Simulation of the interaction between blood flow and atherosclerotic plaque

It has been well accepted that over 50% of cerebral ischemic events are the result of rupture of vulnerable carotid atheroma and subsequent thrombosis. Such strokes are potentially preventable by carotid interventions. Selection of patients for intervention is currently based on the severity of carotid luminal stenosis. It has been, however, widely accepted that luminal stenosis alone may not be an adequate predictor of risk. To evaluate the effects of degree of luminal stenosis and plaque morphology on plaque stability, we used a coupled nonlinear time-dependent model with flow-plaque interaction simulation to perform flow and stress/strain analysis for stenotic artery with a plaque. The Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the fluid. The Ogden strain energy function was used for both the fibrous cap and the lipid pool. The plaque Principal stresses and flow conditions were calculated for every case when varying the fibrous cap thickness from 0.1 to 2mm and the degree of luminal stenosis from 10% to 90%. Severe stenosis led to high flow velocities and high shear stresses, but a low or even negative pressure at the throat of the stenosis. Higher degree of stenosis and thinner fibrous cap led to larger plaque stresses, and a 50% decrease of fibrous cap thickness resulted in a 200% increase of maximum stress. This model suggests that fibrous cap thickness is critically related to plaque vulnerability and that, even within presence of moderate stenosis, may play an important role in the future risk stratification of those patients when identified in vivo using high resolution MR imaging.

Process Analytical Technology Approach on Fluid Bed Granulation and Drying : Identifying Critical Relationships and Constructing the Design Space

Fluid bed granulation is a key pharmaceutical process which improves many of the powder properties for tablet compression. Dry mixing, wetting and drying phases are included in the fluid bed granulation process. Granules of high quality can be obtained by understanding and controlling the critical process parameters by timely measurements. Physical process measurements and particle size data of a fluid bed granulator that are analysed in an integrated manner are included in process analytical technologies (PAT). Recent regulatory guidelines strongly encourage the pharmaceutical industry to apply scientific and risk management approaches to the development of a product and its manufacturing process. The aim of this study was to utilise PAT tools to increase the process understanding of fluid bed granulation and drying. Inlet air humidity levels and granulation liquid feed affect powder moisture during fluid bed granulation. Moisture influences on many process, granule and tablet qualities. The approach in this thesis was to identify sources of variation that are mainly related to moisture. The aim was to determine correlations and relationships, and utilise the PAT and design space concepts for the fluid bed granulation and drying. Monitoring the material behaviour in a fluidised bed has traditionally relied on the observational ability and experience of an operator. There has been a lack of good criteria for characterising material behaviour during spraying and drying phases, even though the entire performance of a process and end product quality are dependent on it. The granules were produced in an instrumented bench-scale Glatt WSG5 fluid bed granulator. The effect of inlet air humidity and granulation liquid feed on the temperature measurements at different locations of a fluid bed granulator system were determined. This revealed dynamic changes in the measurements and enabled finding the most optimal sites for process control. The moisture originating from the granulation liquid and inlet air affected the temperature of the mass and pressure difference over granules. Moreover, the effects of inlet air humidity and granulation liquid feed rate on granule size were evaluated and compensatory techniques used to optimize particle size. Various end-point indication techniques of drying were compared. The ∆T method, which is based on thermodynamic principles, eliminated the effects of humidity variations and resulted in the most precise estimation of the drying end-point. The influence of fluidisation behaviour on drying end-point detection was determined. The feasibility of the ∆T method and thus the similarities of end-point moisture contents were found to be dependent on the variation in fluidisation between manufacturing batches. A novel parameter that describes behaviour of material in a fluid bed was developed. Flow rate of the process air and turbine fan speed were used to calculate this parameter and it was compared to the fluidisation behaviour and the particle size results. The design space process trajectories for smooth fluidisation based on the fluidisation parameters were determined. With this design space it is possible to avoid excessive fluidisation and improper fluidisation and bed collapse. Furthermore, various process phenomena and failure modes were observed with the in-line particle size analyser. Both rapid increase and a decrease in granule size could be monitored in a timely manner. The fluidisation parameter and the pressure difference over filters were also discovered to express particle size when the granules had been formed. The various physical parameters evaluated in this thesis give valuable information of fluid bed process performance and increase the process understanding.

Microcontinuum approach to the pulsatile flow in tubes with and without longitudinal vibration

A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.

Laminar flow of a suspension in a curved pipe with varying curvature

The laminar flow of a fairly concentrated suspension (in which the volume fraction Z of the solid particles < 0.4) in a spatially varying periodically curved pipe has been examined numerically. Unlike the case of interacting suspension flows, the particles are found to flow in a well-mixed fashion, altering both the axial and circumferential velocities and consequently the fluid flux in the tube, depending on their diffusivity and inertia. The magnitude of shear stress at the wall is enhanced, suggesting that, if applied to vascular system, the vascular wall could be prone to ulceration during pathological situations like polycythemia. The delay in adaptation of the deviation in Poiseuille flow velocity to the curvature changes is also discussed in detail.

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

Flow between torsionally oscillating disks rotating about different axes at different speeds

The flow of an incompressible viscous fluid confined between two parallel infinite disks performing torsional oscillations with the same frequency, but rotating about different axes with different speeds has been studied. The solutions are presented for the symmetric and asymmetric first harmonic and steady streaming. The interesting features of the symmetric and asymmetric flow are discussed for the cases of small and large Womersley parameter at different ratios of the rotation speeds. The forces acting on one of the disks are also calculated.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Oscillatory flow in an elastic tube of variable cross-section

An oscillatory flow of a viscous incompressible fluid in an elastic tube of variable cross section has been investigated at low Reynolds number. The equations governing, the flow are derived under the assumption that the variation of the cross-section is slow in the axial direction for a tethered tube. The problem is then reduced to that of solving for the excess pressure from a second order ordinary differential equation with complex valued Bessel functions as the coefficients. This equation has been solved numerically for geometries of physiological interest and a comparison is made with some of the known theoretical and experimental results.

Flow over a cylinder with a hinged-splitter plate

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a hinged-splitter plate in the wake of a circular cylinder. The splitter plate can rotate about the hinge at the base of the cylinder due to the unsteady fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted as in the rigid splitter plate case. In our study, we investigate this problem in the limit where the stiffness and internal damping associated with the hinge are negligible, and the mass ratio of the splitter plate is small. The experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re, Re>4000. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force, and has been observed previously for transversely oscillating cylinders with no restorin force. In the present case, the saturation tip amplitude level can be tip to 0.45D, where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter ratio (L/D) is crucial in determining the character and magnitude of the oscillations. For small splitter plate length (L/D <= 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The nondiinensional oscillation frequencies (fD/U) on the other hand are found to continuously vary with L/D from fD/U approximate to 0.2 at L/D = 1 to fD/U approximate to 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D >= 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D >= 5.0. In the present case of the hinged-splitter plate, the sudden transition seen as the splitter plate length (L/D) is increased from 3 to 4 may be attributed to the fact that the wake vortices are no longer able to synchronize with the plate motions for larger splitter plate lengths. Hence, as observed in other vortex-induced vibration problems, the oscillations becomeaperiodic and the amplitude reduces dramatically.

On the magnetohydrodynamic flow between eccentrically rotating disks

The steady flow of an incompressible, viscous, electrically conducting fluid between two parallel, infinite, insulated disks rotating with different angular velocities about two noncoincident axes has been investigated; under the application of a uniform magnetic field in the axial direction. The solutions for the symmetric and asymmetric velocities are presented. The interesting feature arising due to the magnetic field is that in the central region the flow attains a uniform rotation with mean angular velocity at all rotation speeds for sufficiently large Hartmann number. In this case the flow adjusts to the rotational velocities of the disks mainly in the boundary layers near the disks. The forces on the disks are found to increase due to the presence of the applied magnetic field.

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.

A hydrodynamical study of the flow in renal tubules

The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.

Mass transfer effects on the generalised vortex flow over a stationary surface with or without magnetic field

The effect of injection and suction on the generalised vortex flow of a steady laminar incompressible fluid over a stationary infinite disc with or without magnetic field under boundary-layer approximations has been studied. The coupled nonlinear ordinary differential equations governing the self-similar flow have been numerically solved using the finite-difference scheme. The results indicate that the injection produces a deeper inflow layer and de-stabilises the motion while suction or magnetic field suppresses the inflow layer and produces stability. The effect of decreasingn, the parameter characterising the nature of vortex flow, is similar to that of increasing the injection rate.