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This paper entails the application of the energy shaping methodology to control a flexible, elastic Cosserat rod model of a single octopus arm. The principal focus and novel contribution of this work is two-fold: (i) reduced order controloriented modeling of the realistic internal muscular architecture in an octopus arm; and (ii) incorporation of such models into the energy shaping methodology, extending our prior work by formally accounting for muscle constraints. Extension of the control scheme to the under-actuated muscle control case involves two steps: (i) design of a desired potential energy function whose static minimizer solves a given control task; and (ii) implementing the resulting energy shaping control input into the dynamic model. Due to the muscle actuator constraints, the desired potential energy function may not be arbitrarily chosen. Indeed, the desired energy must now satisfy a partial differential equation, known as the matching condition, which is derived for the infinite dimensional Hamiltonian control system. A particular solution to those matching conditions is described, paving the way to the application of energy shaping methodology. The overall control design methodology including muscle models is implemented and demonstrated in a dynamic simulation environment. Results of several bio-inspired numerical experiments involving the control of octopus arms are reported.

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an effective-friction modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes ‘diffracting’ while traversing rows of posts, similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design.

The hydrodynamics of aneurysm blood flow is thought to be a critical factor in the evolution and potential rupture of blood vessel walls. The ability to predict which aneurysms may grow or rupture has eluded researchers and practicing clinicians. On the other hand, it is expected that local flow patterns, pressures, and wall shear stress play a role in the aneurysm life. In this study, the impact of waveform on these parameters was studied. A baseline waveform, taken from a patient, was applied to an aneurysm geometry. Then the waveform was modified by increasing and decreasing both the flowrates and the cardiac rate. In total, seven cases were investigated. It was found that there were remarkable similarities in the patterns of flow and wall stresses for the cases. These similarities existed throughout the cardiac cycle. It was also found that there was a reduced pressure variable that provides a universal relationship that characterizes all of the cases. It was seen that the maximum wall shear occurs at the neck of the aneurysm and scales with the peak systolic velocity. Finally, it is shown that the flow distribution to the multiple outlets does not appreciably depend on the details of the inlet waveform. All cases had a flow distribution that was within 2%.

Purpose: Estimating microstructural parameters of skeletal muscle from diffusion MRI (dMRI) signal requires understanding the relative importance of both microstructural and dMRI sequence parameters on the signal. This study seeks to determine the sensitivity of dMRI signal to variations in microstructural and dMRI sequence parameters, as well as assess the effect of noise on sensitivity. Methods: Using a cylindrical myocyte model of skeletal muscle, numerical solutions of the Bloch-Torrey equation were used to calculate global sensitivity indices of dMRI metrics (FA, RD, MD, λ 1 , λ 2 , λ 3) for wide ranges of microstructural and dMRI sequence parameters. The microstructural parameters were: myocyte diameter, volume fraction, membrane permeability, intra-and extracellular diffusion coefficients, and intra-and extracellular T 2 times. Two separate pulse sequences were examined, a PGSE and a generalized diffusion-weighted sequence that accommodates a larger range of diffusion times. The effect of noise and signal averaging on the sensitivity of the dMRI metrics was examined by adding synthetic noise to the simulated signal. Results: Among the examined parameters, the intracellular diffusion coefficient has the strongest effect, and myocyte diameter is more influential than permeability for FA and RD. The sensitivity indices do not vary significantly between the two pulse sequences. Also, noise strongly affects the sensitivity of the dMRI signal to microstructural variations. Conclusions: With the identification of key microstructural features that affect dMRI measurements, the reported sensitivity results can help interpret dMRI measurements of skeletal muscle in terms of the underlying microstructure and further develop parsimonious dMRI models of skeletal muscle.