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Cancer pathology is unique to a given individual, and developing personalized diagnostic and treatment protocols are a primary concern. Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the…
Overall survival (OS) is the gold standard for assessing patient benefit and cost-effectiveness of new cancer drugs. However, it is often difficult to use OS as the primary endpoint in randomized clinical trials (RCTs) for patients with…
Most human carcinomas exhibit telomere abnormalities early in the carcinogenesis process suggesting that crisis caused by telomere shortening may be a necessary event leading to human carcinomas. Epidemiological records of the age at which…
Prostate cancer was the third most common cancer in 2020 internationally, coming after breast cancer and lung cancer. Furthermore, in recent years prostate cancer has shown an increasing trend. According to clinical experience, if this…
Employing a novel two-dimensional computational model we have simulated the feedback between angiogenesis and tumor growth dynamics. Analyzing vessel formation and elongation towards the concentration gradient of the tumor-derived…
The fitness of somatic cells of metazoan, the ability of proliferation and survival, depends on microenvironment. In somatic evolution, a mutated cell in a tissue clonally expands abnormally because of its high fitness as normal cells in a…
Cancer has become one of the most widespread diseases in the world. Specifically, breast cancer is diagnosed more often than any other type of cancer. However, breast cancer patients and their individual tumors are often unique. Identifying…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…
Purpose. Patients with advanced cancer may undergo multiple lines of treatment, switching therapies as their disease progresses. Motivated by a study of metastatic prostate cancer, we develop a microsimulation framework to study therapy…
Metastatic Progression remains the leading cause of cancer-related mortality, yet predicting whether a primary tumor will metastasize and where it will disseminate directly from histopathology remains a fundamental challenge. Although…
When confronted with an undesired cell population, such as bacterial infections or tumors, we seek the most effective treatment, designed to eliminate the population as rapidly as possible. A common practice is to monitor the cells…
Cancer is increasingly a global health issue. Seconding cardiovascular diseases, cancers are the second biggest cause of death in the world with millions of people succumbing to the disease every year. According to the World Health…
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…
We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the…
Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of `seed-soil' relationships. Preceeding this biological mechanism is the physical process of…
A biological transition from a state N to a state T is characterized by a rearrangement of the gene expression profile in the system, quantitatively measured through the differential expression of genes. In contrast, changes in genetic…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
Due to over-metabolism, the tumour cells become hypoxic. To overcome this situation tumour cells secret several chemical substrates to attract nearby blood vessels towards it (angiogenesis). Transition from avascular to vascular tumour is…
The incidence of malignant melanoma continues to increase worldwide. This cancer can strike at any age; it is one of the leading causes of loss of life in young persons. Since this cancer is visible on the skin, it is potentially detectable…
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation…