined the staff of the United States Commission on Civil Rights^[4]

Kenneth joined the staff of

Its dispersion and absorption are represented by the empirical formula:

${\displaystyle \epsilon ^{*}-\epsilon _{\infty }={\dfrac {\epsilon _{0}-\epsilon _{\infty }}{1+(i\omega \tau _{0})^{1-\alpha }}}}$

In this equation ${\displaystyle \epsilon ^{*}}$ is the complex dielectric constant, ${\displaystyle {\epsilon _{0}}}$ and ${\displaystyle \epsilon _{\infty }}$ are the "static" and "infinite frequency" dielectric constants, ${\displaystyle \omega =2\pi }$ times the frequency, and ${\displaystyle \tau _{0}}$ is a generalized relaxation time. The parameter ${\displaystyle \alpha }$ 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.^[8] The impedance ${\displaystyle Z}$ is given by:

${\displaystyle Z=R_{\infty }+{\frac {R_{0}-R_{\infty }}{1+({\tfrac {jf}{f_{c}}})^{1-\alpha }}}}$

Where ${\displaystyle R_{0}}$ and ${\displaystyle R_{\infty }}$ are the resistances at zero frequency (i.e. DC) and infinity, respectively. ${\displaystyle f_{c}}$ is often referred to as the characteristic frequency. 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 ${\displaystyle S}$ is in series with a capacitor ${\displaystyle C}$ and this combination is placed in parallel with a resistance ${\displaystyle R}$. In this case ${\displaystyle R_{0}=R}$ and ${\displaystyle R_{\infty }\ ={\tfrac {RS}{R+S}}}$. It can be shown that ${\displaystyle f_{c}}$ is given by ${\displaystyle f_{c}={\tfrac {1}{2\pi C(R+S)}}}$.

Electrical measurements of tissues

In a series of papers in 1930s -- 1940s, he experimentally studied the electric properties of living tissues, such as Nitella,^[9] frog eggs,^[10] and most famously, the squid giant axon.^[11][12]

Figure 4 of ^[11] is sometimes used as artistic representations of biophysics. It also appeared, rotated 90 degrees, in Swedish apartments as modern art.^[13]

See also

• Action potential
• Cable theory
• Dendrite

References