Estimating anisotropy directly via neural timeseries.

Area of Science:

• Dynamical Systems Theory
• Computational Neuroscience
• Theoretical Physics

Background:

• Isotropy describes systems uniform in all directions, while anisotropy indicates directional variations.
• Quantifying anisotropy is crucial for understanding complex systems, including neural networks.
• Existing methods may not fully capture the nuanced directional properties of biological systems.

Purpose of the Study:

• To derive a generalized scalable field theoretic Lagrangian for estimating anisotropy.
• To develop a computational methodology for quantifying anisotropy in time-series data.
• To apply the method to in vivo neural data for biological insights.

Main Methods:

• Derivation of a generalized scalable discretized field theoretic Lagrangian.
• Generation of synthetic isotropic and anisotropic data.
• Bayesian model inversion and reduction for data discrimination.
• Application to murine calcium imaging data from rest and task states.

Main Results:

• Successfully discriminated between synthetic isotropic and anisotropic datasets, demonstrating proof of principle.
• Developed a method to estimate anisotropy directly from time-series data of arbitrary dimensionality.
• Quantified anisotropy in different murine brain states (rest vs. task) and cortical regions.
• Showed that anisotropy can be estimated in an empirical in vivo biological setting.

Conclusions:

• The derived Lagrangian and methodology provide a robust framework for quantifying anisotropy in dynamical systems.
• The approach is applicable to biological systems, offering new insights into neural organization.
• This work facilitates the study of neural system growth and development (ontogenetically and phylogenetically).