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https://eprints.maths.manchester.ac.uk/cgi/oai2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:587
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https://eprints.maths.manchester.ac.uk/587/
Part 1: the reconstruction problem
Lionheart, William
Polydorides, Nicholas
Borsic, Andrea
35 Partial differential equations
65 Numerical analysis
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
This book section provides a comprehensive introduction to reconstruction algorithms in Electrical Impedance Tomography (EIT) aimed at graduate students starting their research in this area.
Institute of Physics
Holder, David
2004-12-31
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/587/1/reconstruction.pdf
Lionheart, William and Polydorides, Nicholas and Borsic, Andrea (2004) Part 1: the reconstruction problem. In: Electrical Impedance Tomography: Methods, History and Applications. Series in Medical Physics and Biomedical Engineering . Institute of Physics, Bristol, pp. 3-64. ISBN 0750309520
http://www.crcpress.com/shopping_cart/products/product_detail.asp?sku=IP234&parent_id=&pc=
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:691
2017-10-20T14:12:22Z
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https://eprints.maths.manchester.ac.uk/691/
Stochastic Resonance in Vision: Models and Data
Tham, Carole
92 Biology and other natural sciences
87 Biological and medical physics
Stochastic resonance (SR) is a phenomenon whereby small amounts of additive noise can greatly enhance the performance of a non-linear signal processing system. It is well known that many sensory systems are non-linear in nature and the phenomenon of SR has been widely studied in them. Perhaps one underexplored area of research is the visual system, in particular the retina and this pro ject aims to explore to what extent SR is or could be utilised in the retina. The thesis is organised as follows: In chapter one I look at the historical development of SR from its conception as an explanation of the periodic occurrence of ice ages to applications in sensory systems. The structure of the retina is explored in chapter two and I explain why SR might be expected to occur in visual systems. The mathematics of the problem is detailed in chapter three, showing why SR arises in systems containing a threshold type non-linearity. The phenomenon is extensively studied experimentally in chapter four, with many different stimuli being tested. These are broadly organised into two types of task, detection and discrimination, with each stimulus carefully designed to probe a different aspect of the phenomenon. In the final chapter overall conclusions are drawn, the scope for future work is explored, including the description of a retina model and the possibilities for practical applications are raised.
The thesis contains novel receiver operating characteristic (ROC) curves, used to demonstrate that SR can occur in systems containing a threshold type non-linearity. I go on to show that noise can be used to enhance the perceptibility of some signals. However, this enhanced perception is shown to be limited to low level visual tasks.
2006-11-30
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/691/1/CaroleTham_finalDraft.pdf
Tham, Carole (2006) Stochastic Resonance in Vision: Models and Data. Doctoral thesis, The University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:842
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https://eprints.maths.manchester.ac.uk/842/
Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour?
Riley, C. J.
Muldoon, M. R.
Huke, J. P.
Broomhead, D. S.
34 Ordinary differential equations
35 Partial differential equations
92 Biology and other natural sciences
05 Statistical physics, thermodynamics, and nonlinear dynamical systems
82 Physical chemistry and chemical physics molecular physics
87 Biological and medical physics
In biological systems, chemical reactions often take place in complex spatial environments. For example, the translation of m-RNA to produce protein within eukaryotic cells takes place within the extremely crowded cytoplasmic environment and appears to require the spatial coordination of many translation factors. It is important, therefore, to understand the transport processes within such an environment. While there is growing interest in both experimental and computational studies of such environments, it is also important to develop suitable mathematical models. Here, as an example of such a model, we study a reaction-diffusion equation defined on the Sierpinski gasket. Both experimental and computational studies of analogous systems have shown power law behaviour and associated deviations from mass action kinetics. The analysis presented here allows us to distinguish the roles of the fractal domain and of the discreteness of molecular interactions in producing this effect. Indeed, we show that the fractal domain alone is insufficient.
2007-09-04
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/842/1/fraclett2.pdf
Riley, C. J. and Muldoon, M. R. and Huke, J. P. and Broomhead, D. S. (2007) Does Reaction-diffusion Dynamics on a Fractal Space Imply Power Law Behaviour? [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:885
2017-10-20T14:12:29Z
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https://eprints.maths.manchester.ac.uk/885/
Migration and proliferation dichotomy in tumor cell invasion
Fedotov, Sergei
Lomin, Alexander
87 Biological and medical physics
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting-time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/885/1/Migration.pdf
Fedotov, Sergei and Lomin, Alexander (2007) Migration and proliferation dichotomy in tumor cell invasion. Physical Review Letters, 98 (11). 118101/1-118101/4. ISSN 1079-7114
http://scitation.aip.org/dbt/dbt.jsp?KEY=PRLTAO&Volume=98&Issue=11
10.1103/PhysRevLett.98.118101
10.1103/PhysRevLett.98.118101
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1080
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https://eprints.maths.manchester.ac.uk/1080/
Chest Impedance Imaging Using Trigonometric Current Patterns
McLeod, Christopher N.
Shi, Yu
Denyer, Christopher
Lidgey, F. John
Lionheart, William R.B.
Paulson, Kevin S.
Pidcock, Michael K.
87 Biological and medical physics
This paper reports the results from the application of the 32 channel Oxford Brookes Adaptve Current Tomograph, OXBACT-III to the chest of a human volunteer. A frame rate of 10 per second was achieved using trigonometric drive currents.
1995
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1080/1/Heidelberg-chest-eit.pdf
McLeod, Christopher N. and Shi, Yu and Denyer, Christopher and Lidgey, F. John and Lionheart, William R.B. and Paulson, Kevin S. and Pidcock, Michael K. (1995) Chest Impedance Imaging Using Trigonometric Current Patterns. In: IX. International Conference on Electrical Bio-impedance, Annual Meeting, 1995, Heidelberg.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1083
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https://eprints.maths.manchester.ac.uk/1083/
Image reconstruction in electrical impedance tomography
Breckon, William Robert
35 Partial differential equations
65 Numerical analysis
78 Optics, electromagnetic theory
87 Biological and medical physics
This thesis is concerned with Electrical Impedance Tomogaphy (EIT), a medical imaging technique in which pictures of the electrical conductivity distribution of the body are formed from current and voltage data taken on the body surface. The focus of the thesis is on the mathematical aspects of reconstructing the conductivity image from the measured data (the reconstruction problem). The reconstruction problem is particularly difficult and in this thesis it is investigated analytically and numerically. The aim of this investigation is to understand why the problem is difficult and to find
numerical solution methods which respect the difficulties encountered. The analytical investigation of this non-linear inverse problem for an elliptic partial differential equation shows that while the forward mapping is analytic the inverse mapping is discontinuous. A rigorous treatment of the linearisation of the problem is given, including proofs of forms of linearisation assumed by previous authors. It is shown that the derivative of the forward problem is compact. Numerical
calculations of the singular value decomposition (SVD) are given including plots of singular values and images of the singular functions. The SVD is used to settle a controversy concerning current drive patterns.
Reconstruction algorithms are investigated and use of Regularised Newton methods is suggested. A formula for the second derivative of the forward mapping is derived which proves too computationally expensive to calculate. Use of Tychonov regularisation as well as filtered SVD and
iterative methods are discussed. The similarities, and differences, between EIT and X-Ray Computed Tomography (X-Ray CT) are illuminated. This leads to an explanation of methods used by other authors for EIT reconstuction based on X-Ray CT. Details of the author's own implementation of a regularised Newton method are given. Finally the idea of adaptive current patterns is investigated. An algorithm is given for the experimental determination of optimal
current patterns and the integration of this technique with
regularised Newton methods is explored. Promising numerical results from this technique are given.
The thesis concludes with a discussion of some outstanding problems in EIT and points to possible routes for their solution. An appendix gives brief details of the design and development of the Oxford Polytechnic Adaptive Current Tomograph.
1990-05
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1083/1/Breckon_PhD_Image_reconstruction_EIT.pdf
Breckon, William Robert (1990) Image reconstruction in electrical impedance tomography. Doctoral thesis, Oxford Polytechnic.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1091
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https://eprints.maths.manchester.ac.uk/1091/
A measure of the information content of EIT data
Adler, Andy
Youmaran, Richard
Lionheart, William R.B.
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
We ask: how many bits of information (in the Shannon sense) do we
get from a set of EIT measurements? Here, the term information in measurements (IM) is denotned as: the decrease in uncertainty about the contents of a medium, due to a set of measurements. This decrease in uncertainly is quantified by the change from the the inter-class model, q, denotned by the prior information, to the intra-class model, p, given by the measured data (corrupted by noise). IM is measured by the expected relative entropy (Kullback-Leibler divergence) between distributions q and
p, and corresponds to the channel capacity in an analogous communications system.
Based on a Gaussian model of the measurement noise, Σ_n, and a prior model of the image element covariances Σ_x, we calculate
IM= (1/2) Σ log_2([SNR]_i + 1), where [SNR]_i
is the signal to noise ratio for each independent measurement calculated from the prior and noise models. For an example, we consider saline tank measurements from a 16 electrode EIT system, with a 2 cm radius non-conductive target, and calculate IM= 179 bits. Temporal sequences of frames are considered, and formulae for IM as a function of temporal image element correlations are derived. We suggest that this measure may allow novel insights into questions such as distinguishability limits, optimal measurement schemes and data fusion
2008-04-24
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1091/1/adler-2008-EIT-information.pdf
Adler, Andy and Youmaran, Richard and Lionheart, William R.B. (2008) A measure of the information content of EIT data. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1111
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https://eprints.maths.manchester.ac.uk/1111/
GREIT: towards a consensus EIT algorithm for lung images,
Adler, Andy
Arnold, John
Bayford, Richard
Borsic, Andrea
Brown, Brian
Dixon, Paul
Faes, Theo
Frerichs, Inez
Gagnon, Herve
Garber, Yvo
Grychtol, Bartlomiej
Hahn, Gunter
Lionheart, William
Malik, Anjum
Stocks, Janet
Tizzard, Andrew
Weiler, Norbert
Wolf, Gerhard
87 Biological and medical physics
Recently, electrical impedance tomogra-
phy (EIT) has begun to see a signi¯cant clinical in-
terest for monitoring of ventilated patients. The key
capability of EIT is to provide real-time images of
the distribution of ventilation in the patient's lungs.
However, most clinical and physiological research in
lung EIT is done using older and proprietary algo-
rithms; this is an obstacle to interpretation of EIT
results because the reconstructed images are not well
characterized. To address this issue, we are devel-
oping a consensus linear reconstruction algorithm for
lung EIT, called GREIT (Graz consensus Reconstruc-
tion algorithm for EIT). This algorithm is being de-
veloped in three phases: 1) selection of the "ingre-
dients" and evaluation methodology (this paper), 2)
evaluation and experience with GREIT variants, and
3) consensus and definition of the GREIT algorithm.
Algorithms evaluation criteria are identified to be: a)
quantitative output for all positions, b) reconstructed
position error (low and uniform), c) resolution (small
PSF, uniform, few artefacts), d) good noise perfor-
mance, e) low sensitivity to electrode and boundary
movement, f) good performance on clinical and exper-
imental data. This approach represents the consensus
of a large and representative group of experts in EIT
algorithm and clinical applications. All software and
data to implement and test GREIT will be made avail-
able under an open source license which allows free
research and commercial use.
2008-06
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1111/1/GREIT-EIT2008.pdf
Adler, Andy and Arnold, John and Bayford, Richard and Borsic, Andrea and Brown, Brian and Dixon, Paul and Faes, Theo and Frerichs, Inez and Gagnon, Herve and Garber, Yvo and Grychtol, Bartlomiej and Hahn, Gunter and Lionheart, William and Malik, Anjum and Stocks, Janet and Tizzard, Andrew and Weiler, Norbert and Wolf, Gerhard (2008) GREIT: towards a consensus EIT algorithm for lung images,. In: 9th EIT conference 2008, 16-18th June 2008, Dartmouth New Hampshire.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1113
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https://eprints.maths.manchester.ac.uk/1113/
Evaluating Deformation Corrections in Electrical Impedance Tomography
Boyle, Alistair
Lionheart, William R.B.
Gomez-Laberge, Camille
Adler, Andy
87 Biological and medical physics
Electrical Impedance Tomography (EIT) uses
the difference in measurements between surface electrodes to
reconstruct an image of the conductivity of the contained
medium. However, changes in measurements result from
changes in internal conductivity and changes in the shape
of the medium relative to the electrode positions. Failure to
account for shape changes results in a conductivity image with
significant artifacts. Previous work to address shape changes
in EIT has shown that: a) theoretically, for an infinite number
of electrodes, non-conformal changes in boundary shapes and
electrode locations can be uniquely determined (Lionheart,
1998); and b) in some cases, conductivity and shape changes
can be recovered using a combined image reconstruction model
of both conductivity and shape changes (Soleimani et al, 2006).
This work has shown that the shape change problem can
be partially addressed. In this paper, we explore the limits
of compensation for boundary movement in EIT, using three
approaches: first, a theoretical model is developed to separate
a deformation vector field into conformal and non-conformal
components, from which the reconstruction limits may be
determined; next, finite element models are constructed from
which EIT measurements are simulated; finally, an experimental
phantom is constructed using a deformable gasket
and stainless steel electrodes in a saline medium, from which
boundary deformation measurements are acquired.
2008-06
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1113/1/boyle-EIT2008-elec_move_phantom.pdf
Boyle, Alistair and Lionheart, William R.B. and Gomez-Laberge, Camille and Adler, Andy (2008) Evaluating Deformation Corrections in Electrical Impedance Tomography. In: 9th EIT conference 2008, 16-18th June 2008, Dartmouth College, New Hampshire.
http://engineering.dartmouth.edu/eit2008/EIT_Conference_2008.pdf
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1114
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https://eprints.maths.manchester.ac.uk/1114/
Simple FEMs aren’t as good as we thought: experiences developing EIDORS v3.3
Adler, Andy
Borsic, Andrea
Polydorides, Nick
Lionheart, William R.B.
87 Biological and medical physics
In this paper, we 1: announce EIDORS
version 3.3, and clarify the new features and changes
to the software. Brie
y, the new version includes: a)
interfaces to FEM generation (distmesh, netgen) and
dual model solvers, b) new algorithms (total varia-
tion, electrode movement solver, temporal solvers),
c) a data repository with in vivo and simulated data
and models, d) faster algorithms with better caching,
and e) improved graphics and extensive tutorials.
2: we review the use of dual models in EIT, and
the architecture to support their use in EIDORS. 3:
we discuss accuracy limitations to the single-order
tetrahedral nite element models that are used in
much EIT research. We recommend that models
be used of at least 104 elements (for 2D FEMs) and
106 elements (for 3D FEMs). FEM accuracy may
be partially addressed using dual model solvers, for
which EIDORS v3.3 provides support.
2008-06
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1114/1/adler-EIT2008-FEM-challenges.pdf
Adler, Andy and Borsic, Andrea and Polydorides, Nick and Lionheart, William R.B. (2008) Simple FEMs aren’t as good as we thought: experiences developing EIDORS v3.3. In: 9th EIT conference 2008, 16-18th June 2008, Dartmouth College, New Hampshire.
http://engineering.dartmouth.edu/eit2008/EIT_Conference_2008.pdf
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1370
2017-11-08T18:18:32Z
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https://eprints.maths.manchester.ac.uk/1370/
Elongated S-cone stimuli reveal the importance of the
intermediate temporal filter
Baraas, Rigmor C.
Kulikowski, Janus J.
Muldoon, Mark R.
92 Biology and other natural sciences
87 Biological and medical physics
The relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli were studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although stimulus elongation apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. Stimulus elongation increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of the intermediate temporal frequency-selective filters to detection, the so-called first transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue stimuli.
2009-12-14
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1370/1/Baraas_Submitted100909.pdf
Baraas, Rigmor C. and Kulikowski, Janus J. and Muldoon, Mark R. (2009) Elongated S-cone stimuli reveal the importance of the intermediate temporal filter. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1401
2017-10-20T14:12:47Z
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74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/1401/
Bar-like S-cone stimuli reveal the importance of an
intermediate temporal filter
Baraas, Rigmor C.
Kulikowski, Janus J.
Muldoon, Mark R.
92 Biology and other natural sciences
87 Biological and medical physics
The relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli were studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although stimulus elongation apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. Stimulus elongation increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of the intermediate temporal frequency-selective filters to detection, the so-called first transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue stimuli.
2010-04
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1401/1/Baraas_Kulikowski_Muldoon_JOSAA.pdf
Baraas, Rigmor C. and Kulikowski, Janus J. and Muldoon, Mark R. (2010) Bar-like S-cone stimuli reveal the importance of an intermediate temporal filter. Journal of the Optical Society of America A, 27 (4). pp. 766-780. ISSN 1749-9097
10.1364/JOSAA.27.000766
10.1364/JOSAA.27.000766
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1698
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https://eprints.maths.manchester.ac.uk/1698/
Shape Deformation in Two-Dimensional
Electrical Impedance Tomography
Boyle, Alistair
Adler, Andy
Lionheart, William R.B.
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
Electrical Impedance Tomography (EIT) uses mea- surements from surface electrodes to reconstruct an image of the conductivity of the contained medium. However, changes in measurements result from both changes in internal conductivity and changes in the shape of the medium relative to the electrode positions. Failure to account for shape changes results in a conductivity image with significant artifacts. Previous work to address shape changes in EIT has shown that in some cases boundary shape and electrode location can be uniquely deter- mined for isotropic conductivities; however, for geometrically conformal changes, this is not possible. This prior work has shown that the shape change problem can be partially addressed. In this paper, we explore the limits of compensation for boundary movement in EIT, using three approaches: first, a theoretical model was developed to separate a deformation vector field into conformal and non-conformal components, from which the reconstruction limits may be determined; next, finite element models were used to simulate EIT measurements from a domain whose boundary has been deformed; finally, an experimental phantom was constructed from which boundary deformation measurements were acquired. Results, both in simulation and with experimental data, suggest that some electrode movement and boundary distortions can be reconstructed based on conduc- tivity changes alone while reducing image artifacts in the process.
2011-11-18
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1698/1/boyle_conformal_movement_ieee-draft7.pdf
Boyle, Alistair and Adler, Andy and Lionheart, William R.B. (2011) Shape Deformation in Two-Dimensional Electrical Impedance Tomography. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1853
2017-11-08T18:18:34Z
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https://eprints.maths.manchester.ac.uk/1853/
State transitions in a model of intermittent seizure dynamics
Goodfellow, M
Rummel, C
Garry, D
Baier, G
Schindler, K
Glendinning, P
87 Biological and medical physics
We present a neural mass model of intermittent transitions into electroencephalographic (EEG) seizure rhythms in epilepsy. The route to intermittent dynamics is identied as Type 1 and state transition statistics are explored. It is demonstrated that a single framework can give rise to different distributions for seizure and non-seizure lengths in line with variability observed clinically. Further investigation of this model can give insight into the possible mechanisms underlying spontaneous seizure transitions in the epileptic brain.
2012-08-03
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1853/1/NeuralMassIntermitMG_submit.pdf
Goodfellow, M and Rummel, C and Garry, D and Baier, G and Schindler, K and Glendinning, P (2012) State transitions in a model of intermittent seizure dynamics. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2062
2017-11-08T18:18:36Z
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https://eprints.maths.manchester.ac.uk/2062/
Sensitivity matrix and reconstruction algorithm for EIT assuming axial uniformity
Jerbi, Karim
Lionheart, William
Vauhkonen, Paivi
Vauhkonen, Marko
35 Partial differential equations
87 Biological and medical physics
References Cited By Metrics
In electrical impedance tomography (EIT) two-dimensional models continue to be applied despite their known inability to provide correct reconstruction. In this paper, a reconstruction algorithm that assumes a translationally invariant conductivity distribution is described. A more precise forward solver is obtained by taking off-slice currents into consideration. An appropriate sensitivity matrix is derived. Numerical evidence for the improvement in precision compared to two-dimensional reconstruction is given.
2013-11-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2062/1/Jerbi_Sensitivity.pdf
Jerbi, Karim and Lionheart, William and Vauhkonen, Paivi and Vauhkonen, Marko (2013) Sensitivity matrix and reconstruction algorithm for EIT assuming axial uniformity. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2308
2017-10-20T14:13:19Z
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2308/
Time series of EIT chest images using singular value decomposition and Fourier transform
Kerrouche, N
McLeod, CN
Lionheart, WRB
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
The aim of this study is to propose a useful method for exploring regional ventilation and perfusion in the chest. The paper describes two methods based on singular value decomposition (SVD) and Fourier transform (FT) respectively. This work shows that power spectral density (PSD) and phase images (derived from the Fourier transform) are easier to interpret and more useful tools for exploiting in vivo EIT data in healthy volunteers in order to explore the cardiovascular and respiratory systems
2001-02
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2308/1/fftsvd-colour.pdf
Kerrouche, N and McLeod, CN and Lionheart, WRB (2001) Time series of EIT chest images using singular value decomposition and Fourier transform. Physiological Measurement, 22. pp. 147-157. ISSN 0967-3334
http://iopscience.iop.org/0967-3334/22/1/318/
10.1088/0967-3334/22/1/318
10.1088/0967-3334/22/1/318
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2312
2017-10-20T14:13:20Z
7374617475733D707562
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7375626A656374733D4D5343:4D53435F3635
7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2312/
Single Scan Parameterization of Space-Variant Point Spread Functions in Image Space via a Printed Array: Impact for two PET/CT Scanners
Kotasidis, FA
Matthews, JC
Angelis, GI
Noonan, PJ
Jackson, A
Price, P
Lionheart, WR
Reader, AJ
45 Integral equations
65 Numerical analysis
87 Biological and medical physics
Incorporation of a resolution model during statistical image reconstruction often produces images of improved resolution and signal-to-noise ratio. A novel and practical methodology to rapidly and accurately determine the overall emission and detection blurring component of the system matrix using a printed point source array within a custom-made Perspex phantom is presented. The array was scanned at different positions and orientations within the field of view (FOV) to examine the feasibility of extrapolating the measured point source blurring to other locations in the FOV and the robustness of measurements from a single point source array scan. We measured the spatially-variant image-based blurring on two PET/CT scanners, the B-Hi-Rez and the TruePoint TrueV. These measured spatially-variant kernels and the spatially-invariant kernel at the FOV centre were then incorporated within an ordinary Poisson ordered subset expectation maximization (OP-OSEM) algorithm and compared to the manufacturer's implementation using projection space resolution modelling (RM). Comparisons were based on a point source array, the NEMA IEC image quality phantom, the Cologne resolution phantom and two clinical studies (carbon-11 labelled anti-sense oligonucleotide [11C]-ASO and fluorine-18 labelled fluoro-l-thymidine [18F]-FLT). Robust and accurate measurements of spatially-variant image blurring were successfully obtained from a single scan. Spatially-variant resolution modelling resulted in notable resolution improvements away from the centre of the FOV. Comparison between spatially-variant image-space methods and the projection-space approach (the first such report, using a range of studies) demonstrated very similar performance with our image-based implementation producing slightly better contrast recovery (CR) for the same level of image roughness (IR). These results demonstrate that image-based resolution modelling within reconstruction is a valid alternative to projection-based modelling, and that, when using the proposed practical methodology, the necessary resolution measurements can be obtained from a single scan. This approach avoids the relatively time-consuming and involved procedures previously proposed in the literature.
2011-04-13
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2312/1/Single_Scan_Parameterization_of_Space_Variant_Point_Spread_Functions_in_Image_Space_via_a_Printed_Array_Impact_for_two_PETCT_Scanners%281%29.pdf
Kotasidis, FA and Matthews, JC and Angelis, GI and Noonan, PJ and Jackson, A and Price, P and Lionheart, WR and Reader, AJ (2011) Single Scan Parameterization of Space-Variant Point Spread Functions in Image Space via a Printed Array: Impact for two PET/CT Scanners. Physics in Medicine and Biology, 56 (10). p. 2917. ISSN 1361-6560
http://iopscience.iop.org/0031-9155/56/10/003
10.1088/0031-9155/56/10/003
10.1088/0031-9155/56/10/003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2315
2017-10-20T14:13:20Z
7374617475733D707562
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2315/
POMPUS: an optimized EIT reconstruction algorithm
Paulson, K
Lionheart, W
Pidcock, M
47 Operator theory
02 Mathematical methods in physics
87 Biological and medical physics
Electrical impedance tomography (EIT) is a non-invasive imaging technique which aims to image the impedance of material within a test volume from electrical measurements made on the surface. The reconstruction of impedance images is an ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. This paper defines an experimental measurement in EIT and calculates optimal experiments which maximize the distinguishability between the region to be imaged and a best estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. We describe a reconstruction algorithm, known as POMPUS, which is based on the use of optimal experiments. We have shown that, given some mild constraints, if POMPUS converges, it converges to a stationary point of our objective function. It is demonstrated to be many times faster than standard, Newton based, reconstruction algorithms. Results using synthetic data indicate that the images produced by POMPUS are comparable to those produced by these standard algorithms.
1995
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2315/1/POMPUS.pdf
Paulson, K and Lionheart, W and Pidcock, M (1995) POMPUS: an optimized EIT reconstruction algorithm. Inverse Problems, 11 (2). pp. 426-437. ISSN 0266-5611
http://iopscience.iop.org/0266-5611/11/2/010/pdf/0266-5611_11_2_010.pdf
10.1088/0266-5611/11/2/010
10.1088/0266-5611/11/2/010
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2316
2017-10-20T14:13:20Z
7374617475733D707562
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2316/
Space variant PSF parameterization in image space using printed point source arrays on the HiRez PET/CT
Kotasidis, F.A.
Angelis, G.I.
Matthews, J.C.
Lionheart, W.R.B
Reader, A.J
47 Operator theory
02 Mathematical methods in physics
87 Biological and medical physics
A new practical and computationally efficient method for deriving and applying the space-variant blurring component of the system matrix is proposed and applied to the HiRez PET/CT scanner. The point spread function (PSF) was sampled at 14400 locations within the field-of-view (FOV) using an array of 120 18-F printed point sources. An HP printer was modified to print the sources on a sheet of A4 paper. To provide enough annihilating material for the positrons and move the array accurately within the FOV a Perspex phantom was designed. The reconstructed PSFs were parameterized in image space and modeled with a pair of multidimensional (3-D) Gaussian distributions. Through the fitting of appropriate functions, model parameters were interpolated and extrapolated for the remaining positions in the FOV. Image reconstruction with resolution modeling was implemented using the expectation maximization algorithm (OP-OSEM) and space variant image based convolution operations. Initial analysis shows significant improvements in the resolution using space variant kernels (reduction of FWHM from 5.5mm down to 2mm at 20cm radially). The improvements are more pronounced at the edge of the FOV when compared to the space invariant method where the discrepancy between the measured space variant blurring kernel and the invariant kernel are larger. Using the printer for producing radioactive point sources, the PSF was sampled at 14400 positions in less than 24h. Parameterizing the kernels in image space also provides a computation efficient alternative to projection space PSF parameterization with similar resolution improvements (a uniform resolution of 2mm throughout the FOV) and minimal increase in the reconstruction time.
2010-07-01
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2316/1/05548459.pdf
Kotasidis, F.A. and Angelis, G.I. and Matthews, J.C. and Lionheart, W.R.B and Reader, A.J (2010) Space variant PSF parameterization in image space using printed point source arrays on the HiRez PET/CT. 2010 IEEE International Conference on Imaging Systems and Techniques (IST),. 129 -134.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548459
10.1109/IST.2010.5548459
10.1109/IST.2010.5548459
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2324
2017-10-20T14:13:20Z
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74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2324/
Uniqueness, Shape, and Dimension in EIT
Lionheart, William R
35 Partial differential equations
47 Operator theory
87 Biological and medical physics
We briefly review the known mathematical results on uniqueness of solution in electrical impedance tomography (EIT). Generally, a real or complex conductivity is determined uniquely by complete boundary data. Uniqueness results are also known for planar resistor networks. However, it is common to make gross errors in the forward modeling of the electrical fields and this may result in no consistent solution. In particular, a two-dimensional model is often used when data are collected from a three-dimensional domain. The boundary shape is often inaccurately known, and commonly modeled by a circle. No model conductivity consistent with measured data exists when the dimension or the boundary shape is wrong.
1999-04
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2324/1/LIONHEART-1999-Annals_of_the_New_York_Academy_of_Sciences.pdf
Lionheart, William R (1999) Uniqueness, Shape, and Dimension in EIT. Annals of the New York Academy of Sciences, 873. pp. 466-471.
http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1999.tb09495.x/abstract
10.1111/j.1749-6632.1999.tb09495.x
10.1111/j.1749-6632.1999.tb09495.x
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2369
2017-10-20T14:13:22Z
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2369/
A Narrowband Level Set Method Applied to EIT in Brain for Cryosurgery Monitoring
Soleimani, Manuchehr
Dorn, Oliver
Lionheart, William RB
47 Operator theory
65 Numerical analysis
87 Biological and medical physics
In this paper we investigate the feasibility of applying a novel level set reconstruction technique to electrical imaging of the human brain. We focus particularly on the potential application of Electrical Impedance Tomography (EIT) to cryosurgery monitoring. In this application, cancerous tissue is treated by a local freezing technique using a small needle-like cryosurgery probe. The interface between frozen and non-frozen tissue can be expected to have a relatively high contrast in conductivity and we treat the inverse problem of locating and monitoring this interface during the treatment. A level set method is used as a powerful and flexible tool for tracking the propagating interfaces during the monitoring process. For calculating sensitivities and the Jacobian when deforming the interfaces we employ an adjoint formula rather than a direct differentiation technique. Particulary we are using a narrowband technique for this procedure. This combination of an adjoint technique and a narrowband technique for calculating Jacobians results in a computationally efficient and extremely fast method for solving the inverse problem. Moreover, due to the reduced number of unknowns in each step of the narrowband approach compared to a pixel- or voxel-based technique, our reconstruction scheme tends to be much more stable. We demonstrate that our new method also outperforms its pixel-/ voxel-based counterparts in terms of image quality in this application.
2006-11
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2369/1/Cry_Brian_Revised.pdf
Soleimani, Manuchehr and Dorn, Oliver and Lionheart, William RB (2006) A Narrowband Level Set Method Applied to EIT in Brain for Cryosurgery Monitoring. IEEE Transactions on Biomedical Engineering, 53 (11). 2257- 2264. ISSN 0018-9294
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1710167
10.1109/TBME.2006.877112
10.1109/TBME.2006.877112
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2379
2017-10-20T14:13:22Z
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74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/2379/
The effects of tomographic scans with fewer radiographs on the image reconstruction
Coban, S.B.
Withers, P.J.
Lionheart, W.R.B.
65 Numerical analysis
81 Materials science
87 Biological and medical physics
Reconstructing a 2D slice or a 3D volume from a set of insufficient tomographic data is a difficult problem, and it is often tackled with analytical reconstruction algorithms. However, these types of methods fall short on delivering a quality image due to the severe artefacts introduced by the insufficiency of the data. The presented work shows the effects of taking tomographic scans with fewer radiographs on the quality of the reconstructed images. The aim here is to show the advantages of using iterative reconstruction methods over analytical methods, which are demonstrated by a quantitative comparison.
2015-09-03
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2379/1/tosca_scoban.pdf
Coban, S.B. and Withers, P.J. and Lionheart, W.R.B. (2015) The effects of tomographic scans with fewer radiographs on the image reconstruction. In: Tomography for Scientific Advancement Symposium, 3-4 September 2015, University of Manchester, United Kingdom.
http://www.nhm.ac.uk/content/dam/nhmwww/our-science/dpts-facilities-staff/Coreresearchlabs/ToScA%20Programme%202015.pdf
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2477
2017-10-20T14:13:26Z
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74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2477/
Absolute Conductivity Reconstruction in Magnetic Induction
Tomography Using a Nonlinear Method
Soleimani, Manuchehr
Lionheart, William
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
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Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential V, a so called A, A-V formulation. A theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise
2006-12
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2477/1/Final_Revised_MIT.pdf
Soleimani, Manuchehr and Lionheart, William (2006) Absolute Conductivity Reconstruction in Magnetic Induction Tomography Using a Nonlinear Method. IEEE Transactions on Medical Imaging, 25 (12). pp. 1521-1530. ISSN 0278-0062
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4016173&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4016173
10.1109/TMI.2006.884196
10.1109/TMI.2006.884196
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2488
2017-10-20T14:13:27Z
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2488/
Characterization of objects by electrosensing fish
based on the first order polarization tensor
Ahmad Khairuddin, Taufiq K
Lionheart, William R B
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
Weakly electric fish generate electric current and use hundreds of voltage
sensors on the surface of their body to navigate and locate food. Experiments [G.
von der Emde and S. Fetz, J. Exp Biol, 210, 3082�3095, 2007] show that they can
discriminate between differently shaped conducting or insulating objects by using
electrosensing. One approach to electrically identify and characterize the object with a
lower computational cost rather than full shape reconstruction is to use the first order
Polarization Tensor (PT) of the object.
In this paper, by considering experimental work on Peters� elephantnose fish
Gnathonemus petersii, we investigate the possible role of the first order PT in the
ability of the fish to discriminate between objects of different shape. We also suggest
some experiments that might be performed to further investigate the role of the first
order PT in electrosensing fish. Finally, we speculate on the possibility of electrical
cloaking or camouflage in prey of electrosensing fish and what might be learnt from
the fish in human remote sensing.
2016
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2488/1/fishpaper-taufiqlionheart-v3.pdf
Ahmad Khairuddin, Taufiq K and Lionheart, William R B (2016) Characterization of objects by electrosensing fish based on the first order polarization tensor. Bioinspiration & Biomimetics. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2565
2017-10-20T14:13:30Z
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https://eprints.maths.manchester.ac.uk/2565/
The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles
Shearer, T.
Thorpe, C.T.
Screen, H.R.C.
81 Materials science
87 Biological and medical physics
A nonlinear elastic microstructural model is used to investigate the relationship between structure and function in energy-storing and positional tendons. The model is used to fit mechanical tension test data from the equine common digital extensor tendon (CDET) and superficial digital flexor tendon (SDFT), which are used as archetypes of positional and energy-storing tendons, respectively. The fibril crimp and fascicle helix angles of the two tendon types are used as fitting parameters in the mathematical model to predict their values. The outer fibril crimp angles were predicted to be 15.1° ± 2.3° in the CDET and 15.8° ± 4.1° in the SDFT, and the average crimp angles were predicted to be 10.0° ± 1.5° in the CDET and 10.5° ± 2.7° in the SDFT. The crimp angles were not found to be statistically significantly different between the two tendon types (p = 0.572). By contrast, the fascicle helix angles were predicted to be 7.9° ± 9.3° in the CDET and 29.1° ± 10.3° in the SDFT and were found to be statistically highly significantly different between the two tendon types (p < 0.001). This supports previous qualitative observations that helical substructures are more likely to be found in energy-storing tendons than in positional tendons and suggests that the relative compliance of energy-storing tendons may be directly caused by these helical substructures.
2017
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2565/1/The_relative_compliance_of_energy-storing_tendons_may_be_due_to_the_helical_fibril_arrangement_of_their_fascicles.pdf
Shearer, T. and Thorpe, C.T. and Screen, H.R.C. (2017) The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles. Journal of the Royal Society Interface, 14. p. 20170261.
http://rsif.royalsocietypublishing.org/content/14/133/20170261
10.1098/rsif.2017.0261
10.1098/rsif.2017.0261
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2828
2021-07-14T07:32:21Z
7374617475733D696E7072657373
7375626A656374733D4D5343:4D53435F3435
7375626A656374733D50414353:504143535F3630:504143535F3631
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7375626A656374733D50414353:504143535F3830:504143535F3837
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2828/
Diffraction tomography inversion and the transverse ray transform
Lionheart, William R.B.
Korsunsky, Alexander M.
45 Integral equations
61 Structure of solids and liquids; crystallography
81 Materials science
87 Biological and medical physics
We show that a reciprocal space squared intensity map of a material can be recovered, for each characteristic length scale, from diffraction tomography data by a simple slice-by-slice reconstruction method. Moreover if the reciprocal space map can be represented by a finite sum of spherical harmonic components for each length scale then the coefficients of that expansion can be recovered from inverting the transverse ray transform (TRT), where the data are polynomial coefficients of the azimuthal diffraction pattern for each length scale.
2021-07
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2828/1/fully3d_LionheartKorsunsky_v2.pdf
Lionheart, William R.B. and Korsunsky, Alexander M. (2021) Diffraction tomography inversion and the transverse ray transform. Proceedings of 16th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine. (In Press)
https://kuleuvencongres.be/fully3d-2021