Neuron arbor geometry is sensitive to the limited-range fractal properties of their dendrites

Study of prediction model for high-grade meningioma using fractal geometry combined with radiological features

PURPOSE

To establish a prediction model combining fractal geometry and radiological features, which consider the complexity of tumour morphology advancing beyond the limitations of previous models.

METHODS

A total of 227 patients at the First Affiliated Hospital of Harbin Medical University from July 2021 to November 2023 were included. Fractal geometry was calculated and the radiomics features were extracted from regions of interest (ROIs). Weighted Gene Co-Expression Network Analysis (WGCNA) was employed for preliminary screening to identify those that were significantly associated with high-grade meningioma. In the training cohort, the least absolute shrinkage and selection operator (LASSO) regression was employed for further screening the radiomics features. Area under curve (AUC) was to evaluate models' performance.

RESULTS

In entire patient cohort, low-grade meningiomas had significantly lower fractal dimensions (P = 0.01), while high-grade meningiomas had higher lacunarity (P = 0.049). Fractal dimension (OR 6.8, 95% CI 1.49-36.51, P = 0.017), lacunarity (OR 3.7, 95% CI 1.36-11.75, P = 0.014), and Rscore (OR 2.8, 95% CI 1.55-5.75, P = 0.002) were independent risk factors for high-grade meningiomas. The final results demonstrated that the "fractal geometry + radiological features (semantic features + radiomics features)" model exhibited the most optimal performance in predicting high-grade meningioma, with an AUC of 0.854 in the training cohort and 0.757 in the validation cohort.

CONCLUSION

Significant differences in fractal dimension and lacunarity exist between high-grade and low-grade meningiomas, which can be potential predictive factors. The developed predictive model demonstrated good performance in predicting high-grade meningiomas.

Evolution of Retinal Neuron Fractality When Interfacing with Carbon Nanotube Electrodes

Exploring how neurons in the mammalian body interact with the artificial interface of implants can be used to learn about fundamental cell behavior and to refine medical applications. For fundamental and applied research, it is crucial to determine the conditions that encourage neurons to maintain their natural behavior during interactions with non-natural interfaces. Our previous investigations quantified the deterioration of neuronal connectivity when their dendrites deviate from their natural fractal geometry. Fractal resonance proposes that neurons will exhibit enhanced connectivity if an implant's electrode geometry is matched to the fractal geometry of the neurons. Here, we use in vitro imaging to quantify the fractal geometry of mouse retinal neurons and show that they change during interaction with the electrode. Our results demonstrate that it is crucial to understand these changes in the fractal properties of neurons for fractal resonance to be effective in the in vivo mammalian system.

Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties

Imagine a world in which damaged parts of the body - an arm, an eye, and ultimately a region of the brain - can be replaced by artificial implants capable of restoring or even enhancing human performance. The associated improvements in the quality of human life would revolutionize the medical world and produce sweeping changes across society. In this chapter, we discuss several approaches to the fabrication of fractal electronics designed to interface with neural networks. We consider two fundamental functions - stimulating electrical signals in the neural networks and sensing the location of the signals as they pass through the network. Using experiments and simulations, we discuss the favorable electrical performances that arise from adopting fractal rather than traditional Euclidean architectures. We also demonstrate how the fractal architecture induces favorable physical interactions with the cells they interact with, including the ability to direct the growth of neurons and glia to specific regions of the neural-electronic interface.

Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons.To investigate fractal resonance, we first determine the degree to which neurons are fractal and the impact of this fractality on their functionality. By analyzing three-dimensional images of rat hippocampal neurons, we find that the way their dendrites fork and weave through space is important for generating their fractal-like behavior. By modeling variations in neuron connectivity along with the associated energetic and material costs, we highlight how the neurons' fractal dimension optimizes these constraints. To simulate neuron interactions with implant interfaces, we distort the neuron models away from their natural form by modifying the dendrites' fork and weaving patterns. We find that small deviations can induce large changes in fractal dimension, causing the balance between connectivity and cost to deteriorate rapidly. We propose that implant surfaces should be patterned to match the fractal dimension of the neurons, allowing them to maintain their natural functionality as they interact with the implant.