Download All Hands Meeting 2005

Model-based Visualization of Cardiac Virtual Tissue
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
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
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
Ventricular Fibrillation – The Killer
Normal rhythm
Ventricular fibrillation
How does it start?
How can we stop it?
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Model-based Visualization of Cardiac Virtual Tissue
Ventricular Fibrillation – Re-entry
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Model-based Visualization of Cardiac Virtual Tissue
Cardiac Virtual Tissue
Model cardiac tissue
as a continuous
excitable medium
Iion
~
Vm    ( D
Vm) 
t
Cm
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
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
Simplified and detailed models
Fenton Karma 4 variable
LuoRudy2 – 14 variable
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Model-based Visualization of Cardiac Virtual Tissue
The Visualization Challenge
Impossible!
(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
Reduce the data
U
V
W
D
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Model-based Visualization of Cardiac Virtual Tissue
Move into ‘Phase Space’
U
V
W
x = 55, y = 91
Observation 1:
3 k x k images can be expressed as k x k points
in 3-dimensional space
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Model-based Visualization of Cardiac Virtual Tissue
CVT data sets – Phase Space
Visualization
Using a 2D slice of Fenton Karma 3 variable CVT
1. Normal action potential propagation
through homogeneous tissue
2. Re-entrant behaviour in heterogeneous
tissue
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Model-based Visualization of Cardiac Virtual Tissue
FK3, Homogenous tissue, no re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue
FK3, Heterogeneous tissue, re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue
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
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
From ‘Phase Space’ to Image
U
V
W
x = 55, y = 91
Observation 2: M k x k images represented as
1 composite k x k image
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Model-based Visualization of Cardiac Virtual Tissue
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
According to Density - Form images using hyperdimensional histograms using histogram sizes
x = 55, y = 91
x = 55, y = 91
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Model-based Visualization of Cardiac Virtual Tissue
According to Position - Form images using hyperdimensional histograms using histogram IDs
x = 55, y = 91
x = 55, y = 91
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Model-based Visualization of Cardiac Virtual Tissue
FK3, Homogenous tissue, no re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue
FK3, Heterogeneous tissue, re-entrant behaviour
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Model-based Visualization of Cardiac Virtual Tissue
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
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
Fenton Karma three variable model
Action Potential
Model-based Representation
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Model-based Visualization of Cardiac Virtual Tissue
Luo Rudy 2 fourteen variable model
Action potential
Model-based representation
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Model-based Visualization of Cardiac Virtual Tissue
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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