Related papers: From Radiation Dose to Cellular Dynamics: A Discre…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
The move towards personalized treatment and digital twins for cancer therapy requires a complete understanding of the mathematical models upon which these optimized simulation-based strategies are formulated. This study investigates the…
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…
Numerical simulations are performed on a stochastic model based on Monte Carlo damage simulation process and Markov Chain Monte Carlo techniques to investigate the formation and evaluation of isolated and multiple DNA damage and cellular…
Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects such as DNA mutation or bystander…
Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
In multi-stage radiotherapy, a patient is treated in several stages separated by weeks or months. This regimen has been motivated mostly by radiobiological considerations, but also provides an approach to reduce normal tissue dose by…
Cancer is a disease driven by random DNA mutations and the interaction of many complex phenomena. To improve the understanding and ultimately find more effective treatments, researchers leverage computer simulations mimicking the tumor…
Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple,…
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.…
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…
It has long been known that radiation biology plays an important role and it is necessary for radiotherapy treatments. The radiation effects on normal and malignant tissues after exposure range from a femtosecond to months and years…
Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…
Radiation therapy is a critical component of cancer treatment. However, the delivery of radiation poses inherent challenges, particularly in minimizing radiation exposure to healthy organs surrounding the tumor site. One significant…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
Radiation therapy has remained as one of the main cancer treatment modalities and a highly cost-effective single modality treatment of cancer care. Typical regimens for fractionated external beam radiotherapy comprise a constant dose…
Electroporation is increasingly used as a percutaneous ablation technique for tumours located near vital structures. Although effective, tumour regrowth may still occur. At the same time, in vitro studies on cell monolayers have shown that…
A mathematical model for time development of metastases and their distribution in size and carrying capacity is presented. The model is used to theoretically investigate anti-cancer therapies such as surgery and chemical treatments…
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…