The concept of Bioimpedance from the start: Evolution and personal historical reminiscences

Herman P. Schwan

Bioengineering Department, University of Pennsylvania

Philadelphia PA 19104

Introduction

I first comment on appropriate terminology for presentation of bioimpedance data by:

1. pointing out some principal considerations,

2. stating personal preference. My choice is largely motivated by my relevant experience. The presentation in terms of admittance components indicates at once underlying mechanisms, while the presentation in impedance components hides this simple picture as I shall demonstrate,

3. the pertinent history and usage applied by pioneers of the field.

I shall talk about some of the great contributors such as Hoeber, Fricke and Cole, their choice of terminology and personal contacts. I next present a summary of my bioimpedance work and how it was influenced by them. I conclude with a few remarks on non linearity. Prediction of the onset of non linearity is fairly straightforward if one is aware of mechanism more readily apparent from admittance data.

On Terminology

We can use both impedance and admittance presentations depending what we want to demonstrate. Usually it makes more sense to use admittance terminology for several reasons:

1. Consider electrolytes and water. Their conductivity s and permittivity e are frequency independent up to several GHz. Their volume specific Z components are not, as seen from eq.5 of table 1. Thus impedivitty data change with frequency and the frequency range of change varies with salt concentrations. The simplicity of the admittivity data directly indicate responsible mechanism, i.e. ion mobility and the polarity of the water molecule . Thus Y component terms s and e appear to be more “real”, but not Z-terms. Clearly, in this case it makes more sense to use the admittivity presentation.

2. The admittance circle peaks at a frequency identical with the characteristic frequency w_o=1/2pT of relaxation processes of the Debye type (T relaxation time). The impedance circle tops at a frequency which is different from this characteristic w_o and hence different from the frequency where the admittance circle tops. The circle in the admittance plane peaks when G = 0.5 (G₀+G_∞). The circle of the impedance plane peaks when R = 0.5(R_o+R_∞). This happens at a frequency which differs from the one where the admittance circle peaks by the square root of G_o/G_∞ This value is large for the b- and g-dispersion ranges of tissues. We prefer the use of admittance data s and e since they more directly relate to the Maxwell-Wagner b-dispersion of tissues and cell suspensions and the Debye g-dispersion of water.

Table 1. Definitions.

Electrical sample properties:

Z = R + jX (1)

(Z Impedance Z, R Resistance, X Reactance)

Y = 1/Z = G + jwC (2)

(Y Admittance, G conductance, C capacitance)

Volume (unit) specific entities:

"Impedivitty" (introduced by Otto Schmitt)

spec. Z = r = r' + j r" (3)

No terms seem to exist for volume specific quantities r' and r"

Admittivity

s* = s + jwe (4)

(s conductivity, e permitivity, w angular freqency)

r=1/s equals “resistivity" or specific resistance. Hence resistivity r

not equal to volume specific resistance r'. Instead

r' = r [ 1 + (wer)² ] (5)

3. The admittance terminology is used by physicists and physical chemists. Biophysicists prefer it also. Bioengineers are not interested much in mechanisms responsible for frequency dependence and seem to prefer the Z-Terminology, even though no volume specific terms have become accepted or even proposed.

4. What about when frequency dependencies exist, i.e. when relaxation effects contribute to the total frequency-behavior? In such a case the usual treatment is for Debye type relaxations. Then the equivalent frequency response yields the dispersion equation

s* = s_o + (s_∞-s_o) (w/wo)²/ [1+(w/wo)²] (7)

An admittance circle results when one plots the two components of s* against one another. It peaks if the angular frequency w is equal to w_o .So we have a base s_o and an additional relaxation term which is frequency dependent. Since the inverse of a circle is again a circle, the impedance plane plot yields also a circle. But its top frequency is no longer equal to w_o as stated above.

Early historical record.

Early investigators of electrolyte conductivities such as Warburg, Nernst and Kohlrausch used conductivity (or its inverse "resistivity"). A need for a capacitive component was apparently at first recognized after WW1. Electrolytes s and e are frequency independent up to several GHz, but in impedivitty presentations they are strongly frequency-dependent. Thus electrolyte admittance data are consistent with simple theory of ionic conduction, directly apparent from s and e, but not volume specific impedivitty data. The tradition to present what appear to be "real" data rather than complex modifications was retained by the physical chemists after WW1, including Debye. Probably the first extensive collection of tissue data is contained in Rajewsky's book from 1938. Its usage followed the established tradition i.e. use of conductivity or resistivity and dielectric constant..

A few words about laboratories which were active in this field and emerging during the 1920's. They were few in number, and I am not aware of the existence of any formal academic program that would have led to advanced degrees in the field of biophysics or biomedical engineering at these early times. In most of these early institutions engineers joined with physicists and medical doctors, attracted by the possibility to apply the analytical power of the physical scientists and their instrumentation to problems in biology and medicine. There was a good mixture of fundamental and applied research. The more basically oriented work was, in most cases, undertaken to eventually solve problems of practical importance, that is, purpose-oriented basic research. Early research was concerned with the effects of ionizing radiation and x-ray technology, electrophysiology, and studies of the electrical properties of live matter and relevant applications in physical medicine.

I joined such an institution in 1937. The early years at the Kaiser Wilhelm, later Max Planck institute of Biophysics were one of learning about electrode polarization, resolution requirements and instrumental limitations existing at the time. There was also initially an interest in medical applications, yielding an electronic hematocrit instrument which was later patented in the USA and a modest commercial success. It also led to a technique of electronic and rapid cell sedimentation measurements.

Great investigators

Next let me comment on some of the pioneers of the bioimpedance field: Hoeber, Fricke and Cole. The example set by these great investigators had a great influence on the development of the field and myself. First of all it stimulated my interest in biophysics at a time when I tried to finance my studies by accepting a technician's job at one of the first biophysical research centers, the Kaiser Wilhelm Institute of Biophysics. The generosity of its director Boris Rajewsky permitted me to enter a field where a combination of mathematics, physics and engineering could be applied to biological systems with an approach typical of physical scientists. The approach was that of a young aspiring scientist eager to understand why properties were as observed without any motivation by questions formulated by life scientists or medical professionals.

R Hoeber

Hoeber recognized the frequency dependence of the conductivity of blood about 1911. He also determined the erythrocyte's interior conductivity and established the existence of cell membranes. He was a leading German physiologist and President of the University of Kiel when Hitler came to power. He left Germany when he was demoted since he was married to a Jewish woman and accepted a position at the department of physiology at the University of Pennsylvania. I met him there when I came to the USA in 1947. He had read the Naturwissenschaften paper reporting on my recent determination of the erythrocyte's cytoplasmic conductivity. He invited me to lecture before the Philadelphia Physiological Society. He also invited me to his home. He was a very kind man, missing Germany where he had been able to accomplish much before disaster struck Germany when Hitler came to power. Shortly thereafter I was offered a faculty position at Penn's School of Medicine, perhaps with his support. Hoeber was the first to recognize that the conductivity of cell suspensions change with frequency and to conclude the existence of cell membranes. His early work deserves to be recognized as the start of the bioimpedance field and its dispersive character.

H. Fricke

I became aware of Fricke's and Cole's work already in Frankfurt, where I had read many of their papers. Hugo Fricke had studied physics in Copenhagen under Niels Bohr. Then he went to the USA where he held appointments at Harvard and the Cleveland Clinic before joining the Carnegie Foundation Cole Spring Harbor Laboratory. His significant work established him as a leader in the bioimpedance field as well as in ionizing radiation biophysics. It is summarized in table 2.

Tab.2. Summary of H. Fricke's work.

Electrical:

His equipment-

Construction of wide band impedance bridge.

Experimental data - Cell suspension work.

Foundation of b-dispersion. -

First data on colloidal suspensions. -

First diel. property data on amino acids . –

Radiology (equally distinguished) :

Chemical dosimeter, radical formation.

Much of the early bioimpedance work by Cole, Fricke and Curtis was presented at the famed Cold Spring Harbor symposia taking place before WW2. Later, during the war, radiation bioeffects demanded priority. Fricke's work came to a conclusion and he lost his laboratory at Cold Spring Harbor. He stayed on, living simply in his beautiful bungalow situated above the laboratories. I first contacted Fricke shortly after arriving in the USA, asking questions about his work and learning a lot. A few years later I was able to offer him compensation in form of a subcontract, using funds which I had negotiated with ONR and NIH. He published several papers during the late 1950's which are still quoted. Work at Cole Spring Harbor laboratories was started again as I moved my more modern equipment there to measure the dielectric properties of E. Coli. This work was published in Nature. It was the first bacterial work of the sort, establishing the existence of membranes surrounding the cells. We visited now fairly often, spending the night as his guests in his house and joining him while he was singing Danish folks songs and playing the piano. During this time Fricke celebrated his 70th or 75th birthday. The Radiation Research Society honored him by publishing a special issue of its journal. It was entirely dedicated to Fricke, republishing his most important articles. I organized a bioimpedance meeting in Chicago with Cole, Fricke and myself lecturing. Fricke and myself met there with a young man who showed us an impedance cell with a small orifice between the electrodes. His name was Coulter. We thought that it was a clever idea. This cell counter became one of the most successful bioimpedance devices ever. At the Chicago meeting Fricke met with an old coworker, now at Argonne National Laboratories. This led to Fricke's acceptance of a consultant arrangement at Argonne and we lost contact. After several years we visited him and his wife once more and had lunch together at his home. We were all in a good mood. He was quite familiar with the work we had done in the meantime at Penn. He was particularly impressed by my investigations of the a-dispersion of colloidal suspensions. However he suffered from cancer and died shortly thereafter. His wife asked me if I wanted his scientific papers and bring some to fruition. I regret that I did not do so.

Fricke used s and e. He disliked circles which he believed hid the truth and preferred plots of e and s against frequency. Fricke extended Hoebers work significantly. He first measured over a broad RF-range and provided a rigorous theoretical basis of the b-dispersion. Cole mentioned once to me that he considered Fricke the real pioneer of the field. He is also held in high regard in the field of ionizing radiation bioeffects, having first discovered radical formation as the cause of radiation injury.

K.S. Cole.

I decided after arriving in the US in 1947 to investigate electrical and acoustic properties of biological materials over the much broader frequency range which had become available after WW 2. I saw a need to collect data, to explore mechanisms responsible for such data and to better understand the interaction of electromagnetic and acoustic fields with biological matter. I suspect that it was Kenneth Cole who was asked to evaluate the research proposals which I submitted first to the Navy and its Office of Naval Research and then the National Institute of Health. The proposal was approved. Cole was then head of the Navy's Biophysical Research Lab at Bethesda, and Howard Curtis who worked many years with Fricke and then Cole was at Brookhaven and a consultant on the NIH study section evaluating my grant application. I had established contact with both Fricke and Cole shortly after my arrival to the USA, visiting them frequently and learning a great deal. Cole was by training a physicist and had spent a year with Peter Debye in Leipzig. The late Chris Brainerd, former Director of the Moore School of Electrical Engineering at the University of Pennsylvania told me that he met Cole at Bell Laboratories. Cole had become interested in electrical circuit analysis and synthesis and their usefulness as models for the dispersive behavior of cell suspensions. He correctly felt that the engineers at Bell knew a lot about this. That must have happened a few years after Cole's return from Leipzig.

Kacy Cole proved a patient, but hard taskmaster. His papers were not easily read and my colleagues in the medical school's physiology and neurology had trouble to understand them and turned to me for help. I visited Cole, asked questions, understood only half, asked later again and was promptly reminded that I did not read his pertinent paper with care even though he had told me about it. Eventually he accepted me and I became almost a member of his team. When he was asked to write for the third edition his contribution to Glasers Medical Physics, he asked me to be co-author and insisted on my being listed first. Much later, when he had published his famous book, he mailed me a copy with a notation "with admiration for all what you have done". And when we celebrated his 65th and 80th birthday, I was asked to present lectures which were published in the respective conference volumes.

What were Cole's significant scientific contributions? His early work on cell suspensions, the development of the voltage clamp technology and the discovery of the conductivity change with excitation in the squid axon membrane are most important. His cell suspension work equaled in quality that of Fricke, further establishing the basis of the RF- range frequency dependence of dielectric properties. His voltage clamp was a prerequisite of measuring successfully the membrane conductance of the giant squid axon. This work was carried out primarily at Woodshole, where fresh squids had become available and the proper handling of the giant axon established. Cole and Curtis did their famous squid axon work there in1938, work which was to revolutionize and start membrane biophysics. It motivated Hodgkin's and Huxley's work, their equations and subsequent Nobel award and channel discovery. The voltage clamp led in due time to the patch clamp earning Neher and Sackman a Nobel prize. But Cole never got it, to his colleagues disappointment. Finally I must mention the Cole brother's famous papers on the Cole-Cole circle and its semi-logarithmic time constant distribution function. It became probably the most often quoted paper in the fields of dielectrics and bioimpedance.

Cole was also a founder of the biophysical society which is now a huge scientific organization. Last, but not least, I mention Cole's constant phase angle, often invoked in order to explain the observed broadened b-dispersion relaxation response. It motivated me to investigate low frequency properties. If a constant phase element in the membrane holds sway over an extended frequency range then the capacitance must continuously increase as the frequency decreases below the b-dispersion range. I found instead the a-dispersion. This new dispersion demanded an entirely different explanation than provided by the constant phase angle concept. However the initial response to my 1950 lecture about my a-dispersion discovery of muscle at the annual physiological society meeting was disappointing. And my 1954 paper in the German journal Naturwissenschaften did not fare much better. It was Kacy Cole who brought my work to the attention of Fatt and Falk in Katz laboratory. They confirmed in 1964 the a-dispersion and proposed that the intracellular membrane system of muscle cells was the cause of the effect. Now interest increased rapidly in this low frequency effect and many other papers followed.

Cole moved to San Diego after he retired. He was very lonely after his wife's death. But he came every summer to Woodshole where he worked in an small one room laboratory. He did there fine experimental work, proving that Maxwell's mixture equation is almost perfect for poorly conducting particles surrounded by an electrolyte. He asked me to help him to retain this NIH lab. I tried in vain with the NIH biophysics director. Kacy Cole suffered much from almost continuous severe backpain and died a few years later Cole deserves more than any others to be recognized as creator of the biomembrane field by his discovery of the conductivity change with excitation and for providing relevant modern instrumentation. Cole used both admittance and resistance terminology. His rational for impedance is in good part based on the need to correct for the access resistance element which must be considered in single cell preparations. This element is part of the theory of the b-dispersion and, hence, need not be considered separately in cell suspension work.

A summary of our bioimpedance work.

I joined the Airomedical equipment laboratory of the Navy in Philadephia 1947 and the University of Pennsylvania in 1950. At Penn I was soon appointed as head of an existing electromedical laboratory, later to become one of the very early bioengineering departments. I had been able to develop in the Navy high resolution instrumentation of unsurpassed sensitivity and accuracy, extending the frequency range both well below and above the radio frequency-range previously investigated by Cole and Fricke. A great deal was accomplished during the decade prior to my 1957 review, which is more of a monograph summarizing this work. This included collection of many data, instrumental advances and the discovery of additional relaxation mechanism.

Most of our early bioimpedance work during the 1950's and 1960's is summarized in table 3. Not included are our contributions to the nonionizing radiation fields and bioacoustics.

Table 3. Bioimpedance research at University of PA

1. Precision equipment at low and ultrahigh frequencies.

High resolution principles. Role of electrode polarization.

2. Development of four electrode techniques to eliminate electrode polarization

3. a-dispersion in muscle tissue

4. a-dispersion of colloidal particle suspension

5. First tissue and cell suspension data above 100 MHz. Conclusions:

The g-dispersion is due to cell water

Cell water is identical with normal water.

6. Discovery of the ultrahigh (UHF) dispersion of protein bound water.

7. First dielectric data and analysis with Fricke of E coli discovering evidence for its membrane

8. The a-b-g classification of dispersions typical for tissues and cell suspensions through the total frequency range from a few Hz to 10 GHz.

9. Analysis of cytoplasmic conductivity with Pauly.

10. Dielectric analysis of mitochondria, PPLO and vesicle suspensions.

There had been already considerable progress due to Fricke, Cole and others over a more restricted frequency range and there was growing interest in therapeutic and diagnostic applications as well as suspected health hazards resulting from undue exposure. Our initial efforts concentrated on the same frequency range previously explored, i.e. on the dispersion which I later termed b-dispersion and which occurs at RF-frequencies.. We obtained modern instrumentation which became available after world war II. We refined the relevant math, adding simple closed form expressions which permit the easy extraction of cellular parameters from experimental data. We carried out many measurements, applying dielectric spectroscopy to all sorts of cellular systems. This included analyses of E. Coli with Fricke and mitochondria with Pauly and Lester Packer, several vesicle systems with Thompson and with Stoeckenius and pleuropneumonia-like organisms with Morowitz. An analysis of erythrocytes with Pauly led to a better determination of the internal conductivity and its response to osmotic shock. An important result was achieving an understanding of the factors which determine cytoplasmic cell conductivity values.

Data at low and very high frequencies were virtually non existing and we concentrated here our efforts. Our data above 100 MHz together with unpublished data from the Mayo clinic, made available to me by Julia Herrick, extended the range to 10 GHz. They clearly demonstrated the role of water, with biological water being identical with normal water except for a small fraction of protein bound water whose relaxational spectrum we found to occurs between 0.1 GHz and a few GHz.

Another major interest focused on low frequencies. One motivation for this was the concept of a polarization element which is characterized by a frequency independent phase angle. Jonscher used it in his formulation of a "universal dielectric response". It is used in dielectric theories, electrode polarization theories and provides a model for the Cole-Cole distribution function of relaxation times. It is a mathematical tool used in models describing dielectric responses, but its physical basis remains obscure. Its great popularity is due to the fact that the Cole-Cole function yields circular behavior in complex plane plots of dielectric data. However, I noted in the 1950's that circular plots are approximated by almost any logarithmic symmetrical distribution functions. Only at frequencies well above or below the relaxation frequency differences become apparent. The applicability of the Cole-Cole model to tissues and cell suspensions can be tested at low frequencies. However, to do so requires extraordinarily sensitive equipment. I had developed such equipment. Instead of the predicted logarithmic response demanded by the Cole-Cole model I found an entirely new relaxation process for muscle tissue, centered at 80 Hz.

In the meantime I had become interested in colloidal particles suspensions as a model for tissues. Fricke had published a paper about the dielectric behavior of suspensions of small glass spheres. He found that the permittivity increases as the frequency is lowered. But Fricke did not reach the low frequency limit necessary to recognize the a-relaxation effect. Furthermore, it was uncertain to what extent electrode polarization could have contributed to the observed data. He also entertained the idea of an "polarization" element with frequency-independent phase angle. We found also that milk displayed the low frequency dispersion behavior which I had first noted with muscle. Shortly thereafter monodisperse particles became available and Mazcuk and myself carried out extensive measurements on these suspensions, concentrating on the pronounced size dependence of the relaxation time constant. I reported early findings in my 1957 review article on dielectric properties of cell suspensions and at the first Biophysical Conference in the United States. I considered all sorts of possible mechanisms. I concluded that a frequency independent surface conductance could not explain my data. Instead, if surface effects were considered responsible, the surface conductance had to be a frequency dependent admittance. Gerhard Schwarz in Goettingen was also interested in counter ion effects. He joined my laboratory and set out to formulate his relevant theory. We published two papers in 1962. One contained most of our experimental data and a detailed discussion of non applicable concepts. His paper contained the theoretical treatment. Robert Cole wrote me that the discovery of the effect and its explanation were a most significant dielectric contribution during the past decades. Since then many more papers have been published on the dielectric properties of colloidal particles and the theory has been refined.

Has everything been done? There is but little doubt that counterion relaxation is at least in part responsible for the LF- dispersion which I had termed a-dispersion. But Fatt and Falk in Katz's laboratory had convincingly demonstrated that the tubular system in muscle tissue is a strong contributor. Gersing recently demonstrated that gap junctions in liver tissue cause a-dispersion effects. Furthermore membrane conductance properties are well known to be dispersive at low frequencies as may be seen from the linear version of the Hodgkin-Huxley equations. To sort out all these mechanisms remains a task for the future. Further, a theory of counter ion relaxation suitable for biological cells, distinguished by very high permittivities, remains undone.

Nonlinearity is another topic to be addressed.. Their importance is warranted by the fact that in many biomedical applications fields are applied which expose tissue to modest fields which evoke nonlinear responses. It seem to me that it is fairly straightforward to anticipate that nonlinearity occurs at fairly low field strength levels, say of the order of 1 V/cm. At this level typical cell membranes are exposed to membrane induced potentials of the order of 10 mV, i.e. levels where nonlinearity starts as may be concluded from the HH equations. More detailed insight is gained if one is aware of the various mechanism responsible for the dispersive behavior of tissue and the various cellular compartments.

Acknowledgment.

I am grateful to Sverre Grimness and Orjan Martinsen who invited me to participate in this outstanding and well organized meeting. I owe them much and enjoyed our frequent discussions and their great hospitality. Thank you for everything.

Work in my laboratory at the University of Pennsylvania would not have been able to contribute so much to the fundamentals of the field of interest were it not for the outstanding contributions of many colleagues and friends, including Ed Carstensen, Helmut Pauly, Gerhard Schwarz, Shiro Takashima and Ken Foster. Their long association earned our laboratory a unique reputation. - Very important was the influence of the old pioneers. Hoeber's interest led to my appointment at Penn where I found an atmosphere conducive to my program as then perceived. Cole motivated my LF work and the discovery of the a-dispersion, the contact with Fricke led not only to the E. Coli work but subsequently to other work on microorganisms and his own renewed activities during the 1950's. I learned a lot from Fricke and Cole. Perhaps most important was the realization that my original believe that biology was too complex to be analytically understood was wrong. If the right questions are formulated quantitative answers and understanding are achievable as the pioneers had so well demonstrated.

References.

I include only a few references, listing a few of our most often quoted reviews, my summary at the occasion of Schwarz' 70th birthday and the books by Cole, Grant, Takashima and Grimness and Martinsen.

ELECTRICAL PROPERTIES OF TISSUE AND CELL SUSPENSIONS

H.P. Schwan. In: "Advances in Biological and Medical Physics"

J. H. Lawrence and C. A. Tobias, Eds., Vol. V., p. 147, Acad. Press, Inc., New York, 1957

DETERMINATION OF BIOLOGICAL IMPEDANCES

H. P. Schwan. In :"Physical Techniques in Biological Research",W. L. Nastuk, Ed., Vol. 6, pp. 323-406 , Academic Press, New York, 1963

DIELECTRIC SPECTROSCOPY OF BIOLOGCAL MATERIALS AND FIELD INTERACTIONS: THE CONNECTION WITH GERHARD SCHWARZ

H.P. Schwan, Biophysical Chemistry, 85, 273-278. 2000

DIELECTRIC PROPERTIES OF TISSUES - A REVIEW

K.R. Foster and H.P. Schwan,

In: Handbook of Biological Effects of Electro-magnetic Radiation, 2nd Ed., C. Polk and E. Postow, Eds.,CRC Press, Boca Raton,Fla.,pp 25-102 1995.

ELECTRICAL CONDUCTION AND DIELECTRIC BEHAVIOR IN BIOLOGICAL SYSTEMS

H.P. Schwan and S. Takashima, In: Encyclopedia of Applied Physics , Vol.5, 177-200

VCH Publishers, Weinheim, Germany. 1992.

MEMBRANES, IONS AND IMPULSES.

K. S. Cole, University of Califormia Press, Berkeley and Los Angeles 1968.

DIELECTRIC BEHAVIOUR OF BIOLOGICAL MOLECULES IN SOLUTION

E.H. Grant, R.J. Sheppard and G.P. South, Oxford University Press, 1978.

ELECTRICAL PROPERTIES OF BIOPOLYMERS AND MEMBRANES

S. Takashima. Adam Hilger, Bristol and Philadelphia, 1989.

BIOIMPEDANCE AND BIOELECTRICITY BASICS

S. Grimness and O.G. Martinsen. Academic Press, 2000.