Some novel approaches in modelling and image reconstruction for multi-frequency Electrical Impedance Tomography of the human brain

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.

[1]  D. Anderson,et al.  Algorithms for minimization without derivatives , 1974 .

[2]  Ninds,et al.  Effect of Intravenous Recombinant Tissue Plasminogen Activator on Ischemic Stroke Lesion Size Measured by Computed Tomography , 2000, Stroke.

[3]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[4]  M Adamczyk,et al.  Development of a quantitative vancomycin immunoassay for the Abbott AxSYM analyzer. , 1998, Therapeutic drug monitoring.

[5]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[6]  J C Newell,et al.  Imaging cardiac activity by the D-bar method for electrical impedance tomography , 2006, Physiological measurement.

[7]  W. R. Adey,et al.  Measurement of electrical impedance in the human brain , 1964, Neurology.

[8]  S. Saha,et al.  Electrical and Dielectric Properties of Wet Bone as a Function of Frequency , 1984, IEEE Transactions on Biomedical Engineering.

[9]  O. Gandhi Some numerical methods for dosimetry: Extremely low frequencies to microwave frequencies , 1995 .

[10]  Stanley Rush,et al.  Methods of measuring the resistivities of anisotropic conducting media in situ , 1962 .

[11]  Dieter Haemmerich,et al.  In vivo electrical conductivity of hepatic tumours. , 2003, Physiological measurement.

[12]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[13]  E. J. Woo,et al.  Skin impedance measurements using simple and compound electrodes , 2006, Medical and Biological Engineering and Computing.

[14]  R A Harper,et al.  Dielectric properties of fluid-saturated bone. , 1980, IEEE transactions on bio-medical engineering.

[15]  D. Isaacson,et al.  A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays , 1999, IEEE Transactions on Biomedical Engineering.

[16]  Kenneth Levenberg A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[17]  David Isaacson,et al.  Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography , 2004, IEEE Transactions on Medical Imaging.

[18]  R. W. Lau,et al.  The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. , 1996, Physics in medicine and biology.

[19]  R Bragós,et al.  In Vivo and In Situ Ischemic Tissue Characterization Using Electrical Impedance Spectroscopy a , 1999, Annals of the New York Academy of Sciences.

[20]  John G. Webster,et al.  An Impedance Camera for Spatially Specific Measurements of the Thorax , 1978, IEEE Transactions on Biomedical Engineering.

[21]  A Tizzard,et al.  Beyond the linear domain-The way forward in MFEIT image reconstruction of the human head , 2004 .

[22]  Jari P. Kaipio,et al.  Simultaneous reconstruction of electrode contact impedances and internal electrical properties: I. Theory , 2002 .

[23]  I. Imam,et al.  Primary brain tumours , 2021, 700 Essential Neurology Checklists.

[24]  B M Eyüboğlu An interleaved drive electrical impedance tomography image reconstruction algorithm. , 1996, Physiological measurement.

[25]  T Brott,et al.  Greater Cincinnati/Northern Kentucky Stroke Study: Volume of First-Ever Ischemic Stroke Among Blacks in a Population-Based Study , 2001, Stroke.

[26]  Simon R. Arridge,et al.  Novel Large-Scale 3D Electrical Impedance Tomography Modeling of the Human Head , 2007 .

[27]  I Frerichs,et al.  Electrical impedance tomography (EIT) in applications related to lung and ventilation: a review of experimental and clinical activities. , 2000, Physiological measurement.

[28]  Francis X. Hart,et al.  The dielectric properties of meat , 1994 .

[29]  J.P. Kaipio,et al.  Three-dimensional electrical impedance tomography based on the complete electrode model , 1999, IEEE Transactions on Biomedical Engineering.

[30]  R. Rosenthal,et al.  Measurement of the electric resistance of human blood; use in coagulation studies and cell volume determinations. , 1948, The Journal of laboratory and clinical medicine.

[31]  M. Schweiger,et al.  Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography. , 2003, Optics letters.

[32]  K. Foster,et al.  Anisotropy in the dielectric properties of skeletal muscle , 2006, Medical and Biological Engineering and Computing.

[33]  J. Engel Update on surgical treatment of the epilepsies , 1993, Neurology.

[34]  A.C. van Huffelen,et al.  Measurement of the conductivity of the skull, temporarily removed during epilepsy surgery , 2001 .

[35]  Yousef Saad,et al.  On the Relations between ILUs and Factored Approximate Inverses , 2002, SIAM J. Matrix Anal. Appl..

[36]  S. Arridge Optical tomography in medical imaging , 1999 .

[37]  D C Barber,et al.  Problems of cardiac output determination from electrical impedance tomography scans. , 1988, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[38]  David A. Boas,et al.  Robust inference of baseline optical properties of the human head with 3 D segmentation from magnetic resonance imaging , 2022 .

[39]  Gerald S. Russell,et al.  Geodesic photogrammetry for localizing sensor positions in dense-array EEG , 2005, Clinical Neurophysiology.

[40]  K. Boone,et al.  Effect of skin impedance on image quality and variability in electrical impedance tomography: a model study , 1996, Medical and Biological Engineering and Computing.

[41]  David R. Wozny,et al.  The electrical conductivity of human cerebrospinal fluid at body temperature , 1997, IEEE Transactions on Biomedical Engineering.

[42]  S. Saha,et al.  Electric and dielectric properties of wet human cortical bone as a function of frequency , 1992, IEEE Transactions on Biomedical Engineering.

[43]  J. Nocedal Updating Quasi-Newton Matrices With Limited Storage , 1980 .

[44]  Adam David Liston,et al.  Models and image: reconstruction in electrical impedance tomography of human brain function , 2003 .

[45]  D C Barber,et al.  Three-dimensional image reconstruction for electrical impedance tomography. , 1996, Physiological measurement.

[46]  D. A. Driscoll,et al.  Current Distribution in the Brain From Surface Electrodes , 1968, Anesthesia and analgesia.

[47]  C. Vogel Non-convergence of the L-curve regularization parameter selection method , 1996 .

[48]  C. Gabriel Dielectric properties of biological tissue: Variation with age , 2005, Bioelectromagnetics.

[49]  S R Arridge,et al.  Simultaneous reconstruction of internal tissue region boundaries and coefficients in optical diffusion tomography , 2000, Physics in medicine and biology.

[50]  R H Bayford,et al.  A comparison of headnet electrode arrays for electrical impedance tomography of the human head. , 2003, Physiological measurement.

[51]  A. Surowiec,et al.  Radiofrequency dielectric properties of animal tissues as a function of time following death. , 1985, Physics in medicine and biology.

[52]  J. Newell,et al.  Assessment of acute pulmonary edema in dogs by electrical impedance imaging , 1996, IEEE Transactions on Biomedical Engineering.

[53]  H Griffiths,et al.  Systematic errors in multi-frequency EIT. , 2000, Physiological measurement.

[54]  Eric F Darve,et al.  A fast multipole method for Maxwell equations stable at all frequencies , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[55]  Jari P. Kaipio,et al.  Electrical impedance tomography with basis constraints , 1997 .

[56]  W. R. Adey,et al.  Impedance measurements in brain tissue of animals using microvolt singals. , 1962, Experimental neurology.

[57]  W. Landau,et al.  Some relations between resistivity and electrical activity in the cerebral cortex of the cat. , 1955, Journal of cellular and comparative physiology.

[58]  R H Bayford,et al.  The effect of layers in imaging brain function using electrical impedance tomograghy. , 2004, Physiological measurement.

[59]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[60]  Martin Schweiger,et al.  MULTILEVEL PRECONDITIONING FOR 3D LARGE-SCALE SOFT-FIELD MEDICAL APPLICATIONS MODELLING , 2006 .

[61]  V. K. Jindal,et al.  Impedance of goat eye lens at different DC voltages , 1998, Medical and Biological Engineering and Computing.

[62]  Dr D. Jennings,et al.  Front-end architecture for a multifrequency electrical impedance tomography system , 2006, Medical and Biological Engineering and Computing.

[63]  K. Foster,et al.  Dielectric properties of tissues and biological materials: a critical review. , 1989, Critical reviews in biomedical engineering.

[64]  朱善安,et al.  Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study , 2005 .

[65]  B. Blad,et al.  Impedance spectra of tumour tissue in comparison with normal tissue; a possible clinical application for electrical impedance tomography. , 1996, Physiological measurement.

[66]  A Irimajiri,et al.  [Dielectric measurements on the rabbit cornea using a surface electrode]. , 1993, Nippon Ganka Gakkai zasshi.

[67]  Marko Vauhkonen,et al.  Electrical impedance tomography and prior information , 1997 .

[68]  Wolfgang Fichtner,et al.  Efficient Sparse LU Factorization with Left-Right Looking Strategy on Shared Memory Multiprocessors , 2000 .

[69]  W. Koroshetz,et al.  Infarct volume as a surrogate or auxiliary outcome measure in ischemic stroke clinical trials. The RANTTAS Investigators. , 1999, Stroke.

[70]  A. Calderón,et al.  On an inverse boundary value problem , 2006 .

[71]  Thom F. Oostendorp,et al.  The conductivity of the human skull: results of in vivo and in vitro measurements , 2000, IEEE Transactions on Biomedical Engineering.

[72]  Matthias Dümpelmann,et al.  Influence of realistic skull and white matter anisotropy on the inverse problem in EEG/MEG-source localization , 2002 .

[73]  J B Ranck,et al.  Electrical impedance in the subicular area of rats during paradoxical sleep. , 1966, Experimental neurology.

[74]  K. L. Boon,et al.  Electrical conductivity of skeletal muscle tissue: Experimental results from different musclesin vivo , 1984, Medical and Biological Engineering and Computing.

[75]  Keith D Paulsen,et al.  Multi-frequency electrical impedance tomography of the breast: new clinical results , 2004, Physiological measurement.

[76]  Jonathan Richard Shewchuk,et al.  What is a Good Linear Element? Interpolation, Conditioning, and Quality Measures , 2002, IMR.

[77]  S. R. Smith,et al.  Dielectric properties of low-water-content tissues , 1985 .

[78]  G L Kongable,et al.  Innovations in Aneurysmal Subarachnoid Hemorrhage: Intracisternal t‐PA for the Prevention of Vasospasm , 1996, The Journal of neuroscience nursing : journal of the American Association of Neuroscience Nurses.

[79]  J P Morucci,et al.  A direct sensitivity matrix approach for fast reconstruction in electrical impedance tomography. , 1994, Physiological measurement.

[80]  Rudolf Höber,et al.  Messungen der inneren Leitfähigkeit von Zellen , 1913, Pflüger's Archiv für die gesamte Physiologie des Menschen und der Tiere.

[81]  D C Barber,et al.  The effect of the skull of low-birthweight neonates on applied potential tomography imaging of centralised resistivity changes. , 1988, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[82]  J. Ripoll,et al.  Diffuse photon propagation in multilayered geometries , 2006, Physics in medicine and biology.

[83]  H. P. Schwan,et al.  Electrical properties of blood and its constitutents: Alternating current spectroscopy , 1983, Blut: Zeitschrift für die Gesamte Blutforschung.

[84]  Eva Syková,et al.  Diffusion parameters of the extracellular space in human gliomas , 2003, Glia.

[85]  Xavier Tricoche,et al.  Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: A simulation and visualization study using high-resolution finite element modeling , 2006, NeuroImage.

[86]  B. Brown,et al.  Applied potential tomography: possible clinical applications. , 1985, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[87]  R H Bayford,et al.  Validation of a 3D reconstruction algorithm for EIT of human brain function in a realistic head-shaped tank. , 2001, Physiological measurement.

[88]  M N SHALIT THE EFFECT OF METRAZOL ON THE HEMODYNAMICS AND IMPEDANCE OF THE CAT'S BRAIN CORTEX. , 1965, Journal of neuropathology and experimental neurology.

[89]  P J Riu,et al.  A broadband system for multifrequency static imaging in electrical impedance tomography. , 1992, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[90]  Xuetao Shi,et al.  [In vivo measurement of rabbits brain impedance frequency response and the elementary imaging of EIT]. , 2003, Sheng wu yi xue gong cheng xue za zhi = Journal of biomedical engineering = Shengwu yixue gongchengxue zazhi.

[91]  B. Brown,et al.  Recent Developments in Applied Potential Tomography-APT , 1986 .

[92]  A. Surowiec,et al.  Postmortem changes of the dielectric properties of bovine brain tissues at low radiofrequencies. , 1986, Bioelectromagnetics.

[93]  T. X. Zhao,et al.  Electrical impedance and haematocrit of human blood with various anticoagulants. , 1993, Physiological measurement.

[94]  M Nadi,et al.  Dielectric properties of blood: an investigation of haematocrit dependence. , 2003, Physiological measurement.

[95]  J P Kaipio,et al.  Effects of local skull inhomogeneities on EEG source estimation. , 1999, Medical engineering & physics.

[96]  P D Lyden,et al.  A Rapid, Reliable, and Valid Method for Measuring Infarct and Brain Compartment Volumes From Computed Tomographic Scans , 1994, Stroke.

[97]  S R Arridge,et al.  A method for generating patient-specific finite element meshes for head modelling. , 2003, Physics in medicine and biology.

[98]  E. R. Flynn,et al.  A Model for Frequency Dependence of Conductivities of the Live Human Skull , 2004, Brain Topography.

[99]  B H Blott,et al.  High fidelity imaging and high performance computing in nonlinear EIT. , 2000, Physiological measurement.

[100]  Pierre N. Robillard,et al.  Specific-impedance measurements of brain tissues , 1977, Medical and Biological Engineering and Computing.

[101]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[102]  Lior Horesh,et al.  A feasibility study for imaging of epileptic seizures by EIT using a realistic FEM of the head 12th Conf. on Biomedical Application of EIT (Seoul, Korea) , 2006 .

[103]  A. Flisberg,et al.  Brain electrical impedance at various frequencies: the effect of hypoxia , 2004, The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[104]  Don M. Tucker,et al.  Regional head tissue conductivity estimation for improved EEG analysis , 2000, IEEE Transactions on Biomedical Engineering.

[105]  N. J. Avis,et al.  Analytical solution to the three-dimensional electrical forward problem for a circular cylinder , 2000 .

[106]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[107]  R. Sheppard,et al.  The dielectric properties of the cerebellum, cerebrum and brain stem of mouse brain at radiowave and microwave frequencies. , 1983, Physics in Medicine and Biology.

[108]  Lior Horesh,et al.  Specification and calibration of a multi-frequency MEIT system for stroke , 2005 .

[109]  Hermann Scharfetter,et al.  Detection of brain oedema using magnetic induction tomography: a feasibility study of the likely sensitivity and detectability. , 2004, Physiological measurement.

[110]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[111]  J. B. Ranck,et al.  Specific impedance of rabbit cerebral cortex. , 1963, Experimental neurology.

[112]  Rudolf Höber,et al.  Eine Methode, die elektrische Leitfähigkeit im Innern von Zellen zu messen , 1910, Pflüger's Archiv für die gesamte Physiologie des Menschen und der Tiere.

[113]  R Bayford,et al.  Design and calibration of a compact multi-frequency EIT system for acute stroke imaging. , 2006, Physiological measurement.

[114]  H Weinans,et al.  Prediction of mechanical properties of human trabecular bone by electrical measurements , 2005, Physiological measurement.

[115]  E. Somersalo,et al.  Existence and uniqueness for electrode models for electric current computed tomography , 1992 .

[116]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[117]  William R B Lionheart,et al.  Conformal uniqueness results in anisotropic electrical impedance imaging , 1997 .

[118]  Charles F. Dalziel,et al.  Electric shock hazard , 1972, IEEE Spectrum.

[119]  N. Berner,et al.  Modelling the anisotropic electrical properties of skeletal muscle. , 1999, Physics in medicine and biology.

[120]  J. Bogousslavsky,et al.  The Lausanne Stroke Registry: analysis of 1,000 consecutive patients with first stroke. , 1988, Stroke.

[121]  P. Nicholson,et al.  Specific impedance of cerebral white matter. , 1965, Experimental neurology.

[122]  Marc Molinari,et al.  Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction. , 2002, Physiological measurement.

[123]  A. Gabizon,et al.  Alteration of blood-brain-CSF barrier in experimental meningeal carcinomatosis , 1987, Journal of Neuro-Oncology.

[124]  W. R. Adey,et al.  Impedance Changes during Epileptic Seizures , 1966, Epilepsia.

[125]  Patricia Brunner,et al.  Direct reconstruction of tissue parameters from differential multifrequency EIT in vivo , 2006, Physiological measurement.

[126]  J Rosell,et al.  Electrical impedance tomography of the eye: in vitro measurements of the cornea and the lens. , 1996, Physiological measurement.

[127]  Jens Haueisen,et al.  Use of a priori information in estimating tissue resistivities--application to human data in vivo. , 2004, Physiological measurement.

[128]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[129]  J. Latikka,et al.  Conductivity of living intracranial tissues. , 2001, Physics in medicine and biology.

[130]  Thomas C. Ferrée,et al.  Weighted regularization in electrical impedance tomography with applications to acute cerebral stroke , 2002, IEEE Transactions on Medical Imaging.

[131]  Richard H. Bayford,et al.  Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method , 2003, NeuroImage.

[132]  Subrata Saha,et al.  Electric and dielectric properties of wet human cancellous bone as a function of frequency , 2006, Annals of Biomedical Engineering.

[133]  Andrea Borsic,et al.  Regularisation methods for imaging from electrical measurements. , 2002 .

[134]  P Guénon,et al.  [Anatomy of the eye]. , 1988, Soins. Chirurgie.

[135]  Kurt Bryan,et al.  Fast imaging of partially conductive linear cracks using impedance data , 2006 .

[136]  D S Holder,et al.  Imaging of cortical spreading depression by EIT: implications for localization of epileptic foci. , 1994, Physiological measurement.

[137]  Manuchehr Soleimani,et al.  Improving the forward solver for the complete electrode model in EIT using algebraic multigrid , 2005, IEEE Transactions on Medical Imaging.

[138]  D. A. Driscoll,et al.  EEG electrode sensitivity--an application of reciprocity. , 1969, IEEE transactions on bio-medical engineering.

[139]  M. Schweiger,et al.  Gauss–Newton method for image reconstruction in diffuse optical tomography , 2005, Physics in medicine and biology.

[140]  F.J. Garcia Sanchez,et al.  Correlation between low-frequency electric conductivity and permittivity in the diaphysis of bovine femoral bone , 1992, IEEE Transactions on Biomedical Engineering.

[141]  H. Kwan,et al.  Changes in the complex permittivity during spreading depression in rat cortex , 1999, IEEE Transactions on Biomedical Engineering.

[142]  Lior Horesh,et al.  Stroke type differentiation by multi-frequency electrical impedance tomography—a feasibility study , 2005 .

[143]  Lior Horesh,et al.  Review of dielectric properties of the human head for multi-frequency electrical impedance tomography (MFEIT) , 2007 .

[144]  A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields , 1999 .

[145]  L Horesha,et al.  Could synchronized neuronal activity be imaged using Low Frequency Electrical Impedance Tomography (LFEIT) , 2005 .

[146]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[147]  R. Pethig,et al.  Dielectric properties of body tissues. , 1987, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[148]  William R B Lionheart,et al.  A Matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project , 2002 .

[149]  Rudolf Höber,et al.  Ein zweites Verfahren, die Leitfähigkeit im Innern von Zellen zu messen , 1912, Pflüger's Archiv für die gesamte Physiologie des Menschen und der Tiere.

[150]  D C Barber,et al.  Fast reconstruction of resistance images. , 1987, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[151]  David Isaacson,et al.  A direct reconstruction algorithm for electrical impedance tomography , 2002, IEEE Transactions on Medical Imaging.

[152]  J. B. Ranck,et al.  Analysis of specific impedance of rabbit cerebral cortex. , 1963, Experimental neurology.

[153]  D. Geselowitz An application of electrocardiographic lead theory to impedance plethysmography. , 1971, IEEE transactions on bio-medical engineering.

[154]  J. Silny,et al.  Electrical phosphenes: on the influence of conductivity inhomogeneities and small-scale structures of the orbita on the current density threshold of excitation , 2002, Medical and Biological Engineering and Computing.

[155]  P. Hansen Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[156]  Fetsje Bijma,et al.  In vivo measurement of the brain and skull resistivities using an EIT-based method and realistic models for the head , 2003, IEEE Transactions on Biomedical Engineering.

[157]  Carlos H. Muravchik,et al.  Estimating brain conductivities and dipole source signals with EEG arrays , 2004, IEEE Transactions on Biomedical Engineering.

[158]  Andrea Borsic,et al.  Generation of anisotropic-smoothness regularization filters for EIT , 2002, IEEE Transactions on Medical Imaging.

[159]  C. Li,et al.  Specific resistivity of the cerebral cortex and white matter. , 1968, Experimental neurology.

[160]  Marko Vauhkonen,et al.  Simultaneous reconstruction of electrode contact impedances and internal electrical properties: II. Laboratory experiments , 2002 .

[161]  J. D. Munck A linear discretization of the volume conductor boundary integral equation using analytically integrated elements (electrophysiology application) , 1992 .

[162]  Richard Bayford,et al.  Near DC conductivity change measurement of fast neuronal activity during human VEP , 2004 .

[163]  C Gabriel,et al.  Comments on 'dielectric properties of the skin'. , 1997, Physics in medicine and biology.

[164]  G. Crile,et al.  THE ELECTRICAL CONDUCTIVITY OF ANIMAL TISSUES UNDER NORMAL AND PATHOLOGICAL CONDITIONS , 1922 .

[165]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[166]  Michael Chow,et al.  Endothelin Receptor Antagonists and Cerebral Vasospasm: An Update , 2002, Neurosurgery.

[167]  W Hacke,et al.  Barbiturate coma in severe hemispheric stroke , 1997, Neurology.

[168]  A. Morice,et al.  Cardiac and respiratory related electrical impedance changes in the human thorax , 1994, IEEE Transactions on Biomedical Engineering.

[169]  Carretera de Valencia,et al.  The finite element method in electromagnetics , 2000 .

[170]  E. Haber,et al.  A GCV based method for nonlinear ill-posed problems , 2000 .

[171]  Fadil Santosa,et al.  A Method for Imaging Corrosion Damage in Thin Plates from Electrostatic Data , 1995 .

[172]  O. Schenk,et al.  ON FAST FACTORIZATION PIVOTING METHODS FOR SPARSE SYMMETRI C INDEFINITE SYSTEMS , 2006 .

[173]  Tatsuma Yamamoto,et al.  Electrical properties of the epidermal stratum corneum , 2006, Medical and biological engineering.

[174]  Andrei V. Gribok,et al.  Information complexity-based regularization parameter selection for solution of ill conditioned inverse problems , 2002 .

[175]  S. Majumdar,et al.  Trabecular Bone Mineral and Calculated Structure of Human Bone Specimens Scanned by Peripheral Quantitative Computed Tomography: Relation to Biomechanical Properties , 1998, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[176]  Lior Horesh,et al.  Calibration and preliminary human measurements for multifrequency EIT of the human head , 2007 .

[177]  F G HIRSCH,et al.  The electrical conductivity of blood. I: Relationship to erythrocyte concentration. , 1950, Blood.

[178]  R. Macdonald,et al.  Pathophysiology and molecular genetics of vasospasm. , 2001, Acta neurochirurgica. Supplement.

[179]  J Sikora,et al.  The Application of hybrid BEM / FEM methods to solve Electrical Impedance Tomography ’ s forward problem for the human head , 2004 .

[180]  H. Schwan Electrical properties of tissue and cell suspensions. , 1957, Advances in biological and medical physics.

[181]  Lior Horesh,et al.  Design of electrodes and current limits for low frequency electrical impedance tomography of the brain , 2007, Medical & Biological Engineering & Computing.

[182]  R H Smallwood,et al.  Transport of gastric contents. , 1994, Physiological measurement.

[183]  Nuutti Hyvönen,et al.  Complete Electrode Model of Electrical Impedance Tomography: Approximation Properties and Characterization of Inclusions , 2004, SIAM J. Appl. Math..

[184]  Louise C. Enfield Electrical impedance tomography of human brain function , 2005 .

[185]  R H Bayford,et al.  A multi-shell algorithm to reconstruct EIT images of brain function. , 2002, Physiological measurement.

[186]  K. Jellinger,et al.  Ions in the Brain: Normal Function, Seizures, and Stroke , 2004 .

[187]  J. Bamford,et al.  Classification and natural history of clinically identifiable subtypes of cerebral infarction , 1991, The Lancet.

[188]  R H Bayford,et al.  Multi-frequency electrical impedance tomography (EIT) of the adult human head: initial findings in brain tumours, arteriovenous malformations and chronic stroke, development of an analysis method and calibration , 2006, Physiological measurement.

[189]  J C Newell,et al.  Reconstruction of conductivity changes due to ventilation and perfusion from EIT data collected on a rectangular electrode array. , 2001, Physiological measurement.

[190]  K. Foster,et al.  Dielectric properties of mammalian tissues from 0.1 to 100 MHz: a summary of recent data. , 1982, Physics in medicine and biology.

[191]  Hugh McCann,et al.  Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography , 2002, IEEE Transactions on Medical Imaging.

[192]  Matthias Bollhöfer,et al.  A robust ILU with pivoting based on monitoring the growth of the inverse factors , 2001 .

[193]  David Isaacson,et al.  Electrical Impedance Tomography , 2002, IEEE Trans. Medical Imaging.

[194]  J C de Munck,et al.  The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem - a simulation study , 2000, Physiological measurement.

[195]  C D Cone,et al.  Induction of mitosis in mature neurons in central nervous system by sustained depolarization. , 1976, Science.

[196]  L. Geddes,et al.  The specific resistance of biological material—A compendium of data for the biomedical engineer and physiologist , 1967, Medical and biological engineering.

[197]  Stuchly,et al.  DIELECTRIC PROPERTIES OF BIOLOGICAL SUBSTANCES–TABULATED , 1980 .

[198]  Fernando Seoane,et al.  Spectroscopy study of the dynamics of the transencephalic electrical impedance in the perinatal brain during hypoxia , 2005, Physiological measurement.

[199]  D. Oldenburg,et al.  A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems , 2004 .

[200]  Paul B. Colditz,et al.  Cerebral impedance and neurological outcome following a mild or severe hypoxic/ischemic episode in neonatal piglets , 2003, Brain Research.

[201]  J Silny,et al.  A model of the electrical volume conductor in the region of the eye in the ELF range. , 2001, Physics in medicine and biology.

[202]  N. A. Coulter,et al.  Development of turbulence in flowing blood. , 1949, The American journal of physiology.

[203]  J H Calderwood Electrode-skin impedance from a dielectric viewpoint. , 1996, Physiological measurement.

[204]  Yousef Saad,et al.  Multilevel Preconditioners Constructed From Inverse-Based ILUs , 2005, SIAM J. Sci. Comput..

[205]  F. H. Lopes da Silva,et al.  In vivo measurement of the brain and skull resistivities using an EIT-based method and the combined analysis of SEF/SEP data , 2003, IEEE Transactions on Biomedical Engineering.

[206]  J. Rosell,et al.  Multi-frequency static imaging in electrical impedance tomography: Part 1 instrumentation requirements , 1995, Medical and Biological Engineering and Computing.

[207]  Fernando Seoane,et al.  Evolution of Cerebral Bioelectrical Resistance at Various Frequencies During Hypoxia in Fetal Sheep , 2004 .

[208]  Liliana Borcea A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency , 2001 .

[209]  J Töyräs,et al.  Electrical and dielectric properties of bovine trabecular bone—relationships with mechanical properties and mineral density , 2003, Physics in medicine and biology.

[210]  P. Hua,et al.  Finite element modeling of electrode-skin contact impedance in electrical impedance tomography , 1993, IEEE Transactions on Biomedical Engineering.

[211]  S. K. Law,et al.  Thickness and resistivity variations over the upper surface of the human skull , 2005, Brain Topography.

[212]  C. Vogel Computational Methods for Inverse Problems , 1987 .

[213]  A. Oosterom,et al.  Electrical properties of platinum electrodes: Impedance measurements and time-domain analysis , 2006, Medical and Biological Engineering and Computing.

[214]  D. Isaacson,et al.  Electrical impedance tomography of complex conductivity distributions with noncircular boundary , 1997, IEEE Transactions on Biomedical Engineering.

[215]  W. Sutherling,et al.  Conductivities of Three-Layer Live Human Skull , 2004, Brain Topography.

[216]  Peter Herrmann,et al.  Regional Lung Perfusion as Determined by Electrical Impedance Tomography in Comparison With Electron Beam CT Imaging , 2002, IEEE Transactions on Medical Imaging.

[217]  G. Mercato,et al.  Dielectric properties of fluid-saturated bone: a comparison between diaphysis and epiphysis , 2006, Medical and Biological Engineering and Computing.

[218]  E. Somersalo,et al.  Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography , 2000 .

[219]  D S Holder Electrical impedance tomography with cortical or scalp electrodes during global cerebral ischaemia in the anaesthetised rat. , 1992, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[220]  William D. Hurt,et al.  Multiterm Debye Dispersion Relations for Permittivity of Muscle , 1985, IEEE Transactions on Biomedical Engineering.

[221]  C Gabriel,et al.  The dielectric properties of biological tissues: I. Literature survey. , 1996, Physics in medicine and biology.

[222]  R H Bayford,et al.  Using the GRID to improve the computation speed of electrical impedance tomography (EIT) reconstruction algorithms. , 2005, Physiological measurement.

[223]  B. Scheithauer,et al.  Tumors of the Central Nervous System, Atlas of Tumor Pathology , 1995 .

[224]  S. Kaczmarz Approximate solution of systems of linear equations , 1993 .

[225]  A. Dale,et al.  Conductivity tensor mapping of the human brain using diffusion tensor MRI , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[226]  A Tizzard,et al.  Generating accurate finite element meshes for the forward model of the human head in EIT , 2005, Physiological measurement.

[227]  T Ribbe,et al.  Triple-frequency method for measuring blood impedance , 1993, Physiological measurement.

[228]  R. Freund,et al.  A new Krylov-subspace method for symmetric indefinite linear systems , 1994 .

[229]  Yuqi Yao,et al.  Frequency domain optical tomography in human tissue , 1995, Optics + Photonics.

[230]  Grace Wahba,et al.  Spline Models for Observational Data , 1990 .

[231]  D. Attwell,et al.  Interaction of low frequency electric fields with the nervous system: the retina as a model system. , 2003, Radiation protection dosimetry.

[232]  E Gersing,et al.  Tissue impedance spectra and the appropriate frequencies for EIT. , 1995, Physiological measurement.

[233]  S R Arridge,et al.  Optical tomographic reconstruction in a complex head model using a priori region boundary information. , 1999, Physics in medicine and biology.

[234]  Zdzislaw Szczepanik,et al.  Frequency analysis of electrical impedance tomography system , 2000, IEEE Trans. Instrum. Meas..

[235]  T Brott,et al.  Measurements of acute cerebral infarction: lesion size by computed tomography. , 1989, Stroke.

[236]  R H Smallwood,et al.  Mk3.5: a modular, multi-frequency successor to the Mk3a EIS/EIT system. , 2001, Physiological measurement.

[237]  Misha Elena Kilmer,et al.  Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems , 2000, SIAM J. Matrix Anal. Appl..

[238]  Tatsuma Yamamoto,et al.  Dielectric constant and resistivity of epidermal stratum corneum , 1976, Medical and biological engineering.

[239]  J Jossinet,et al.  The impedivity of freshly excised human breast tissue , 1998, Physiological measurement.

[240]  K. Foster,et al.  Dielectric properties of brain tissue between 0.01 and 10 GHz. , 1979, Physics in medicine and biology.

[241]  David Isaacson,et al.  NOSER: An algorithm for solving the inverse conductivity problem , 1990, Int. J. Imaging Syst. Technol..

[242]  V. Morozov On the solution of functional equations by the method of regularization , 1966 .

[243]  J. Schadé,et al.  Changes in the electrical conductivity of cerebral cortex during seizure activity. , 1962, Experimental neurology.

[244]  William R B Lionheart EIT reconstruction algorithms: pitfalls, challenges and recent developments. , 2004, Physiological measurement.

[245]  J Rosell,et al.  Errors in prolonged electrical impedance measurements due to electrode repositioning and postural changes. , 1995, Physiological measurement.

[246]  Stuchly,et al.  Dielectric properties of breast carcinoma and the surrounding tissues , 1988, IEEE Transactions on Biomedical Engineering.

[247]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[248]  Paul L. Nunez,et al.  A Study of Origins of the Time Dependencies of Scalp EEG: I - Theoretical Basis , 1981, IEEE Transactions on Biomedical Engineering.

[249]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[250]  Michael Pidcock,et al.  Ill-Posedness and Non-Linearity in Electrical Impedance Tomography , 1988 .

[251]  A. van Harreveld,et al.  Specific impedance of rabbit's cortical tissue. , 1963, The American journal of physiology.

[252]  Anders M. Dale,et al.  Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy , 2004, NeuroImage.

[253]  A. Surowiec,et al.  In vivo and in vitro dielectric properties of feline tissues at low radiofrequencies. , 1986, Physics in medicine and biology.

[254]  Keith D. Paulsen,et al.  Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography , 2006, IEEE Transactions on Medical Imaging.

[255]  E. Haber Quasi-Newton methods for large-scale electromagnetic inverse problems , 2005 .

[256]  T Iritani,et al.  A study of the electrical bio-impedance of tumors. , 1993, Journal of investigative surgery : the official journal of the Academy of Surgical Research.

[257]  Simon J. Cox,et al.  Efficient Non-Linear 3D Electrical Tomography Reconstruction , 2001 .

[258]  William Robert Breckon Image reconstruction in electrical impedance tomography , 1990 .

[259]  D S Holder,et al.  Detection of cerebral ischaemia in the anaesthetised rat by impedance measurement with scalp electrodes: implications for non-invasive imaging of stroke by electrical impedance tomography. , 1992, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[260]  K. Foster,et al.  Dielectric Permittivity and Electrical Conductivity of Fluid Saturated Bone , 1983, IEEE Transactions on Biomedical Engineering.

[261]  J. Haueisen,et al.  The Influence of Brain Tissue Anisotropy on Human EEG and MEG , 2002, NeuroImage.

[262]  C. J. Kotre,et al.  EIT image reconstruction using sensitivity weighted filtered backprojection. , 1994, Physiological measurement.

[263]  D. Isaacson,et al.  Electrode models for electric current computed tomography , 1989, IEEE Transactions on Biomedical Engineering.

[264]  R H Smallwood,et al.  Multi-frequency imaging and modelling of respiratory related electrical impedance changes. , 1994, Physiological measurement.

[265]  Paul L. Nunez,et al.  A Study of Origins of the Time Dependencies of Scalp EEG: II-Experimental Support of Theory , 1981, IEEE Transactions on Biomedical Engineering.

[266]  M. W. Johnson,et al.  Electrical properties of compact bone. , 1981, Clinical orthopaedics and related research.

[267]  Olaf Schenk,et al.  Maximum-Weighted Matching Strategies and the Application to Symmetric Indefinite Systems , 2004, PARA.

[268]  Lior Horesh,et al.  Non invasive imaging of synchronized neuronal activity using low frequency electrical impedance tomography , 2005 .

[269]  D. S. Holder,et al.  A model of the effect of variations in contact and skin impedance on electrical impedance tomography measurements artefacts , 1995 .

[270]  J. Shewchuk An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[271]  David M. Weinstein,et al.  Biomedical computing and visualization , 2006, ACSC.

[272]  Sverre Grimnes,et al.  Facts and Myths about Electrical Measurement of Stratum corneum Hydration State , 2001, Dermatology.

[273]  I. Duff,et al.  The state of the art in numerical analysis , 1997 .

[274]  E. Haber,et al.  Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach , 2004 .

[275]  Lior Horesh,et al.  Robustness of linear and non-linear reconstructions algorithms for brain EITS. Non-linear—is it worth the effort , 2004 .

[276]  Lior Horesh,et al.  Effects of warping finite element meshes for the forward model of the head in EIT , 2004 .

[277]  Richard H. Bayford,et al.  Applications of GRID in Clinical Neurophysiology and Electrical Impedance Tomography of Brain Function , 2005, HealthGrid.

[278]  E. Hennessy,et al.  Measurements of gastric emptying during continuous nasogastric infusion of liquid feed: electric impedance tomography versus gamma scintigraphy. , 2006, Clinical nutrition.

[279]  J. Rosell,et al.  Skin impedance from 1 Hz to 1 MHz , 1988, IEEE Transactions on Biomedical Engineering.

[280]  L. Ward,et al.  Improved prediction of extracellular and total body water using impedance loci generated by multiple frequency bioelectrical impedance analysis , 1993, Physics in medicine and biology.

[281]  George Biros,et al.  Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange-Newton Solver and Its Application to Optimal Control of Steady Viscous Flows , 2005, SIAM J. Sci. Comput..

[282]  J. B. Ranck,et al.  Specific impedance of cerebral cortex during spreading depression, and an analysis of neuronal, neuroglial, and interstitial contributions , 1964 .

[283]  S OCHS,et al.  Cerebral impedance changes after circulatory arrest. , 1956, The American journal of physiology.

[284]  R H Bayford,et al.  Two-dimensional finite element modelling of the neonatal head. , 2000, Physiological measurement.

[285]  Lutz Jäncke,et al.  Brain size and grey matter volume in the healthy human brain , 2002, Neuroreport.

[286]  S Arridge,et al.  A gradient-based optimisation scheme foroptical tomography. , 1998, Optics express.

[287]  J P Kaipio,et al.  Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns. , 1997, Physiological measurement.

[288]  Jari P. Kaipio,et al.  Tikhonov regularization and prior information in electrical impedance tomography , 1998, IEEE Transactions on Medical Imaging.

[289]  E. Somersalo,et al.  Inverse problems with structural prior information , 1999 .

[290]  H. C. Burger,et al.  Specific electric resistance of body tissues. , 1961, Physics in medicine and biology.

[291]  E. Somersalo,et al.  Approximation errors and model reduction with an application in optical diffusion tomography , 2006 .

[292]  H. Pfützner,et al.  Dielectric analysis of blood by means of a raster-electrode technique , 1984, Medical and Biological Engineering and Computing.

[293]  Herman P. Schwan,et al.  Electric Characteristics of Tissues , 1963 .

[294]  J. B. Ranck,et al.  THE SPECIFIC IMPEDANCE OF THE DORSAL COLUMNS OF CAT: AN INISOTROPIC MEDIUM. , 1965, Experimental neurology.

[295]  P J Vauhkonen,et al.  Errors due to the truncation of the computational domain in static three-dimensional electrical impedance tomography. , 2000, Physiological measurement.

[296]  W. Sutherling,et al.  Conductivities of Three-Layer Human Skull , 2004, Brain Topography.

[297]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[298]  C D Binnie,et al.  Factors limiting the application of electrical impedance tomography for identification of regional conductivity changes using scalp electrodes during epileptic seizures in humans , 2006, Physiological measurement.

[299]  Simon R. Arridge,et al.  Stroke type detection by multi-frequency electrical impedance tomography MFEIT—a feasibility study , 2005 .

[300]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[301]  D S Holder,et al.  Experimental validation of a novel reconstruction algorithm for electrical impedance tomography based on backprojection of Lagrange multipliers. , 1995, Physiological measurement.

[302]  R. Sacco,et al.  Antithrombotic and thrombolytic therapy for ischemic stroke. , 2001, Chest.

[303]  Marom Bikson,et al.  Tissue resistance changes and the profile of synchronized neuronal activity during ictal events in the low-calcium model of epilepsy. , 2004, Journal of neurophysiology.

[304]  D C Barber,et al.  A review of image reconstruction techniques for electrical impedance tomography. , 1989, Medical physics.

[305]  S. Arridge,et al.  Optical imaging in medicine: II. Modelling and reconstruction , 1997, Physics in medicine and biology.

[306]  P Warnell Advanced concepts in the management of cerebral vasospasm associated with aneurysmal subarachnoid hemorrhage. , 1996, Axone.

[307]  Michael Pidcock,et al.  An image reconstruction algorithm for three-dimensional electrical impedance tomography , 2001, IEEE Transactions on Biomedical Engineering.

[308]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2004, Future Gener. Comput. Syst..

[309]  D. Holder,et al.  Large-Scale Non-Linear 3D Reconstruction Algorithms for Electrical Impedance Tomography of the Human Head , 2007 .

[310]  C. Gabriel Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies. , 1996 .

[311]  V. Raicu,et al.  A quantitative approach to the dielectric properties of the skin. , 2000, Physics in medicine and biology.

[312]  C R Falyar Using transcranial Doppler sonography to augment the neurological examination after aneurysmal subarachnoid hemorrhage. , 1999, The Journal of neuroscience nursing : journal of the American Association of Neuroscience Nurses.

[313]  Ananth Ranganathan,et al.  The Levenberg-Marquardt Algorithm , 2004 .