Cancer is a diseases characterized by the uncontrolled abnormal cells growth and the statistics reveals that it is the second factor of human mortality worldwide. Among the different types of tumors, the treatment of brain tumors is immensely challenging. Due to the health hazards that may be caused in newfound clinical therapies, the innovative research on cancer has started by turning to computational methods and has made fundamental changes. Mathematical modeling is able to provide insight into tumor growth and invasion by systematic studies of fundamental constituent processes and thereby reducing the number of costly experiments needed for the development of therapies. These mathematical models are based on biological characteristics and provided a powerful tool for the development of drug properties and preclinical eva‎luations. In this study, a comprehensive model is presented that examines tumor morphology simultaneously with drug delivery, which includes the pharmacokinetic and pharmacodynamic behavior of the drug in two stages of avascular and angiogenic tumor growth. In this model, it is for the first time that drug delivery and tumor dynamics contains the capillary network in relation to the interstitial flow. Continuum and discrete models are two main approaches for describing the evolution of the tumor in mathematical way. In order to simulate a tumor in large-scaled systems, continuum models sounds more suitable than discrete cell ones as a one millimeter radius spheroidal tumor consists of roughly one million cells. Thus, the continuous approach is chosed to describe the tumor dynamics and the tumor interface captures with phase field method. Moreover, the capillary network is produced by discrete-continuous hybrid model in Comsol software. As the angiogenesis is extremely complex due to multiple integrated modulators and feedback loops, a discrete-continuous hybrid model can explain the intercellular growth patterns of capillaries within a tissue and facilitate understanding these complex phenomena. In addition to the tumor morphology, the effect of some parameters related to the drug, such as the association rate the free drug to the cell receptor, the time of drug injection and the interval between each injection, have been investigated. The results show that in accordance with clinical studies, the angiogenesis stage has a significant effect on tumor growth due to the increase in nutrients and oxygen produced by the capillary network. Thus, according to the obtained results, the size of the tumor in a short period after the beginning of the angiogenic stage is about 3 times its size in the avascular stage. Furthermore, the drug can be administered more effectively and the treatment period can be reduced by starting chemotherapy when the active loops have formed in the capillary network. The treatment period can be shortened by five times if the treatment begins by the formation of the active loops opposed to the early stage of angiogenesis or avascular growth. In this regard, chemotherapy is not recommended for tumor treatment in avascular growth. By increasing the association rate of the free drug, the concentration of internalized drug increases and the more drug enters the tumor cells, the more tumor cells are killed. Compared to free drugs with a low affinity to cell receptors, the treatment period can fall down by one third.

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محسن ثقفيان

ابراهيم شيراني، مهدي نيلي احمدآبادي