1. Model-based Visualization of Cardiac Virtual Tissue 1 Model based Visualization of Cardiac Virtual Tissue James Handley, Ken Brodlie – University of Leeds Richard Clayton – University of Sheffield

2. Model-based Visualization of Cardiac Virtual Tissue 2 Tackling two Grand Challenge research questions: What causes heart disease How does a cancer form and grow? Together these diseases cause 61% of all UK deaths.

3. Model-based Visualization of Cardiac Virtual Tissue 3 Why model the heart?  Heart disease is an important health problem.  Worldwide, cardiovascular disease causes 19 million deaths annually, over 5 million between the ages of 30 and 69 years.  Spectrum of acquired and congenital heart disease, multiple disease mechanisms.  All disease mechanisms are difficult to study experimentally.  Heart is simpler (structurally and functionally) than other organs.

4. Model-based Visualization of Cardiac Virtual Tissue 4 Normal rhythmVentricular fibrillation How does it start?How can we stop it? Ventricular Fibrillation – The Killer

5. Model-based Visualization of Cardiac Virtual Tissue 5 Ventricular Fibrillation – Re-entry

6. Model-based Visualization of Cardiac Virtual Tissue 6 Cardiac Virtual Tissue Model cardiac tissue as a continuous excitable medium Solve using finite difference grid. At each timestep  Compute dV due to diffusion  Compute dV due to dynamic response of cell membrane  Different models can be used; simplified and detailed  Update membrane voltage at each grid point

7. Model-based Visualization of Cardiac Virtual Tissue 7 The Visualization Challenge Standard Visualization techniques of 2D and 3D models use a single variable… …but detailed models may have dozens of variables. Can we visualize the entire state of the heart model in a single image (or figure?)

8. Model-based Visualization of Cardiac Virtual Tissue 8 Fenton Karma 4 variable LuoRudy2 – 14 variable Simplified and detailed models

9. Model-based Visualization of Cardiac Virtual Tissue 9 Impossible! The Visualization Challenge (3+1) dimensional 14+ variate data cannot be perfectly visualized in a single picture on a (2+1) dimensional computer screen….. but can we make at least a useful representation in a single image?

10. Model-based Visualization of Cardiac Virtual Tissue 10 UVWD Reduce the data

11. Model-based Visualization of Cardiac Virtual Tissue 11 Move into ‘Phase Space’ x = 55, y = 91 Observation 1: 3 k x k images can be expressed as k x k points in 3-dimensional space U V W

12. Model-based Visualization of Cardiac Virtual Tissue 12 CVT data sets – Phase Space Visualization 1.Normal action potential propagation through homogeneous tissue 2.Re-entrant behaviour in heterogeneous tissue Using a 2D slice of Fenton Karma 3 variable CVT

13. Model-based Visualization of Cardiac Virtual Tissue 13 FK3, Homogenous tissue, no re-entrant behaviour

14. Model-based Visualization of Cardiac Virtual Tissue 14 FK3, Heterogeneous tissue, re-entrant behaviour

15. Model-based Visualization of Cardiac Virtual Tissue 15 Phase Space Visualization Problem: This works for 3 variables – but generalisation for M variables is: M k x k images represented as k x k points in M-dimensional space How do we visualize M-dimensional space??

16. Model-based Visualization of Cardiac Virtual Tissue 16 What does phase space look like for 14 variable Luo Rudy 2? Look at 2D projections - Here are 13 phase space representations of action potential against other variables But.. can we get a single, composite picture - if possible, in the original space?

17. Model-based Visualization of Cardiac Virtual Tissue 17 From ‘Phase Space’ to Image x = 55, y = 91 Observation 2: M k x k images represented as 1 composite k x k image W V U

18. Model-based Visualization of Cardiac Virtual Tissue 18 Assigning Value to a Point in Phase Space We look first at two general techniques: –Value according to density of points in that point’s neighbourhood of phase space –Value according to position of point in phase space

19. Model-based Visualization of Cardiac Virtual Tissue 19 According to Density - Form images using hyper- dimensional histograms using histogram sizes x = 55, y = 91

20. Model-based Visualization of Cardiac Virtual Tissue 20 According to Position - Form images using hyper- dimensional histograms using histogram IDs x = 55, y = 91

21. Model-based Visualization of Cardiac Virtual Tissue 21 FK3, Homogenous tissue, no re-entrant behaviour

22. Model-based Visualization of Cardiac Virtual Tissue 22 FK3, Heterogeneous tissue, re-entrant behaviour

23. Model-based Visualization of Cardiac Virtual Tissue 23 Model based Approach Why not use knowledge of normal behaviour? Build a model of the expected locations of points in phase space For any simulation, visualize the difference from normal behaviour –The value of a point then becomes the distance of the point from the model –In this way abnormal points are highlighted to the greatest extent

24. Model-based Visualization of Cardiac Virtual Tissue 24 Building the Point-based Model Capture every point in M-dimensional phase space for simulation showing normal behaviour –Typically this generates millions of points over time Model then decimated because: –Many points co-located –Distance calculation is expensive Any point removed is within ‘eps’ of point retained –Typical reduction: 5 million to 500

25. Model-based Visualization of Cardiac Virtual Tissue 25 Fenton Karma three variable model Action Potential Model-based Representation

26. Model-based Visualization of Cardiac Virtual Tissue 26 Luo Rudy 2 fourteen variable model Action potential Model-based representation

27. Model-based Visualization of Cardiac Virtual Tissue 27 Conclusions New insight gained from moving to phase space – particularly for three variables Higher number of variables is challenging – but some merit in mapping M-dimensional phase space back to the image space by assigning phase space properties to pixels Approach will generalise to 3D models: –3 k x k x k volumes will map to k x k x k points in 3D phase space –M k x k x k volumes will map to a composite k x k x k volume (via M-dimensional phase space)