Realtime identification of cardiac substrate anomalies

1
Real-time identification of cardiac substrate
anomalies

• Author Philippe Haldermans
• Promoters dr. Ronald Westra
• dr. ir. Ralf Peeters

13th September 2004
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Contents

• Motivation
• Forward modelling
• Inverse methods
• Results
• Conclusions

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Motivation

• Atrium fibrillation (AF)
• cell triggers
• wave maintenance by substrate anomalies
• New spatial-temporal data ? better image of wave
  propagation (movie)

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Objective

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Forward modelling (1)

• Biophysically detailed models
• Luo-Rudy, Beeler-Reuter,
• Complicated for inverse method
• Cellular automata
• Simple and fast, especially for normal
  propagation
• Absence of parameters for inverse estimation

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Forward modelling (2)

• Fitzhugh-Nagumo model
• Partial differential equation

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Forward modelling (3)

• Discretized in time and space
• Space symmetric estimation
• Time normal estimation

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Experiments (1)

• Types of waves
• Planar
• Spherical
• Spiral
• Different sorts of tissue
• Isotropic Anisotropic
• Homogeneous Inhomogeneous

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Experiments (2)

• Refractory period
• Re-entering waves
• Spiral waves (spiral.avi)
• Figure-8 reentry (figure8.avi)
• Laws of physics
• Rotations
• Snellius law

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Inverse methods

• Rewriting equations ? linear in the parameters
• Iterative linear least squares estimation
• Proof of usefulness
• Robustness for rounding errors
• Effect of noisy data

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Results (1)

• Simulated data
• Good estimation of the parameters
• Method holds even with noisy data
• Able to find anomalies (tissue) (demo)
• Data movies
• Proved in theory ? estimation works
• Practical problems with matlab

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Results (2)

• Real data
• First dataset (movie)
• shows normal propagation
• method finds smooth surface (tissue)
• Second dataset (movie)
• fibrillatory propagation
• no anomalies in the conductivity (tissue)
• example of other problem cell triggering?

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Other inverse methods (1)

• Bayesian approach
• estimation of the uncertainty
• groups of solutions
• prior distribution likelihood function ?
  posterior distribution
• can be used as first estimation for other methods

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Other inverse methods (2)

• Regularization
• Moore-Penrose pseudo-inverse
• Problems with
• Small singular values noisy data
• Possible solutions
• Truncated singular value decomposition
• Tikhonov regularization

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Conclusions

• Identify spatial anomalies in the conductivity
• Fitzhugh-Nagumo ? Realistic properties
• Estimation method works is robust
• Real data
• able to give conductivity
• these examples show no problems in the
  conductivity

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Recommendations (1)

• Other forward model
• Biologically more detailled
• Other properties
• Different inverse method
• Bayesian, regularization,
• Combination least squares with Bayesian

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Recommendations (2)

• Real data
• More datasets
• More information about the data
• Combination with the spatial-temporal data
  measurement ? real-time identification