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This paper studies chaotic behavior in cancer dynamics when a treatment procedure is introduced. Recently introduced virotherapy is considered for the cancer treatment. Chaotic behaviors are investigated by using the Lyapunov Exponent for a set of parameters. The chaotic behavior is studied by using the mathematical model of the cancer dynamics involving the virotherapy. Through simulations and the...
We perform a local sensitivity study taking into account the variation of the parameters and initial conditions applied to a model governing the chronic myelogenous leukemia (CML) evolution, a cancer of the white blood cells. The interaction mechanism between naïve T cells, effector T cells, and CML cancer cells in the body is modeled by a system of ordinary differential equations which defines rates...
This paper is dedicated to develop a fractional order model of the rate of change of cancerous blood cells in Chronic Myeloid Leukaemia using fractional-order differential equations as well as tackling the factors that affect this rate and compare between them. The simulated cases (using MATLAB) prove that the proposed model is doable in terms of the variables positions in the equations and its effect...
Microarray dataset often contains huge number of data, only a fraction of which comprise significant differentially expressed genes. In this article, t-test is applied to identify the precise and interesting genes which are responsible for cause of cancer. After precise identification, a new embedded approach is proposed where in a genetic algorithm (GA) is combined with Artificial neural network...
In this paper we study some features of global behavior of one four-dimensional cancer model described by DePillisand Radunskaya in 2013. We find upper bounds for ultimate dynamics of all types of cells populations involvedinto this model. Also all the ultimate lower bounds. Further, we prove the existence of the bounded positively invariantpolytope. Finally, we demonstrate local stability of the...
Biologists have uncovered some of the most basic mechanisms by which normal cells develop into cancerous tumors. These biological theories can be transformed into adequate mathematical models. For this reason, we attempt to study the evolution of cancer cells using the Markov Chain Processes. Based on Markov chain Processes, cancer chemotherapy will be applied on them to treat the disease. However,...
Pulsed electric fields (PEFs) may be used to control cancer cell population in vitro or to treat cancers in vivo. In both cases, understanding the impact of PEFs on the cell population is critical, particularly as a function of pulse parameters. Generally, cancer cell populations consist of proliferating (dividing) and quiescent (resting) cells. Mathematical models based on coupled differential equations...
Cancer mathematical modeling constitutes an emerging area of research aiming to predict tumors spatial and temporal evolution. Several mathematical and computational models have appeared in the literature addressing the mechanisms that govern tumor progression and invasion. Modeling techniques are initialized based either on the actual tumor geometries derived from imaging modalities (such as serial...
Cancer chemotherapy is a complicated treatment that needs balancing the cell killing with the undesirable toxic side-effects caused by the drugs. Several computational methods have been used in finding the right balance. This paper presents a model-based method to design optimum chemotherapy treatment schedule by using multiple objective particle swarm optimization (MOPSO) algorithm. Three dose plans...
The most effective cancer treatments are the ones that prolong patients' lives while offering a reasonable quality of life during and after treatment. The treatments must also carry out their actions rapidly and with high efficiency such that a very large percentage of tumor cells die or shift into a state where they stop proliferating. Due to biological and micro-environmental variabilities within...
Tumor growth involves numerous biochemical and biophysical processes related to the invasion of surrounding tissue and metastasis. Such phenomena occur at different scales of time and space. The desire to understand the interactions of these complex processes has given rise to various computational models allowing for multiple variable modeling using continuous, discrete and the most recent hybrid...
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