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We investigate the degree to which neurons are fractal, the origin of this fractality, and its impact on functionality. By analyzing three-dimensional images of rat neurons, we show the way their dendrites fork and weave through space is unexpectedly important for generating fractal-like behavior well-described by an ‘effective’ fractal dimension D . This discovery motivated us to create distorted neuron models by modifying the dendritic patterns, so generating neurons across wide ranges of D extending beyond their natural values. By charting the D -dependent variations in inter-neuron connectivity along with the associated costs, we propose that their D values reflect a network cooperation that optimizes these constraints. We discuss the implications for healthy and pathological neurons, and for connecting neurons to medical implants. Our automated approach also facilitates insights relating form and function, applicable to individual neurons and their networks, providing a crucial tool for addressing massive data collection projects (e.g. connectomes).

Controlled assembly of retinal cells on artificial surfaces is important for fundamental cell research and medical applications. We investigate fractal electrodes with branches of vertically-aligned carbon nanotubes and silicon dioxide gaps between the branches that form repeating patterns spanning from micro- to milli-meters, along with single-scaled Euclidean electrodes. Fluorescence and electron microscopy show neurons adhere in large numbers to branches while glial cells cover the gaps. This ensures neurons will be close to the electrodes’ stimulating electric fields in applications. Furthermore, glia won’t hinder neuron-branch interactions but will be sufficiently close for neurons to benefit from the glia’s life-supporting functions. This cell ‘herding’ is adjusted using the fractal electrode’s dimension and number of repeating levels. We explain how this tuning facilitates substantial glial coverage in the gaps which fuels neural networks with small-world structural characteristics. The large branch-gap interface then allows these networks to connect to the neuron-rich branches.

Understanding the impact of the geometry and material composition of electrodes on the survival and behavior of retinal cells is of importance for both fundamental cell studies and neuromodulation applications. We investigate how dissociated retinal cells from C57BL/6J mice interact with electrodes made of vertically-aligned carbon nanotubes grown on silicon dioxide substrates. We compare electrodes with different degrees of spatial confinement, specifically fractal and grid electrodes featuring connected and disconnected gaps between the electrodes, respectively. For both electrodes, we find that neuron processes predominantly accumulate on the electrode rather than the gap surfaces and that this behavior is strongest for the grid electrodes. However, the ‘closed’ character of the grid electrode gaps inhibits glia from covering the gap surfaces. This lack of glial coverage for the grids is expected to have long-term detrimental effects on neuronal survival and electrical activity. In contrast, the interconnected gaps within the fractal electrodes promote glial coverage. We describe the differing cell responses to the two electrodes and hypothesize that there is an optimal geometry that maximizes the positive response of both neurons and glia when interacting with electrodes.

By analyzing reconstructed three-dimensional images of retinal bipolar neurons, we show that their dendritic arbors weave through space in a manner that generates fractal-like behavior quantified by an ‘effective’ fractal dimension. Examining this fractal weave along with traditional morphological parameters reveals a dependence of arbor fractal dimension on the summation of the lengths of the arbor’s dendrites. We discuss the implications of this behavior for healthy neurons and also for the morphological deterioration of unhealthy neurons in response to diseases.

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.

Retinal implant devices are becoming an increasingly realizable way to improve the vision of patients blinded by photoreceptor degeneration. As an electrode material that can improve restored visual acuity, carbon nanotubes (CNTs) excel due to their nanoscale topography, flexibility, surface chemistry, and double-layer capacitance. If vertically aligned carbon nanotubes (VACNTs) are biocompatible with retinal neurons and mechanically robust, they can further improve visual acuity—most notably in subretinal implants—because they can be patterned into high-aspect-ratio, micrometer-size electrodes. We investigated the role of an aluminum (Al) underlayer beneath an iron (Fe) catalyst layer used in the growth of VACNTs by chemical vapor deposition (CVD). In particular, we cultured dissociated retinal cells for three days in vitro (DIV) on unfunctionalized and oxygen plasma functionalized VACNTs grown from a Fe catalyst (Fe and Fe+Pl preparations, where Pl signifies the plasma functionalization) and an Fe catalyst with an Al underlayer (Al/Fe and Al/Fe+Pl preparations). The addition of the Al layer increased the mechanical integrity of the VACNT interface and enhanced retinal neurite outgrowth over the Fe preparation. Unexpectedly, the extent of neurite outgrowth was significantly greater in the Al/Fe than in the Al/Fe+Pl preparation, suggesting plasma functionalization can negatively impact biocompatibility for some VACNT preparations. Additionally, we show our VACNT growth process for the Al/Fe preparation can support neurite outgrowth for up to 7 DIV. By demonstrating the retinal neuron biocompatibility, mechanical integrity, and pattern control of our VACNTs, this work offers VACNT electrodes as a solution for improving the restored visual acuity provided by modern retinal implants.

For well over a century, neuroscientists have been studying the inherent ties between neuronal morphology and functionality. Santiago Ramón y Cajal, in his work that ultimately awarded him a Nobel Prize in 1906, established that neurons function as the fundamental unit of the nervous system. Ramón y Cajal himself recognized the relationship between neuronal form and function by proposing the wiring economy principle, which states that the nervous system’s complex network of neurons is efficiently wired in a way that minimizes wiring length. The research within this dissertation works towards the goal of optimizing the design of the electrode-neuron interface of medical implants by building upon Ramón y Cajal’s foundational ideas and integrating them with the techniques of fractal analysis.The dissertation begins by addressing the question of how electrode geometry impacts the morphology of the networks of neurons and glia interfacing with the electrode. This was done by interacting dissociated mouse retinal cell cultures in vitro with vertically aligned carbon nanotube (VACNT) electrodes grown on a silicon dioxide (SiO2) substrate and patterned into Euclidean and fractal geometries. The VACNT-SiO2 material system was shown to perform exceptionally well at guiding neurons onto the VACNTs and glia onto the surrounding SiO2. Furthermore, the electrode geometries that performed the best at supporting a healthy network of neurons and glia were those that balanced providing a large VACNT electrode area with maintaining connectedness in the surrounding SiO2 surface and allowing it to interpenetrate the VACNT electrode.Following these in vitro experiments, three-dimensional models of pyramidal neurons from the CA1 region of the rat hippocampus were reconstructed using confocal microscopy. The fractal properties of the neurons and how these relate to their functionality were then analyzed. It was then demonstrated that the natural, fractal behavior of the neurons, though limited in its scaling range, was sufficient to provide the neurons with an optimal balance between connectivity and building and operating costs.The dissertation concludes by reviewing the results of these studies, providing directions for future work, and discussing the implications regarding electrode design.This dissertation includes previously published co-authored material.