Towards continuous EIT monitoring for hemorrhagic stroke patients.

The practical implementation of continuous monitoring of stroke patients by Electrical Impedance Tomography (EIT) is addressed. In a previous paper, we have demonstrated EIT sensitivity to cerebral hemodynamics, using scalp-mounted electrodes, very low-noise measurements, and a novel image reconstruction method. In the present paper, we investigate the potential to adapt that system for clinical application, by using 50% fewer electrodes and by incorporating into the measurement protocol an additional high-frequency measurement to provide an effective reference. Previously published image reconstruction methods for multi-frequency EIT are substantially improved by exploiting the forward calculations enabled by the detailed head model, particularly to make the referencing method more robust and to attempt to remove the effects of modelling error. Images are presented from simulation of a typical hemorrhagic stroke and its growth. These results are encouraging for exploration of the potential clinical benefit of the methodology in long-term monitoring of hemorrhagic stroke.

Tomographic imaging of carbon dioxide in the exhaust plume of large commercial aero-engines.

We report here the first implementation of chemically specific imaging in the exhaust plume of a gas turbine typical of those used for propulsion in commercial aircraft. The method used is chemical species tomography (CST) and the target species is CO2, absorbing in the near-infrared at 1999.4 nm. A total of 126 beams propagate transverse to the plume axis, along 7 m paths in a coplanar geometry, to probe a central region of diameter ≈1.5m. The CO2 absorption spectrum is measured using tunable diode laser spectroscopy with wavelength modulation, using the second harmonic to first harmonic (2f/1f) ratio method. The engine is operated over the full range of thrust, while data are recorded in a quasi-simultaneous mode at frame rates of 1.25 and 0.3125 Hz. Various data inversion methodologies are considered and presented for image reconstruction. At all thrust levels a persistent ring structure of high CO2 concentration is observed in the central region of the measurement plane, with a raised region in the middle of the plume assumed to be due to the engine's boat tail. With its potential to target various exhaust species, the CST method outlined here offers a new approach to turbine combustion research, turbine engine development, and aviation fuel research and development.

Scalp-Mounted Electrical Impedance Tomography of Cerebral Hemodynamics.

An Electrical Impedance Tomography (EIT) system has been developed for dynamic three-dimensional imaging of changes in conductivity distribution in the human head, using scalp-mounted electrodes. We attribute these images to changes in cerebral perfusion. At 100 frames per second (fps), voltage measurement is achieved with full-scale signal-to-noise ratio of 105 dB and common-mode rejection ratio > 90 dB. A novel nonlinear method is presented for 3-D imaging of the difference in conductivity distribution in the head, relative to a reference time. The method achieves much reduced modelling error. It successfully localizes conductivity inclusions in experimental and simulation tests, where previous methods fail. For > 50 human volunteers, the rheoencephalography (REG) waveform is observed in EIT voltage measurements for every volunteer, with peak-to-peak amplitudes up to approx. 50 µVrms. Images are presented of the change in conductivity distribution during the REG/cardiac cycle, at 50 fps, showing maximum local conductivity change of approx. 1% in grey/white matter. A total of 17 tests were performed during short (typically 5s) carotid artery occlusions on 5 volunteers, monitored by Transcranial Doppler ultrasound. From EIT measurements averaged over complete REG/cardiac cycles, 13 occlusion tests showed consistently decreased conductivity of cerebral regions on the occluded side, and increased conductivity on the opposite side. The maximum local conductivity change during occlusion was approx. 20%. The simplicity of the carotid artery intervention provides a striking validation of the scalp-mounted measurement system in imaging cerebral hemodynamics, and the REG images indicate its unique combination of sensitivity and temporal resolution.

Finite element modelling and image reconstruction for Lorentz force electrical impedance tomography.

OBJECTIVE: We propose a numerical framework to simulate the Lorentz force electrical impedance tomography (LFEIT) measurements on accurate electrode models and an image reconstruction scheme for which data on two pairs of electrodes are sufficient. APPROACH: The adopted finite element-based complete electrode model encompasses the electrode's geometry and contact impedance, accounting for the power losses at the contact interface. For image reconstruction, we suggest an approach based on a modified J-substitution algorithm that requires LFEIT and impedance measurements on two pairs of sensors, essentially necessitating no more than three boundary electrodes. MAIN RESULTS: The results of our simulation study suggest that electrode modelling has a significant impact on the measurements and electrode model inaccuracies may be detrimental to the image reconstruction. For image reconstruction, we suggest an approach based on a modified J-substitution algorithm that requires LFEIT and impedance measurements on two pairs of sensors, essentially necessitating no more than three boundary electrodes. SIGNIFICANCE: This allows for shorter acquisition times, less sonication noise during the acoustic modulation, a simpler measurement setup, and eventually a more succinct and efficient image reconstruction process.

Constrained models for optical absorption tomography.

We consider the inverse problem of concentration imaging in optical absorption tomography with limited data sets. The measurement setup involves simultaneous acquisition of near-infrared wavelength-modulated spectroscopic measurements from a small number of pencil beams equally distributed among six projection angles surrounding the plume. We develop an approach for image reconstruction that involves constraining the value of the image to the conventional concentration bounds and a projection into low-dimensional subspaces to reduce the degrees of freedom in the inverse problem. Effectively, by reparameterizing the forward model, we impose, simultaneously, spatial smoothness and a choice among three types of inequality constraints, namely, positivity, boundedness, and logarithmic boundedness in a simple way that yields an unconstrained optimization problem in a new set of surrogate parameters. Testing this numerical scheme with simulated and experimental phantom data indicates that the combination of affine inequality constraints and subspace projection leads to images that are qualitatively and quantitatively superior to unconstrained regularized reconstructions. This improvement is more profound in targeting concentration profiles of small spatial variation. We present images and convergence graphs from solving these inverse problems using Gauss-Newton's algorithm to demonstrate the performance and convergence of our method.

Tackling modelling error in the application of electrical impedance tomography to the head.

In the head application of Electrical Impedance Tomography (EIT), reconstruction of voltage measurements for a conductivity distribution image using an ordinary method, the absolute imaging approach, is impossible due to the traditional ignorance of modelling error. The modelling error comes from the inaccuracy of geometry and structure, which are unable to be known accurately in practice, and are usually large in head application of EIT. Difference imaging is an alternative approach which is able to reduce the size of this error, but it introduces other kinds of error. In this work, we demonstrate that in situations like head EIT, the nonlinear difference imaging approach can reconstruct difference conductivity effectively: the reduced modelling error and the new errors arising are able to be ignored, because they are much smaller than the original modelling error. The magnitude of conductivity change in the head-like situation is also investigated, and a selection scheme for the initial guess in the reconstruction process is also proposed.

Improving the forward solver for the complete electrode model in EIT using algebraic multigrid.

Image reconstruction in electrical impedance tomography is an ill-posed nonlinear inverse problem. Linearization techniques are widely used and require the repeated solution of a linear forward problem. To account correctly for the presence of electrodes and contact impedances, the so-called complete electrode model is applied. Implementing a standard finite element method for this particular forward problem yields a linear system that is symmetric and positive definite and solvable via the conjugate gradient method. However, preconditioners are essential for efficient convergence. Preconditioners based on incomplete factorization methods are commonly used but their performance depends on user-tuned parameters. To avoid this deficiency, we apply black-box algebraic multigrid, using standard commercial and freely available software. The suggested solution scheme dramatically reduces the time cost of solving the forward problem. Numerical results are presented using an anatomically detailed model of the human head.

Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography.

In this paper, we review some numerical techniques based on the linear Krylov subspace iteration that can be used for the efficient calculation of the forward and the inverse electrical impedance tomography problems. Exploring their computational advantages in solving large-scale systems of equations, we specifically address their implementation in reconstructing localized impedance changes occurring within the human brain. If the conductivity of the head tissues is assumed to be real, the pre-conditioned conjugate gradients (PCGs) algorithm can be used to calculate efficiently the approximate forward solution to a given error tolerance. The performance and the regularizing properties of the PCG iteration for solving ill-conditioned systems of equations (PCGNs) is then explored, and a suitable preconditioning matrix is suggested in order to enhance its convergence rate. For image reconstruction, the nonlinear inverse problem is considered. Based on the Gauss-Newton method for solving nonlinear problems we have developed two algorithms that implement the PCGN iteration to calculate the linear step solution. Using an anatomically detailed model of the human head and a specific scalp electrode arrangement, images of a simulated impedance change inside brain's white matter have been reconstructed.