Modeling Electrical Potential in Multi-Dendritic Neurons Using Bessel Functions

Understanding the distribution of electrical potential within neurons is critical for advancing our comprehension of neuronal signaling and communication. Neurons, the fundamental units of the nervous system, rely on complex electrochemical processes to transmit information. The intricate structure of neurons, especially those with multiple dendrites, plays a crucial role in how these electrical signals are generated, propagated, and integrated. Despite significant progress in neuroscience, accurately modeling the electrical potential within neurons with elaborate dendritic architectures remains a challenge. This article introduces a novel approach to modeling the electrical potential in multi-dendritic neurons using Bessel functions, which offers a more precise and detailed representation of these processes. The proposed method involves solving the electric potential diffusion equation in cylindrical coordinates, a mathematical framework that naturally aligns with the geometry of dendrites. The radial and axial components of the solution are expressed using Bessel functions and sinusoidal functions, respectively. Bessel functions are particularly well-suited for this purpose due to their ability to describe waveforms in cylindrical systems, making them ideal for capturing the spatial variations in electrical potential within the cylindrical shape of dendrites. By leveraging this mathematical approach, we obtain a complete representation of the potential distribution across the neuron, from the soma (cell body) through the dendrites to the synaptic terminals. This model accurately captures the spatial variations of electrical potential in different regions of the neuron, including areas with complex dendritic arborizations, which are branching structures that significantly influence the neuron’s electrical characteristics. Simulation results underscore the effectiveness of this approach in reproducing realistic neuronal behavior. The model successfully mimics the way electrical signals propagate and interact within dendritic structures, providing crucial insights into the underlying mechanisms of signal integration and transmission in neurons.