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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…
The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis. An improved understanding of apoptosis can significantly enhance our knowledge of…
We extend the semiclassical two-step model for strong-field ionization that describes quantum interference and accounts for the Coulomb potential beyond the semiclassical perturbation theory to the hydrogen molecule. In the simplest case of…
Ionizing radiation is known to delay the cell cycle progression. In particular after particle exposure significant delays have been observed and it has been shown that the extent of delay affects the expression of damage such as chromosome…
The nanometric track-structure of energetic ion beams in biological media determines the direct physical damage to living cells, which is one of the main responsibles of their killing or inactivation during radiotherapy treatments or under…
We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
Tumor development is characterized by a compromised balance between cell life and death decision mechanisms, which are tighly regulated in normal cells. Understanding this process provides insights for developing new treatments for fighting…
Ion-induced cell killing has been reported to depend on the irradiation dose but also on the projectile parameters. In this paper we focus on two approaches developed and extensively used to predict cell survival in response to ion…
Statistical and computational methods are widely used in today's scientific studies. Using a female fertility potential in childhood cancer survivors as an example, we illustrate how these methods can be used to extract insight regarding…
Systems biology and whole-cell modelling are demanding increasingly comprehensive mathematical models of cellular biochemistry. These models require the development of simplified models of specific processes which capture essential…
In oncology, treating cancer with a beam of photons is a well established therapeutic technique, developed over 100 years, and today over 50% of cancer patients will undergo traditional X-ray radiotherapy. However, ionizing radiation…
It has been postulated that the delivery of radiotherapy at ultra-high dose rates ("FLASH") reduces normal tissue toxicities by depleting them of oxygen. The fraction of normal tissue and cancer cells surviving radiotherapy depends on dose…
We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines…
A bio-heat transfer model for biological tissues in a micro-scale and periodical settings is investigated . It is assumed that the model is a two-component system consisting of solid particles representing tissue cells and interconnected…
We present a mechanistic biomathematical model of molecular radiotherapy of thyroid disease. The general model consists of a set of differential equations describing the dynamics of different populations of thyroid cells with varying…
We present a semiclassical two-step model for strong-field ionization that accounts for path interferences of tunnel-ionized electrons in the ionic potential beyond perturbation theory. Within the framework of a classical trajectory…
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…
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, could be treated as periodic bi-domain structures, which…
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…
We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In…