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Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype…
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…
We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…
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…
It is proposed that cancer results from the breakdown of universal control mechanisms which developed in mutual association as part of the historical process that brought individual cells together into multi-cellular communities. By…
Clusters of circulating tumor cells (CTCs), although rare, may account for more than 95% of metastases. Inflammatory breast cancer (IBC) is a highly aggressive subtype that chiefly metastasizes via CTC clusters. Theory suggests that…
Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…
Cancer is a complex disease driven by dynamic regulatory shifts that cannot be fully captured by individual molecular profiling. We employ a data-driven approach to construct a coarse-grained dynamic network model based on hallmark…
In this paper, we describe a dataset relating to cellular and physical conditions of patients who are operated upon to remove colorectal tumours. This data provides a unique insight into immunological status at the point of tumour removal,…
Tumors are extremely heterogeneous and comprise of a number of intratumor microenvironments or sub-regions. These tumor microenvironments may interact with eac based on complex high-level relationships, which could provide important insight…
Large variability between cell lines brings a difficult optimization problem of drug selection for cancer therapy. Standard approaches use prediction of value for this purpose, corresponding e.g. to expected value of their distribution.…
According to official statistics, cancer is considered as the second leading cause of human fatalities. Among different types of cancer, brain tumor is seen as one of the deadliest forms due to its aggressive nature, heterogeneous…
The majority of cancer treatments end in failure due to Intra-Tumor Heterogeneity (ITH). ITH in cancer is represented by clonal evolution where different sub-clones compete with each other for resources under conditions of Darwinian natural…
Early detection and quantification of tumour growth would help clinicians to prescribe more accurate treatments and provide better surgical planning. However, the multifactorial and heterogeneous nature of lung tumour progression hampers…
Colorectal Cancer (CRC) is the second most common cause of cancer death in the world, ad can be identified by the location of the primary tumor in the large intestine: right and left colon, and rectum. Based on the location, CRC shows…
Recent studies have identified highly tumorigenic cells with stem cell-like characteristics in human cancers, termed cancer stem cells (CSCs). CSCs are resistant to conventional radiotherapy and chemotherapy owing to their high DNA repair…
The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and…
Distant spreading of primary lesions is modulated by the vascular dynamics of circulating tumor cells (CTCs) and their ability to establish metastatic niches. While the mechanisms regulating CTC homing in specific tissues are yet to be…
Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. That is why, it is crucial to understand metastases evolution in…
We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be…