All Hands Meeting 2005

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

• 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
Ventricular Fibrillation The Killer
Normal rhythm
Ventricular fibrillation
How does it start?
How can we stop it?
5
Ventricular Fibrillation Re-entry
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
The Visualization Challenge
Standard Visualization techniques of 2D and 3D
models use a single variable
Can we visualize the entire state of the heart
model in a single image (or figure?)
8
Simplified and detailed models
LuoRudy2 14 variable
Fenton Karma 4 variable
9
The Visualization Challenge
Impossible!
(31) dimensional 14 variate data cannot be
perfectly visualized in a single picture on a
(21) dimensional computer screen
.. but can we make at least a useful
representation in a single image?
10
Reduce the data
U
V
W
D
11
Move into Phase Space
U
V
W
Observation 1 3 k x k images can be expressed
as k x k points in 3-dimensional space
12
CVT data sets Phase Space Visualization
Using a 2D slice of Fenton Karma 3 variable CVT

• Normal action potential propagation through
  homogeneous tissue
• Re-entrant behaviour in heterogeneous tissue

13
FK3, Homogenous tissue, no re-entrant behaviour
14
FK3, Heterogeneous tissue, re-entrant behaviour
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
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
From Phase Space to Image
U
V
W
Observation 2 M k x k images represented as 1
composite k x k image
18
Assigning Value to a Point in Phase Space

• We look first at two general techniques
• Value according to density of points in that
  points neighbourhood of phase space
• Value according to position of point in phase
  space

19
According to Density - Form images using
hyper-dimensional histograms using histogram sizes
20
According to Position - Form images using
hyper-dimensional histograms using histogram IDs
21
FK3, Homogenous tissue, no re-entrant behaviour
22
FK3, Heterogeneous tissue, re-entrant behaviour
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
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
Fenton Karma three variable model
Model-based Representation
Action Potential
26
Luo Rudy 2 fourteen variable model
Action potential
Model-based representation
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)