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

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The Fractal Geometry of the Brain

Part of the book series: Advances in Neurobiology ((NEUROBIOL,volume 36))

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Abstract

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.

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Acknowledgments

R.P. Taylor is a Cottrell Scholar of the Research Council for Science Advancement. This research was supported by the W. M. Keck Foundation, the Living Legacy Foundation, the Ciminelli Foundation, and the University of Oregon. We thank M.-T. Perez (Lund University, Sweden) for useful discussions along with providing training for retinal cultures and immunocytochemistry, M. Pluth (University of Oregon, USA) for providing the opportunity and training for the fluorescence microscopy imaging system, W. Griffiths and C.M. Niell (University of Oregon) for discussions, B. Aleman, D. Miller, and K. Zappitelli (University of Oregon) for their contributions to the development of the VACNT synthesis process, J. Levine (University of Oregon) for stereoscopic imaging of the VACNTs, and S.A. Brown (University of Canterbury, New Zealand) and R.D. Montgomery (University of Oregon) for nanoflower development.

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Authors and Affiliations

  1. Physics Department, University of Oregon, Eugene, OR, USA

    C. Rowland, S. Moslehi, J. H. Smith & R. P. Taylor

  2. School of Pharmacy, University of Auckland, Auckland, New Zealand

    B. Harland

  3. School of Psychology, Speech and Hearing, University of Canterbury, Christchurch, New Zealand

    J. Dalrymple-Alford

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  1. C. Rowland
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Correspondence to R. P. Taylor .

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  1. Computational NeuroSurgery (CNS) Lab & Macquarie Neurosurgery Macquarie Medical School, Faculty of Medicine, Human and Health Sciences, Macquarie University, Sydney, NSW, Australia

    Antonio Di Ieva

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Rowland, C., Moslehi, S., Smith, J.H., Harland, B., Dalrymple-Alford, J., Taylor, R.P. (2024). Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?. In: Di Ieva, A. (eds) The Fractal Geometry of the Brain. Advances in Neurobiology, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-47606-8_44

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