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

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!

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

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 .

𝜀1

xω

 

 background

perturbation

x

1

1

0

0

 

 xω

𝜀2

Method: Fraction model

?

Conductivity Tissue spectra Fraction values

𝜀1𝜀2

Method: Fraction reconstruction

Conductivity Fractions

Markov Random field regularization:

Method: Fraction reconstructionNumerical validation

Fractions

ModelMinimize…

…subject to

Step 1. Gradient projection

Step 2. Damped Gauss-Newton

repe

at

Results: Use of difference dataPhantom

Fractions Absolute Conductivities

Difference data Absolute data

Results: Use of all multifrequency dataPhantom

Fractions

All frequencies Single frequency

WFD Conductivities

Results: Use of nonlinear methodModel

Fractions WFD Conductivities

Nonlinear method Linear method

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?

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

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

emma.malone.11@ucl.ac.uk