Table of contents

The interdisciplinary nature of biomedical applications of electrical impedance tomography (EIT) sets many challenges that require an integrated approach to problem solving. This issue of Physiological Measurement follows a tradition of special issues on EIT, providing the opportunity for mathematicians, engineers, physicists and clinicians to present the results of this challenging work and demonstrate the interdisciplinary approach to their research. The Fourth Conference on Biomedical Applications of Electrical Impedance Tomography, held at UMIST, Manchester in April 2003, follows the successful Mummy Range Workshop on Electrical Impedance Tomography, which was held during August 2002 in Colorado. The 2003 conference was the first non-funded conference to take place after the successful series of EPRSC-funded EIT conferences organized by David Holder in London. The commitment of the EIT community to this conference shows that the state of EIT research is still healthy with new researchers joining the research community each year. It was heartening for the organizers that so many from distant countries were able to attend this meeting at a time when international travel was overshadowed by an epedemic of SARS and war. Plans are already in place for the next conference in Poland, which will be combined with ICEBI XII, but will still keep it own identity as the fifth meeting in this series.

The main themes of this special issue include a larger contribution of clinical applications, which is encouraging. New themes are emerging, including MREIT, bringing together EIT and magnetic resonance imaging, while the use of inductively coupled systems for EIT also continues to grow.

In terms of technical developments, there appear to be a wealth of new mathematical methods and hardware, but these new methods have yet to be evaluated and applied to clinical systems. The importance of the numerical algorithm cannot be underestimated, but there remains a gap between the application of new methods to simulated data and to real medical problems. Unfortunately many clinical studies have not exploited the best available algorithms but simply settled for simple algorithms which have known limitations. Often the results are inconclusive. Interdisciplinary gatherings such as this, the first of the UK meetings to be hosted by a mathematics department, actively encourage collaboration across disciplinary boundaries. It is our hope that the fruit of this meeting will be a strengthening of such collaborations.

Another issue, which needs addressing, is the need to involve more physicians in the research community; for EIT to be accepted and validated as a viable clinical tool, the role of medical doctors cannot be underestimated. It is also important that the biomedical EIT research community develops links with those working on applications of electrical imaging in geophysics, industrial process monitoring and non-destructive testing, as well as related inverse problems such as optical absorption and scattering tomography and other optical and low-frequency electromagnetic imaging methods.

The future of EIT looks healthy, as demonstrated by the collection of papers in this special issue, which provides evidence of significant advances in all areas of this research field.

A new method for the measurement of pulmonary gas exchange during inhalational anaesthesia is described which measures fresh gas and exhaust gas flows using carbon dioxide as an extractable marker gas. The theoretical precision of the method was compared by Monte Carlo modelling with other approaches which use marker gas dilution. A system was constructed for automated measurement of uptake of oxygen, nitrous oxide, volatile anaesthetic agent and elimination of carbon dioxide by an anaesthetized patient. The accuracy and precision of the method was tested in vitro on a lung gas exchange simulator, by comparison with simultaneous measurements made using nitrogen as marker gas and the Haldane transformation. Good agreement was obtained for measurement of simulated uptake or elimination of all gases studied over a physiologically realistic range of values. Mean bias for oxygen and nitrous oxide uptake was 0.003 l min⁻¹, for isoflurane 0.0001 l min⁻¹ and for carbon dioxide 0.001 l min⁻¹. Limits of agreement lay within 10% of the mean uptake rate for nitrous oxide, within 5% for oxygen and isoflurane and within 1% for carbon dioxide. The extractable marker gas method allows accurate and continuous measurement of gas exchange in an anaesthetic breathing system with any inspired gas mixture.

The axial red blood cell velocity pulse was quantified throughout its period by a high-speed video microscopy method, using images of erythrocytes moving near the microvessel axis. In 10 mesenteric precapillary arterioles (8 to 12 µm in diameter) from six rabbits, axial velocities ranged from 0.46 (the minimum of all the end diastolic values) to 4.8 mm s⁻¹ (the maximum of all the peak systolic values). With the velocity pulse shape properly quantified, a correct estimation of the average velocity over time can be made and hence, appropriate quantification of blood flow. Average velocity ranged between 1.14 mm s⁻¹ (8 µm arterioles) and 1.98 mm s⁻¹ (9 µm arterioles). Also, with the velocity pulse shape known, an estimation of the magnitude of the pulsation can be made by introducing Pourcelot's resistive index (RI) in the microvascular haemodynamics (diameter less than 15 µm). The results of this study reveal that RI in the precapillary arterioles is quite high ranging between 0.56 (8 µm arterioles) and 0.74 (12 µm arterioles). Observing the velocity pulse diagrams in different diameters, quantitative information is obtained for the first time on how the velocity pulse shape flattens as it proceeds to the capillary bed.

High-frequency ultrasound techniques are introduced for three-dimensional imaging and thickness estimation of fresh heart valve cusps. Images of porcine aortic valve specimens were acquired within a 12 × 8 × 8 mm³ volume using a VisualSonics VS40 micro-imaging system operating at a 40 MHz centre frequency. Two image volumes were obtained from each of six left coronary cusps. One volume was acquired with the specimen submerged in distilled water and the second volume was acquired through either Hanks physiologic solution or coronary perfusion solution (CPS). The fibrosa, spongiosa and ventricularis were most readily distinguished when the specimen was imaged in distilled water. Colour thickness maps were computed from B-mode image data, and the mean and standard deviations of the thickness were determined for each cusp. In 11 of 12 trials, the image analysis algorithm yielded valid thickness estimates over greater than 98% of the region examined. Mean thickness estimates obtained with specimens submerged in Hanks solution or CPS ranged from 0.66 to 1.03 mm, and submersion in distilled water increased the mean thickness by 20–40%. This observation suggests that the cusps osmotically absorbed water. Information provided by high-frequency ultrasound is expected be valuable for characterizing the morphological properties of heart valves.

Pulse wave velocity (PWV) is an indicator associated with the arterial stiffness. Although this technique has been used in the diagnosis of systemic arterial hypertension (SAH), it cannot supply alone enough information about the pathogenesis of this disturbance. This paper aims to determine the compliance of brachial-radial arterial segment by applying a three-element windkessel model, and by using the same pressure waveforms acquired to calculate the PWV. The proposed method to determine the arterial compliance was evaluated with a physical simulation of the arterial system, where parameters were known, resulting in an estimation error of 0.73 × 10⁻⁷ cm⁵ dyne⁻¹. In a clinical study the estimated compliance was statistically different (p < 0.01) in a controlled group ((3.12 ± 3.53) × 10⁻⁷ cm⁵ dyne⁻¹) and in an SAH group ((1.04 ± 0.74) × 10⁻⁷ cm⁵ dyne⁻¹). It was observed that the PWV value calculated using the maximum of the first derivative of the pressure waveform upstroke as characteristic points was the best correlated (r = −0.71) with the determined compliance. Because SAH normally results, among other causes, from a decreased arterial compliance the results suggest that the determined compliance could be used concomitantly with PWV to supply more diagnostic information about the pathogenesis of SAH.

A new method for non-invasive measurement of the human state of hydration is presented. This method is based on frequency-dependent absorptiometry of radio-waves passing through tissues. A device utilizing this method was constructed and applied to 12 young (24 ± 1) male volunteers, who were dehydrated for 1–2.5% of their weight by performance of a physical effort (two 30 min bouts of treadmill walking/running at 2, 3, 4, 5, 6 and 7 mph, 5 min at each speed, separated by 10 min rest), under moderate heat stress (40 °C, 40% RH). Hypohydration level was determined by body weight measurements taken before each session, after 30 min and at the end of each session. Concomitantly, measurements of radio frequency (RF) absorption were taken. Each volunteer underwent the heat stress exercise twice: one in which no drinking was permitted, and another with free drinking. A correlation (R² = 0.734) between weight loss and a change in the radio-waves absorption pattern was observed in most of the volunteers, in both hypo and euhydration sessions. Further work to establish the reproducibility and validity of the RF methodology in larger and different populations, i.e., females, other age groups and different health conditions, is already being researched.

The measurement of the electrical impedance inside the esophagus provides information about its status, and is being explored in the study of the gastroesophageal reflux. This paper presents theoretical computation of impedance inside the esophagus. The results of the numerical solution for a simple geometry are compared against the solution formulated from the Green's function approach. The effect of the electrode configuration on the resulting impedance is studied as an application of the methodology developed in this paper. The results of this paper will be useful in the design of an intraluminal impedance catheter as well as in the interpretation of the resulting impedance signals

Intact heart muscles are believed to contract synchronously to produce maximum effective work at a minimum energy cost. Temporal correlation coefficients between the left ventricular volume and muscle contraction were introduced to assess the synchronicity of left ventricular contraction (synchronous contraction index, SCI), and applied to eight normal volunteers. Area-contraction and length-shortening parallel to and perpendicular to the long axis were computed from electrocardiogram (ECG)-gated single-photon emission computed tomographies (SPECT) using a homemade computer programme. The cardiac wall was divided into nine segments, and the average values of accumulation of perfusion agents, amplitude of contraction and SCI were obtained in each segment. The area-SCI was 91.4% ± 4.3% and relatively uniform over the whole cardiac wall (p = 0.014, analysis of variance (ANOVA)), whereas the accumulation and amplitude of contraction varied significantly in different segments (p < 0.0001, ANOVA). This study suggested that in normal subjects the myocardial contraction was synchronous, and that the amplitude of contraction was not spatially uniform.

When an electric field is applied to cartilage, current-generated stress gradients are produced and stress deformation occurs. Since differential phase optical coherence tomography (DP-OCT) is sensitive to tiny surface displacement, these tiny displacements are induced electrokinetically in cartilage and the electric-current-induced stress gradients were measured with DP-OCT. The electrokinetic surface displacement of cartilage was characterized by applying sinusoidal voltages with two amplitudes (5 and 10 V) and different frequencies (1.0, 0.5 and 0.2 Hz). The results show that by application of DP-OCT the surface displacement increased with increasing applied voltage and decreased with increasing excitation frequency. In the electrokinetic response of cartilage, measured optical phase delay between the surface displacement response and excitation waveform varies inversely with the excitation frequency. Since the streaming potential and other electrokinetic effects in cartilage are directly proportional to proteoglycan density, application of an electric field in cartilage combined with DP-OCT measurements may provide a sensitive indicator of cartilage viability.

A novel instrument has been devised for the in vivo examination of the dynamic biomechanical properties of skin. These properties include stiffness and viscoelasticity. The advantage of the device is its ability to examine the skin dynamically, thereby eliminating preconditioning effects. Furthermore, it is portable, hand-held and easy to operate in the clinical environment. The objective of this study was to determine the accuracy and reliability of the dynamic biomechanical skin measurement (DBSM) probe. The accuracy was determined by examining a series of silicone elastomer specimens. A comparison of the shear modulus (G*), obtained from a static indentation system, with stiffness, obtained from the DBSM probe, was performed. The reliability was determined by examining both silicone elastomers and forearm volar skin in vivo. In both cases assessment was by six different operators (inter-reliability) and also by an individual operator (intra-reliability). Statistical analysis was performed using Levene's test of homogeneity and analysis of variance to ascertain if there were significant differences between operators (inter-reliability) and with one individual operator (intra-reliability). It can be concluded, from this study, that the DBSM probe is accurate (R² = 0.96, p = 0.01). It is also inter- and intra-reliable when assessing elastomer stiffness and skin stiffness. However, phase lag was not found to be a useful indicator of device reliability. It is anticipated that this device will be used to examine dermatological conditions and the benefits, or otherwise, of treatment. The DBSM probe promises to contribute to the objective measurement of physical properties of the skin in future investigative studies.

The sounds associated with the five classical Korotkoff phases are clinically important for measuring systolic and diastolic blood pressures. The frequency ranges of the sounds have already been described simply using the overall peak frequencies within each phase by Fourier methods. However, such analysis may be missing potentially useful clinical information. The aim of this study was to compare features associated with the different phases of the Korotkoff sounds obtained during blood pressure measurement using a joint time–frequency analysis (JTFA) technique. A single operator recorded Korotkoff sounds from 25 healthy subjects using a measurement system comprising cardiology stethoscope, microphone, amplifier and recording system for computer sound digitization, and a MiniDisc system for playback to the cardiologist for Korotkoff phase classification. We have shown that using this system the phase classification by the cardiologist is repeatable, with no significant differences found in the number of sounds allocated to phases on two separate recording assessments. The digitized sounds were processed using a MATLAB-based short-time Fourier transform JTFA technique and differences in time, frequency and amplitude characteristics between the phases compared. It was found that on average, phase III had the largest overall amplitude and high frequency energy. Phase II had the greatest high frequency component and longest murmur, and was visibly the most complex phase in terms of time and frequency content. In contrast, phases IV and V had the lowest amplitude and frequency components. Overall, the statistically significant transitions between phases were: phase I to II with increases in high frequency (224 to 275 Hz) (p < 0.01) and sound duration (49 to 98 ms) (p < 0.0001), II to III with a significant decrease in sound duration (to 37 ms) (p < 0.0001), III to IV with decreases in maximum amplitude (0.95 to 0.25), highest frequency (262 to 95 Hz), and relative high frequency energy of the sounds (0.61 to 0.10) (all p < 0.0001), and IV to V with decreases in the maximum amplitude (0.25 to 0.13) (p < 0.0002) and high frequency energy (0.10 to 0.03) (p < 0.005). This study has demonstrated that joint time–frequency analysis of Korotkoff sounds was able to identify characteristic differences associated with the different phases classified by the expert cardiologist. Ultimately, exploiting the joint time and frequency characteristics of the sounds may improve blood pressure measurement and help to assess the stiffness of the peripheral arteries.

It has previously been shown that extreme changes in ambient air temperature can affect whole-body bioelectrical impedance. The purpose of this study was to determine if more moderate changes in ambient air temperature, such as those experienced in most laboratory settings, would also affect bioelectric impedance analysis (BIA). In addition, to elucidate the mechanism responsible for changes in BIA with ambient air temperature, both skin blood flow (SBF) and the electrode–skin interface temperature were independently manipulated to determine their effect on BIA. During the first part of the study, nine healthy volunteers had their BIA measured in five different ambient air temperatures (15, 20, 25, 30 and 35 °C). Mean BIA was 513 Ω under the 15 °C condition and decreased significantly (p < 0.05) to 486 Ω in the 35 °C trial. However, no significant change was found in mean BIA between the 20 and 25 °C trials, which is the temperature range seen in most laboratories. Thus, moderate changes in ambient air temperature have only minor effects on BIA. In the second and third parts of the study, the electrode–skin interface temperature and SBF were independently manipulated using ice packs and electric heating pads placed over the four BIA electrodes. The results showed that BIA was inversely related to SBF (r = −0.95), and strongly suggest that changes in SBF, not electrode–skin interface temperature, are responsible for the changes seen in BIA.

We review developments, issues and challenges in electrical impedance tomography (EIT) for the 4th Conference on Biomedical Applications of Electrical Impedance Tomography, held at Manchester in 2003. We focus on the necessity for three-dimensional data collection and reconstruction, efficient solution of the forward problem, and both present and future reconstruction algorithms. We also suggest common pitfalls or 'inverse crimes' to avoid.

Electrical impedance tomography (EIT) has promise for imaging brain function with rings of scalp electrodes, but hitherto human images have been collected and reconstructed using a simple algorithm in which the head was modelled as a homogeneous sphere. The purpose of this work was to assess the improvement in image quality which could be achieved by adding layers to represent the cerebro-spinal fluid (CSF), skull and scalp in the forward model employed by the reconstruction algorithm. Solutions to the forward model were produced analytically and using the linear finite element method (FEM). This was undertaken for computer simulated data when a spherical conductivity change of 10%, radius 5 mm, was moved through 29 positions within a head modelled as four concentric spheres of radius 80–92 mm in order to verify the accuracy of the linear FEM by comparison with the analytical method. Test data were also recorded in a 93.5 mm, spherical, saline-filled tank in which the skull was simulated by a hollow sphere of plaster of Paris, 5 mm thick and a 20 × 20 mm right-cylindrical Perspex object, a 100% conductivity decrease, was moved through 39 positions. The best images were achieved by reconstruction with a four- or three-shell analytical model, giving a spatial accuracy of 5.8 ± 2.2 mm for computer simulated or 14.0 ± 5.8 mm for tank data. Mean FWHM was 57 mm and 91 mm in the XY-plane and along the z-axis, respectively. Reconstruction with a homogeneous analytical model gave localization errors greater by about 50–300%, but a reduction in FWHM of about 5% of the image diameter. Unexpectedly, reconstruction with FEM models gave poorer results similar to the analytical homogeneous case. This confirms that addition of shells to the forward model improves image quality as expected with an analytical model for reconstruction, but that the FEM method employed, which used a medium mesh and a linear element computation, requires improvement in order to yield the expected benefits.

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour.

Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring.

This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

Tikhonov regularization has been widely used in electrical tomography to deal with the ill-posedness of the inverse problem. However, due to the fact that discontinuities are strongly penalized, this approach tends to produce blurred images. Recently, a lot of interest has been devoted to methods with edge-preserving properties, such as those related to total variation, wavelets and half-quadratic regularization. In the present work, the performance of an edge-preserving regularization method, called ARTUR, is evaluated in the context of magnetic induction tomography (MIT). ARTUR is a deterministic method based on half-quadratic regularization, where complementary a priori information may be introduced in the reconstruction algorithm by the use of a nonnegativity constraint. The method is first tested using an MIT analytical model that generates projection data given the position, the radius and the magnetic permeability of a single nonconductive cylindrical object. It is shown that even in the presence of strong Gaussian additive noise, it is still able to recover the main features of the object. Secondly, reconstructions based on real data for different configurations of conductive nonmagnetic cylindrical objects are presented and some of their parameters estimated.

The focal underdetermined system solver (FOCUSS) algorithm is a recursive algorithm to find the localized energy solution. It is an initialization-dependent algorithm. The generalized vector sample pattern matching (GVSPM) method has been applied to solve the inverse problem of electrical impedance tomography (EIT) and obtain smooth reconstructed images. By combining the GVSPM solution as the initial estimation of the FOCUSS algorithm, an idea termed the GVSPM-FOCUSS method is presented in this paper to improve the spatial resolution and precision of localization for EIT images. The comparisons are carried out between the EIT images reconstructed with the GVSPM-FOCUSS method and the GVSPM method alone. The effectiveness is verified by simulated and tank data for a model of a two-dimensional homogeneous circular disk.

An unfortunate occurrence in experimental measurements with electrical impedance tomography is electrodes which become detached or poorly connected, such that the measured data cannot be used. This paper develops an image reconstruction methodology which allows use of the remaining valid data. A finite element model of the EIT difference imaging forward problem is linearized as z = Hx, where z represents the change in measurements and x the element log conductivity changes. Image reconstruction is represented in terms of a maximum a posteriori (MAP) estimate as x = inv(H^tinv(R_n) + inv(R_x))H^tinv(R_n)z, where R_x and R_n represent the a priori estimates of image and measurement noise crosscorrelations, respectively. Using this formulation, missing electrode data can be naturally modelled as infinite noise on all measurements using the affected electrodes. Simulations indicate position error and resolution are close (±10%) to the values calculated without missing electrode data as long as the target was further than 10% of the medium diameter from the affected electrode. Applications of this technique to experimental data show good results in terms of removing artefacts from images.

In electrical impedance tomography (EIT), measurements of developed surface potentials due to applied currents are used for the reconstruction of the conductivity distribution. Practical implementation of EIT systems is known to be problematic due to the high sensitivity to noise of such systems, leading to a poor imaging quality. In the present study, the performance of an induced current EIT (ICEIT) system, where eddy current is applied using magnetic induction, was studied by comparing the voltage measurements to simulated data, and examining the imaging quality with respect to simulated reconstructions for several phantom configurations. A 3-coil, 32-electrode ICEIT system was built, and an iterative modified Newton–Raphson algorithm was developed for the solution of the inverse problem. The RMS norm between the simulated and the experimental voltages was found to be 0.08 ± 0.05 mV (<3%). Two regularization methods were implemented and compared: the Marquardt regularization and the Laplacian regularization (a bounded second-derivative regularization). While the Laplacian regularization method was found to be preferred for simulated data, it resulted in distinctive spatial artifacts for measured data. The experimental reconstructed images were found to be indicative of the angular positioning of the conductivity perturbations, though the radial sensitivity was low, especially when using the Marquardt regularization method.

A new image reconstruction algorithm is proposed to visualize static conductivity images of a subject in magnetic resonance electrical impedance tomography (MREIT). Injecting electrical current into the subject through surface electrodes, we can measure the induced internal magnetic flux density B = (B_x, B_y, B_z) using an MRI scanner. In this paper, we assume that only the z-component B_z is measurable due to a practical limitation of the measurement technique in MREIT. Under this circumstance, a constructive MREIT imaging technique called the harmonic B_z algorithm was recently developed to produce high-resolution conductivity images. The algorithm is based on the relation between ∇²B_z and the conductivity requiring the computation of ∇²B_z. Since twice differentiations of noisy B_z data tend to amplify the noise, the performance of the harmonic B_z algorithm is deteriorated when the signal-to-noise ratio in measured B_z data is not high enough. Therefore, it is highly desirable to develop a new algorithm reducing the number of differentiations. In this work, we propose the variational gradient B_z algorithm where B_z is differentiated only once. Numerical simulations with added random noise confirmed its ability to reconstruct static conductivity images in MREIT. We also found that it outperforms the harmonic B_z algorithm in terms of noise tolerance. From a careful analysis of the performance of the variational gradient B_z algorithm, we suggest several methods to further improve the image quality including a better choice of basis functions, regularization technique and multilevel approach. The proposed variational framework utilizing only B_z will lead to different versions of improved algorithms.

In biomedical magnetic induction tomography (MIT), measurement precision may be improved by incorporating some form of primary field compensation/cancellation scheme. Schemes which have been described previously include gradiometric approaches and the use of 'back-off' coils. In each of these methods, however, the primary field cancellation was achieved only for a single transmitter/receiver combination. For the purpose of imaging, it would be desirable for a fully electronically scanned MIT system to provide a complete set of measurements, all with the primary field cancelled. A single channel suitable for incorporation into an MIT system with planar-array geometry is described. The transmitter is a 6-turn coil of wire 5 cm in diameter. The receiver is a surface mount inductor, of inductance 10 µH, mounted such that, in principle, no net primary field flux threads it. The results of measurements carried out with the single channel system suggest that the signal due to the primary excitation field can be reduced on average by a factor of 298 by the sensor geometry over the operating frequency range 1–10 MHz. The standard deviation and drift of the signal with the system adjusted for maximum primary field cancellation, expressed as a percentage of the signal when the receiver coil was rotated until its axis of sensitivity lay along the primary field, were 0.0009% and 0.009%, respectively. The filter time constant used was 30 ms.

Magnetic resonance–electrical impedance tomography (MREIT) algorithms fall into two categories: those utilizing internal current density and those utilizing only one component of measured magnetic flux density. The latter group of algorithms have the advantage that the object does not have to be rotated in the magnetic resonance imaging (MRI) system. A new algorithm which uses only one component of measured magnetic flux density is developed. In this method, the imaging problem is formulated as the solution of a non-linear matrix equation which is solved iteratively to reconstruct resistivity. Numerical simulations are performed to test the algorithm both for noise-free and noisy cases. The uniqueness of the solution is monitored by looking at the singular value behavior of the matrix and it is shown that at least two current injection profiles are necessary. The method is also modified to handle region-of-interest reconstructions. In particular it is shown that, if the image of a certain xy-slice is sought for, then it suffices to measure the z-component of magnetic flux density up to a distance above and below that slice. The method is robust and has good convergence behavior for the simulation phantoms used.

We conducted a short study on 8 volunteer subjects to establish whether physiological changes occurring as a result of the menstrual cycle affect tissue electrical properties. For this study subjects submitted to electrical impedance tomographic breast measurement four times, over two cycles at two different points in the cycle. Statistical analysis based on reconstructed values of conductivity and permittivity were conducted using the t-test for difference of means. The results were inconsistent, with some subjects showing a difference between the two phases and in all tests, while others showed differences only in some of the tests. At this time we can only conclude that a difference is more likely than not, although it could be a phenomenon only measurable in some individuals and not others. It seems that a larger study may be in order to establish this fact definitively.

Electrical impedance tomography (EIT) has been used in the recent past for a number of clinical applications. In this work we present recent tomographic and spectroscopic findings for breast imaging from clinical exams completed at Dartmouth. The results presented here are based on 18 normal and 24 abnormal subjects. The participants were classified as normal or abnormal using the American College of Radiology (ACR) indexing system for mammograms. The EIT data were collected for ten discrete frequencies in the range 10 kHz–1 MHz using a single array of 16 electrodes. The finite element method was used to reconstruct the images. The images were examined visually and were compared with mammograms. The results were also analyzed based on zonal averages of property values and breast tissue radiodensities. Statistical analysis showed a significance difference between the mean conductivity and permittivity values of normal and abnormal subjects for various zones defined on the reconstructed images. Tissues with high radiodensity also had increased conductivity and permittivity.

The measurement of hepatic iron overload is of particular interest in cases of hereditary hemochromatosis or in patients subject to periodic blood transfusion. The measurement of plasma ferritin provides an indirect estimate but the usefulness of this method is limited by many common clinical conditions (inflammation, infection, etc). Liver biopsy provides the most quantitative direct measurement of iron content in the liver but the risk of the procedure limits its acceptability. This work studies the feasibility of a magnetic induction (MI) low-cost system to measure liver iron overload. The excitation magnetic field (B₀, frequency: 28 kHz) was produced by a coil, the perturbation produced by the object (ΔB) was detected using a planar gradiometer. We measured ten patients and seven volunteers in supine and prone positions. Each subject was moved in a plane parallel to the gradiometer several times to estimate measurement repeatability. The real and imaginary parts of ΔB/B₀ were measured. Plastic tanks filled with water, saline and ferric solutions were measured for calibration purposes. We used a finite element model to evaluate the experimental results. To estimate the iron content we used the ratio between the maximum values for real and imaginary parts of ΔB/B₀ and the area formed by the Nyquist plot divided by the maximum imaginary part. Measurements in humans showed that the contribution of the permittivity is stronger than the contribution of the permeability produced by iron stores in the liver. Defined iron estimators show a limited correlation with expected iron content in patients (R ⩽ 0.56). A more precise control of geometry and position of the subjects and measurements at multiple frequencies would improve the method.

Planar gradiometers (PGRAD) have particular advantages compared to solenoid receiver coils in magnetic induction tomography (MIT) for biological objects. A careful analysis of the sensitivity maps has to be carried out for perturbations within conducting objects in order to understand the performance of a PGRAD system and the corresponding implications for the inverse problem of MIT. We calculated and measured sensitivity maps for a single MIT-channel and a cylindrical tank (diameter 200 mm) with a spherical perturbation (diameter 50 mm) and with conductivities in the physiological range (0.4–0.8 S m⁻¹). The excitation coil (EXC) was a solenoid (diameter 100 mm) with its axis perpendicular to the cylinder axis. As receiver a PGRAD was used. Calculations were carried out with a finite element model comparing the PGRAD and a solenoid receiver coil with its axis perpendicular to the excitation coil axis (SC90). The measured and simulated sensitivity maps agree satisfactorily within the limits of unavoidable systematic errors. In PGRAD the sensitivity is zero on the coil axis, exhibiting two local extrema near the receiver and a strong increase of the sensitivity with the distance from the coil axis. In SC90 the sensitivity map is morphologically very similar to that of the PGRAD. The maps are completely different from those known in EIT and may thus cause different implications for the inverse problem. The SC90 can, in principle, replace the mechanically and electrically more complicated PGRAD, however, the immunity to far sources of electromagnetic interference is worse, thus requiring magnetic shielding of the system.

Electrical impedance spectroscopy (EIS) has been previously reported as a technique for non invasive assessment of tissue change. Our previous in vivo studies demonstrated the ability of EIS to non-invasively detect and longitudinally follow tumor growth. This study was designed to determine the ability of EIS to detect tumors at a very early stage post-implantation. Complex impedance measurements were collected from eight rats with one control and one tumor implanted leg six or seven days after tumor cell inoculation. Legs were also imaged with computed tomography (CT) and ultrasound (US) in an effort to determine EIS resolution and sensitivity. Six of the animals were sacrificed immediately after imaging, and tissue was collected for histology and later co-registration of the pathology with the imaging techniques. Results show that EIS is able to repeatedly detect small tumors (<3 mm) and tumor-associated changes, whereas CT and US were not routinely capable of detecting pathological developments on this scale.

The detection and continuous monitoring of brain oedema is of particular interest in clinical applications because existing methods (invasive measurement of the intracranial pressure) may cause considerable distress for the patients. A new non-invasive method for continuous monitoring of an oedema promises the use of multi-frequency magnetic induction tomography (MIT). MIT is an imaging method for reconstructing the changes of the conductivity Δκ in a target object. The sensitivity of a single MIT-channel to a spherical oedematous region was analysed with a realistic model of the human brain. The model considers the cerebrospinal fluid around the brain, the grey matter, the white matter, the ventricle system and an oedema (spherical perturbation). Sensitivity maps were generated for different sizes and positions of the oedema when using a coaxial coil system. The maps show minimum sensitivity along the coil axis, and increasing values when moving the perturbation towards the brain surface. Parallel to the coil axis, however, the sensitivity does not vary significantly. When assuming a standard deviation of 10⁻⁷ for the relative voltage change due to the system's noise, a centrally placed oedema with a conductivity contrast of 2 with respect to the background and a radius of 20 mm can be detected at 100 kHz. At higher frequencies the sensitivity increases considerably, thus suggesting the capability of multi-frequency MIT to detect cerebral oedema.

Electrical impedance endotomography (EIE) is a modality where the electrodes are located around an insulating core placed inside the region of interest. This approach results in significant differences with respect to conventional EIT. The paper examines the sensitivity distribution of bipolar current patterns and the influence of the spacing between the drive electrodes using a two-dimensional (2D) mathematical model. The number of pixels of sensitivity above a given sensitivity threshold decreases faster with the distance to the probe for diametric and adjacent drive than for other bipolar drive patterns. The reconstruction of images from datasets collected in vitro using a 16-electrode probe confirmed the feasibility of the method at least within a range extending to three times the radius of the probe, under the described experimental conditions. Reduction of system noise, multiple-current patterns and the use of remote current and voltage electrodes are potential methods to increase the sensitivity range. Further work includes the improvement of the model to account for finite length electrodes and the miniaturization of the probe.

The holy grail of neuroimaging would be to have an imaging system, which could image neuronal electrical activity over milliseconds. One way to do this would be by imaging the impedance changes associated with ion channels opening in neuronal membranes in the brain during activity. In principle, we could measure this change by using electrical impedance tomography (EIT) but it is close to its threshold of detectability. With the inherent limitation in the use of electrodes, we propose a new scheme based on recording the magnetic field resulting from an injected current with superconducting quantum interference devices (SQUIDs), used in magnetoencephalography (MEG). We have performed a feasibility study using computer simulation. The head was modelled as concentric spheres to mimic the scalp, skull, cerebrospinal fluid and brain using the finite element method. The magnetic field 1 cm away from the scalp was estimated. An impedance change of 1% in a 2 cm radius volume in the brain was modelled as the region of depolarization. A constant current of 100 µA was injected into the head from diametrically opposite electrodes. The model predicts that the standing magnetic field is about 10 pT and changed by about 3 fT (0.03%) on depolarization. The spectral noise density in a typical MEG system in the frequency band 1–100 Hz is about 7 fT, so this places the change at the limit of detectability. This is similar to electrical recording, as in conventional EIT systems, but there may be advantages to MEG in that the magnetic field directly traverses the skull and instrumentation errors from the electrode–skin interface will be obviated.

Electrical impedance tomography is an imaging modality being investigated for use in detection of breast cancer. Use of higher frequencies than have typically been employed may benefit the detection processes. In this current work we discuss the design and initial implementation of a system having a bandwidth of 10 MHz. Previous investigations into high frequency designs have proven more difficult than anticipated and shown that careful selection of systems architecture is critical to achieving broadband performance above 1 MHz. The design for this new system is based on a digital signal processor (DSP) which is used for control, signal generation and signal processing. Signal generation and detection, software design and preliminary system specifications are discussed.

The technique of contactless imaging of resistivity distribution inside conductive objects, which can be applied in medical diagnostics, has been suggested and analyzed. The method exploits the interaction of a high-frequency electric field with a conductive medium. Unlike electrical impedance tomography, no electric current is injected into the medium from outside. The interaction is accompanied with excitation of high-frequency currents and redistribution of free charges inside the medium leading to strong and irregular perturbation of the field's magnitude outside and inside the object. Along with this the considered interaction also leads to small and regular phase shifts of the field in the area surrounding the object. Measuring these phase shifts using a set of electrodes placed around the object enables us to reconstruct the internal structure of the medium. The basics of this technique, which we name electric field tomography (EFT), are described, simple analytical estimations are made and requirements for measuring equipment are formulated. The realizability of the technique is verified by numerical simulations based on the finite elements method. Results of simulation have confirmed initial estimations and show that in the case of EFT even a comparatively simple filtered backprojection algorithm can be used for reconstructing the static resistivity distribution in biological tissues.

In this study the performance of an axial gradiometer sensor for magnetic induction tomography was investigated and the results of measurements to determine the precision and sensitivity of the sensor were undertaken. In the first part of the study a single gradiometer sensor was used and the noise and drift were measured for two excitation current values at a single frequency of 600 kHz. The variations of the real and imaginary received signal components with conductivity were then obtained for samples with 0–5 S m⁻¹. Both sets of measurements were repeated using two different forms of capacitive shielding. In the second part of the study the results of preliminary measurements obtained with a 2 × 2 planar matrix of axial gradiometers are given. The results of a simulation of a similar matrix using a commercial electromagnetic field calculation programme are also presented for comparison. For the sample utilized, the sensor output showed a linear variation with conductivity for the imaginary component of 0.033 mV S⁻¹ m using an excitation current of 316 mA at 600 kHz. No apparent correlation with conductivity for the real component was observed. The noise and drift of the imaginary component of the sensor output were 0.001 mV and 0.006 mV respectively, for the same excitation current. The results of the planar matrix measurements and simulations suggest that significant sensitivity is provided by using the measurement coils of the adjacent sensors. The measurement results however suggest that large improvements in the sensor noise and drift performance are required for these data to be of use.

An ultrasonic device for the diagnosis of acute compartment syndrome is described and results on six human cadaveric legs are presented. The ultrasonic device uses a pulsed phase locked loop (PPLL) to measure sub-micrometer displacements of the fascia wall. These displacements occur as a result of volume expansion of the muscle compartment of the lower leg and are related to changes in intramuscular pressure (IMP). In the cadaveric tests, the PPLL detected changes in compartment diameter resulting from IMP changes of 1 mmHg and from infusions of 0.25 ml saline increments. Based on these results, the ultrasonic PPLL appears to have the potential to become a low-cost, portable and noninvasive alternative to current methods for diagnosing acute compartment syndrome.