Measurement of the electrical impedance of biological tissue in vitro and in vivo has entered prominently into three classes of biological research and biomedical applications. Pioneered some half century ago by Fricke (1) and perfected by his followers Cole and Curtis (2), measurements of the electrical self-impedance of a variety of cell and tissue systems were made across the audio, lower radio, and even into the medium to high radio frequencies. These data were examined most commonly in the more familiar impedance domain comprised of resistance and reactance rather than in the electrically equivalent admittance domain of conductance and susceptance, thus giving, unintentionally, an implicit preference to serially organized circuit models.
Data from these experiments, plotted parametrically as a function of frequency on the complex impedance plane, formed accurate loci of characteristic forms so closely identifiable with equivalent components in a circuit model that usefully quantitative physiological analysis could often be made by visual inspection or at most by simple constructions with ruler, compass and protractor. Because of the geometric simplicity with which the complex dielectric constant can be identified and measured in these plots, this otherwise somewhat esoteric concept of a partially imaginary dielectric constant has gained wide acceptance. By incorporating a partially balanced bridge procedure, these techniques were extended to make the classic measurements showing the dynamic change of impedance in the nerve axon membrane during the passage of the nerve impulse (3).
This basic package of techniques, perfected over some thirty years, especially
by Schwan and his students and co-workers (4), has yielded a body of well worked
out theory and measurement procedures that is well known and accepted in biophysical
circles as characterizing biological cells, tissues, and electrical systems.
From these studies have evolved the concepts of biologically characterizing
molecular and macromolecular complex relaxations which in turn have popularized
the acceptance of dielectric constant as a complex quantity and recognition
of electrical phase angle as a meaningful term in biology.
In the course of these studies, samples of a considerable variety of tissues have been measured (5) and the general form of variation of reactance and resistance with frequency determined. There has never been developed, however, an “atlas” of tissue impedance characteristics as a data base large enough and statistically consistent enough to permit clinical assessment of tissue normality or abnormality on other than a very gross basis.
Lack of enthusiasm for such work on a clinical basis is quite understandable in view of the very great polarization and trauma errors introduced by the necessary electrode systems required for in vivo measurements, not to mention the intractability of the mathematical models appropriate to tissues histologically linked intimately in complicated pathways with adjacent tissues. Maintaining physiological integrity and adequate perfusion while “isolating” the tissues electrically by “guard ring” or other sophisticated bioelectric tricks is indeed difficult, Cutting out a suitable biopsy sample for in vitro measurement is also very difficult, not only from the point of view of maintaining it in normal status without ischemia, hypoxia or self-toxicity, but because of the sheer mechanical difficulty of surgically removing a “core” of desired shape and size after
excision. The tissue property to be measured is likely to be overwhelmed by uncertainties in the equivalent circuit model or in its specifications. Electrical isolation problems are also very severe, especially in the in vivo cases, as the unfamiliar displacement current, and at higher frequency the radiation currents of the measurement and from ambient interference, assert themselves as errors.
Variations in tissue system impedances associated with physiological activity
have been much more widely utilized medically. Even though the change in cerebral
or thoracic impedance associated with the pulsatile blood flow pattern may be
only one tenth of one percent of the total background impedance, such impedance
changes can be readily measured, especially if they are measured as scalar impedance
magnitude changes instead of component resistance and reactance measurements.
This procedure, developed in our laboratories in 1956 (6), has had
considerable utility under the names of Impedance Plethysmography or Impedance
Rheography and has seen use in establishing perfusion patterns and has been
developed, for example, by Kubicek and his associates into a measure believed
to give a quantitative estimate of ventricular stroke volume (7) and as a commercial
instrument for sensing pulse pattern of the dynamic plethysmogram (8).
The “four terminal's version of this measurement technique, extensively discussed, tested, and championed by Nyboer (9) and later by Allison and others (10), escapes much of the electrode problem by using separate driving and sensing electrodes, keeping the desired tissues to be measured, as much as possible, common to both circuits, and making the measurement a “mutual” impedance measurement. Such measurements are classed as “two port” electrical system measurements.
Seeking a unifying model to pull these measurements together and to permit extension to more precise clinical applications, we need an element of analysis that is easily incorporated as an infinitesimal into differential equation formulations of tissue models. It must, however, preserve the complex domain characteristics required of impedance spectrometry. This unit element we find well expressed in terms of Impedivity or Specific Impedance (11). This set of measures I am seeking to introduce into regular Biophysical use (12).
Impedivity follows logically from the familiar “resistivity” as used in describing the specific resistance of solutions in physical chemistry and of first class conductors in classical physics. It is the impedance of a unit cube of the material measured between opposite faces and dimensionally specified typically in ohms-cm. While most commonly treated as an isotropic quantity, it is amenable to tensor expansion for anisotropic tissues and does not lose its validity when properly defined in inhomogeneous tissues.
Impedance being a series model concept, the orthogonally resolved components of impedivity will naturally be resistivity for the “real” part and reactivity for the “imaginary” part where the reactivity will carry a negative sign for most biological components at ordinary frequencies, thus implying a “capacitive” characteristic. According to long established tradition, negative biological reactances are often plotted upward to satisfy esthetic tastes.
Closely following the classical usage, impedivity leads to an obvious inverse measure for parallel-organized equivalence, admittivity. Admnittivity , the complex quantity, is comprised of conductivity and susceptivity , where conductivity is the real and susceptivity the imaginary part.
Now in building up the medical atlas of tissue impedivity spectrometry, it
is not enough merely to tabulate resistivity and reactivity as functions of
frequency. We must utilize some at least pseudo-orthogonal three-variable phase-space
display for ready perception of these spectral patterns, and modest changes
in them that typical pathological variations, such as ischemia or neoplastic
invasion, will produce.
Several display modes have been utilized but to date no one has emerged as clear best choice. We are especially interested in utilizing multidimensional visual hyperspace displays to allow the human to serve as his own good pattern recognizer. The complex plane display, in which reactivity is plotted vertically against resistivity horizontally, with frequency as a tagged parameter, has the special advantage of generating arcs of circles with depressed centers easily related to equivalent phase angle of the “dielectric”. Small changes in such arcs with physiological or pathological shifts do not show up to advantage when plotted together. The “Incremental Impedivity” (6) is, however, a sensitive display.
One can plot reactivity and resistivity separately against frequency or against log frequency to good advantage, while sometimes the complementary admittivity plot of conductivity and susceptivity against frequency will be revealing. Obviously the parametric admittivity dimension needs to be similarly explored.
We anticipate that “out-of-band normalization” will prove a valuable tool in mutual impedivity spectrometry even though we do not yet have enough experience to prove this prediction. Expecting, as we do, that successive characteristic relaxations with changing frequency will be the essence of the impedivity fingerprint of normality versus abnormality, we can take the ratio of measured to standard complex impedivity at a frequency away from important relaxation frequencies as a normalizing factor. Using this technique, we can bring measurements made on similar but not anatomically identical forms into nominal coincidence.
Utilization of the Lissajous elliptic pattern to express phase and amplitude equivalents of impedivity has led to the “flying bagel” display in which a series of ellipses express by their height the magnitude of Impedivity, and by their “openness” the extent of deviation from in-phase or purely real status. Used as a differential vector index, this display is easily perceived but needs an indication of direction of rotation, i.e. lead or lag of phase. This can be achieved by adding an arrow, a notch, or a radar type ‘‘louse“ on the ellipses.
Given a three dimensional display as described later, these problems become greatly simplified, as the real and imaginary components can both be at right angles to the frequency axis.
In those few fortunate cases where we can use guard ring techniques or can
constrain driving currents to flow uniformly and always parallel to the flow
lines associated with the sensing electrodes, and where tissue is homogeneous
and Isotropic, we can define a unit of “Mutual Impedivity” that applies to the
tissues in the region showing mutually parallel current flow lines for the driving
and sensing electrodes. Each unit of tissue volume can be thought of as contributing
an element of output voltage for every unit of current density flowing through
it, resulting in a transfer operator having the dimensions of a voltage per
unit current per unit volume. As thus defined, Mutual Impedivity is a conceptual
advance but of little practical use.
Reaching into transfer impedance theory as developed for Spatial Vector Electrocardiography (13), we can devise a much more flexible and applicable version of a mutual impedivity that is still compatible with the above special case where current flows and sensing patterns are still parallel and uniform.
As developed for quantitative electrocardiographic use, transfer impedance is defined as the ratio of the potential difference or voltage produced In a specified “lead” to the localized current source moment, wherever it may be anatomically, that is producing the output voltage and will ordinarily be expressed in ohms/cm. Naturally this transfer impedance quantity must be a vector with magnitude and direction both free to change with location and defined wherever sources may exist and hence it will be a field function, a vector point function. A “lead”, used here in the standard electrocardiographic sense, may be merely two electrodes or It may express a linearly weighted combination of potentials from several electrodes, even including amplification in some cases.
A “lead”, thus defined, can Integrate, with locally merging weighting factors, the contributions from many dipole current moment sources as in the myocardial case. Each dipole contribution is simply the scalar product of its vector strength with the transfer impedance field vector at its location. Originally our effort was to make the transfer impedance operator uniform in strength and direction throughout the heart region, but occasionally we undertook by “cancellation” techniques to make it “selective” so as to emphasize one region in preference to another, or even to make sensitivity zero at some locus for which the lead was to be made unresponsive.
The famous Maxwell Helmholtz reciprocity principle applied to the field case
yields a very simple inverse. If we devise a lead with a scalar current of algebraic
magnitude I and measure the electric gradient at a chosen locus, the electric
gradient per unit current will vary in just the same field pattern as the transfer
impedance previously measured after being normalized by the magnitude of local
impedivity. (14)
If we utilize two different leads on the same tissue system and apply the transfer impedance rule to one and the inverse to the other, we develop a mutual impedivity algorithm where the output voltage in one lead is equal to the scalar current driving the other, multiplied by the volume integral of the scalar product of the two transfer impedance fields normalized by the local impedivity at each point. We thus have a volume measure of mutual impedance expressed in terms of the distribution of local impedivity and a scalar product of two vector point functions expressing the geometrical anatomical relation between the source and sensing electrodes.
As there is in this reformulation no requirement for keeping very small or closely controlled the polarization impedance of the several electrodes, many different electrical combinational arrangements of input and output can be made out of a few dozen electrodes so that it must be evident that an analog of the CAT (Computer Assisted Tomography) roentgenographic reconstruction array can be developed. The principal differences, good and bad, are the vectorial, spatially dispersed nature of the input-output operator and the absence of a simple geometric reconstruction rule. One has only the benefits of a knowledge of typical anatomy, specific measurements on the individual patient and the continuity equation combined with the impedivity generalization of Chin's law.
Obviously one can make reasonable electrode choices to cause current flow lines to stay strong and mainly parallel to sensing electrode vector lines where detection is desired and to make one or the other weak, or the direction nearly orthogonal, where sensing is to be suppressed.
Presumably one could use a standard torso, limb, head or other body element as a reference standard on which to perform calculations , thus allowing it to “stand in” for the specific subject. It is most fortunate that the measurement involves a “phasor” or two-variable spectrum so that observations from the standard “phantom” can be normalized at an out-of-band frequency to show in-band normality or pathology.
Attempts of this sort to reconstruct the impedance anatomy can be expected
to give relatively poor anatomical localization, but for the selected internal
locality a non-invasive and possibly accurate and descriptive index of tissue
health.
It would be very satisfying clinically to have a non-invasive tissue measure that is sensitive to physiological status of tissue otherwise than by exercise of its contractile or other functions. Certainly we do not now have even crude classifying measures of the several body tissues with respect to fibrosity, fattiness, saline content or blood to muscle ratio, ischemic or hypoxic state, etc.
Certainly development of the in vitro atlas of tissue impedivity, the construction of a set of suitable mutual impedivity phantoms and the selection of good candidate electrode patterns will have to precede the writing of an effective anatomical impedivity spectrometry computer reconstruction program. It is not too soon, however, to program for specific body targets; lungs, adipose tissue, limb segments, peripheral perfusion models, large muscle status, etc. We should also plan to use “electrode systems of convenience” such as the several fingers, body apertures and accessible parallel planes of tissue.
No mention has been made, however, of the artifacts to be expected with respiratory and/or circulatory movements while measurements are made or for display modalities. With respect to the former problem, we have high hopes for utilization of the VCRS technique, not only to reduce measurement “noise” but even to make useful data out of this variance.
The VCRS procedure (15) utilizes the phase-lock-loop technique now becoming very popular in communication and control electronic engineering, to allow the patient being measured to breathe quite normally under computer instruction while in effect locking his respiratory and cardiac systems into a stationary, but not fixed frequency, synchronism. One can thus be guaranteed practically identical circulatory-respiratory status at corresponding points along typically a five heart-beat sequence.
One can thus generate samples from as many cycles as necessary, then selecting samples in accordance with the computer timing, or alternatively utilize different beats to sense component change with the element of the cycle. This beat variability is the focus of a current examination of the mechanism of the vague heart control, beat to beat and day to day.
Finally we come to the problem of display for the multidimensional data created by this or other reconstruction analysis. Here we would like to encourage utilization of two new versions of an old SVEC display form. (16)
In the original version of this display, two separate cathode ray tubes were utilized. By one or another optical path arrangement, each eye was allowed to see only its own tube, while to the observer there appeared to be only one tube. By synthesizing left and right eye projections separately on the respective tubes, one could have the observer “see” the desired pattern in space, could rotate it, move it about, or otherwise manipulate it. With such displays there is always a difficult alignment and image registration problem and the optical system is complicated.
It is now relatively easy to generate raster patterns and to swap line or dot patterns on a CRO face on a millisecond basis under computer refresh control. We thus present left and right eye patterns alternating above visual flicker perceiving frequencies and within the central stereo
perception limit and need only an eye control that is correspondingly fast to see the spatial pattern which can equally well be black and white or trichromatic.
PLZT solid state electrooptic lenses used as clip-on eyeglasses accomplish this switching ideally and permit viewing by several observers from a single CRO with minimal distortion but are at present expensive. Similar results can be had less elegantly utilizing electromechanical Moire' switching eyeglass clip-ons or even mechanical chopping viewers. There appears to be a possibility of utilizing Fresnel lens techniques to present banded viewpoints for alternate raster scans of the CRO tube so that the viewer can, without glasses, see the full stereoscopic display. The implied vertical raster scan, instead of the conventional horizontal one, presents a mild challenge to the microcomputer designer and programmer. These displays all permit the observer to view at least three orthogonal dimensions simultaneously and can be extended to additional dimensionality by chromatic coding.
In summary, mutual impedivity spectrometry has a promising but not yet proven
medical diagnostic utility. Whether it will ultimately be capable of detailed
anatomical reconstruction by computer synthesis is problematical, but it is
very likely that localized non-invasive analysis of reasonably accessible tissue
will be possible. Before significant success with reconstruction can be expected,
a large amount of effort will have to be expended on developing “an atlas of
tissue impedivity spectra”. This work is now starting on surgically isolated
tissue samples. In vivo measurement presents technical electrical measurement
problems that are severe but apparently soluble, at least from audio up to megahertz
frequencies.