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Electrode position and size in electrical impedance myography
Clinical Neurophysiology 116 (2005) 290–299 www.elsevier.com/locate/clinph
Electrode position and size in electrical impedance myography Seward B. Rutkove*, Ramon A. Partida, Gregory J. Esper, Ronald Aaron, Carl A. Shiffman The Department of Neurology, Division of Neuromuscular Diseases, Harvard Medical School, Beth Israel Deaconess Medical Center and the Department of Physics, Northeastern University, Boston, MA 02215, USA Accepted 3 September 2004 Available online 7 October 2004
Abstract Objective: Linear-electrical impedance myography (EIM) is a non-invasive technique for the evaluation of muscle, in which highfrequency alternating current is injected into the body via two surface electrodes, and the resulting voltage pattern over a selected muscle is measured using a second, larger set of electrodes. The precise location and size of the electrodes can be critical to the data obtained, and in this study the effects of variation in these factors were evaluated. Methods: Linear-EIM was performed in 5 subjects while varying the location of the current injecting electrodes and in an additional 8 subjects while varying the position of the voltage electrodes. Results: The major outcome variable, the ‘spatially averaged phase’ (qavg), decreased as the ipsilateral current injecting electrode was moved farther from the voltage electrodes, reaching a plateau 15–20 cm distant. As for the voltage electrode array, distal–proximal shifts resulted in the greatest changes, with variation in qavg being as high as 14% per cm; circumferential shifts around the limb had more modest effects. Conclusions: Linear-EIM results depend systematically on current and voltage electrode positions, but with reasonable care variation can be minimized. Significance: With proper attention to electrode placement, linear-EIM has sufficient reproducibility to become an important clinical tool in neuromuscular disease evaluation. q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. Keywords: Electromyography; Impedance; Muscle; Electrical current; Distance; Electrode
1. Introduction Electrical impedance myography (EIM), previously called localized bioimpedance analysis, is a form of neuromuscular evaluation in which high frequency alternating current is injected into the body via two surface electrodes—the current electrodes—and the resulting voltage pattern over a selected muscle or muscle group is measured using a second and larger set—the voltage electrodes (Aaron and Shiffman, 2000; Shiffman et al., 1999). EIM has several potential advantages over
* Corresponding author. Address: The Department of Neurology, Division of Neuromuscular Diseases, Harvard Medical School, Beth Israel Deaconess Medical Center, 330 Brookline Avenue, TCC-810, Boston, MA 02215, USA. Tel.: C1 617 667 8130; fax: C1 617 667 8747. E-mail address: [email protected] (S.B. Rutkove).
conventional electromyographic techniques: it is noninvasive, entirely painless, and can provide a quantitative rapid assessment of the muscle condition to be used in following disease progression or remission. The basic form of the technique is ‘linear-EIM,’ in which the voltage electrodes are placed along a line over the region of interest and the current is injected far from that region (Fig. 1). An early study of the quadriceps (Rutkove et al., 2002) has indicated that linear-EIM will have value in the assessment of neuromuscular disease, especially in terms of evaluating changes in disease severity over time. As an example, Fig. 2 shows the deterioration in the ‘spatially averaged phase,’ qavg (a key EIM parameter defined below) for three amyotrophic lateral sclerosis patients. While geometrical factors, such as muscle girth and shape, can impact EIM measurements, theory shows that these factors tend to cancel in the calculation of the spatially averaged phase,
1388-2457/$30.00 q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2004.09.002
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Fig. 1. Voltage electrode array configuration in linear-EIM for the study of biceps.
which primarily reflects properties of cell membranes (Shiffman et al., 2001). In fact, the same study included examination of the thighs of 45 healthy subjects and 25 patients with various neuromuscular diseases affecting the quadriceps, and it showed that EIM can be useful in detecting neuromuscular diseases despite wide variations in sizes and shapes of the thigh, and differences in age and gender. Fig. 3 illustrates this via a receiver-operating characteristic plot for the proposition that subjects with spatially averaged phase above a critical value are healthy and those below are diseased. The area under the curve of such a plot is taken as a measure of the test’s accuracy, and values above 0.9 are generally regarded as superior (Swets, 1988). The area under the curve in the present case is 0.95, supporting the view that EIM can discriminate between diseased and normal states of the quadriceps. In this case, the optimum cut-off between normal and diseased tissue is
Fig. 2. An example of the potential clinical value of EIM. Spatially averaged phase values for 3 patients with amyotrophic lateral sclerosis over time, demonstrating a clear decrease in phase consistent with the progressive course of the disease.
Fig. 3. Receiver operating characteristic curve demonstrating the accuracy of linear-EIM in differentiating neuromuscular disease patients from normal subjects. A perfect test would have an area under the curve (AUC) of 1.0.
qavgz8.28, representing a balance between high sensitivity, 0.85, and specificity, 0.95. The mechanism for the reduction in phase with disease remains uncertain and is a subject of continuing study. However, here we simply introduce the mathematical definition of qavg as an aid to discussing factors which can lead to inaccuracies in its measurement. With reference to Fig. 1, we can use ‘zn’ to represent the distance of the nth voltage electrode from the first, usually taken as the most distal one of the array. Measurements of the resistance, R and reactance, X, for the intervals z1 to z2, z1 to z3,., give R(zn) and X(zn), from which the phase q(zn)Zarctan{X(zn)/ R(zn)} is calculated. This is found to vary smoothly along a limb, allowing one to define the function q(z) by ordinary low-order polynomial fits. qavg is then calculated by analytic integration over a specified interval (or, as a rough guide during the measurements, simply as the average of the qn). Two examples of q(z) along the thigh are given in Fig. 4, one for a typical healthy subject and the other for a subject of similar age with advanced inclusion body myositis. Such ‘phase curves’ clearly offer much more information than the spatially averaged values alone, but their interpretation in terms of tissue parameters is mathematically difficult. Since qavg is theoretically relatively insensitive to differences in shapes and cross-sectional areas of the measured regions, it has been adopted as a phenomenological index of muscle condition. The results in Figs. 2–4 pertain to the muscles of the thigh, and they were obtained under research conditions using a specific protocol for electrode placement. If EIM is to be used as a clinical tool, it will be necessary to evaluate many different muscle regions and to establish that the results are reproducible for healthy individuals under ordinary clinical conditions. While the theory underlying EIM is generally understood, a number of technical issues concerning testing strategies must be addressed before the method can be effectively implemented. Variations in
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Fig. 4. Example of two phase versus z curves along the thigh, (A) for a 71 years old normal adult man (B) for 76 years old man with inclusion body myositis. Note differences in absolute values of phase and the sign of their slopes at equivalent points along the thigh.
current and voltage electrode placement may lead to significant changes in the primary outcome variables. For example, a strong dependence of q on z makes qavg sensitive to the length and location of the region over which the voltage electrodes lay. Unlike conventional nerve conduction studies, where the active electrode is placed over the motor point of the muscle in order to achieve the largest amplitude response, a similar focus cannot be defined for linear-EIM. Rather, the voltage electrodes are placed over the muscle(s) of interest in an attempt to sample ‘as much of the muscle as possible,’ and strict adherence to specified electrode placement protocols is required if one is to obtain reproducible outcomes. Some variability in the positioning of electrodes is of course inevitable, given the inherent difficulties in placing electrodes in identical locations on the same person over time or on different people whose muscle and limb shapes vary. Similarly, variation in the location of the current injecting electrodes also affects EIM results. This is because the impedance depends not only on the voltage electrode positions but also on the current distribution deep into the tissue below them. In particular, the spreading of flow lines as they emerge from the current electrodes can have significant effect on the measurements unless those electrodes are placed far from the voltage measuring region. Ideally, the current electrodes should be placed as far from the region of interest as is needed to ensure that the impedance is insensitive to inconsistencies in their placement. A major purpose of this study, then, is to find what qualifies as sufficiently distant for current electrode placement, in the context of reproducibility criteria based on realistic clinical needs. It will become clear that achieving adequate distance is anatomically impossible for some muscles, and therefore a second goal is to determine the sensitivity of qavg to distance over a wide range, in order to
make quantitative estimates of the precision needed to achieve a specified reproducibility in such cases. These estimates will also be useful when the current electrodes are deliberately placed close to the voltage measuring region in order to focus more narrowly the direction or the range of the currents. This variant of the linear-EIM technique may assist in identifying localized abnormalities and diseases, for example focal neurogenic atrophy. To these ends we evaluate the effects of varying current electrode position for three fixed voltage electrode array locations (over biceps, forearm flexor compartment, and tibialis anterior) and the effects of shifts in the voltage electrode array over biceps and tibialis anterior for fixed current electrode positions. While the primary aim is to assess the repeatability of EIM under clinical as opposed to laboratory conditions, this report also includes discussion of some fundamental questions concerning the technique.
2. Methods 2.1. Apparatus The technique of EIM has been described in detail elsewhere (Rutkove et al., 2002; Shiffman et al., 1999) and we outline here the features of the measuring system used in this study. Impedance data were obtained using a modified RJL model 101-A instrument (RJL Electronics, Clinton Twshp, MI), which supplied a constant 0.8 mA current at a fixed frequency of 50 kHz. Signals from computer-selected pairs of voltage electrodes were returned to the impedance instrument, which converted them into analog signals proportional to the resistance and reactance values. These were digitized and transmitted to the computer for display and further processing. In particular, graphs of resistance, R, and reactance, X, versus distance along the voltage electrode array were produced, and values of the phase q(z) and its spatial average, qavg, were calculated as described above. The impedances involved in this work lie at the few tens-ofohms level at phases of the order of 108, so that a precision of 1% in qavg requires noise levels in the few tens-ofmicrovolts range. This is easily obtained by digital signal averaging of a few hundred samples per voltage measurement, which requires about 0.01 s. Consequently, insofar as strictly electronic aspects of the measurements are concerned, random errors in qavg are of little concern in the present context. (Systematic errors associated with the instrumentation are discussed in detail in previous work (Shiffman et al., 1999)). Much more serious are transient electrochemical effects, primarily drifts in the properties of the voltage electrode–skin interface, which are dealt with in the Discussion. As a check against such drifts, each determination of the spatially averaged phase is repeated 2 or 3 times for the same electrode array, and it is the mean of these which is reported here as the quantity qavg.
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2.2. Electrodes and placement Voltage sensing was performed via disposable 5.5 mm wide strip electrodes (part number 019-766400, Nicolet Biomedical, Madison, WI), cut to lengths of 9, 4.5, or 2.25 cm. Current injection used either 20 cm2 Nicolet Disposable Ground Plate Electrodes (part number 019400500) or 3.1 cm2 Nicolet Dipsosable Recording electrodes (part number 019-400400). In all cases, measurements were made with the subject in a supine posture with the arm and leg outstretched and resting on the examining table. After briefly cleaning the relevant areas of the skin with alcohol, voltage electrodes were placed along a line parallel to the limb axis so as to lie over the greatest muscle bulk. In the current electrode studies, different ‘standard’ voltage electrode arrays were adopted for the different muscle regions, all using the 4.5 cm long strips. For the biceps, 6 electrodes were placed 2.5 cm apart starting 2 cm proximal to the biceps tendon (Fig. 1). For the forearm flexor compartment (current electrode studies only), five electrodes were placed starting 2.5 cm distal to the antecubital fossa and extending toward the hand at 2.5 cm intervals, and for the tibialis anterior, six electrodes were placed at 2.5 cm separation, starting 2.5 cm distal to the fibular head, just lateral to the anterior surface of the tibia. Current electrodes were placed at various locations which will be described, but for clarity of reference, we note that the electrode distal to the voltage electrode array on its limb is designated as ‘C1’. The other is identified as ‘C2’, regardless of its location on the body, e.g. whether it be placed on the contralateral arm, contralateral leg, trunk, or ipsilateral arm proximal to voltage electrode array. C1 position changes were studied for all three muscle groups, whereas C2 position changes were studied only for biceps. In the voltage electrode studies, the current electrodes were maintained on the ipsilateral hand and contralateral wrist for the biceps and on the distal foot and contralateral calf for the tibialis anterior. Three variations in voltage electrode placement were examined for each subject in the same session, and the results were compared to those for the relevant standard voltage configuration defined in the previous paragraph. Particular attention was paid to removing any electrode gel remaining from a previous placement, and the initial electrode positions were recorded on the skin using an indelible marker to facilitate accurate subsequent placements. 1. Circumferential shifts: Measurements were made using the standard configuration, then with the voltage electrode array positioned 2 cm medially, and then 2 cm laterally. The pre-existing array was removed in each case, and the 4.5 cm long electrodes were used throughout. 2. Distal–proximal shifts: Rather than shifting the voltage electrodes, we simply recalculated the impedances for the standard configuration, first using only electrodes
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V1–V5 (the most distal 5) and then using electrodes V2–V6 (the most proximal 5). This has the effect of creating a five-electrode array that is shifted proximally by 2.5 cm, the inter-electrode distance. 3. Electrode size: The 4.5 cm long voltage electrodes of the standard configuration were replaced in turn by the 2.25 and 9 cm versions.
2.3. Subjects In the current electrode studies, 5 normal subjects (4 men and 1 woman, median age 39 years, range 25–53 years) participated. For the voltage electrode studies, 8 normal subjects (6 men and 2 women, mean age 40 years, ranging from 27 to 69 years) participated. All subjects completed a brief neurological history and examination to confirm that no underlying disease was present. The study was approved by the hospital’s institutional review board, and written informed consent was obtained from all participants. 2.4. Data analysis Like all physiologic parameters, there are appreciable variations in EIM values amongst normal subjects, and what is relevant to this study are the fractional changes in phase that occur when current and voltage electrodes are shifted. For the current electrode studies, the results are presented for each subject in terms of percentage changes with respect to the values at a common (distant) reference point. For the voltage electrode studies, results are given in the form of the average percentage change in qavg for the group of subjects, i.e. the average of individual values of 100(qavg(shifted)K qavg(standard configuration))/qavg(standard configuration)), which we abbreviate by Dq/qo.
3. Results 3.1. Current electrode studies Distance of C1 from the voltage electrode array. As shown in Figs. 5–7, increasing the distance between C1 and the voltage electrode array had the effect of reducing the phase until a ‘plateau’ was reached at large separations. Typical variations in qavg on these plateaus are within G2 to G3% of the value for the most distant placement, and the sensitivities to electrode shift are of the order of a few tenths of a percent per cm. In the cases of the biceps and the forearm flexor compartment, such essentially constant values of the phase were found for distances larger than 10–15 cm, while for the tibialis anterior, that was not achieved until C1 was approximately 20 cm distant. At shorter distances, qavg was found to rise significantly, in qualitatively the same way for the three regions and the five
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Fig. 5. C1 position dependence of the average phase in biceps. The average phase appears to reach a near steady value when the distance between the distal current electrode (C1) and the voltage electrode array (measured along the axis of the arm) is greater than 10–15 cm.
subjects, though much more dramatically in some cases than in others. As shown, two exceptions to these trends were found, however, in which the phase dropped slightly from its upward trend as C1 reached its most proximal position. C1 electrode size. The data in Figs. 5–7 were obtained using the 20 cm2 rectangular ground plate electrodes, which may be rather large for some clinical applications, and less detailed measurements were made using 3.1 cm2 circular electrodes to estimate the electrode area effect. With sufficiently distant placement, the phase was approximately the same for the two sizes, with slightly higher values for the smaller area. For example, in the case of the biceps with C1 at 20 cm (i.e. on its plateau, [see Fig. 5]) qavg was on average only 1.2% higher for the smaller electrode relative to the larger one. On the other hand, the area dependence appears to be quite marked if it is placed on a rapidly rising part of the phase versus distance curve. In the one subject on whom it was studied, qavg was 6.448 for the 20 cm2 electrode at
Fig. 6. C1 position dependence of the average phase in finger flexor compartment of forearm. A 10–15 cm distance leads to the greatest stability of results.
Fig. 7. C1 position dependence of the average phase in tibialis anterior. A 15–20 cm distance produces the most consistent results.
10 cm compared with 8.258 for the 3.1 cm2 one at the same location. C1 circumferential displacements. Up to this point, C1 was maintained on the same side of the limb as the muscles studied (i.e. on the anterior forearm, hand and leg). However, this is not a critical requirement if the electrode is sufficiently distant. For example, shifting C1 from the palm to the posterior hand had negligible effect on the phase for the biceps. However, significant changes were seen when an intermediate distance was chosen and C1 was methodically repositioned around the arm (anterior to posterior and back to the original position). Fig. 8 demonstrates this for the 5 subjects, using 6 locations on a loop 10 cm from the voltage electrode array at its closest approach. This figure also testifies to the overall reproducibility of the measurements, the two sets of anterior values (‘A’ in the figure) differing by only 1% (rms) or about 0.18.
Fig. 8. Circumferential position dependence of the average phase in biceps. C1 (small disk electrode) was placed at a fixed intermediate distance from the voltage electrode array, and rotated around the arm (in the following order: anterior, lateral, posterior, medial, and back to anterior).
S.B. Rutkove et al. / Clinical Neurophysiology 116 (2005) 290–299 Table 1 Dependence of qavg for the biceps on C2 location
3.2. Voltage electrode studies
C2 locationa
qavg group meanGSD (degrees)
Extremes of variation with respect to contralateral wrist (degrees)
Contralateral wrist Contralateral palm Contralateral biceps Contralateral medial calf Ipsilateral medial calf Back of neck 4 cm proximal to array on ipsilateral arm
7.22G0.64 7.28G0.63 7.23G0.61 7.12G0.59 7.12G0.61 6.99G0.57 9.31G1.20
– K0.01 to K0.06 to K0.25 to K0.18 to K0.38 to C0.87 to
a
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C0.14 C0.16 C0.05 K0.04 K0.02 C3.64
C1 is on the ipsilateral palm throughout.
Note that the smaller area current electrode was of necessity used for these measurements. Distance of C2 from the voltage electrode array. The symmetric relationship between the current electrodes requires that similar ‘plateaus of insensitivity’ should exist for C2 at sufficient distance as are shown for C1 in Figs. 5–7. We have conducted one study to confirm this, involving 7 locations for C2 and the same 6-element voltage electrode array (on the biceps) and C1 location (on the ipsilateral palm.) The contralateral wrist location was taken as the reference position for C2, and the differences in qavg between that location and each of the six others was measured for each member of the group. The results are summarized in Table 1.
Circumferential shifts. Fig. 9 shows the effect on qavg of 2 cm shifts in the lateral and medial directions, for (a) the biceps and (b) the tibialis anterior. The coding of the points indicates the eight subjects, and while there is considerable variation amongst them, one can see that differences between the standard and shifted configurations amount to only a few percent in a 1 cm wide band centered on the reference position. The results are summarized in Table 2 in the form of percentage phase error per cm of shift. Distal–proximal shifts. Table 3 shows group average values of Dq/qo due to proximal shifts along the limb axis for the two muscles. The negative signs on the biceps entries designate a decrease in qavg for proximal shifts, and it is significant that that was the case individually for all 8 subjects. In contrast, qavg increased for proximal shifts along the TA for every subject except one. The preponderance of increases in qavg for the TA and decreases for the biceps with the same proximal electrode shift in both muscles argues that the changes reflect intrinsic anatomical features of the regions, rather than random effects. Voltage electrode size. Fig. 10 shows the effect of changing the length of the electrodes, with the points coded as in Fig. 9. Shortening the voltage electrodes evidently has a much greater effect than lengthening them, i.e. 9 and 6% change per cm for the biceps and TA cases, respectively, compared to 2 and 3% change per cm for lengthening them. Taking the most extreme case, an electrode length variation of 1 mm would have less than 1% effect on the phase results.
Fig. 9. Effect of 2 cm circumferential shifts of the electrode array on qavg, the spatially averaged phase. Dq/qo is the fractional change in qavg with respect to the reference position for the array, as defined in the text. (a) Biceps, (b) tibialis anterior.
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Table 2 Effect of circumferential shifts of the voltage electrode array Muscle
Shift direction
Group average fractional change (%/cm)GSD
Extremes of variation (%/cm)
Biceps
Medial Lateral Medial
5G3 0.3G2 K1.3G3
K0.2 to 10 K2.5 to 3.5 K6 to 2
Tibialis anterior
Lateral
2.5G1.5
K0.3 to 5
Table 3 Effect of distal–proximal shifts of the voltage electrode array Muscle
Group average fractional change (%/cm)GSD
Extremes of variation (%/cm)
Biceps Tibialis anterior
K11.4G2.5 2.6G2.8
K6.4 to K14 K1 to 7.6
4. Discussion Reproducibility is the sine qua non for the transfer of a new technique from the research laboratory to the clinic. In the case of linear-EIM, positioning of the various electrodes on the body is a key issue, since too stringent a requirement for precise placement could well make acceptable
repeatability difficult to achieve in practice. Assessing the implication of the results depends on whether linear-EIM is to be used in longitudinal studies (e.g. following the progression of disease in individual patients over time) or in cross-sectional studies of population groups (e.g. as an aid in neuromuscular diagnosis). In cross-sectional studies one is confronted with the question of how one chooses an appropriate size and location for the voltage electrode array and the location of the current electrodes when subjects have substantially different limb lengths and shapes. In longitudinal studies, on the other hand, that question is essentially irrelevant. Furthermore, errors due to shifts of the voltage electrode array from one testing session to the next are substantially correctable with the aid of photographs of the relevant area taken on each occasion. The results for the 45 normal subjects and 25 neuromuscular disease patients depicted in Fig. 3 offer a reasonable estimate for the extent of variation in crosssectional studies that can be expected for qavg, and it serves as a context in which to interpret the effects of possible inconsistencies in electrode positioning in clinical practice. In those measurements on the thigh (with C1 on the ipsilateral calf and C2 on the contralateral thigh) it was found that qavg ranged from as much as 148 in healthy subjects to less than 28 in some subjects with neuromuscular disease. Given this scale of variation, the present study
Fig. 10. Effect of electrode length on qavg. Dq/qo is the fractional change in qavg with length, with respect to the 4.5 cm reference electrode length. (a) Biceps, (b) tibialis anterior.
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indicates that linear-EIM is virtually insensitive to variations in current electrode placement, size or shape, provided that the electrodes can be placed more than 15– 20 cm from the voltage-measuring region. This has been shown explicitly for C1, but for theoretical reasons, it also holds true for C2. While no detailed centimeter-by-centimeter repositioning of C2 was performed in this study, the data do show insensitivity to location if C2 is placed sufficiently distant. In the case of biceps studied here, relative stability of measurements was achieved when C2 was placed at or more distant from the neck (Table 1). A more subtle feature of Table 1 deserves mention as well. For all but the nearest placement of C2 the extremes of variation in column 3 are of the same order of magnitude as the estimated random noise for the system and therefore should not be considered significantly different from zero. At the same time, the standard deviations in qavg in column 2 are very nearly the same and substantially larger than that noise estimate. The straightforward interpretation of these facts is that the standard deviations in column two are due to genuine subject-to-subject differences in the tissue under the voltage electrodes. By the same token, the much larger standard deviation for the last entry in the table must be taken as strong evidence that the effect of such differences on qavg is indeed greatly magnified when current electrodes are placed close to voltage electrode region. Also, the results in Figs. 5–7 for ‘distant’ placements of C1 suggest that G0.1 to G0.28 can be taken as an estimate for the random errors in measurements on individual subjects. This has particular relevance in the context of longitudinal studies, i.e. in terms of the time which would be needed to decide if a significant change in phase has occurred, say in a drug trial. Using Fig. 2 as an example, the 0.158 per week decline in qavg for the amyotrophic lateral sclerosis patient followed the longest period shows that only a few weeks would be needed to detect a statistically significant change. Placement of current electrodes at distances of 15–20 cm away from the electrode array will not be possible when studying muscle groups such as the intrinsic muscles of the hand or foot, and the data for the three areas examined here show that the phase can be quite sensitive to position when close placements of the current electrodes are required. Moreover, it is possible that placement of the current electrodes near the voltage electrode array may be advantageous in some situations, for example to reduce the spatial range of the currents when studying a specific muscle or muscle group. In either case, individual protocols will need to be developed for the positions, sizes and shapes of the current electrodes, and it will be important to determine how serious minor departures from the prescribed locations are likely to be. If the present results are a valid guide, it is likely that some protocols will make relatively stringent demands on positioning. A sense of this can be
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gleaned by studying the phase versus distance curves of Figs. 5–7. These have slopes of as much as 15% per cm at small distances, in which case achieving repeatability no worse than the random errors would require that the near current electrode be placed within 1–2 mm of the prescribed position. Of course many clinical situations will not demand such high accuracy, and positioning constraints will be correspondingly looser. Two fundamental questions are prompted by the current and voltage electrode shift data. First, how can one explain the results, i.e. are they physically reasonable? And second, if the phase attributed to a muscle can depend on where the current or voltage electrodes are placed, then what is the ‘real’ phase for that muscle? The answers to both hinge on the fact that the reactance of muscle is much larger for currents flowing perpendicular to fibers than for currents flowing parallel to them. With respect to the first question, in a non-invasive technique such as EIM, currents in the neighborhood of the current electrodes must flow predominantly across muscle fibers and hence are characterized by much larger values of phase than those further away, where the direction of the flow lines is more nearly parallel to the bundled fiber structure of the muscle (Aaron et al., 1997). As a consequence, the farther the current electrodes are from the voltage-measuring region, the lower the measured phase will be. The dependence on electrode area also follows from essentially the same qualitative considerations, as indeed is suggested by the observation that there is virtually no area dependence at large current electrode distances. Mathematical treatments of both questions have been pursued and support these conclusions, albeit in a different context and for strictly homogeneous and highly simplified muscle shapes (Rush, 1962; Shiffman and Aaron, 1998). We note, however, that the theory does not explain the reductions in phase observed at very low current–voltage electrode separations in the two cases noted earlier. The basic answer to second question is that all the measured phases are ‘real,’ but that the phase is a joint property of the muscle and of the distribution of currents flowing through it. One can define microscopic phase variables which do characterize the tissue per se, but as the previous discussion suggests, there must be two such variables, one for the component of the current parallel to the fibers and another for the transverse component. qavg certainly depends on those genuinely physiological parameters, but it also depends on the relative strengths of the longitudinal and transverse currents. These in turn are determined in large part by the local anatomical structure, such as the degree of flare of the thigh or forearm musculature or the convexity of the biceps brachii, a theoretical treatment of which is provided in earlier work (Shiffman et al., 2001). But they are also determined by the location of the current electrodes, as variation in placement will lead to different current distributions within the tissue.
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As for the voltage electrodes, errors due to incorrect placement of the array can be regarded as combination of: (i) shifts of the array along the circumference of the limb, maintaining its axis parallel to the limb axis (‘circumfercircumferential’ shifts), (ii) shifts of the array along the limb axis (‘distal–proximal’ shifts), (iii) tilting of the array axis relative to the limb axis, and (iv) changes in the transverse dimension of the array, i.e. in the length of the voltage electrodes. Of these, the first two are the most important, and we will show that the third, the tilt effect, can be adequately estimated from the circumferential shift data. The list does not include effects due to variations in the internal structure of the array, such as irregularities in electrode spacing or the electrode strips not being exactly parallel to one another. Barring extreme cases these do not lead to errors in qavg, as will be discussed below. Also, changes in the dimension of the array should not really be regarded as a serious source of error, since the length of the electrodes can certainly be controlled adequately. However, electrode length can have an indirect effect on the accuracy and reproducibility of the results, and we include a brief examination of that issue below. Our data suggests that distal–proximal shifts have the greatest effect on qavg with Dq/qo as high as 14% per cm for individual patients (the largest found in this study, on the biceps in two subjects). As Table 1 shows, circumferential shifts have group average values for Dq/qo lying in the 0– 5% per cm range, and individual values as high as 10% per cm. As for the question of electrode length, the dependence of qavg on circumferential shift dictates that a finite length electrode measures an average of the sub-surface electrical potentials which it overlies. This undoubtedly contributes to the observed dependence of qavg on length, but part of the effect is due to electrochemical properties of the electrodeskin-fat-layer complex, whose contribution is inversely proportional to electrode area. Since electrode length can easily be controlled, the relevant issue here is that the electrochemical properties generally change with time, which may lead to significant drift in R and X and hence in qavg. Comparing the observed R(t) and X(t) for long intervals after application of the voltage electrodes with simulations based on resistor–capacitor models of the electrode-skin-fat layer interface shows that the drift is away from the most accurate values rather than towards them, and it is advisable to make measurements within minutes of placing them on the skin. (This applies to the Ag/AgCl electrodes used in this study; the reverse was true for the tin-based electrodes used in our early work (Shiffman et al., 1999), where it was necessary to heat the electrode–skin area for 4–5 min to hasten stabilization of the measurements. These drifts involve what is called the ‘voltage divider effect,’ and they depend on the input characteristics of the impedance measuring instrument as well as on the area and conditions at the electrode–skin
interface. They can be reduced by increasing the input impedance of the instrument, and the use of active low capacitance probes is recommended for the most accurate work.) The remaining major factor affecting reproducibility is the ‘tilt’ of the electrode array with respect to the limb axis. This was not studied experimentally, since order of magnitude estimates of its effect can be established from basic theory. For example, rotating a point electrode version of the array by an angle f leads to a voltage change which is always less than what would be found for a circumferential shift equal to L sin f, where L is the axial length of the array. Thus if L was 20 cm and the tilt angle 38, the error could be as large as that due to a 1 cm circumferential shift. While this calculation is oversimplified, it is sufficient for showing that care must be taken to position the electrode array parallel to the axis of the limb. Finally, the discussion so far has focused on positioning of the voltage electrode array, as if it were a manufactured object with a fixed, pre-determined configuration of the actual electrodes. It is therefore important to point out that test-to-test inconsistencies in the spacing of the voltage electrodes within the array will not affect the qavg results, assuming that extreme variations are avoided. As explained earlier, qavg is determined using low-order polynomials fitted to the q(zn) data, and as long as the actual z values are used, no error is introduced by moderate irregularities in their spacing. We note also that errors due to inconsistency in voltage electrode separation and alignment could be avoided entirely by the use of pre-fabricated arrays. In summary, the major reproducibility problem facing EIM is two-fold: first, how does one determine anatomically equivalent locations for the electrodes in subjects of different body sizes and shapes, and second, how accurately must electrode placement conform to any chosen scheme so as to achieve the desired reproducibility of results. This study shows that for those muscles where the current electrodes can be placed at sufficient distance, neither of these issues is of practical concern insofar as placement of the current electrodes is concerned. But the results may still be sensitive to the location of the voltage electrodes. This is particularly important for cross-sectional studies, where many centimeters of difference in relevant anatomical dimensions are involved. The receiver operating characteristic curve shown in Fig. 3 does offer promise of success in at least some cross-sectional studies, but it remains to be seen whether linear-EIM will find utility as a diagnostic tool, given these high sensitivities to errors in electrode placement. On the other hand, linear-EIM appears to be ideally suited for longitudinal studies, where variation in electrode placement can be kept to a minimum. In particular, the study shows that for individual patients, qavg can be measured with sufficient relative accuracy that changes even as small as a few percent could safely be considered as having
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physiological rather than instrumental or methodological origin. Acknowledgements This study was supported by the National Institutes of Health, Grant RO1-NS42037-01A2 and Grant RR01032 to the Beth Israel Deaconess Medical Center General Clinical Research Center. References Aaron R, Shiffman C. Using localized impedance measurements to study muscle changes in injury and disease. Ann N Y Acad Sci 2000;904: 171–80.
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Aaron R, Huang M, Shiffman C. Anisotropy of human muscle via noninvasive impedance measurements. Phys Med Biol 1997;42:1245–62. Rush S. Methods of measuring resistivities of anisotropic conducting media. J Res Natl Bureau Stand 1962;66C:217–22. Rutkove S, Aaron R, Shiffman C. Localized bioimpedance analysis in the evaluation of neuromusclar disease. Muscle Nerve 2002;25:390–7. Shiffman C, Aaron R. Angular dependence of resistance in non-invasive electrical measurements of human muscle: the tensor model. Phys Med Biol 1998;43:1317–22. Shiffman C, Aaron R, Amoss V, Therrien J, Coomler K. Resistivity and phase in localized BIA. Phys Med Biol 1999;44:2409–29. Shiffman C, Aaron R, Altman A. Spatial dependence of the phase in localized bioelectrical impedance analysis. Phys Med Biol 2001;46: N97–N104. Swets J. Measuring the accuracy of diagnostic systems. Science 1988;240: 1285–93.
Electrode position and size in electrical impedance myography Seward B. Rutkove*, Ramon A. Partida, Gregory J. Esper, Ronald Aaron, Carl A. Shiffman The Department of Neurology, Division of Neuromuscular Diseases, Harvard Medical School, Beth Israel Deaconess Medical Center and the Department of Physics, Northeastern University, Boston, MA 02215, USA Accepted 3 September 2004 Available online 7 October 2004
Abstract Objective: Linear-electrical impedance myography (EIM) is a non-invasive technique for the evaluation of muscle, in which highfrequency alternating current is injected into the body via two surface electrodes, and the resulting voltage pattern over a selected muscle is measured using a second, larger set of electrodes. The precise location and size of the electrodes can be critical to the data obtained, and in this study the effects of variation in these factors were evaluated. Methods: Linear-EIM was performed in 5 subjects while varying the location of the current injecting electrodes and in an additional 8 subjects while varying the position of the voltage electrodes. Results: The major outcome variable, the ‘spatially averaged phase’ (qavg), decreased as the ipsilateral current injecting electrode was moved farther from the voltage electrodes, reaching a plateau 15–20 cm distant. As for the voltage electrode array, distal–proximal shifts resulted in the greatest changes, with variation in qavg being as high as 14% per cm; circumferential shifts around the limb had more modest effects. Conclusions: Linear-EIM results depend systematically on current and voltage electrode positions, but with reasonable care variation can be minimized. Significance: With proper attention to electrode placement, linear-EIM has sufficient reproducibility to become an important clinical tool in neuromuscular disease evaluation. q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. Keywords: Electromyography; Impedance; Muscle; Electrical current; Distance; Electrode
1. Introduction Electrical impedance myography (EIM), previously called localized bioimpedance analysis, is a form of neuromuscular evaluation in which high frequency alternating current is injected into the body via two surface electrodes—the current electrodes—and the resulting voltage pattern over a selected muscle or muscle group is measured using a second and larger set—the voltage electrodes (Aaron and Shiffman, 2000; Shiffman et al., 1999). EIM has several potential advantages over
* Corresponding author. Address: The Department of Neurology, Division of Neuromuscular Diseases, Harvard Medical School, Beth Israel Deaconess Medical Center, 330 Brookline Avenue, TCC-810, Boston, MA 02215, USA. Tel.: C1 617 667 8130; fax: C1 617 667 8747. E-mail address: [email protected] (S.B. Rutkove).
conventional electromyographic techniques: it is noninvasive, entirely painless, and can provide a quantitative rapid assessment of the muscle condition to be used in following disease progression or remission. The basic form of the technique is ‘linear-EIM,’ in which the voltage electrodes are placed along a line over the region of interest and the current is injected far from that region (Fig. 1). An early study of the quadriceps (Rutkove et al., 2002) has indicated that linear-EIM will have value in the assessment of neuromuscular disease, especially in terms of evaluating changes in disease severity over time. As an example, Fig. 2 shows the deterioration in the ‘spatially averaged phase,’ qavg (a key EIM parameter defined below) for three amyotrophic lateral sclerosis patients. While geometrical factors, such as muscle girth and shape, can impact EIM measurements, theory shows that these factors tend to cancel in the calculation of the spatially averaged phase,
1388-2457/$30.00 q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2004.09.002
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Fig. 1. Voltage electrode array configuration in linear-EIM for the study of biceps.
which primarily reflects properties of cell membranes (Shiffman et al., 2001). In fact, the same study included examination of the thighs of 45 healthy subjects and 25 patients with various neuromuscular diseases affecting the quadriceps, and it showed that EIM can be useful in detecting neuromuscular diseases despite wide variations in sizes and shapes of the thigh, and differences in age and gender. Fig. 3 illustrates this via a receiver-operating characteristic plot for the proposition that subjects with spatially averaged phase above a critical value are healthy and those below are diseased. The area under the curve of such a plot is taken as a measure of the test’s accuracy, and values above 0.9 are generally regarded as superior (Swets, 1988). The area under the curve in the present case is 0.95, supporting the view that EIM can discriminate between diseased and normal states of the quadriceps. In this case, the optimum cut-off between normal and diseased tissue is
Fig. 2. An example of the potential clinical value of EIM. Spatially averaged phase values for 3 patients with amyotrophic lateral sclerosis over time, demonstrating a clear decrease in phase consistent with the progressive course of the disease.
Fig. 3. Receiver operating characteristic curve demonstrating the accuracy of linear-EIM in differentiating neuromuscular disease patients from normal subjects. A perfect test would have an area under the curve (AUC) of 1.0.
qavgz8.28, representing a balance between high sensitivity, 0.85, and specificity, 0.95. The mechanism for the reduction in phase with disease remains uncertain and is a subject of continuing study. However, here we simply introduce the mathematical definition of qavg as an aid to discussing factors which can lead to inaccuracies in its measurement. With reference to Fig. 1, we can use ‘zn’ to represent the distance of the nth voltage electrode from the first, usually taken as the most distal one of the array. Measurements of the resistance, R and reactance, X, for the intervals z1 to z2, z1 to z3,., give R(zn) and X(zn), from which the phase q(zn)Zarctan{X(zn)/ R(zn)} is calculated. This is found to vary smoothly along a limb, allowing one to define the function q(z) by ordinary low-order polynomial fits. qavg is then calculated by analytic integration over a specified interval (or, as a rough guide during the measurements, simply as the average of the qn). Two examples of q(z) along the thigh are given in Fig. 4, one for a typical healthy subject and the other for a subject of similar age with advanced inclusion body myositis. Such ‘phase curves’ clearly offer much more information than the spatially averaged values alone, but their interpretation in terms of tissue parameters is mathematically difficult. Since qavg is theoretically relatively insensitive to differences in shapes and cross-sectional areas of the measured regions, it has been adopted as a phenomenological index of muscle condition. The results in Figs. 2–4 pertain to the muscles of the thigh, and they were obtained under research conditions using a specific protocol for electrode placement. If EIM is to be used as a clinical tool, it will be necessary to evaluate many different muscle regions and to establish that the results are reproducible for healthy individuals under ordinary clinical conditions. While the theory underlying EIM is generally understood, a number of technical issues concerning testing strategies must be addressed before the method can be effectively implemented. Variations in
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Fig. 4. Example of two phase versus z curves along the thigh, (A) for a 71 years old normal adult man (B) for 76 years old man with inclusion body myositis. Note differences in absolute values of phase and the sign of their slopes at equivalent points along the thigh.
current and voltage electrode placement may lead to significant changes in the primary outcome variables. For example, a strong dependence of q on z makes qavg sensitive to the length and location of the region over which the voltage electrodes lay. Unlike conventional nerve conduction studies, where the active electrode is placed over the motor point of the muscle in order to achieve the largest amplitude response, a similar focus cannot be defined for linear-EIM. Rather, the voltage electrodes are placed over the muscle(s) of interest in an attempt to sample ‘as much of the muscle as possible,’ and strict adherence to specified electrode placement protocols is required if one is to obtain reproducible outcomes. Some variability in the positioning of electrodes is of course inevitable, given the inherent difficulties in placing electrodes in identical locations on the same person over time or on different people whose muscle and limb shapes vary. Similarly, variation in the location of the current injecting electrodes also affects EIM results. This is because the impedance depends not only on the voltage electrode positions but also on the current distribution deep into the tissue below them. In particular, the spreading of flow lines as they emerge from the current electrodes can have significant effect on the measurements unless those electrodes are placed far from the voltage measuring region. Ideally, the current electrodes should be placed as far from the region of interest as is needed to ensure that the impedance is insensitive to inconsistencies in their placement. A major purpose of this study, then, is to find what qualifies as sufficiently distant for current electrode placement, in the context of reproducibility criteria based on realistic clinical needs. It will become clear that achieving adequate distance is anatomically impossible for some muscles, and therefore a second goal is to determine the sensitivity of qavg to distance over a wide range, in order to
make quantitative estimates of the precision needed to achieve a specified reproducibility in such cases. These estimates will also be useful when the current electrodes are deliberately placed close to the voltage measuring region in order to focus more narrowly the direction or the range of the currents. This variant of the linear-EIM technique may assist in identifying localized abnormalities and diseases, for example focal neurogenic atrophy. To these ends we evaluate the effects of varying current electrode position for three fixed voltage electrode array locations (over biceps, forearm flexor compartment, and tibialis anterior) and the effects of shifts in the voltage electrode array over biceps and tibialis anterior for fixed current electrode positions. While the primary aim is to assess the repeatability of EIM under clinical as opposed to laboratory conditions, this report also includes discussion of some fundamental questions concerning the technique.
2. Methods 2.1. Apparatus The technique of EIM has been described in detail elsewhere (Rutkove et al., 2002; Shiffman et al., 1999) and we outline here the features of the measuring system used in this study. Impedance data were obtained using a modified RJL model 101-A instrument (RJL Electronics, Clinton Twshp, MI), which supplied a constant 0.8 mA current at a fixed frequency of 50 kHz. Signals from computer-selected pairs of voltage electrodes were returned to the impedance instrument, which converted them into analog signals proportional to the resistance and reactance values. These were digitized and transmitted to the computer for display and further processing. In particular, graphs of resistance, R, and reactance, X, versus distance along the voltage electrode array were produced, and values of the phase q(z) and its spatial average, qavg, were calculated as described above. The impedances involved in this work lie at the few tens-ofohms level at phases of the order of 108, so that a precision of 1% in qavg requires noise levels in the few tens-ofmicrovolts range. This is easily obtained by digital signal averaging of a few hundred samples per voltage measurement, which requires about 0.01 s. Consequently, insofar as strictly electronic aspects of the measurements are concerned, random errors in qavg are of little concern in the present context. (Systematic errors associated with the instrumentation are discussed in detail in previous work (Shiffman et al., 1999)). Much more serious are transient electrochemical effects, primarily drifts in the properties of the voltage electrode–skin interface, which are dealt with in the Discussion. As a check against such drifts, each determination of the spatially averaged phase is repeated 2 or 3 times for the same electrode array, and it is the mean of these which is reported here as the quantity qavg.
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2.2. Electrodes and placement Voltage sensing was performed via disposable 5.5 mm wide strip electrodes (part number 019-766400, Nicolet Biomedical, Madison, WI), cut to lengths of 9, 4.5, or 2.25 cm. Current injection used either 20 cm2 Nicolet Disposable Ground Plate Electrodes (part number 019400500) or 3.1 cm2 Nicolet Dipsosable Recording electrodes (part number 019-400400). In all cases, measurements were made with the subject in a supine posture with the arm and leg outstretched and resting on the examining table. After briefly cleaning the relevant areas of the skin with alcohol, voltage electrodes were placed along a line parallel to the limb axis so as to lie over the greatest muscle bulk. In the current electrode studies, different ‘standard’ voltage electrode arrays were adopted for the different muscle regions, all using the 4.5 cm long strips. For the biceps, 6 electrodes were placed 2.5 cm apart starting 2 cm proximal to the biceps tendon (Fig. 1). For the forearm flexor compartment (current electrode studies only), five electrodes were placed starting 2.5 cm distal to the antecubital fossa and extending toward the hand at 2.5 cm intervals, and for the tibialis anterior, six electrodes were placed at 2.5 cm separation, starting 2.5 cm distal to the fibular head, just lateral to the anterior surface of the tibia. Current electrodes were placed at various locations which will be described, but for clarity of reference, we note that the electrode distal to the voltage electrode array on its limb is designated as ‘C1’. The other is identified as ‘C2’, regardless of its location on the body, e.g. whether it be placed on the contralateral arm, contralateral leg, trunk, or ipsilateral arm proximal to voltage electrode array. C1 position changes were studied for all three muscle groups, whereas C2 position changes were studied only for biceps. In the voltage electrode studies, the current electrodes were maintained on the ipsilateral hand and contralateral wrist for the biceps and on the distal foot and contralateral calf for the tibialis anterior. Three variations in voltage electrode placement were examined for each subject in the same session, and the results were compared to those for the relevant standard voltage configuration defined in the previous paragraph. Particular attention was paid to removing any electrode gel remaining from a previous placement, and the initial electrode positions were recorded on the skin using an indelible marker to facilitate accurate subsequent placements. 1. Circumferential shifts: Measurements were made using the standard configuration, then with the voltage electrode array positioned 2 cm medially, and then 2 cm laterally. The pre-existing array was removed in each case, and the 4.5 cm long electrodes were used throughout. 2. Distal–proximal shifts: Rather than shifting the voltage electrodes, we simply recalculated the impedances for the standard configuration, first using only electrodes
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V1–V5 (the most distal 5) and then using electrodes V2–V6 (the most proximal 5). This has the effect of creating a five-electrode array that is shifted proximally by 2.5 cm, the inter-electrode distance. 3. Electrode size: The 4.5 cm long voltage electrodes of the standard configuration were replaced in turn by the 2.25 and 9 cm versions.
2.3. Subjects In the current electrode studies, 5 normal subjects (4 men and 1 woman, median age 39 years, range 25–53 years) participated. For the voltage electrode studies, 8 normal subjects (6 men and 2 women, mean age 40 years, ranging from 27 to 69 years) participated. All subjects completed a brief neurological history and examination to confirm that no underlying disease was present. The study was approved by the hospital’s institutional review board, and written informed consent was obtained from all participants. 2.4. Data analysis Like all physiologic parameters, there are appreciable variations in EIM values amongst normal subjects, and what is relevant to this study are the fractional changes in phase that occur when current and voltage electrodes are shifted. For the current electrode studies, the results are presented for each subject in terms of percentage changes with respect to the values at a common (distant) reference point. For the voltage electrode studies, results are given in the form of the average percentage change in qavg for the group of subjects, i.e. the average of individual values of 100(qavg(shifted)K qavg(standard configuration))/qavg(standard configuration)), which we abbreviate by Dq/qo.
3. Results 3.1. Current electrode studies Distance of C1 from the voltage electrode array. As shown in Figs. 5–7, increasing the distance between C1 and the voltage electrode array had the effect of reducing the phase until a ‘plateau’ was reached at large separations. Typical variations in qavg on these plateaus are within G2 to G3% of the value for the most distant placement, and the sensitivities to electrode shift are of the order of a few tenths of a percent per cm. In the cases of the biceps and the forearm flexor compartment, such essentially constant values of the phase were found for distances larger than 10–15 cm, while for the tibialis anterior, that was not achieved until C1 was approximately 20 cm distant. At shorter distances, qavg was found to rise significantly, in qualitatively the same way for the three regions and the five
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Fig. 5. C1 position dependence of the average phase in biceps. The average phase appears to reach a near steady value when the distance between the distal current electrode (C1) and the voltage electrode array (measured along the axis of the arm) is greater than 10–15 cm.
subjects, though much more dramatically in some cases than in others. As shown, two exceptions to these trends were found, however, in which the phase dropped slightly from its upward trend as C1 reached its most proximal position. C1 electrode size. The data in Figs. 5–7 were obtained using the 20 cm2 rectangular ground plate electrodes, which may be rather large for some clinical applications, and less detailed measurements were made using 3.1 cm2 circular electrodes to estimate the electrode area effect. With sufficiently distant placement, the phase was approximately the same for the two sizes, with slightly higher values for the smaller area. For example, in the case of the biceps with C1 at 20 cm (i.e. on its plateau, [see Fig. 5]) qavg was on average only 1.2% higher for the smaller electrode relative to the larger one. On the other hand, the area dependence appears to be quite marked if it is placed on a rapidly rising part of the phase versus distance curve. In the one subject on whom it was studied, qavg was 6.448 for the 20 cm2 electrode at
Fig. 6. C1 position dependence of the average phase in finger flexor compartment of forearm. A 10–15 cm distance leads to the greatest stability of results.
Fig. 7. C1 position dependence of the average phase in tibialis anterior. A 15–20 cm distance produces the most consistent results.
10 cm compared with 8.258 for the 3.1 cm2 one at the same location. C1 circumferential displacements. Up to this point, C1 was maintained on the same side of the limb as the muscles studied (i.e. on the anterior forearm, hand and leg). However, this is not a critical requirement if the electrode is sufficiently distant. For example, shifting C1 from the palm to the posterior hand had negligible effect on the phase for the biceps. However, significant changes were seen when an intermediate distance was chosen and C1 was methodically repositioned around the arm (anterior to posterior and back to the original position). Fig. 8 demonstrates this for the 5 subjects, using 6 locations on a loop 10 cm from the voltage electrode array at its closest approach. This figure also testifies to the overall reproducibility of the measurements, the two sets of anterior values (‘A’ in the figure) differing by only 1% (rms) or about 0.18.
Fig. 8. Circumferential position dependence of the average phase in biceps. C1 (small disk electrode) was placed at a fixed intermediate distance from the voltage electrode array, and rotated around the arm (in the following order: anterior, lateral, posterior, medial, and back to anterior).
S.B. Rutkove et al. / Clinical Neurophysiology 116 (2005) 290–299 Table 1 Dependence of qavg for the biceps on C2 location
3.2. Voltage electrode studies
C2 locationa
qavg group meanGSD (degrees)
Extremes of variation with respect to contralateral wrist (degrees)
Contralateral wrist Contralateral palm Contralateral biceps Contralateral medial calf Ipsilateral medial calf Back of neck 4 cm proximal to array on ipsilateral arm
7.22G0.64 7.28G0.63 7.23G0.61 7.12G0.59 7.12G0.61 6.99G0.57 9.31G1.20
– K0.01 to K0.06 to K0.25 to K0.18 to K0.38 to C0.87 to
a
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C0.14 C0.16 C0.05 K0.04 K0.02 C3.64
C1 is on the ipsilateral palm throughout.
Note that the smaller area current electrode was of necessity used for these measurements. Distance of C2 from the voltage electrode array. The symmetric relationship between the current electrodes requires that similar ‘plateaus of insensitivity’ should exist for C2 at sufficient distance as are shown for C1 in Figs. 5–7. We have conducted one study to confirm this, involving 7 locations for C2 and the same 6-element voltage electrode array (on the biceps) and C1 location (on the ipsilateral palm.) The contralateral wrist location was taken as the reference position for C2, and the differences in qavg between that location and each of the six others was measured for each member of the group. The results are summarized in Table 1.
Circumferential shifts. Fig. 9 shows the effect on qavg of 2 cm shifts in the lateral and medial directions, for (a) the biceps and (b) the tibialis anterior. The coding of the points indicates the eight subjects, and while there is considerable variation amongst them, one can see that differences between the standard and shifted configurations amount to only a few percent in a 1 cm wide band centered on the reference position. The results are summarized in Table 2 in the form of percentage phase error per cm of shift. Distal–proximal shifts. Table 3 shows group average values of Dq/qo due to proximal shifts along the limb axis for the two muscles. The negative signs on the biceps entries designate a decrease in qavg for proximal shifts, and it is significant that that was the case individually for all 8 subjects. In contrast, qavg increased for proximal shifts along the TA for every subject except one. The preponderance of increases in qavg for the TA and decreases for the biceps with the same proximal electrode shift in both muscles argues that the changes reflect intrinsic anatomical features of the regions, rather than random effects. Voltage electrode size. Fig. 10 shows the effect of changing the length of the electrodes, with the points coded as in Fig. 9. Shortening the voltage electrodes evidently has a much greater effect than lengthening them, i.e. 9 and 6% change per cm for the biceps and TA cases, respectively, compared to 2 and 3% change per cm for lengthening them. Taking the most extreme case, an electrode length variation of 1 mm would have less than 1% effect on the phase results.
Fig. 9. Effect of 2 cm circumferential shifts of the electrode array on qavg, the spatially averaged phase. Dq/qo is the fractional change in qavg with respect to the reference position for the array, as defined in the text. (a) Biceps, (b) tibialis anterior.
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Table 2 Effect of circumferential shifts of the voltage electrode array Muscle
Shift direction
Group average fractional change (%/cm)GSD
Extremes of variation (%/cm)
Biceps
Medial Lateral Medial
5G3 0.3G2 K1.3G3
K0.2 to 10 K2.5 to 3.5 K6 to 2
Tibialis anterior
Lateral
2.5G1.5
K0.3 to 5
Table 3 Effect of distal–proximal shifts of the voltage electrode array Muscle
Group average fractional change (%/cm)GSD
Extremes of variation (%/cm)
Biceps Tibialis anterior
K11.4G2.5 2.6G2.8
K6.4 to K14 K1 to 7.6
4. Discussion Reproducibility is the sine qua non for the transfer of a new technique from the research laboratory to the clinic. In the case of linear-EIM, positioning of the various electrodes on the body is a key issue, since too stringent a requirement for precise placement could well make acceptable
repeatability difficult to achieve in practice. Assessing the implication of the results depends on whether linear-EIM is to be used in longitudinal studies (e.g. following the progression of disease in individual patients over time) or in cross-sectional studies of population groups (e.g. as an aid in neuromuscular diagnosis). In cross-sectional studies one is confronted with the question of how one chooses an appropriate size and location for the voltage electrode array and the location of the current electrodes when subjects have substantially different limb lengths and shapes. In longitudinal studies, on the other hand, that question is essentially irrelevant. Furthermore, errors due to shifts of the voltage electrode array from one testing session to the next are substantially correctable with the aid of photographs of the relevant area taken on each occasion. The results for the 45 normal subjects and 25 neuromuscular disease patients depicted in Fig. 3 offer a reasonable estimate for the extent of variation in crosssectional studies that can be expected for qavg, and it serves as a context in which to interpret the effects of possible inconsistencies in electrode positioning in clinical practice. In those measurements on the thigh (with C1 on the ipsilateral calf and C2 on the contralateral thigh) it was found that qavg ranged from as much as 148 in healthy subjects to less than 28 in some subjects with neuromuscular disease. Given this scale of variation, the present study
Fig. 10. Effect of electrode length on qavg. Dq/qo is the fractional change in qavg with length, with respect to the 4.5 cm reference electrode length. (a) Biceps, (b) tibialis anterior.
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indicates that linear-EIM is virtually insensitive to variations in current electrode placement, size or shape, provided that the electrodes can be placed more than 15– 20 cm from the voltage-measuring region. This has been shown explicitly for C1, but for theoretical reasons, it also holds true for C2. While no detailed centimeter-by-centimeter repositioning of C2 was performed in this study, the data do show insensitivity to location if C2 is placed sufficiently distant. In the case of biceps studied here, relative stability of measurements was achieved when C2 was placed at or more distant from the neck (Table 1). A more subtle feature of Table 1 deserves mention as well. For all but the nearest placement of C2 the extremes of variation in column 3 are of the same order of magnitude as the estimated random noise for the system and therefore should not be considered significantly different from zero. At the same time, the standard deviations in qavg in column 2 are very nearly the same and substantially larger than that noise estimate. The straightforward interpretation of these facts is that the standard deviations in column two are due to genuine subject-to-subject differences in the tissue under the voltage electrodes. By the same token, the much larger standard deviation for the last entry in the table must be taken as strong evidence that the effect of such differences on qavg is indeed greatly magnified when current electrodes are placed close to voltage electrode region. Also, the results in Figs. 5–7 for ‘distant’ placements of C1 suggest that G0.1 to G0.28 can be taken as an estimate for the random errors in measurements on individual subjects. This has particular relevance in the context of longitudinal studies, i.e. in terms of the time which would be needed to decide if a significant change in phase has occurred, say in a drug trial. Using Fig. 2 as an example, the 0.158 per week decline in qavg for the amyotrophic lateral sclerosis patient followed the longest period shows that only a few weeks would be needed to detect a statistically significant change. Placement of current electrodes at distances of 15–20 cm away from the electrode array will not be possible when studying muscle groups such as the intrinsic muscles of the hand or foot, and the data for the three areas examined here show that the phase can be quite sensitive to position when close placements of the current electrodes are required. Moreover, it is possible that placement of the current electrodes near the voltage electrode array may be advantageous in some situations, for example to reduce the spatial range of the currents when studying a specific muscle or muscle group. In either case, individual protocols will need to be developed for the positions, sizes and shapes of the current electrodes, and it will be important to determine how serious minor departures from the prescribed locations are likely to be. If the present results are a valid guide, it is likely that some protocols will make relatively stringent demands on positioning. A sense of this can be
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gleaned by studying the phase versus distance curves of Figs. 5–7. These have slopes of as much as 15% per cm at small distances, in which case achieving repeatability no worse than the random errors would require that the near current electrode be placed within 1–2 mm of the prescribed position. Of course many clinical situations will not demand such high accuracy, and positioning constraints will be correspondingly looser. Two fundamental questions are prompted by the current and voltage electrode shift data. First, how can one explain the results, i.e. are they physically reasonable? And second, if the phase attributed to a muscle can depend on where the current or voltage electrodes are placed, then what is the ‘real’ phase for that muscle? The answers to both hinge on the fact that the reactance of muscle is much larger for currents flowing perpendicular to fibers than for currents flowing parallel to them. With respect to the first question, in a non-invasive technique such as EIM, currents in the neighborhood of the current electrodes must flow predominantly across muscle fibers and hence are characterized by much larger values of phase than those further away, where the direction of the flow lines is more nearly parallel to the bundled fiber structure of the muscle (Aaron et al., 1997). As a consequence, the farther the current electrodes are from the voltage-measuring region, the lower the measured phase will be. The dependence on electrode area also follows from essentially the same qualitative considerations, as indeed is suggested by the observation that there is virtually no area dependence at large current electrode distances. Mathematical treatments of both questions have been pursued and support these conclusions, albeit in a different context and for strictly homogeneous and highly simplified muscle shapes (Rush, 1962; Shiffman and Aaron, 1998). We note, however, that the theory does not explain the reductions in phase observed at very low current–voltage electrode separations in the two cases noted earlier. The basic answer to second question is that all the measured phases are ‘real,’ but that the phase is a joint property of the muscle and of the distribution of currents flowing through it. One can define microscopic phase variables which do characterize the tissue per se, but as the previous discussion suggests, there must be two such variables, one for the component of the current parallel to the fibers and another for the transverse component. qavg certainly depends on those genuinely physiological parameters, but it also depends on the relative strengths of the longitudinal and transverse currents. These in turn are determined in large part by the local anatomical structure, such as the degree of flare of the thigh or forearm musculature or the convexity of the biceps brachii, a theoretical treatment of which is provided in earlier work (Shiffman et al., 2001). But they are also determined by the location of the current electrodes, as variation in placement will lead to different current distributions within the tissue.
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As for the voltage electrodes, errors due to incorrect placement of the array can be regarded as combination of: (i) shifts of the array along the circumference of the limb, maintaining its axis parallel to the limb axis (‘circumfercircumferential’ shifts), (ii) shifts of the array along the limb axis (‘distal–proximal’ shifts), (iii) tilting of the array axis relative to the limb axis, and (iv) changes in the transverse dimension of the array, i.e. in the length of the voltage electrodes. Of these, the first two are the most important, and we will show that the third, the tilt effect, can be adequately estimated from the circumferential shift data. The list does not include effects due to variations in the internal structure of the array, such as irregularities in electrode spacing or the electrode strips not being exactly parallel to one another. Barring extreme cases these do not lead to errors in qavg, as will be discussed below. Also, changes in the dimension of the array should not really be regarded as a serious source of error, since the length of the electrodes can certainly be controlled adequately. However, electrode length can have an indirect effect on the accuracy and reproducibility of the results, and we include a brief examination of that issue below. Our data suggests that distal–proximal shifts have the greatest effect on qavg with Dq/qo as high as 14% per cm for individual patients (the largest found in this study, on the biceps in two subjects). As Table 1 shows, circumferential shifts have group average values for Dq/qo lying in the 0– 5% per cm range, and individual values as high as 10% per cm. As for the question of electrode length, the dependence of qavg on circumferential shift dictates that a finite length electrode measures an average of the sub-surface electrical potentials which it overlies. This undoubtedly contributes to the observed dependence of qavg on length, but part of the effect is due to electrochemical properties of the electrodeskin-fat-layer complex, whose contribution is inversely proportional to electrode area. Since electrode length can easily be controlled, the relevant issue here is that the electrochemical properties generally change with time, which may lead to significant drift in R and X and hence in qavg. Comparing the observed R(t) and X(t) for long intervals after application of the voltage electrodes with simulations based on resistor–capacitor models of the electrode-skin-fat layer interface shows that the drift is away from the most accurate values rather than towards them, and it is advisable to make measurements within minutes of placing them on the skin. (This applies to the Ag/AgCl electrodes used in this study; the reverse was true for the tin-based electrodes used in our early work (Shiffman et al., 1999), where it was necessary to heat the electrode–skin area for 4–5 min to hasten stabilization of the measurements. These drifts involve what is called the ‘voltage divider effect,’ and they depend on the input characteristics of the impedance measuring instrument as well as on the area and conditions at the electrode–skin
interface. They can be reduced by increasing the input impedance of the instrument, and the use of active low capacitance probes is recommended for the most accurate work.) The remaining major factor affecting reproducibility is the ‘tilt’ of the electrode array with respect to the limb axis. This was not studied experimentally, since order of magnitude estimates of its effect can be established from basic theory. For example, rotating a point electrode version of the array by an angle f leads to a voltage change which is always less than what would be found for a circumferential shift equal to L sin f, where L is the axial length of the array. Thus if L was 20 cm and the tilt angle 38, the error could be as large as that due to a 1 cm circumferential shift. While this calculation is oversimplified, it is sufficient for showing that care must be taken to position the electrode array parallel to the axis of the limb. Finally, the discussion so far has focused on positioning of the voltage electrode array, as if it were a manufactured object with a fixed, pre-determined configuration of the actual electrodes. It is therefore important to point out that test-to-test inconsistencies in the spacing of the voltage electrodes within the array will not affect the qavg results, assuming that extreme variations are avoided. As explained earlier, qavg is determined using low-order polynomials fitted to the q(zn) data, and as long as the actual z values are used, no error is introduced by moderate irregularities in their spacing. We note also that errors due to inconsistency in voltage electrode separation and alignment could be avoided entirely by the use of pre-fabricated arrays. In summary, the major reproducibility problem facing EIM is two-fold: first, how does one determine anatomically equivalent locations for the electrodes in subjects of different body sizes and shapes, and second, how accurately must electrode placement conform to any chosen scheme so as to achieve the desired reproducibility of results. This study shows that for those muscles where the current electrodes can be placed at sufficient distance, neither of these issues is of practical concern insofar as placement of the current electrodes is concerned. But the results may still be sensitive to the location of the voltage electrodes. This is particularly important for cross-sectional studies, where many centimeters of difference in relevant anatomical dimensions are involved. The receiver operating characteristic curve shown in Fig. 3 does offer promise of success in at least some cross-sectional studies, but it remains to be seen whether linear-EIM will find utility as a diagnostic tool, given these high sensitivities to errors in electrode placement. On the other hand, linear-EIM appears to be ideally suited for longitudinal studies, where variation in electrode placement can be kept to a minimum. In particular, the study shows that for individual patients, qavg can be measured with sufficient relative accuracy that changes even as small as a few percent could safely be considered as having
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physiological rather than instrumental or methodological origin. Acknowledgements This study was supported by the National Institutes of Health, Grant RO1-NS42037-01A2 and Grant RR01032 to the Beth Israel Deaconess Medical Center General Clinical Research Center. References Aaron R, Shiffman C. Using localized impedance measurements to study muscle changes in injury and disease. Ann N Y Acad Sci 2000;904: 171–80.
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