electrical impedance tomography: image algorithms and applications
DESCRIPTION
Electrical ImpedanceTomography:Image Algorithms andApplicationsTRANSCRIPT
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 1
Electrical Impedance Tomography:
Image Algorithms and Applications
Andy Adler
Assistant Professor, SITE, U.Ottawa
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 2
Outline
• Electrical Impedance Tomography• Physics• Image Reconstruction• Applications• Future Work
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 3
Electrical Impedance Tomography
• Relatively new medical imaging technique (early 1990’s)
• Body Surface Electrodes apply current patterns and measure the resulting voltages
• Distribution of conductivity is calculated
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 4
EIT: Block Diagram
+
+
CurrentSource
Amplifiers
Controler
Dataacquisition
Medium
+
Imaging SystemΩ
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 5
EIT: Applications
• EIT can image physiological processes involving movement of conductive fluids and gasses
• Lungs• Heart / perfusion• GI tract• Brain• Breast
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 6
EIT: Advantages
EIT is a relatively low resolution imaging modality, but
• Non-invasive• Non-cumbersome• Suitable for monitoring• Underlying technology is low cost
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 7
Application: Breathing
Chest images of tidal breathing in normal
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 8
Application: Heart Beat
EIT signal in ROI around heart and ECG
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 9
Non-invasive
0.1
1
10
100
30 100 300 1K 3K 10K 30K
Frequency (Hz)
Current(mA)
Percentile 99Percentile 50Percentile 1EIT system
Thresholds for cutaneous perception of electric current vs. frequency and EIT system
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 10
EIT: Physics
• Within medium there is E and J.
•
dtd
od
c
EJ
EJ
εε
σ
=
=
( )EJ ojωεεσ −=
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 11
EIT: Physics
In the absence of magnetic fields
No charge build up in conductive medium
We have
V−∇=E
0J =−=•∇t∂
∂ρ
( ) Ω=∇−•∇ in 0Vj oωεεσ
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 12
Image Reconstruction:Static Imaging
Static imaging reconstructs the absolute conductivity from measurements.
Algorithms:• Iterative (Newton-Raphson)• Layer Stripping
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 13
CurrentInjection
Patient
andEIT data
measurement
Real Data
Finite Element Model
EIT datasimulation Simulation Data
Does simulationapproximate
real data
Finishedyes
Updateconductivitydistribution
no
Block Diagram of Iterative Algorithm
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 14
Static Imaging Difficulties
• Extremely sensitive to uncertainties in electrode position
• Ill-conditioned problem• Numerical instability
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 15
Dynamic Imaging
• Calculate change in conductivity distribution from change in measurements
• Inverse problem linearized• Much reduced sensitivity to electrode
and hardware errors.• Very suitable for physiological imaging:
lung, heart, GI
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 16
Dynamic imaging techniques
• Backprojection: Voltages are “projected” along the equipotential lines.
Equipotential Region
Current Injection I+_I
M+M_
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 17
Inverse Techniques
• We can pose dynamic imaging as linear inverse, using a sensitivity matrix
j
jhhj δ
δσσ )()( +−=
zzz
σ∆= Hz
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 18
Inverse Techniques
• Classic least-squares inverse
( ) zHHHx
Hxztt 1
ˆ−
=
=
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 19
Matrix Techniques
However, problem is:• ill-conditioned: measurements depend
much more on data near electrodes than in centre
• ill-formed: more unknowns than measurements
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 20
Regularized Imaging
Given Linear Model:
Maximum A Posteriori (MAP) estimate is:
( ) ( )∞−−−−− ++=
+=
xRRHRHRHx
nHxz
11111ˆ xnt
xnt z µµ
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 21
Regularized Imaging• Parameters W, Q, , represent a priori
statistical knowledge of problem
[ ]( ) ( )[ ] [ ]
[ ]
==
−==
=
∞∞∞∞
∞
22
21
00
σσ
nnR
xxxxx-xx-xR
x x
n
x
t
ttt
E
EE
E
∞x
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 22
Advantages of Regularization
• Stabilizes ill-conditioned inverse• Introduction of a priori information• Control of resolution-noise performance
trade-off• MAP inverse justifies the formulation in
terms of Bayesian statistics
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 23
Regularized Inverse
Parameters:• W: models measurement noise• Q: penalizes image features which are
greater than data supports• : represents the background
conductivity distribution (heart,lungs,etc)• : “hyper-parameter” amount of
regularization
∞x
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 24
Noise – Resolution Tradeoff
F: Meas: No Noise Reconst: NF= 2.0G: Meas: -3dB SNR Reconst: NF= 2.0
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 25
Noise – Resolution Tradeoff
F: Meas: No Noise Reconst: NF= 0.4G: Meas: -3dB SNR Reconst: NF= 0.4
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 26
Electrode Movement
• Electrodes on chest move during breathing
• Figure shows rough movement pattern of rib cage
A B
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 27
Electrode Movement
• FEM of electrical and mechanical properties of thorax to simulate
• Signal from expansion shown to contribute 10-20% of conductivity signal
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 28
Applications: Lung Function and Disease
Monitoring of lung function is important in ICU. Issues are:
• Distribution of ventilation• Ventilation – perfusion match• Lung Edema• Flow limitation (obstructive lung
disease)
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 29
Lung function tests
• Patients with obstructive lung disease (emphysema, bronchitis) tend to dynamically hyperinflate: lower inspiration than expiration.
• Simulated with PEEP (positive end expiratory pressure)
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 30
Lung Function: Protocol
• Initially, inflations to 3 kPa• dog expires to the applied PEEP• ventilation stopped, and dog expires against PEEP for 15 s
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 31
Lung Function
A: image of section thorax due to ∆VL 800 mlB: image due to a ∆VL 400 where left main
stem bronchus was plugged.
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 32
• Volume estimates by EIT, Pao and Pes, after step volume increases of 100ml, 500ml, 900ml.
• Note that EIT signal does not display overshoot
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 33
Pulmonary Edema
• Pulmonary Edema (lungs filled with fluid) plagues ICU patients for heart disease, accident victims
• Typical monitoring techniques are invasive (Swan-Ganz catheter)
• We looked at EIT ability to monitor level of Edema.
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 34
Pulmonary Edema: Results
• Change in lung liquid volume by EIT vs liquid volume instilled
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 35
Imaging
• Algorithms to use data from internal electrodes
• How to manage electrode artefacts• Arbitrary electrode placements• Image interpretation and error bounds
given artefacts and noise
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A.Adler, Oct 28, 2002 Electrical Impedance Tomography 36
Applications of interest
• Longer term monitoring in ICU• Small animal lung function• Contrast agents• Inhomogeneous ventilation on smaller
scale