Numerical studies of contoured shock tube for murine powdered vaccine delivery system

A unique form of powdered delivery system, a biolistic system, has been developed. This novel technology is to accelerate particles in micro-particle form by a gas flow behind a travelling shock wave, so that they can attain sufficient momentum to penetrate the skin and thus achieve a pharmacological effect. One of the most recent developments is a mouse biolistic system, used in immunological studies. These studies require powdered vaccine to be delivered into the epidermis of the mouse with a narrow and highly controllable velocity distribution and a uniform spatial distribution. In this paper, Computational Fluid Dynamics (CFD) has been utilized to characterize the complete operation of a prototype mouse biolistic system. The key features of the gas dynamics and gas-particle interaction are discussed. Introduction A needle-free epidermal powdered delivery system, a biolistic system, has been developed at University of Oxford (Bellhouse et al, 1994, [1]). The underlying principle of the system is to accelerate a pre-measured dose of vaccine and drugs in microparticle form to an appropriate momentum by a high speed gas flow in order to penetrate the outer layer of the skin to achieve a pharmacological effect. The biolistic system has shown many advantages over conventional needle and syringe, in terms of effectiveness, cost and health risk. The system can deliver powdered vaccine into a desired layer of skin or tissue to achieve the optimal effect. When antigenic compounds are delivered to skin or mucosa, the biolistic system requires less material to elicit the equivalent immune response [2, 12]. The formulation of vaccines in powder form can also improve stability, making transport and storage simple and inexpensive. Recently, the mouse biolistic system, has been used in particle impact and immunological studies [7, 13, 14]. These studies require powdered vaccine preferably to be delivered into specific epidermis of the mouse skin with a narrow and controllable velocity range and uniform spatial distribution. In this paper, Computational Fluid Dynamics (CFD) is utilized to simulate the gas and particle dynamics of a mouse biolistic system. The performance of this system is investigated in a series of numerical simulations. The main features of the starting process are presented. Predicted gas and particles characteristics within prototype system are compared with experimental data. The primary emphasis of this study is to gain new insights into the nozzle starting process and the interaction between the gas and particles. Representative results for a variant of the nozzle contour are given. Murine biolistic system Figure 1 shows a schematic of the mouse biolistic system, a variation of the Contoured Shock Tube system(CST). Key aspects of principles of operation are described by Kendall (see reference [6]). Essentially, the rupture of the diaphragms forms a primary shock wave, which propagates downstream and initiates an unsteady gas flow, as in a classical shock tube [15]. A quasi-state supersonic flow (QSSF) is subsequently established. In the course of these processes, particles are entrained in the gas flow and accelerated towards the nozzle exit. The gas is deflected, while the particles maintain a sufficient momentum to breach the stratum corneum and target the underlying cells in the viable epidermis. Figure 1: A schematic of the murine biolistics system. The system is optimized such that the bulk of the particle cloud is accelerated in the QSSF and not in the starting process. This is achieved by the choice of system geometry, gas species, operation pressure and particles. The upstream termination boundary of the particle delivery window is defined by the reflected expansion wave. Therefore an emphasis is placed upon gaining new insights in to the nozzle starting process and the gasparticle interactions. The characteristics of the steady flow generated by the prototype mouse biolistic system have been analyzed theoretically with ideal shock relations. For a nominal diaphragm burst pressure of 2070kPa, the primary shock Mach number ( Mas) is 2.343, the pressure for both Regions 2 and 3 in the shock tube is 632 kPa, and Mach numbers for Regions 2 and 3 (using standard shock tube nomenclature) are 1.133 and 0.787, respectively. The correctly expanded Mach number for helium at the nozzle exit is 2.11. The CFD Model In order to better understand the physical mechanics and help optimize the design, CFD is utilized to characterize the operation of the mouse biolistic system, illustrated in Figure 1. For the solution, Fluent, a commercial available CFD software package [3], is employed to numerically simulate the multispecies gas flow and the interaction with the particles. Discrete and numerical solutions can be obtained by solving the governing partial differential equations (PDEs) using the finite volume method to determine the real gas flow field. The convective flux is discretized by an upwinding Roe vector difference splitter, and viscous term by the central difference. Time integration has been explicitly performed. Due to the unsteady motion of the shock wave process, a coupled explicit solver is chosen. An overall second order scheme is satisfied spatially and temporally. For an efficient, time-accurate solution of the preconditioned equations, a multi-stage scheme is employed. Modelling of particle dynamics requires knowledge of the fluid flow field as well as the variation of the drag coefficient with relative Reynolds and Mach numbers. It is evident that there is great discrepancy between the correlations proposed for the particle drag coefficient. These discrepancies stem from the different ranges of Reynolds and Mach number covered, gas flows, particle sizes and density ranges and the particle concentration. Regarding to our particular application, which consists of both subsonic and supersonic unsteady flow region, the correlation of Igra and Takayama [5], covering a wider range of Reynolds number (200 to 101,000), is implemented to determine the unsteady drag coefficient. Some validation of this approach with prototypes of biolistic systems have been conducted through extensive comparison with experimental data [9, 10, 11] and computational results from the CFX calculations [4]. Results and discussion The flow fields under consideration have circular cross sections and are assumed to be axisymmetric. The emphasis is on the events after diaphragm rupture, thus the gas filling process is not simulated. The diaphragm (shown in Figure 1) initially separates high-pressure driver gas (mixture of helium and air) and driven gas (air) at atmospheric pressure. In this study, a single diaphragm is assumed for simplicity, and no attempt is made to consider the effects of non-ideal diaphragm rupture. Similarly, we have not included the effects of tissue surface deformation, studied by Kendall et al [8]. The calculation is started with the instant rupture of the diaphragm when the driver mixture gas pressure reaches the pressure of 2.07 MPa, which has been approximately determined from the experiments. Gas flow The calculated and experimental history of the static pressure in the driver chamber (23 mm upstream of the diaphragm), is shown in Figure 2. The time zero is taken as the rupture of the diaphragm. The measured pressure is rather oscillatory and the level is higher than that CFD prediction. This discrepancy is attributed to the assumption of a closed gas filling system after diaphragm rupture, and perhaps a weak area change influence caused by the ruptured diaphragm and the unsteady expansion. This phenomenon is consistent with other biolistic systems [9, 4]. Time (μs) P re ss ur e (k P a) 0.0 100.0 200.0 300.0 400.0 500.0 0 50