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Determining the extent to which a patient is benefiting from cancer therapy is challenging. Criteria for quantifying the extent of "tumor response" observed within a few cycles of treatment have been established for various types of solid…
We present a multiagent-based model that captures the interactions between different types of cells with their microenvironment, and enables the analysis of the emergent global behavior during tissue regeneration and tumor development.…
Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with…
In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes involved in tumor growth, such as oxygen diffusion, carcinogen penetration, and…
Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual…
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system…
Targeted therapeutic interventions utilizing low-inten\-sity ultrasound (LIUS) exhibit substantial potential for hindering the proliferation of cancer stem cells. This investigation introduces a multiscale model and computational framework…
We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the…
Although there are various types of cancer treatments, none of these currently take into account the effect of ageing of the immune system and hence altered responses to cancer. Recent studies have shown that in vitro stimulation of T cells…
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…
CAR-T cell therapies have demonstrated significant success in treating B-cell leukemia in children and young adults. However, their effectiveness in treating B-cell lymphomas has been limited. Unlike leukemia, lymphoma often manifests as…
We use a stochastic birth-death model for a population of cells to estimate the normal tissue complication probability (NTCP) under a particular radiotherapy protocol. We specifically allow for interaction between cells, via a nonlinear…
Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical…
We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is…
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer…
Inhibiting a signalling pathway concerns controlling the cellular processes of a cancer cell's viability, cell division, and death. Assay protocols created to see if the molecular structures of the drugs being tested have the desired…
Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer…
Imaging demonstrates that preclinical and human tumors are heterogeneous, i.e. a single tumor can exhibit multiple regions that behave differently during both normal development and also in response to treatment. The large variations…