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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
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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.
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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.
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Model-based Visualization of Cardiac Virtual Tissue 4 Normal rhythmVentricular fibrillation How does it start?How can we stop it? Ventricular Fibrillation – The Killer
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Model-based Visualization of Cardiac Virtual Tissue 5 Ventricular Fibrillation – Re-entry
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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
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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?)
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Model-based Visualization of Cardiac Virtual Tissue 8 Fenton Karma 4 variable LuoRudy2 – 14 variable Simplified and detailed models
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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?
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Model-based Visualization of Cardiac Virtual Tissue 10 UVWD Reduce the data
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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
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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
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Model-based Visualization of Cardiac Virtual Tissue 13 FK3, Homogenous tissue, no re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue 14 FK3, Heterogeneous tissue, re-entrant behaviour
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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??
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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?
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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
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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
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Model-based Visualization of Cardiac Virtual Tissue 19 According to Density - Form images using hyper- dimensional histograms using histogram sizes x = 55, y = 91
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Model-based Visualization of Cardiac Virtual Tissue 20 According to Position - Form images using hyper- dimensional histograms using histogram IDs x = 55, y = 91
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Model-based Visualization of Cardiac Virtual Tissue 21 FK3, Homogenous tissue, no re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue 22 FK3, Heterogeneous tissue, re-entrant behaviour
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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
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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
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Model-based Visualization of Cardiac Virtual Tissue 25 Fenton Karma three variable model Action Potential Model-based Representation
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Model-based Visualization of Cardiac Virtual Tissue 26 Luo Rudy 2 fourteen variable model Action potential Model-based representation
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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)
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