ABSTRACT
This chapter examines a cable model which incorporates nonuniformities in the dendritic diameter, the membrane resistivity and the electrotonic lengths. The physiological significance of dendritic tapering in neurons has long been of interest to neuromorphologists and theorists. Tapering is a physical nonuniformity in that diameter varies with the distance from the origin. Tapering can be modelled mathematically by a modified cable equation. The term tapering has been used to describe at least two different morphological traits—the tapering of individual dendritic branches, hereafter called branch tapering, and the occurrence of electrotonic mismatches at branchpoints, hereafter called a step change in the equivalent diameter. Compartmental models are based on multiple ordinary differential equations rather than on a single partial differential equation. The implicit backward finite difference method is commonly used because it provides sufficient accuracy with the short computation times while avoiding the instabilities inherent with forward difference methods.
