Multifrequency electrical impedance tomography with total variation regularization

Multifrequency electrical impedance tomography (MFEIT) reconstructs the distribution of conductivity by exploiting the dependence of tissue conductivity on frequency. MFEIT can be performed on a single instance of data, making it promising for applications such as stroke and cancer imaging, where it is not possible to obtain a 'baseline' measurement of healthy tissue. A nonlinear MFEIT algorithm able to reconstruct the volume fraction distribution of tissue rather than conductivities has been developed previously. For each volume, the fraction of a certain tissue should be either 1 or 0; this implies that the sharp changes of the fractions, representing the boundaries of tissue, contain all the relevant information. However, these boundaries are blurred by traditional regularization methods using [Formula: see text] norm. The total variation (TV) regularization can overcome this problem, but it is difficult to solve due to its non-differentiability. Because the fraction must be between 0 and 1, this imposes a constraint on the MFEIT method based on the fraction model. Therefore, a constrained optimization method capable of dealing with non-differentiable problems is required. Based on the primal and dual interior point method, we propose a new constrained TV regularized method to solve the fraction reconstruction problem. The noise performance of the new MFEIT method is analysed using simulations on a 2D cylindrical mesh. Convergence performance is also analysed through experiments using a cylindrical tank. Finally, simulations on an anatomically realistic head-shaped mesh are demonstrated. The proposed MFEIT method with TV regularization shows higher spatial resolution, particularly at the edges of the perturbation, and stronger noise robustness, and its image noise and shape error are 20% to 30% lower than the traditional fraction method.

A Reconstruction-Classification Method for Multifrequency Electrical Impedance Tomography

Multifrequency Electrical Impedance Tomography is an imaging technique which distinguishes biological tissues by their unique conductivity spectrum. Recent results suggest that the use of spectral constraints can significantly improve image quality. We present a combined reconstruction-classification method for estimating the spectra of individual tissues, whilst simultaneously reconstructing the conductivity. The advantage of this method is that a priori knowledge of the spectra is not required to be exact in that the constraints are updated at each step of the reconstruction. In this paper, we investigate the robustness of the proposed method to errors in the initial guess of the tissue spectra, and look at the effect of introducing spatial smoothing. We formalize and validate a frequency-difference variant of reconstruction-classification, and compare the use of absolute and frequency-difference data in the case of a phantom experiment.

Mapping cortical haemodynamics during neonatal seizures using diffuse optical tomography: a case study

Seizures in the newborn brain represent a major challenge to neonatal medicine. Neonatal seizures are poorly classified, under-diagnosed, difficult to treat and are associated with poor neurodevelopmental outcome. Video-EEG is the current gold-standard approach for seizure detection and monitoring. Interpreting neonatal EEG requires expertise and the impact of seizures on the developing brain remains poorly understood. In this case study we present the first ever images of the haemodynamic impact of seizures on the human infant brain, obtained using simultaneous diffuse optical tomography (DOT) and video-EEG with whole-scalp coverage. Seven discrete periods of ictal electrographic activity were observed during a 60 minute recording of an infant with hypoxic-ischaemic encephalopathy. The resulting DOT images show a remarkably consistent, high-amplitude, biphasic pattern of changes in cortical blood volume and oxygenation in response to each electrographic event. While there is spatial variation across the cortex, the dominant haemodynamic response to seizure activity consists of an initial increase in cortical blood volume prior to a large and extended decrease typically lasting several minutes. This case study demonstrates the wealth of physiologically and clinically relevant information that DOT-EEG techniques can yield. The consistency and scale of the haemodynamic responses observed here also suggest that DOT-EEG has the potential to provide improved detection of neonatal seizures.

Multifrequency electrical impedance tomography using spectral constraints

Multifrequency electrical impedance tomography (MFEIT) exploits the dependence of tissue impedance on frequency to recover an image of conductivity. MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. We present a method for performing MFEIT using spectral constraints. Boundary voltage data is employed directly to reconstruct the volume fraction distribution of component tissues using a nonlinear method. Given that the reconstructed parameter is frequency independent, this approach allows for the simultaneous use of all multifrequency data, thus reducing the degrees of freedom of the reconstruction problem. Furthermore, this method allows for the use of frequency difference data in a nonlinear reconstruction algorithm. Results from empirical phantom measurements suggest that our fraction reconstruction method points to a new direction for the development of multifrequency EIT algorithms in the case that the spectral constraints are known, and may provide a unifying framework for static EIT imaging.

The influence of high intensity terahertz radiation on mammalian cell adhesion, proliferation and differentiation

Understanding the influence of exposure of biological systems to THz radiation is becoming increasingly important. There is some evidence to suggest that THz radiation can influence important activities within mammalian cells. This study evaluated the influence of the high peak power, low average power THz radiation produced by the ALICE (Daresbury Laboratory, UK) synchrotron source on human epithelial and embryonic stem cells. The cells were maintained under standard tissue culture conditions, during which the THz radiation was delivered directly into the incubator for various exposure times. The influence of the THz radiation on cell morphology, attachment, proliferation and differentiation was evaluated. The study demonstrated that there was no difference in any of these parameters between irradiated and control cell cultures. It is suggested that under these conditions the cells are capable of compensating for any effects caused by exposure to THz radiation with the peak powers levels employed in these studies.

Calibration methods for a multi-channel multi-frequency EIT system

Multi-channel multi-frequency electrical impedance tomography (EIT) systems require a careful calibration to minimize systematic errors. We describe novel calibration methods for the recently developed KHU Mark1 EIT system. Current source calibration includes maximization of output resistance and minimization of output capacitance using multiple generalized impedance converters. Phase and gain calibrations are used for voltmeters. Phase calibration nulls out the total system phase shift in measured voltage data. Gain calibrations are performed in two steps of intra- and inter-channel calibrations. Intra-channel calibration for each voltmeter compensates frequency dependence of its voltage gain and also discrepancy between design and actual gains. Inter-channel calibration compensates channel-dependent voltage gains of all voltmeters. Using the calibration methods described in this paper, we obtained 1 MOmega minimal output impedance of the current source in the frequency range 10 Hz-500 kHz. The reciprocity error was as small as 0.05% after intra- and inter-channel voltmeter calibrations. To demonstrate effects of calibration in reconstructed images, we used a homogenous phantom from which uniform images should be produced. Reconstructed time- and frequency-difference images using uncalibrated data showed spurious anomalies. By using calibrated data, standard deviations of time- and frequency-difference images of the homogenous phantom were reduced by about 40% and 90%, respectively.

Multi-frequency EIT system with radially symmetric architecture: KHU Mark1

We describe the development of a multi-frequency electrical impedance tomography (EIT) system (KHU Mark1) with a single balanced current source and multiple voltmeters. It was primarily designed for imaging brain function with a flexible strategy for addressing electrodes and a frequency range from 10 Hz-500 kHz. The maximal number of voltmeters is 64, and all of them can simultaneously acquire and demodulate voltage signals. Each voltmeter measures a differential voltage between a pair of electrodes. All voltmeters are configured in a radially symmetric architecture in order to optimize the routing of wires and minimize cross-talk. We adopted several techniques from existing EIT systems including digital waveform generation, a Howland current generator with a generalized impedance converter (GIC), digital phase-sensitive demodulation and tri-axial cables. New features of the KHU Mark1 system include multiple GIC circuits to maximize the output impedance of the current source at multiple frequencies. The voltmeter employs contact impedance measurements, data overflow detection, spike noise rejection, automatic gain control and programmable data averaging. The KHU Mark1 system measures both in-phase and quadrature components of trans-impedances. By using a script file describing an operating mode, the system setup can be easily changed. The performance of the developed multi-frequency EIT system was evaluated in terms of a common-mode rejection ratio, signal-to-noise ratio, linearity error and reciprocity error. Time-difference and frequency-difference images of a saline phantom with a banana object are presented showing a frequency-dependent complex conductivity of the banana. Future design of a more innovative system is suggested including miniaturization and wireless techniques.

Design and calibration of a compact multi-frequency EIT system for acute stroke imaging

A new, compact UCLH Mk 2.5 EIT system has been developed and calibrated for EIT imaging of the head. Improvements include increased input and output impedances, increased bandwidth and improved CMRR (80 dB) and linearity over frequencies and load (0.2% on a single channel, +/-0.7% on a saline tank over 20 Hz-256 kHz and 10-65 Omega). The accuracy of the system is sufficient to image severe acute stroke according to the specification from recent detailed anatomical modelling (Horesh et al 2005 3rd European Medical and Biological Engineering Conference EMBEC'05). A preliminary human study has validated the main specifications of the modelling, the range of trans-impedance from the head (8-70 Omega) using a 32 electrode, 258 combination protocol and contact impedances of 300 Omega to 2.7 kOmega over 20 Hz to 256 kHz.

Singularity Characteristics of Needle EMG IP Signals

Clinical electromyography (EMG) interference pattern (IP) signals can reveal more diagnostic information than their constituents, the motor unit action potentials (MUAPs). Singularities and irregular structures typically characterize the mathematically defined content of information in signals. In this paper, a wavelet transform method is used to detect and quantify the singularity characteristics of EMG IP signals using the Lipschitz exponent (LE) and measures derived from it. The performance of the method is assessed in terms of its ability to discriminate healthy, myopathic and neuropathic subjects and how it compares with traditionally used Turns Analysis (TA) methods and a method recently developed by the authors, interscale wavelet maximum (ISWM). Highly significant intergroup differences were found using the LE method. Most of the singularity measures have a performance similar to that of ISWM and considerably better than that of TA. Some measures such as the ratio of the mean LE value to the number of singular points in the signal have considerably superior performance to both methods. These findings add weight to the view that wavelet analysis methods offer an effective way forward in the quantitative analysis of EMG IP signal to assist the clinician in the diagnosis of neuromuscular disorders.

Applications of GRID in clinical neurophysiology and Electrical Impedance Tomography of brain function

The computational requirements in Neurophysiology are increasing with the development of new analysis methods. The resources the GRID has to offer are ideally suited for this complex processing. A practical implementation of the GRID, Condor, has been assessed using a local cluster of 920 PCs. The reduction in processing time was assessed in spike recognition of the Electroencephalogram (EEG) in epilepsy using wavelets and the computationally demanding task of non-linear image reconstruction with Electrical Impedance Tomography (EIT). Processing times were decreased by 25 and 40 times respectively. This represents a substantial improvement in processing time, but is still sub optimal due to factors such as shared access to resources and lack of checkpoints so that interrupted jobs had to be restarted. Future work will be to use these methods in non-linear EIT image reconstruction of brain function and methods for automated EEG analysis, if possible with further optimized GRID middleware.

The spatial resolution improvement of EIT images by GVSPM-FOCUSS algorithm

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.

The application of the generalized vector sample pattern matching method for EIT image reconstruction

This paper presents a new application of a generalized vector sample pattern matching (GVSPM) method for image reconstruction of conductivity changes in electrical impedance tomography. GVSPM is an iterative method for linear inverse problems. The key concept of the GVSPM is that the objective function is defined in terms of an angular component between the inner product of the known vector and solution of a system of equations. Comparisons are presented between images of simulated and experimental data, reconstructed using truncated singular value decomposition and GVSPM. In both cases, a normalized sensitivity matrix is constructed using the finite volume method to solve the forward problem.