Fractal Electrodes as a Generic Interface for Stimulating Neurons

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 Microelectrodes for More Energy-Efficient Cervical Vagus Nerve Stimulation

Vagus nerve stimulation (VNS) has the potential to treat various peripheral dysfunctions, but the traditional cuff electrodes for VNS are susceptible to off-target effects. Microelectrodes may enable highly selective VNS that can mitigate off-target effects, but they suffer from the increased impedance. Recent studies on microelectrodes with non-Euclidean geometries have reported higher energy efficiency in neural stimulation applications. These previous studies use electrodes with mm/cm-scale dimensions, mostly targeted for myelinated fibers. This study evaluates fractal microelectrodes for VNS in a rodent model (N = 3). A thin-film device with fractal and circle microelectrodes is fabricated to compare their neural stimulation performance on the same radial coordinate of the nerve. The results show that fractal microelectrodes can activate C-fibers with up to 52% less energy (p = 0.012) compared to circle microelectrodes. To the best of the knowledge, this work is the first to demonstrate a geometric advantage of fractal microelectrodes for VNS in vivo.

Modeling of dielectric resonator antenna array for retina photoreceptors

The retina encompasses several cone and rod photoreceptors at fovea region i.e., 90 million cells of rod photoreceptors and 4.5million cells of cone photoreceptors. The overall photoreceptors determine the vision of every human. An electromagnetic dielectric resonator antenna has been presented for retina photoreceptors in order to model them at fovea and its peripheral retina with the respected angular spectrum. Three coloring primary system of human eye (R, G, B) can be realized based on the model. Three miscellaneous models i.e., simple, graphene coated, and interdigital models have been presented in this paper. The nonlinear property of interdigital structures is one of the best advantages to use for creating the capacitor. The capacitance property helps improving the upper band of visible spectrum. The absorption of light for graphene as an energy harvesting material and its conversion into electrochemical signals is making it one of the best models. The mentioned three electromagnetic models of human photoreceptors have been expressed as a receiver antenna. The proposed electromagnetic models based on dielectric resonator antenna (DRA) are being analyzed for cones and rods photoreceptors of retina in the human eye by Finite Integral Method (FIM) utilized by CST MWS. The results show that the models are so fine for vision spectrum due to its localized near field enhancement property. The results indicate fine parameters of S 11 (return loss below -10 dB) with invaluable resonants in a wide range of frequencies from 405 THz to 790 THz (vision spectrum), appropriate S 21 (insertion loss 3-dB bandwidth), very good field distribution of electric and magnetic fields for flowing the power and electrochemical signals. Finally, mfERG clinical and experimental results validate the numeric results by the normalized output to input ratio of these models and it points out that these models can stimulate the electrochemical signals in photoreceptor cells for the best suiting of realizing the new retinal implants.

Comparison of fractal and grid electrodes for studying the effects of spatial confinement on dissociated retinal neuronal and glial behavior

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.

Graphene coated dielectric resonator antenna for modeling the photoreceptors at visible spectrum

The absorption of light is very important task for retina photoreceptors. Graphene is an energy harvesting material and one of the best models for the electromagnetic wave absorption and its conversion into signals. In this paper, an electromagnetic modeling of human retinal photoreceptors has been presented based on graphene coated material as a receiver antenna. The proposed electromagnetic model based on dielectric resonator antenna (DRA) is being analyzed for retina photoreceptors of human eye (cones and rods) by Finite Integral Method (FIM) collaborated with CST MWS. The results show that the model is good for vision spectrum with a proper field enhancement in cone photoreceptor due to its sensitivity to light. The results indicate proper S₁₁ (return loss below −10 dB) with invaluable resonances in a wide range of frequencies from 405 THz to 790 THz (vision spectrum), suitable S₂₁ (insertion loss 3-dB bandwidth), very good field distribution for flowing the power within desired radiation characteristics. The drawbacks of conventional model (no coating) have been resolved by presenting this one at blue spectrum specifically. Finally, mfERG clinical and experimental results show that this model can stimulate the electrochemical voltages and currents in photoreceptor cells.

Controlled assembly of retinal cells on fractal and Euclidean electrodes

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.

Bio-inspired strategies for next-generation perovskite solar mobile power sources

Smart electronic devices are becoming ubiquitous due to many appealing attributes including portability, long operational time, rechargeability and compatibility with the user-desired form factor. Integration of mobile power sources (MPS) based on photovoltaic technologies with smart electronics will continue to drive improved sustainability and independence. With high efficiency, low cost, flexibility and lightweight features, halide perovskite photovoltaics have become promising candidates for MPS. Realization of these photovoltaic MPS (PV-MPS) with unconventionally extraordinary attributes requires new 'out-of-box' designs. Natural materials have provided promising designing solutions to engineer properties under a broad range of boundary conditions, ranging from molecules, proteins, cells, tissues, apparatus to systems in animals, plants, and humans optimized through billions of years of evolution. Applying bio-inspired strategies in PV-MPS could be biomolecular modification on crystallization at the atomic/meso-scale, bio-structural duplication at the device/system level and bio-mimicking at the functional level to render efficient charge delivery, energy transport/utilization, as well as stronger resistance against environmental stimuli (e.g., self-healing and self-cleaning). In this review, we discuss the bio-inspired/-mimetic structures, experimental models, and working principles, with the goal of revealing physics and bio-microstructures relevant for PV-MPS. Here the emphasis is on identifying the strategies and material designs towards improvement of the performance of emerging halide perovskite PVs and strategizing their bridge to future MPS.

Investigation of Fractal Carbon Nanotube Networks for Biophilic Neural Sensing Applications

We propose a carbon-nanotube-based neural sensor designed to exploit the electrical sensitivity of an inhomogeneous fractal network of conducting channels. This network forms the active layer of a multi-electrode field effect transistor that in future applications will be gated by the electrical potential associated with neuronal signals. Using a combination of simulated and fabricated networks, we show that thin films of randomly-arranged carbon nanotubes (CNTs) self-assemble into a network featuring statistical fractal characteristics. The extent to which the network's non-linear responses will generate a superior detection of the neuron's signal is expected to depend on both the CNT electrical properties and the geometric properties of the assembled network. We therefore perform exploratory experiments that use metallic gates to mimic the potentials generated by neurons. We demonstrate that the fractal scaling properties of the network, along with their intrinsic asymmetry, generate electrical signatures that depend on the potential's location. We discuss how these properties can be exploited for future neural sensors.

How neurons exploit fractal geometry to optimize their network connectivity

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).

Novel Electrode Designs for Neurostimulation in Regenerative Medicine: Activation of Stem Cells

Neural stem and progenitor cells (i.e., neural precursors) are found within specific regions in the central nervous system and have great regenerative capacity. These cells are electrosensitive and their behavior can be regulated by the presence of electric fields (EFs). Electrical stimulation is currently used to treat neurological disorders in a clinical setting. Herein we propose that electrical stimulation can be used to enhance neural repair by regulating neural precursor cell (NPC) kinetics and promoting their migration to sites of injury or disease. We discuss how intrinsic and extrinsic factors can affect NPC migration in the presence of an EF and how this impacts electrode design with the goal of enhancing tissue regeneration. We conclude with an outlook on future clinical applications of electrical stimulation and highlight technological advances that would greatly support these applications.

The Roles of an Aluminum Underlayer in the Biocompatibility and Mechanical Integrity of Vertically Aligned Carbon Nanotubes for Interfacing with Retinal Neurons

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.

Fractal solar panels: Optimizing aesthetic and electrical performances

Solar energy technologies have been plagued by their limited visual appeal. Because the electrical power generated by solar panels increases with their surface area and therefore their occupancy of the observer’s visual field, aesthetics will play an increasingly critical role in their future success in urban environments. Inspired by previous psychology research highlighting the aesthetic qualities of fractal patterns, we investigated panel designs featuring fractal electrodes. We conducted behavioral studies which compared observers’ preferences for fractal and conventional bus-bar electrode patterns, along with computer simulations which compared their electrical performances. This led us to develop a hybrid electrode pattern which best combines the fractal and bus-bar designs. Here we show that the new hybrid electrode matches the electrical performance of bus-bars in terms of light transmission and minimizing electrical power losses, while benefiting from the superior aesthetics of fractal patterns. This innovative integration of psychology and engineering studies provides a framework for developing novel electrode patterns with increased implementation and acceptance.

Characteristics of prosthetic vision in rats with subretinal flat and pillar electrode arrays

Objective

Retinal prostheses aim to restore sight by electrically stimulating the surviving retinal neurons. In clinical trials of the current retinal implants, prosthetic visual acuity does not exceed 20/550. However, to provide meaningful restoration of central vision in patients blinded by age-related macular degeneration (AMD), prosthetic acuity should be at least 20/200, necessitating a pixel pitch of about 50 μm or lower. With such small pixels, stimulation thresholds are high due to limited penetration of electric field into tissue. Here, we address this challenge with our latest photovoltaic arrays and evaluate their performance in vivo.

Approach

We fabricated photovoltaic arrays with 55 and 40 μm pixels (a) in flat geometry, and (b) with active electrodes on 10 μm tall pillars. The arrays were implanted subretinally into rats with degenerate retina. Stimulation thresholds and grating acuity were evaluated using measurements of the visually evoked potentials (VEP).

Main results

With 55 μm pixels, we measured grating acuity of 48 ± 11 μm, which matches the linear pixel pitch of the hexagonal array. This geometrically corresponds to a visual acuity of 20/192 in a human eye, matching the threshold of legal blindness in the US (20/200). With pillar electrodes, the irradiance threshold was nearly halved, and duration threshold reduced by more than three-fold, compared to flat pixels. With 40 μm pixels, VEP was too low for reliable measurements of the grating acuity, even with pillar electrodes.

Significance

While being helpful for treating a complete loss of sight, current prosthetic technologies are insufficient for addressing the leading cause of untreatable visual impairment—AMD. Subretinal photovoltaic arrays may provide sufficient visual acuity for restoration of central vision in patients blinded by AMD.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Modeling the Improved Visual Acuity Using Photodiode Based Retinal Implants Featuring Fractal Electrodes

Electronically restoring vision to patients blinded by severe retinal degenerations is rapidly becoming a realizable feat through retinal implants. Upon receiving an implant, previously blind patients can now detect light, locate objects, and determine object motion direction. However, the restored visual acuity (VA) is still significantly below the legal blindness level (VA < 20/200). The goal of this research is to optimize the inner electrode geometry in photovoltaic subretinal implants in order to restore vision to a VA better than blindness level. We simulated neural stimulation by 20 μm subretinal photovoltaic implants featuring square or fractal inner electrodes by: (1) calculating the voltage generated on the inner electrode based on the amount of light entering the photodiode, (2) mapping how this voltage spreads throughout the extracellular space surrounding retinal bipolar neurons, and (3) determining if these extracellular voltages are sufficient for neural stimulation. By optimizing the fractal inner electrode geometry, we show that all neighboring neurons can be stimulated using an irradiance of 12 mW/mm², while the optimized square only stimulates ~10% of these neurons at an equivalent irradiance. The 20 μm fractal electrode can thus theoretically restore VA up to 20/80, if other limiting factors common to retinal degenerations, such as glia scarring and rewiring of retinal circuits, could be reduced. For the optimized square to stimulate all neighboring neurons, the irradiance has to be increased by almost 300%, which is very near the maximum permissible exposure safety limit. This demonstration that fractal electrodes can stimulate targeted neurons for long periods using safe irradiance levels highlights the possibility for restoring vision to a VA better than the blindness level using photodiode-based retinal implants.

Electrochemical Evaluations of Fractal Microelectrodes for Energy Efficient Neurostimulation

Advancements in microfabrication has enabled manufacturing of microscopic neurostimulation electrodes with smaller footprint than ever possible. The smaller electrodes can potentially reduce tissue damage and allow better spatial resolution for neural stimulation. Although electrodes of any shape can easily be fabricated, substantial effort have been focused on identification and characterization of new materials and surface morphology for efficient charge injection, while maintaining simple circular or rectangular Euclidean electrode geometries. In this work we provide a systematic electrochemical evaluation of charge injection capacities of serpentine and fractal-shaped platinum microelectrodes and compare their performance with traditional circular microelectrodes. Our findings indicate that the increase in electrode perimeter leads to an increase in maximum charge injection capacity. Furthermore, we found that the electrode geometry can have even more significant impact on electrode performance than having a larger perimeter for a given surface area. The fractal-shaped microelectrodes, despite having smaller perimeter than other designs, demonstrated superior charge injection capacity. Our results suggest that electrode design can significantly affect both Faradaic and non-Faradaic electrochemical processes, which may be optimized to enable a more energy efficient design for neurostimulation.