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Journal of Drug Delivery
Volume 2013, Article ID 172529, 13 pages
http://dx.doi.org/10.1155/2013/172529
Research Article

A Mathematical Model for Thermosensitive Liposomal Delivery of Doxorubicin to Solid Tumour

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

Received 9 October 2012; Accepted 13 December 2012

Academic Editor: Andreas G. Tzakos

Copyright © 2013 Wenbo Zhan and Xiao Yun Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Goodman, A. Gilman, L. Brunton, J. Lazo, and K. Parker, Goodman & Gilman's the Pharmacological Basis of Therapeutics, McGraw-Hill, New York, 2005.
  2. E. Saltiel and W. McGuire, “Doxorubicin (Adriamycin) cardiomyopathy. A critical review,” Western Journal of Medicine, vol. 139, no. 3, pp. 332–341, 1983. View at Google Scholar · View at Scopus
  3. P. K. Singal and N. Iliskovic, “Doxorubicin-induced cardiomyopathy,” The New England Journal of Medicine, vol. 339, no. 13, pp. 900–905, 1998. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Storm, Q. G. C. M. van Hoesel, G. de Groot, W. Kop, P. A. Steerenberg, and F. C. Hillen, “A comparative study of the antitumor effect, cardiotoxicity and nephrotoxicity of doxorubicin given as a bolus, continuous infusion or entrapped in liposomes in the Lou/M Wsl rat,” Cancer Chemotherapy and Pharmacology, vol. 24, no. 6, pp. 341–348, 1989. View at Google Scholar · View at Scopus
  5. M. H. Gaber, N. Z. Wu, K. Hong, S. K. Huang, M. W. Dewhirst, and D. Papahadjopoulos, “Thermosensitive liposomes: extravasation and release of contents in tumor microvascular networks,” International Journal of Radiation Oncology Biology Physics, vol. 36, no. 5, pp. 1177–1187, 1996. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Zou, M. Yamagishi, I. Horikoshi, M. Ueno, X. Gu, and R. Perez-Soler, “Enhanced therapeutic effect against liver W256 carcinosarcoma with temperature-sensitive liposomal Adriamycin administered into the hepatic artery,” Cancer Research, vol. 53, no. 13, pp. 3046–3051, 1993. View at Google Scholar · View at Scopus
  7. N. Z. Wu, R. D. Braun, M. H. Gaber et al., “Simultaneous measurement of liposome extravasation and content release in tumors,” Microcirculation, vol. 4, no. 1, pp. 83–101, 1997. View at Google Scholar · View at Scopus
  8. T. P. Chelvi, S. K. Jain, and R. Ralhan, “Hyperthermia-mediated targeted delivery of thermosensitive liposome-encapsulated melphalan in murine tumors,” Oncology Research, vol. 7, no. 7-8, pp. 393–398, 1995. View at Google Scholar · View at Scopus
  9. H. Harashima, M. Tsuchihashi, S. Iida, H. Doi, and H. Kiwada, “Pharmacokinetic/pharmacodynamic modeling of antitumor agents encapsulated into liposomes,” Advanced Drug Delivery Reviews, vol. 40, no. 1-2, pp. 39–61, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Harashima, S. Iida, Y. Urakami, M. Tsuchihashi, and H. Kiwada, “Optimization of antitumor effect of liposomally encapsulated doxorubicin based on simulations by pharmacokinetic/pharmacodynamic modeling,” Journal of Controlled Release, vol. 61, no. 1-2, pp. 93–106, 1999. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Tsuchihashi, H. Harashima, and H. Kiwada, “Development of a pharmacokinetic/pharmacodynamic (PK/PD)-simulation system for doxorubicin in long circulating liposomes in mice using peritoneal P388,” Journal of Controlled Release, vol. 61, no. 1-2, pp. 9–19, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. A. W. El-Kareh and T. W. Secomb, “A mathematical model for comparison of bolus injection, continuous infusion, and liposomal delivery of doxorubicin to tumor cells,” Neoplasia, vol. 2, no. 4, pp. 325–338, 2000. View at Google Scholar · View at Scopus
  13. R. F. Greene, J. M. Collins, and J. F. Jenkins, “Plasma pharmacokinetics of adriamycin and adriamycinol: implications for the design of in vitro experiments and treatment protocols,” Cancer Research, vol. 43, no. 7, pp. 3417–3421, 1983. View at Google Scholar · View at Scopus
  14. P. Rubin and G. Casarett, “Microcirculation of tumors part I: anatomy, function, and necrosis,” Clinical Radiology, vol. 17, no. 3, pp. 220–229, 1966. View at Google Scholar · View at Scopus
  15. L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection,” Microvascular Research, vol. 37, no. 1, pp. 77–104, 1989. View at Google Scholar · View at Scopus
  16. L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors II. Role of heterogeneous perfusion and lymphatics,” Microvascular Research, vol. 40, no. 2, pp. 246–263, 1990. View at Publisher · View at Google Scholar · View at Scopus
  17. L. T. Baxter and R. K. Jain, “Transport of fluid and macromolecules in tumors. III. Role of binding and metabolism,” Microvascular Research, vol. 41, no. 1, pp. 5–23, 1991. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. M. F. Goh, H. L. Kong, and C. H. Wang, “Simulation of the delivery of doxorubicin to hepatoma,” Pharmaceutical Research, vol. 18, no. 6, pp. 761–770, 2001. View at Publisher · View at Google Scholar · View at Scopus
  19. J. R. Less, T. C. Skalak, E. M. Sevick, and R. K. Jain, “Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions,” Cancer Research, vol. 51, no. 1, pp. 265–273, 1991. View at Google Scholar · View at Scopus
  20. F. Yuan, M. Dellian, D. Fukumura et al., “Vascular permeability in a human tumor xenograft: molecular size dependence and cutoff size,” Cancer Research, vol. 55, no. 17, pp. 3752–3756, 1995. View at Google Scholar · View at Scopus
  21. W. M. Deen, “Hindered transport of large molecules in liquid-filled pores,” AIChE Journal, vol. 33, no. 9, pp. 1409–1425, 1987. View at Google Scholar · View at Scopus
  22. S. Eikenberry, “A tumor cord model for Doxorubicin delivery and dose optimization in solid tumors,” Theoretical Biology and Medical Modelling, vol. 6, no. 1, article 16, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. F. Yuan, M. Leunig, Shi Kun Huang, D. A. Berk, D. Papahadjopoulos, and R. K. Jain, “Microvascular permeability and interstitial penetration of sterically stabilized (stealth) liposomes in a human tumor xenograft,” Cancer Research, vol. 54, no. 13, pp. 3352–3356, 1994. View at Google Scholar · View at Scopus
  24. N. Z. Wu, D. Da, T. L. Rudoll, D. Needham, A. R. Whorton, and M. W. Dewhirst, “Increased microvascular permeability contributes to preferential accumulation of stealth liposomes in tumor tissue,” Cancer Research, vol. 53, no. 16, pp. 3765–3770, 1993. View at Google Scholar · View at Scopus
  25. A. Gabizon, R. Catane, B. Uziely et al., “Prolonged circulation time and enhanced accumulation in malignant exudates of doxorubicin encapsulated in polyethylene-glycol coated liposomes,” Cancer Research, vol. 54, no. 4, pp. 987–992, 1994. View at Google Scholar · View at Scopus
  26. N. Z. Wu, B. Klitzman, G. Rosner, D. Needham, and M. W. Dewhirst, “Measurement of material extravasation in microvascular networks using fluorescence video-microscopy,” Microvascular Research, vol. 46, no. 2, pp. 231–253, 1993. View at Publisher · View at Google Scholar · View at Scopus
  27. R. K. Jain, “Transport of molecules in the tumor interstitium: a review,” Cancer Research, vol. 47, no. 12, pp. 3039–3051, 1987. View at Google Scholar · View at Scopus
  28. K. A. Granath and B. E. Kvist, “Molecular weight distribution analysis by gel chromatography on sephadex,” Journal of Chromatography A, vol. 28, no. C, pp. 69–81, 1967. View at Google Scholar · View at Scopus
  29. W. M. Saltzman and M. L. Radomsky, “Drugs released from polymers: diffusion and elimination in brain tissue,” Chemical Engineering Science, vol. 46, no. 10, pp. 2429–2444, 1991. View at Google Scholar · View at Scopus
  30. L. J. Nugent and R. K. Jain, “Extravascular diffusion in normal and neoplastic tissues,” Cancer Research, vol. 44, no. 1, pp. 238–244, 1984. View at Google Scholar · View at Scopus
  31. E. A. Swabb, J. Wei, and P. M. Gullino, “Diffusion and convection in normal and neoplastic tissues,” Cancer Research, vol. 34, no. 10, pp. 2814–2822, 1974. View at Google Scholar · View at Scopus
  32. M. B. Wolf, P. D. Watson, and D. R. C. Scott, “Integral-mass balance method for determination of solvent drag reflection coefficient,” American Journal of Physiology, vol. 253, no. 1, p. 22/1, 1987. View at Google Scholar · View at Scopus
  33. D. J. Kerr, A. M. Kerr, R. I. Freshney, and S. B. Kaye, “Comparative intracellular uptake of adriamycin and 4'-deoxydoxorubicin by non-small cell lung tumor cells in culture and its relationship to cell survival,” Biochemical Pharmacology, vol. 35, no. 16, pp. 2817–2823, 1986. View at Google Scholar · View at Scopus
  34. R. E. Eliaz, S. Nir, C. Marty, and F. C. Szoka, “Determination and modeling of kinetics of cancer cell killing by doxorubicin and doxorubicin encapsulated in targeted liposomes,” Cancer Research, vol. 64, no. 2, pp. 711–718, 2004. View at Publisher · View at Google Scholar · View at Scopus
  35. J. Robert, A. Illiadis, and B. Hoerni, “Pharmacokinetics of adriamycin in patients with breast cancer: correlation between clinical short-term response,” European Journal of Cancer and Clinical Oncology, vol. 18, no. 8, pp. 739–745, 1982. View at Google Scholar · View at Scopus
  36. C. Liu, J. Krishnan, and X. Y. Xu, “A systems-based mathematical modelling framework for investigating the effect of drugs on solid tumours,” Theoretical Biology & Medical Modelling, vol. 8, pp. 45–65, 2011. View at Google Scholar
  37. M. Winter, Basic Clinical Pharmacokinetics, Plasma Protein Binding, Lippincott Williams & Wilkins, Philadelphia, Pa, USA, 4th edition, 2003.
  38. L. Z. Benet and P. Zia-Amirhosseini, “Basic principles of pharmacokinetics,” Toxicologic Pathology, vol. 23, no. 2, pp. 115–123, 1995. View at Google Scholar · View at Scopus
  39. K. A. Rodvold, D. A. Rushing, and D. A. Tewksbury, “Doxorubicin clearance in the obese,” Journal of Clinical Oncology, vol. 6, no. 8, pp. 1321–1327, 1988. View at Google Scholar · View at Scopus
  40. M. Dalmark and H. H. Storm, “A Fickian diffusion transport process with features of transport catalysis. Doxorubicin transport in human red blood cells,” Journal of General Physiology, vol. 78, no. 4, pp. 349–364, 1981. View at Google Scholar · View at Scopus
  41. R. T. Tong, Y. Boucher, S. V. Kozin, F. Winkler, D. J. Hicklin, and R. K. Jain, “Vascular normalization by vascular endothelial growth factor receptor 2 blockade induces a pressure gradient across the vasculature and improves drug penetration in tumors,” Cancer Research, vol. 64, no. 11, pp. 3731–3736, 2004. View at Publisher · View at Google Scholar · View at Scopus
  42. J. C. Parker, M. A. Perry, and A. E. Taylor, “Permeability of the microvascular barrier,” in Edema, N. C. Staub and A. E. Taylor, Eds., pp. 143–187, Raven Press, New York, NY, USA, 1984. View at Google Scholar
  43. K. Aukland and R. K. Reed, “Interstitial-lymphatic mechanisms in the control of extracellular fluid volume,” Physiological Reviews, vol. 73, no. 1, pp. 1–78, 1993. View at Google Scholar · View at Scopus
  44. H. Sarin, “Physiologic upper limits of pore size of different blood capillary types and another perspective on the dual pore theory of microvascular permeability,” Journal of Angiogenesis Research, vol. 2, no. 1, article 14, 2010. View at Publisher · View at Google Scholar · View at Scopus
  45. T. Tagami, M. Ernsting, and S. D. Li, “Optimization of a novel and improved thermosensitive liposome formulated with DPPC and a Brij surfactant using a robust in vitro system,” Journal of Controlled Release, vol. 154, no. 3, pp. 290–297, 2011. View at Google Scholar
  46. M. Afadzi, C. Davies, and Y. H. Hansen, “Ultrasound stimulated release of liposomal calcein,” in Ultrasonics Symposium (IUS), vol. 2010, pp. 11–14, IEEE Conference, October 2010.
  47. J. Kirk, S. Houlbrook, N. S. A. Stuart, I. J. Stratford, A. L. Harris, and J. Carmichael, “Differential modulation of doxorubicin toxicity to multidrug and intrinsically drug resistant cell lines by anti-oestrogens and their major metabolites,” British Journal of Cancer, vol. 67, no. 6, pp. 1189–1195, 1993. View at Google Scholar · View at Scopus
  48. L. M. Levasseur, H. K. Slocum, Y. M. Rustum, and W. R. Greco, “Modeling of the time-dependency of in vitro drug cytotoxicity and resistance,” Cancer Research, vol. 58, no. 24, pp. 5749–5761, 1998. View at Google Scholar · View at Scopus
  49. S. Ozawa, Y. Sugiyama, Y. Mitsuhashi, T. Kobayashi, and M. Inaba, “Cell killing action of cell cycle phase-non-specific antitumor agents is dependent on concentration-time product,” Cancer Chemotherapy and Pharmacology, vol. 21, no. 3, pp. 185–190, 1988. View at Google Scholar · View at Scopus