Abstract:Many of nature’s fractal objects benefit from the favorable functionality that results from their pattern repetition at multiple scales. Our recent research focused on the importance of fractal scaling in establishing connectivity between neurons. Fractal dimension DA of the neuron arbors was shown to relate to the optimization of competing functional constraints—the ability of dendrites to connect to other neurons versus the costs associated with building the dendrites. Here, we consider whether pathological … Show more
“…Analysis of the fractal characteristics of these pathological neurons may provide biomarkers for their early detection, similar to how fractal dimension can differentiate the stages of cancer (Elkington et al, 2022). It is important to note that high resolution imaging would likely be required to accurately detect prodromal changes affecting a neuron's fractal characteristics, as well as automation to characterize large numbers of samples (Rowland et al, 2022). As such, a goal of future studies is to apply our technique to publicly accessible repositories of images from experiments, for example online libraries such as NeuroMorpho.Org (Ascoli et al, 2007) with a much larger number of neurons featuring a range of pathological conditions.…”
Fractal geometry is a well-known model for capturing the multi-scaled complexity of many natural objects. By analyzing three-dimensional images of pyramidal neurons in the rat hippocampus CA1 region, we examine how the individual dendrites within the neuron arbor relate to the fractal properties of the arbor as a whole. We find that the dendrites reveal unexpectedly mild fractal characteristics quantified by a low fractal dimension. This is confirmed by comparing two fractal methods—a traditional “coastline” method and a novel method that examines the dendrites’ tortuosity across multiple scales. This comparison also allows the dendrites’ fractal geometry to be related to more traditional measures of their complexity. In contrast, the arbor’s fractal characteristics are quantified by a much higher fractal dimension. Employing distorted neuron models that modify the dendritic patterns, deviations from natural dendrite behavior are found to induce large systematic changes in the arbor’s structure and its connectivity within a neural network. We discuss how this sensitivity to dendrite fractality impacts neuron functionality in terms of balancing neuron connectivity with its operating costs. We also consider implications for applications focusing on deviations from natural behavior, including pathological conditions and investigations of neuron interactions with artificial surfaces in human implants.
“…Analysis of the fractal characteristics of these pathological neurons may provide biomarkers for their early detection, similar to how fractal dimension can differentiate the stages of cancer (Elkington et al, 2022). It is important to note that high resolution imaging would likely be required to accurately detect prodromal changes affecting a neuron's fractal characteristics, as well as automation to characterize large numbers of samples (Rowland et al, 2022). As such, a goal of future studies is to apply our technique to publicly accessible repositories of images from experiments, for example online libraries such as NeuroMorpho.Org (Ascoli et al, 2007) with a much larger number of neurons featuring a range of pathological conditions.…”
Fractal geometry is a well-known model for capturing the multi-scaled complexity of many natural objects. By analyzing three-dimensional images of pyramidal neurons in the rat hippocampus CA1 region, we examine how the individual dendrites within the neuron arbor relate to the fractal properties of the arbor as a whole. We find that the dendrites reveal unexpectedly mild fractal characteristics quantified by a low fractal dimension. This is confirmed by comparing two fractal methods—a traditional “coastline” method and a novel method that examines the dendrites’ tortuosity across multiple scales. This comparison also allows the dendrites’ fractal geometry to be related to more traditional measures of their complexity. In contrast, the arbor’s fractal characteristics are quantified by a much higher fractal dimension. Employing distorted neuron models that modify the dendritic patterns, deviations from natural dendrite behavior are found to induce large systematic changes in the arbor’s structure and its connectivity within a neural network. We discuss how this sensitivity to dendrite fractality impacts neuron functionality in terms of balancing neuron connectivity with its operating costs. We also consider implications for applications focusing on deviations from natural behavior, including pathological conditions and investigations of neuron interactions with artificial surfaces in human implants.
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