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Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than…
The mathematical modeling of tumor growth has a long history, and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using mathematical tools from statistical…
With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high…
The present work introduces a rigorous stochastic model, named Generalized Stochastic Microdosimetric Model (GSM2), to describe biological damage induced by ionizing radiation. Starting from microdosimetric spectra of energy deposition in…
Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
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…
Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…
Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease.…
Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are…
Computational models and simulations are not just appealing because of their intrinsic characteristics across spatiotemporal scales, scalability, and predictive power, but also because the set of problems in cancer biomedicine that can be…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
In concurrent chemoradiotherapy, chemotherapeutic agents are administered during the course of radiotherapy to enhance the primary tumor control. However, that often comes at the expense of increased risk of normal-tissue complications. The…
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…
We present a novel application of Tensor Network methods in cancer treatment as a potential tool to solve the dose optimization problem in radiotherapy. In particular, the Intensity-Modulated Radiation Therapy (IMRT) technique - that allows…
Cancer is one of the most common diseases worldwide, posing a serious threat to human health and leading to the deaths of a large number of people. It was observed during the drug administration in chemotherapy that immune cells, cancer…
The interplay between tumor cells and macrophages plays a central regulatory role in cancer progression. In this study, we developed a mathematical model that incorporates tumor cells, M1 type macrophages, M2 type macrophages and an M3 type…
Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}.…
In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…
Markov Decision Processes and Dynamic Treatment Regimes have grown increasingly popular in the treatment of diseases, including cancer. However, cancer treatment often impacts quality of life drastically, and people often fail to take…