Rheology of the vitreous body. Part I: Viscoelasticity of human vitreous

On the mechanochemical theory of biological pattern formation with application to vasculogenesis

We first describe the Murray-Oster mechanical theory of pattern formation, the biological basis of which is experimentally well documented. The model quantifies the interaction of cells and the extracellular matrix via the cell-generated forces. The model framework is described in quantitative detail. Vascular endothelial cells, when cultured on gelled basement membrane matrix, rapidly aggregate into clusters while deforming the matrix into a network of cord-like structures tessellating the planar culture. We apply the mechanical theory of pattern formation to this culture system and show that neither strain-biased anisotropic cell traction nor cell migration are necessary for pattern formation: isotropic, strain-stimulated cell traction is sufficient to form the observed patterns. Predictions from the model were confirmed experimentally.

Age-related changes in vitreous mobility as measured by video B scan ultrasound

Many vitreoretinal disorders increase in incidence with age. The vitreous is known to liquefy and separate from the retina in aging patients. Liquefaction and partial vitreous separation alter the biomechanics of the vitreous and change the tractional forces exerted by the vitreous on the retina. These forces may play a role in the development of a variety of vitreoretinal pathologies including retinal tears, cystoid macular edema, and macular holes. The purpose of this study is to test the hypothesis that the biomechanical properties of the vitreous change with aging and can be quantified by analysis of kinetic B scan ultrasound recordings. Kinetic B scan ultrasound recordings were made of the vitreous gel of 38 subjects from ages 18 to 91 during standard eye motions. The recordings were graded for speckle density (hyperreflective areas on ultrasound) and were examined for the presence or absence of posterior vitreous detachment. Tracking of the speckles on a polar grid allowed for the calculation of the angle travelled by the speckle relative to the angle travelled by the eye. The recordings were also analysed for "overshoot time", or the amount of time that the speckles continued to travel after the cessation of eye movement. The vitreous of subjects of age less than 46 years demonstrated significantly less speckle density (P < 0.001), less overshoot time (P < 0.001), and less angle travelled by the speckle relative to the angle travelled by the eye when compared to older subjects (P = 0.006). The presence or absence of PVD as diagnosed by kinetic ultrasound was not a significant predictor for speckle density, overshoot time, or ratio of angular motions. The results indicate that aging affects the biomechanics of the vitreous in ways which can be quantified with kinetic ultrasound analysis using the grading system described above.

A method of imaging viscoelastic parameters with acoustic radiation force

Acoustic radiation force has been proposed as a method of interrogating the mechanical properties of tissue. One simple approach applies a series of focused ultrasonic pulses to generate an acoustic radiation force, then processes the echoes returned from these pulses to estimate the radiation-force-induced displacement as a function of time. This process can be repeated at a number of locations to acquire data for image formation. In previous work we have formed images of tissue stiffness by depicting the maximum displacement induced at each tissue location after a finite period of insonification. While these maximum displacement images are able to differentiate materials of disparate mechanical properties, they exploit only a fraction of the information available. In this paper we show that the time-displacement curves acquired from tissue mimicking phantoms exhibit a viscoelastic response which is accurately described by the Voigt model. We describe how the viscous and elastic parameters of this model may be determined from experimental data. Finally, we show phantom images that depict not only the maximum local displacement, but also the viscous and elastic model parameters. These images offer complementary information about the target.

A model for the fluid motion of vitreous humour of the human eye during saccadic movement

During saccadic motion the eyewall moves in a manner similar to a sinusoid or at least can be represented by a sine Fourier series. Motion of the vitreous is induced by the saccade and the vitreo-retinal interface is subjected to a time-dependent shear. This force may be a significant factor for retinal tearing in the neighbourhood of small retinal holes or tears. An analytical viscoelastic model and a numerical, Newtonian model of the motion of the vitreous are presented and compared. Under sinusoidal boundary motion the analytical model shows that a viscous wave propagates inward toward the axis of rotation and the characteristic length of this wave is a function of the Womersley number. The numerical solution indicates that the vitreous moves similarly to the analytical result with small secondary motion; however, this motion allows complete recirculation of the vitreous over large timescales. Excellent agreement is found between the analytical and numerical models. The time-dependent fluid shear is evaluated and from the analytical solution the maximum value of this is found to be proportional to R0 square root of v(omega)3, where R0 is the eye radius, v the modified complex viscosity and omega the sinusoidal frequency. This indicates that myopes have a larger shear force exerted on them by virtue of the larger eye size. Further work is directed toward a model which links the stress found in the sclera to that exerted on the vitreo-retinal interface by the vitreous fluid motion.

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G''(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G''(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G'' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G'' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.