Simulation-based feasibility study of monitoring of intracerebral hemorrhages and detection of secondary hemorrhages using electrical impedance tomography.

Purpose: We present a simulation-based feasibility study of electrical impedance tomography (EIT) for continuous bedside monitoring of intracerebral hemorrhages (ICH) and detection of secondary hemorrhages. Approach: We simulated EIT measurements for six different hemorrhage sizes at two different hemorrhage locations using an anatomically detailed computational head model. Using this dataset, we test the ICH monitoring and detection performance of our tailor-made, patient-specific stroke-monitoring algorithm that utilizes a novel combination of nonlinear region-of-interest difference imaging, parallel level sets regularization and a prior-conditioned least squares algorithm. We compare the results of our algorithm to the results of two reference algorithms, a total variation regularized absolute imaging algorithm and a linear difference imaging algorithm. Results: The tailor-made stroke-monitoring algorithm is capable of indicating smaller changes in the simulated hemorrhages than either of the reference algorithms, indicating better monitoring and detection performance. Conclusions: Our simulation results from the anatomically detailed head model indicate that EIT equipped with a patient-specific stroke-monitoring algorithm is a promising technology for the unmet clinical need of having a technology for continuous bedside monitoring of brain status of acute stroke patients.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models.

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T1 relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T1 maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object.

Dual-Modal Electrical Imaging of Two-Phase Flow-Experimental Evaluation of the State Estimation Approach.

Accurate measurement of two-phase flow quantities is essential for managing production in many industries. However, the inherent complexity of two-phase flow often makes estimating these quantities difficult, necessitating the development of reliable techniques for quantifying two-phase flow. In this paper, we investigated the feasibility of using state estimation for dynamic image reconstruction in dual-modal tomography of two-phase oil-water flow. We utilized electromagnetic flow tomography (EMFT) to estimate velocity fields and electrical tomography (ET) to determine phase fraction distributions. In state estimation, the contribution of the velocity field to the temporal evolution of the phase fraction distribution was accounted for by approximating the process with a convection-diffusion model. The extended Kalman filter (EKF) and fixed-interval Kalman smoother (FIKS) were used to reconstruct the temporally evolving velocity and phase fraction distributions, which were further used to estimate the volumetric flow rates of the phases. Experimental results on a laboratory setup showed that the FIKS approach outperformed the conventional stationary reconstructions, with the average relative errors of the volumetric flow rates of oil and water being less than 4%. The FIKS approach also provided feasible uncertainty estimates for the velocity, phase fraction, and volumetric flow rate of the phases, enhancing the reliability of the state estimation approach.

Embedded Quantitative MRI T1ρ Mapping Using Non-Linear Primal-Dual Proximal Splitting.

Quantitative MRI (qMRI) methods allow reducing the subjectivity of clinical MRI by providing numerical values on which diagnostic assessment or predictions of tissue properties can be based. However, qMRI measurements typically take more time than anatomical imaging due to requiring multiple measurements with varying contrasts for, e.g., relaxation time mapping. To reduce the scanning time, undersampled data may be combined with compressed sensing (CS) reconstruction techniques. Typical CS reconstructions first reconstruct a complex-valued set of images corresponding to the varying contrasts, followed by a non-linear signal model fit to obtain the parameter maps. We propose a direct, embedded reconstruction method for T1ρ mapping. The proposed method capitalizes on a known signal model to directly reconstruct the desired parameter map using a non-linear optimization model. The proposed reconstruction method also allows directly regularizing the parameter map of interest and greatly reduces the number of unknowns in the reconstruction, which are key factors in the performance of the reconstruction method. We test the proposed model using simulated radially sampled data from a 2D phantom and 2D cartesian ex vivo measurements of a mouse kidney specimen. We compare the embedded reconstruction model to two CS reconstruction models and in the cartesian test case also the direct inverse fast Fourier transform. The T1ρ RMSE of the embedded reconstructions was reduced by 37-76% compared to the CS reconstructions when using undersampled simulated data with the reduction growing with larger acceleration factors. The proposed, embedded model outperformed the reference methods on the experimental test case as well, especially providing robustness with higher acceleration factors.

Corrections to "Sensitivity Analysis Highlights the Importance of Accurate Head Models for Electrical Impedance Tomography Monitoring of Intracerebral Hemorrhagic Stroke".

In the above paper [1] there are two errors which we correct here. An important reference was omitted.

Sensitivity Analysis Highlights the Importance of Accurate Head Models for Electrical Impedance Tomography Monitoring of Intracerebral Hemorrhagic Stroke.

OBJECTIVE: Electrical impedance tomography (EIT) has been proposed as a novel tool for diagnosing stroke. However, so far, the clinical feasibility is unresolved. In this study, we aim to investigate the need for accurate head modeling in EIT and how the inhomogeneities of the head contribute to the EIT measurement and affect its feasibility in monitoring the progression of a hemorrhagic stroke. METHODS: We compared anatomically detailed six- and three-layer finite element models of a human head and computed the resulting scalp electrode potentials and the lead fields of selected electrode configurations. We visualized the resulting EIT measurement sensitivity distributions, computed the scalp electrode potentials, and examined the inverse imaging with selected cases. The effect of accurate tissue geometry and conductivity values on the EIT measurement is assessed with multiple different hemorrhagic perturbation locations and sizes. RESULTS: Our results show that accurate tissue geometries and conductivity values inside the cranial cavity, especially the highly conductive cerebrospinal fluid, significantly affect EIT measurement sensitivity distribution and measured potentials. CONCLUSIONS: We can conclude that the three-layer head models commonly used in EIT literature cannot depict the current paths correctly in the head. Thus, our study highlights the need to consider the detailed geometry of the cerebrospinal fluid (CSF) in EIT. SIGNIFICANCE: The results clearly show that the CSF should be considered in the head EIT calculations.

Data-Driven Regularization Parameter Selection in Dynamic MRI.

In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One problem in CS approaches is determining the regularization parameters, which control the balance between data fidelity and regularization. We propose a data-driven approach for the total variation regularization parameter selection, where reconstructions yield expected sparsity levels in the regularization domains. The expected sparsity levels are obtained from the measurement data for temporal regularization and from a reference image for spatial regularization. Two formulations are proposed. Simultaneous search for a parameter pair yielding expected sparsity in both domains (S-surface), and a sequential parameter selection using the S-curve method (Sequential S-curve). The approaches are evaluated using simulated and experimental DCE-MRI. In the simulated test case, both methods produce a parameter pair and reconstruction that is close to the root mean square error (RMSE) optimal pair and reconstruction. In the experimental test case, the methods produce almost equal parameter selection, and the reconstructions are of high perceived quality. Both methods lead to a highly feasible selection of the regularization parameters in both test cases while the sequential method is computationally more efficient.

Quantitative susceptibility mapping of articular cartilage: Ex vivo findings at multiple orientations and following different degradation treatments.

PURPOSE: We investigated the feasibility of quantitative susceptibility mapping (QSM) for assessing degradation of articular cartilage by measuring ex vivo bovine cartilage samples subjected to different degradative treatments. Specimens were scanned at several orientations to study if degradation affects the susceptibility anisotropy. T2*-mapping, histological stainings, and polarized light microscopy were used as reference methods. Additionally, simulations of susceptibility in layered geometry were performed. METHODS: Samples (n = 9) were harvested from the patellae of skeletally mature bovines. Three specimens served as controls, and the rest were artificially degraded. MRI was performed at 9.4T using a 3D gradient echo sequence. QSM and T2* images and depth profiles through the centers of the samples were compared with each other and the histological findings. A planar isotropic model with depth-wise susceptibility variation was used in the simulations. RESULTS: A strong diamagnetic contrast was seen in the deep and calcified layers of cartilage, while T2* maps reflected the typical trilaminar structure of the collagen network. Anisotropy of susceptibility in cartilage was observed and was found to differ from the T2* anisotropy. Slight changes were observed in QSM and T2* following the degradative treatments. In simulations, anisotropy was observed. CONCLUSIONS: The results suggest that QSM is not sensitive to cartilage proteoglycan content, but shows sensitivity to the amount of calcification and to the integrity of the collagen network, providing potential for assessing osteoarthritis. The simulations suggested that the anisotropy of susceptibility might be partially explained by the layered geometry of susceptibility in cartilage.

PET Reconstruction With an Anatomical MRI Prior Using Parallel Level Sets.

The combination of positron emission tomography (PET) and magnetic resonance imaging (MRI) offers unique possibilities. In this paper we aim to exploit the high spatial resolution of MRI to enhance the reconstruction of simultaneously acquired PET data. We propose a new prior to incorporate structural side information into a maximum a posteriori reconstruction. The new prior combines the strengths of previously proposed priors for the same problem: it is very efficient in guiding the reconstruction at edges available from the side information and it reduces locally to edge-preserving total variation in the degenerate case when no structural information is available. In addition, this prior is segmentation-free, convex and no a priori assumptions are made on the correlation of edge directions of the PET and MRI images. We present results for a simulated brain phantom and for real data acquired by the Siemens Biograph mMR for a hardware phantom and a clinical scan. The results from simulations show that the new prior has a better trade-off between enhancing common anatomical boundaries and preserving unique features than several other priors. Moreover, it has a better mean absolute bias-to-mean standard deviation trade-off and yields reconstructions with superior relative l2-error and structural similarity index. These findings are underpinned by the real data results from a hardware phantom and a clinical patient confirming that the new prior is capable of promoting well-defined anatomical boundaries.

Nonlinear Difference Imaging Approach to Three-Dimensional Electrical Impedance Tomography in the Presence of Geometric Modeling Errors.

OBJECTIVE: To evaluate the recently proposed nonlinear difference imaging approach to electrical impedance tomography (EIT) in realistic 3-D geometries. METHODS: In this paper, the feasibility of nonlinear difference approach-based EIT is tested using simulation studies in 3-D geometries of thorax and larynx, and with an experimental study of a thorax-shaped water tank. All test cases exhibit severe modeling errors due to uncertainty in the boundary shape of the body. RESULTS: In all test cases, the conductivity change reconstructed with nonlinear difference imaging outperforms the conventional reconstructions qualitatively and quantitatively. CONCLUSION: The results demonstrate that the nonlinear difference reconstructions tolerate geometrical modeling errors at least to the same extent as the conventional linear approach and produce quantitatively more accurate information on the conductivity change. SIGNIFICANCE: Physiological processes that produce changes in the electrical conductivity of the body can be monitored with difference imaging based on EIT. The wide popularity of linearized difference imaging in EIT is mainly based on its good tolerance for the ubiquitous modeling errors, which are predominantly caused by inexact knowledge of the body geometry. However, the linearized difference imaging produces only qualitative information on the conductivity change, and the feasibility of the estimates also depends on the selection of the linearization point which ideally should be equal to the conductivity of the initial state. Based on the findings of this paper, these problems can be avoided by nonlinear difference imaging, and potentially the approach can enable quantitative imaging of conductivity change in medical applications.

Nonlinear approach to difference imaging in diffuse optical tomography.

Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.

Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography.

Diffuse optical tomography is a highly unstable problem with respect to modeling and measurement errors. During clinical measurements, the body shape is not always known, and an approximate model domain has to be employed. The use of an incorrect model domain can, however, lead to significant artifacts in the reconstructed images. Recently, the Bayesian approximation error theory has been proposed to handle model-based errors. In this work, the feasibility of the Bayesian approximation error approach to compensate for modeling errors due to unknown body shape is investigated. The approach is tested with simulations. The results show that the Bayesian approximation error method can be used to reduce artifacts in reconstructed images due to unknown domain shape.

Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach.

Diffuse optical tomography is highly sensitive to measurement and modeling errors. Errors in the source and detector coupling and positions can cause significant artifacts in the reconstructed images. Recently the approximation error theory has been proposed to handle modeling errors. In this article, we investigate the feasibility of the approximation error approach to compensate for modeling errors due to inaccurately known optode locations and coupling coefficients. The approach is evaluated with simulations. The results show that the approximation error method can be used to recover from artifacts in reconstructed images due to optode coupling and position errors.

Approximation error method can reduce artifacts due to scalp blood flow in optical brain activation imaging.

Diffuse optical tomography can image the hemodynamic response to an activation in the human brain by measuring changes in optical absorption of near-infrared light. Since optodes placed on the scalp are used, the measurements are very sensitive to changes in optical attenuation in the scalp, making optical brain activation imaging susceptible to artifacts due to effects of systemic circulation and local circulation of the scalp. We propose to use the Bayesian approximation error approach to reduce these artifacts. The feasibility of the approach is evaluated using simulated brain activations. When a localized cortical activation occurs simultaneously with changes in the scalp blood flow, these changes can mask the cortical activity causing spurious artifacts. We show that the proposed approach is able to recover from these artifacts even when the nominal tissue properties are not well known.

Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information.

Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term.

Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography.

Electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors. This instability is especially severe when absolute imaging is considered. With clinical measurements, accurate knowledge about the body shape is usually not available, and therefore an approximate model domain has to be used in the computational model. It has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect. In this paper, we adapt the so-called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape. This approach has previously been shown to be applicable to a variety of modeling errors, such as coarse discretization in the numerical approximation of the forward model and domain truncation. We evaluate the approach with a simulated example of thorax imaging, and also with experimental data from a laboratory setting, with absolute imaging considered in both cases. We show that the related modeling errors can be efficiently compensated for by the approximation error approach. We also show that recovery from simultaneous discretization related errors is feasible, allowing the use of computationally efficient reduced order models.

Corrections to linear methods for diffuse optical tomography using approximation error modelling.

Linear reconstruction methods in diffuse optical tomography have been found to produce reasonable good images in cases in which the variation in optical properties within the medium is relatively small and a reference measurement with known background optical properties is available. In this paper we examine the correction of errors when using a first order Born approximation with an infinite space Green's function model as the basis for linear reconstruction in diffuse optical tomography, when real data is generated on a finite domain with possibly unknown background optical properties. We consider the relationship between conventional reference measurement correction and approximation error modelling in reconstruction. It is shown that, using the approximation error modelling, linear reconstruction method can be used to produce good quality images also in situations in which the background optical properties are not known and a reference is not available.

Approximation errors and model reduction in three-dimensional diffuse optical tomography.

Model reduction is often required in diffuse optical tomography (DOT), typically because of limited available computation time or computer memory. In practice, this means that one is bound to use coarse mesh and truncated computation domain in the model for the forward problem. We apply the (Bayesian) approximation error model for the compensation of modeling errors caused by domain truncation and a coarse computation mesh in DOT. The approach is tested with a three-dimensional example using experimental data. The results show that when the approximation error model is employed, it is possible to use mesh densities and computation domains that would be unacceptable with a conventional measurement error model.

3D shape based reconstruction of experimental data in Diffuse Optical Tomography.

Diffuse optical tomography (DOT) aims at recovering three-dimensional images of absorption and scattering parameters inside diffusive body based on small number of transmission measurements at the boundary of the body. This image reconstruction problem is known to be an ill-posed inverse problem, which requires use of prior information for successful reconstruction. We present a shape based method for DOT, where we assume a priori that the unknown body consist of disjoint subdomains with different optical properties. We utilize spherical harmonics expansion to parameterize the reconstruction problem with respect to the subdomain boundaries, and introduce a finite element (FEM) based algorithm that uses a novel 3D mesh subdivision technique to describe the mapping from spherical harmonics coefficients to the 3D absorption and scattering distributions inside a unstructured volumetric FEM mesh. We evaluate the shape based method by reconstructing experimental DOT data, from a cylindrical phantom with one inclusion with high absorption and one with high scattering. The reconstruction was monitored, and we found a 87% reduction in the Hausdorff measure between targets and reconstructed inclusions, 96% success in recovering the location of the centers of the inclusions and 87% success in average in the recovery for the volumes.

Electrical impedance tomography problem with inaccurately known boundary and contact impedances.

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmUller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.