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Time-Difference Electrical Impedance Tomography with a Blood Flow Model as Prior Information for Stroke Monitoring
Abstract
Continuous monitoring of brain hemodynamics is important to quickly detect changes in healthy cerebral blood flow, helping physician decision-making in the treatment of the patient. Resistivity changes in the brain happen as a result of the pulsatile characteristic of the blood in the arteries or pathological conditions such as ischemia. We developed a dynamic model of cerebral circulation capable of portraying variations in resistivities in arteries within a cardiac cycle. From the hypothesis that the resistivity changes in the brain can be detected by Electrical Impedance Tomography (EIT), we included this model as prior information in time-difference image reconstruction algorithm. With this prior information, image reconstruction of the brain with pre-existing ischemia was possible, showing that EIT is a potential technique for brain hemodynamic monitoring.KeywordsBlood flow modelElectrical impedance tomographyDifference imagingStroke
... Electrical impedance tomography (EIT) is a non-invasive and radiation-free imaging technique [1] which can create impedance images of the target area [2]. It has been used in numerous biomedical applications, such as lung-ventilation monitoring [3], [4], cardiac activities monitoring [5], breast cancer monitoring [6] [7], and cerebral blood flow monitoring [8]. In addition, neural EIT has been introduced recently [9] as the EIT technique becomes more advanced. ...
Objective. The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications. Approach. The atlas was constructed based on 3D magnetic resonance images (MRI) of 107 human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. T1w+T2w MRI images were used to segment the main structures of the head while angiography MRI was used to segment the main arteries. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier–Stokes equation in the main arteries and their vascular territories. Main results. High-resolution, multi-frequency and time-varying anatomical atlases of resistivity, conductivity and relative permittivity were created and evaluated using a forward problem solver for EIT. The atlas was successfully used to simulate electrical impedance tomography measurements indicating the necessity of signal-to-noise between 100 and 125 dB to identify vascular changes due to the cardiac cycle, corroborating previous studies. The source code of the atlas and solver are freely available to download. Significance. Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. Anatomical atlases are important tools for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g. machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers.
When a main artery of the brain occludes, a cellular response involving multiple cell types follows. Cells directly affected by the lack of glucose and oxygen in the neuronal core die by necrosis. In the periphery surrounding the ischemic core (the so-called penumbra) neurons, astrocytes, microglia, oligodendrocytes, pericytes, and endothelial cells react to detrimental factors such as excitotoxicity, oxidative stress, and inflammation in different ways. The fate of the neurons in this area is multifactorial, and communication between all the players is important for survival. This review focuses on the latest research relating to synaptic loss and the release of apoptotic bodies and other extracellular vesicles for cellular communication in stroke. We also point out possible treatment options related to increasing neuronal survival and regeneration in the penumbra.
Cerebral vasospasm is a prolonged but reversible narrowing of cerebral arteries beginning days after subarachnoid hemorrhage. Progression to cerebral ischemia is tied mostly to vasospasm severity, and its pathogenesis lies in artery encasement by blood clot, although the complex interactions between hematoma and surrounding structures are not fully understood. The delayed onset of vasospasm provides a potential opportunity for its prevention. It is disappointing that recent randomized, controlled trials did not demonstrate that the endothelin antagonist clazosentan, the cholesterol-lowering agent simvastatin, and the vasodilator magnesium sulfate improve patient outcome. Minimizing ischemia by avoiding inadequate blood volume and pressure, administering the calcium antagonist nimodipine, and intervention with balloon angioplasty, when necessary, constitutes current best management. Over the past two decades, our ability to manage vasospasm has led to a significant decline in patient morbidity and mortality from vasospasm, yet it still remains an important determinant of outcome after aneurysm rupture.
Electrical Impedance Tomography (EIT) is a recently developed imaging technique. Small insensible currents are injected into the body using electrodes. Measured voltages are used for reconstruction of images of the internal dielectric properties of the body. This imaging technique is portable, safe, rapid, inexpensive and has the potential to provide a new method for imaging in remote or acute situations, where other large scanners, such as MRI, are either impractical or unavailable. It has been in use in clinical research for about two decades but has not yet been adopted into routine clinical practice. One potentially powerful clinical application lies in its use for imaging acute stroke, where it could be used to distinguish haemorrhage from infarction. Hitherto, image reconstruction has mainly been for the more tractable case of changes in impedance over time. For acute stroke, it is best operated in multiple frequency mode, where data is collected at multiple frequencies and images can be recovered with higher fidelity. Whereas the eventual idea appears to be good, there are several important issues which affect the likelihood of its success in producing clinically reliable images. These include limitations in accuracy of finite element modelling, image reconstruction, and accuracy of recorded voltage data due to noise and confounding factors. The purpose of this work was to address these issues in the hope that, at the end, a clinical study of EIT in acute stroke would have a much greater chance of success. In order to address the feasibility of this application, a comprehensive literature review regarding the dielectric properties of human head tissues in normal and pathological states was conducted in this thesis. Novel generic tools were developed in order to enable modelling and non-linear image reconstruction of large-scale problems, such as those arising from the head EIT problem.
Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright © 2009 John Wiley & Sons, Ltd.
Cerebral hemodynamics and metabolism are frequently impaired in a wide range of neurological diseases, including traumatic brain injury and stroke, with several pathophysiological mechanisms of injury. The resultant uncoupling of cerebral blood flow and metabolism can trigger secondary brain lesions, particularly in early phases, consequently worsening the patient's outcome. Cerebral blood flow regulation is influenced by blood gas content, blood viscosity, body temperature, cardiac output, altitude, cerebrovascular autoregulation, and neurovascular coupling, mediated by chemical agents such as nitric oxide (NO), carbon monoxide (CO), eicosanoid products, oxygen-derived free radicals, endothelins, K+, H+, and adenosine. A better understanding of these factors is valuable for the management of neurocritical care patients. The assessment of both cerebral hemodynamics and metabolism in the acute phase of neurocritical care conditions may contribute to a more effective planning of therapeutic strategies for reducing secondary brain lesions. In this review, the authors have discussed concepts of cerebral hemodynamics, considering aspects of clinical importance.
This paper develops a mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography (ECCT). The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, 29.5 omega.cm were studied. Values of "effective" contact impedance zeta used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 omega.cm2, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an "effective" contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field.
MFEIT (multi-frequency electrical impedance tomography) could distinguish between ischaemic and haemorrhagic stroke and permit the urgent use of thrombolytic drugs in patients with ischaemic stroke. The purpose of this study was to characterize the UCLH Mk 2 MFEIT system, designed for this purpose, with 32 electrodes and a multiplexed 2 kHz to 1.6 MHz single impedance measuring circuit. Data were collected in seven subjects with brain tumours, arteriovenous malformations or chronic stroke, as these resembled the changes in haemorrhagic or ischaemic stroke. Calibration studies indicated that the reliable bandwidth was only 16-64 kHz because of front-end components placed to permit simultaneous EEG recording. In raw in-phase component data, the SD of 16-64 kHz data for one electrode combination across subjects was 2.45 +/- 0.9%, compared to a largest predicted change of 0.35% estimated using the FEM of the head. Using newly developed methods of examining the most sensitive channels from the FEM, and nonlinear imaging constrained to the known site of the lesion, no reproducible changes between pathologies were observed. This study has identified a specification for accuracy in EITS in acute stroke, identified the size of variability in relation to this in human recordings, and presents new methods for analysis of data. Although no reproducible changes were identified, we hope this will provide a foundation for future studies in this demanding but potentially powerful novel application.
Electrical Impedance Tomography (EIT) is a non-invasive image reconstruction technique, whereby current is injected by electrodes and electric potential is measured by electrodes. In some electronic hardware implementations, only two electrodes inject current simultaneously, and are denominated pair-wise current injection. Several possibilities of pair-wise current injection (electric current patterns) and electric potential measurement (single-ended and differential) have been addressed in the literature. Considering pair-wise current injection, the skip-m current pattern can be defined as a pair-wise injection strategy in which the number of non-current injecting electrodes enclosed between two injection electrodes is m. Single-ended electric potential measurements consist of measurements with a common potential reference. Differential electric potential measurements consist of pair-wise measurements between two electrodes. A theoretical analysis based on control theory is presented to show that some current and measurement pattern strategies convey less information than others. This hypothesis is verified by the analysis of the matrix containing possible measurement vectors, with respect to its rank, condition number and singular values. Additionally, a novel approach is proposed to analyse current and measurement patterns based on uncertainty estimation of difference images by the correlation matrix linearization of the reconstructed impedance matrix. The results show that single-ended potential measurements are usually better when compared to differential electric potential measurements. A conclusion supported by both points of view is that the cross current pattern (diametral) is the least informative for these symmetrical domains.
The article discusses the discretization of linear inverse problems. When an inverse problem is formulated in terms of infinite-dimensional function spaces and then discretized for computational purposes, a discretization error appears. Since inverse problems are typically ill-posed, neglecting this error may have serious consequences to the quality of the reconstruction. The Bayesian paradigm provides tools to estimate the statistics of the discretization error that is made part of the measurement and modelling errors of the estimation problem. This approach also provides tools to reduce the dimensionality of inverse problems in a controlled manner. The ideas are demonstrated with a computed example.
Electrical Impedance Tomography (EIT) is a non-invasive method that aims to create an electrical conductivity map of a volume. In particular, it can be applied to study the human head. The method consists on the injection of an unperceptive and known current through two electrodes attached to the scalp, and the measurement of the resulting electric potential distribution at an array of sensors also placed on the scalp. In this work, we propose a parametric estimation of the brain, scalp and skull conductivities using EIT over an spherical model of the head. The forward problem involves the computation of the electric potential on the surface, for given the conductivities and the injection electrode positions, while the inverse problem consists on estimating the conductivities given the sensor measurements. In this study, the analytical solution to the forward problem based on a three layer spherical model is first described. Then, some measurements are simulated adding white noise to the solutions and the inverse problem is solved in order to estimate the brain, skull and scalp conductivity relations. This is done with a least squares approach and the Nelder-Mead multidimensional unconstrained nonlinear minimization method.
An effective resistivity is defined for axisymmetric flow through a circular tube with a uniform electric field in the longitudinal direction. The resistivity of flowing blood is found to be a function of the shear rate profile. Under axisymmetric conditions shear rate profiles are a function of a single parameter: the reduced average velocity, which is the average velocity divided by the radius of the tube. The resistivity of human blood was investigated while the blood was in laminar flow in a circular tube with different constant flow rates. The relative change in resistivity in % is given by: -0.45.H.(1 - exp[-0.26.((v)/R)0.39]); where H is the packed cell volume in % and (v)/R is the reduced average velocity in s-1. In accelerating flow the resistivity change is synchronous with the change in flow rate, but in decelerating flow there is an exponential decay characterized by a relaxation time tau. For packed cell volumes of 36.4% and 47.5% tau was estimated to be 0.21 s, for a packed cell volume of 53.7% tau was estimated to be 0.29 s. The resistivity changes in elastic tubes are influenced by both velocity changes and changes in diameter, but in opposite directions.
A parametric model was developed to describe the variation of dielectric properties of tissues as a function of frequency. The experimental spectrum from 10 Hz to 100 GHz was modelled with four dispersion regions. The development of the model was based on recently acquired data, complemented by data surveyed from the literature. The purpose is to enable the prediction of dielectric data that are in line with those contained in the vast body of literature on the subject. The analysis was carried out on a Microsoft Excel spreadsheet. Parameters are given for 17 tissue types.
Malignancy provokes regional changes to vessel shape. Characteristic vessel tortuosity abnormalities appear early during tumor development, affect initially healthy vessels, spread beyond the confines of tumor margins, and do not simply mirror tissue perfusion. The ability to detect and quantify tortuosity abnormalities on high-resolution magnetic resonance angiography (MRA) images offers a new approach to the noninvasive diagnosis of malignancy. This report evaluates a computerized, statistical method of analyzing the shapes of vessels extracted from MRA in diagnosing cancer.
The regional vasculature of 34 healthy subjects was compared with the tumor-associated vasculature of 30 brain tumors before surgical resection. The operator performing the analysis was blinded to the diagnosis. Vessels were segmented from an MRA of each subject, a region of interest was defined in each tumor patient and was mapped to all healthy controls, and a statistical analysis of vessel shape measures was then performed over the region of interest. Many difficult cases were included, such as pinpoint, hemorrhagic, and irradiated tumors, as were hypervascular benign tumors. Tumors were identified as benign or malignant on the basis of histological evaluation.
A discriminant analysis performed at the study's conclusion successfully classified all but one of the 30 tumors as benign or malignant on the basis of vessel tortuosity.
Quantitative, statistical measures of vessel shape offer a new approach to the diagnosis and staging of disease. Although the methods developed under the current report must be tested against a new series of cases, initial results are promising.
Blood flow in the circle of Willis (CoW) is modelled using the 1-D equations of pressure and flow wave propagation in compliant vessels. The model starts at the left ventricle and includes the largest arteries that supply the CoW. Based on published physiological data, it is able to capture the main features of pulse wave propagation along the aorta, at the brachiocephalic bifurcation and throughout the cerebral arteries. The collateral ability of the complete CoW and its most frequent anatomical variations is studied in normal conditions and after occlusion of a carotid or vertebral artery (VA). Our results suggest that the system does not require collateral pathways through the communicating arteries to adequately perfuse the brain of normal subjects. The communicating arteries become important in cases of missing or occluded vessels, the anterior communicating artery (ACoA) being a more critical collateral pathway than the posterior communicating arteries (PCoAs) if an internal carotid artery (ICA) is occluded. Occlusions of the VAs proved to be far less critical than occlusions of the ICAs. The worst scenario in terms of reduction in the mean cerebral outflows is a CoW without the first segment of an anterior cerebral artery combined with an occlusion of the contralateral ICA. Furthermore, in patients without any severe occlusion of a carotid or VA, the direction of flow measured at the communicating arteries corresponds to the side of the CoW with an absent or occluded artery. Finally, we study the effect of partial occlusions of the communicating arteries on the cerebral flows, which again confirms that the ACoA is a more important collateral pathway than the PCoAs if an ICA is occluded.
Non-invasive hemodynamic monitoring by electrical impedance tomography
- M Proença
Desenvolvimento de um modelo dinâmico da circulação cerebral para tomografia por impedância elétrica. Master’s thesis
- R G Beraldo
Influence of current injection pattern and electric potential measurement strategies in electrical impedance tomography
- O L Silva
- R G Lima
- T C Martins
- OL Silva
Gaussian process emulators for 1D vascular models
- A Melis