CОВРЕМЕННОЕ СОСТОЯНИЕ ТЕРАПИИ БЫСТРЫМИ НЕЙТРОНАМИ

.В первой части статьи представлен анализ возможностей клинического применения терапии быстрыми нейтронами (ТБН), технические и статистические данные, а также биологические свойства быстрых нейтронов по сравнению с другими методами лучевой терапии. Рассматривается ситуация с клиническим применением бор-нейтрон захватной терапии (БНЗТ). Вторая часть статьи посвящена опыту применения ТБН на исследовательских реакторах FRM I и FRM II Технического университета Мюнхена в Гархинге (Германия)

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Analysis of Oscillations and Defect Measures for the Quasineutral Limit in Plasma Physics

We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in $3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly converges towards an incompressible velocity vector field $u$ and the density fluctuation $\rho^{\lambda}-1$ weakly converges to zero. In general the limit velocity field cannot be expected to satisfy the incompressible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self interacting wave packets. We shall provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover we will be able to identify an explicit pseudo parabolic pde satisfied by the leading correctors terms. Our results include all the previous results in literature, in particular we show that the formal limit holds rigorously in the case of well prepared data.Comment: Submitted pape

First steps towards a fast-neutron therapy planning program

<p>Abstract</p> <p>Background</p> <p>The Monte Carlo code GEANT4 was used to implement first steps towards a treatment planning program for fast-neutron therapy at the FRM II research reactor in Garching, Germany. Depth dose curves were calculated inside a water phantom using measured primary neutron and simulated primary photon spectra and compared with depth dose curves measured earlier. The calculations were performed with GEANT4 in two different ways, simulating a simple box geometry and splitting this box into millions of small voxels (this was done to validate the voxelisation procedure that was also used to voxelise the human body).</p> <p>Results</p> <p>In both cases, the dose distributions were very similar to those measured in the water phantom, up to a depth of 30 cm. In order to model the situation of patients treated at the FRM II MEDAPP therapy beamline for salivary gland tumors, a human voxel phantom was implemented in GEANT4 and irradiated with the implemented MEDAPP neutron and photon spectra. The 3D dose distribution calculated inside the head of the phantom was similar to the depth dose curves in the water phantom, with some differences that are explained by differences in elementary composition. The lateral dose distribution was studied at various depths. The calculated cumulative dose volume histograms for the voxel phantom show the exposure of organs at risk surrounding the tumor.</p> <p>Conclusions</p> <p>In order to minimize the dose to healthy tissue, a conformal treatment is necessary. This can only be accomplished with the help of an advanced treatment planning system like the one developed here. Although all calculations were done for absorbed dose only, any biological dose weighting can be implemented easily, to take into account the increased radiobiological effectiveness of neutrons compared to photons.</p

Efficacy and complications of neurosurgical treatment of acromegaly

The aim of the study was to evaluate the frequency of occurrence of pituitary failure following neurosurgery and the efficacy of transsphenoidal tumour resection in acromegalic patients. We retrospectively evaluated 85 patients (60 female and 25 male), of mean age 43.9 ± 13.2 years, treated by transsphenoidal neurosurgery. Macroadenoma and microadenoma of pituitary were found in 66 (77.6%) and 19 (22.4%) of these patients, respectively. Criteria of cure following neurosurgery were: basal GH < 2.5 μg/l, GH at 120 min in OGTT < 1.0 μg/l and serum concentration of IGF-1 within normal ranges for age and sex. After surgery 32 patients (37.6%) were cured and 53 patients (62.4%) required somatostatin analogue treatment. In patients cured by surgery, lower levels of basal GH (P < 0.05), IGF-1 (P < 0.001), GH at 120 min in OGTT and smaller size of pituitary tumour (P < 0.05) were found at diagnosis, as compared to patients in whom surgery was unsuccessful. Significant correlation between basal serum level of GH at diagnosis and size of pituitary tumour was found (P < 0.001). Invasive tumours were found in 45 of 53 (84.9%) patients not cured and in only 8 of 32 (25.0%) patients cured (P < 0.001). Impaired function of pituitary anterior lobe after surgery was observed in 30% and 4% of patients with macro- and microadenoma, respectively (P < 0.05). The efficacy of neurosurgery is affected by concentration of basal serum GH and IGF-1, GH at 120 min in OGTT, tumour size and invasiveness. Hypopituitarism after surgery is more frequent in patients with macroadenoma. Pituitary insufficiency, as a consequence of surgery, was found in 21% of patients with normal pituitary function prior to operation

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from the knowledge of the present mass density field, the latter being inferred from the 3D distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales -- a few Mpc -- where multi-streaming becomes significant. Above 6 Mpc/h we propose and implement an effective Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge (1781). After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than cubic time complexity in N and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60% of exactly reconstructed points. We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge-Ampere equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. Self-contained discussion of relevant notions and techniques is provided.Comment: 26 pages, 14 figures; accepted to MNRAS. Version 2: numerous minour clarifications in the text, additional material on the history of the Monge-Ampere equation, improved description of the auction algorithm, updated bibliography. Version 3: several misprints correcte

Oxidant-NO dependent gene regulation in dogs with type I diabetes: impact on cardiac function and metabolism

<p>Abstract</p> <p>Background</p> <p>The mechanisms responsible for the cardiovascular mortality in type I diabetes (DM) have not been defined completely. We have shown in conscious dogs with DM that: <it>1</it>) baseline coronary blood flow (CBF) was significantly decreased, <it>2</it>) endothelium-dependent (ACh) coronary vasodilation was impaired, and <it>3</it>) reflex cholinergic NO-dependent coronary vasodilation was selectively depressed. The most likely mechanism responsible for the depressed reflex cholinergic NO-dependent coronary vasodilation was the decreased bioactivity of NO from the vascular endothelium. The goal of this study was to investigate changes in cardiac gene expression in a canine model of alloxan-induced type 1 diabetes.</p> <p>Methods</p> <p>Mongrel dogs were chronically instrumented and the dogs were divided into two groups: one normal and the other diabetic. In the diabetic group, the dogs were injected with alloxan monohydrate (40-60 mg/kg iv) over 1 min. The global changes in cardiac gene expression in dogs with alloxan-induced diabetes were studied using Affymetrix Canine Array. Cardiac RNA was extracted from the control and DM (n = 4).</p> <p>Results</p> <p>The array data revealed that 797 genes were differentially expressed (P < 0.01; fold change of at least ±2). 150 genes were expressed at significantly greater levels in diabetic dogs and 647 were significantly reduced. There was no change in eNOS mRNA. There was up regulation of some components of the NADPH oxidase subunits (gp91 by 2.2 fold, P < 0.03), and down-regulation of SOD1 (3 fold, P < 0.001) and decrease (4 - 40 fold) in a large number of genes encoding mitochondrial enzymes. In addition, there was down-regulation of Ca²⁺cycling genes (ryanodine receptor; SERCA2 Calcium ATPase), structural proteins (actin alpha). Of particular interests are genes involved in glutathione metabolism (glutathione peroxidase 1, glutathione reductase and glutathione S-transferase), which were markedly down regulated.</p> <p>Conclusion</p> <p>our findings suggest that type I diabetes might have a direct effect on the heart by impairing NO bioavailability through oxidative stress and perhaps lipid peroxidases.</p

A user's guide to optimal transport

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below