Inverse problem of EIT using spectral constraints
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Inverse problem of EIT using spectral constraints
Emma Malone1, Gustavo Santos1, David Holder1, Simon Arridge2
1 Department of Medical Physics and Bioengineering, University College London, UK 2 Department of Computer Science, University College London, UK
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Introduction: EIT of acute stroke
Ischaemic
Haemorrhagic
• Stroke is the leading cause of disability and third cause of mortality in industrialized nations.
• Clot-busting drugs can improve the outcome of ischaemic stroke, but they need to be administered FAST!
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Simple FD
Weighted FDJun et al (2009), Phys. Meas., 30(10), 1087-99.
Nonlinear absolute
Introduction: Multifrequency EIT
background
perturbation
High sensitivity to errors
Very limited application
Limited application
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Method: Fraction model
The following assumptions are made:
1. the domain is composed of a known number T of tissues with distinct conductivity,
2. the conductivity of each tissue is known for all measurement frequencies,
3. the conductivity of the nth element is given by the linear combination of the conductivities of the component tissues
where and .
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𝜀1
xω
background
perturbation
x
1
1
0
0
xω
𝜀2
Method: Fraction model
?
Conductivity Tissue spectra Fraction values
𝜀1𝜀2
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Method: Fraction reconstruction
Conductivity Fractions
Markov Random field regularization:
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Method: Fraction reconstructionNumerical validation
Fractions
ModelMinimize…
…subject to
Step 1. Gradient projection
Step 2. Damped Gauss-Newton
repe
at
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Results: Use of difference dataPhantom
Fractions Absolute Conductivities
Difference data Absolute data
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Results: Use of all multifrequency dataPhantom
Fractions
All frequencies Single frequency
WFD Conductivities
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Results: Use of nonlinear methodModel
Fractions WFD Conductivities
Nonlinear method Linear method
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Discussion
Advantages:• Simultaneous and direct use of all multifrequency data• Nonlinear reconstruction method• Use of difference data
Disadvantage:Requires accurate knowledge of tissue spectra.
Temperature?Flow rate?Cell count?
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Hiltunen P, Prince S J D, & Arridge S (2009). A combined reconstruction-classification method for diffuse optical tomography. Physics in medicine and biology, 54(21), 6457–76.
Future work
Hidden variable
Tissue properties
1. Reconstruction
2. Classification
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Centre for Medical Imaging and Computing (CMIC)
Electrical Impedance Tomography (EIT) Research Group
Department of Medical Physics and Bioengineering, University College London
Thank for your attention