Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models.

We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.

Labile haemoglobin as a glycaemic biomarker for patient-specific monitoring of diabetes: mathematical modelling approach.

Diabetes mellitus constitutes a major health problem and its clinical presentation and progression may vary considerably. A number of standardized diagnostic and monitoring tests are currently used for diabetes. They are based on measuring either plasma glucose, glycated haemoglobin or both. Their main goal is to assess the average blood glucose concentration. There are several sources of interference that can lead to discordances between measured plasma glucose and glycated haemoglobin levels. These include haemoglobinopathies, conditions associated with increased red blood cell turnover or the administration of some therapies, to name a few. Therefore, there is a need to provide new diagnostic tools for diabetes that employ clinically accessible biomarkers which, at the same time, can offer additional information allowing us to detect possible conflicting cases and to yield more reliable evaluations of the average blood glucose level concentration. We put forward a biomathematical model to describe the kinetics of two patient-specific glycaemic biomarkers to track the emergence and evolution of diabetes: glycated haemoglobin and its labile fraction. Our method incorporates erythrocyte age distribution and utilizes a large cohort of clinical data from blood tests to support its usefulness for diabetes monitoring.

Photoionization with orbital angular momentum beams.

Intense laser ionization expands Einstein's photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of an intense ultraviolet beam bearing OAM, envisaging new scenarios for quantum optics.

Isotropic versus anisotropic modeling of photorefractive solitons.

The question of the isotropic versus anisotropic modeling of incoherent spatial screening solitons in photorefractive crystals is addressed by a careful theoretical and numerical analysis. Isotropic, or local, models allow for an extended spiraling of two interacting scalar solitons, and for a prolonged propagation of vortex vector solitons, whereas anisotropic, nonlocal, models prevent such phenomena. In the context of Kukhtarev's material equations, the difference in behavior is traced to the continuity equation for the current density. We further show that neither an indefinite spiraling of two solitons nor stable propagation of vortex vector solitons is generally possible in both isotropic and anisotropic models. Such systems do not conserve angular momentum, even in the case of an isotropic change in the index of refraction.

Solitonlike beam propagation along light-induced singularity of space charge in fast photorefractive media.

We investigate light beam propagation in a fast photorefractive medium placed in an alternating electric ac field to enhance the nonlinear response. It is shown that the joint action of the optical and material nonlinearities leads to formation of a narrow singularity of the light-induced space charge at the intensity maximum and to self-trapping of the light energy near the corresponding discontinuity of the index profile. Owing to the strong saturation of the material nonlinearity, the trapped beam propagates over long distances with only a weak loss of its power.

Dipole-mode vector solitons in anisotropic nonlocal self-focusing media.

We demonstrate, theoretically and experimentally, that dipole-mode vector solitons created in biased photorefractive media possess a number of anisotropy-driven properties, such as stability of a selected orientation, wobbling, and incomplete rotation, owing to the anisotropic nonlocal response of the photorefractive non-linearity. Such features are found for higher-order (multipole) vector solitons, and they are carefully verified in an experiment.