Circuit modeling of the electrical impedance: part III. Disuse following bone fracture

Scaling and the frequency dependence of Nyquist plot maxima of the electrical impedance of the human thigh

OBJECTIVE

To define and elucidate the properties of reduced-variable Nyquist plots.

APPROACH

Non-invasive measurements of the electrical impedance of the human thigh. A retrospective analysis of the electrical impedances of 154 normal subjects measured over the past decade shows that 'scaling' of the Nyquist plots for human thigh muscles is a property shared by healthy thigh musculature, irrespective of subject and the length of muscle segment. Here the term scaling signifies the near and sometimes 'perfect' coalescence of the separate X versus R plots into one 'reduced' Nyquist plot by the simple expedient of dividing R and X by X _m , the value of X at the reactance maximum. To the extent allowed by noise levels one can say that there is one 'universal' reduced Nyquist plot for the thigh musculature of healthy subjects.

MAIN RESULTS

There is one feature of the Nyquist curves which is not 'universal', however, namely the frequency f _m at which the maximum in X is observed. That is found to vary from 10 to 100 kHz. depending on subject and segment length. Analysis shows, however, that the mean value of 1/f _m is an accurately linear function of segment length, though there is a small subject-to-subject random element as well. Also, following the recovery of an otherwise healthy victim of ankle fracture demonstrates the clear superiority of measurements above about 800 kHz, where scaling is not observed, in contrast to measurements below about 400 kHz, where scaling is accurately obeyed.

SIGNIFICANCE

The ubiquity of 'scaling' casts new light on the interpretation of impedance results as they are used in electrical impedance myography and bioelectric impedance analysis.

Pre-contraction dynamic electrical impedance myography of the forearm finger flexors

Electrical activity in the sensory-motor and supplementary motor areas of the cerebral cortex is known to occur during a 'readiness interval', extending up to 2 s before the relevant muscle actually contracts. This paper presents evidence that there are also changes in the properties of the muscle itself during a similar preparatory period, as revealed by dynamic electrical impedance myography. 11 healthy subjects aged 23.5 ± 2.5 years were asked to perform a series of isometric gripping exercises during which the force, resistance and reactance of the forearm finger flexor muscles were monitored. A change in reactance, ΔX, or resistance, ΔR, which occurred before the generation of force, ΔF, was dubbed a 'PIC', shorthand for precontraction impedance change (subject to criteria to rule out the possibility of simple 'noise'), of which 1206 qualified in the entire subject cohort. Such PIC's are statistically well correlated when expressed in terms of differences between PIC and force onset times (r ≈ 0.9, p ≈ 0). This is demonstrated using a variation on the 'computer of average transients' method. Precontraction impedance changes (PICs) occurring as much as 2 s before the onset of force generation were found, in qualitative agreement with precontraction EEG activity reported in the literature. Also, a subset of PIC's was found in which the scaled and time-shifted ΔX(t) was virtually identical to ΔF(t). Since the occurrence and timing of all the PICs depend on oral commands, it is clear that the auditory cortex is likely involved, but the detailed mechanism coupling brain activity with PICs is not known.

Evaluation of Electrical Impedance as a Biomarker of Myostatin Inhibition in Wild Type and Muscular Dystrophy Mice

Objectives

Non-invasive and effort independent biomarkers are needed to better assess the effects of drug therapy on healthy muscle and that affected by muscular dystrophy (mdx). Here we evaluated the use of multi-frequency electrical impedance for this purpose with comparison to force and histological parameters.

Methods

Eight wild-type (wt) and 10 mdx mice were treated weekly with RAP-031 activin type IIB receptor at a dose of 10 mg kg⁻¹ twice weekly for 16 weeks; the investigators were blinded to treatment and disease status. At the completion of treatment, impedance measurements, in situ force measurements, and histology analyses were performed.

Results

As compared to untreated animals, RAP-031 wt and mdx treated mice had greater body mass (18% and 17%, p < 0.001 respectively) and muscle mass (25% p < 0.05 and 22% p < 0.001, respectively). The Cole impedance parameters in treated wt mice, showed a 24% lower central frequency (p < 0.05) and 19% higher resistance ratio (p < 0.05); no significant differences were observed in the mdx mice. These differences were consistent with those seen in maximum isometric force, which was greater in the wt animals (p < 0.05 at > 70 Hz), but not in the mdx animals. In contrast, maximum force normalized by muscle mass was unchanged in the wt animals and lower in the mdx animals by 21% (p < 0.01). Similarly, myofiber size was only non-significantly higher in treated versus untreated animals (8% p = 0.44 and 12% p = 0.31 for wt and mdx animals, respectively).

Conclusions

Our findings demonstrate electrical impedance of muscle reproduce the functional and histological changes associated with myostatin pathway inhibition and do not reflect differences in muscle size or volume. This technique deserves further study in both animal and human therapeutic trials.

Adverse effects of near current-electrode placement in non-invasive bio-impedance measurements

A major problem confronting application of impedance techniques to studies of disease is the extraction of intrinsic properties of the tissue from the measured impedances, which unavoidably involve geometric factors as well. Amongst the foremost are the sizes and locations of the measuring electrode arrays, and this paper addresses one of these, the location of current injecting electrodes. Tetrapolar impedance measurements on a 17.5 cm segment of the thigh gave R and X values three to four times larger when the current injecting electrodes were placed 2.5 cm from the sensing electrodes than when very distant placement was used. The frequency dependences of R and X were affected as well, though the X versus R plots still showed virtually perfect depressed-center semicircles, as in the Cole model. R(f) and X(f) for the set of contiguous 2.5 cm wide sub-segments show that these behaviors can be explained by a combination of the transverse orientation of current flow lines near the injecting electrodes and the anisotropy of the resistivity associated with the bundled fiber structure of muscle tissue. The measured impedance was found to be a separable function of geometric and intrinsic tissue variables, but far more complicated than is implicit in the usual cylindrical models. The results also suggest that many full and segmental body composition studies in the literature may be prone to substantial errors due to too close placement of the current injecting electrodes.