State and parameter estimation for canonic models of neural oscillators

Area of Science:

• Computational Neuroscience
• Systems Biology
• Control Theory

Background:

• Model neurons like Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar are crucial for understanding neural dynamics.
• Recovering state and parameter values from experimental data is essential for validating and refining these models.

Purpose of the Study:

• To develop a method for reconstructing state and parameter values of model neurons from in-vitro membrane potential measurements.
• To address the challenge of non-existence of parameter-independent diffeomorphisms for transforming neuron models into adaptive canonic observer forms.

Main Methods:

• The study proposes a novel reconstruction method applicable to a broad class of model neurons.
• The method relies on in-vitro measurements of membrane potentials.
• It requires mild conditions on the richness of the measured signal.

Main Results:

• State and parameter reconstruction is demonstrated to be possible for a large class of model neurons.
• The proposed method allows reconstruction up to an equivalence class.
• This overcomes limitations of traditional control theory approaches for these specific models.

Conclusions:

• The developed method offers a viable approach for parameter and state recovery in complex model neurons.
• This advancement facilitates more accurate computational neuroscience research and model development.
• The findings have implications for understanding neuronal behavior from experimental data.