model based visualization of cardiac virtual tissue

Model-based Visualization of Cardiac Virtual Tissue

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Model based Visualization of Cardiac Virtual Tissue

James Handley, Ken Brodlie – University of LeedsRichard Clayton – University of Sheffield


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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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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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Normal rhythm Ventricular fibrillation

How does it start? How can we stop it?

Ventricular Fibrillation – The Killer


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Ventricular Fibrillation – Re-entry


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Cardiac Virtual Tissue

Model cardiac tissue as a continuous excitable medium m

ionm

C

IVD

tVm )

~(

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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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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Fenton Karma 4 variable LuoRudy2 – 14 variable

Simplified and detailed models


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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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U V W D

Reduce the data


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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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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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FK3, Homogenous tissue, no re-entrant behaviour


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FK3, Heterogeneous tissue, re-entrant behaviour


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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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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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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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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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According to Density - Form images using hyper-dimensional histograms using

histogram sizes

x = 55, y = 91

x = 55, y = 91


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According to Position - Form images using hyper-dimensional histograms using

histogram IDs

x = 55, y = 91

x = 55, y = 91


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FK3, Homogenous tissue, no re-entrant behaviour


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FK3, Heterogeneous tissue, re-entrant behaviour


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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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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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Fenton Karma three variable model

Action Potential Model-based Representation


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Luo Rudy 2 fourteen variable model

Action potential Model-based representation


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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)

model based visualization of cardiac virtual tissue

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