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
Introduction: EIT of acute stroke
• 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!
Ischaemic
Haemorrhagic
Introduction: Multifrequency EIT
Nonlinear absolute
High sensitivity to errors
Simple FD
Very limited application
perturbation
background
Weighted FD
Limited application
Jun et al (2009), Phys. Meas., 30(10), 1087-99.
Method: Fraction model
The following assumptions are made:
1. the domain is composed of a known number T of tissues
distinct conductivity,
2. the conductivity of each tissue
frequencies,
with
is known for all measurement
3. the conductivity of the nth element is given by the linear combination of the
conductivities of the component tissues
where
and
.
Method: Fraction model
𝜀1
perturbation
1
0
ω
x
𝜀2
x
1
background
0
ω
Conductivity
Tissue spectra
x
Fraction values
𝜀1
𝜀2
?
Method: Fraction reconstruction
Conductivity
Markov Random field regularization:
Fractions
Method: Fraction reconstruction
Numerical validation
Minimize…
Model
…subject to
Fractions
repeat
Step 1. Gradient projection
Step 2. Damped Gauss-Newton
Results: Use of difference data
Phantom
Difference data
Fractions
Absolute data
Absolute Conductivities
Results: Use of all multifrequency data
Phantom
All frequencies
Fractions
Single frequency
WFD Conductivities
Results: Use of nonlinear method
Model
Nonlinear method
Fractions
Linear method
WFD Conductivities
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?
Future work
Tissue properties
Hidden variable
1. Reconstruction
2. Classification
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.
Thank for your attention
emma.malone.11@ucl.ac.uk
Centre for Medical Imaging and Computing (CMIC)
Electrical Impedance Tomography (EIT) Research Group
Department of Medical Physics and Bioengineering, University College London