B H Blott

Adaptive mesh refinement techniques for electrical impedance tomography

Adaptive mesh refinement techniques can be applied to increase the efficiency of electrical impedance tomography reconstruction algorithms by reducing computational and storage cost as well as providing problem-dependent solution structures. A self-adaptive refinement algorithm based on an a posteriori error estimate has been developed and its results are shown in comparison with uniform mesh refinement for a simple head model.

Imaging of free-space interference patterns used to manufacture fiber Bragg gratings

A technologically important use of the free-space interference patterns formed by phase gratings is in the creation of the refractive-index variation along optical fiber Bragg gratings. The patterns can be imaged directly by use of a tapered optical fiber tip, which acts as a local probe of the optical field. We present measurements of these patterns under varying conditions and compare them with theoretical predictions. In discussing the results within the context of fiber grating manufacture, we also demonstrate the effects of incident-beam misalignment and wave-front curvature.

Electrical impedance tomography with compensation for electrode positioning variations.

Ideally electrical impedance tomography (EIT) should not be oversensitive to electrode positions, but this conflicts with efforts to produce high-resolution images. Two procedures are presented that balance reducing the sensitivity to electrode position errors with generating practicable EIT images. The first provides a criterion based on electrode sensitivity for regularizing the reconstruction through spectral expansion. The main consequences of this are that smoother images are produced and the number of artefacts and their magnitude are generally reduced. The second modification uses the recorded data to compensate for electrode movements that have occurred after the reference data were measured. Image smoothness is used as the criterion for the readjustment. Computer simulation tests have shown that this modification produces improved image fidelity.

Optimal imaging with adaptive mesh refinement in electrical impedance tomography

In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical chi2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.

Dye permeability at phase transitions in single and binary component phospholipid bilayers

By encapsulating a pH-sensitive dye, phenol red, in multilamellar liposomes of DMPC, DPPC and DMPC/DPPC mixtures, the permeability of these phospholipid bilayers to dye as a function of temperature has been studied. For both DMPC and DPPC liposomes, dye release begins well below the main gel-to-liquid-crystalline phase transition (24 degrees C and 42 degrees C, respectively) at temperatures corresponding to the onset of the pretransition (about 14 degrees C and 36 degrees C, respectively) with DPPC liposomes exhibiting a permeability anomaly at the main phase transition (42 degrees C). The perturbation occurring in the bilayer structure that allows the release of encapsulated phenol red (approx. 5 A diameter) is not sufficient to permit the release of encapsulated haemoglobin (approx. 20 A diameter, negatively charged). In liposomes composed of a range of DMPC/DPPC mixtures, dye release commences at the onset of the pretransition range (determined by optical absorbance measurements) and increases with increasing temperature until the first appearance of liquid crystalline phase after which no further dye release occurs. Interestingly, the dye retaining properties of DMPC and DPPC liposomes well below their respective pretransition temperature regions are very different: DMPC liposomes release much encapsulated dye at incubation temperatures of 5 degrees C whilst DPPC liposomes do not.

EIT data noise evaluation in the clinical environment

In the clinical environment the reliable interpretation of EIT images depends on the quality of the data. In the electrically noisy hospital environment the system performance needs to be assessed for each clinical investigation. From the model of noise presented, a figure of merit for comparisons of system performance with a known standard, or with previous studies, can be generated. The method depends on calculating the variances of the differences in reciprocity measurements as a function of the distance between the current drive electrodes and the receive voltage electrodes. These measurements fit the noise model, with minimal interference from physiological variability, and permit a figure of merit to be calculated which is a representation of the noise at the point to the system. Typical figures of merit are 7.36 +/- 0.03 microV for a test card and 10.50 +/- 16 microV for subject data.

High fidelity imaging and high performance computing in nonlinear EIT

We show that nonlinear EIT provides images with well defined characteristics when smoothness of the image is used as a constraint in the reconstruction process. We use the gradient of the logarithm of resistivity as an effective measure of image smoothness, which has the advantage that resistivity and conductivity are treated with equal weight. We suggest that a measure of the fidelity of the image to the object requires the explicit definition and application of such a constraint. The algorithm is applied to the simulation of intra-ventricular haemorrhaging (IVH) in a simple head model. The results indicate that a 5% increase in the blood content of the ventricles would be easily detectable with the noise performance of contemporary instrumentation. The possible implementation of the algorithm in real time via high performance computing is discussed.

Evanescent field imaging of an optical fiber Bragg grating

We have investigated the evanescent field associated with an optical fiber Bragg grating using the sub-wavelength imaging properties of scanning near-field optical microscopy (SNOM). Imaging of either the field distribution within the grating, or the periodic refractive index changes along the grating can be performed by tuning the launched light on or off the grating resonance. These measurements reveal non-uniformity in the resonant standing-wave pattern that occur due to phase errors in the refractive index profile of the grating under study.

Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction

Non-linear electrical impedance tomography reconstruction algorithms usually employ the Newton-Raphson iteration scheme to image the conductivity distribution inside the body. For complex 3D problems, the application of this method is not feasible any more due to the large matrices involved and their high storage requirements. In this paper we demonstrate the suitability of an alternative conjugate gradient reconstruction algorithm for 3D tomographic imaging incorporating adaptive mesh refinement and requiring less storage space than the Newton-Raphson scheme. We compare the reconstruction efficiency of both algorithms for a simple 3D head model. The results show that an increase in speed of about 30% is achievable with the conjugate gradient-based method without loss of accuracy.

Nonlinear reconstruction constrained by image properties in electrical impedance tomography.

It is proposed that image quality, for example the degree of roughness, in electrical impedance tomography is the essential measure required to regularize nonlinear reconstruction. Most previously published work has addressed efficiency, stabilization and speed of reconstruction and has overlooked the targeted image qualities. The measure of quality adopted is the mean square gradient of the logarithm of resistivity which, in combination with the chi2 statistic as a measure of the fit to the data, is minimized by iteration until convergence to a stable image is achieved. This penalty function is invariant to the scale of the resistivity and to the interchange of resistivity and conductivity. The algorithm is tested on computer simulated data and on measurements from a cylindrical tank of electrolyte. The results demonstrate the increased image definition that it would be possible to achieve as data acquisition systems are improved. The images show how a reduction in resolution can be traded for reduced noise artefacts, by selecting an appropriate target chi2.