A new PET prototype for proton therapy: comparison of data and Monte Carlo simulations

Ion beam therapy is a valuable method for the treatment of deep-seated and radio-resistant tumors thanks to the favorable depth-dose distribution characterized by the Bragg peak. Hadrontherapy facilities take advantage of the specific ion range, resulting in a highly conformal dose in the target volume, while the dose in critical organs is reduced as compared to photon therapy. The necessity to monitor the delivery precision, i.e. the ion range, is unquestionable, thus different approaches have been investigated, such as the detection of prompt photons or annihilation photons of positron emitter nuclei created during the therapeutic treatment. Based on the measurement of the induced β+ activity, our group has developed various in-beam PET prototypes: the one under test is composed by two planar detector heads, each one consisting of four modules with a total active area of 10 × 10 cm2. A single detector module is made of a LYSO crystal matrix coupled to a position sensitive photomultiplier and is read-out by dedicated frontend electronics. A preliminary data taking was performed at the Italian National Centre for Oncological Hadron Therapy (CNAO, Pavia), using proton beams in the energy range of 93–112 MeV impinging on a plastic phantom. The measured activity profiles are presented and compared with the simulated ones based on the Monte Carlo FLUKA package.

Análisis y diseño de multiplicadores y mezcladores mediante el método de Monte Carlo en la banda de THz = Analysis and design of multipliers and mixers via Monte Carlo modelling at THz bands

La región del espectro electromagnético comprendida entre 100 GHz y 10 THz alberga una gran variedad de aplicaciones en campos tan dispares como la radioastronomía, espectroscopíamolecular, medicina, seguridad, radar, etc. Los principales inconvenientes en el desarrollo de estas aplicaciones son los altos costes de producción de los sistemas trabajando a estas frecuencias, su costoso mantenimiento, gran volumen y baja fiabilidad. Entre las diferentes tecnologías a frecuencias de THz, la tecnología de los diodos Schottky juega un importante papel debido a su madurez y a la sencillez de estos dispositivos. Además, los diodos Schottky pueden operar tanto a temperatura ambiente como a temperaturas criogénicas, con altas eficiencias cuando se usan como multiplicadores y con moderadas temperaturas de ruido en mezcladores. El principal objetivo de esta tesis doctoral es analizar los fenómenos físicos responsables de las características eléctricas y del ruido en los diodos Schottky, así como analizar y diseñar circuitos multiplicadores y mezcladores en bandas milimétricas y submilimétricas. La primera parte de la tesis presenta un análisis de los fenómenos físicos que limitan el comportamiento de los diodos Schottky de GaAs y GaN y de las características del espectro de ruido de estos dispositivos. Para llevar a cabo este análisis, un modelo del diodo basado en la técnica de Monte Carlo se ha considerado como referencia debido a la elevada precisión y fiabilidad de este modelo. Además, el modelo de Monte Carlo permite calcular directamente el espectro de ruido de los diodos sin necesidad de utilizar ningún modelo analítico o empírico. Se han analizado fenómenos físicos como saturación de la velocidad, inercia de los portadores, dependencia de la movilidad electrónica con la longitud de la epicapa, resonancias del plasma y efectos no locales y no estacionarios. También se ha presentado un completo análisis del espectro de ruido para diodos Schottky de GaAs y GaN operando tanto en condiciones estáticas como variables con el tiempo. Los resultados obtenidos en esta parte de la tesis contribuyen a mejorar la comprensión de la respuesta eléctrica y del ruido de los diodos Schottky en condiciones de altas frecuencias y/o altos campos eléctricos. También, estos resultados han ayudado a determinar las limitaciones de modelos numéricos y analíticos usados en el análisis de la respuesta eléctrica y del ruido electrónico en los diodos Schottky. La segunda parte de la tesis está dedicada al análisis de multiplicadores y mezcladores mediante una herramienta de simulación de circuitos basada en la técnica de balance armónico. Diferentes modelos basados en circuitos equivalentes del dispositivo, en las ecuaciones de arrastre-difusión y en la técnica de Monte Carlo se han considerado en este análisis. El modelo de Monte Carlo acoplado a la técnica de balance armónico se ha usado como referencia para evaluar las limitaciones y el rango de validez de modelos basados en circuitos equivalentes y en las ecuaciones de arrastredifusión para el diseño de circuitos multiplicadores y mezcladores. Una notable característica de esta herramienta de simulación es que permite diseñar circuitos Schottky teniendo en cuenta tanto la respuesta eléctrica como el ruido generado en los dispositivos. Los resultados de las simulaciones presentados en esta parte de la tesis, tanto paramultiplicadores comomezcladores, se han comparado con resultados experimentales publicados en la literatura. El simulador que integra el modelo de Monte Carlo con la técnica de balance armónico permite analizar y diseñar circuitos a frecuencias superiores a 1 THz. ABSTRACT The terahertz region of the electromagnetic spectrum(100 GHz-10 THz) presents a wide range of applications such as radio-astronomy, molecular spectroscopy, medicine, security and radar, among others. The main obstacles for the development of these applications are the high production cost of the systems working at these frequencies, highmaintenance, high volume and low reliability. Among the different THz technologies, Schottky technology plays an important rule due to its maturity and the inherent simplicity of these devices. Besides, Schottky diodes can operate at both room and cryogenic temperatures, with high efficiency in multipliers and moderate noise temperature in mixers. This PhD. thesis is mainly concerned with the analysis of the physical processes responsible for the characteristics of the electrical response and noise of Schottky diodes, as well as the analysis and design of frequency multipliers and mixers at millimeter and submillimeter wavelengths. The first part of the thesis deals with the analysis of the physical phenomena limiting the electrical performance of GaAs and GaN Schottky diodes and their noise performance. To carry out this analysis, a Monte Carlo model of the diode has been used as a reference due to the high accuracy and reliability of this diode model at millimeter and submillimter wavelengths. Besides, the Monte Carlo model provides a direct description of the noise spectra of the devices without the necessity of any additional analytical or empirical model. Physical phenomena like velocity saturation, carrier inertia, dependence of the electron mobility on the epilayer length, plasma resonance and nonlocal effects in time and space have been analysed. Also, a complete analysis of the current noise spectra of GaAs and GaN Schottky diodes operating under static and time varying conditions is presented in this part of the thesis. The obtained results provide a better understanding of the electrical and the noise responses of Schottky diodes under high frequency and/or high electric field conditions. Also these results have helped to determine the limitations of numerical and analytical models used in the analysis of the electrical and the noise responses of these devices. The second part of the thesis is devoted to the analysis of frequency multipliers and mixers by means of an in-house circuit simulation tool based on the harmonic balance technique. Different lumped equivalent circuits, drift-diffusion and Monte Carlo models have been considered in this analysis. The Monte Carlo model coupled to the harmonic balance technique has been used as a reference to evaluate the limitations and range of validity of lumped equivalent circuit and driftdiffusion models for the design of frequency multipliers and mixers. A remarkable feature of this reference simulation tool is that it enables the design of Schottky circuits from both electrical and noise considerations. The simulation results presented in this part of the thesis for both multipliers and mixers have been compared with measured results available in the literature. In addition, the Monte Carlo simulation tool allows the analysis and design of circuits above 1 THz.

Feasibility assessment of the interactive use of a Monte Carlo algorithm in treatment planning for intraoperative electron radiation therapy

This work analysed the feasibility of using a fast, customized Monte Carlo (MC) method to perform accurate computation of dose distributions during pre- and intraplanning of intraoperative electron radiation therapy (IOERT) procedures. The MC method that was implemented, which has been integrated into a specific innovative simulation and planning tool, is able to simulate the fate of thousands of particles per second, and it was the aim of this work to determine the level of interactivity that could be achieved. The planning workflow enabled calibration of the imaging and treatment equipment, as well as manipulation of the surgical frame and insertion of the protection shields around the organs at risk and other beam modifiers. In this way, the multidisciplinary team involved in IOERT has all the tools necessary to perform complex MC dosage simulations adapted to their equipment in an efficient and transparent way. To assess the accuracy and reliability of this MC technique, dose distributions for a monoenergetic source were compared with those obtained using a general-purpose software package used widely in medical physics applications. Once accuracy of the underlying simulator was confirmed, a clinical accelerator was modelled and experimental measurements in water were conducted. A comparison was made with the output from the simulator to identify the conditions under which accurate dose estimations could be obtained in less than 3 min, which is the threshold imposed to allow for interactive use of the tool in treatment planning. Finally, a clinically relevant scenario, namely early-stage breast cancer treatment, was simulated with pre- and intraoperative volumes to verify that it was feasible to use the MC tool intraoperatively and to adjust dose delivery based on the simulation output, without compromising accuracy. The workflow provided a satisfactory model of the treatment head and the imaging system, enabling proper configuration of the treatment planning system and providing good accuracy in the dosage simulation.

Hybrid Monte Carlo dose algorithm for low energy X-rays intraoperative radiation therapy

Low energy X-rays Intra-Operative Radiation Therapy (XIORT) treatment delivered during surgery (ex: INTRABEAM, Carl Zeiss, and Axxent, Xoft) can benefit from accurate and fast dose prediction in a patient 3D volume.

Monte Carlo limit cycle characterization

The fixed point implementation of IIR digital filters usually leads to the appearance of zero-input limit cycles, which degrade the performance of the system. In this paper, we develop an efficient Monte Carlo algorithm to detect and characterize limit cycles in fixed-point IIR digital filters. The proposed approach considers filters formulated in the state space and is valid for any fixed point representation and quantization function. Numerical simulations on several high-order filters, where an exhaustive search is unfeasible, show the effectiveness of the proposed approach.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project

We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.