Y.Z. Ider

Electrical impedance tomography: induced-current imaging achieved with a multiple coil system

An experimental study of induced-current electrical impedance tomography verifies that image quality is enhanced by employing six rather than three induction coils by increasing the number of independent measurements. However, with an increasing number of coils, the inverse problem becomes more sensitive to measurement noise. Using 16 electrodes to measure surface voltages, it is possible to collect 6/spl times/15=90 independent measurements. For comparison purposes, images of two-dimensional conductivity perturbations are reconstructed by using the data for three and six coils with the truncated pseudoinverse algorithm. By searching for the optimal truncation index that minimizes the noise error plus the resolution error, the signal-to-noise ratio of the data acquisition system was established as 58 db. Images obtained with this six-coil system reveal the sizes and locations of the conductivity perturbations. This system also provides images within the central region of the object space, a capability not achieved in previous experimental studies using only three circular coils. Nevertheless, the three-coil system can identify the conductivity perturbations near the periphery. However, it displays shifts in the locations and spread in the sizes of perturbations near the center of the object.

Electrical impedance tomography using induced currents

The mathematical basis of a new imaging modality, induced current electrical impedance tomography (EIT), is investigated, The ultimate aim of this technique is the reconstruction of conductivity distribution of the human body, from voltage measurements made between electrodes placed on the surface, when currents are induced inside the body by applied time varying magnetic fields. In this study the two-dimensional problem is analyzed. A specific 9-coil system for generating nine different exciting magnetic fields (50 kHz) and 16 measurement electrodes around the object are assumed, The partial differential equation for the scaler potential function in the conductive medium is derived and finite element method (FEM) is used for its solution. Sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular value decomposition of the sensitivity matrix shows that there are 135 independent measurements. It is found that measurements are less sensitive to changes in conductivity of the objects interior. While in this respect induced current EIT is slightly inferior to the technique of injected current EIT (using Sheffield protocol), its sensitivity matrix is better conditioned. The images obtained are found to be comparable to injected current EIT images In resolution. Design of a coil system for which parameters such as sensitivity to inner regions and condition number of the sensitivity matrix are optimum, remains to be made.

Electrical impedance tomography of translationally uniform cylindrical objects with general cross-sectional boundaries

An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.

Measurement of AC magnetic field distribution using magnetic resonance imaging

Electric currents are applied to body in numerous applications in medicine such as electrical impedance tomography, cardiac defibrillation, electrocautery, and physiotherapy. If the magnetic field within a region is measured, the currents generating these fields can be calculated using the curl operator. In this study, magnetic fields generated within a phantom by currents passing through an external wire is measured using a magnetic resonance imaging (MRI) system. A pulse sequence that is originally designed for mapping static magnetic field inhomogeneity is adapted. AC current in the form of a burst sine wave is applied synchronously with the pulse sequence. The frequency of the applied current is in the audio range with an amplitude of 175-mA rms. It is shown that each voxel value of sequential images obtained by the proposed pulse sequence is modulated similar to a single-tone broadband frequency modulated (FM) waveform with the AC magnetic field strength determining the modulation index. An algorithm is developed to calculate the AC magnetic field intensity at each voxel using the frequency spectrum of the voxel signal. Experimental results show that the proposed algorithm can be used to calculate AC magnetic field distribution within a conducting sample that is placed in an MRI system.

A new technique for line interference monitoring and reduction in biopotential amplifiers

Hardware developed to record the common mode line frequency signal on the body simultaneously with the ECG lead signals of a 15-channel computerized cardiograph is described. This interference reference signal and its quadrature, obtained by software, are linearly combined to be subtracted from any one of the channels to reduce the interference to below the quantization level of the 12 b A/D converter. Coefficients of the linear combination are estimated using linear regression, which is applied to the relatively isoelectric regions of the data, excluding the QRS complexes. Since the interference reference signal is available in real time, simultaneously with the ECG signals, another software approach is adopted in which an adaptive interference reduction algorithm is used to cope with varying interference. A recursive-least-squares algorithm with forgetting factor is used to update the coefficients. This updating mechanism is gated by the output of a software QRS detector. Results regarding the performance of both the offline and the adaptive algorithms are given, and the effects of nonisoelectric portions of the ECG lead signals on the estimation of the coefficients are quantified.<<ETX>>

A comparative study of several exciting magnetic fields for induced current EIT

In this study, the selection of coil configuration parameters (coil radius and coil centre shift) for induced current EIT using circular coils is investigated. An alternative coil configuration is suggested, which produces approximately linear (spatially) magnetic fields in order to strengthen the currents in the central region. Injected current EIT, with Sheffield data collection protocol, and induced current EIT, with two different coil configurations, are compared with respect to singular-value patterns, sensitivity distributions and imaging performances. It is observed that for the proposed alternative coil configuration the measurements are more sensitive to inner region conductivity perturbations when compared to injected current EIT and induced current EIT using circular coils. The images obtained by induced current EIT are comparable to that obtained by injected current EIT.

Determination of the boundary of an object inserted into a water-filled cylinder

In order to circumvent the electrode position determination problem in static electrical impedance tomography, it is possible to insert the object to be imaged into a water-filled cylinder on which the electrodes are at fixed and known positions. It has previously been shown that if the boundary of the internally placed object and the conductivity of the salty water in the cylinder are known, then a significant improvement in the conductivity image of the object is obtained. An algorithm for finding the boundary of an internally placed object is developed based on the finite element method (FEM). The boundary is assumed to obey a parametric model and the parameters are estimated by inverting a matrix representing the sensitivity of the boundary voltage measurements to parameter variations. The algorithm assumes that the objects internal conductivity is uniform and known. Simulation studies show that if the internal conductivity is not uniform to the extent found in the arm cross-sections, up to 9% error in the boundary, as measured from a centrally placed reference point, may result. It is also shown that if previous knowledge about the boundary shape is used to model the boundary with fewer numbers of parameters, then the boundary may be found with less error.

Magnetic resonance-conductivity imaging using 0.15 tesla MRI scanner

A novel imaging method for electrical impedance tomography is implemented. In this method, the magnetic flux density generated by current flowing in a 2D slice is measured using a MRI scanner and the recorded data is used to reconstruct relative conductivity images. The measurements are done from all parts of the imaging region, and therefore sensitivity is space independent. The magnetic flux density is extracted from phase images of the MRI image and a sensitivity based image reconstruction algorithm is used to reconstruct relative conductivity images. The magnetic flux density measured and the conductivity image reconstructed for an insulator object placed in the middle of the imaging region are presented.

Magnetic resonance conductivity imaging

A new imaging modality combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI), by utilizing both the voltage measurements from EIT and magnetic field measurements from MRI, is proposed and tested using simulated data. It has been shown that, high resolution and absolute conductivity images can be obtained.

Measuring AC magnetic field distribution using MRI

Electric currents are applied to body in numerous applications in medicine, such as electrical impedance tomography, cardiac defibrillators, electrocautery and some treatment methods in physiotherapy. If the magnetic field within a region is measured, the currents generating these fields can be calculated using the curl operator. In this study, magnetic fields generated by AC currents injected into a phantom are measured using MRI. A pulse sequence that is originally designed for mapping static magnetic field is used. AC currents in the form of burst sine waves are applied synchronously with the pulse sequence. Results show that this method can be used in applications where the frequency of the currents is in the audio range and the amplitude is a few milliamperes or larger depending on SNR.