(625i) The Development of A General Mathematical Model for the Prediction of Tumor Growth Based On Experimental Data

Mathematical modeling of growth kinetics is important in predicting the behavior of many biological systems such as tumor size, population dynamics and disease progression.  In many cases it is important to accurately describe the growth of biological system, such as the planning of chemotherapeutics for cancer patients or tracking the growth of bio-film in industrial pipes. Logistic and Gompertz are two models in particular that have been studied to a great extent in biological and medical systems.   A series of hyperbolastic models H1, H2, and H3 were proposed by Tabataba that more accurately describe both systems of Ehrlich tumor growth and broiler growth kinetics then previous models.  Upon observation of the hyperbolastic models, it appears that each took a specific form of a generalized model.  It was found that a generalized form could become the proposed models with the addition of two or three assumptions.  We perform a comparative study of the previously proposed hyperbolastic models and a generalized form H₀.  The results of this comparison show that the assumptions that make up the earlier proposed hyperbolastic models are not necessarily correct; as the generalized model produced the smallest error in modeling both Ehrlich tumor growth and broiler growth kinetics.