Geometrical modelling of neuronal clustering and development
Ali H Rafati1, Maryam Ardalan1,2,3, Regina T Vontell4
1Translational Neuropsychiatry Unit, Department of Clinical Medicine, Aarhus University, 8000 Aarhus C, Denmark.
Heliyon
|July 18, 2022
Summary
This study introduces a novel mathematical model for neuronal development, using fractal geometry to simulate neuron growth and electrical field interactions. The model offers a new platform for understanding brain structure and function.
Area of Science:
- Theoretical Neuroscience
- Computational Neuroscience
- Biophysics
Background:
- Neuronal development involves complex dynamic geometry.
- Understanding the interplay between neuronal structure and electrical activity is crucial.
Purpose of the Study:
- To design an innovative mathematical model for geometric neuronal development.
- To model the spatial interaction between neuronal electrical fields.
Main Methods:
- Utilized a fractal cylinder and 'surface of revolution' for geometric neuron generation (pyramidal/sphere).
- Modeled adjacent neuron effects using a 'normal vector surface'.
- Simulated neuronal-electrical field interaction using Van der Pol oscillator and Laplacian vector fields.
Main Results:
- Demonstrated a model for inside-out neuronal growth.
- Showcased transformation of neuronal geometry and clustering into equivalent vector fields representing electrical activity.
- Verified spatial simulation of neuronal-electrical field interaction.
Conclusions:
- The developed model provides a flexible platform for studying neuronal geometry and electrical fields.
- This approach inspires future complex geometrical and electrical modeling of neural systems.
Keywords:
Geometrical modellingMathematicsNeuritesNeuronal developmentNeuronal shapeNeuronal-electrical field interactionVector field
