Related papers: Efficient modeling of chemotherapy regimens using …
We propose a new model of cancer growth based on nonextensive entropy. The evolution equation depends on the nonextensive parameter q. The exponential, the logistic, and the Gompertz growth laws are particular cases of the generalized…
We present a mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to a Gompertz growth function. We present local stability analysis and bifurcation plots for relevant model parameters to…
In this work, we combine a new form of the cell survival fraction developed in [29] with the Gompertz cell growth model. The result is an equation that models the cell growth/death under a radiation dose and can be applied in a conventional…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
The problem of chemotherapy treatment optimization can be defined in order to minimize the size of the tumor without endangering the patient's health; therefore, chemotherapy requires to achieve a number of objectives, simultaneously. For…
Comparing both, the more conventional Gompertz tumor growth law (GL) and the ``Universal'' law (UL), recently proposed and applied to cancer,we have investigated the growth law's implications on various radiotherapy regimen. According to…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the…
In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune…
We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…
A macroscopic model of the tumor Gompertzian growth is proposed. This approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor factors.…
The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…
Chemotherapy is one of the primary modalities of cancer treatment. Chemotherapy drug administration is a complex problem that often requires expensive clinical trials to evaluate potential regimens. One way to alleviate this burden and…
Despite internal complexity, tumor growth kinetics follow relatively simple macroscopic laws that have been quantified by mathematical models. To resolve this further, quantitative and discriminant analyses were performed for the purpose of…
In this paper, a tractable methodology is proposed to approximate stochastic optimal feedback treatment in the context of mixed immuno-chemo therapy of cancer. The method uses a fixed-point value iteration that approximately solves a…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy as well as immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population…
In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by…
In radiation therapy, mathematical methods have been used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to critical surrounding structures minimal. This optimization problem…
Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…