Numerical investigation of the pharmacokinetics and pharmacodynamics of the chemotherapeutic drug in avascular and vascular stages of a brain tumor.

One of the most commonly used approaches for treating solid tumors is the systemic delivery of chemotherapeutic drugs. However, our understanding of the factors influencing treatment efficacy through this method is still limited. This study presents a comprehensive and realistic mathematical model that incorporates the dynamics of tumor growth, capillary network extension, and drug delivery in a coupled and simultaneous manner. The model covers two stages of tumor growth: avascular and vascular. For tumor growth, a continuum model is employed using the phase field interface-capturing method. The neo-vascularization process is modeled using a hybrid discrete-continuum approach. Additionally, a multi-scale model is used to describe the pharmacokinetics of doxorubicin, considering various agents. The study investigates the effect of haptotaxis and reveals that a higher haptotaxis coefficient leads to faster tumor growth (up to 2.6 times) and a quicker progression to angiogenesis. The impact of tumor-related and drug-related parameters is also examined, including tumor size, tumor sensitivity to the drug, chemotherapy initialization, treatment cycle duration, drug affinity to cells, and drug dose. The findings indicate that chemotherapy is more effective during the angiogenesis stage when active loops have formed. Other clinical methods such as radiotherapy and surgery may be more appropriate during the avascular stage or the transition period between angiogenesis initialization and loop formation. The penetration depth of the drug decreases by approximately 50% with an increase in the drug binding rate to surface-cell receptors. As a result, high-associate-rate drugs are preferred for chemotherapy after active loops have formed, while low-associate-rate drugs are suitable for earlier stages.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.