Magic angles and fibre stretch in arterial tissue: Insights from the linear theory

Soft skeletons transmit force with variable gearing

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

On the tension-compression switch hypothesis in arterial mechanics

The tension-compression switch hypothesis for soft tissue proposes that when collagen fibres are compressed they do not contribute to the mechanical response which is then assumed to be the isotropic response of the extra-cellular matrix in which they are embedded. Such an assumption would seem reasonable. However, three difficulties with its use are discussed here. First it is shown that the admittedly scant experimental evidence available suggests that it does not have a completely sound physical basis. The possible paradoxical nature of the tension-compression switch has been previously identified by other authors. If the fibres are predicted to be in compression by an anisotropic model, then the resulting isotropic stretch of the fibres predicted by the tension-compression switch can be tensile. Thus the fibres can have a duality of being simultaneously tensile and compressive if the tension-compression switch is employed. This is illustrated here with a particular emphasis on the nature of the isotropic stretching of the fibres when compressed and the essential role of the linear theory when predicting the mechanical response for non-linear deformations of arterial tissue. Finally it is shown that use of the tension-compression switch can result in the failure of some models to predict the mechanical response in the material characterisation tests that were used to determine the values of their material constants. Thus some anisotropic models can have better predictive capability without the tension-compression switch.