Torpedo formation and Purkinje cell loss: modeling their relationship in cerebellar disease

Torpedo formation and Purkinje cell (PC) loss represent standard and inter-related cerebellar responses to injury. Surprisingly, the nature of their relationship has not been carefully characterized across a range of normal and disease states. Are brains with more torpedoes expected to have fewer PCs? We quantified torpedoes and PCs in four groups: essential tremor (ET), spinocerebellar ataxia (SCA), multiple system atrophy-cerebellar (MSA-C), and controls. Brains from 100 individuals (58 ET, 27 controls, 7 SCA, 8 MSA-C) were available at the New York Brain Bank. After complete neuropathological assessment, a standard parasagittal neocerebellar block was harvested; a 7-μm thick section was stained with Luxol fast blue/hematoxylin and eosin; and torpedoes and PCs were quantified. For a given PC count, SCA and MSA-C cases often had higher torpedo counts than ET cases or controls. Furthermore, the relationship between torpedo and PC counts was complex. The correlation between torpedo and PC counts was negative in ET cases (i.e., individuals with more torpedoes had fewer PCs [i.e., more PC loss]) whereas the relationship was positive in MSA-C cases (i.e., individuals with fewer PCs [i.e., more PC loss] had fewer torpedoes). Patients with SCA showed both patterns. When all diagnostic groups were combined, the correlation was best fit by a quadratic (i.e., parabolic) model rather than a simple linear model; this model incorporated data on the negative correlation in ET cases, the mixed results in SCA cases, and the positive correlation in MSA-C cases (r = 0.636). The relationship between torpedo and PC counts was complex and heterogeneous across a range of cerebellar disease states, and was best characterized by a quadratic rather than a simple model. With more severe cerebellar disease, torpedoes can be quite numerous and are likely a common feature of surviving PCs, but eventually, dramatic loss of PC leads to a paradoxical reduction in observable torpedoes.