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.

Using Fractal Iconography to Emulate Nature's Aesthetics.

This year's cover artists are members of a team of physicists and psy-chologists who create human-centered designs based on psychology experiments that investigate the positive impacts of viewing fractal patterns. These positive impacts include reduced physiological stress levels and enhanced cognitive skills. Here, the team explores the concept of 'fractal iconography' as an approach to employing computers to generate naturalistic art. Adopting this approach, three forms of fractal patterning ('fractal icons') are combined in a variety of ways to generate the rich complexity of nature's scenery. These composite fractals are remarkably effective at conveying nature's aesthetic power.

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).

An Eye for Nature.

Artists have a long tradition of capturing the essence of Nature in their creative works. This year's cover artist, Tallmadge Doyle, uses copper plates to create prints of the complex visual textures found in Nature's scenery. Originating from careful observation, her images then undergo a stylistic evolution toward a personalized artistic vision of Nature's textures.

Complement C5a-Induced Changes in Neutrophil Morphology During Inflammation.

The complement and neutrophil defence systems, as major components of innate immunity, are activated during inflammation and infection. For neutrophil migration to the inflamed region, we hypothesized that the complement activation product C5a induces significant changes in cellular morphology before chemotaxis. Exposure of human neutrophils to C5a dose- and time-dependently resulted in a rapid C5a receptor-1 (C5aR1)-dependent shape change, indicated by enhanced flow cytometric forward-scatter area values. Similar changes were observed after incubation with zymosan-activated serum and in blood neutrophils during murine sepsis, but not in mice lacking the C5aR1. In human neutrophils, Amnis high-resolution digital imaging revealed a C5a-induced decrease in circularity and increase in the cellular length/width ratio. Biomechanically, microfluidic optical stretching experiments indicated significantly increased neutrophil deformability early after C5a stimulation. The C5a-induced shape changes were inhibited by pharmacological blockade of either the Cl-/HCO3--exchanger or the Cl- -channel. Furthermore, actin polymerization assays revealed that C5a exposure resulted in a significant polarization of the neutrophils. The functional polarization process triggered by ATP-P2X/Y-purinoceptor interaction was also involved in the C5a-induced shape changes, because pretreatment with suramin blocked not only the shape changes but also the subsequent C5a-dependent chemotactic activity. In conclusion, the data suggest that the anaphylatoxin C5a regulates basic neutrophil cell processes by increasing the membrane elasticity and cell size as a consequence of actin-cytoskeleton polymerization and reorganization, transforming the neutrophil into a migratory cell able to invade the inflammatory site and subsequently clear pathogens and molecular debris.

Fractal Electrodes as a Generic Interface for Stimulating Neurons.

The prospect of replacing damaged body parts with artificial implants is being transformed from science fiction to science fact through the increasing application of electronics to interface with human neurons in the limbs, the brain, and the retina. We propose bio-inspired electronics which adopt the fractal geometry of the neurons they interface with. Our focus is on retinal implants, although performance improvements will be generic to many neuronal types. The key component is a multifunctional electrode; light passes through this electrode into a photodiode which charges the electrode. Its electric field then stimulates the neurons. A fractal electrode might increase both light transmission and neuron proximity compared to conventional Euclidean electrodes. These advantages are negated if the fractal's field is less effective at stimulating neurons. We present simulations demonstrating how an interplay of fractal properties generates enhanced stimulation; the electrode voltage necessary to stimulate all neighboring neurons is over 50% less for fractal than Euclidean electrodes. This smaller voltage can be achieved by a single diode compared to three diodes required for the Euclidean electrode's higher voltage. This will allow patients, for the first time, to see with the visual acuity necessary for navigating rooms and streets.

Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots.

Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers' creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery.

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

Fractal images induce fractal pupil dilations and constrictions.

Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed.

The art and science of hyperbolic tessellations.

The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.

A smart micro-drill for cochleostomy formation: a comparison of cochlear disturbances with manual drilling and a human trial.

BACKGROUND: Cochleostomy formation is a key stage of the cochlear implantation procedure. Minimizing the trauma sustained by the cochlea during this step is thought to be a critical feature in hearing preservation cochlear implantation. The aim of this paper is firstly, to assess the cochlea disturbances during manual and robotic cochleostomy formation. Secondly, to determine whether the use of a smart micro-drill is feasible during human cochlear implantation. MATERIALS AND METHODS: The disturbances within the cochlea during cochleostomy formation were analysed in a porcine specimen by creating a third window cochleostomy, preserving the underlying endosteal membrane, on the anterior aspect of the basal turn of the cochlea. A laser vibrometer was aimed at this third window, to assess its movement while a traditional cochleostomy was performed. Six cochleostomies were performed in total, three manually and three with a smart micro-drill. The mean and peak membrane movement was calculated for both manual and smart micro-drill arms, to represent the disturbances sustained within cochlea during cochleostomy formation. The smart micro-drill was further used to perform live human robotic cochleostomies on three adult patients who met the National Institute of Health and Clinical Excellence criteria for undergoing cochlear implantation. RESULTS: In the porcine trial, the smart micro-drill preserved the endosteal membrane in all three cases. The velocity of movement of the endosteal membrane during manual cochleostomy is approximately 20 times higher on average and 100 times greater in peak velocity, than for robotic cochleostomy. The robot was safely utilized in theatre in all three cases and successfully created a bony cochleostomy while preserving the underlying endosteal membrane. CONCLUSIONS: Our experiments have revealed that controlling the force of drilling during cochleostomy formation and opening the endosteal membrane with a pick will minimize the trauma sustained by the cochlea by a factor of 20. Additionally, the smart micro-drill can safely perform a bony cochleostomy in humans under operative conditions and preserve the integrity of the underlying endosteal membrane.

Impact of small-angle scattering on ballistic transport in quantum dots.

Disorder increasingly affects performance as electronic devices are reduced in size. The ionized dopants used to populate a device with electrons are particularly problematic, leading to unpredictable changes in the behavior of devices such as quantum dots each time they are cooled for use. We show that a quantum dot can be used as a highly sensitive probe of changes in disorder potential and that, by removing the ionized dopants and populating the dot electrostatically, its electronic properties become reproducible with high fidelity after thermal cycling to room temperature. Our work demonstrates that the disorder potential has a significant, perhaps even dominant, influence on the electron dynamics, with important implications for "ballistic" transport in quantum dots.

The transience of virtual fractals.

Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.

Fractal electronic devices: simulation and implementation.

Many natural structures have fractal geometries that exhibit useful functional properties. These properties, which exploit the recurrence of patterns at increasingly small scales, are often desirable in applications and, consequently, fractal geometry is increasingly employed in diverse technologies ranging from radio antennae to storm barriers. In this paper, we explore the application of fractal geometry to electrical devices. First, we lay the foundations for the implementation of fractal devices by considering diffusion-limited aggregation (DLA) of atomic clusters. Under appropriate growth conditions, atomic clusters of various elements form fractal patterns driven by DLA. We perform a fractal analysis of both simulated and physical devices to determine their spatial scaling properties and demonstrate their potential as fractal circuit elements. Finally, we simulate conduction through idealized and DLA fractal devices and show that their fractal scaling properties generate novel, nonlinear conduction properties in response to depletion by electrostatic gates.

Artistic forms and complexity.

We discuss the inter-relationship between various concepts of complexity by introducing a complexity 'triangle' featuring objective complexity, subjective complexity and social complexity. Their connections are explored using visual and musical compositions of art. As examples, we quantify the complexity embedded within the paintings of the Jackson Pollock and the musical works of Johann Sebastian Bach. We discuss the challenges inherent in comparisons of the spatial patterns created by Pollock and the sonic patterns created by Bach, including the differing roles that time plays in these investigations. Our results draw attention to some common intriguing characteristics suggesting 'universality' and conjecturing that the fractal nature of art might have an intrinsic value of more general significance.

The art and science of foam bubbles.

Art and science become inevitably intertwined in our appreciation of nature's forms. This concept is demonstrated by the creative team responsible for the cover images of Nonlinear Dynamics, Psychology, and Life Sciences. Denis Weaire, Stefan Hutzler, Wiebke Drenckhan form a leading international collaboration with photographers Tim Durham and Michael Boran that explores the physics of bubble patterns. The images they generate capture and manipulate the striking aesthetic impact of foam bubbles. Furthermore, the foams exhibit a balance between simplicity and intricacy that symbolizes many of the complex systems that permeate nature and society.

Science and art: emergence of patterns from nature's chaos, through parallels between Edward Lorenz and Yves Klein.

Famous stories achieve their enduring appeal because they capture the essence of the times from which they emerge. This is true for both art and science. At critical moments in history, these two worlds become intertwined through a shared quest to understand the world around them. Questions hang in the air and, remarkably, accidents deliver the answers. In this chapter, I will explore the relationship between science and art as Edward Lorenz's discoveries unfolded to shed new light on the sensitive patterns hidden within nature's processes.

The museum of unnatural form: a visual and tactile experience of fractals.

A remarkable computer technology is revolutionizing the world of design, allowing intricate patterns to be created with mathematical precision and then 'printed' as physical objects. Contour crafting is a fabrication process capable of assembling physical structures the sizes of houses, firing the imagination of a new generation of architects and artists (Khoshnevisat, 2008). Daniel Della-Bosca has jumped at this opportunity to create the 'Museum of Unnatural Form' at Griffith University. Della-Bosca's museum is populated with fractals sculptures - his own versions of nature's complex objects - that have been printed with the new technology. His sculptures bridge the historical divide in fractal studies between the abstract images of mathematics and the physical objects of Nature (Mandelbrot, 1982). Four of his fractal images will be featured on the cover of NDPLS in 2009.

An autonomous surgical robot for drilling a cochleostomy: preliminary porcine trial.

OBJECTIVE: To produce an autonomous drilling robot capable of performing a bony cochleostomy whilst minimising the damage to the underlying cochlear endosteum. DESIGN: In this laboratory based study, a robotic drill was designed to measure the changes in force and torque experienced by the tool point during the drilling process. This information is used to predict the point of breakthrough and stop the drill prior to damaging the underlying endosteal membrane. SETTING: Aston University. PARTICIPANTS: Five porcine cochleas. MAIN OUTCOMES MEASURES: An assessment was made of whether a successful bony cochleostomy was performed, the integrity of endosteal membrane was then assessed. RESULTS: The autonomous surgical robotic drill successfully performed a bony cochleostomy and stopped without damaging the endosteal membrane in all five cases. CONCLUSIONS: The autonomous surgical robotic drill can perform a cochleostomy whilst minimising the trauma to the endosteal membrane. The system allows information about the state of the drilling process to be derived using force and torque data from the tool point. This information can be used to effectively predict drill breakthrough and implement a control strategy to minimise drill penetration beyond the far surface.