We base our simulation on c.s. group 6, located on the proximal end of the tibia of each leg of the American cockroach, Periplaneta americana. We modeled the tibia as a hollow tube of circular cross-section. Using tibial dimensions measured from the rear leg of an adult male, we calculated the area of the cuticular cross section, as well as its first, second, and polar moments of area. With the tibia immobilized at its proximal end, we calculated the effects of applying three kinds of forces to the distal end: bending up and down, axial pulling and pushing, and axial twisting (torsional force).
We used statics equations to calculate the internal loading (at the level of the tibial cross-section intersecting c.s. group 6) that results from applying force to the tibia. Using standard formulae from the mechanics of materials and a few reasonable assumptions, we then calculated the resulting stresses in the tibial wall at the location of c.s. group 6. From the stresses, we calculated the normal and shear strains in the cuticle for each type of force we applied, using a modulus of elasticity of 9.4 GPa and a Poisson's ratio of 0.3.
Previous experimental work by others has shown that compressional strain across the short axis of the c.s. will cause it to fire. C.s. group 6 consists of two subgroups: a proximal subgroup oriented along the long axis of the tibia, and a slightly more distal subgroup oriented across the tibia at right angles to the first. We evaluated the pattern of firing of the two c.s. subgroups to be expected due to each of the forces we applied, assuming that axial strain would excite the proximal subgroup and circumferential strain would excite the more distal subgroup. The pattern of firing predicted by our strain analysis agrees qualitatively with the actual pattern of firing recorded by Zill & Moran (J. exp. Biol. 91, 1-24, 1981) when they applied similar forces to an actual tibia. Next we converted force to a series of action potentials using the data of Zill & Moran, and using a power law to model the adaptation of the firing frequency of the sense organ after the onset of the stimulus (step response), we simulated the pattern of firing of the two c.s. subgroups. Our simulated pattern agrees remarkably well with the actual pattern of firing recorded by Zill & Moran when they applied similar bending and axial forces to an actual tibia. Zill & Moran report a small response to torsional force that we did not find, but analysis of their method of twisting the tibia shows that they introduced a bending force more than sufficient to account for the c.s. activity they report. Overall, simulation of the step response of campaniform sensilla shows promising aspects for future integration in a dynamic simulation.
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