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Topological approximate Bayesian computation for parameter inference of an angiogenesis model.

Thomas Thorne1, Paul D W Kirk2,3,4, Heather A Harrington5,6

  • 1Department of Computer Science, University of Surrey, Guildford GU2 7XH, UK.

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We introduce a novel method combining topological data analysis (TDA) with Approximate Bayesian Computation (ABC) for parameter inference in spatial biological models. This approach enhances the analysis of spatial patterns, outperforming traditional methods.

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Area of Science:

  • Computational Biology
  • Systems Biology
  • Mathematical Biology

Background:

  • Parameter inference is crucial for understanding biological mechanisms, with Approximate Bayesian Computation (ABC) widely used for stochastic and ordinary differential equation models.
  • Inference in spatial models remains a challenge, despite advances in topological data analysis (TDA) for characterizing spatial patterns.

Purpose of the Study:

  • To develop and evaluate a novel method for parameter inference in spatial biological models.
  • To combine topological data analysis (TDA) with Approximate Bayesian Computation (ABC) for enhanced spatial parameter inference.

Main Methods:

  • We propose a method integrating TDA with ABC to infer parameters in the Anderson-Chaplain model of angiogenesis.
  • The approach utilizes TDA to analyze spatial patterns within the model's parameter space.

Main Results:

  • The proposed TDA-enhanced ABC method demonstrates superior performance compared to ABC approaches relying on simpler spatial statistics.
  • This study successfully infers parameters for a well-studied model of angiogenesis.

Conclusions:

  • Combining TDA with ABC offers a powerful framework for spatial parameter inference in biological systems.
  • This work represents a significant step towards a general methodology for analyzing spatial patterns in complex biological models.