An experimental method for measuring the mean length of cerebellar parallel fibers: validation and derivation of a correction factor by computational simulation and probability analysis.

The length of cerebellar parallel fibers is important for information integration by the Purkinje cells. Based on the Copernican principle for analyzing the length of stochastic events, we have recently devised a stochastic method to estimate the mean length of parallel fibers within a given cerebellar region. The purpose of the present report is to provide validation of this methodology via computational simulations. We create virtual parallel fibers with known lengths and program each step of our stochastic method for computational simulation. We then compare the observed mean length obtained from our computational simulation with the known mean length of the virtual parallel fibers. In particular, we investigate the effect of cutting parallel fibers into segments during histological sectioning. Our computational results reveal an over-estimation factor ranging from 1.0 (no correction is necessary) to 2.0 as the parallel fiber segmentation becomes increasingly severe. Based on probability theory considerations, we have confirmed the existence of this over-estimation. We have further determined the cause of this over-estimation to be an artificial consequence of one of the sampling steps in our stochastic method. These results provide validation of our methodology, as well as a correction factor, which can be derived directly from the experimentally measured parameters and used to obtain the true mean length of parallel fibers. Potential applications of the stochastic method include a comparative analysis of the length of parallel fibers as an approach to gain clues about cerebellar circuit principles and function. In addition, the stochastic method may also find promising applications in other functionally important axonal systems in the brain.