A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin’s lymphoma: Investigation of the current protocol through theoretical modelling results

Doxorubicin treatment outcomes for non-Hodgkin’s lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature vessels, vascular structural adaptation and NHL cell-cycle kinetics in addition to Doxorubicin pharmacokinetics (PK) and pharmacodynamics (PD). Simulations provide qualitative estimations of the effect of Doxorubicin on high-grade (HG), intermediate-grade (IG) and low-grade (LG) NHL. Simulation results imply that if the interval between successive drug applications is prolonged beyond a certain point, treatment will be inefficient due to effects caused by heterogeneous blood flow in the system.

[1]  S. Korenman Williams Textbook of Endocrinology; Williams Textbook of Endocrinology CD-ROM , 2003 .

[2]  M. Chaplain,et al.  Continuous and discrete mathematical models of tumor-induced angiogenesis , 1998, Bulletin of mathematical biology.

[3]  T. Tong,et al.  Cancer statistics, 1994 , 1994, CA: a cancer journal for clinicians.

[4]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[5]  M. Chaplain,et al.  Mathematical modelling of tumour invasion and metastasis , 2000 .

[6]  Leszek Wojnar,et al.  Image Analysis , 1998 .

[7]  Z. Agur,et al.  A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. , 1992, Mathematical biosciences.

[8]  H. Minn,et al.  Increased glucose metabolism in untreated non-Hodgkin's lymphoma: a study with positron emission tomography and fluorine-18-fluorodeoxyglucose. , 1995, Blood.

[9]  T. Kwok,et al.  The response to cytotoxic drugs of EMT6 cells treated either as intact or disaggregated spheroids. , 1985, British Journal of Cancer.

[10]  J. Lankelma,et al.  A mathematical model of drug transport in human breast cancer. , 2000, Microvascular research.

[11]  C Haanen,et al.  Cell cycle kinetics in malignant lymphoma studied with in vivo iododeoxyuridine administration, nuclear Ki-67 staining, and flow cytometry. , 1992, Blood.

[12]  E. Smeland,et al.  Proliferation and apoptosis in malignant and normal cells in B-cell non-Hodgkin's lymphomas. , 1998, British Journal of Cancer.

[13]  Mark A. J. Chaplain,et al.  A mathematical model of vascular tumour growth and invasion , 1996 .

[14]  Z. Agur,et al.  A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth , 2004, Angiogenesis.

[15]  H. Honda,et al.  Formation of the branching pattern of blood vessels in the wall of the avian yolk sac studied by a computer simulation , 1997, Development, growth & differentiation.

[16]  Mikhail V. Blagosklonny,et al.  The Restriction Point of the Cell Cycle , 2002, Cell cycle.

[17]  R K Jain,et al.  Delivery of molecular medicine to solid tumors: lessons from in vivo imaging of gene expression and function. , 2001, Journal of controlled release : official journal of the Controlled Release Society.

[18]  A. Pries,et al.  Structural adaptation and stability of microvascular networks: theory and simulations. , 1998, The American journal of physiology.

[19]  Cell cycle kinetics in malignant lymphoma studied with in vivo iododeoxyuridine administration, nuclear Ki-67 staining, and flow cytometry. , 1992 .

[20]  M. Tsujimoto,et al.  Relationships between the in vitro cytotoxicity and transport characteristics of pirarubicin and doxorubicin in M5076 ovarian sarcoma cells, and comparison with those in Ehrlich ascites carcinoma cells , 2002, Cancer Chemotherapy and Pharmacology.

[21]  Philip K Maini,et al.  A design principle for vascular beds: the effects of complex blood rheology. , 2005, Microvascular research.

[22]  Maurice W. Van Allen,et al.  Handbook of Physiology: A Critical, Comprehensive Presentation of Physiological Knowledge and Concepts , 1960 .

[23]  Charles F. Code,et al.  Handbook of Physiology; a Critical, Comprehensive Presentation of Physiological Knowledge and Concepts , 2011 .

[24]  G Enden,et al.  A numerical study of plasma skimming in small vascular bifurcations. , 1994, Journal of biomechanical engineering.

[25]  A. Deutsch,et al.  Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. , 2002, In silico biology.

[26]  S. Barranco Cellular and molecular effects of adriamycin on dividing and nondividing cells. , 1984, Pharmacology & therapeutics.

[27]  Zvia Agur,et al.  Randomness, synchrony and population persistence , 1985 .

[28]  M A Konerding,et al.  3D microvascular architecture of pre-cancerous lesions and invasive carcinomas of the colon , 2001, British Journal of Cancer.

[29]  Zvia Agur,et al.  Reduction of cytotoxicity to normal tissues by new regimens of cell-cycle phase-specific drugs , 1988 .

[30]  F. Willemse,et al.  Image analysis in immunohistochemistry. Factors with a possible influence on the performance of VIDAS version 2.0, a commercially available true color image analysis system. , 1993, Analytical and quantitative cytology and histology.

[31]  D. Darland,et al.  Blood vessel maturation: vascular development comes of age. , 1999, The Journal of clinical investigation.

[32]  E. T. Gawlinski,et al.  A cellular automaton model of early tumor growth and invasion. , 2001, Journal of theoretical biology.

[33]  C Sebban,et al.  Prognostic significance of received relative dose intensity in non-Hodgkin's lymphoma patients: application to LNH-87 protocol. The GELA. (Groupe d'Etude des Lymphomes de l'Adulte). , 1993, Annals of oncology : official journal of the European Society for Medical Oncology.

[34]  S. V. Sotirchos,et al.  Glucose diffusivity in multicellular tumor spheroids. , 1988, Cancer research.

[35]  E. T. Gawlinski,et al.  A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism , 2001 .

[36]  A. Pries,et al.  Resistance to blood flow in microvessels in vivo. , 1994, Circulation research.

[37]  D. Pode,et al.  Selective ablation of immature blood vessels in established human tumors follows vascular endothelial growth factor withdrawal. , 1999, The Journal of clinical investigation.

[38]  ScienceDirect Bulletin of mathematical biology , 1973 .

[39]  B Zackrisson,et al.  Cell kinetic analysis of non‐Hodgkin's lymphomas using in vivo iododeoxyuridine incorporation and flow cytometry , 1995, Hematological oncology.

[40]  J. Gaddum,et al.  The Pharmacological Basis of Therapeutics , 1966 .

[41]  P. Maini,et al.  A cellular automaton model for tumour growth in inhomogeneous environment. , 2003, Journal of theoretical biology.

[42]  Stanley J. Wiegand,et al.  Vascular-specific growth factors and blood vessel formation , 2000, Nature.

[43]  G M Saidel,et al.  Diffusion model of tumor vascularization and growth , 1977, Bulletin of mathematical biology.

[44]  S. McDougall,et al.  Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies , 2002, Bulletin of mathematical biology.

[45]  L. Goodman,et al.  The Pharmacological Basis of Therapeutics , 1941 .

[46]  J. H. Scarffe,et al.  Cancer Medicine , 1982, British Journal of Cancer.

[47]  J. Whittaker,et al.  Combination chemotherapy including epirubicin for the management of non-Hodgkin's lymphoma. , 1987, European journal of cancer & clinical oncology.

[48]  B. Couderc,et al.  The management of adult aggressive non-Hodgkin's lymphomas. , 2000, Critical reviews in oncology/hematology.