Impedance of skeletal muscle from 1 Hz to 1 MHz

Lean regional muscle volume estimates using explanatory bioelectrical models in healthy subjects and patients with muscle wasting

BACKGROUND

The availability of non-invasive, accessible, and reliable methods for estimating regional skeletal muscle volume is paramount in conditions involving primary and/or secondary muscle wasting. This work aimed at (i) optimizing serial bioelectrical impedance analysis (S_BIA ) by computing a conductivity constant based on quantitative magnetic resonance imaging (MRI) data and (ii) investigating the potential of S_BIA for estimating lean regional thigh muscle volume in patients with severe muscle disorders.

METHODS

Twenty healthy participants with variable body mass index and 20 patients with idiopathic inflammatory myopathies underwent quantitative MRI. Anatomical images and fat fraction maps were acquired in thighs. After manual muscle segmentation, lean thigh muscle volume (lV_MRI ) was computed. Subsequently, multifrequency (50 to 350 kHz) serial resistance profiles were acquired between current skin electrodes (i.e. ankle and hand) and voltage electrodes placed on the anterior thigh. In vivo values of the muscle electrical conductivity constant were computed using data from S_BIA and MRI gathered in the right thigh of 10 healthy participants. Lean muscle volume (lV_BIA ) was derived from S_BIA measurements using this newly computed constant. Between-day reproducibility of lV_BIA was studied in six healthy participants.

RESULTS

Electrical conductivity constant values ranged from 0.82 S/m at 50 kHz to 1.16 S/m at 350 kHz. The absolute percentage difference between lV_BIA and lV_MRI was greater at frequencies >270 kHz (P < 0.0001). The standard error of measurement and the intra-class correlation coefficient for lV_BIA computed from measurements performed at 155 kHz (i.e. frequency with minimal difference) against lV_MRI were 6.1% and 0.95 in healthy participants and 9.4% and 0.93 in patients, respectively. Between-day reproducibility of lV_BIA was as follows: standard error of measurement = 4.6% (95% confidence interval [3.2, 7.8] %), intra-class correlation coefficient = 0.98 (95% confidence interval [0.95, 0.99]).

CONCLUSIONS

These findings demonstrate a strong agreement of lean muscle volume estimated using S_BIA against quantitative MRI in humans, including in patients with severe muscle wasting and fatty degeneration. S_BIA shows promises for non-invasive, fast, and accessible estimation and follow-up of lean regional skeletal muscle volume for transversal and longitudinal studies.

Electrical Impedance Myography and Its Applications in Neuromuscular Disorders

Electrical impedance myography (EIM) refers to the specific application of electrical bioimpedance techniques for the assessment of neuromuscular disorders. In EIM, a weak, high-frequency electrical current is applied to a muscle or muscle group of interest and the resulting voltages measured. Among its advantages, the technique can be used noninvasively across a variety of disorders and requires limited subject cooperation and evaluator training to obtain accurate and repeatable data. Studies in both animals and human subjects support its potential utility as a primary diagnostic tool, as well as a biomarker for clinical trial or individual patient use. This review begins by providing an overview of the current state and technological advances in electrical impedance myography and its specific application to the study of muscle. We then provide a summary of the clinical and preclinical applications of EIM for neuromuscular conditions, and conclude with an evaluation of ongoing research efforts and future developments.

Contactless remote induction of shear waves in soft tissues using a transcranial magnetic stimulation device

This study presents the first observation of shear waves induced remotely within soft tissues. It was performed through the combination of a transcranial magnetic stimulation device and a permanent magnet. A physical model based on Maxwell and Navier equations was developed. Experiments were performed on a cryogel phantom and a chicken breast sample. Using an ultrafast ultrasound scanner, shear waves of respective amplitudes of 5 and 0.5 μm were observed. Experimental and numerical results were in good agreement. This study constitutes the framework of an alternative shear wave elastography method.

Review of temperature dependence of thermal properties, dielectric properties, and perfusion of biological tissues at hyperthermic and ablation temperatures

The application of supraphysiological temperatures (>40°C) to biological tissues causes changes at the molecular, cellular, and structural level, with corresponding changes in tissue function and in thermal, mechanical and dielectric tissue properties. This is particularly relevant for image-guided thermal treatments (e.g. hyperthermia and thermal ablation) delivering heat via focused ultrasound (FUS), radiofrequency (RF), microwave (MW), or laser energy; temperature induced changes in tissue properties are of relevance in relation to predicting tissue temperature profile, monitoring during treatment, and evaluation of treatment results. This paper presents a literature survey of temperature dependence of electrical (electrical conductivity, resistivity, permittivity) and thermal tissue properties (thermal conductivity, specific heat, diffusivity). Data of soft tissues (liver, prostate, muscle, kidney, uterus, collagen, myocardium and spleen) for temperatures between 5 to 90°C, and dielectric properties in the frequency range between 460 kHz and 3 GHz are reported. Furthermore, perfusion changes in tumors including carcinomas, sarcomas, rhabdomyosarcoma, adenocarcinoma and ependymoblastoma in response to hyperthmic temperatures up to 46°C are presented. Where appropriate, mathematical models to describe temperature dependence of properties are presented. The presented data is valuable for mathematical models that predict tissue temperature during thermal therapies (e.g. hyperthermia or thermal ablation), as well as for applications related to prediction and monitoring of temperature induced tissue changes.

Electrical impedance spectroscopy and diagnosis of tendinitis

There have been a number of studies that investigate the usefulness of bioelectric signals in diagnoses and treatment in the medical field. Tendinitis is a musculoskeletal disorder with a very high rate of occurrence. This study attempts to examine whether electrical impedance spectroscopy (EIS) can detect pathological changes in a tendon and find the exact location of the lesion. Experimental tendinitis was induced by injecting collagenase into one side of the patellar tendons in rabbits, while the other side was used as the control. After measuring the impedance in the tendinitis and intact tendon tissue, the dissipation factor was computed. The real component of impedance and the dissipation factor turned out to be lower in tendinitis than in intact tissues. Moreover, the tendinitis dissipation factor spectrum showed a clear difference from that of the intact tendon, indicating its usefulness as a tool for detecting the location of the lesion. Pathologic findings from the tissues that were obtained after measuring the impedance confirmed the presence of characteristics of tendinitis. In conclusion, EIS is a useful method for diagnosing tendinitis and detecting the lesion location in invasive treatment.

Transthoracic atrial defibrillation energy thresholds are correlated to uniformity of current density distributions

Previous studies have shown that successful defibrillation depends on the uniformity of current density in the heart and the percentage of total current reaching the heart. This study uses an anatomically-realistic finite element computer model of the human torso for external atrial defibrillation to (1) examine the defibrillation energy thresholds and current density distributions for common clinical paddle placements and (2) investigate the effects of electrode shifts on these defibrillation parameters. The model predicts atrial defibrillation threshold (AD FT) energy by requiring a voltage gradient of 5 V/cm over at least 95% of atrial myocardium. This study finds that variation in electrode placement by only a few centimeters increases ADFTs by up to 46% with a corresponding change of 38% between the average current density in the left and right atria and 34% between the heterogeneity indices of atrial current density distributions. Additionally, the heterogeneity index, or degree of uniformity, is linearly correlated to the ADFT (R2=0.9). We suggest that uniformity of current density distribution, in addition to minimum current density, may be an important parameter to use for predicting successful defibrillation when testing new electrode placements.

Simultaneous double external DC shock techniques for atrial fibrillation: a simulation study

The success rate of direct current cardioversion (DCC), the most common method to convert atrial fibrillation (AF) to sinus rhythm (SR), depends on various factors including AF duration, prior anti-arrhythmic therapy, electrode position and size, transthoracic impedance, and the use of biphasic versus monophasic shocks. Recent, small clinical studies have reported using quadruple electrodes to deliver higher energy, in order to increase DCC success rates in refractory patients. This study aims to computationally model and compare double shock defibrillation with conventional single shock DCC, based on the two parameters, defibrillation threshold (DFT) and heterogeneity index (HI). DFT is the energy required to achieve a voltage gradient of 5 V/cm over 95% of the atrial myocardium. HI, calculated as the (95(th)-5(th))/50(th) percentile of atrial electric field magnitudes, is a measure of non-uniformity. The electric field distributions in the myocardium were generated for over five thousand different conventional and quadruple electrode placements with electrodes of two different sizes. Results show that there is a significant decrease in DFT (p0.01) and HI (p0.01) with increase in electrode size and quantity.

Modeling upper and lower limb muscle volume by bioelectrical impedance analysis

Most studies employing bioelectrical impedance analysis (BIA) for estimating appendicular skeletal muscle mass using descriptive BIA models rely on statistical rather than biophysical principles. The aim of the present study was to evaluate the feasibility of estimating arm and leg muscle volume (MV) based on multiple bioimpedance measurements and using a recently proposed mathematical model and to compare this technique to conventional segmental BIA at high and low frequencies. MV of the arm and leg, respectively, was determined in 15 young, healthy, active men [age 22 ± 2 (SD) yr, total body fat 15.6 ± 5.1%] by magnetic resonance imaging (MRI) and BIA using a conventional and new bioimpedance model. MRI-determined MV for leg and arm was 6,268 ± 1,099 and 1,173 ± 172 cm3, respectively. Estimated MV by the new BIA model [leg: 6,294 ± 1,155 cm3 (50 kHz), 6,278 ± 1,103 cm3 (500 kHz); arm: 1,216 ± 172 cm3 (50 kHz), 1,155 ± 157 cm3 (500 kHz)] was not statistically different from MRI-determined MV (leg: P= 0.958; arm: P= 0.188). The new BIA model was superior to conventional BIA and performed best at 500 kHz for estimating leg MV as indicated by the lower relative total error [new: 3.6% (500 kHz), 5.2% (50 kHz); conventional: 7.6% (500 kHz) and 8.3% (50 kHz)]. In contrast, the new BIA model, both at 50 and 500 kHz, did not improve the accuracy for estimating arm MV [new: 10.8% (500 kHz), 10.6% (50 kHz); conventional: 11.8% (500 kHz), 11.4% (50 kHz)]. It was concluded that modeling of multiple BIA measurements has advantages for the determination of lower limb muscle volume in healthy, active adult men.

Finite element computer modeling of transthoracic atrial defibrillation

Placement of external electrodes can significantly affect the success rate of transthoracic atrial defibrillation, but studies have not led to agreement on optimal electrode placements. This study aims to (1) develop an anatomically realistic, finite element model of the human torso for external atrial defibrillation, (2) investigate model parameters of skeletal muscle conductivity and anisotropy and the presence of subcutaneous fat, and (3) investigate clinical defibrillation parameters of electrode size, shape, and location. The model predicts atrial defibrillation threshold (ADFT) energy by requiring a voltage gradient of 5 V/cm over at least 95% of atrial myocardium. The model compares favorably with a clinical study of 301 patients that reported an anterior-posterior electrode position required approximately 20% less energy than an anterior-anterior position. Results indicate that a change in electrode size has a different effect for different electrode placements. This study finds that variation in electrode placement by only a few centimeters can change ADFTs by up to 51%. This is the first computer model of transthoracic atrial defibrillation to our knowledge. Our computer model is not limited to a few empirically selected electrode placements as in clinical studies and can test any location, size, and number of electrode placements.

Left ventricular volume measurement in mice by conductance catheter: evaluation and optimization of calibration

The conductance catheter (CC) allows thorough evaluation of cardiac function because it simultaneously provides measurements of pressure and volume. Calibration of the volume signal remains challenging. With different calibration techniques, in vivo left ventricular volumes (VCC) were measured in mice ( n = 52) with a Millar CC (SPR-839) and compared with MRI-derived volumes (VMRI). Significant correlations between VCC and VMRI [end-diastolic volume (EDV): R2 = 0.85, P < 0.01; end-systolic volume (ESV): R2 = 0.88, P < 0.01] were found when injection of hypertonic saline in the pulmonary artery was used to calibrate for parallel conductance and volume conversion was done by individual cylinder calibration. However, a significant underestimation was observed [EDV = −17.3 μl (−22.7 to −11.9 μl); ESV = −8.8 μl (−12.5 to −5.1 μl)]. Intravenous injection of the hypertonic saline bolus was inferior to injection into the pulmonary artery as a calibration method. Calibration with an independent measurement of stroke volume decreased the agreement with VMRI. Correction for an increase in blood conductivity during the in vivo experiments improved estimation of EDV. The dual-frequency method for estimation of parallel conductance failed to produce VCC that correlated with VMRI. We conclude that selection of the calibration procedure for the CC has significant implications for the accuracy and precision of volume estimation and pressure-volume loop-derived variables like myocardial contractility. Although VCC may be underestimated compared with MRI, optimized calibration techniques enable reliable volume estimation with the CC in mice.

The contribution of the lungs to thoracic impedance measurements: a simulation study based on a high resolution finite difference model

A high resolution electrical finite difference model of the human thorax based on a 43 slice MRI data set along with lead field theory was used to examine the contribution of the lungs to the total impedance for a typical mid-thoracic 2D EIT eight and sixteen electrode configuration. Regional analysis of the thoracic sources of impedance revealed that the maximum contribution of lungs to the total impedance was approximately 22% for the eight electrode array and 25% for the sixteen electrode array. Analysis of impedance distribution of the lungs using a mid-thoracic application showed that the contribution of impedance of each slice followed closely the volume of the lungs in the given slice. This suggests that the mid-thoracic application gives results reflecting the entire lung. The contributions of the lung impedance for the various electrode positions showed that the eight electrode configuration had a more smooth change between adjacent electrodes compared to the 16 electrode arrangement.

Electrical impedance in bovine skeletal muscle as a model for the study of neuromuscular disease

Electrical impedance myography (EIM) consists of a set of bioimpedance methods configured for neuromuscular disease assessment, in which high-frequency electrical current is applied to a limb and the consequent surface voltage pattern over a muscle is evaluated. Prior human work has shown that the EIM parameters of resistance, reactance and phase change in different neuromuscular disease states including neurogenic and myopathic conditions. These parameters are also sensitive to the angle at which current is applied and measured relative to muscle fiber direction, a characteristic known as anisotropy. In order to obtain insights into the impedance characteristics of mammalian skeletal muscle without the confounding effects of an overlying skin-fat layer, bone and irregular muscle shape, we performed EIM on three 'nearly ideal' round 16 cm diameter, 1 cm equal thickness pieces of bovine rectus abdominis muscle. Using a standardized tetrapolar electrode array with 50 kHz electrical current, we identified strong anisotropy in the measured reactance and phase, with weaker anisotropy identified for resistance. We also found that increasing amounts of muscle maceration, a rough model of myopathic or traumatic muscle fiber injury, reduced phase and muscle anisotropy when current was injected perpendicular to the muscle fibers. These findings support that EIM parameters, including muscle anisotropy, are likely to be sensitive to the pathological changes that occur in neuromuscular disease states.

Calculation of magnetic field-induced current densities for humans from EAS countertop activation/deactivation devices that use ferromagnetic cores

Compliance testing of electronic article surveillance (EAS) devices requires that induced current densities in central nervous system (CNS) tissues, i.e. brain and the spinal cord, be less than the prescribed safety limits. Even though ferromagnetic cores are mostly used for activation/deactivation of embedded magnetic tags, assumed equivalent air-core coils with guessed increased number of ampere turns have always been used to calculate the magnetic fields for the proximal region to which a customer is exposed. We show that at low frequencies up to several kilohertz, duality of electric and magnetic circuits may be exploited such that the shaped high reluctance core is modelled as though it was a higher conductivity electric circuit of the corresponding shape. The proposed procedure is tested by examples of two magnetic cores typical of countertop activation/deactivation devices. The equivalent exposure magnetic fields obtained from the dual electric fields are shown to be in excellent agreement (within +/-5%) with those measured for these ferromagnetic EAS devices. The previously proposed impedance method is then used to calculate the induced current densities for a 1.974 x 1.974 x 2.93 mm resolution anatomic model of a human. For the two considered EAS systems using excitation currents of 5000 A turns at 200 Hz, the maximum 1 cm2 area-averaged induced current densities in the CNS tissues are calculated and found to be less than the ICNIRP safety limits.

Effect of cooling and re-warming on cerebral and whole body electrical impedance

Cerebral electrical impedance is useful for the detection of cerebral edema following hypoxia in newborn infants. Thus it may be useful for determining neurological outcome or monitoring treatment. Hypothermia is a promising new therapy currently undergoing trials, but will alter impedance measurements. This study aimed to define the relationship between temperature and both cerebral and whole body electrical impedance, and to derive correction factors for adjustment of impedance measurements during hypothermia. In eight anaesthetized 1-2 day old piglets rectal, tympanic and scalp temperatures were monitored continuously. Following baseline readings at a rectal temperature of 39 degrees C, piglets were cooled to 32 degrees C. Four piglets were re-warmed. Cerebral and whole body impedance were measured at each 0.5 degrees C as rectal temperature decreased. There was a strong linear relationship between both cerebral and whole body impedance and each of the temperatures measured. There was no difference in the relationship between impedance and rectal, tympanic or scalp temperatures. The relationship for impedance and rectal temperature was the same during cooling and re-warming. Using the correction factors derived it will be possible to accurately monitor cerebral and whole body fluid distribution during hypothermic treatment.

In vitro measurement of myocardial impedivity anisotropy with a miniature rectangular tube

Due to rapid change of fiber orientation, it is difficult to measure myocardial impedivity separately in a longitudinal or transverse fiber direction without mutual influence in the two directions. Previously published values of the longitudinal and the transverse myocardial impedivity were derived indirectly from measurements that mixed the impedivity in all directions. Those values are questionable because the derivations were based on a simplified uniform myocardial fiber model. In this paper, a miniature rectangular tube was devised to facilitate direct measurement of myocardial impedivity in a uniform fiber direction. The average transverse-to-longitudinal ratio of the measured in vitro swine myocardial impedivity was about 1.66 from 1 Hz to 1 kHz and dropped to 1.25 at 1 MHz. The result is important for accurate modeling of the electrical property of myocardium in biomedical research of radio-frequency cardiac catheter ablation.

Comparison of various safety guidelines for electronic article surveillance devices with pulsed magnetic fields

The paper uses the two methods suggested in both the ICNIRP and proposed IEEE safety guidelines for compliance testing of security systems based on time-varying magnetic fields being introduced for electronic article surveillance (EAS), radiofrequency identification, and other applications. For nonsinusoidal pulses that are often used, the two procedures are to treat the exposure as a multifrequency exposure with various frequency components or to calculate the peak induced current densities or electric fields treating the highest of the pulses of duration t(p) as a single frequency, half sinusoid of the same duration and frequency 1/(2t(p)). Using either of the procedures, the induced current densities (J) or electric fields (E) are compared to the basic restrictions on J or E for compliance testing. Using a heterogeneous, tissue-classified anatomic model of the human body, we calculate the induced J and E for the various tissues for a realistic, EAS system for two typical nonsinusoidal pulses to show that the two methods give substantially different results. While the approximate but simpler method of treating the pulse as a half sinusoid results in peak induced J or E that may be compliant with safety guidelines, the rigorous method of treating such exposures as multifrequency exposures gives induced current densities or electric fields that may be up to twice as large, thus making such systems potentially noncompliant with the safety guidelines. Since it is more accurate, it is suggested that safety assessment based on the Fourier analysis leading to multifrequency components be used for compliance testing of such devices.

FEM analysis of predicting electrode-myocardium contact from RF cardiac catheter ablation system impedance

We used the finite-element method (FEM) to model and analyze the resistance between the catheter tip electrode and the dispersive electrode during radio-frequency cardiac catheter ablation for the prediction of myocardium-electrode contact. We included deformation of the myocardial surface to achieve accurate modeling. For perpendicular catheter contact, we measured the side view of myocardial deformation using X-ray projection imaging. We averaged the deformation contour from nine samples, and then incorporated the contour information into our FEM model. We measured the resistivity of the bovine myocardium using the four-electrode method, and then calculated the resistance change as the catheter penetrated into the myocardium. The FEM result of resistance versus catheter penetration depth matches well with our experimental data.

In-vivo measurement of swine myocardial resistivity

We used a four-terminal plunge probe to measure myocardial resistivity in two directions at three sites from the epicardial surface of eight open-chest pigs in-vivo at eight frequencies ranging from 1 Hz to 1 MHz. We calibrated the plunge probe to minimize the error due to stray capacitance between the measured subject and ground. We calibrated the probe in saline solutions contained in a metal cup situated near the heart that had an electrical connection to the pig's heart. The mean of the measured myocardial resistivity was 319 ohm x cm at 1 Hz down to 166 ohm x cm at 1 MHz. Statistical analysis showed the measured myocardial resistivity of two out of eight pigs was significantly different from that of other pigs. The myocardial resistivity measured with the resistivity probe oriented along and across the epicardial fiber direction was significantly different at only one out of the eight frequencies. There was no significant difference in the myocardial resistivity measured at different sites.

Error analysis of tissue resistivity measurement

We identified the error sources in a system for measuring tissue resistivity at eight frequencies from 1 Hz to 1 MHz using the four-terminal method. We expressed the measured resistivity with an analytical formula containing all error terms. We conducted practical error measurements with in-vivo and bench-top experiments. We averaged errors at all frequencies for all measurements. The standard deviations of error of the quantization error of the 8-bit digital oscilloscope with voltage averaging, the nonideality of the circuit, the in-vivo motion artifact and electrical interference combined to yield an error of +/- 1.19%. The dimension error in measuring the syringe tube for measuring the reference saline resistivity added +/- 1.32% error. The estimation of the working probe constant by interpolating a set of probe constants measured in reference saline solutions added +/- 0.48% error. The difference in the current magnitudes used during the probe calibration and that during the tissue resistivity measurement caused +/- 0.14% error. Variation of the electrode spacing, alignment, and electrode surface property due to the insertion of electrodes into the tissue caused +/- 0.61% error. We combined the above errors to yield an overall standard deviation error of the measured tissue resistivity of +/- 1.96%.

Changes in electrical resistivity of swine liver after occlusion and postmortem

The resistivity of swine liver tissue was measured in vivo, during induced ischaemia and post-mortem, so that associated changes in resistivity could be quantified. Plunge electrodes, the four-terminal method and a computer-automated measurement system were used to acquire resistivities between 10Hz and 1 MHz. Liver resistivity was measured in vivo in three animals at 11 locations. At 10 Hz, resistivity was 758 +/- 170 ohm x cm. At 1 MHz, the resistivity was 250 +/- 40 ohm x cm. The resistivity time course was measured during the first 10 min after the liver blood supply in one animal had been occluded. Resistivity increased steadily during occlusion. The change in resistivity of an excised tissue sample was measured during the first 12h after excision in one animal. Resistivity increased during the first 2h by 53% at 10 Hz and by 32% at 1 MHz. After 2h, resistivity decreased, probably owing to membrane breakdown. The resistivity data were fitted to a Cole-Cole circle, from which extracellular resistance Re, intracellular resistance Ri and cell membrane capacitance Cm were estimated. Re increased during the first 2h by 95% and then decreased, suggesting an increase in extracellular volume. Cm increased during the first 4 h by 40%, possibly owing to closure of membrane channels, and then decreased, suggesting membrane breakdown. Ri stayed constant during the initial 6h and then increased.

Calculation of induced current densities for humans by magnetic fields from electronic article surveillance devices

This paper illustrates the use of the impedance method to calculate the electric fields and current densities induced in millimetre resolution anatomic models of the human body, namely an adult and 10- and 5-year-old children, for exposure to nonuniform magnetic fields typical of two assumed but representative electronic article surveillance (EAS) devices at 1 and 30 kHz, respectively. The devices assumed for the calculations are a solenoid type magnetic deactivator used at store checkouts and a pass-by panel-type EAS system consisting of two overlapping rectangular current-carrying coils used at entry and exit from a store. The impedance method code is modified to obtain induced current densities averaged over a cross section of 1 cm2 perpendicular to the direction of induced currents. This is done to compare the peak current densities with the limits or the basic restrictions given in the ICNIRP safety guidelines. Because of the stronger magnetic fields at lower heights for both the assumed devices, the peak 1 cm2 area-averaged current densities for the CNS tissues such as the brain and the spinal cord are increasingly larger for smaller models and are the highest for the model of the 5-year-old child. For both the EAS devices, the maximum 1 cm2 area-averaged current densities for the brain of the model of the adult are lower than the ICNIRP safety guideline, but may approach or exceed the ICNIRP basic restrictions for models of 10- and 5-year-old children if sufficiently strong magnetic fields are used.

Development of a multifrequency conductance catheter-based system to determine LV function in mice

Transgenic mice offer a valuable way to relate gene products to phenotype, but the ability to assess the cardiovascular phenotype with pressure-volume analysis has lagged. Conductance measurement offers a method to generate an instantaneous left ventricular (LV) volume signal in the mouse but has been limited by the volume signal being a combination of blood and LV muscle. We hypothesized that by developing a mouse conductance system that operates at several simultaneous frequencies, we could identify and correct for the myocardial contribution to the instantaneous volume signal. This hypothesis is based on the assumption that mouse myocardial conductivity will vary with frequency, whereas mouse blood conductivity will not. Consistent with this hypothesis, we demonstrated that at higher excitation frequency, greater end-diastolic and end-systolic conductance are detected, as well as a smaller difference between the two. We then empirically solved for LV blood volume using two frequencies. We combined measured resistivity of mouse myocardium with an analytic approach and extracted an estimate of LV blood volume from the raw conductance signal. Development of a multifrequency catheter-based system to determine LV function could be a tool to assess cardiovascular phenotype in transgenic mice.

Estimation of skeletal muscle mass by bioelectrical impedance analysis

The purpose of this study was to develop and cross-validate predictive equations for estimating skeletal muscle (SM) mass using bioelectrical impedance analysis (BIA). Whole body SM mass, determined by magnetic resonance imaging, was compared with BIA measurements in a multiethnic sample of 388 men and women, aged 18-86 yr, at two different laboratories. Within each laboratory, equations for predicting SM mass from BIA measurements were derived using the data of the Caucasian subjects. These equations were then applied to the Caucasian subjects from the other laboratory to cross-validate the BIA method. Because the equations cross-validated (i.e., were not different), the data from both laboratories were pooled to generate the final regression equation SM mass (kg) = [(Ht<SUP>2</SUP>/ <IT>R</IT> x 0.401) + (gender x 3.825) + (age x -0. 071)] + 5.102 where Ht is height in centimeters; R is BIA resistance in ohms; for gender, men = 1 and women = 0; and age is in years. The r(2) and SE of estimate of the regression equation were 0.86 and 2.7 kg (9%), respectively. The Caucasian-derived equation was applicable to Hispanics and African-Americans, but it underestimated SM mass in Asians. These results suggest that the BIA equation provides valid estimates of SM mass in healthy adults varying in age and adiposity.

Estimation of parallel conductance by dual-frequency conductance catheter in mice

The conductance catheter method has substantially enhanced the characterization of in vivo cardiovascular function in mice. Absolute volume determination requires assessment of parallel conductance (V(p)) offset because of conductivity of structures external to the blood pool. Although such a determination is achievable by hypertonic saline bolus injection, this method poses potential risks to mice because of volume loading and/or contractility changes. We tested another method based on differences between blood and muscle conductances at various catheter excitation frequencies (20 vs. 2 kHz) in 33 open-chest mice. The ratio of mean frequency-dependent signal difference to V(p) derived by hypertonic saline injection was consistent [0.095 +/- 0.01 (SD), n = 11], and both methods were strongly correlated (r(2) = 0.97, P < 0.0001). This correlation persisted when the ratio was prospectively applied to a separate group of animals (n = 12), with a combined regression relation of V(p(DF)) = 1.1 * V(p(Sal)) - 2.5 [where V(p(DF)) is V(p) derived by the dual-frequency method and V(p(Sal)) is V(p) derived by hypertonic saline bolus injection], r(2) = 0.95, standard error of the estimate = 1.1 microl, and mean difference = 0.6 +/- 1.4 microl. Varying V(p(Sal)) in a given animal resulted in parallel changes in V(p(DF)) (multiple regression r(2) = 0.92, P < 0.00001). The dominant source of V(p) in mice was found to be the left ventricular wall itself, since surrounding the heart in the chest with physiological saline or markedly varying right ventricular volumes had a minimal effect on the left ventricular volume signal. On the basis of V(p) and flow probe-derived cardiac output, end-diastolic volume and ejection fraction in normal mice were 28 +/- 3 microl and 81 +/- 6%, respectively, at a heart rate of 622 +/- 28 min(-1). Thus the dual-frequency method and independent flow signal can be used to provide absolute volumes in mice.

Assessing regional muscle mass with segmental measurements of bioelectrical impedance in obese women during weight loss

Tetrapolar bioelectrical impedance analysis (BIA) offers the possibility of determining the bioconductor volume in discrete segments of the body, because the resistivities of bone, fat, and skeletal muscle differ considerably. We tested this hypothesis by measuring BIA and anthropometry of defined segments of the right thighs of women before and during a controlled weight-loss program. Eight women, aged 22 to 32 years, with a body mass index of 37.8 +/- 1.6 (mean +/- SE) kg/m2 underwent determinations of body composition with dual-energy X-ray absorptiometry (DXA) and regional BIA measurements (800 microA at 50 kHz) before the program, and monthly thereafter for four months during weight loss. BIA measurements were made with spot-detector electrodes positioned 10 cm apart on the anterior of the thigh, and source electrodes placed on the right hand and foot. The physical volume of the thigh segment decreased by 29 +/- 3% (p < 0.0001), with a modest change in its electrical volume (8 +/- 0.2%; p < 0.05) during weight loss. Muscle (181 +/- 49 g; p < 0.05) and fat mass (702 +/- 95 g; p < 0.001) also declined. The electrical or bioconductor volume correlated with DXA determinations of muscle mass (r = 0.91, p < 0.0001), whereas physical volume correlated with fat mass (r = 0.95, p < 0.0001). These findings support the hypothesis that BIA is a valid method to assess regional muscle mass in humans.

Systematic errors in multi-frequency EIT

Systematic errors have been measured with a multi-frequency data-collection system operating between 10.24 and 81.92 kHz. The errors were present even though a conventional background measurement on a uniform saline phantom had already been subtracted. Errors due to changes in transimpedance between the calibration and the tissue measurements, cable movement and electrode-skin contact impedance were simulated giving a total systematic error estimate equivalent to a 9% change in tissue conductivity. It was shown that more than 89% of the image was above the total error magnitude, indicating that most of the image revealed true changes in tissue conductivity. In three human subjects, the largest conductivity changes were in two regions, located posteriorly on either side of the midline, and were interpreted as due to the erector spinae muscles. These regions showed increases in conductivity of 73-104%. Identification of other anatomical features was difficult because of the poor spatial resolution of the images.

Effects of sample geometry and electrode configuration on measured electrical resistivity of skeletal muscle

Over the past 40 years, researchers from a variety of scientific backgrounds have been using Rush's equations to analyze results of their electrophysiological studies. A lack of understanding of the constraints and the domain in which these equations are valid, often results in situations in which it is challenging to evaluate and compare results obtained by different investigators. In this paper, we reanalyzed the conditions for which Rush's equations were derived, and using mathematical modeling, computer simulation and in vitro measurements, we delineated areas of their appropriate application. Our studies showed that both sample geometry and test electrode configuration affect the measured tissue electrical resistivities: 1) The sample can be considered semi-infinite only if its dimensions are > 50 inter-electrode separation distances (IESD), and thickness > 2.5 IESD, 2) smaller sample sizes increase the transversally measured resistivity, 3) semi-infinite samples thinner than 2.5 IESD, and samples tested with needle electrodes demonstrate reduced anisotropy, and 4) when surface-spot electrodes are longitudinally aligned, as the IESD/tissue thickness ratio decreases, the measured resistivity increases. Our conclusion is that in most experimental situations, it is necessary to use modeling techniques to decouple the electrode configuration/sample geometry influence from the measured tissue resistivity.

Analysis of defibrillation efficacy from myocardial voltage gradients with finite element modeling

Increasing defibrillation efficacy by lowering the defibrillation threshold (DFT) is an important goal in positioning implantable cardioverter-defibrillator electrodes. Clinically, the DFT is difficult to estimate noninvasively. It has been suggested that the DFT relates to the myocardial voltage gradient distribution, but this relation has not been quantitatively demonstrated. We analyzed the relation between the experimentally measured DFT's and the simulated myocardial voltage gradients provided by finite element modeling. We performed a series of experiments in 11 pigs to measure the DFT's, and created and solved three-dimensional subject-specific finite element models to assess the correlation between the computed myocardial voltage gradient histograms and the DFT's. Our data show a statistically significant correlation between the DFT and the left ventricular voltage gradient distribution, with the septal region being more significant (correlation coefficient of 0.74) than other myocardial regions. The correlation between the DFT and the right ventricular and the atrial voltage gradient, on the other hand, is not significant.

Specific absorption rates and induced current densities for an anatomy-based model of the human for exposure to time-varying magnetic fields of MRI

A 6-mm resolution, 30-tissue anatomy-based model of the human body is used to calculate specific absorption rate (SAR) and the induced current density distributions for radiofrequency and switched gradient magnetic fields used for MRI, respectively. For SAR distributions, the finite-difference time-domain (FDTD) method is used including modeling of 16-conductor birdcage coils and outer shields of dimensions that are typical of body and head coils and a new high-frequency head coil proposed for the 300-400 MHz band. SARs at 64, 128, and 170 MHz have been found to increase with frequency (f) as f(k) where k is on the order of 1.1-1.2. The tables of the calculated maximum 1 kg and 100 g SAR may be used to calculate the maximum RF currents and/or magnetic fields that may be used in order not to exceed the safety guidelines. Because of the low frequencies associated with switched gradient magnetic fields, a quasi-static impedance method is used for calculation of induced current densities that are compared with the safety guidelines.

An electrical impedance index to distinguish between normal and cancerous tissues

Bioimpedance measurements have previously shown that cancerous tissues in many cases have a higher characteristic frequency than normal tissues. This paper tries to find an index which is sensitive to variation in the characteristic frequency but is independent of the impedance value itself. Calculated indexes from several publications in most cases show values larger than one for cancerous tissues and less than one for normal tissues.

Changes in the noninvasive, in vivo electrical impedance of three xenografts during the necrotic cell-response sequence

PURPOSE

To investigate the noninvasive, in vivo use of electrical impedance spectroscopy (EIS) as a method for observing the real-time, cellular-level responses of a volume of tissue to therapies. Here, we studied the EIS response during the development and progression of hyperthermia-induced coagulative necrosis in three diverse human xenografts.

METHODS AND MATERIALS

A necrotic cell response sequence was selectively induced in three types of subcutaneously-grown human tumor xenografts by applying hyperthermia at 44.5 degrees C. The electrical impedance of the tumors was measured from 100 Hz to 10 MHZ, noninvasively, in vivo during the treatments. From the full spectrum EIS, ratios between resistivities at selected frequencies (p-ratios) were used as indicators of the changes in the electrical impedance spectra of each tumor's cell population.

RESULTS

The rho-ratios consistently demonstrated characteristic, early, rapid increases which coincided with cell and organelle swelling typical of early necrosis. These increases subsequently slowed, but no decrease began before the end of treatment, unlike previous, similarly treated, thermo-sensitive EMT6 mouse tumors. This was consistent with the xenograft histology, which revealed ubiquitous, early-stage coagulative necrosis, with no gross plasma membrane damage at the end of treatment. The extent of both the necrosis and p-ratio changes were similar to those seen early in the EMT6 tumor treatment. Within several days after treatment, the xenograft volumes regressed nearly completely, suggesting completion of the cell populations' necrotic response (lysing) during this period. Consistent with this, extended EIS measurements over a 24-h posttreatment period allowed tracking of the necrotic response sequence through this lysing phase for one type of xenograft.

CONCLUSION

The change in the electrical impedance of a volume of tumor tissue which occurs during and/or after a hyperthermia treatment can be correlated with the extent of necrosis observed histologically in the cell population.

Defibrillation efficacy of different electrode placements in a human thorax model

The objective of this study was to measure the defibrillation threshold (DFT) associated with different electrode placements using a three-dimensional anatomically realistic finite element model of the human thorax. Coil electrodes (Endotak DSP, model 125, Guidant/CPI) were placed in the RV apex along the lateral wall (RV), withdrawn 10 mm away from the RV apex along the lateral wall (RVprox), in the RV apex along the anterior septum (RVseptal), and in the SVC. An active pulse generator (can) was placed in the subcutaneous prepectoral space. Five electrode configurations were studied: RV-->SVC, RVprox-->SVC, RVSEPTAL-->SVC, RV-->Can, and RV-->SVC + Can. DFTs are defined as the energy required to produce a potential gradient of at least 5 V/cm in 95% of the ventricular myocardium. DFTs for RV-->SVC, RVprox-->SVC, RVseptal-->SVC, RV-->Can, and RV-->SVC + Can were 10, 16, 7, 9, and 6 J, respectively. The DFTs measured at each configuration fell within one standard deviation of the mean DFTs reported in clinical studies using the Endotak leads. The relative changes in DFT among electrode configurations also compared favorably. This computer model allows measurements of DFT or other defibrillation parameters with several different electrode configurations saving time and cost of clinical studies.

Comparison of cardiac-induced endogenous fields and power frequency induced exogenous fields in an anatomical model of the human body

Time-domain potentials measured at 64 points on the surface of a large canine heart, considered comparable with those of a human heart, were used to calculate the electric fields and current densities within various organs of the human body. A heterogeneous volume conductor model of an adult male with a resolution of approximately 6 mm3 and 30 segmented tissue types was used along with the admittance method and successive over-relaxation to calculate the voltage distribution throughout the torso and head as a function of time. From this time-domain voltage description, values of [E(t)] and [J(t)] were obtained, allowing for maximum values to be found within the given tissues of interest. Frequency analysis was then used to solve for [E(f)] and [J(f)] in the various organs, so that average, minimum and maximum values within specific bandwidths (0-40, 40-70 and 70-100 Hz) could be analysed. A comparison was made between the computed results and measured data from both EKG waveforms and isopotential surface maps for validation, with good agreement in both amplitude and shape between the computed and measured results. These computed endogenous fields were then compared with exogenous fields induced in the body from a 60 Hz high-voltage power line and a 60 Hz uniform magnetic field of 1 mT directed from the front to the back of the body. The high-voltage power line EMFs and 1 mT magnetic field were used as 'bench' marks for comparison with several safety guidelines for power frequency (50/60 Hz) EMF exposures. The endogenous electric fields and current densities in most of the tissues (except for organs in close proximity to the heart, for example lungs, liver, etc) in the frequency band 40-70 Hz were found to be considerably smaller, between 5% and 10%, than those induced in the human body by the electric and magnetic fields generated by the 60 Hz sources described above.

Geometric effects on resistivity measurements with four-electrode probes in isotropic and anisotropic tissues

We studied via computer simulation the effects of electrode diameter, electrode length, interelectrode spacing, and tissue size on the accuracy of measured tissue resistivities and anisotropy ratios obtained with the widely used four-electrode technique. Such measurements commonly assume an ideal situation in which the four electrodes are infinitesimally small and the tissue is semi-infinite. Our study shows that these geometric factors can significantly affect measured resistivities, particularly for anisotropic tissues. The measured anisotropy ratio is decreased by either 1) increasing the electrode diameter or length relative to the interelectrode spacing of the probe or 2) decreasing tissue size. We have provided an equation for estimating errors in the measured anisotropy ratio from the parameters of electrode and tissue geometries. The simulation findings are supported by our in vitro experimental results.

The effect of changing excitation frequency on parallel conductance in different sized hearts

OBJECTIVE

An important component of the ventricular volume measured using the conductance catheter technique is due to parallel conductance (Vc), which results from the extension of the electric field beyond the ventricular blood pool. Parallel conductance volume is normally estimated using the saline dilution method (Vc(saline dilution)), in which the conductivity of blood in the ventricle is transiently increased by injection of hypertonic saline. A simpler alternative has been reported by Gawne et al. [12]. Vc(dual frequency) is estimated from the difference in total conductance measured at two exciting frequencies and the method is based on the assumption that parallel conductance is mainly capacitive and hence is negligible at low frequency. The objective of this study was to determine whether the dual frequency technique could be used to substitute the saline dilution method to estimate Vc in different sized hearts.

METHODS

The accuracy and linearity of a custom-built conductance catheter (CC) system was initially assessed in vitro. Subsequently, a CC and micromanometer were inserted into the left ventricle of seven 5 kg pigs (group 1) and six 50 kg pigs (group 2). Cardiac output was determined using thermodilution (group 1) and an ultrasonic flow probe (group 2) from which the slope coefficient (alpha) was determined. Steady state measurements and Vc estimated using saline dilution were performed at frequencies in the range of 5-40 kHz. All measurements were made at end-expiration. Finally, Vc was estimated from the change in end-systolic conductance between 5 kHz and 40 kHz using the dual frequency technique of Gawne et al. [12].

RESULTS

There was no change in measured volume of a simple insulated cylindrical model when the stimulating frequency was varied from 5-40 kHz. Vc(saline dilution) varied significantly with frequency in group 1 (8.63 +/- 2.74 ml at 5 kHz; 11.51 +/- 2.65 ml at 40 kHz) (p = 0.01). Similar results were obtained in group 2 (69.43 +/- 27.76 ml at 5 kHz; 101.24 +/- 15.21 ml at 40 kHz) (p < 0.001). However, the data indicate that the resistive component of the parallel conductance is substantial (Vc at 0 Hz estimated as 8.01 ml in group 1 and 62.3 ml in group 2). There was an increase in alpha with frequency in both groups but this did not reach significance. The correspondence between Vc(dual frequency) and Vc(saline dilution) methods was poor (group 1 R2 = 0.69; group 2 R2 = 0.22).

CONCLUSION

At a lower excitation frequency of 5 kHz a smaller percentage of the electric current extends beyond the blood pool so parallel conductance is reduced. While parallel conductance is frequency dependent, it has a substantial resistive component. The dual frequency method is based on the assumption that parallel conductance is negligible at low frequencies and this is clearly not the case. The results of this study confirm that the dual frequency technique cannot be used to substitute the saline dilution technique.

Regularized reconstruction in electrical impedance tomography using a variance uniformization constraint

This paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography. Our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on finding a proper way to cope with the ill-posed nature of the problem, mainly caused by strong attenuation phenomena; this is done by devising regularization techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regularization matrix is determined by space-uniformization of the variance of the reconstructed condictivities. Both methods are nonsupervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography.