Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age. The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. We then formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size: cells consume oxygen which in turns fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. This allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy

Calculation of Exclusive Cross Sections with the Lorentz Integral Transform Method

The longitudinal structure function of the d(e,e'p) exclusive cross section is calculated with the Lorentz integral transform method. In this approach final state interaction is fully taken into account, but without using a final state wave function. Cross sections are obtained via the inversion of the transform. It is shown that the inversion results are very stable. The comparison to a conventional calculation with an explicit np final state wave function shows that the obtained results are also very precise. Thus the method opens up the possibility to obtain exclusive cross sections for reactions with more than two particles, where it is generally very difficult to calculate the exact final state wave function.Comment: LaTeX, 15 pages, 8 ps figure

Semantic variation operators for multidimensional genetic programming

Multidimensional genetic programming represents candidate solutions as sets of programs, and thereby provides an interesting framework for exploiting building block identification. Towards this goal, we investigate the use of machine learning as a way to bias which components of programs are promoted, and propose two semantic operators to choose where useful building blocks are placed during crossover. A forward stagewise crossover operator we propose leads to significant improvements on a set of regression problems, and produces state-of-the-art results in a large benchmark study. We discuss this architecture and others in terms of their propensity for allowing heuristic search to utilize information during the evolutionary process. Finally, we look at the collinearity and complexity of the data representations that result from these architectures, with a view towards disentangling factors of variation in application.Comment: 9 pages, 8 figures, GECCO 201

On the apparent absence of broad iron lines in Seyfert galaxies

We present an analysis of XMM-Newton observations of eleven Seyfert galaxies that appear to be missing a broad iron K alpha line. These objects represent a challenge to the established paradigm for active galactic nuclei, where a relatively cold accretion disc feeds the central black hole. In that paradigm, X-ray illumination of the accretion disc should lead to continuum and fluorescence emission from iron which is broadened and shifted by relativistic effects close the hole. We extend the work of Nandra et al. (2007), who found no evidence for such a component in an earlier analysis of these objects, by testing a variety of more complex relativistic reflection models. Specifically, we consider the possibility that the disc is highly ionised, and/or that the the reflection is heavily blurred by strong relativistic effects in a Kerr geometry. We find that in 8/11 of the observations with no apparent broad iron line, the fit is significantly improved when an ionised or strongly blurred reflector is included, and that all 11 observations allow for such a component. The disc inclinations are found generally to be around 60 degrees, which when combined with a steep emissivity profile results in strong relativistic blurring of the reflection, rendering the K alpha line difficult to distinguish from the underlying continuum. Nevertheless, relativistic reflection does appear to be present, and the strength of the smeared reflection is similar to that expected from a flat disc illuminated by a point source. Such blurred reflection and the associated steep radial emissivity profiles are consistent with the gravitational light bending of the continuum photons close to the black hole.Comment: 9 pages, 2 figures. Accepted for publication in MNRA

Primary photodynamic therapy with verteporfin for pigmented posterior pole cT1a choroidal melanoma: a 3-year retrospective analysis

AIMS: To investigate the outcomes of primary photodynamic therapy (PDT) for pigmented posterior pole cT1a choroidal melanoma. METHODS: Retrospective interventional consecutive case series of 26 patients (26 eyes) with pigmented posterior pole cT1a choroidal melanoma, who were treated with 3 sessions of PDT and followed-up thereafter. RESULTS: Included were 11 males and 15 females that presented at a median age of 66 years (mean: 64) with transformed naevi (n=11) or suspicious lesions (n=15) with ≥3 risk factors for growth, with lipofuscin in all. In all cases, diagnosis was clinically based (no tissue biopsy). Tumour control was achieved in 16 (62%) patients in a median follow-up time of 29 months (mean: 27). Ten patients failed treatment by form of radial expansion, diagnosed in a median time of 13 months (mean: 12) from last treatment. By Kaplan-Meier analysis, success rate after 1, 2 and 3 years was 85%, 59% and 51%, respectively. On statistical analysis, number of suspicious features was found to be the only risk factor predicting failure (P=0.046). One patient developed macula-sparing branch retinal artery occlusion after treatment. Following PDT, subretinal fluid resolved in all cases and visual acuity significantly improved in all treatment-success cases (P=0.043). There were no cases of metastatic spread. CONCLUSION: Primary PDT resulted in tumour regression of small, pigmented choroidal melanoma in 62% after a mean of 27 months. Treatment was more effective in tumours with three or less risk factors for growth, and resulted with fluid elimination and significant improvement in vision in treatment-success cases

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the Chemical Master Equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provide the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species are order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.Comment: 33 pages, 9 figures, accepted for publication in the Journal of Chemical Physic

On the critical amplitude in oscillating rolling element bearings

Small oscillating amplitudes (~0. 1°) and larger (> 1°) can both lead to wear, w hich complicates the evaluation of the operating conditions. In this work, a simulation model is used to discuss critical amplitudes. The parametric study, which includes 125 simulations, shows the effect of load and coefficient of friction on the frictional work density for amplitudes ranging from 0.1 to 2.5°. The study concludes that the frictional work density increases with the oscillating amplitude up to a certain point, where it becomes almost constant in relation to the amplitude. This point is reached when the amplitude is so large that a continuous overlapping of the contact zone no longer occurs. It is precisely this point that marks the critical oscillation amplitude

Imagenología por resonancia magnética por detección remota: guías de ondas

En la presente tesis se muestra la posibilidad de emplear guías de ondas, a campos magnéticos principales menores a 7 Tesla, como medio para transferir la información proveniente de la relajación de los espines nucleares en estudios de Imagenología por Resonancia Magnética (IRM), y ser detectadas a una distancia superior a 50cm de dónde se generaron. De igual forma se plantea un esquema novedoso que muestra que es posible generar imágenes con la antena de recepción fuera del imán empleando una guía de ondas de placas paralelas y obtener señales más allá de 150cm. Se muestra que la introducción de este nuevo hardware no afecta el comportamiento normal de un sistema de IRM clínico y que la calidad de la imagen es comparable con la forma de adquisición convencional. El estado del arte indica una frecuencia mínima de 300MHz para una guía cilíndrica con un diámetro de por lo menos 58cm, lo que se obtiene únicamente con sistemas de IRM de cuerpo entero a 7Tesla, que se emplean solamente en investigación. Nuestro diseño no comparte la problemática de la frecuencia de corte, y con ello se plantea la posibilidad de experimentos multinucleares dentro de la misma guía de ondas. Utilizando las guías de ondas en IRM se puede generar un campo magnético homogéneo sobre la muestra. En este trabajo mostramos la homogeneidad del campo magnético obtenida por medio de una adquisición con la guía de ondas de placas paralelas. Se construyeron dos prototipos de guías de ondas, el primero se utilizó para demostrar los conceptos mencionados anteriormente y tenía una longitud de 200cm. El segundo tuvo la finalidad de obtener imágenes in vivo. Se obtuvieron imágenes de una pierna de un voluntario; este prototipo tuvo una longitud de 60cm. Por medio del cálculo de la tasa de absorción específica (SAR, del Inglés Specific Absorption Rate) mostramos que es seguro el empleo de la guía de ondas de palcas paralelas en estudios de imagenología de extremidades

Antena volumétrica tipo magnetrón para 7 Tesla

El diseño de la antena magnetrón volumétrica fue concebido en base a la teoría desarrollada por P. Mansfield en 1990 de la ‘High Frequency Cavity Resonator Designs for NMR’ que propone una antena de volumen sintonizada sin capacitores, que no ha sido construida; y la antena desarrollada por A. O. Rodríguez en 2006 ‘Magnetron Surface Coil for Brain MR Imaging’. De igual forma se tomaron algunas consideraciones de la antena de volumen ‘Jaula de Pájaro’. Dentro del trabajo se encontró, al simular el campo magnético generado por la antena a , y al variar el número de cavidades sobre las placas terminales que se mantenía un campo más homogéneo con 6 cavidades. El primer diseño presentado es la antena polarizada linealmente, que a pesar de que obtuvo imágenes el consumo de potencia excedía los límites de seguridad de los amplificadores del sistema. Al polarizar la antena en cuadratura obtuvimos una considerable disminución en el consumo de potencia y con la ayuda de un circuito de desacople pudimos optimizar la sintonización de los canales. Debido al diseño de la capacitancia distribuida por medio de las cavidades resonantes, se logró construir una antena que sólo consta de dos capacitores fijos, que balancean el circuito de ajuste de impedancia y sintonización. Se obtuvieron imágenes de un fantoma de agua destilada y se compararon con imágenes obtenidas con una antena jaula de pájaro con el mismo número de piernas que la magnetrón volumétrica y con los mismos parámetro de adquisición. Se mostró que la antena desarrollada mostraba una notable mejoría en la intensidad de señal recibida y en la homogeneidad del campo producido. Como primera aproximación de la utilización de la antena desarrollada obtuvimos imágenes de rata in vivo, en las cuales se observa una buena resolución que hace a esta antena un buen candidato para imagenología de roedores