Hypoxic Cell Waves around Necrotic Cores in Glioblastoma: A Biomathematical Model and its Therapeutic Implications

Glioblastoma is a rapidly evolving high-grade astrocytoma that is distinguished pathologically from lower grade gliomas by the presence of necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded by hypercellular regions known as "pseudopalisades" originated by local tumor vessel occlusions that induce collective cellular migration events. This leads to the formation of waves of tumor cells actively migrating away from central hypoxia. We present a mathematical model that incorporates the interplay among two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our simulations reveal the formation of a traveling wave of tumor cells that reproduces the observed histologic patterns of pseudopalisades. Additional simulations of the model equations show that preventing the collapse of tumor microvessels leads to slower glioma invasion, a fact that might be exploited for therapeutic purposes.Comment: 29 pages, 9 figure

Driving defect modes of Bose-Einstein condensates in optical lattices

We present an approximate analytical theory and direct numerical computation of defect modes of a Bose-Einstein condensate loaded in an optical lattice and subject to an additional localized (defect) potential. Some of the modes are found to be remarkably stable and can be driven along the lattice by means of a defect moving following a step-like function defined by the period of Josephson oscillations and the macroscopic stability of the atoms.Comment: 4 pages, 5 figure

Estudio fitoquímico de especies de Eupatorium : síntesis de dimeros del Precoceno II

Del Eupatorium Eternbergianum se han aislado 2-hidroxi-4 5-dimetoxibenzaldehido pammaradienol acetato de dammaradienol spathulenol 12-hidroxi-euparina persicogenina sakuranetina los nuevos productos eupatarona y sternbina (5 3 4 - t rihidroxi-7-metoxi-flavanona). Se han asignado las posiciones de resonancias de los carbonos en los espectros de rmn del dammaradienol de su acetato y de la da mmaradienona. Se aislo tambien el precoceno-ii que posee gran actividad antialatotrodica. es el compuesto más abundante del e. ferrerae se hanobtenido tres nuevos sesquiterpenos: los angelato tiglato e isobutirato de iso-2 3-desoxo-hilliardinol y los ya conocidos epoxi-decompostina acetato de taraxerol friedelina y epifrizoelinol. Se ha estudiado la dimerizacion del precoceno-ii utilizando gel de suice impregnada con no sub 3 ag o con cl sub 3 fe y se ha determinado la estructura de los dimeros obtenidos. se aislaron y estudiaron los productos del fotolisis de uno de estos dimeros

CAR T cells for T-cell leukemias: Insights from mathematical models

Immunotherapy has the potential to change the way all cancer types are treated and cured. Cancer immunotherapies use elements of the patient immune system to attack tumor cells. One of the most successful types of immunotherapy is CAR-T cells. This treatment works by extracting patient's T-cells and adding to them an antigen receptor allowing tumor cells to be recognized and targeted. These new cells are called CAR-T cells and are re-infused back into the patient after expansion in-vitro. This approach has been successfully used to treat B-cell malignancies (B-cell leukemias and lymphomas). However, its application to the treatment of T-cell leukemias faces several problems. One of these is fratricide, since the CAR-T cells target both tumor and other CAR-T cells. This leads to nonlinear dynamical phenomena amenable to mathematical modeling. In this paper we construct a mathematical model describing the competition of CAR-T, tumor and normal T-cells and studied some basic properties of the model and its practical implications. Specifically, we found that the model reproduced the observed difficulties for in-vitro expansion of the therapeutic cells found in the laboratory. The mathematical model predicted that CAR-T cell expansion in the patient would be possible due to the initial presence of a large number of targets. We also show that, in the context of our mathematical approach, CAR-T cells could control tumor growth but not eradicate the disease

Dissipative solitons which cannot be trapped

In this paper we study the behavior of dissipative solitons in systems with high order nonlinear dissipation and show how they cannot survive under the effect of trapping potentials both of rigid wall type or asymptotically increasing ones. This provides an striking example of a soliton which cannot be trapped and only survives to the action of a weak potential