Abstract
In this paper we introduce a new growth model called T growth model. This model is capable of representing sigmoidal growth as well as biphasic growth. This dual capability is achieved without introducing additional parameters. The T model is useful in modeling cellular proliferation or regression of cancer cells, stem cells, bacterial growth and drug dose-response relationships. We recommend usage of the T growth model for the growth of tumors as part of any system of differential equations. Use of this model within a system will allow more flexibility in representing the natural rate of tumor growth. For illustration, we examine some systems of tumor-immune interaction in which the T growth rate is applied. We also apply the model to a set of tumor growth data.
Highlights
In biomedical sciences, the analysis of growth is usually characterized by a rate at which the population size changes
We suggest the usage of model (1) in systems involving immunotherapy to boost the immune system to fight tumor cells
The T growth model introduced in this paper follows the tradition of the hyperbolastic growth models in which hyperbolic functions are introduced into the growth model for the purpose of adding to the flexibility of the model and enabling the model to represent certain patterns of growth common to biological settings. This model is introduced with the dual goals of improving the representation of certain patterns of biological growth, biphasic growth and the goal of providing a flexible but accurate growth model with a small number of parameters that can be incorporated as the growth assumptions in a system of differential equations
Summary
The analysis of growth is usually characterized by a rate at which the population size changes. Beyond the variables in the system, sometimes terms representing particular therapies, such as chemotherapy or immunotherapy, can be included This direction of modeling has progressed in numerous directions, modeling important biological issues including issues such as evasion of the immune response, the effects of various therapies, and the role of myeloid cells in specific immune responses. The study of Kareva, et al (2010) deals with the role of myeloid cells in activating a specific immune response, and this model includes the inhibitory effect of tumor growth on the maturation of myeloid cells, diminishing the immune response as the tumor develops Another important direction in this field of research is the application of optimal control theory to these systems. Biphasic growth is a common occurrence in tumor growth, and introduction of this new model into the systems of ODEs will allow us to study its effects within the tumor-immune dynamics
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