The efficacy of cancer chemotherapy can be greatly enhanced by thermally targeted nanoparticle liposome drug delivery system. A new theoretical model coupling heat and mass transfer has been developed to study the spatial and transient drug distributions. In this model, the influence of tumor cell apoptosis and necrosis in drug transport is also considered, in addition to the tumor microvasculature permeability to nanoliposomes. The model predictions agree well with our previous experimental results, and it has been used to simulate the nanoparticle drug distribution in the tumor under hyperthermic conditions. Results show that hyperthermia alone only enhances drug accumulation in the periphery of a tumor with 1 cm in radius, and the tumor cells in the central region are hardly damaged due to poor drug diffusion. Apoptosis or necrosis of the tumor cells could significantly influence the drug penetration and should be accounted for in drug diffusion modeling to accurately predict the therapeutic effect. Simulation study on the combined radio frequency ablation and liposomal doxorubicin delivery shows more effective treatment outcome, especially for larger tumors. The present model can be used to predict the treatment outcome and optimize the clinical protocol.
1.
Szoka
, F. C.
, 1991, “Liposomal Drug Delivery: Current Status and Future Prospects
,” Membrane Fusion
, J.
Wilschut
and D.
Hoekstra
, eds., Marcel Dekker
, New York
, pp. 845
–890
.2.
Gabizon
, A.
, Catane
, R.
, Uziely
, B.
, Kaufman
, B.
, Safra
, T.
, Cohen
, R.
, Martin
, F.
, Huang
, A.
, and Barenholz
, Y.
, 1994, “Prolonged Circulation Time and Enhanced Accumulation in Malignant Exudates of Doxorubicin Encapsulated in Polyethylene-Glycol Coated Liposomes
,” Cancer Res.
, 54
(4
), pp. 987
–992
. 0008-54723.
Nagayasu
, A.
, Uchiyama
, K.
, and Kiwada
, H.
, 1999, “The Size of Liposomes: A Factor Which Affects Their Targeting Efficiency to Tumors and Therapeutic Activity of Liposomal Antitumor Drugs
,” Adv. Drug Delivery Rev.
0169-409X, 40
(1–2
), pp. 75
–87
.4.
Kong
, G.
, Braun
, R. D.
, and Dewhirst
, M. W.
, 2000, “Hyperthermia Enables Tumor-Specific Nanoparticle Delivery: Effect of Particle Size
,” Cancer Res.
, 60
(16
), pp. 4440
–4445
. 0008-54725.
Ning
, S.
, Macleod
, K.
, Abra
, R. M.
, Huang
, A. H.
, and Hahn
, G. M.
, 1994, “Hyperthermia Induces Doxorubicin Release From Long-Circulating Liposomes and Enhances Their Anti-Tumor Efficacy
,” Int. J. Radiat. Oncol., Biol., Phys.
, 29
(4
), pp. 827
–834
. 0360-30166.
Dvorak
, J.
, Zoul
, Z.
, Melichar
, B.
, Petera
, J.
, Vesely
, P.
, Vosmik
, M.
, and Dolezel
, M.
, 2004, “Liposomal Doxorubicin Combined With Regional Hyperthermia: Reducing Systemic Toxicity and Improving Locoregional Efficacy in the Treatment of Solid Tumors
,” J. Chemother.
, 16
, pp. 34
–36
. 1120-009X7.
Urano
, M.
, Kuroda
, M.
, and Nishimura
, Y.
, 1999, “For the Clinical Application of Thermochemotherapy Given at Mild Temperatures
,” Int. J. Hyperthermia
, 15
(2
), pp. 79
–107
. 0265-67368.
Liu
, P.
, Zhang
, A.
, Xu
, Y.
, and Xu
, L. X.
, 2005, “Study of Non-Uniform Nanoparticle Liposome Extravasation in Tumor
,” Int. J. Hyperthermia
, 21
(3
), pp. 259
–270
. 0265-67369.
Kong
, G.
, and Dewhirst
, M. W.
, 1999, “Hyperthermia and Liposomes
,” Int. J. Hyperthermia
, 15
(5
), pp. 345
–370
. 0265-673610.
Xu
, L. X.
, Zhu
, L.
, and Holmes
, K. R.
, 1998, “Thermoregulation in the Canine Prostate During Transurethral Microwave Hyperthermia, Part I: Temperature Response
,” Int. J. Hyperthermia
, 14
(1
), pp. 29
–37
. 0265-673611.
Maruyama
, K.
, Unezaki
, S.
, Takahashi
, N.
, and Iwatsuru
, M.
, 1993, “Enhanced Delivery of Doxorubicin to Tumor by Long-Circulating Thermosensitive Liposomes and Local Hyperthermia
,” Biochim. Biophys. Acta
, 1149
(2
), pp. 209
–216
. 0006-300212.
Gaber
, M. H.
, Wu
, N. Z.
, Hong
, K.
, Huang
, S. K.
, Dewhirst
, M. W.
, and Papahadjopoulos
, D.
, 1996, “Thermosensitive Liposomes: Extravasation and Release of Contents in Tumor Microvascular Networks
,” Int. J. Radiat. Oncol., Biol., Phys.
0360-3016, 36
(5
), pp. 1177
–1187
.13.
Ribba
, B.
, Marron
, K.
, Agur
, Z.
, Alarcon
, T.
, and Maini
, P. K.
, 2005, “A Mathematical Model of Doxorubicin Treatment Efficacy for Non-Hodgkin’s Lymphoma: Investigation of the Current Protocol Through Theoretical Modelling Results
,” Bull. Math. Biol.
, 67
(1
), pp. 79
–99
. 0092-824014.
Tzafriri
, A. R.
, Lerner
, E. I.
, Flashner-Barak
, M.
, Hinchcliffe
, M.
, Ratner
, E.
, and Parnas
, H.
, 2005, “Mathematical Modeling and Optimization of Drug Delivery From Intratumorally Injected Microspheres
,” Clin. Cancer Res.
, 11
, pp. 826
–834
. 1078-043215.
Ward
, J. P.
, and King
, J. R.
, 2003, “Mathematical Modelling of Drug Transport in Tumor Multicell Spheroids and Monolayer Cultures
,” Math. Biosci.
0025-5564, 181
(2
), pp. 177
–207
.16.
Lankelma
, J.
, Luque
, R. F.
, Dekker
, H.
, Schinkel
, W.
, and Pinedo
, H. M.
, 2000, “A Mathematical Model of Drug Transport in Human Breast Cancer
,” Microvasc. Res.
, 59
(1
), pp. 149
–161
. 0026-286217.
Lankelma
, J.
, Luque
, R. F.
, Dekker
, H.
, and Pinedo
, H. M.
, 2003, “Simulation Model of Doxorubicin Activity in Islets of Human Breast Cancer Cells
,” Biochim. Biophys. Acta
, 1622
(3
), pp. 169
–178
. 0006-300218.
Magni
, P.
, Simeoni
, M.
, Poggesi
, I.
, Rocchetti
, M.
, and De Nicolao
, G.
, 2006, “A Mathematical Model to Study the Effects of Drugs Administration on Tumor Growth Dynamics
,” Math. Biosci.
, 200
(2
), pp. 127
–151
. 0025-556419.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 2003, “A Mathematical Model for Cisplatin Cellular Pharmacodynamics
,” Neoplasia
, 5
(2
), pp. 161
–169
. 1522-800220.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 2005, “Two-Mechanism Peak Concentration Model for Cellular Pharmacodynamics of Doxorubicin
,” Neoplasia
, 7
(7
), pp. 705
–713
. 1522-800221.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 2004, “A Theoretical Model for Intraperitoneal Delivery of Cisplatin and the Effect of Hyperthermia on Drug Penetration Distance
,” Neoplasia
, 6
(2
), pp. 117
–127
. 1522-800222.
Maruyama
, K.
, Ishida
, O.
, Takizawa
, T.
, and Moribe
, K.
, 1999, “Possibility of Active Targeting to Tumor Tissues With Liposomes
,” Adv. Drug Delivery Rev.
, 40
(1–2
), pp. 89
–102
. 0169-409X23.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 2000, “A Mathematical Model for Comparison of Bolus Injection, Continuous Infusion, and Liposomal Delivery of Doxorubicin to Tumor Cells
,” Neoplasia
, 2
(4
), pp. 325
–338
. 1522-800224.
Lankelma
, J.
, Dekker
, H.
, Luque
, F. R.
, Luykx
, S.
, Hoekman
, K.
, van der Valk
, P.
, van Diest
, P. J.
, and Pinedo
, H. M.
, 1999, “Doxorubicin Gradients in Human Breast Cancer
,” Clin. Cancer Res.
, 5
(7
), pp. 1703
–1707
. 1078-043225.
Jang
, S. H.
, Wientjes
, M. G.
, Lu
, D.
, and Au
, J. L.
, 2003, “Drug Delivery and Transport to Solid Tumors
,” Pharm. Res.
, 20
(9
), pp. 1337
–1350
. 0724-874126.
Gabizon
, A.
, Shmeeda
, H.
, and Barenholz
, Y.
, 2003, “Pharmacokinetics of Pegylated Liposomal Doxorubicin—Review of Animal and Human Studies
,” Clin. Pharmacokinet
, 42
(5
), pp. 419
–436
. 0312-596327.
Elliott
, G. D.
, and McGrath
, J. J.
, 1999, “Freezing Response of Mammary Tissue: A Mathematical Study
,” Heat Mass Transfer
0947-7411, 44
, pp. 59
–64
.28.
Chato
, J. C.
, 1987, “Thermal Properties of Tissues
,” Handbook of Bioengineering
, Vols. 9.1–9.13
, R.
Skalak
and S.
Chien
, eds., McGraw-Hill
, New York
.29.
Zhang
, A.
, Xu
, L. X.
, Sandison
, G. A.
, and Zhang
, J.
, 2003, “A Microscale Model for Prediction of Breast Cancer Cell Damage During Cryosurgery
,” Cryobiology
0011-2240, 47
(2
), pp. 143
–154
.30.
Xu
, L. X.
, Zhu
, L.
, and Holmes
, K. R.
, 1998, “Thermoregulation in the Canine Prostate During Transurethral Microwave Hyperthermia, Part II: Blood Flow Response
,” Int. J. Hyperthermia
, 14
(1
), pp. 65
–73
. 0265-673631.
Siegal
, T.
, Horowitz
, A.
, and Gabizon
, A.
, 1995, “Doxorubicin Encapsulated in Sterically Stabilized Liposomes for the Treatment of a Brain Tumor Model: Biodistribution and Therapeutic Efficacy
,” J. Neurosurg.
, 83
(6
), pp. 1029
–1037
. 0022-308532.
Nugent
, L. J.
, and Jain
, R. K.
, 1984, “Extravascular Diffusion in Normal and Neoplastic Tissues
,” Cancer Res.
, 44
(1
), pp. 238
–244
. 0008-547233.
Yuan
, F.
, Leunig
, M.
, Huang
, S. K.
, Berk
, D. A.
, Papahadjopoulos
, D.
, and Jain
, R. K.
, 1994, “Microvascular Permeability and Interstitial Penetration of Sterically Stabilized (Stealth) Liposomes in a Human Tumor Xenograft
,” Cancer Res.
, 54
(13
), pp. 3352
–3356
. 0008-547234.
Qian
, F.
, Stowe
, N.
, Liu
, E. H.
, Saidel
, G. M.
, and Gao
, J.
, 2003, “Quantification of In Vivo Doxorubicin Transport From PLGA Millirods in Thermoablated Rat Livers
,” J. Controlled Release
, 91
(1–2
), pp. 157
–166
. 0168-365935.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 2004, “A Theoretical Model for Intraperitoneal Delivery of Cisplatin and the Effect of Hyperthermia on Drug Penetration Distance
,” Neoplasia
, 6
(2
), pp. 117
–127
. 1522-800236.
Tsuchihashi
, M.
, Harashima
, H.
, and Kiwada
, H.
, 1999, “Development of a Pharmacokinetic/Pharmacodynamic (PK/PD)-Simulation System for Doxorubicin in Long Circulating Liposomes in Mice Using Peritoneal P388
,” J. Controlled Release
, 61
(1–2
), pp. 9
–19
. 0168-365937.
Zhu
, L.
, Mi
, Z.
, and Xu
, L. X.
, 1998, “Temperature Distribution in Prostate During Transurethral Radio Frequency Thermotherapy Treatment of Benign Prostatic Hyperplasia
,” Advances in Heat Mass Transfer in Biotechnology
, HTD-Vol.362/BED-Vol.40, ASME
, New York, NY
, pp. 117
–122
.38.
Jain
, R. K.
, 1987, “Transport of Molecules Across Tumor Vasculature
,” Cancer Metastasis Rev.
, 6
(4
), pp. 559
–593
. 0891-999239.
Chen
, B.
, and Fu
, B. M.
, 2004, “An Electrodiffusion-Filtration Model for Effects of Endothelial Surface Glycocalyx on Microvessel Permeability to Macromolecules
,” ASME J. Biomech. Eng.
0148-0731, 126
(5
), pp. 614
–624
.40.
Dreher
, M. R.
, Liu
, W.
, Michelich
, C. R.
, Dewhirst
, M. W.
, Yuan
, F.
, and Chilkoti
, A.
, 2006, “Tumor Vascular Permeability, Accumulation, and Penetration of Macromolecular Drug Carriers
,” J. Natl. Cancer Inst.
, 98
(5
), pp. 335
–344
. 0027-887441.
El-Kareh
, A. W.
, and Secomb
, T. W.
, 1997, “Theoretical Models for Drug Delivery to Solid Tumors
,” Crit. Rev. Biomed. Eng.
, 25
(6
), pp. 503
–571
. 0278-940X42.
El-Kareh
, A. W.
, Braunstein
, S. L.
, and Secomb
, T. W.
, 1993, “Effect of Cell Arrangement and Interstitial Volume Fraction on the Diffusivity of Monoclonal Antibodies in Tissue
,” Biophys. J.
, 64
(5
), pp. 1638
–1646
. 0006-349543.
Jang
, S. H.
, Wientjes
, M. G.
, Lu
, D.
, and Au
, J. L. S.
, 2003, “Drug Delivery and Transport to Solid Tumors
,” Pharm. Res.
, 20
(9
), pp. 1337
–1350
. 0724-874144.
Liu
, P.
, and Xu
, L. X.
, 2006, “Enhanced Efficacy of Anti-Tumor Liposomal Doxorubicin by Hyperthermia
,” 28th Annual International Conference IEEE Engineering Medicine and Biology Society
.45.
Weinstein
, J. N.
, Magin
, R. L.
, Yatvin
, M. B.
, and Zaharko
, D. S.
, 1979, “Liposomes and Local Hyperthermia: Selective Delivery of Methotrexate to Heated Tumors
,” Science
, 204
, pp. 188
–191
. 0036-807546.
Ahmed
, M.
, and Goldberg
, S. N.
, 2004, “Combination Radiofrequency Thermal Ablation and Adjuvant IV Liposomal Doxorubicin Increases Tissue Coagulation and Intratumoral Drug Accumulation
,” Int. J. Hyperthermia
, 20
(7
), pp. 781
–802
. 0265-673647.
Zhu
, L.
, and Xu
, L. X.
, 1999, “Evaluation of the Effectiveness of Transurethral RF Hyperthermia in the Canine Prostate: Temperature Distribution Analysis
,” ASME J. Biomech. Eng.
0148-0731, 121
(6
), pp. 584
–590
.48.
Schuder
, G.
, Pistorius
, G.
, Fehringer
, M.
, Feifel
, G.
, Menger
, M. D.
, and Vollmar
, B.
, 2000, “Complete Shutdown of Microvascular Perfusion Upon Hepatic Cryothermia Is Critically Dependent on Local Tissue Temperature
,” Br. J. Cancer
, 82
(4
), pp. 794
–799
. 0007-092049.
Sun
, J. Q.
, Zhang
, A.
, and Xu
, L. X.
, 2008, “Evaluation of Alternative Cooling and Heating for Tumor Treatment
,” Int. J. Heat Mass Transfer
, 51
(23–24
), pp. 5478
–5485
. 0017-931050.
Lee
, J. M.
, Han
, J. K.
, Kim
, S. H.
, Lee
, J. Y.
, Choi
, S. H.
, and Choi
, B. I.
, 2004, “Hepatic Bipolar Radiofrequency Ablation Using Perfused-Cooled Electrodes: A Comparative Study in the Ex Vivo Bovine Liver
,” Br. J. Radiol.
, 77
, pp. 944
–949
. 0007-128551.
Eddy
, H. A.
, 1980, “Alterations in Tumor Microvasculature During Hyperthermia
,” Radiology
, 137
(2
), pp. 515
–21
. 0033-841952.
Greenstein
, A.
, and Koontz
, W. W.
, Jr., 2002, “Does Local Hyperthermia Affect Metastasis of a Human Prostate Carcinoma Grown in Athymic Nude Mice?
,” Int. J. Hyperthermia
, 18
, pp. 285
–291
. 0265-673653.
Salsbury
, A. J.
, 1975, “The Significance of the Circulating Cancer Cell
,” Cancer Treat Rev.
, 2
, pp. 55
–72
. 0305-7372Copyright © 2009
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