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 Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles, and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary, and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.Comment: 25 pp, 11 figure

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

Multifrequency methods for Electrical Impedance Tomography

Multifrequency Electrical Impedance Tomography (MFEIT) is an emerging imaging modality which exploits the dependence of tissue impedance on frequency to recover images of conductivity. Given the low cost and portability of EIT scanners, MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. Whereas time-difference, or dynamic, EIT is an established technique for monitoring lung ventilation, MFEIT has received less attention in the literature, and the imaging methodology is at an early stage of development. MFEIT holds the unique potential to form images from static data, but high sensitivity to noise and modelling errors must be overcome. The subject of this doctoral thesis is the investigation of novel techniques for including spectral information in the image reconstruction process. The aim is to improve the ill-posedness of the inverse problem and deliver the first imaging methodology with sufficient robustness for clinical application. First, a simple linear model for the conductivity is defined and a simultaneous multifrequency method is developed. Second, the method is applied to a realistic numerical model of a human head, and the robustness to modelling errors is investigated. Third, a combined image reconstruction and classification method is developed, which allows for the simultaneous recovery of the conductivity and the spectral information by introducing a Gaussian-mixture model for the conductivity. Finally, a graph-cut image segmentation technique is integrated in the imaging method. In conclusion, this work identifies spectral information as a key resource for producing MFEIT images and points to a new direction for the development of MFEIT algorithms

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 l2 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

Correction of electrode modelling errors in multi-frequency EIT imaging

The differentiation of haemorrhagic from ischaemic stroke using electrical impedance tomography (EIT) requires measurements at multiple frequencies, since the general lack of healthy measurements on the same patient excludes time-difference imaging methods. It has previously been shown that the inaccurate modelling of electrodes constitutes one of the largest sources of image artefacts in non-linear multi-frequency EIT applications. To address this issue, we augmented the conductivity Jacobian matrix with a Jacobian matrix with respect to electrode movement. Using this new algorithm, simulated ischaemic and haemorrhagic strokes in a realistic head model were reconstructed for varying degrees of electrode position errors. The simultaneous recovery of conductivity spectra and electrode positions removed most artefacts caused by inaccurately modelled electrodes. Reconstructions were stable for electrode position errors of up to 1.5 mm standard deviation along both surface dimensions. We conclude that this method can be used for electrode model correction in multi-frequency EIT

Regional admittivity reconstruction with multi-frequency complex admittance data using contactless capacitive electrical tomography

Tomographic imaging of the electrical properties distribution within biological subjects such as the human body has been an active research goal in electrical tomography (ET). As the electrical properties of a living tissue vary with the excitation frequency, measuring the frequency-dependent behaviour of the effective dielectric can increase the possibilities for tissue characterisation, and thus enhance the potential for extended clinical applications. The ET system generally enables to capture the changes in effective dielectric properties at low spatial resolution, therefore, the complete complex admittance spectrum can be reconstructed by ET to enrich the information content and further provide better diagnostic. In this work, we demonstrate a novel contactless ET system which relies on the capacitive coupled principle, the capacitive coupled electrical tomography (CCET). Except the non-contact measuring characteristic, the capacitance-based imaging principle enables the system to obtain the measurements at higher excitation frequencies. These characteristics give CCET great potential in future medical application, as the high-frequency component of complex impedance plays a dominant role in establishing the link between the microscopic cell structures and the macroscopic admittivity images obtained from multi-frequency ET systems. In this paper, we used multi-frequency electrical signals from 320 kHz to 14 MHz to conduct the single and multiple inclusions test with different biological samples. Both the reconstructed tomographic images and the Cole-Cole plots confirm the ability of CCET in characterising different objects.</p

Identification of an inclusion in multifrequency electric impedance tomography

International audienceThe multifrequency electrical impedance tomography is considered in order to image a conductivity inclusion inside a homogeneous background medium by injecting one current. An original spectral decomposition of the solution of the forward conductivity problem is used to retrieve the Cauchy data corresponding to the extreme case of perfect conductor. Using results based on the unique continuation we then prove the uniqueness of multifrequency electrical impedance tomography and obtain rigorous stability estimates. Our results in this paper are quite surprising in inverse conductivity problem since in general infinitely many input currents are needed in order to obtain the uniqueness in the determination of the conductivity