Calderón's method on an elliptical domain

Calderón's Method with a Spatial Prior for 2-D EIT Imaging of Ventilation and Perfusion

Bedside imaging of ventilation and perfusion is a leading application of 2-D medical electrical impedance tomography (EIT), in which dynamic cross-sectional images of the torso are created by numerically solving the inverse problem of computing the conductivity from voltage measurements arising on electrodes due to currents applied on electrodes on the surface. Methods of reconstruction may be direct or iterative. Calderón’s method is a direct reconstruction method based on complex geometrical optics solutions to Laplace’s equation capable of providing real-time reconstructions in a region of interest. In this paper, the importance of accurate modeling of the electrode location on the body is demonstrated on simulated and experimental data, and a method of including a priori spatial information in dynamic human subject data is presented. The results of accurate electrode modeling and a spatial prior are shown to improve detection of inhomogeneities not included in the prior and to improve the resolution of ventilation and perfusion images in a human subject.

A Three Dimensional Calderon-Based Method for EIT on the Cylindrical Geometry

OBJECTIVE

Electrical impedance tomography (EIT) is an imaging modality in which voltage data arising from currents applied on the boundary are used to reconstruct the conductivity distribution in the interior. This paper provides a novel direct (noniterative) 3-D reconstruction algorithm for EIT in the cylindrical geometry.

METHODS

The algorithm is based on Calderón's method [Calderón, 1980], and is implemented for data collected on two or four rows of electrodes on the boundary of a cylinder.

RESULTS

The effectiveness of the method to localize inhomogeneities in the plane of the electrodes and in the z-direction is demonstrated on simulated and experimental data.

CONCLUSIONS AND SIGNIFICANCE

The results from simulated and experimental data show that the method is effective for distinguishing in-plane and nearby out-of-plane inhomogeneities with good spatial resolution in the vertical z direction with computational efficiency.

A DIRECT RECONSTRUCTION ALGORITHM FOR THE ANISOTROPIC INVERSE CONDUCTIVITY PROBLEM BASED ON CALDERÓN'S METHOD IN THE PLANE

A direct reconstruction algorithm based on Calderón's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.

A second order Calderón's method with a correction term and a priori information

Calderón's method is a direct linearized reconstruction method for the inverse conductivity problem with the attribute that it can provide absolute images of both conductivity and permittivity with no need for forward modeling. In this work, an explicit relationship between Calderón's method and the D-bar method is provided, facilitating a "higher-order" Calderón's method in which a correction term is included, derived from the relationship to the D-bar method. Furthermore, a method of including a spatial prior is provided. These advances are demonstrated on simulated data and on tank data collected with the ACE1 EIT system.

Real-Time Implementation of Calderón's Method on Subject-Specific Domains

A real-time implementation of Calderón's method for the reconstruction of a 2-D conductivity from electrical impedance tomography data is presented, in which domain-specific modeling is taken into account. This is the first implementation of Calderón's method that accounts for correct modeling of non-symmetric domain boundaries in image reconstruction. The domain-specific Calderón's method is derived and reconstructions from experimental tank data are presented, quantifying the distortion when correct modeling is not included in the reconstruction algorithm. Reconstructions from human subject volunteers are presented, demonstrating the method's effectiveness for imaging changes due to ventilation and perfusion in the human thorax.

EIT Imaging of admittivities with a D-bar method and spatial prior: experimental results for absolute and difference imaging

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a noise-robust regularized image reconstruction method. In this work, the a priori D-bar method for complex admittivities is demonstrated effective on experimental tank data for absolute imaging for the first time. Additionally, the method is adjusted for, and tested on, time-difference imaging scenarios. The ability of the method to be used for conductivity, permittivity, absolute as well as time-difference imaging provides the user with great flexibility without a high computational cost.

Electrical impedance tomography imaging of the cardiopulmonary system

PURPOSE OF REVIEW

This review article summarizes the recent advances in electrical impedance tomography (EIT) related to cardiopulmonary imaging and monitoring on the background of the 30-year development of this technology.

RECENT FINDINGS

EIT is expected to become a bedside tool for monitoring and guiding ventilator therapy. In this context, several studies applied EIT to determine spatial ventilation distribution during different ventilation modes and settings. EIT was increasingly combined with other signals, such as airway pressure, enabling the assessment of regional respiratory system mechanics. EIT was for the first time used prospectively to define ventilator settings in an experimental and a clinical study. Increased neonatal and paediatric use of EIT was noted. Only few studies focused on cardiac function and lung perfusion. Advanced radiological imaging techniques were applied to assess EIT performance in detecting regional lung ventilation. New approaches to improve the quality of thoracic EIT images were proposed.

SUMMARY

EIT is not routinely used in a clinical setting, but the interest in EIT is evident. The major task for EIT research is to provide the clinicians with guidelines how to conduct, analyse and interpret EIT examinations and combine them with other medical techniques so as to meaningfully impact the clinical decision-making.