Large strain behaviour of brain tissue in shear: some experimental data and differential constitutive model.

In this paper, some experimental measurements of the behaviour of bovine brain tissue under large shear strains in vitro are reported, and a constitutive model which is consistent with the data is developed. It was determined that brain tissue is not strain-time separable, showing slower relaxation at higher strains, and that the stresses in shear are not linear with increasing shear strain. The new constitutive model is a differential model, including both an "elastic" term, of the Mooney type and a nonlinear viscoelastic term. The latter allows for the change in relaxation behaviour with strain, by modifying an upper convected multimode Maxwell model with a damping function. The model shows good agreement with the experimental shear results and could be used to describe other types of data.

Stiffness properties of the human lumbar spine: a lumped parameter model.

OBJECTIVE: To characterise with a mechanical model, the force-displacement response of the human lumbar spine to postero-anterior loading. DESIGN: Single case with repetition. BACKGROUND: Previous attempts to characterise the spine's force-displacement response have been simplistic and only considered the loading curve. These approaches ignored valuable information such as viscosity, non-linear elasticity and inertia of the lumbar spine. METHODS: The Spinal Assessment Machine applied a postero-anterior load to the spines of 23 asymptomatic subjects and measured the force-displacement response. The data was analysed by two methods; by a traditional linear regression of part of the loading curve and by a new method where an equation including non-linear stiffness and damping was used to characterise the whole force-displacement relationship. RESULTS: The equation developed was found to account for virtually all of the variance in the raw data (R2 > 0.993). Four elements derived by the equation determine the contributions of linear elasticity, non-linear elasticity, linear viscosity and non-linear viscosity to the overall stiffness. CONCLUSIONS: Considering the excellent fit of the new equation to the raw data and its poor correlation with existing measures, it is proposed that the traditional measures provide an incomplete description of the force-displacement response. Relevance. Therapists use their perception of the force-displacement response of the spine to select the type of manipulative treatment to apply. To study this aspect of patient care, devices capable of measuring spinal stiffness have been developed, however to date the obtained data has been analysed only simply. A lumped parameter mechanical model incorporating non-linear damping and stiffness provides a more complete description of the force-displacement response and thus may offer added insight into the manipulative treatment of spinal pain.

Linear viscoelastic properties of bovine brain tissue in shear.

We report the results from a series of rheological tests of fresh bovine brain tissue. Using a standard Bohlin VOR shear rheometer, shear relaxation and oscillating strain sweep experiments were performed on disks of brain tissue 30 mm in diameter, with a thickness of 1.5-2 mm. The strain sweep experiment showed that the viscoelastic strain limit is of the order of 0.1% strain. Shear relaxation data do not indicate the presence of a long-term elastic modulus, indicating fluid-like behavior. A relaxation spectrum was calculated by inverting the experimental data and used to predict oscillatory response, which agreed well with measured data.

The role of hydrodynamic interaction in the locomotion of microorganisms.

A general Boundary Element Method is presented and benchmarked with existing Slender Body Theory results and reflection solutions for the motion of spheres and slender bodies near plane boundaries. This method is used to model the swimming of a microorganism with a spherical cell body, propelled by a single rotating flagellum. The swimming of such an organism near a plane boundary, midway between two plane boundaries or in the vicinity of another similar organism, is investigated. It is found that only a small increase (less than 10%) results in the mean swimming speed of an organism swimming near and parallel to another identical organism. Similarly, only a minor propulsive advantage (again, less than 10% increase in mean swimming speed) is predicted when an organism swims very close and parallel to plane boundaries (such as a microscopic plate and (or) a coverslip, for example). This is explained in terms of the flagellar propulsive advantage derived from an increase in the ratio of the normal to tangential resistance coefficients of a slender body being offset by the apparently equally significant increase in the cell body drag. For an organism swimming normal to and toward a plane boundary, however, it is predicted that (assuming it is rotating its flagellum, relative to its cell body, with a constant angular frequency) the resulting swimming speed decreases asymptotically as the organism approaches the boundary.

On the flow of a non-Newtonian liquid induced by intestine-like contractions.

This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.