15th Australasian Fluid Mechanics ConferenceThe University of Sydney, Sydney, Australia13-17 December 2004

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

Y. Liu ∗, N. K. Truong and M.A.F. Kendall

The PowderJect Centre for Gene and Drug Delivery ResearchDepartment of Engineering Science, University of Oxford

Oxford OX2 6PE, United Kingdom∗Email:yi.liu@eng.ox.ac.uk

Abstract

A unique form of powdered delivery system, a biolistic system,has been developed. This novel technology is to accelerate par-ticles in micro-particle form by a gas flow behind a travellingshock wave, so that they can attain sufficient momentum to pen-etrate the skin and thus achieve a pharmacological effect. Oneof the most recent developments is a mouse biolistic system,used in immunological studies. These studies require powderedvaccine to be delivered into the epidermis of the mouse with anarrow and highly controllable velocity distribution and a uni-form spatial distribution. In this paper, Computational FluidDynamics (CFD) has been utilized to characterize the completeoperation of a prototype mouse biolistic system. The key fea-tures of the gas dynamics and gas-particle interaction are dis-cussed.

Introduction

A needle-free epidermal powdered delivery system, a biolisticsystem, has been developed at University of Oxford (Bellhouseet al, 1994, [1]). The underlying principle of the system is toaccelerate a pre-measured dose of vaccine and drugs in micro-particle form to an appropriate momentum by a high speed gasflow in order to penetrate the outer layer of the skin to achievea pharmacological effect.

The biolistic system has shown many advantages over conven-tional needle and syringe, in terms of effectiveness, cost andhealth risk. The system can deliver powdered vaccine into a de-sired layer of skin or tissue to achieve the optimal effect. Whenantigenic compounds are delivered to skin or mucosa, the biolis-tic system requires less material to elicit the equivalent immuneresponse [2, 12]. The formulation of vaccines in powder formcan also improve stability, making transport and storage simpleand inexpensive.

Recently, the mouse biolistic system, has been used in particleimpact and immunological studies [7, 13, 14]. These studies re-quire powdered vaccine preferably to be delivered into specificepidermis of the mouse skin with a narrow and controllable ve-locity range and uniform spatial distribution.

In this paper, Computational Fluid Dynamics (CFD) is utilizedto simulate the gas and particle dynamics of a mouse biolisticsystem. The performance of this system is investigated in a se-ries of numerical simulations. The main features of the startingprocess are presented. Predicted gas and particles characteris-tics within prototype system are compared with experimentaldata. The primary emphasis of this study is to gain new insightsinto the nozzle starting process and the interaction between thegas and particles. Representative results for a variant of the noz-zle contour are given.

Murine biolistic system

Figure 1 shows a schematic of the mouse biolistic system, avariation of the Contoured Shock Tube system(CST). Key as-

pects of principles of operation are described by Kendall (seereference [6]). Essentially, the rupture of the diaphragms formsa primary shock wave, which propagates downstream and initi-ates an unsteady gas flow, as in a classical shock tube [15]. Aquasi-state supersonic flow (QSSF) is subsequently established.In the course of these processes, particles are entrained in thegas flow and accelerated towards the nozzle exit. The gas is de-flected, while the particles maintain a sufficient momentum tobreach the stratum corneum and target the underlying cells inthe viable epidermis.

Figure 1: A schematic of the murine biolistics system.

The system is optimized such that the bulk of the particle cloudis accelerated in the QSSF and not in the starting process. Thisis achieved by the choice of system geometry, gas species, oper-ation pressure and particles. The upstream termination bound-ary of the particle delivery window is defined by the reflectedexpansion wave. Therefore an emphasis is placed upon gain-ing new insights in to the nozzle starting process and the gas-particle interactions.

The characteristics of the steady flow generated by the prototypemouse biolistic system have been analyzed theoretically withideal shock relations. For a nominal diaphragm burst pressureof 2070kPa, the primary shock Mach number (Mas) is 2.343,the pressure for both Regions 2 and 3 in the shock tube is 632kPa, and Mach numbers for Regions 2 and 3 (using standardshock tube nomenclature) are 1.133 and 0.787, respectively.The correctly expanded Mach number for helium at the nozzleexit is 2.11.

The CFD Model

In order to better understand the physical mechanics and helpoptimize the design, CFD is utilized to characterize the opera-tion of the mouse biolistic system, illustrated in Figure 1.

For the solution, Fluent, a commercial available CFD softwarepackage [3], is employed to numerically simulate the multi-species gas flow and the interaction with the particles. Discreteand numerical solutions can be obtained by solving the govern-ing partial differential equations (PDEs) using the finite volumemethod to determine the real gas flow field. The convective fluxis discretized by an upwinding Roe vector difference splitter,and viscous term by the central difference. Time integration hasbeen explicitly performed. Due to the unsteady motion of theshock wave process, a coupled explicit solver is chosen. Anoverall second order scheme is satisfied spatially and tempo-rally. For an efficient, time-accurate solution of the precondi-tioned equations, a multi-stage scheme is employed.

Modelling of particle dynamics requires knowledge of the fluidflow field as well as the variation of the drag coefficient withrelative Reynolds and Mach numbers. It is evident that thereis great discrepancy between the correlations proposed for theparticle drag coefficient. These discrepancies stem from the dif-ferent 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 bothsubsonic and supersonic unsteady flow region, the correlationof Igra and Takayama [5], covering a wider range of Reynoldsnumber (200 to 101,000), is implemented to determine the un-steady drag coefficient.

Some validation of this approach with prototypes of biolisticsystems have been conducted through extensive comparisonwith experimental data [9, 10, 11] and computational resultsfrom the CFX calculations [4].

Results and discussion

The flow fields under consideration have circular cross sectionsand are assumed to be axisymmetric. The emphasis is on theevents after diaphragm rupture, thus the gas filling process isnot simulated. The diaphragm (shown in Figure 1) initially sep-arates high-pressure driver gas (mixture of helium and air) anddriven gas (air) at atmospheric pressure. In this study, a singlediaphragm is assumed for simplicity, and no attempt is made toconsider 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 theinstant rupture of the diaphragm when the driver mixture gaspressure reaches the pressure of 2.07MPa, which has been ap-proximately determined from the experiments.

Gas flow

The calculated and experimental history of the static pressurein the driver chamber (23 mm upstream of the diaphragm), isshown in Figure 2. The time zero is taken as the rupture of thediaphragm. The measured pressure is rather oscillatory and thelevel is higher than that CFD prediction. This discrepancy isattributed to the assumption of a closed gas filling system afterdiaphragm rupture, and perhaps a weak area change influencecaused by the ruptured diaphragm and the unsteady expansion.This phenomenon is consistent with other biolistic systems [9,4].

Time (µs)

Pre

ssur

e(k

Pa)

0.0 100.0 200.0 300.0 400.0 500.00

500

1000

1500

2000

2500

CFD SimulationExperment.1Experment.2Experment.3

Figure 2: Calculated and measured pressure history.

In Figure 3, the simulated Pitot pressure history is comparedwith corresponding measurements from a centrally located Pitotprobe of 3mmdownstream of the nozzle exit. The CFD hasoverestimated the Pitot pressure. This is largely due to poorspatial sensitivity of the probe in the supersonic flow (the diam-eter of the Pitot probe is about 2mm, comparing with 4mmof

nozzle exit diameter), which is not considered in the simulation.

Time (µs)

Pre

ssur

e(k

Pa)

0.0 100.0 200.0 300.0 400.0 500.00

500

1000

1500

2000

CFD SimulationExperment.1Experment.2Experment.3

A B

Figure 3: Calculated and measured Pitot pressure history.

In general, however, all the simulated pressure histories in Fig-ure 2 and 3 are in good agreement with the measurements. Thetermination time of the starting process (”A” in Figure 3) is rea-sonable modelled. It demonstrates that shock, compression, ex-pansion waves, and interactions between waves and the bound-ary layer are reasonably predicted by the numerical method em-ployed.

Further investigation is obtained through examining the se-quences of the flow field. Closer examination of the formationof the secondary shock is achieved at time of 89.3µsand 107.4µsafter diaphragm rupture as shown in Figure 4.1 and 4.2. Thecontact surface between the primary shock and the secondaryshock can be identified in the lower half of flow field. The con-tours within the QSSF, identified in Figure 3 to be 152.5µs., areshown in Figure 4.3.

Particle flow

The particle trajectories are advanced simultaneously with thegenerated gas flow field. In the calculation, the particles areassumed to be initially arranged in a matrix representing all thedifferent possible positions within the vaccine particle cassette.

Figure 5 plots the calculated particle impact velocity as a func-tion of radius. Particles were assumed as sphere with a densityof 19,320kg/m3. The velocity plots clearly show that the par-ticles are achieved velocity of approximately 640m/s with areasonably uniform.

Finally, the key gas flow regimes and the particles cloud trajec-tories are shown together in the calculated space-time (x-t) dia-gram, Figure 6. The representation of the gas flow is achievedby plotting the CFD calculation, in the typical form of contoursof pressure. It can be seen that the particles have been acceler-ated to the nozzle exit, avoiding the starting process secondaryshock and the reflected expansion wave, and thereby remainingin the quasi-steady supersonic flow (QSSF).

Alternative nozzle design

The other feature of Figure 6, illustrates oblique shocks associ-ated with a weak overexpanded nozzle flow, and resulting sep-arated flow. This observation leads to a new design of the su-personic nozzle to achieve a quasi-steady correctly expandedsupersonic flow and a more uniform particle impact velocity.The results are present here.

Figure 7 shows the instantaneous velocity contours in the QSSFstate obtained with an alternative,correctly expanded nozzle de-sign. The uniformity of gas velocity distribution is further illus-trated in Figure 8.

1

3

3

5

5

7

9

11

13

15

17

17

21 25

29

31 1100.029 1040.027 980.025 920.023 860.021 800.019 740.017 680.015 620.013 560.011 500.09 440.07 380.05 320.03 260.01 200.0

Velocity (m/s)

3

5

7

7

9

9

11

13

13 17

31 8.00E+0529 7.52E+0527 7.04E+0525 6.56E+0523 6.08E+0521 5.60E+0519 5.12E+0517 4.64E+0515 4.16E+0513 3.68E+0511 3.20E+059 2.72E+057 2.24E+055 1.76E+053 1.28E+051 8.00E+04

Pressure (Pa)

(1) Time=89.3µs

1

1

3

3

5 59

13 15

23

31 1.0E+0629 9.4E+0527 8.8E+0525 8.2E+0523 7.6E+0521 7.0E+0519 6.4E+0517 5.8E+0515 5.2E+0513 4.6E+0511 4.0E+059 3.4E+057 2.8E+055 2.2E+053 1.6E+051 1.0E+05

Pressure (Pa)

1

1

3

3

5

5

7

7 99

11

11

13

13

15

15

15

17 19

19

2325

27

29

31 1150.029 1090.027 1030.025 970.023 910.021 850.019 790.017 730.015 670.013 610.011 550.09 490.07 430.05 370.03 310.01 250.0

Velocity (m/s)

(2) Time=107.4µs

1

1

1

3

3

3

3

7

11 1113

15

21

21

23

31 9.0E+0529 8.5E+0527 8.0E+0525 7.5E+0523 7.0E+0521 6.5E+0519 6.0E+0517 5.5E+0515 5.0E+0513 4.5E+0511 4.0E+059 3.5E+057 3.0E+055 2.5E+053 2.0E+051 1.5E+05

Pressure (Pa)

13 55

77

9

911

11

13

1515

17

17

19

21

21

2323

2729

29

31 1100.029 1040.027 980.025 920.023 860.021 800.019 740.017 680.015 620.013 560.011 500.09 440.07 380.05 320.03 260.01 200.0

Velocity (m/s)

(3) Time=152.5µs

Figure 4: Instantaneous contour plots of velocity and pressure.

Figure 9 plots the calculated particle trajectories. The velocityplots clearly show that the particles are accelerated to a moreuniform velocity. The improvement in impact velocity distri-bution is further illustrated by comparison with Figure 5. It isworthwhile to mention that the nozzle exit diameter has been re-duced to 3.8mm, still achieving a equivalent impact area. A sta-tistic analysis of impact velocity, shown in Figure 10, provides626m/s of a mean velocity, with 1.61m/s standard deviation.

Conclusions

A CFD model has been implemented to gain new insights intothe mouse biolistic system used to accelerate vaccines in micro-

Radius (mm)

Vel

ocity

(m/s

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00570

580

590

600

610

620

630

640

650

660

670

Φ2.7µm Gold particle

Nozzle edge

Figure 5: Calculated impact velocity of murine device.

Axial position (mm)

Tim

e(µ

s)

-60 -40 -20 0 20 40 600

50

100

150

200

250 2.00E+061.90E+061.80E+061.70E+061.60E+061.50E+061.40E+061.30E+061.20E+061.10E+061.00E+069.00E+058.00E+057.00E+056.00E+055.00E+054.00E+053.00E+052.00E+051.00E+05

Pressure (Pa)

Figure 6: Constructed x-t characteristics from simulations.

1

3

35

7

7

99

1111 13

13

15

17

17

19 19

2123

25

25

27

27

29

31

31 1100.029 1040.027 980.025 920.023 860.021 800.019 740.017 680.015 620.013 560.011 500.09 440.07 380.05 320.03 260.01 200.0

Velocity (m/s)

Figure 7: The Contour plot of velocity.

Radius (mm)

Vel

ocity

(m/s

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.000

200

400

600

800

1000

1200

137.14 µs154.75 µs172.76 µs191.73 µs233.00 µs

Time after diaphragm rupture

Figure 8: Velocity profiles along radius.

particle form to impart the skin. Fluent is utilized to simulatethe unsteady gas flow and the interaction with the particles by acoupled explicit solver.

Radius (mm)

Vel

ocity

(m/s

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00570

580

590

600

610

620

630

640

650

660

670

Φ2.7µm Gold particle

Nozzle edge

Figure 9: The impact velocity of new design murine device.

Impact velocity (m/s)

629.50

628.50

627.50

626.50

625.50

624.50

623.50

622.50

621.50

620.50

Particle impact velocity statistic analysis

Par

ticle

num

bers

50

40

30

20

10

0

Std. Dev = 1.61

Mean = 625.57

N = 160.00

Figure 10: The statistic analysis of new design murine device.

Simulated pressure histories agree well with the correspondingstatic and Pitot pressure measurements. These calculations havebeen used to further explore the gas flow field, with an emphasison the nozzle starting process. The quasi-steady supersonic flowwindow has been accordingly determined. The action of thegas flow in accelerating the particles was calculated within themodelled flow field. The main features of the gas dynamics andgas-particle interaction are presented.

The preliminary results demonstrate the overall capability of anew designed supersonic nozzle to deliver the particles to theskin targets with a more uniform velocity and spatial distribu-tion.

Acknowledgements

The authors wish to thank professor B. J. Bellhouse, Powder-ject Centre for Gene and Drug Delivery Research, Universityof Oxford, for his encouragement of this work. This work wassupported by PowderJect plc. and Chiron Vaccines. Their sup-port is gratefully acknowledge.

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