Silny J. Intraluminal Multiple Electric Impedance Procedure for Measurement of Gastrointestinal Motility // Journal of Gastrointestinal Motility 1991; 3(3):151-162).

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Авторы: Silny J.

Intraluminal Multiple Electric Impedance Procedure for Measurement of Gastrointestinal Motility

Jiri Silny

Helmholtz-Institute for Biomedical Engineering, University of Technology, Aachen, Germany

A new catheter-related procedure for high-resolution measurements of gastrointestinal motility is presented. The method is based on simultaneous acquisition of the electric impedance in the surrounding body volume conductor from a number of annular electrodes, successively arranged on the catheter. The impedance of a volume conductor around the catheter, consisting of a bolus, the organ wall, body fluids, and so forth, has a characteristic value for each segment and phase of contraction wave, as theoretical and experimental investigations revealed. A calculation on the basis of a simplified model reveals that the impedance changes as a logarithmic function of the bolus thickness, in which the highest sensitivity is advantageously obtained at a small lumen size and utilizing unipolar or bipolar electrode setups. The high resolution in time, space, and amplitude of the changes in the bolus shape allow us to use this impedance method for evaluation of functional stages in each measuring segment and of the beginning, end, and type of contraction wave, as well as their characteristics. The unique mechanical properties of the catheter (thinner than 3 mm, several meters long, flexible, closed surface) and the ability to distribute more than 32 measuring segments of different lengths on the catheter make this procedure suitable even for long-term physiologic and pathologic studies of gastrointestinal motility. (Journal of Gastrointestinal Motility 1991; 3(3):151-162)

Key Words: intraluminal electric impedance measurement.

One of the most important functions of the gastrointestinal tract (GIT) is the transport of food and fermented material from one digestive or resorption stage to another. This is based on propulsive mechanisms distributed along the whole length of the organ. In this way, one or several contracted segments of varying lengths push the pulpy or liquid food through a muscular tube, leading to the mixture and movement of its contents. These contraction waves are produced by smooth and striated muscles embedded circularly and longitudinally in the organ wall. The organs of the GIT are separated by sphincters, which allow flow in only one direction under physiologic conditions.

The bolus in an organ can be segmented, mixed, or moved in different directions depending on the degree of the wall contraction and the direction of the contraction movement. The parameters of the transport and mixing processes in the organs of the GIT differ considerably in adaptation to the graded digestion in the alimentary tract. For example, just one parameter, the average transport velocity, comes to 3 to 4 cm/s in the main transport organ, the esophagus (1), whereas it is slower than 1 to 2 cm/s in the intestine (2).

The transport and mixing processes in each organ of the GIT also differ in time and space and are subject to numerous physiologic and psychological influences. The resulting peristaltic activity can therefore be characterized as a time- and space-dependent, nonstationary process. These contraction patterns have been used for diagnosis of dysfunctions of the GIT. The following general measurement rules should be followed to obtain accurate results.
  1. The chosen procedure should record all phases of the peristaltic waves completely and without distortion.
  2. The measurement procedure must not impair the function of the organ.
  3. Using discrete sensors the peristaltic activity of the whole organ can be recorded completely and simultaneously only with a high number of sensors.
  4. The patient should not be impaired by the measurement procedure.
Generally, all catheter-related procedures have an essential advantage over other methods because a thin intraluminal probe with many sensors can be adapted closely to the long and tube-shaped organs. From the numerous methods developed for the intraluminal measurement (3) only perfusion manometry and catheters with miniature solid-state pressure sensors have been widely introduced into clinical routine (4). However, they have shown many limitations and deficiencies. For example, in perfusion manometry the measured dynamics of the pressure changes are strongly restricted by the diameter, length, and compliance of the whole system (3). In addition, catheter diameter may influence the function of the organs.

Catheters with semiconductor pressure micro-transducers do show excellent dynamic characteristics, but they are costly and relatively fragile (5). Therefore it is necessary to look for new and better procedures for the measurement of peristaltic waves in the organs of the GIT. In this context a new procedure is presented here in which the peristaltic wave is simultaneously measured by intraluminal electric impedance changes near many annular electrodes placed sequentially on the catheter.

Intracorporal and extracorporal applications of the electric impedance technique for the characterization of different physiologic processes and anatomic structures have already been suggested and partly proved many times in experiments (6, 7). A theoretical approach to the determination of the motility in the organs of the GIT by means of intraluminal electric impedance measurement, however, has not yet been presented systematically in the literature. The impedance measurement of the intracardiac volume and related problems have been dealt with extensively (6, 8, 9). But, as the transport processes in the GIT are basically different from the heart pump function, the deduced principle cannot be translated to this problem. Therefore this paper deals not only with an explanation and the experimental proof of this procedure in the esophagus and intestine, but also with calculations of the electric fields and impedance conditions around the catheter before, during, and after a contraction wave.

Phases of the Motility Wave

The mechanical transports as well as the mixing of food and fermented material take place in all the organs of the GIT with comparable mechanisms (5). Narrowing or complete constriction of neighboring segments in an organ lead to segmentation and mixing of the contents. A contracted segment that moves at a velocity, V, pushes the bolus in front of it. A contraction wave at a given time can be divided in a simplified way into four typical phases, as shown schematically in Figure 1.

Fig 1. Phases I-IV of mechanical peristaltic activity in the esophagus, 1 = saliva film, 2 = organ wall, 3 = bolus, 4 = body

During the resting phase I the wall muscles are relaxed with the exception of the sphincter regions. In the resting state the organ walls lie smooth or folded together and swim on a thin fluid film. In phase II the organ wall is extended by the bolus. It remains to be seen how far this extension is affected by the force of the pressed bolus or by active opening mechanisms. A fully contracted segment that pushes the bolus is associated with phase III. In phase IV the muscular tube is relaxed again and the organ walls can touch each other. The fluid film, which is transported away with the bolus, is slowly built up again. Distribution of different physical characteristics, such as wall tension, lumen size, or pressure in the muscle tube, can be used for the quantitative description of the contraction wave. In phases I and IV the wall tension and pressure are clearly at their lowest values, whereas the lumen size can differ from its minimum value (phase III). Phase II is marked by increased wall tension and maximal lumen size. In this phase the pressure shows only a very small increase, which is frequently difficult to measure. The wall tension and pressure are at their maximum values in phase III, whereas the lumen size reaches its minimum here. Measurement of wall tension and lumen size would yield the best distinction between the different phases of the contraction wave. Unfortunately, however, there are no sensors that can directly register the wall tension in situ without injuring the wall. By measuring changes of pressure during a contraction wave we can recognize only phase III, in which the organ is totally contracted. Most procedures widely used in clinical practice for the determination of motility, such as perfusion catheters or solid-state transducers (5), give the wall pressure of only a small wall segment.
The change in the lumen size during the contraction wave could be the second most important parameter besides wall tension, as it changes from phase to phase. A catheter-related electric impedance technique adapted to this special problem could represent the change in the lumen size in a simple way. Results of a rough estimation of the impedance around an annular measurement electrode and its relationship to the phases of the contraction wave and different parameters are presented below.

Impedance Measurements: Theoretical Approach

For measuring impedance a plastic catheter is placed in the esophagus or intestine. Metallic cylinder electrodes with a radius of p0 and length of L = 2l are attached at a distance of d on the catheter (Fig. 2). The ring electrodes are connected with terminals outside the body by means of thin wires which run inside the catheter. This setup can be used to measure an impedance ZB between two electrodes on the catheter (bipolar measurement) and impedance values Zu between one electrode on the catheter and one large reference electrode on the body surface (unipolar arrangement).

Fig 2. Intraluminal electric impedance catheter in the esophageal tube during deglutition with characteristics of the catheter and of the volume conductor, and electric conductivities of the body σB, the wall σw, and the bolus σF. 1 = saliva film, 2 = organ wall, 3 = bolus, 4 = body, 5 = air, 6 = impedance catheter electrode

The question is how these impedances change depending on different parameters in bipolar or unipolar configuration when a contraction wave runs along the catheter. For the calculations in the Appendix, the following simplifications are made:
  1. Impedances Zu and ZB are replaced by resistances Ru, and RB.
  2. Cylindrical electrodes are simulated by concentric finite length line sources.
  3. Bolus, muscular wall, and body around the catheter are modeled by two concentric cylindrical layer conductors of infinite axial extension and conductivities, σ1 and σ2, where the outer conductor also extends infinitely in radial direction (see Fig. 14).
Thus the first layer can be used for the simulation of the organ wall in phase III (σ1 = σw); the bolus in phase II (σ1 = σF); and the bolus and the wall in phase II, if the conductivities of the bolus oy and the wall ov are comparable (σ1 = σw = σF).

The second layer {outer infinite conductor) represents the body in phase III (σ2 = σB); an equivalent conductor for the wall and the body in phase II (σ2 = σBw + σB); and the body in phase II, if σF ≈ σw (σ2  =  σB).
The most important results of the calculations in the Appendix are visualized in Figures 3 to 9.

Fig. 3. Normalized impedance in the unipolar measuring arrangement as a function of the bolus layer thickness D for different ratios σ1/σ2 and a given electrode geometry (ρo = 1.5 mm, l = 2 mm)
The resistances Ru and RB in Equations (16) and (18) (see Appendix) are in a logarithmic relationship to the thickness D of layer I (see Fig. 14), and they depend on the conductivities σ1 and σ2. Figures 3 and 4 depict the connection between the products σ1Ru, σ1RB, and D for a realistic variation of thickness D and the ratio of conductivities σ12, as well as for practicable dimensions of the catheter. The radius po of the catheter and length L of each electrode as well as the distance between the electrodes should be determined for the construction of the catheter. Practice has shown that catheters with ρo - 1.5 mm, L = 3-4 mm, and d = 1- 2 cm can be constructed relatively easily, that they have good mechanical properties, and that they provide a precise enough solution of motility in esophagus, stomach, and intestines. The effect on organ function of a catheter with a diameter of 3 mm can also be tolerated for most sections of the GIT. Therefore, in all graphs parameters within these ranges are introduced as examples. For the chosen configurations, the bipolar setup gives a nearly double resistance value RB (Figs. 3 and 4).

Fig. 4. Normalized impedance in the bipolar measuring arrangement as a function of the bolus layer thickness D for different ratios σ12 and a given electrode geometry (ρo = 1.5 mm, l = 2 mm, d = 10 mm)

Here the sensitivity ΔR/ΔD, as a ratio between the resistance change and a small variation of the thickness D, decreases with the thickness D in both the unipolar and the bipolar arrangements. Furthermore, the sensitivity is higher in the bipolar arrangement than in the unipolar array. The rate of increase depends on the electrode size, the interelectrode spacing, and the thickness D. In Figures 3 and 4, we can distinguish between two regions with σ1 > σ2 and σ1 < σ2. The courses of the resistances are symmetrical about the axis σ1 = σ2 for different reciprocal values of σ12 in both setups. These graphs allow explanation of the change in resistance in the individual phases of the contraction wave in the esophagus and intestine, as discussed below. Figure 5 plots the resistance dependency of the length / of the half electrode at a predefined thickness D and conductivity ratios σ12 as well as a possible catheter configuration. The resistance diminishes slowly with l especially in the unipolar configuration.

Fig. 5. Changes of normalized impedance as a function of the electrode length in the unipolar and bipolar arrangements for different ratios σ12 and a predefined electrode geometry (ρo = 1-5 mm, d = 2 cm)

The variation of the interelectrode spacing d in the bipolar setup causes a strong change in the resistance RB only at very short distances (Fig. 6). In the range of realistic interelectrode spacing d > 0.5 cm, only a weak increase of the resistance can be noticed. Figures 7 and 8 show the normalized longitudinal distribution of the normal component of the  current density within the boundary ρ = ρ1 (see Fig. 14) for both unipolar and bipolar arrays arid different parameters of the catheter and conductors, chosen as examples (see Eq. [20] in Appendix). Both plots demonstrate the longitudinal sensitivity (see Eq. [22] in Appendix) of the unipolar and bipolar setups for given example parameters.

Fig. 6. Changes of normalized impedance as a function of the electrode distance in the bipolar array for different  ratios σ12and for a given geometry of the measuring setup (ρ= 1.5 mm, l = 1.5 mm)

Fig. 7. Longitudinal selectivity of the unipolar arrangement derived from the normal component of the current density within the boundary ρ = ρ1 for given electrode geometry (ρ0 = 1.5 mm, l=2 mm) and different thicknesses of the bolus layer (a, D = 1 mm; b, D = 5 mm) as well as for given conductivities (σ1  = 4 mS/cm, σ2 = 0.4 mS/cm)

Fig. 8. Longitudinal selectivity of the bipolar arrangement derived from the normal component of the current density in the boundary p = Pi for a given electrode radius p0 = 1.5 mm, different electrode distances, and chosen thicknesses of the bolus (a, D = 1 mm, d = 10 mm; b, D = 1 mm, d = 5 mm; c, D = 5 mm, d = 10 mm) at given conductivities (σ1  = 4 mS/cm, σ2 = 0.4 mS/cm)

Figure 9 presents the notated longitudinal bandwidth for 90% of the total current (see Eq. [21] in Appendix) and selectivity as a function of thickness D for unipolar and bipolar measurements. In both cases a reduction of the longitudinal bandwidth and an increase in selectivity follows the decrease of the layer thickness. This comparison shows that the bipolar array has a greater bandwidth and a much higher selectivity. The sudden loss of sensitivity in the middle of the bipolar arrangement (Fig. 8) could be considered a disadvantage. No essential information, however, is lost through this characteristic if the distance between the electrodes is shorter than the length of the bolus. This condition can be fulfilled in practice.

Fig. 9. Longitudinal bandwidth and selectivity of the unipolar and bipolar arrangements in the boundary ρ = ρ1 as a function of the bolus layer thickness D in unipolar and bipolar setups (ρ0 = 1.5 mm, l=2 mm, d = 10 mm, σ1  = 4 mS/cm, (σ2 = 0.4 mS/cm)

Experimental Proof


A setup as shown in Figure 10 was used in the first experimental investigations of the impedance method in the esophagus and intestine. The essential parts of the equipment are an impedance catheter (10) and impedance-voltage transducers for eight channels. There are nine thin metal ring electrodes mounted on the lower part of a 2-m-long plastic catheter with a diameter of 3 mm. The center distance between each 0.4-cm-long electrode is 2 cm. Each electrode is connected with a thin wire that runs inside the catheter over a connector to the rows of a crossbar distributor (see the horizontal lines in Fig. 10).

Fig. 10. Setup  for   electrical  impedance  measurement: (•) connected; (O) unconnected

The tenth row is contacted with a reference electrode 200 cm2 in size. This metal electrode is attached to the surface of the thorax using a conductive gel. In the vertical direction of the crossbar distributor eight impedance-voltage transducers are connected with their virtual inputs. Depending on the wiring of the distributor we can obtain a bipolar (channel 1 in Fig. 10) or unipolar (channel 8 in Fig. 10) setup for each channel. The specifications of each impedance-voltage transducer are as follows:
  • measurement frequency 1 kHz,
  • measurement current < 6 μA,
  • sensitivity 1 mV/Ω,
  • decoupling between two channels > 40 dB,
  • channel frequency response DC-100 Hz.
During the investigations all signals are depicted online and simultaneously on an eight-channel scope and also recorded on a PCM tape (Stellavox 4 S 17/ W). The evaluation of the signals takes place off-line by measuring extended signal segments on the scope, using a cursor. The curves are documented on an eight-channel comb writer (Uniscript UD210, Picker Co.).

Impedans of food

As theoretical consideration has shown, the electric conductivity σF of the organ contents has a great influence on the measured impedance. Especially in the esophagus, the transported bolus can assume very different conductivities depending on the kind of food. Therefore we carried out a preliminary study to determine the conductivity for some soft foods, liquids, and saliva. The four-electrode measurements (11) are applied in an air-tight measurement container (area 1 cm2, length 1 cm) at 1 kHz frequency and a current of 6 μA.

Table 1 gives a set of measured conductivities and their standard deviations, both related to a preset temperature, measuring frequency, and some additional data from the literature.
Table 1. Conductivities of Different Tissues, Fluids, and Soft Foods
Tissues, Fluids and Soft Foods Average Conductivity at 1 kHz mS/cm Standard Deviation (mS/cm) No. of Samples Temp.
Physiologic saline solution 0.9%
0.9 ±0.32
45   36 
Stomach and duodenal contents 
Bile duct fluids
±1.3  6
Skeletal muscle*
Average conductivity of body fluids* 
Drinking water
Milk (3.5% fat)
0.9  ±0.02
Thick custard-based dessert flavored with vanilla, chocolate, etc.
Curds with different fruits 2.3

Measurement in the Esophagus

Figure 11 presents three typical courses of the impedance change measured simultaneously in different parts of the esophagus before, during, and after an arbitrarily chosen swallowing of yoghurt. The upper signal marks with the arrow S the beginning of the swallowing process in the region of the larynx. The three impedance curves Z1, Z7, and Z8 can be subdivided into four characteristic phases following the sequences of the contraction wave (Figs. 1 and 2). To check these courses we consider first the constraint sequence of the functional phases and the conformity with the theoretically derived connections. Moreover, experimental investigations with combined catheters (bipolarly measured impedance and manometry), the results of which will soon be published, confirm these theoretically derived connections. In this respect phase III (Fig. 11) promises to give the best confirmation of the theoretical approach, as here only the organ wall with a low conductivity is located between the catheter and the highly conductive volume conductor of the body. This phase corresponds to an entirely contracted segment, and therefore the impedance has in each segment a characteristic and reproducible value of С independent of the swallowed food.

Fig. 11. Impedance changes in the bipolar setup in the esophagus during deglutition of 15 ml of yoghurt: phases I, II, III, and IV of a peristaltic contraction A = bolus front, b = maximal bolus diameter, С = constriction, S = beginning of swallowing, T = time difference; 1 = saliva, 2 = wall of muscular tube, 3  = bolus

The impedance values in points С (Fig. 11) reach about 1.5 kΩ in all three curves Z1, Z7, and Z8. From this value the average conductivity of the esophageal wall σW can be estimated. For example, a realistic value of σW = σ1 = 0.35 mS/cm results from Figure 4, point 1, considering the wall thickness to be 3 mm and the conductivity of the surrounding body to be σB = σ2 = 7 mS/cm, as some in vitro measurements with pig esophagus have indicated. Phase II corresponds to the filling of each organ segment with food. By choosing appropriate food with a conductivity σF » σW the bolus of a known conductivity σF = σ1 is modeled by layer I (see Fig. 14). The infinite conductor II represents the organ wall and the surrounding body in this example. Thereby the conductivity of the wall is decisive for the introduced equivalent conductivity σ2, as its value is several times lower than the conductivity of the body (if σ» σW then σ2 ≈ σW) (see Eqs. [16] and [18] in Appendix). A growing diameter of yoghurt bolus with a conductivity σF = σ1 = 3.2 mS/ cm (Table 1) and σ1 ≈ σ= 0.35 mS/cm (σ1/σ2) causes a decrease of impedance (upper part of Fig. 4). The functional relation between Z and D (Fig. 4) allows an assessment of the thickness D from the measured impedance in phase II (Fig. 2). The minimal impedance value of 270 Ω in point В (Fig. 11) results from Figure 4, point 2, a realistic maximum bolus layer thickness of D = 4 mm. From the delay between two arbitrary points AM and AN or СM and CN and the central distance between the channels M and N the average velocity of the bolus front V`MN and of tne contraction wave VMN can be calculated. Furthermore, the time difference TAC between the points AM and CM, the velocities V`MN and Vmn and the longitudinal bandwidth B, (see Appendix) allow us to estimate the bolus length for each measuring segment M:

in front of the bolus BL = ТAC • VM - В9, and
directly behind it BL' = TAC • V'M - B9 

Figure 12 depicts impedance shapes in two groups recorded one after the other at seven neighboring measuring segments of 2-cm length from the same upper esophagus part in a healthy human being. These records are alternatively results of unipolar and bipolar measurements by swallowing 20 ml of the same meal (yoghurt). The shapes of both recording groups reflect the theoretically derived results in the Appendix, which are illustrated in Figures 3 to 9. The bipolar setup shows the double amplitude value in phases I, II, and IV in comparison to the unipolar arrangement. This ratio is lower in phase III because the impedance of the reference electrode is added in the unipolar setup and it distinctly increases the lowest value. The maximal thickness of the bolus with D = 4.4 mm and D = 4.1 mm results from Figure 3 and Figure 4, point 3, for the channels 1-2 (Fig. 12A) in the bipolar setup (B = 350 Ω, С = 2 kΩ) and for channels 1-15 (Fig. 12B) in the unipolar setup (B = 180 Ω, С = 1.1 kΩ), respectively. As both recording groups indicate, the bolus is formed by the  narrow muscular tube  and will therefore be longer and thinner toward the distal end of the esophagus. The average velocity of the contraction wave shows a small difference with 7.5 cm/s in the bipolar arrangement and 6.2 cm/s in the unipolar arrangement. The average velocity of the bolus front VB = 26 cm/s is similar for both setups. The impedances and their changes in phase IV and the following phase I result from the relaxation process in the muscular tube between two consecutive deglutitions. After the constriction of a segment (phase III), the relaxation which follows leads to a gradual increase of lumen in phases IV and I. The saliva of low conductivity (Table 1) soaks into the space between the catheter and the wall and causes a slow increase of impedance. In phase IV the catheter is centered by the neighboring contracting segment, whereas in phase I the catheter can take on different sizes in the strong folded structure of the esophagus. Therefore the impedance in different phases I can reach variable values after different acts of deglutition. The measurement of the impedance changes at different segments in the esophagus supplies similar curves with a time delay. The analysis of the time and space factors offers additional interesting parameters concerning the contraction wave, the bolus transit, and the bolus or lumen shape. Further theoretical and experimental investigations are required to evaluate these connections. 

Fig. 12. Impedance measurement of the contraction wave in the esophagus during the swallowing of 15 ml of yoghurt acquired by a bipolar (ZB) and a unipolar (Zu,) setup as shown in Figure 10

Small intestine measurments

In these investigations the impedance catheter (Fig. 10) is inserted through the nose, esophagus, and stomach into different parts of the small intestine. The final position of the catheter is checked by x-ray, whereafter the catheter is attached to the nose. Figure 13 demonstrates a record of the motility with eight impedance channels from a 16-cm-long region of the proximal jejunum in a volunteer 20 minutes after a meal, for example. In all traces recurrent resting (R) and active (A) phases appear simultaneously. The impedances in the resting states have a similar value of 214 ± 17 Ω with each trace as well in the interchanneling comparison. The active phases are manifested by oscillations of the impedance around the resting level. On the average the maximum of the impedance amounts to 300 Ω and the minimum to about 100 Ω in this phase. Table 1 shows that the electrical conductance of the bolus in the small intestine generally has a high electric conductivity of about 8 to 12 mS/cm, which is comparable to the conductivity of the body fluids (11). In the volume conductor considered, consisting of the bolus, the organ wall, and the body fluids, the impedance along the catheter can change in connection with the transit of a bolus only if the conductivity of the intestine wall is lower than the conductivity of the body and of the bolus. These conclusions coincide with common experience, that tissues like muscles or epithelia have essentially lower conductances than blood or body fluids (11). The conductivity of the intestine wall, σW = σ1 =2.1 mS/cm, can be estimated for the maximum impedance of 300 Ω under the assumption of the conductivity, σB = σ2 = 7 mS/cm, in the remaining body and a layer thickness of the organ wall of D = 3 mm, as shown in Figure 4, point 4. The plot for σF = 8 mS/cm and the ratio σ12 = σFW = 4 in Figure 4 characterizes the change of the impedance as a function of the thickness D. Consequently, the maximum impedance of 300 Ω in the traces in Figure 13 corresponds to the constriction D = 0 in the measuring segment, and the minimum of 100 Ω indicates a bolus layer thickness of D = 4.5 mm (point 5 in Fig. 4). If the catheter radius is 1.5 mm, the outside diameter of the bolus could maximally reach 12 mm. In the same way, for the resting state with an impedance of 214 Ω only a thin bolus layer (D < 1 mm) can be derived. The impedance patterns in Figure 13 demonstrate the typical contraction activity of the small intestine, known as the migrating motor complex (2). In the active phase the frequency varies between 10 and 12 contractions per minute. Only some strong contraction waves fully occlude or dilate the intestinal tube. These intensive peristaltic waves are propulsive in most cases. An average transit rate of 1.5 cm/s results from the time and space comparison between channels one and eight. 

Fig. 13. Impedance tracings from the jejunum recorded with the bipolar setup shown in Figure 10.


A new approach for intraluminal evaluation of gastrointestinal motility, based on multiple electric impedance measurements, has been verified in theoretical and experimental studies.

In the theoretical considerations several simplifications discussed below have been made to describe the measuring problem analytically. At a frequency of 1 kHz, the impedance of the tissue can be replaced by a resistance without any essential error, as the capacitive reactance is low (11).  The annular electrodes are modeled by concentric finite-length line sources. In this way, an ellipsoid forms the fictitious electrode surface with a desirable nonuniform distribution of current density. On the other hand, the surface area of such a model is dependent on the surrounding volume conductor, and this area is generally greater than the surface of the modeled cylindrical electrode. Underestimation of the impedance, especially in the case of a thin bolus, is the consequence of this simplification. The volume conductor around the electrodes is simulated by two concentric cylindrical layer conductors of different conductivities and infinite extension of both layers in the longitudinal direction and of the outer conductor in the radial direction. To discuss these points one must consider the electric field around the electrode. The current density  decreases  rapidly with  increasing distance from the electrode. Within a radius of about 2.5 times the length of a slim electrode the current density comes down to a few percent. This means that only a small pick-up area of the volume conductor around a short electrode with a small radius is responsible for the measured impedance. In the case of such a limited area it is possible to decide on the advantageous division into two representative layers without making an essential mistake in the simulation. The small pick-up area also allows the assumption of an infinite layer extension, as both the bolus and the investigated organ are much longer. Despite these inaccuracies, the results offer important information about the influence of various parameters on the impedance. Essential parameters are, for example, geometry of the electrodes as well as thickness and conductivity of the bolus in unipolar or bipolar measuring arrangements. According to the calculations the impedance is a reciprocal function of the logarithm of the bolus layer thickness D in both the unipolar and bipolar setups. Consequently, a change in a thin bolus advantageously produces  a much stronger impedance alteration than the same thickness change would in the case of a thick bolus. The sensitivity of these changes is about twice as high in the bipolar arrangement as in the unipolar setup. The procedure measures an average impedance from one  interval,   which  is  denoted  as  a  longitudinal bandwidth. The longitudinal bandwidth grows with the bolus thickness in both arrangements.

Moreover, it is also determined by the electrode length in both arrangements, and by the distance of the electrodes in the bipolar array. The longitudinal bandwidth of the bipolar array, and thus the distance between the electrode pair, should be shorter than the expected bolus length. Otherwise, due to the characteristics of the bipolar setup, the transit of the bolus will cause two responses. At an appropriate electrode distance the bipolar setup supplies a much better longitudinal selectivity than the unipolar array. This advantage is very important if the measuring segments are arranged successively. Experimental investigations have been carried out in healthy volunteers to verify the theoretical approach. The intraluminal multiple impedance measurements in the esophagus and in the small intestine yielded traces that characterized the mechanical peristaltic activity in detail. In each trace, which represents one organ segment of predefined length, it is possible to distinguish between the resting states, the bolus transit, and the contraction of the wall. This applies to both the unipolar and the bipolar arrangements. The features of the unipolar and bipolar impedance measurements are compared in a separate esophageal study. Both arrangements directly supply distinct motility curves without breathing artifacts or other disturbances. The sensitivity and selectivity are evidently higher in the bipolar than in the unipolar setup, as was predicted theoretically. The advantage of the unipolar arrangement could be the requirement for only half the number of measuring electrodes on the catheter for the same number of channels if the interchannel spacing is greater than the distance between the measuring electrode pair in the bipolar setup.

From each impedance trace a number of parameters can be derived, which describe an average activity in a defined organ segment. The starting and final time or the duration of the bolus transit as well as the extrema of impedance are important characteristics of each channel. On the basis of several impedance tracings the contractile patterns can be classified as segmenting, propulsive, or repropulsive functions. For the propulsive or repropulsive activities the average transit rate of the contraction wave and the bolus front can be calculated from the time delay of two events in different traces and the longitudinal distance between these channels. Moreover, on the basis of all parameters, the estimation of the bolus or lumen shape along the measuring catheter also seems to be possible. These connections as well as the experimental comparisons of the impedance procedure with other established manometric methods would go beyond the scope of this article, however, and will therefore be treated in a forthcoming paper.


For the continuous support of this work I want to thank the director of the Helraholtz-Institute, Prof. Dr. rer. nat. G. Rau, Aachen.

Appendix: Resistance of Ring Electrodes in an Infinite Volume Conductor

In the first analytical approach the fields of the electrodes are simulated by centric current line sources with a length L (13,14). The problem is assumed to be quasistatic. In the cylindrical coordinate system the distance between one point P and a point of the line sources e1 or e2 is r1(ξ) or r2(ξ) (Fig. 14).

Fig. 14. Line sources in an infinite two-layer conductor in cylindrical coordinates for simulation of the measuring electrodes and the electric volume conductor of the body around the catheter in unipolar and bipolar setups. Only the upper half of the symmetrical plane is depicted (left, unipolar setup; right bipolar setup)

Homogenous volume conductor

In a homogeneous and isotropic infinitely extended volume conductor with a conductivity σ every point of the line sources (Fig. 14) with a current


builds up a cylinder-symmetrical potential contribution


in an arbitrary point P(p, z) (12). The potential of the whole line source (Fig. 2) in a point P(p, z)


is given by the addition of all contributions.

The unipolar resistance RUH of the electrode e1(ρ = ρ0, z = 0) or e2(ρ = ρ0, z = d) in an infinite homogeneous volume conductor is given from Eq. (3)


For the bipolar setup (Fig. 14), it follows in the same manner:




represents the mutual influence of the line source e1 and sink e2.

As in Eq. (3) and (5)


in Eq. (5)


have to be valid.
Inhomogeneous volume conductor

In this part the electric volume conductor around the electrodes in each of the four phases of the contraction wave (Fig. 2) is simplified by one cylindrical layer I with a various conductivity σ1 and thickness D, which encircles the catheter and lies in a homogeneous, infinitely extended volume conductor II with a conductivity σ2 (Fig. 14). In the simulation of phase III (Fig. 2) the volume conductor II represents, for example, the conducting medium of the body fluids. Such a problem may be solved by the method of images (5) in a direct manner following the treatment in Eq. (1) to Eq. (8). The influence of layer II on the potential distribution of a current line source e1 (Fig. 14) in layer I can be considered by an additional image line sink e3, which lies symmetrical to the axis in a distance ρ2 and supplies the current I'. Thus the contribution of a point of the line source (Fig. 14) is given in layer I by


Accordingly, we replace in в\ a new line source with the current I" to obtain the potential distribution in layer II of a source point


Equations (9) and (10) must satisfy Laplace's equation, which for surface of discontinuity demands this boundary condition:


These demands can be fulfilled if


Substituting Equations (1) and (12) into (9) and (10) and integration of the resulting equations according to Equation (3) gives, with the notation


the potential function in layer II from two electrodes


and in layer I


The resistance of an electrode in Figure 2 (unipolar arrangement) results from Equations (15), (9), and (4) in


where D = ρ1 - ρ0 is the thickness of layer I (Fig. 14). Accordingly, the resistance of a bipolar set up RB in Figure 2 can be expressed as


Substituting Equations (6), (15), and (16) into (17) gives


The last term in Equation (18) depicts the mutual influence of the image source e1 and e3 (R13). Only a part of RU (Eq. 16) and R13 changes with D.

The  distribution  of the  current  density  in  the boundary ρ = ρ1,


can be used advantageously to compare some characteristics of the unipolar and bipolar arrangements in reference to the longitudinal extension of the measured region. Only the current density component in the direction of the normal


resulting from Equations (19), (13), and (14) is important for the change of Ru and RB depending on the thickness D.

We introduce segments of length B5 and B9 that comply with


where B5 and B9 define longitudinal bandwidth in which 50% or 90% of the total current It1) flows.

In other words, the part of resistance RU or RB that characterized the change of the thickness D in layer I is determined to 50% or 90% in a longitudinal segment that is B5 or B9 wide.

Finally, for the longitudinal selectivity the notation


is adopted.

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