Related papers: Structural Derivative Model for Tissue Radiation R…
The inverse geometric approach to the modeling of the growth of circular objects revealing required features, such as the velocity of the growth and fractal behavior of their contours, is presented. It enables to reproduce some of the…
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…
Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and…
We propose a dynamical model for the secondary structure of DNA, which is based on the finite stacking enthalpies used in thermodynamics calculations. In this model, the two strands can separate and the bases are allowed to rotate…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor…
We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive…
Motivated by an ongoing collaboration with clinical oncologists and pathologists, we develop a hybrid partial differential equation--ordinary differential equation (PDE--ODE) framework that captures (i) competition between susceptible and…
After injury, if regeneration can be observed in hydra, planaria and some vertebrates, regeneration is rare in mammals and particularly in humans. In this paper, we investigate the mechanisms by which biological tissues recover after…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
In this paper, a mixed-effect modeling scheme is proposed to construct a predictor for different features of cancer tumor. For this purpose, a set of features is extracted from two groups of patients with the same type of cancer but with…
A new alternate method for evaluating linear response theory is formally developed, and results are presented. This method involves the time-evolution of the system using TDHF and is constructed directly on top of a static Hartree-Fock…
The pattern of radiation energy deposition in substances at the microscopic level of lattice, molecule size, or the cell's nucleus is not uniform. The energy of radiation is transferred to the substance medium in the form of discrete,…
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…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
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…
We revisit the controversial "abscopal" effect in the context of Personalized Ultra-Fractionated Stereotactic Adaptive Radiotherapy (PULSAR). By allowing long interval between fractions, PULSAR may enhance systemic immune activation and…