Tumor shapes effect on metastatic state: A theoretical derivation embedding thermodynamic laws

Breaching away cells from an original primary tumor site and spreading throughout the body is hallmark definition of metastasis. To get the bottom line of this phenomenon, mathematical and thermodynamically based techniques have been developed and are being increasingly applied to help, decipher and forecast tumor pattern disturbing and treatment response. Becoming a primary tumor to metastatic one, remains as hot topic in many studies. In this study, an extensive complicated mathematical model was used and by embedding thermodynamic laws, three primary oversimplifying hypothetical tumors’ shape e.g. cylindrical, spherical, ellipsoidal were theoretically studied. After extracting within tumor flux pressures, we tried to compare aforementioned tumor shapes in terms of becoming a metastatic one e.g. cell rupturing. Our results shown it was not explicitly possible to address which tumor shapes shall get metastatic state (tear down in much earlier time than other shapes), as it was heavily dependent on tumor parameter values. The results of this study could be fairy appealing for both cancer model developer experts, medicines and cancer systems biologist as well.