Electrical Impedance Tomography: advances in Image Reconstruction

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1 Electrical Impedance Tomography: advances in Image Reconstruction Andy Adler Systems and Computer Engineering, Carleton U, Ottawa, Canada

2 Outline Electrical Impedance Tomography Imaging the lungs Measurement Difficulties and solutions Electrode Errors Electrode Movement 3D Imaging / Electrode Placement Temporal Filtering EIDORS Project

3 Lung images A: image of section thorax due to VL 800 ml B: image due to a VL 400 where left main stem bronchus was plugged.

4 Volume estimates by EIT, Pao and Pes, after step volume increases of 00ml, 500ml, 900ml. Note that EIT signal does not display overshoot Time (s)

5 Pulmonary Oedema: model using fluid instillation Change in lung liquid volume by EIT vs liquid volume instilled

6 Iterative (Absolute) Image Reconstruction Patient Current Injection and EIT data measurement Real Data Finite Element Model Does simulation approximate real data yes no Finished EIT data simulation Simulation Data Update conductivity distribution

7 Absolute Imaging Difficulties Extremely sensitive to uncertainties in electrode position Need to know where electrodes are to and electrode shape to mm Absolutely must do 3D Numerical instability Slow reconstructions Is muscle in chest isotropic?

8 Difference Imaging: Example

9 Difference Imaging Calculate from conductivity measurements Inverse problem linearized reduced sensitivity to electrode and hardware errors. Suitable for physiological imaging: lung, heart, GI

10 Image Reconstruction Forward Model (linearized) Measurements (difference) Image (difference) = + noise Jacobian System is underdetermined

11 Image Reconstruction Regularized linear Inverse Model 2 + Penalty Function Norm weighted by measurement accuracy Way to introduce prior knowledge into solution

12 Noise Resolution Tradeoff Lots of Regularization (large penalty) Little Regularization (small penalty) No Noise -3dB SNR

13 Applications Electrode Errors Electrode Movement 3D Imaging / Electrode Placement Temporal Filtering

14 Electrode Measurement Errors Experimental measurements with EIT quite often show large errors from one electrode Causes aren t always clear Electrode Detaching Skin movement Sweat changes contact impedance Electronics Drift?

15 Example of electrode errors A B C Bad Electrode Images measured in anaesthetised, ventilated dog A. Image of 700 ml ventilation B. Image of 00 ml saline instillation in right lung C. Image of 700 ml ventilation and 00 ml saline

16 Measurements with bad electrode Bad Electrode X X X X X X X X X X X X X X X X X X X X X X X X bad measurement X measurement at current injection

17 Zero bad data solution Traditional solution (in the sense that I ve done this) Error Here Replace With zero 2-2 σ σ σ 3-2 σ 4

18 Regularized imaging solution Electrode errors are large measurement noise on affected electrode Error Here 2-2 σ σ 2-2 Low SNR here Replace With zero -2 σ 3-2 σ 4

19 Simulation Small targets simulated at different radial positions Position in % of medium diameter Bad Electrode Data simulated with 2D FEM with 024 elements not same as inverse model

20 Simulation results for opposite drive No Electrode Errors Zero Affected Measurements Regularized Image

21 How does this work with real data? A B C Bad Electrode A. Image of 700 ml ventilation B. Image of 00 ml saline instillation in right lung C. Image of 700 ml ventilation and 00 ml saline

22 Electrode Movement A B Electrodes move with breathing with posture change Simulations show broad central artefact in images

23 Imaging Electrode Movement Forward model image includes movement = + noise Jacobian now includes measurement change due to movement image now includes x,y sensor movement

24 Images of electrode movement Simulation: tank twisted in 3D y x

25 Top slice Middle slice Bottom slice Simulation Standard Algorithm with electrode movement

26 3D Electrode Arrangements using 6 electrodes Aligned Offset

27 Electrode Sequencing Can put electrodes anywhere; algorithm knows and can interpret data Electrode Placement strategies to evaluate Planar Planar-Offset Planar-Opposite Zigzag Zigzag-Offset Zigzag-Opposite Square

28 Planar Planar-Offset

29 Zigzag Zigzag-Offset

30 Planar- Opposite ZigZag- Opposite

31 Square

32 3D placement summary Planar Planar-Offset Planar-Opposite Zigzag Zigzag-Offset Zigzag-Opposite - - Square Resolution Vert. Posn Error Radial Posn Error Qualitative Image Noise Performance Layer Offset Error Layer Sep Error

33 Recommended 3D placement Planar and Planar-offset strategies are most robust. Planar placement is easiest

34 EIT makes fast measurements. Can we use this fact? Measurement sequence Jacobian Image sequence = n -n n past now future past now future

35 Temporal Reconstruction Temporal Penalty Functions likely quite likely unlikely Standard EIT approaches to not take this into account

36 GN vs. Temporal Inverse. Noise free data (IIRC tank) 2. Data with added 6dB SNR noise Gauss-Newton solver Solve time = 5.33 s (with caching) = 0.22 s Temporal solver (4 time steps) Solve time = 34.8 s (with caching) = 0.60 s

37 Gauss Newton vs. Temporal Inverse (6db SNR) Gauss-Newton solver Solve time = 5.33 s (with caching) = 0.22 s Temporal solver (4 time steps) Solve time = 34.8 s (with caching) = 0.60 s

38 Non-blurring EIT Traditional EIT will dramatically blur reconstructed contrasts Iterative (ie slower) techniques exist to remove blur Problem still low spatial resolution

39 Total Variation images

40 EIDORS: community-based extensible software for EIT Andy Adler, William R.B. Lionheart 2 Systems and Computer Engineering, Carleton University, Ottawa, Canada 2 School of Mathematics, University of Manchester, U.K.

41 EIDORS Tutorial Introduction to EIDORS Goal Features Examples (worked together) Forward solutions Inverse solutions Examples (worked alone) Based on EIDORS tutorial (with V3.)

42 Goal: software community Project: Electrical Impedance and Diffuse Optical Tomography Reconstruction Software

43 Blobby the Walrus?. EIT images blobby objects in aqueous media; Blobby the Walrus is a fat animal that lives in water. 2. Walrus is EIDORS logo 3. Walruses are much funnier than a talk about software architecture. Images credit: Genny Anderson

44 EIDORS Features Open-source: License: GNU General Public License. Free to use, modify, and distribute modifications. May be used in a commercial product Hosted on Sourceforge.net Software is available for download (version 2.0) CVS access to latest developer versions Group members can modify Anyone can read and download

45 Web Site Walrus This Tutorial Release Version Developer Version

46 Features Language independence: Octave (octave.org, ver 2.9) Matlab (version 6.0). Usage examples: new software is based on demos. simple and more complex usage examples. Tests: Software is intrinsically difficult to test. Numerical software is probably more difficult Implement of regression test scripts

47 Features Pluggable code base: Object-oriented: Packaging and Abstraction. Don t use the Matlab OO framework Instead, EIDORS designed as "Pluggable" software using function pointers.

48 Features Automatic matrix caching: Save computationally expensive variables ie Jacobian, Image priors. Caching complicates software Caching managed in eidors_obj

Features Generalized data formats: EIT has a wide variety of stimulation, measurements general EIT data format : fwd_model electrode positions

49 Features Generalized data formats: EIT has a wide variety of stimulation, measurements general EIT data format : fwd_model electrode positions contact impedances stimulation and measurement patterns. Interface software for common EIT systems: Load data from some EIT systems Please contribute

50 getting started Download Run tutorial examples Join Mailing list Sign up as developer at: sourceforge.net Contribute your code

51 Tutorials Also tutorial.shtml In eidors-v3. distribution Tutorials

52 Summary EIT and Image Reconstruction Electrode Errors Electrode Movement Temporal Filtering EIDORS Project Significant recent developments in EIT image algorithms will improve EIT s clinical applicability

53 Is backprojection bad? Yes No Mathematical Model poorly understood artifacts Pushes objects into centre Can t handle arbitrary electrode placements No 3D Must be done on a circular thorax No Handles position Error Maybe good enough for rough model

54 What do clinical people want from algorithm people? Better accuracy? More stable Automatic detection of errors How much more accurate data (ie. electrode placement) are clinical people prepared to make

EIT: reflections on two weeks of EIT research in Kiel. Andy Adler SCE, Carleton University, Ottawa, Canada

EIT: reflections on two weeks of EIT research in Kiel Andy Adler SCE, Carleton University, Ottawa, Canada Applications: Breathing Me in 1993. Data from 7 fps system (Guardo 1991) Application: Heart Beat