Related papers: Mathematical modeling of the metastatic process
Recent advances in types and extent of medical imaging technologies has led to proliferation of multimodal quantitative imaging data in cancer. Quantitative medical imaging data refer to numerical representations derived from medical…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical…
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
This paper presents a comprehensive survey of various established mathematical models pertaining to Somitogenesis, a biological process. The study begins by revisiting and replicating the findings from prominent research papers in this…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…
The long-term efficacy of targeted therapeutics for cancer treatment can be significantly limited by the type of therapy and development of drug resistance, inter alia. Experimental studies indicate that the factors enhancing acquisition of…
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…
Computational pathology is part of precision oncology medicine. The integration of high-throughput data including genomics, transcriptomics, proteomics, metabolomics, pathomics, and radiomics into clinical practice improves cancer treatment…
Recurrence and metastasis have been regarded as two of the greatest obstacles for curing cancer. Cancer stem cell (CSC) have been found. They contribute to cancer development with the distinct feature of recurrence and resistance to the…
Atherosclerosis is one of the principle pathologies of cardiovascular disease with blood cholesterol a significant risk factor. The World Health Organisation estimates that approximately 2.5 million deaths occur annually due to the risk…
Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
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…
Research into somatic mutations in cancer cell DNA and their role in tumour growth and progression between successive stages is crucial for improving our understanding of cancer evolution. Mathematical and computer modelling can provide…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Mathematical and computational modelling in oncology has played an increasingly important role in not only understanding the impact of various approaches to treatment on tumour growth, but in optimizing dosing regimens and aiding the…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…