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

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The Fractal Geometry of the Brain

Abstract

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.

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References

  1. Lewis PM, Rosenfeld JV. Electrical stimulation of the brain and the development of cortical visual prostheses: an historical perspective. Brain Res. 2016;1630:208–24.

    Article  CAS  PubMed  Google Scholar 

  2. Marlow CA, et al. Unified model of fractal conductance fluctuations for diffusive and ballistic semiconductor devices. Phys Rev B. 2006;73:195318.

    Article  Google Scholar 

  3. Micolich AP, et al. Evolution of fractal patterns during a classical-quantum transition. Phys Rev Lett. 2001;87:036802.

    Article  CAS  PubMed  Google Scholar 

  4. Sachrajda AS, et al. Spin-controlled resonances in the magnetotransport in quantum dots. Phys Rev B. 1993;47:6811–4.

    Article  CAS  Google Scholar 

  5. Taylor RP, Sachrajda AS, Zawadzki P, Coleridge PT, Adams JA. Aharonov-Bohm oscillations in the Coulomb blockade regime. Phys Rev Lett. 1992;69:1989–92.

    Article  CAS  PubMed  Google Scholar 

  6. Jang J, et al. Implantation of electronic visual prosthesis for blindness restoration. Opt Mater Express. 2019;9:3878–94.

    Article  Google Scholar 

  7. Chenais NAL, Airaghi Leccardi MJI, Ghezzi D. Photovoltaic retinal prosthesis restores high-resolution responses to single-pixel stimulation in blind retinas. Commun Mater. 2021;2:1–16.

    Article  Google Scholar 

  8. Prévot P-H, et al. Behavioural responses to a photovoltaic subretinal prosthesis implanted in non-human primates. Nat Biomed Eng. 2020;4:172–80.

    Article  PubMed  Google Scholar 

  9. Tong W, Meffin H, Garrett DJ, Ibbotson MR. Stimulation strategies for improving the resolution of retinal prostheses. Front Neurosci. 2020;14:262.

    Article  PubMed  PubMed Central  Google Scholar 

  10. Lorach H, et al. Photovoltaic restoration of sight with high visual acuity. Nat Med. 2015;21:476–82.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Palanker D, Le Mer Y, Mohand-Said S, Muqit M, Sahel JA. Photovoltaic restoration of central vision in atrophic age-related macular degeneration. Ophthalmology. 2020;127:1097–104.

    Article  PubMed  Google Scholar 

  12. Palanker D, Le Mer Y, Mohand-Said S, Sahel JA. Simultaneous perception of prosthetic and natural vision in AMD patients. Nat Commun. 2022;13:513.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Edwards TL, et al. Assessment of the electronic retinal implant alpha AMS in restoring vision to blind patients with end-stage retinitis pigmentosa. Ophthalmology. 2018;125:432–43.

    Article  PubMed  Google Scholar 

  14. Hariz M. My 25 stimulating years with DBS in Parkinson’s disease. J Parkinsons Dis. 2017;7:S33–41.

    Article  PubMed  PubMed Central  Google Scholar 

  15. Fan X, Agid Y. At the origin of the history of glia. Neuroscience. 2018;385:255–71.

    Article  CAS  PubMed  Google Scholar 

  16. Von Bartheld CS, Bahney J, Herculano-Houzel S. The search for true numbers of neurons and glial cells in the human brain: a review of 150 years of cell counting. J Comp Neurol. 2016;524:3865–95.

    Article  Google Scholar 

  17. Zhang Y, Barres BA. Astrocyte heterogeneity: an underappreciated topic in neurobiology. Curr Opin Neurobiol. 2010;20:588–94.

    Article  CAS  PubMed  Google Scholar 

  18. Smith JH, et al. How neurons exploit fractal geometry to optimize their network connectivity. Sci Rep. 2021;11:2332.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Rowland C, et al. Investigating fractal analysis as a diagnostic tool that probes the connectivity of hippocampal neurons. Front Physiol. 2022;13:932598.

    Article  PubMed  PubMed Central  Google Scholar 

  20. Rowland C, et al. Neuron arbor geometry is sensitive to the fractal properties of their dendrites. Front Netw Physiol. 2023;3:1072815.

    Article  PubMed  PubMed Central  Google Scholar 

  21. Seidel D, et al. How a measure of tree structural complexity relates to architectural benefit-to-cost ratio, light availability, and growth of trees. Ecol Evol. 2019;9:7134–42.

    Article  PubMed  PubMed Central  Google Scholar 

  22. Hou C, Gheorghiu S, Huxley VH, Pfeifer P. Reverse engineering of oxygen transport in the lung: adaptation to changing demands and resources through space-filling networks. PLoS Comput Biol. 2010;6:e1000902.

    Article  PubMed  PubMed Central  Google Scholar 

  23. Bronikowski MJ. CVD growth of carbon nanotube bundle arrays. Carbon. 2006;44:2822–32.

    Article  CAS  Google Scholar 

  24. Yunyu W, Li B, Ho P, Yao Z, Shi L. Effect of supporting layer on growth of carbon nanotubes by thermal chemical vapor deposition. Appl Phys Lett. 2006;89:183113.

    Article  Google Scholar 

  25. Zhao B, et al. Exploring advantages of diverse carbon nanotube forests with tailored structures synthesized by supergrowth from engineered catalysts. ACS Nano. 2009;3:108–14.

    Article  CAS  PubMed  Google Scholar 

  26. Chen Y-C, et al. An active, flexible carbon nanotube microelectrode array for recording electrocorticograms. J Neural Eng. 2011;8:034001.

    Article  PubMed  Google Scholar 

  27. David-Pur M, Bareket-Keren L, Beit-Yaakov G, Raz-Prag D, Hanein Y. All-carbon-nanotube flexible multi-electrode array for neuronal recording and stimulation. Biomed Microdevices. 2014;16:43–53.

    Article  CAS  PubMed  Google Scholar 

  28. Bareket-Keren L, Hanein Y. Carbon nanotube-based multi electrode arrays for neuronal interfacing: progress and prospects. Front Neural Circuits. 2013;6:22.

    Article  Google Scholar 

  29. Fabbro A, Bosi S, Ballerini L, Prato M. Carbon nanotubes: artificial nanomaterials to engineer single neurons and neuronal networks. ACS Chem Neurosci. 2012;3:611–8.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Krukiewicz K, Janas D, Vallejo-Giraldo C, Biggs MJP. Self-supporting carbon nanotube films as flexible neural interfaces. Electrochim Acta. 2019;295:253–61.

    Article  CAS  Google Scholar 

  31. Hu H, Ni Y, Montana V, Haddon RC, Parpura V. Chemically functionalized carbon nanotubes as substrates for neuronal growth. Nano Lett. 2004;4:507–11.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Nick C, Yadav S, Joshi R, Thielemann C, Schneider JJ. Growth and structural discrimination of cortical neurons on randomly oriented and vertically aligned dense carbon nanotube networks. Beilstein J Nanotechnol. 2014;5:1575–9.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Sorkin R, et al. Process entanglement as a neuronal anchorage mechanism to rough surfaces. Nanotechnology. 2009;20:015101.

    Article  PubMed  Google Scholar 

  34. Flanagan LA, Ju Y-E, Marg B, Osterfield M, Janmey PA. Neurite branching on deformable substrates. Neuroreport. 2002;13:2411–5.

    Article  PubMed  PubMed Central  Google Scholar 

  35. Georges PC, Miller WJ, Meaney DF, Sawyer ES, Janmey PA. Matrices with compliance comparable to that of brain tissue select neuronal over glial growth in mixed cortical cultures. Biophys J. 2006;90:3012–8.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Watterson WJ, et al. The roles of an aluminum underlayer in the biocompatibility and mechanical integrity of vertically aligned carbon nanotubes for interfacing with retinal neurons. Micromachines (Basel). 2020;11:546.

    Article  PubMed  Google Scholar 

  37. Gabay T, et al. Carbon nanotube based neuro-chip for engineering, recording and stimulation of cultured networks. In: The 13th international conference on solid-state sensors, actuators and microsystems, 2005. Digest of technical papers. TRANSDUCERS ’05, vol. 2. IEEE; 2005. p. 1226–9.

    Chapter  Google Scholar 

  38. Wang K, Fishman HA, Dai H, Harris JS. Neural stimulation with a carbon nanotube microelectrode array. Nano Lett. 2006;6:2043–8.

    Article  CAS  PubMed  Google Scholar 

  39. Mazzatenta A, et al. Interfacing neurons with carbon nanotubes: electrical signal transfer and synaptic stimulation in cultured brain circuits. J Neurosci. 2007;27:6931–6.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Cellot G, et al. Carbon nanotubes might improve neuronal performance by favouring electrical shortcuts. Nat Nanotechnol. 2009;4:126–33.

    Article  CAS  PubMed  Google Scholar 

  41. Lovat V, et al. Carbon nanotube substrates boost neuronal electrical signaling. Nano Lett. 2005;5:1107–10.

    Article  CAS  PubMed  Google Scholar 

  42. Fairbanks MS, Taylor RP. Measuring the scaling properties of temporal and spatial patterns: from the human eye to the foraging albatross. In: Nonlinear dynamical systems analysis for the behavioral sciences using real data. Boca Raton: CRC Press; 2010.

    Google Scholar 

  43. Moslehi S, et al. Controlled assembly of retinal cells on fractal and Euclidean electrodes. PLoS One. 2022;17:e0265685.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Butterwick A, et al. Effect of shape and coating of a subretinal prosthesis on its integration with the retina. Exp Eye Res. 2009;88:22–9.

    Article  CAS  PubMed  Google Scholar 

  45. Thanihaichelvan M, et al. Metallic-semiconducting junctions create sensing hot-spots in carbon nanotube FET aptasensors near percolation. Biosens Bioelectron. 2019;130:408–13.

    Article  CAS  PubMed  Google Scholar 

  46. Plank NOV, Ishida M, Cheung R. Positioning of carbon nanotubes using soft-lithography for electronics applications. J Vac Sci Technol B. 2005;23:3178–81.

    Article  CAS  Google Scholar 

  47. Zheng HY, Plank NOV. Facile fabrication of carbon nanotube network thin film transistors for device platforms. Int J Nanotechnol. 2017;14:505–18.

    Article  CAS  Google Scholar 

  48. Thanihaichelvan M, et al. Data on liquid gated CNT network FETs on flexible substrates. Data Brief. 2018;21:276–83.

    Article  PubMed  PubMed Central  Google Scholar 

  49. Browning LA, et al. Investigation of fractal carbon nanotube networks for biophilic neural sensing applications. Nanomaterials. 2021;11:636.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Fan JA, et al. Fractal design concepts for stretchable electronics. Nat Commun. 2014;5:3266.

    Article  PubMed  Google Scholar 

  51. Zhang J, et al. Integrated device for optical stimulation and spatiotemporal electrical recording of neural activity in light-sensitized brain tissue. J Neural Eng. 2009;6:055007.

    Article  PubMed  PubMed Central  Google Scholar 

  52. Zrenner E. Will retinal implants restore vision? Science. 2002;295:1022–5.

    Article  CAS  PubMed  Google Scholar 

  53. Cogan SF. Neural stimulation and recording electrodes. Annu Rev Biomed Eng. 2008;10:275–309.

    Article  CAS  PubMed  Google Scholar 

  54. Watterson WJ, Montgomery RD, Taylor RP. Fractal electrodes as a generic interface for stimulating neurons. Sci Rep. 2017;7:6717.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Watterson WJ, Montgomery RD, Taylor RP. Modeling the improved visual acuity using photodiode based retinal implants featuring fractal electrodes. Front Neurosci. 2018;12:277.

    Article  PubMed  PubMed Central  Google Scholar 

  56. Charlier J-C, Blase X, Roche S. Electronic and transport properties of nanotubes. Rev Mod Phys. 2007;79:677–732.

    Article  CAS  Google Scholar 

  57. Obaid A, et al. Massively parallel microwire arrays integrated with CMOS chips for neural recording. Sci Adv. 2020;6:eaay2789.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Pampaloni NP, et al. Sculpting neurotransmission during synaptic development by 2D nanostructured interfaces. Nanomedicine. 2018;14:2521–32.

    Article  CAS  PubMed  Google Scholar 

  59. Einevoll GT, Franke F, Hagen E, Pouzat C, Harris KD. Towards reliable spike-train recordings from thousands of neurons with multielectrodes. Curr Opin Neurobiol. 2012;22:11–7.

    Article  CAS  PubMed  Google Scholar 

  60. Buzsáki G. Large-scale recording of neuronal ensembles. Nat Neurosci. 2004;7:446–51.

    Article  PubMed  Google Scholar 

  61. Piret G, Perez M-T, Prinz CN. Support of neuronal growth over glial growth and guidance of optic nerve axons by vertical nanowire arrays. ACS Appl Mater Interfaces. 2015;7:18944–8.

    Article  CAS  PubMed  Google Scholar 

  62. Chapman CAR, Chen H, Stamou M, Lein PJ, Seker E. Mechanisms of reduced astrocyte surface coverage in cortical neuron-glia co-cultures on nanoporous gold surfaces. Cell Mol Bioeng. 2016;9:433–42.

    Article  CAS  PubMed  Google Scholar 

  63. Mata D, et al. Diels–Alder functionalized carbon nanotubes for bone tissue engineering: in vitro/in vivo biocompatibility and biodegradability. Nanoscale. 2015;7:9238–51.

    Article  CAS  PubMed  Google Scholar 

  64. Abu-Saude M, Morshed BI. Characterization of a novel polypyrrole (PPy) conductive polymer coated patterned vertical CNT (pvCNT) dry ECG electrode. Chemosensors. 2018;6:27.

    Article  Google Scholar 

  65. Latora V, Marchiori M. Economic small-world behavior in weighted networks. Eur Phys J B. 2003;32:249–63.

    Article  CAS  Google Scholar 

  66. Achard S, Bullmore E. Efficiency and cost of economical brain functional networks. PLoS Comput Biol. 2007;3:e17.

    Article  PubMed  PubMed Central  Google Scholar 

  67. Liu J, et al. Control of neuronal network organization by chemical surface functionalization of multi-walled carbon nanotube arrays. Nanotechnology. 2011;22:195101.

    Article  PubMed  PubMed Central  Google Scholar 

  68. Shefi O, Golding I, Segev R, Ben-Jacob E, Ayali A. Morphological characterization of in vitro neuronal networks. Phys Rev E. 2002;66:021905.

    Article  Google Scholar 

  69. Luo L, O’Leary DDM. Axon retraction and degeneration in development and disease. Annu Rev Neurosci. 2005;28:127–56.

    Article  CAS  PubMed  Google Scholar 

  70. Fields RD, Stevens-Graham B. New insights into neuron-glia communication. Science. 2002;298:556–62.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Shein M, et al. Engineered neuronal circuits shaped and interfaced with carbon nanotube microelectrode arrays. Biomed Microdevices. 2009;11:495–501.

    Article  CAS  PubMed  Google Scholar 

  72. Villegas JC, et al. Multiwalled carbon nanotubes hinder microglia function interfering with cell migration and phagocytosis. Adv Healthc Mater. 2014;3:424–32.

    Article  CAS  PubMed  Google Scholar 

  73. Hatten ME, Mason CA. Mechanisms of glial-guided neuronal migration in vitro and in vivo. Experientia. 1990;46:907–16.

    Article  CAS  PubMed  Google Scholar 

  74. Fishell G, Hatten ME. Astrotactin provides a receptor system for CNS neuronal migration. Development. 1991;113:755–65.

    Article  CAS  PubMed  Google Scholar 

  75. Moslehi S, et al. Comparison of fractal and grid electrodes for studying the effects of spatial confinement on dissociated retinal neuronal and glial behavior. Sci Rep. 2022;12:17513.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Zhong Y, Bellamkonda RV. Dexamethasone-coated neural probes elicit attenuated inflammatory response and neuronal loss compared to uncoated neural probes. Brain Res. 2007;1148:15–27.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Fox D. Neuroscience: brain buzz. Nature. 2011;472:156–9.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

RPT is a Cottrell Scholar of the Research Council for Science Advancement. This research was supported (RPT) by the W. M. Keck Foundation, the Living Legacy Foundation, the Ciminelli Foundation, and the University of Oregon, and (MTP) by the Swedish Research Council (# 2016-03757), NanoLund at Lund University, Stiftelsen för Synskadade if.d. Malmöhus Län, Crown Princess Margareta’s Committee for the Blind. We thank M. Pluth (University of Oregon) for providing the opportunity and training for the fluorescence microscopy imaging system. Microscopy instrumentation was supported by the NSF (CHE-1531189). We thank C.M.Niell (University of Oregon) for his collaboration in the discussion of the results, B. Aleman, D. Miller, and K. Zappitelli (University of Oregon) for their contributions to the development of the VACNT synthesis process. The CN California Polytechnic State University T thin films were fabricated by L.A. Browning in collaboration with N.O.V. Plank (Victoria University, Wellington, New Zealand) and imaged by M. P. Dierkes (California Polytechnic State University).

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Moslehi, S. et al. (2024). Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties. 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_43

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