Related papers: Deterministic Partial Differential Equation Model …
Deterministic Lateral Displacement (DLD) devices are widely used in microfluidics for label-free, size-based separation of particles and cells, with particular promise in isolating circulating tumor cells (CTCs) for early cancer…
Stellar cores may be considered as a nuclear reactor that play important role in injecting new synthesized elements in the interstellar medium Helium burning is an important stage that contribute to the synthesis of key elements such as…
A determinant formalism in combination with \emph{ab initio} calculations proposed recently has paved a new way for simulating and interpreting x-ray excitation spectra. The new method systematically takes into account many-electron effects…
Starting from the radiative transfer equation and its usual boundary conditions, the objective of this work is to design Monte Carlo algorithms estimating the specific intensity spatial and angular derivatives as well as its geometric…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…
This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma…
In this paper we study a problem in radiotherapy treatment planning, where the evolution of the radiation field is governed by a deterministic Boltzmann transport equation. We show existence, uniqueness and regularity of solutions to an…
The paper presents alternative statistical methods for biological dosimetry, such as the Bayesian and Monte Carlo method. The classical Gaussian and robust Bayesian fit algorithms for the linear, linear-quadratic as well as saturated and…
We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of…
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…
The $\mu$Dose system was developed to allow the measurement of environmental levels of natural radioactive isotopes. The system records $\alpha$ and $\beta$ particles along with four decay pairs arising from subsequent decays of…
Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given…
Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…
We present a novel application of Tensor Network methods in cancer treatment as a potential tool to solve the dose optimization problem in radiotherapy. In particular, the Intensity-Modulated Radiation Therapy (IMRT) technique - that allows…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded as a level set…