Topological Sholl Descriptors For Neuronal Clustering and Classification

Abstract

Variations in neuronal morphology among cell classes, brain regions, and animal species are thought to underlie known heterogeneities in neuronal function. Thus, accurate quantitative descriptions and classification of large sets of neurons is essential for functional characterization. However, unbiased computational methods to classify groups of neurons are currently scarce. We introduce a novel, robust, and unbiased method to study neuronal morphologies. We develop mathematical descriptors that quantitatively characterize structural differences among neuronal cell types and thus classify them. Each descriptor that is assigned to a neuron is a function of a distance from the soma with values in real numbers or more general metric spaces. Standard clustering methods enhanced with detection and metric learning algorithms are then used to objectively cluster and classify neurons. Our results illustrate a practical and effective approach to the classification of diverse neuronal cell types, with the potential for discovery of putative subclasses of neurons.

Towards modelling cold-water coral reef-scale crumbling: Including morphological variability in mechanical surrogate models

“…We then introduced four topological descriptors that represent morphological features of the branching coral structure, adopting those proposed by Khalil et al [37] to study neuronal morphology. These descriptors associate a function to a given coral skeleton whose independent variable is either the path, δ , or radial, r , distance from the skeletal root (Figure 4d).…”

“…Where x is the normalised path, δ i , or radial, r i , distance from the skeletal root. The corresponding vector for each coral skeleton, V C , is: This vectorization allows us to optimize classification of the data [37].…”

Between neurons and networks: investigating mesoscale brain connectivity in neurological and psychiatric disorders

“…Their findings highlight the importance of specific measures like branching density, size, tortuosity, bifurcation angles, arbor flatness, and topological asymmetry in capturing meaningful features of dendritic trees. Similarly, Khalil et al (2021) extracted L-measure metrics and modified Sholl descriptors from the NeuroMorpho database and used PCA and KNN clustering to classify neuronal types.…”

Stability of topological descriptors for neuronal morphology

“…Stability results for the TMD algorithm with respect to the bottleneck distance were given by Kanari et al [8,SI,Section 4]. Khalil et al [10] state the TMD is stable against perturbations to an embedding of T in Euclidean space for the 1-Wasserstein distance when f is the Euclidean distance of the vertices to the soma; however Lipschitz bounds for this kind of stability are not provided. We prove in Section 3 that the TMD is stable against perturbations of arbitrary functional information f , and against certain perturbations of the underlying rooted tree T .…”

“…The TMDs of different neurons can be vectorized using persistence images, which can be averaged, interpreted and compared. Khalil et al [10] state the TMD is stable for the 1-Wasserstein distance against perturbations to an embedding of T in Euclidean space when f the Euclidean distance of the vertices to the soma; no quantification or bounds are given measuring the stability of these perturbations. Here, we prove 1-Wasserstein stability of the TMD against perturbations to any function f and to a class of perturbations to the structure of T .…”