Simulating ECG and solving inverse problem with a genetic algorithm

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Simulating ECG and solving inverse problem with a
genetic algorithm
Matja Depolli
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Topics

• Electrical properties of myocardium (muscular
  tissue of the heart)
• An ECG
• ECG simulation
• Inverse problem
• Optimization and differential evolution
• Achievements
• Goals and future work

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ECG
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Heart anatomy
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Action potential

• Property of a single cell
• Electric charge of a cell responds to an external
  signal (change of electric charge of neighbouring
  cell)
• A way of transmitting order to contract across
  the whole heart muscle

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Heart model
Action potentials
AV node
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Heart model

• Three distinct layers of cells (endocard,
  mid-cells, epicard)
• Simplified Purkinje fibers (transmit signal along
  the wall)
• Simplifications shape, constant wall width,
  uniform properties of all cells of the same
  layer, ignored some conductive paths within the
  heart

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ECG leads (electrodes)
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Simulated ECG
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Inverse problem
Action potentials
ECG
Parameters
Inverse problem
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Inverse problem

• Typically ill-posed
• solution might not exist
• more than one solution
• solution(s) might not depend continuously on the
  data
• solution might be highly sensitive to changes in
  data

yf(x)
xg(y)
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Inverse problem

• Sensitivity of solution to changes in data
• quantization error (finite precision)

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ECG ? APs

• Solution exists
• Expect more than one solution
• Expect very different solutions (expressing
  different mechanisms of U wave genesis)
• Solutions not sensitive to small perturbations of
  data
• Measured ECGs vary, but solutions should be the
  same.

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Optimization

• A typical way of handling inverse problems
• Optimization is an inverse problem
• Optimization of distance between the function
  value and desired value

yf(x)
yf(x)-y1
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Differential evolution

• Optimization of functions with real parameters
• Steady state evolutionary algorithm
• C X1 F(X2 - X3)

C
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Differential evolution

• No background knowledge of the problem is needed
• Small number of parameters
• Multiple solutions per run
• Easily parallelizable

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Differential evolution

• Mapping on the presented problem
• Fitness function similarity between the
  simulated and measured ECG (curve matching)
• Action potentials are modeled with analytic
  functions with real-valued parameters

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3x
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Achievements
Inside
Outside
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Achievements

• Learned a lot about the problem
• A new mechanism of U wave genesis was found
  (article published in Journal of Cardiovascular
  Electrophysiology)
• In-vivo measurements taken into account

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Goals

• A general algorithm for efficient solving of
  inverse problems (like the problem of U wave
  genesis)
• Improvements on the simulator
• including more parameters
• increasing ability to simulate ECG genesis
• ability to simulate defective heart

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Future work

• Improving models simulator
• Improving the search algorithm
• Improving the fitness function
• Parallelize algorithms
• Putting more parameters in optimization process