Related papers: Deterministic Partial Differential Equation Model …
We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological…
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…
Deterministic models for radiation transport describe the density of radiation particles moving through a background material. In radiation therapy applications, the phase space of this density is composed of energy, spatial position and…
We consider the problem of estimating a dose-response curve. Continuous treatments arise often in practice, e.g. in the form of time spent on an operation, distance traveled to a location or dosage of a drug. Letting $A$ denote a continuous…
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.…
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting…
Electroporation is a very useful tool for drug delivery into various diseased tissues of the human body. This technique helps to improve the clinical treatment by transferring drugs into the targeted cells rapidly. In electroporation, drug…
In radiotherapy, the dose-volume histogram (DVH) curve is an important means of evaluating the clinical feasibility of tumor control and side effects in normal organs against actual treatment. Fractionation, distributing the amounts of…
In order to study 4-body atomic collisions such as excitation-ionization, transfer with target excitation, and double electron capture, the calculation of a nine-dimensional numerical integral is often required. This calculation can become…
In this paper, we consider a mathematical model for the invasion of host tissue by tumour cells in a $d$-dimensional bounded domain, $d\leq 3$. This model consists of a system of differential equations describing the evolution of cancer…
The new statistical approach for calculation of radiation processes with heavy multielectron ions in plasma is developed. The method consists in consideration of atomic structure as a condensed medium, characterized by the spectrum of…
Cancer is a primary cause of morbidity and mortality worldwide. The radiotherapy plays a more and more important role in cancer treatment. In the radiotherapy, the dose distribution maps in patient need to be calculated and evaluated for…
Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely…
Personalized cancer treatments based on the molecular profile of a patient's tumor are an emerging and exciting class of treatments in oncology. As genomic tumor profiling is becoming more common, targeted treatments to specific molecular…
A model for beam customization with collimators and a range-compensating filter based on the phase-space theory for beam transport is presented for dose distribution calculation in treatment planning of radiotherapy with protons and heavier…
This work addresses computing techniques for dose calculations in treatment planning with proton and ion beams, based on an efficient kernel-convolution method referred to as grid-dose spreading (GDS) and accurate heterogeneity-correction…
Differential cross sections for electromagnetic dissociation in nucleus-nucleus collisions are calculated. The kinetic energy distribution is parameterized with a Boltzmann distribution and the angular distribution is assumed isotropic in…
The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments…
Accurate dose calculation is vitally important for proton therapy. Pencil beam (PB) model-based dose calculation is fast but inaccurate due to the approximation when dealing with inhomogeneities. Monte Carlo (MC) dose calculation is the…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…