Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure

Structural Systems Inspired by the Architecture of Skeletal Muscle

Modern engineering applications call for structural and material systems that exhibit advanced performance. To achieve this performance, researchers often look to nature for inspiration. Skeletal muscle is a multifunctional system with remarkable versatility and robustness, offering a great example on how to effectively store, convert, and release energy for force generation and shape change. To date, most efforts seeking to emulate muscle have focused on its bulk characteristics. However, it has recently been shown that many of muscle’s advantageous properties arise from the assembly and geometry of its microscale constituents. This dissertation will aim to develop new concepts for structural and material systems inspired by a fundamental understanding of the assembly of muscle’s constituent elements into contractile units. This is achieved by exploiting two key ingredients expressed by these constituents: metastability, which is the existence of multiple stable conformations for a prescribed global geometry, and ¬¬local conformation changes to switch between these stable topologies. Rather than faithfully emulating or seeking to explain the complex chemo-mechanical processes that govern muscle contraction, the major contributions of this thesis arise from the exploitation of the aforementioned key features within the context of engineered structures and materials systems. First, a fundamental metastable unit is studied under harmonic excitation. Experimental, numerical, and analytical investigations uncover the coexistence of multiple response regimes with significantly different amplitudes. These distinct regimes are exploited to achieve highly adaptable energy dissipation characteristics that vary by up to two orders of magnitude among them, even as excitation parameters are held constant. On the other hand, introducing asymmetry by varying a static bias parameter allows for smooth, finer variation of energy dissipation performance. Then, inspired by the ability of the myofibril lattice in skeletal muscle to trap strain energy that can be released on-demand, this thesis explores structural systems that leverage asymmetric multistability for energy capture and storage. The initial kinetic energy from impulsive excitation is shown to trigger state transitions that result in the capture of recoverable strain energy in higher-potential states. Reverse transitions to lower-energy states exploit this stored energy to facilitate efficient deployment and length change in the structure. Lastly, the effect of myofibril lattice spacing in skeletal muscle, and shear-like motions of adjacent filaments during contraction, serves as inspiration for the development of an architected modular material system that uses transverse confinements in conjunction with oblique, shear-like motions to give rise to sudden state transitions. Numerical results provide insight into the experimentally-observed behaviors, revealing that these energy-releasing transitions correspond to discrete changes in reaction force magnitude and direction Mechanical response properties can be tailored by strategic variation of transverse confinement and system geometry. Analytical tools using relatively simple models are developed to offer meaningful prediction of the above features. The overall outcomes of this thesis reveal great potential to develop high-performance, versatile, and adaptable structural and material systems by exploiting fundamental features of skeletal muscle architecture.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145893/1/kidambi_1.pd

Multistable Phase Regulation for Robust Steady and Transitional Legged Gaits

We develop robust methods that allow specification, control, and transition of a multi-legged robot’s stepping pattern—its gait—during active locomotion over natural terrain. Resulting gaits emerge through the introduction of controllers that impose appropriately-placed repellors within the space of gaits, the torus of relative leg phases, thereby mitigating against dangerous patterns of leg timing. Moreover, these repellors are organized with respect to a natural cellular decomposition of gait space and result in limit cycles with associated basins that are well characterized by these cells, thus conferring a symbolic character upon the overall behavioral repertoire. These ideas are particularly applicable to four- and six-legged robots, for which a large variety of interesting and useful (and, in many cases, familiar) gaits exist, and whose tradeoffs between speed and reliability motivate the desire for transitioning between them during active locomotion. We provide an empirical instance of this gait regulation scheme by application to a climbing hexapod, whose “physical layer” sensor-feedback control requires adequate grasp of a climbing surface but whose closed loop control perturbs the robot from its desired gait. We document how the regulation scheme secures the desired gait and permits operator selection of different gaits as required during active climbing on challenging surfaces

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

A Metastable Modular Structure Approach for Shape Morphing, Property Tuning and Wave Propagation Tailoring

The emerging concept of reconfigurable mechanical metamaterials has received increasing attention for realizing future advanced multifunctional adaptive structural systems partially due to their advantages over conventional bulk materials that are beneficial and desirable in many engineering applications. However, some of the critical challenges remain unaddressed before the concept can effectively and efficiently achieve real-world impacts. For instance, in the state-of-art, modules of mechanical metamaterials only reconfigure collectively to achieve global topology adaptation. As a result, the structure merely exhibits limited number of configurations that are discretely different from each other, which greatly undermines the benefits and impact of the reconfiguration effect. Additionally, most of the metamaterials investigations are focusing on the “materials” characteristics assuming infinite domain without considering the “structure” aspect of the systems. The effects of having finite domains and boundary conditions will generate new research issues and phenomena that are critical to real-world systems. To address the challenges and fundamentally advance the state of the art of multifunctional adaptive structures, this dissertation seeks to create a paradigm shift by exploiting and harnessing metastable modular mechanics and dynamics. Through developing new analysis and synthesis methodologies and conducting rigorous analytical, numerical, and experimental investigations, this research creates a new class of reconfigurable metastructure that can achieve mechanical property and topology adaptation as well as adaptive non-reciprocal vibration/wave transmission. The intellectual merit of this dissertation lies in introducing metastable modules that can be synergistically assembled and individually tuned to realize near continuous topology and mechanical property adaptation and elucidating the intricate nonlinear dynamics afforded by the metastructure. This research reveals different kinds of nonlinear instabilities that are able to facilitate the onset of supratransmission, a bandgap transmission phenomenon pertained to nonlinear periodic metastructure. In addition, utilizing this novel phenomenon, supratransmission, together with inherent spatial asymmetry of strategically configured constituents, the proposed metastructure is shown to be able to facilitate unprecedented broadband non-reciprocal vibration and wave transmission and on-demand adaptation. Since the proposed approach depends primarily on scale-independent principles, the broader impact of this dissertation is that the proposed metastructure could foster a new generation of reconfigurable structural and material systems with unprecedented adaptation and unconventional vibration control and wave transmission characteristics that are applicable to vastly different length scales for a wide spectrum of applications.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147525/1/wuzhen_1.pd

Programmable Multistable Mechanisms: Design, modeling, characterization and applications

Multistable Mechanisms are mechanical devices having more than one stable state. Since these mechanisms can maintain different deformations with zero force, they are advantageous for low power environments such as wristwatches and medical devices. In this thesis, I introduce programmable multistable mechanisms (PMMs), a new family of multistable mechanisms where the number, position, and stiffness of stable states can be controlled by programming inputs modifying the boundary conditions. PMMs can be synthesized by combining bistable mechanisms. This method was used to produce the T-mechanism, a PMM consisting of two double parallelogram mechanisms (DPMs) connected orthogonally where each DPM consists of two parallel beams connected centrally by a rigid block and axially loaded by programming input. An analytical model based on Euler-Bernoulli beam theory was derived to describe qualitatively the stability behaviour of the T-mechanism. The model approximates the mechanism's stiffness by a sixth order polynomial from which the reaction force and strain energy expressions can be estimated. These explicit formulas provide analytical expressions for the number, position, and stiffness of stable and unstable states as functions of the programming inputs. The qualitative stability behavior was represented by the programming diagram, bifurcation diagrams and stiffness maps relating the number, position and stiffness of stable states with the programming inputs. In addition, I showed that PMMs have zero stiffness regions functioning as constant-force multistable mechanisms. Numerical simulations validated these results. Experimental measurements were conducted on the T-mechanism prototype manufactured using electro-discharge machining. An experimental setup was built to measure the reaction force of the mechanism for different programming inputs. I verified the possible configurations of the T-mechanism including monostability bistability, tristability, quadrastability, zero stiffness regions, validating my analytical and numerical models. Compared to classical multistable mechanisms which are displaced between their stable states by imposing a direct displacement, PMMs can be displaced by modifying mechanism strain energy. This property increases the repeatability of the mechanism as the released energy is independent of the driving parameters, which can be advantageous for mechanical watches and medical devices. Accurate timekeepers require oscillators having repeatable period independent of their energy source. However, the balance wheel spiral spring oscillator used in all mechanical watches, suffers from isochronism defect, i.e., its oscillation period depends on its amplitude. I addressed this problem by introducing novel detached constant force escapements for mechanical wristwatches based on PMMs. In the medical domain, I applied PMMs to construct a retinal vein cannulation needle for the treatment of retinal vein occlusion. PMMs based needles produce sufficient repeatable puncturing energy with a predefined stroke independent of the operator input. Numerical simulations were used to model and dimension our proposed tool and satisfy the strict requirements of ophthalmologic operations. The tool was manufactured using 3D femto-laser printing of glass. An experimental setup was built to characterize the tool's mechanical behavior and to verify my computations. The tool was applied successfully to cannulate retinal veins of pig eyes

Chaotic exploration and learning of locomotion behaviours

We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage