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Software for Analysis of Heart Rate and Blood Pressure Time-series Data from the Valsalva Maneuver

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Robust data assimilation with noise: Applications to cardiac dynamics.

Christopher D Marcotte¹, Flavio H Fenton², Matthew J Hoffman³

¹School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

Chaos (Woodbury, N.Y.)

|March 23, 2021

Summary

Stochastic modeling improves cardiac excitation pattern reconstruction by accounting for uncertainties. Combining stochastic processes enhances data assimilation accuracy and ensemble spread, outperforming classical methods.

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Area of Science:

Computational Biology
Biophysics
Applied Mathematics

Background:

Cardiac excitation pattern reconstruction faces challenges from model and observation errors, and hidden variables.
Accurate state reconstructions require addressing uncertainties in model specification and dynamics.

Purpose of the Study:

To introduce and evaluate stochastic modeling methods for improved state reconstruction in cardiac dynamics.
To enhance ensemble-based data assimilation by incorporating model uncertainties.

Main Methods:

Developed two classes of stochastic modeling methods: stochastic differential equation formalism and parameter space perturbation.
Applied these methods to one- and three-dimensional cardiac systems with fast-slow time-scale separation.
Investigated the role of time-scale separation in formulating stochastic assimilation schemes.

Main Results:

Stochastic forcing term formulation, based on slow or fast time scales, is analogous to ensemble inflation techniques.
Careful parameter selection is crucial to prevent over-driving the data assimilation process.
Combining stochastic processes improved assimilation error and ensemble spread compared to classical methods.

Conclusions:

Stochastic modeling offers a robust approach to managing uncertainties in cardiac dynamics reconstruction.
The proposed methods enhance the accuracy and reliability of data assimilation in complex biological systems.
Further research can optimize parameter choices for specific cardiac models and assimilation tasks.