Quantitative Classification of Cerebellar Foliation in Cartilaginous Fishes (Class: Chondrichthyes) Using Three-Dimensional Shape Analysis and Its Implications for Evolutionary Biology

Abstract

A true cerebellum appeared at the onset of the chondrichthyan (sharks, batoids, and chimaerids) radiation and is known to be essential for executing fast, accurate, and efficient movement. In addition to a high degree of variation in size, the corpus cerebellum in this group has a high degree of variation in convolution (or foliation) and symmetry, which ranges from a smooth cerebellar surface to deep, branched convexities and folds, although the functional significance of this trait is unclear. As variation in the degree of foliation similarly exists throughout vertebrate evolution, it becomes critical to understand this evolutionary process in a wide variety of species. However, current methods are either qualitative and lack numerical rigor or they are restricted to two dimensions. In this paper, a recently developed method for the characterization of shapes embedded within noisy, three-dimensional data called spherical wave decomposition (SWD) is applied to the problem of characterizing cerebellar foliation in cartilaginous fishes. The SWD method provides a quantitative characterization of shapes in terms of well-defined mathematical functions. An additional feature of the SWD method is the construction of a statistical criterion for the optimal fit, which represents the most parsimonious choice of parameters that fits to the data without overfitting to background noise. We propose that this optimal fit can replace a previously described qualitative visual foliation index (VFI) in cartilaginous fishes with a quantitative analog, i.e. the cerebellar foliation index (CFI). The capability of the SWD method is demonstrated in a series of volumetric images of brains from different chondrichthyan species that span the range of foliation gradings currently described for this group. The CFI is consistent with the qualitative grading provided by the VFI, delivers a robust measure of cerebellar foliation, and can provide a quantitative basis for brain shape characterization across taxa.

Comparative Brain Morphology of the Greenland and Pacific Sleeper Sharks and its Functional Implications

“…Morphologically, the corpus cerebellum varies substantially in size, level of convolution (a.k.a. foliation) and symmetry in cartilaginous fishes 27,30,74,134–136 , and it has been suggested that this may reflect performance differences in cerebellar-dependent functions and behaviors 132 . Both S .…”

“…High-resolution (100 μm isotropic), T1-weighted images were acquired using a 3D FLASH sequence with RF spoiling. Images were produced with high contrast between gray and white matter in cartilaginous fish brains 86,136 , from which structural characteristics were derived (Fig. 2A,B).…”

“…A grade of 1 corresponded to a smooth cerebellar surface with no folding, increasing in complexity to a grade of 5, which corresponded to extreme foliation with deep, branched grooves 30 . Although not as quantitatively rigorous as other methods 136 , the visual foliation index score was available on the greatest number of species 10,27,74 , thereby facilitating a broad comparative analysis.…”

Unveiling the third dimension in morphometry with automated quantitative volumetric computations

“…The model order has physical significance as a measure of an objects complexity, and consequently can have biological and evolutionary significance, as was demonstrated in our study to characterize of cerebellar foliations in elasmobranch brains [73], which has implications in the quantification and comparison of the cerebellum in different species of elasmobranchs where variation in cerebellar foliations has been shown to be related to species habitat and predation strategies and has evolutionary significance [74][75][76].…”

JEDI:JointEstimationDiffusionImaging of macroscopic and microscopic tissue properties

“…We fit, then get segmentation afterwards, essentially “for free”. Moreover, an important practical aspect of this method is that the entire process takes on the order of 12 s, whereas that of the “standard” method takes about 12 h. This method has been used to quantitatively classify cerebellar foliation in cartilaginous fishes (eg, sharks) which has important implications for evolutionary biology, and for cortical thickness measurements in Alzheimer’s Disease. It is also at the heart of our entire suite of programs.…”