Utilising Surrogate Models to Approximate Cardiac Potentials when Solving Inverse Problems via Bayesian Techniques

Abbish Kamalakkannan, Peter Johnston, Barbara Johnston
Griffith University


Aims: Solving inverse problems is computationally expensive, if not infeasible, under certain scenarios. For example, large numbers of forward solutions are required when solving inverse problems using Bayesian techniques. This work studies the benefits and limitations of implementing a surrogate model to approximate the solution of the bidomain equations on an electrode array, so that the potentials can be used to determine the bidomain cardiac conductivities and fibre rotation angle.

Methods: Based on generalised polynomial chaos techniques, a surrogate model is developed to approximate the cardiac potentials on a multi-electrode array, for a given applied current, set of six cardiac conductivities and cardiac fibre rotation angle. Utilising the surrogate model and a set of synthetically generated cardiac potentials contaminated with measurement noise, we employ a novel inverse approach to retrieve the conductivities and the fibre rotation angle through Bayesian Inference. The accuracy of the retrieved cardiac parameters is analysed to determine the benefits and limitations of using this surrogate model.

Results: A surrogate model, developed using a polynomial chaos expansion of relatively low order (3-5), can approximate the cardiac potentials of the bidomain model accurately while maintaining high computational efficiency. When coupled with Bayesian Inference, the resulting surrogate model retrieves the fibre rotation angle and the extracellular cardiac conductivities accurately (relative errors<0.13%), while the intracellular conductivities are retrieved to a lesser degree of accuracy. Higher-order polynomial expansions (6-9) help reduce errors in the intracellular conductivity approximations; however, they come at the cost of longer surrogate model training times.

Conclusion: A surrogate model can be used to overcome computational limitations associated with applying Bayesian techniques to find the bidomain cardiac conductivities. A lower-order expansion (3-5) can be used to retrieve the extracellular conductivities accurately; however, it is recommended that a higher-order expansion (6-9) be used if accurate intracellular conductivities are required.