The preparation of HEMA-MPC films for ocular drug delivery

There is a need to prolong drug residence time using a biocompatible formulation in the subconjunctival space after surgery to treat glaucoma. Drug releasing discs were prepared with 2-(hydroxyethyl)methacrylate (HEMA) and 2-methacryloyl-oxyethyl phosphorylcholine (MPC). The ratio of bound water (Wb) to free water (Wf) ratio increased from 1:0.3 to 1:6.8 with increasing MPC (0 to 50%, w/w). The optimal balance between water content, SR and mechanical strength were obtained with 10% MPC (w/w) hydrogels. Water-alcohol mixtures were examined to facilitate loading of poorly soluble drugs, and they showed greater hydrogel swelling than either water or alcohol alone. The SR was 1.2 ± 0.02 and 3.3 ± 0.1 for water and water:ethanol (1:1) respectively. HEMA-MPC (10%) discs were loaded with dexamethasone using either water:ethanol (1:1) or methanol alone. Drug release was examined in an outflow rig model that mimics the subconjunctival space in the eye. Dexamethasone loading increased from 0.3 to 1.9 mg/disc when the solvent was changed from water:ethanol (1:1) to methanol with the dexamethasone half-life (t½) increasing from 1.9 to 9.7 days respectively. These encouraging results indicate that HEMA-MPC hydrogels have the potential to sustain the residence time of a drug in the subconjunctival space of the eye

Steady streaming within a periodically rotating sphere

We consider the flow in a spherical chamber undergoing periodic torsional oscillations about an axis through its centre, and analyse it both theoretically and experimentally. We calculate the flow in the limit of small-amplitude oscillations in the form of a series expansion in powers of the amplitude, finding that at second order, a steady streaming flow develops consisting of two toroidal cells. This streaming behaviour is also observed in our experiments. We find good quantitative agreement between theory and experiments, and we discuss the dependence of the steady streaming behaviour as both the oscillation frequency and amplitude are varied

Mixing processes in the vitreous chamber induced by eye rotations

In this paper, we study a model of flow in the vitreous humour in the posterior chamber of the human eye, induced by saccadic eye rotations. We concentrate on the effect of the shape of the chamber upon the mixing properties of the induced flows. We make particle image velocimetry measurements of the fluid velocity in a transparent plastic (Perspex)model of the posterior chamber during sinusoidal torsional oscillations about a vertical axis. We use a Newtonian fluid to model the vitreous humour, which is most realistic when either the vitreous humour is liquefied or has been replaced by purely viscous tamponade fluids. The model of the posterior chamber is a sphere with an indentation, representing the effect of the lens. In spite of the purely periodic forcing, a steady streaming flow is generated, which plays a fundamental role in the mixing processes in the domain. The streaming flow differs markedly from that in a perfect sphere, and its topological characteristics change substantially as the frequency of oscillation varies. We discuss the flow characteristics in detail and show that, for physiological parameter values, the Peclet number (based on a suitable measure of the steady streaming velocity) is large, suggesting that advection strongly dominates over diffusion for mass transport phenomena. We also compute particle trajectories based on the streaming velocity and use these to investigate the stirring properties of the flow

Steady streaming in the liquefied vitreous due to saccadic eye movements

The posterior chamber of the eye has an approximately spherical shape, and is filled with vitreous humor, a transparent material with viscoelastic properties. The vitreous has the mechanical roles of supporting the eye shape, promoting the adherence between the retina and the choroid, and acting as a barrier between the anterior and posterior segments of the eye that inhibits both heat diffusion and molecular transport. Sometimes, particularly in elderly people, the fluid in the posterior chamber has almost Newtonian properties. This can be as a consequence of liquefaction of the vitreous humor due to synchisys (degradation of the collagenous framework of the vitreous humor), or after a vitrectomy, a surgical procedure in which the vitreous humor is replaced by tamponade fluids (typically silicone oils). Since intra-vitreal drug injection is increasingly used to treat retinal diseases, and the efficacy of this procedure depends on molecular transport processes following injection, much of the biomechanical research on the vitreous humor has focused on understanding these processes. Many authors have considered purely diffusive transport or alternatively purely advective transport due to creeping bulk flow [3,4]. However, when the vitreous is liquefied, rotational motion of the eye is also likely to induce significant fluid flow

Experimental and theoretical study of the steady streaming in a sphere subject to periodic torsional oscillations

We study by theoretical and experimental means the steady streaming generated in a sphere subject to periodic torsional oscillations. The experimental setup consists of a Perspex cylindrical container in which a spherical cavity is carved. The container is filled with glycerol and is then set in motion by a computer controlled motor. PIV measurements of the streaming flow are taken on the equatorial plane normal to the axis of rotation. The problem is also studied theoretically by assuming small amplitude rotations and developing a perturbation solution in terms of this small parameter. At second order the steady streaming flow is reproduced. The streaming flow is axis-symmetric and consists of two toroidal circulation cells, one in each hemisphere. Theoretical results and experimental measurements are in very good quantitative agreement

Flow in the vitreous humour of the eye induced by saccadic eyeball motion

Certain retinal conditions are treated by direct drug injection into the vitreous humour; the subsequent delivery will be affected by vitreous motion driven by saccades of the eyeball. We model the saccades as small-amplitude sinusoidal oscillations, and the vitreous humour as a Newtonian fluid. Treating the vitreous chamber as a sphere, we obtain an oscillating flow plus a correction that includes a steady streaming flow on vertical planes, and we argue that both components have comparable importance for drug transport. In reality however, the vitreous chamber has an indentation due to the lens. Accounting for this leads to a perturbation in the flow field. The oscillatory component includes a vortex formed behind the lens every half period that migrates into the interior, and the steady streaming has two counter-rotating vortices

Mathematical modeling of the circulation in the liver lobule

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises

The first international workshop on the role and impact of mathematical in medicine: A collective account

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