2011 Noise titration for detecting determinism and nonlinearity in dynamics underlying biomedical data

Elise Roulin
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The increasing amount of data produced in biomedicine leads scientists to treat them using a statistical approach. Such a descriptive approach does not provide any inference of the underlying causality until its determinisitic nature is not proved. Up to now, the sole satisfactory proof for the determinism underlying experimental data is provided by global modelling, that is, when a set of differential of difference equations captures the measured dynamics. In the case of biological systems, getting a global model remains a very challenge task and was rarely successful. The "noise titration" technqiue, based on a comparison between one-step-ahead prediction produced by linear and nonlinear polynomial models, was presented as an alternative technique. Nevertheless, it was shown that it fails to discriminate deterministic from stochastic dynamics. Its critical analysis is here developed exhibit various influent factors depending on the technique itself as well as on the measured data. We show that noise titration, when correctly applied, can be a good marker to track dynamical change. Applied to two experimental dynamics, ventilation (continuous time series of the airflow) and cardiac activity (RR-intervals), it is shown that noise titration is more efficient to characterize the latter than the former.

The Ph.D. Thesis can be doawnloaded here

* References

  • E. Roulin, U. S. Freitas & C. Letellier, Working conditions for safe detection of nonlinearity and noise titration, Physical Review E, 83, 046225, 2011. online
  • U. Freitas, E. Roulin, J.-F. Muir & C. Letellier, Identifying chaos from heart rate : The right task ?, Chaos, 19, 028505, 2009. Online
  • C. Letellier, E. Roulin & O. E. Rössler, Inequivalent topologies of chaos in simple equations, Chaos, Solitons & Fractals, 28, 337-360, 2006. Online
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