Microenvironmental Dynamics of Adenoid Cystic Carcinoma in Lacrimal Galand: A Mathematical Modeling Approach

Adenoid Cystic Carcinoma in lacrimal gland is extremely life threatening malignant tumor despite of being rare. Death is inevitable for the affected person, so to speak. Because metastasis into distant organs like lungs and bones is frequently observed in case of this tumor. On the other hand, for its complex molecular dynamics and low incidence rate, the treatment strategies are very limited. And the typical strategies can prevent tumor recurrence locally but, they do not have any influence on distant metastasis and mortality rate. So, it is urgent to move forward to targeted therapies. For this reason, it is essential to identify the changes occurring inside the tumor miceroenvironment. To explore this underlying dynamics, we developed a non-linear mathematical model incorporating the key variables of the tumor microenvironment such as number of tumor cells, oxygen level, nutrient level and blood vessels. The model is analyzed both analytically and numerically. To simulate the model numerically, Runge-Kutta 4th order has been applied. This study aligns with with the basic features of the lacrimal gland ACC describing severe hypoxic environment, low nutrient adaptive metabolic reprogramming and elevated abnormal vasculature structure. Most importantly, the study identifies that oxygen and nutrient supply rate by blood vessels are the bifurcating parameters that is the key drivers of the tumor microenvironment. The variation of these parameters can induce qualitative changes in the steady state from tumor free equilibrium to chemotherapy resistant state. If the oxygen and nutrient supply is reduced bellow a threshold level, it lead tumor to therapy resistance. From this observation it is understood that applying therapy before oxygen and nutrient levels fall below their thresholds makes tumor control possible. Moreover, this insight opens new avenues for the development of adaptive therapies targeting low oxygen and low nutrient tumor environments.

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