25

Impedance Plethysmography

Determination of the cardiac stroke volume is an area in which accurate, easily applied, noninvasive methods are needed. Impedance cardiography is easy to apply, noninvasive, and also cheap; however, it has serious methodological limitations, which are discussed below. We also provide a brief overview of other applications of impedance plethysmography.

The magnetic method corresponding to electric impedance plethysmography is called

Otto H. Schmitt first suggested that the concept of lead field could be used in connection with impedance plethysmography. David Geselowitz (1971) mathematically proved this relationship between the measured impedance changes and the changes in conductivity within a volume conductor. John Lehr (1972) later presented another proof of this relationship. In the following we give the result of Geselowitz using the terminology and sign convention of this book. (Note that Geselowitz (1971) defined the lead fields as the electric fields per reciprocal current and we define them as the current fields per unit reciprocal current. These are, of course, directly related by Ohm's law.)

(25.1) |

where | ΔZ | = impedance change [Ω/m³] |

t_{0}, t_{1} | = time instants | |

Δσ | = conductivity change between the two time instants [S/m = 1/Ω·m] | |

_{LE} | = lead field of the voltage measurement electrodes for unit reciprocal current [1/m^{2}] | |

_{LI} | = lead field of the current feeding electrodes for unit current [1/m^{2}] | |

v | = volume [m^{3}] |

In Equation 25.1, the region *v* consists of an inhomogeneous volume conductor whose conductivity (as a function of position) at time *t*_{0} is σ(*t*_{0}). At *t*_{1}, this has changed to σ(*t*_{1}), and it is this change (*t*_{1}) - (*t*_{0}) = Δσ which is responsible for the measured impedance change ΔZ. Thus Equation 25.1 describes how the changes in volume conductor conductivity are converted into the impedance change evaluated from a measured voltage (at the voltage electrode pair) divided by applied current (at the current electrode pair). Note that the 4-electrode impedance method underlies Equation 25.1.

A special case of Equation 25.1 is one where we consider σ(*t*_{1}) = εσ(*t*_{0}), where ε is very small:

(25.2) |

where all variables are evaluated at *t*_{0}. Equation 25.2 describes how the macroscopic resistivity *Z* (impedance per unit volume) is derived from the spatial distribution of conductivity σ weighted by the dot product of the lead fields of the current and voltage electrodes. Note the similarity between Equation 25.2 and the fundamental equation of the lead field theory, Equation 11.30 (or 11.52), which describes the electric signal in the lead produced by a volume source formed by a distribution of the impressed current ^{i}. In these equations the corresponding variables are the measured signals: *V*_{LE} and *Z* (= measured voltage per applied current), the distributions of sensitivity: _{LE} in both of them, as well as the source distributions: ^{i} and _{LI}.

If the introduction of the current is done with the same electrodes as the voltage measurement is made, the sensitivity distribution, that is the lead field _{LE} is the same as the distribution of the applied current _{LI}. This technique is, however, seldom used because of the artifact due to the electrode impedance. If the current-feeding electrodes are different from those of the voltage measurement electrodes, the sensitivity distribution is the dot product of the lead fields of the voltage electrodes _{LE} and the current electrodes _{LI}. Thus, any previous discussion in this book on the electric and magnetic lead fields in general (Chapters 11 and 12), in the head (Chapters 13 and 14) or in the thorax (Chapters 15 ... 18 and 20) may readily be applied to impedance plethysmography. Just as in the study of electrocardiography, one can design electrode systems for impedance measurement to give special emphasis to particular regions (the aorta, the ventricles, etc.). One can even have situations where the dot product is negative in a particular region so that if the conductivity increases in that region, the impedance *Z* will also increase. Some examples can be found in Plonsey and Collin (1977) and Penney (1986).

While Equation 25.1 is a suitable theoretical basis for impedance plethysmography, we are still left with considerable uncertainty how varies throughout the heart and torso or in what way the circulation modifies the thorax structure and conductivity as a function of time throughout the cardiac cycle. Further research is required to develop a physiologically adequate circulation model. Note, however, that Equation 25.1 may be more readily applied over a longer time frame (*t*_{1} - *t*_{0}) to, say, the growth of a localized tumor in the thorax (other regions remaining the same).

In measuring bioelectric sources the reactive component of tissue impedance is not important because the frequency range is under 1 kHz. Actually, in Section 7.2.4 it was shown that it can be omitted with the assumption of quasistationarity. In impedance plethysmography (and tomography) the frequency dependence of tissue impedance is a factor which can be utilized for increasing the selectivity of the system. Because the impedance of different tissues has different reactive components, the impedance may be measured with applied currents at different frequencies (Lozano, Rosell, and Pallás-Areny, 1990). The frequencies may be selected so that the separation of certain tissues is maximized. With appropriate filtering the measurement may be done simultaneously with different frequencies in order to save measurement time.

A useful method for illustrating the behavior of tissue impedance as a function of frequency is the Cole-Cole plot (Cole and Cole, 1941). In this presentation, real component

(25.3) |

where | Z_{f} | = impedance (as a function of frequency f ) |

R_{0} | = resistance at f = 0 | |

R | = resistance at f = | |

τ | = time constant (R_{2}C) |

The Cole-Cole plot is a semicircle with radius (*R*_{ 0} - *R* )/2 which intercepts the real axis at *R*_{ 0} and *R*, a conclusion that can be verified by noting that the real (Re) and imaginary (Im) parts of Equation 25.3 satisfy

(25.4) |

The right-hand side of Equation 25.4 is a constant where one recognizes the equation to be that of a circle whose center is at Im = 0, Re = (*R*_{ 0} - *R* )/2 with a radius of (*R*_{ 0} - *R* )/2, as stated. In the three-element circuit of Figure 25.1A, *R*_{0} = *R*_{1} + *R*_{2}, *R* = *R*_{ 1} , and τ = *R*_{2}*C*.

In practice, the center of the semicircle is not necessarily on the real axis, but is located beneath it. The equation representing practical measurements may be described by Equation 25.5 (Schwan, 1957):

(25.5) |

In the corresponding Cole-Cole plot, shown in Figure 25.1C, the depression angle is φ = (1 - α)π/2. Figure 25.2 shows the depression of the semicircle in the Cole-Cole plots for the transverse and longitudinal impedances of skeletal muscle as measured by Epstein and Foster (1983).

The reactive component of human blood has been studied, for example, by Tanaka et al. (1970) and Zhao (1992). The reactive component of tissue impedance seems to have an important role in impedance plethysmography, as will be discussed later in this Chapter in connection with determining body composition..

(B) Cole-Cole plot for impedance with a single time constant.

(C) The depressed Cole-Cole plot.

(B) longitudinal impedances of skeletal muscle.(Redrawn from Epstein and Foster, 1983.)

The impedance of the thorax is measured longitudinally by four band electrodes, shown in Figure 25.3. In the physical arrangement of the outer pair, one electrode is placed around the abdomen and the other around the upper part of the neck. For the inner electrode pair, one electrode is placed around the thorax at the level of the joint between the

Figure 25.4 presents a typical thorax impedance curve (

The amount of blood in the thorax changes as a function of the heart cycle. During systole, the right ventricle ejects an amount of blood into the lungs which equals the stroke volume. At the same time blood flows from the lungs to the left atrium. The effect of these changes in the distribution of blood in the thorax as a function of the heart cycle can be determined by measuring the impedance changes of the thorax. The problem is to determine cardiac stroke volume as a function of changes in thoracic impedance.

**Fig. 25.5** Simplified cylindrical model of the average thorax containing a uniform blood and tissue compartment for determining the net torso impedance.

(25.6) |

where | Z | = longitudinal impedance of the model |

Z_{b} | = impedance of the blood volume | |

Z_{t} | = impedance of the tissue volume |

The relationship between the impedance change of the thorax and the impedance change of the blood volume is found by differentiating Equation 25.6 with respect to *Z*_{b}:

(25.7) |

The impedance of the blood volume with blood resistivity ρ_{b} based on the cylindrical geometry of Figure 25.5, is:

(25.8) |

where | ρ_{b} | = blood resistivity |

A_{b} | = cross-section of the blood area | |

l | = length of the thorax model |

The relationship between changes in blood volume *v*_{b} and the blood volume impedance is found by solving for the blood volume in Equation 25.8 and differentiating:

(25.9) |

where | v_{b} | = blood volume |

We finally derive the dependence of the change in blood volume on the change in thoracic impedance by solving for *dZ*_{b} in Equation 25.7 and substituting it into Equation 25.9:

(25.10) |

As was mentioned earlier, during systole, the right ventricle ejects a volume of blood into the lungs. Subsequently, blood flows away from the lungs to the left atrium. The stroke volume can thus be determined from the impedance curve by extrapolating to the impedance (Δ

In this extrapolation, it is assumed that if no blood were to flow away from the thorax during systole, the thorax impedance would continuously decrease during systole at a rate equal to the maximum rate of decrease of Z. Thus, Δ

The value of Δ

(25.11) |

Assuming that Δ*t* equals the ejection time *t*_{e}, Δ*Z* can be determined from equation

(25.12) |

With the above assumptions, the impedance change Δ*Z* can be determined by multiplying the ejection time by the minimum value of the first derivative of the impedance curve (that is, the maximum slope magnitude; the reader must remember that the slope is negative).

Finally, the formula for determining the stroke volume is obtained by substituting Equation 25.12 into Equation 25.10, which gives:

(25.13) |

where | SV | = stroke volume [ml] |

ρ_{b} | = resistivity of the blood [Ω·cm] | |

l | = mean distance between the inner electrodes [cm] | |

Z | = mean impedance of the thorax [Ω] | |

= absolute value of the maximum deviation of the first derivative signal during systole [Ω/s] | ||

t_{e} | = ejection time [s] |

The ejection time can be determined from the first-derivative impedance curve with the help of the phonocardiogram or carotid pulse. Then, the impedance curve itself is used only for control purposes (e.g., checking the breathing).

The resistivity of the blood is of the order of 160 Ωcm. Its value depends on hematocrit, as discussed in Section 7.4.

Sakamoto et al. (1979) constructed an anatomically more realistic model in which changes in vena cava, heart, lungs, aorta, and torso shape were investigated (see Figure 25.8). The model permits an examination of the effect of conductivity changes of component structures on the measured impedance. The weakness in this work is that one does not know what quantitative changes in conductivity are brought about as a result of real or simulated blood circulation. Sakamoto et al. (1979) also did studies with dogs and humans where they measured the isopotential lines on the surface of the thorax.

Witsoe and Kottke (1967) conducted experiments with dogs, using venous occlusion achieved by an inflated ball. In these experiments the origin of the impedance signal was found to be contributed totally by the left ventricle. (This is also seen in humans.) Stroke volume measurements with impedance plethysmography on patients with aortic valve insufficiency give values that are too high.

Penney (1986) summarized a number of studies and estimated, on the base of these observations, the contributions to the impedance signal shown in Table 25.1.

Contributing organ | Contribution |

Vena cava and right atrium | +20% |

Right ventricle | -30% |

Pulmonary artery and lungs | +60% |

Pulmonary vein and left atrium | +20% |

Left ventricle | -30% |

Aorta and thoracic musculature | +60% |

Source: Penney (1986) |

Mohapatra (1981) conducted a critical analysis of a number of hypotheses concerning the origin of the cardiac impedance signal. He concluded that it was due to cardiac hemodynamics only. Furthermore, the signal reflects both a change in the blood velocity as well as change in blood volume. The changing speed of ejection has its primary effect on the systolic behavior of ΔZ whereas the changing volume (mainly of the atria and great veins) affects the diastolic portion of the impedance curve.

These facts point out that the weakest feature of impedance plethysmography is that the source of the signal is not accurately known. Additional critical comments may be found in Mohapatra (1988).

impedance signal in impedance cardiography.

Event in the cardiac cycle | Notch |

Atrial contraction | A |

Closure of tricuspid valve | B |

Closure of aortic valve | X |

Closure of pulmonic valve | Y |

Opening snap of mitral valve | O |

Third heart sound | Z |

Source: Lababidi et al., (1970) |

The first-derivative impedance curve can be used with some accuracy in timing various events in the cardiac cycle. The ejection time can be determined as the time between where the *dZ/dt* curve crosses the zero line after the B point, and the X point. However, in general, the determination of ejection time from the dZ/dt curve is more complicated. Thus, the need of the phonocardiogram in determining the ejection time depends on the quality and clarity of the dZ/dt curve. Though the timing of the various notches of the dZ/dt curve is well known, the origins of the main deflections are not well understood.

Hill, Jaensen, and Fling (1967) have introduced a critical comment concerning the effect of the contact impedance on the signal: they claim that the entire signal is an electrode artifact. Based on the preceding arguments and the experiments concerning the origin of the signal (Lababidi et al., 1971; Baker, Hill, and Pale, 1974) these claims can be ignored.

The effect of changes in the mean thoracic impedance has also been investigated (Hill and Lowe, 1973). Placement of a defibrillator back electrode under the back of a supine patient changed the mean impedance recorded by the instrument by up to 20%, but did not have any significant influence on the stroke volume value determined by the instrument, because of a simultaneous change in (

(25.14) |

where | ΔZ | = change of the impedance of the thorax |

Z | = mean value of the impedance of the thorax | |

v_{tx} | = volume of the thorax between the inner electrode pair |

They used the Fick principle as a reference for evaluating stroke volume. (The Fick principle determines the cardiac output from the oxygen consumption and the oxygen contents of the atrial and venous bloods.) In a study of six subjects at various exercise levels, the correlation between the impedance and Fick cardiac outputs was *r* = 0.962, with an estimated standard error of 12% of the average value of the cardiac output.

Harley and Greenfield (1968) performed two series of experiments with simultaneous dye dilution and impedance techniques. They estimated Δ*Z* from the impedance curve itself, instead of using the first-derivative technique. In the first experiment, 13 healthy male subjects were examined before and after an intravenous infusion of isoproterenol. The mean indicator dilution cardiac output was 6.3 /min before and 9.5 /min after infusion. The ratios of the cardiac outputs measured with impedance plethysmography and indicator dilution were 1.34 and 1.23, respectively. This difference (p > .2) was not significant. The second experiment included 24 patients with heart disease, including aortic and mitral insufficiencies. A correlation coefficient of *r* = .26 was obtained for this data. The poor correlation was caused in those cases with aortic and mitral insufficiency.

Bache, Harley, and Greenfield (1969) performed an experiment with eight patients with various types of heart disease excluding valvular insufficiencies. As a reference they used the pressure gradient technique. Individual correlation coefficients ranged from .58 to .96 with an overall correlation coefficient as low as .28.

Baker et al. (1971) compared the impedance and radioisotope dilution values of cardiac output for 17 normal male subjects before and after exercise. The regression function for this data was *CO*_{Z} = 0.80·*CO*_{I} + 4.3 with a correlation coefficient *r* = .58. The comparison between the paired values before and after exercise showed better correlation for the impedance technique. Baker examined another group of 10 normal male subjects by both impedance and dye techniques. In 21 measurements the regression function was *CO*_{Z} = 1.06·*CO*_{D} + 0.52, with correlation coefficient *r* = .68. In addition to this set of data, the impedance cardiac output was determined by using individual resistivity values determined from the hematocrit. The relation between resistivity and Hct was, however, not mentioned.

In this case, the regression function was *CO*_{Z} = 0.96·*CO*_{D} + 0.56 with correlation coefficient *r* = .66. A set of measurements was performed also on 11 dogs using electromagnetic flowmeters and the impedance technique. A comparison of 214 paired data points was made with intravenous injections of epinephrine, norepinephrine, acetylcholine, and isoproterenol. Values of the correlation coefficients from each animal ranged from 0.58 to 0.98 with a mean value of 0.92. The first two experiments of this paper are also presented in Judy et al. (1969).

A comparison of impedance cardiac output to Fick systemic cardiac output in patients with left to right shunts showed the correlation to be poor:

Baker, Hill, and Pale (1974) compared impedance and dye dilution cardiac outputs in three dogs and got a correlation of

Malmivuo (1974) compared impedance and Fick methods in 18 patients without valvular incompetencies, but with one subject having a left to right shunt. For this special subject a comparison was made to pulmonary blood flow. The regression function was

Malmivuo, Orko, and Luomanmäki (1975) compared impedance and Fick methods in 11 patients with atrial fibrillation and without intracardiac shunts or valvular insufficiencies. The regression function was

In evaluating the significance of a particular correlation coefficient between impedance and reference methods, Penney points out that the reference methods themselves are not completely consistent. For example, if one considers the correlation coefficient

Concerning the accuracy of impedance plethysmography in determining peripheral blood flow, there are much fewer data available as few detailed experiments have been published. van de Water et al.(1971) reported on a series of measurements in a hind limb of a dog using an electromagnetic flowmeter as a reference method. A correlation of

From this it is easy to deduce that if the impedance measurement is made with electrodes placed on one side of the head only or if, when using circular band electrodes, the electrodes are relatively close to each other, the major part of the signal comes from the blood flow in the scalp, not from that in the brain area. This shading effect of the skull does not show up as clearly in the EEG-measurement, because no bioelectric sources exist outside the skull (Malmivuo, 1992).

Van de Water et al. (1971) infused 400 cm³ of saline in 25 cm³ increments into a thoracic cavity of a dog weighing 15 kg. The regression formula between the infused saline volume and the thoracic impedance was

The method undoubtedly has some disadvantages. These include the errors caused by aortic valve insufficiency, severe mitral valve insufficiency, and shunts in the circulation in, for example, septal defects or tetralogy of Fallot. The method does not give any indication of the presence of these pathologies, and they must therefore be diagnosed by other means. The method is also difficult to apply to patients with atrial fibrillation.

On the other hand, impedance plethysmography is noninvasive and harmless. The accuracy of the method in careful examinations in patients, excluding the previously mentioned groups, gives promising results. The accuracy in determining the absolute value of cardiac output seems to be of the same order as the accuracy of the dilution methods. The accuracy in determining changes in cardiac output seems to be still higher.

As noted in the previous section, extreme care should be followed in applying impedance plethysmography to measuring the blood flow in the brain area to ensure that the recorded signal really originates mostly from the intracranial region..

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