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In this paper, a new stochastic framework to determine optimal combination therapies in colon cancer-induced immune response is presented. The dynamics of colon cancer is described through an It\"o stochastic process, whose probability…
The number of new cancer cases is expected to increase by about 50% in the next 20 years, and the need for chemotherapy treatments will increase accordingly. Chemotherapy treatments are usually performed in outpatient cancer centers where…
Background: Gliomas are the most common brain tumors, which vary from low to high-grade. Despite the improvements in imaging techniques in the last decade, all parts of the tumor are not visible in these images, due to having a threshold of…
One primary goal of precision medicine is to estimate the individualized treatment rules (ITRs) that optimize patients' health outcomes based on individual characteristics. Health studies with multiple treatments are commonly seen in…
This paper introduces a method for estimating the shape and location of an embedded tumor. The approach utilizes shape optimization techniques, applying the coupled complex boundary method. By rewriting the problem -- characterized by a…
The development of mathematical models of cancer informed by time-resolved measurements has enabled personalised predictions of tumour growth and treatment response. However, frequent cancer monitoring is rare, and many tumours are treated…
Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients and become fatal after a few years. Current clinical handling includes surgery as first line treatment. Cytotoxic therapies (radiotherapy RT or…
In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak…
In cancer research, the role of the extracellular matrix (ECM) and its associated matrix-degrading enzyme (MDE) has been a significant area of focus. This study presents a numerical algorithm designed to simulate a previously established…
Protein/Peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and highthroughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having…
A dynamical system model for tumor -- immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. A characteristic…
Fluence map optimization for intensity-modulated radiation therapy planning can be formulated as a large-scale inverse problem with competing objectives and constraints associated with the tumors and organs-at-risk. Unfortunately,…
Tumor development is an evolutionary process in which a heterogeneous population of cells with differential growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to…
Radiotherapy is used to treat cancer patients by damaging DNA of tumor cells using ionizing radiation. Photons are the most widely used radiation type for therapy, having been put into use soon after the first discovery of X-rays in 1895.…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…
We formulate and analyze a mathematical model describing immune response to avascular tumor under the influence of immunotherapy and chemotherapy and their combinations as well as vaccine treatments. The effect of vaccine therapy is…
Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for…
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…
Glioblastoma, the most aggressive primary brain tumor, poses a severe clinical challenge due to its diffuse microscopic infiltration, which remains largely undetected on standard MRI. As a result, current radiotherapy planning employs a…
Immunotherapy emerges as promising approach for treating cancer. Encouraging findings have validated the efficacy of immunotherapy medications in addressing tumors, resulting in prolonged survival rates and notable reductions in toxicity…