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Templated Open Flocs of Nanorods for Enhanced Pulmonary Delivery with Pressurized Metered Dose Inhalers

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Abstract

Purpose

A novel concept is presented for the formation of stable suspensions composed of low density flocs of high aspect ratio drug particles in hydrofluoroalkane (HFA) propellants, and for subdividing (templating) the flocs with aerosolized HFA droplets to achieve high fine particle fractions with a pressurized metered dose inhaler.

Methods

Bovine serum albumin (BSA) nanorods, produced by thin film freezing (TFF), were added to HFA to form a suspension. Particle properties were analyzed with an Anderson cascade impactor (ACI), static and dynamic light scattering and optical microscopy.

Results

The space filling flocs in HFA were stable against settling for one year. The pMDI produced high fine particle fractions (38–47%) with an emitted dose of 0.7 mg/actuation. The atomized HFA droplets break apart, that is template, the highly open flocs. Upon evaporation of HFA, capillary forces shrink the templated flocs to produce porous particles with optimal aerodynamic diameters for deep lung delivery.

Conclusions

Open flocs composed of nanorods, stable against settling, may be templated during actuation with a pMDI to produce optimal aerodynamic diameters and high fine particle fractions. This concept is applicable to a wide variety of drugs without the need for surfactants or cosolvents to stabilize the primary particles.

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References

  1. R. U. Agu, M. I. Ugwoke, M. Armand, R. Kinget, and N. Verbeke. The lung as a route for systemic delivery of therapeutic proteins and peptides. Respir. Res. 2:198–209 (2001) doi:10.1186/rr58.

    Article  PubMed  CAS  Google Scholar 

  2. A. L. Adjei, and P. K. Gupta. Inhalation delivery of therapeutic peptides and proteins. Int. J. Pharm. 159:259 (1997).

    Article  Google Scholar 

  3. S. White, D. B. Bennett, S. Cheu, P. W. Conley, D. B. Guzek, S. Gray, J. Howard, R. Malcolmson, J. M. Parker, P. Roberts, N. Sadrzadeh, J. D. Schumacher, S. Seshadri, G. W. Sluggett, C. L. Stevenson, and N. J. Harper. EXUBERA: pharmaceutical development of a novel product for pulmonary delivery of insulin. Diabetes Technol. Ther. 7:896–906 (2005) doi:10.1089/dia.2005.7.896.

    Article  PubMed  CAS  Google Scholar 

  4. S. A. Shoyele, and A. Slowey. Prospects of formulating proteins/peptides as aerosols for pulmonary drug delivery. Int. J. Pharm. 314:1–8 (2006) doi:10.1016/j.ijpharm.2006.02.014.

    Article  PubMed  CAS  Google Scholar 

  5. H. M. Courrier, N. Butz, and T. F. Vandamme. Pulmonary drug delivery systems: recent developments and prospects. Crit. Rev. Ther. Drug Carr. Syst. 19:425–498 (2002) doi:10.1615/CritRevTherDrugCarrierSyst.v19.i45.40.

    Article  CAS  Google Scholar 

  6. M. J. Kwon, J. H. Bae, J. J. Kim, K. Na, and E. S. Lee. Long acting porous microparticle for pulmonary protein delivery. Int. J. Pharm. 333:5–9 (2007) doi:10.1016/j.ijpharm.2007.01.016.

    Article  PubMed  CAS  Google Scholar 

  7. J. S. Patton, and P. R. Byron. Inhaling medicines: delivering drugs to the body through the lungs. Nature Reviews Drug Discovery. 6:67–74 (2007) doi:10.1038/nrd2153.

    Article  PubMed  CAS  Google Scholar 

  8. V. Codrons, F. Vanderbist, R. K. Verbeeck, M. Arras, D. Lison, V. Preat, and R. Vanbever. Systemic delivery of parathyroid hormone (1–34) using inhalation dry powders in rats. J. Pharm. Sci. 92:938–950 (2003) doi:10.1002/jps.10346.

    Article  PubMed  CAS  Google Scholar 

  9. L. Garcia-Contreras, and H. D. C. Smyth. Liquid-spray or dry-powder systems for inhaled delivery of peptide and proteins? American Journal of Drug Delivery. 3:29–45 (2005) doi:10.2165/00137696-200503010-00004.

    Article  CAS  Google Scholar 

  10. D. Traini, P. Young, P. Rogueda, and R. Price. The use of AFM and surface energy measurements to investigate drug–canister material interactions in a model pressurized metered dose inhaler formulation. Aerosol Sci. Tech. 40:227–236 (2006) doi:10.1080/02786820500543316.

    Article  CAS  Google Scholar 

  11. P. Rogueda. Novel hydrofluoroalkane suspension formulations for respiratory drug delivery. Expert Opinion on Drug Delivery. 2:625–638 (2005) doi:10.1517/17425247.2.4.625.

    Article  PubMed  CAS  Google Scholar 

  12. R. O. Williams III, and J. Liu. Formulation of a protein with propellant HFA 134a for aerosol delivery. Eur. J. Pharm. Sci. 7:137–144 (1999) doi:10.1016/S0928-0987(98)00015-3.

    Article  PubMed  CAS  Google Scholar 

  13. R. O. Williams III, M. Repka, and J. Liu. Influence of propellant composition on drug delivery from a pressurized metered-dose inhaler. Drug Dev. Ind. Pharm. 24:763–770 (1998) doi:10.3109/03639049809082724.

    Article  PubMed  CAS  Google Scholar 

  14. K. A. Johnson. Interfacial phenomena and phase behavior in metered dose inhaler formulations. In A. J. Hickey (ed.), Inhalation Aerosols: Physical and Biological Basis for Therapy, Vol. 221. Lung Biology in Health and Disease, 2007.

  15. E. A. Quinn, R. T. Forbes, A. C. Williams, M. J. Oliver, L. McKenzie, and T. S. Purewal. Protein conformational stability in the hydrofluoroalkane propellants tetrafluoroethane and heptafluoropropane analyzed by Fourier transform Raman spectroscopy. Int. J. Pharm. 186:31–41 (1999) doi:10.1016/S0378-5173(99)00135-0.

    Article  PubMed  CAS  Google Scholar 

  16. M. J. Oliver, L. McKenzie, W. D. Graffiths, G. R. Morgan, and N. O’Kelly. Initial assessment of a protein formulated in pressurized MDIS for pulmonary delivery. In RDD VII, 2000.

  17. C. Benfait. Kos reports achievement of new research and development milestones. Kos Press Release (2004).

  18. J. Heyder, J. Gebhart, G. Rudolf, C. F. Schiller, and W. Stahlhofen. Deposition of particles in the human respiratory tract in the size range 0.005–15 µm. J. Aerosol Sci. 17:811–825 (1986) doi:10.1016/0021-8502(86)90035-2.

    Article  Google Scholar 

  19. A. Ben-Jebria, D. Chen, M. L. Eskew, R. Vanbever, R. Langer, and D. A. Edwards. Large porous particles for sustained protection from carbachol-induced bronchoconstriction in guinea pigs. Pharm. Res. 16:555–561 (1999) doi:10.1023/A:1018879331061.

    Article  PubMed  CAS  Google Scholar 

  20. N. Tsapis, D. Bennett, B. Jackson, D. A. Weitz, and D. A. Edwards. Trojan particles: large porous carriers of nanoparticles for drug delivery. Proc. Natl. Acad. Sci. U. S. A. 99:12001–12005 (2002) doi:10.1073/pnas.182233999.

    Article  PubMed  CAS  Google Scholar 

  21. L. A. Dellamary, T. E. Tarara, D. J. Smith, C. H. Woelk, A. Adractas, M. L. Costello, H. Gill, and J. G. Weers. Hollow porous particles in metered dose inhalers. Pharm. Res. 17:168–174 (2000) doi:10.1023/A:1007513213292.

    Article  PubMed  CAS  Google Scholar 

  22. Y.-F. Maa, P.-A. Nguyen, T. Sweeney, S. J. Shire, and C. C. Hsu. Protein inhalation powders: spray drying vs spray freeze drying. Pharm. Res. 16:249–254 (1999) doi:10.1023/A:1018828425184.

    Article  PubMed  CAS  Google Scholar 

  23. Y.-F. Maa, and H. R. Costantino. Spray freeze-drying of biopharmaceuticals: applications and stability considerations. In H. R. Costantino, and M. J. Pikal (eds.), Biotechnology: Pharmaceutical Aspects. 2. Lyophilization of Biopharmaceuticals, Vol. 2, American Association of Pharmaceutical Scientists, Arlington, 2004, pp. 519–561.

    Google Scholar 

  24. Z. Yu, A. S. Garcia, K. P. Johnston, and R. O. Williams III. Spray freezing into liquid nitrogen for highly stable protein nanostructured microparticles. Eur. J. Pharm. Biopharm. 58:529–537 (2004) doi:10.1016/j.ejpb.2004.04.018.

    Article  PubMed  CAS  Google Scholar 

  25. J. D. Engstrom, D. T. Simpson, E. Lai, R. O. Williams III, and K. P. Johnston. Morphology of protein particles produced by spray freezing of concentrated solutions. Eur. J. Pharm. Biopharm. 65:149–162 (2007) doi:10.1016/j.ejpb.2006.08.005.

    Article  PubMed  CAS  Google Scholar 

  26. J. D. Engstrom, D. T. Simpson, C. Cloonan, E. Lai, R. O. Williams III, G. B. Kitto, and K. P. Johnston. Stable high surface area lactate dehydrogenase particles produced by spray freezing into liquid nitrogen. Eur. J. Pharm. Biopharm. 65:163–174 (2007) doi:10.1016/j.ejpb.2006.08.002.

    Article  PubMed  CAS  Google Scholar 

  27. Z. Yu, K. P. Johnston, and R. O. Williams III. Spray freezing into liquid versus spray-freeze drying: Influence of atomization on protein aggregation and biological activity. Eur. J. Pharm. Sci. 27:9–18 (2006) doi:10.1016/j.ejps.2005.08.010.

    Article  PubMed  CAS  Google Scholar 

  28. Z. Yu, T. L. Rogers, J. Hu, K. P. Johnston, and R. O. Williams III. Preparation and characterization of microparticles containing peptide produced by a novel process: spray freezing into liquid. Eur. J. Pharm. Biopharm. 54:221–228 (2002) doi:10.1016/S0939-6411(02)00050-4.

    Article  PubMed  CAS  Google Scholar 

  29. J. D. Engstrom, E. S. Lai, B. Ludher, B. Chen, T. E. Milner, G. B. Kitto, R. O. Williams III, and K. P. Johnston. Formation of stable submicron protein particles by thin film freezing. Pharm. Res. 25:1334–1346 (2008) doi:10.1007/s11095-008-9540-4.

    Article  PubMed  CAS  Google Scholar 

  30. S. D. Webb, S. L. Golledge, J. L. Cleland, J. F. Carpenter, and T. W. Randolph. Surface adsorption of recombinant human interferon-γ in lyophilized and spray-lyophilized formulations. J. Pharm. Sci. 91:1474–1487 (2002) doi:10.1002/jps.10135.

    Article  PubMed  CAS  Google Scholar 

  31. X. C. Nguyen, J. D. Herberger, and P. A. Burke. Protein powders for encapsulation: a comparison of spray-freeze drying and spray drying of darbepoetin alfa. Pharm. Res. 21:507–514 (2004) doi:10.1023/B:PHAM.0000019306.89420.f0.

    Article  PubMed  CAS  Google Scholar 

  32. Y.-F. Maa, and S. J. Prestrelski. Biopharmaceutical powders: particle formation and formulation considerations. Curr. Pharm. Biotechnol. 1:283–302 (2000) doi:10.2174/1389201003378898.

    Article  PubMed  CAS  Google Scholar 

  33. I. Gonda. Development of a systematic theory of suspension inhalation aerosols. I. A framework to study the effects of aggregation on the aerodynamic behavior of drug particles. Int. J. Pharm. 27:99–116 (1985) doi:10.1016/0378–5173(85)90189-9.

    Article  CAS  Google Scholar 

  34. Y.-H. Liao, M. B. Brown, S. A. Jones, T. Nazir, and G. P. Martin. The effects of polyvinyl alcohol on the in vitro stability and delivery of spray-dried protein particles from surfactant-free HFA 134a-based pressurised metered dose inhalers. Int. J. Pharm. 304:29–39 (2005) doi:10.1016/j.ijpharm.2005.07.013.

    Article  PubMed  CAS  Google Scholar 

  35. M. Keller. Innovations and perspectives of metered dose inhalers in pulmonary drug delivery. Int. J. Pharm. 186:81–90 (1999) doi:10.1016/S0378-5173(99)00132-5.

    Article  PubMed  CAS  Google Scholar 

  36. C. Vervaet, and P. R. Byron. Drug-surfactant-propellant interactions in HFA-formulations. Int. J. Pharm. 186:13–30 (1999) doi:10.1016/S0378-5173(99)00134-9.

    Article  PubMed  CAS  Google Scholar 

  37. F. E. Blondino, and P. R. Byron. Surfactant dissolution and water solubilization in chlorine-free liquified gas propellants. Drug Dev. Ind. Pharm. 24:935–945 (1998) doi:10.3109/03639049809097273.

    Article  PubMed  CAS  Google Scholar 

  38. R. P. S. Peguin, P. Selvam, and S. R. P. da Rocha. Microscopic and thermodynamic properties of the HFA134a-water interface: atomistic computer simulations and tensiometry under pressure. Langmuir. 22:8826–8830 (2006) doi:10.1021/la0608157.

    Article  PubMed  CAS  Google Scholar 

  39. L. Wu, R. P. S. Peguin, P. Selvam, U. Chokshi, and S. R. P. da Rocha. Molecular scale behavior in alternative propellant-based inhaler formulations. In A. J. Hickey (ed), Inhalation Aerosols: Physical and biological basis for therapy, Vol. 221. Lung Biology in Health and Disease, 2007.

  40. R. Vanbever, J. D. Mintzes, J. Wang, J. Nice, D. Chen, R. Batycky, R. Langer, and D. A. Edwards. Formulation and physical characterization of large porous particles for inhalation. Pharm. Res. 16:1735–1742 (1999) doi:10.1023/A:1018910200420.

    Article  PubMed  CAS  Google Scholar 

  41. D. A. Edwards, J. Hanes, G. Caponetti, J. Hrkach, A. Ben-Jebria, M. L. Eskew, J. Mintzes, D. Deaver, N. Lotan, and R. Langer. Large porous particles for pulmonary drug delivery. Science. 276:1868–1871 (1997) doi:10.1126/science.276.5320.1868.

    Article  PubMed  CAS  Google Scholar 

  42. J. Tam, J. T. McConville, R. O. Williams III, and K. P. Johnston. Amorphous cyclosporin A nanodispersions for enhanced pulmonary deposition and dissolution. J. Pharm. Sci. in press (2008) doi:10.1002/jps.21367.

  43. Z. Jiang, and Y. Guan. Flocculation morphology: effect of particulate shape and coagulant species on flocculation. Water Sci. Technol. 53:9–16 (2006) doi:10.2166/wst.2006.339.

    CAS  Google Scholar 

  44. I. Goodarz-Nia, and D. N. Sutherland. Floc simulation. Effects of particle size and shape. Chem. Eng. Sci. 30:407–12 (1975) doi:10.1016/0009-2509(75)85005-6.

    Article  CAS  Google Scholar 

  45. P. C. Hiemenz and R. Rajagopalan. Principles of colloid and surface chemistry, Marcel Dekker, New York, 1997.

  46. A. P. Philipse, and A. M. Wierenga. On the density and structure formation in gels and clusters of colloidal rods and fibers. Langmuir. 14:49–54 (1998) doi:10.1021/la9703757.

    Article  CAS  Google Scholar 

  47. A. P. Philipse. The random contact equation and its implications for (colloidal) rods in packings, suspensions, and anisotropic powders. Langmuir. 12:5971 (1996) doi:10.1021/la960869o.

    Article  CAS  Google Scholar 

  48. R. G. Larson. The structure and rheology of complex fluids. Oxford University Press, New York, 1999.

    Google Scholar 

  49. P. G. Smith Jr., W. Ryoo, and K. P. Johnston. Electrostatically stabilized metal oxide particle dispersions in carbon dioxide. J. Phys. Chem. B. 109:20155–20165 (2005) doi:10.1021/jp0532521.

    Article  PubMed  CAS  Google Scholar 

  50. Y. Kim, S. H. Atwell, and R. G. Bell. Determination of water in pressurized pharmaceutical metered dose aerosol products. Drug Dev. Ind. Pharm. 18:2185–2195 (1992) doi:10.3109/03639049209038756.

    Article  CAS  Google Scholar 

  51. R. O. Williams III, J. Liu, and J. J. Koleng. Influence of metering chamber volume and water level on the emitted dose of a suspension-based pMDI containing propellant 134a. Pharm. Res. 14:438–443 (1997) doi:10.1023/A:1012087130114.

    Article  PubMed  CAS  Google Scholar 

  52. E. Berlin, and M. J. Pallansch. Densities of several proteins and L-amino acids in the dry state. J. Phys. Chem. 72:1887–1889 (1968) doi:10.1021/j100852a004.

    Article  PubMed  CAS  Google Scholar 

  53. P. G. A. Rogueda. HPFP, a model propellant for pMDIs. Drug Dev. Ind. Pharm. 29:39–49 (2003) doi:10.1081/DDC-120016682.

    Article  PubMed  CAS  Google Scholar 

  54. R. Ashayer, P. F. Luckham, S. Manimaaran, and P. Rogueda. Investigation of the molecular interactions in a pMDI formulation by atomic force microscopy. Eur. J. Pharm. Sci. 21:533–543 (2004) doi:10.1016/j.ejps.2003.12.003.

    Article  PubMed  CAS  Google Scholar 

  55. D. Traini, M. Young Paul, P. Rogueda, and R. Price. In vitro investigation of drug particulates interactions and aerosol performance of pressurised metered dose inhalers. Pharm. Res. 24:125–135 (2007) doi:10.1007/s11095-006-9130-2.

    Article  PubMed  CAS  Google Scholar 

  56. S. L. Nail, S. Jiang, S. Chongprasert, and S. A. Knopp. Fundamentals of freeze-drying. In S. L. Nailand, and M. J. Akers (eds.), Pharmaceutical Biotechnology. 14. Development and Manufacture of Protein Pharmaceuticals, Vol. 14, Kluwer, New York, 2002, pp. 281–360.

    Google Scholar 

  57. S. D. Webb, J. L. Cleland, J. F. Carpenter, and T. W. Randolph. A new mechanism for decreasing aggregation of recombinant human interferon-g by a surfactant: slowed dissolution of lyophilized formulations in a solution containing 0.03% polysorbate 20. J. Pharm. Sci. 91:543–558 (2002) doi:10.1002/jps.10033.

    Article  PubMed  CAS  Google Scholar 

  58. J. F. Carpenter, B. S. Chang, W. Garzon-Rodriguez, and T. W. Randolph. Rational design of stable lyophilized protein formulations: theory and practice. In J. F. Carpenter, and M. C. Manning (eds.), Pharmaceutical Biotechnology. 13. Rational Design of Stable Protein Formulations, Vol. 13, Kluwer, New York, 2002, pp. 109–133.

    Google Scholar 

  59. A. Farahnaky, F. Badii, I. A. Farhat, J. R. Mitchell, and S. E. Hill. Enthalpy relaxation of bovine serum albumin and implications for its storage in the glassy state. Biopolymers. 78:69–77 (2005) doi:10.1002/bip.20265.

    Article  PubMed  CAS  Google Scholar 

  60. B. Y. Shekunov, P. Chattopadhyay, H. H. Y. Tong, and A. H. L. Chow. Particle size analysis in pharmaceutics: principles, methods and applications. Pharm. Res. 24:203–227 (2007) doi:10.1007/s11095-006-9146-7.

    Article  PubMed  CAS  Google Scholar 

  61. W. H. Finlay. The mechanics of inhaled pharmaceutical aerosols, Academic,New York, 2001.

  62. A. Sihvola. Electromagnetic mixing formulas and applications, Institute of Electrical Engineers, London, 1999.

  63. W. B. Russel, D. A. Saville, and W. R. Schowalter. Colloidal dispersions, Cambridge University Press, Cambridge, 1989.

  64. D. Traini, P. Rogueda, P. Young, and R. Price. Surface Energy and Interparticle Forces Correlations in Model pMDI Formulations. Pharm. Res. 22:816–825 (2005) doi:10.1007/s11095-005-2599-2.

    Article  PubMed  CAS  Google Scholar 

  65. M. A. Bevan. Effect of adsorbed polymer on the interparticle potential, chemical engineering. Carnegie Mellon University, Pittsburgh, 1999.

    Google Scholar 

  66. P. Tang, J. Greenwood, and J. A. Raper. A model to describe the settling behavior of fractal aggregates. J. Colloid Interface Sci. 247:210–219 (2002) doi:10.1006/jcis.2001.8028.

    Article  PubMed  CAS  Google Scholar 

  67. C. Fargues, and C. Turchiuli. Structural characterization of flocs in relation to their settling performances. Chem. Eng. Res. Des. 82:1517 (2004) doi:10.1205/cerd.82.11.1517.52026.

    Article  CAS  Google Scholar 

  68. H. Abramowitz, P. S. Shah, P. F. Green, and K. P. Johnston. Welding colloidal crystals with carbon dioxide. Macromolecules. 37:7316–7324 (2004) doi:10.1021/ma048961b.

    Article  CAS  Google Scholar 

  69. D. R. Ulrich. Chemical processing of ceramics. Chem. Eng. News. 68:28–40 (1990).

    CAS  Google Scholar 

  70. H. D. C. Smyth, A. J. Hickey, and R. M. Evans. Aerosol generation from propellant-driven metered dose inhalers. In J. Hickey Anthony (ed), Inhalation Aerosols: Physical and Biological Basis for Therapy, Vol. 221, Lung biology in health and disease, 2007, pp. 399–416.

  71. D. L. French, D. A. Edwards, and R. W. Niven. The influence of formulation on emission, deaggregation and deposition of dry powders for inhalation. J. Aerosol Sci. 27:769–783 (1996) doi:10.1016/0021-8502(96)00021-3.

    Article  CAS  Google Scholar 

  72. T. L. Rogers, A. C. Nelsen, J. Hu, J. N. Brown, M. Sarkari, T. J. Young, K. P. Johnston, and R. O. Williams III. A novel particle engineering technology to enhance dissolution of poorly water soluble drugs: spray-freezing into liquid. Eur. J. Pharm. Biopharm. 54:271–280 (2002) doi:10.1016/S0939-6411(02)00063-2.

    Article  PubMed  CAS  Google Scholar 

  73. T. L. Rogers, K. A. Overhoff, P. Shah, P. Santiago, M. J. Yacaman, K. P. Johnston, and R. O. Williams III. Micronized powders of a poorly water soluble drug produced by a spray-freezing into liquid-emulsion process. Eur. J. Pharm. Biopharm. 55:161–72 (2003) doi:10.1016/S0939-6411(02)00193-5.

    Article  PubMed  CAS  Google Scholar 

  74. J. Israelachvili. Intermolecular and surface forces. Academic, San Diego, 1992.

    Google Scholar 

  75. S. Takashima. Proton fluctuation in protein. Experimental study of the Kirkwood–Shumaker theory. J. Phys. Chem. 69:2281–2286 (1965) doi:10.1021/j100891a023.

    Article  CAS  Google Scholar 

  76. R. Tadmor. The London–van der Waals interaction energy between objects of various geometries. J. Phys. Condens. Matter. 13:L195–L202 (2001) doi:10.1088/0953-8984/13/9/101.

    Article  CAS  Google Scholar 

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Acknowledgements

This material is supported in part by the STC Program of the National Science Foundation under Agreement No. CHE987664, the Robert A. Welch Foundation, and the Process Science and Technology Center at the University of Texas. The authors also wish to thank TSI for access to the APS 3321.

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Correspondence to Keith P. Johnston.

Appendix

Appendix

Bruggeman mixing rule

For porous particles or suspensions with a BSA particle volume fraction ϕ, the effective refractive index n e and dielectric constant ɛ e can be calculated from the following Bruggeman mixing relationships

$$\left( {1 - \phi } \right)\frac{{n_{\text{A}} ^2 - n_{\text{e}} ^2 }}{{n_{\text{A}} ^2 + 2n_{\text{e}} ^2 }} + \phi \frac{{n_{\text{B}} ^2 - n_{\text{e}} ^2 }}{{n_{\text{B}} ^2 + 2n_{\text{e}} ^2 }} = 0$$
(9)
$$\left( {1 - \phi } \right)\frac{{\varepsilon _{\text{A}} - \varepsilon _{\text{e}} }}{{\varepsilon _{\text{A}} + 2\varepsilon _{\text{e}} }} + \phi \frac{{\varepsilon _{\text{B}} - \varepsilon _{\text{e}} }}{{\varepsilon _{\text{B}} + 2\varepsilon _{\text{e}} }} = 0$$
(10)

where ϕ can be either ϕ g or ϕ f, the subscript A denotes air or HFA 227, and B denotes BSA.

Attractive van der Waals equations

The Φ vdw is directly proportional to the Hamaker constant A 121 for one particle interacting with another (subscript 1) across solvent, such as HFA 227 or acetonitrile, (subscript 2) as a function of the particle geometry (74). The Hamaker constant A 121 may be approximated by

$$A_{121} = \left( {\sqrt {A_{11} } - \sqrt {A_{22} } } \right)^2 $$
(11)

where A 11 and A 22 are the pure Hamaker constants for BSA and the suspending media interacting across a vacuum, respectively. These values were calculated from Lifshitz theory (74,75). To determine A 11 for porous BSA particles in HFA 227, ɛ e and n e were calculated with the Bruggeman mixing rule (Eqs. 9 and 10) at ϕ = 0.5 in HFA 227 (40,62). The van der Waals attractive potential between identical spherical particles (74)

$$\Phi _{{\text{vdw}}} {\text{ = }} - \frac{{A_{121} R}}{{12h}}$$
(12)

which has an attractive force F vdw given as

$$F_{{\text{vdw}}} = \frac{{A_{121} R}}{{12h^2 }}$$
(13)

where R is the spherical particle radius and h is the separation distance between the particle surfaces and for identical hollow spheres with solid shells (76)

$$\Phi _{{\text{vdw}}} = - \frac{{A_{121} R}}{{12}}\left( {\frac{1}{{h + 2t}} - \frac{2}{{h + t}} + \frac{1}{h}} \right) - \frac{{A_{121} }}{6}\ln \left( {\frac{{h(h + 2t)}}{{(h + t)^2 }}} \right)$$
(14)

where t is the shell thickness. For identical rods, E vdw can be calculated for parallel

$$\Phi _{{\text{vdw}}} = - \frac{{A_{121} LR^{1/2} }}{{24h^{3/2} }}$$
(15)

or crossed cylinders

$$\Phi _{{\text{vdw}}} = - \frac{{A_{121} R}}{{6h}}$$
(16)

where L is the cylinder length. The values from Eq. 15 and 16 were averaged to give equal weight to the two orientations (Table III).

Space filling floc derivation

A vial filled with protein particles of total mass m and primary particle density ρ p into a given volume V of HFA 227 has a volume fraction ϕ v defined as

$$\phi _{\text{v}} = \frac{{{m \mathord{\left/{\vphantom {m {\rho _{\text{p}} }}} \right.\kern-\nulldelimiterspace} {\rho _{\text{p}} }}}}{V}$$
(17)

The volume fraction of particles in a floc ϕ f is

$$\phi _{\text{f}} = \frac{{V_{\text{p}} \cdot k}}{{V_{\text{f}} }}$$
(18)

where V p and V f are the volume of a spherical primary particle and a spherical floc, respectively, and k is the number of primary particles in a floc.

The volume fraction of flocs in HFA ϕ flocs is defined as

$$\phi ^{{\text{flocs}}} = \frac{{V_{\text{f}} \cdot N_{\text{f}} }}{V}$$
(19)

where N f is the total number of flocs in suspension. N f = N p /k where N p  = m/m p is the total number of primary particles in suspension and m p = V p·ρ p is the mass of a primary particle. Substitution into Eq. 19 gives

$$\phi ^{{\text{flocs}}} = \frac{{V_{\text{f}} \cdot m}}{{V_{\text{p}} \cdot k \cdot V \cdot \rho _{\text{p}} }} = \frac{{\phi _{\text{v}} }}{{\phi _{\text{f}} }}$$
(20)

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Engstrom, J.D., Tam, J.M., Miller, M.A. et al. Templated Open Flocs of Nanorods for Enhanced Pulmonary Delivery with Pressurized Metered Dose Inhalers. Pharm Res 26, 101–117 (2009). https://doi.org/10.1007/s11095-008-9707-z

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  • DOI: https://doi.org/10.1007/s11095-008-9707-z

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