Accurate Approximation Series for Optimal Targeting Regions in a Neural Growth Model with a Low –branching Probability

Understanding the complex growth process of dendritic arbors is essential for the medical field and disciplines like Biology and Neurosciences. The establishment of the dendritic patterns has received increasing attention from experimental researchers that seek to determine the cellular mechanisms that play a role in the growth of neural trees. Our goal in this thesis was to prove the recurrence formula for the probability distribution of all possible neural trees, as well as the formulas of the expected number of active branches and their variances. We also derived formulas for the spatial locations of the optimal targeting region for a tree with branching probability. These formulas were necessary for the simplified stochastic computational model that Osan et al have developed in order to examine how changes in branching probability influence the success of targeting neurons located at different distances away from a starting point. INDEX WORDS: Growth of neural trees, Computational model, Stochastic branching probability, Expected number of active branches, Variances, Recurrence formula. ACCURATE APPROXIMATION SERIES FOR OPTIMAL TARGETING REGIONS IN A NEURAL GROWTH MODEL WITH A LOW –BRANCHING PROBABILITY