Radiotherapy Treatment Assessment using DCE-MRI

Abstract

The goal of modern radiotherapy is to precisely deliver a prescribed radiation dose to delineated target volumes that contain a significant amount of tumor cells while sparing the surrounding healthy tissues/organs. Precise delineation of treatment and avoidance volumes is the key for the precision radiation therapy. In recent years, considerable clinical and research efforts have been devoted to integrate MRI into radiotherapy workflow motivated by the superior soft tissue contrast and functional imaging possibility. Dynamic contrast-enhanced MRI (DCE-MRI) is a noninvasive technique that measures properties of tissue microvasculature. Its sensitivity to radiation-induced vascular pharmacokinetic (PK) changes has been preliminary demonstrated. In spite of its great potential, two major challenges have limited DCE-MRI’s clinical application in radiotherapy assessment: the technical limitations of accurate DCE-MRI imaging implementation and the need of novel DCE-MRI data analysis methods for richer functional heterogeneity information.

This study aims at improving current DCE-MRI techniques and developing new DCE-MRI analysis methods for particular radiotherapy assessment. Thus, the study is naturally divided into two parts. The first part focuses on DCE-MRI temporal resolution as one of the key DCE-MRI technical factors, and some improvements regarding DCE-MRI temporal resolution are proposed; the second part explores the potential value of image heterogeneity analysis and multiple PK model combination for therapeutic response assessment, and several novel DCE-MRI data analysis methods are developed.

I. Improvement of DCE-MRI temporal resolution. First, the feasibility of improving DCE-MRI temporal resolution via image undersampling was studied. Specifically, a novel MR image iterative reconstruction algorithm was studied for DCE-MRI reconstruction. This algorithm was built on the recently developed compress sensing (CS) theory. By utilizing a limited k-space acquisition with shorter imaging time, images can be reconstructed in an iterative fashion under the regularization of a newly proposed total generalized variation (TGV) penalty term. In the retrospective study of brain radiosurgery patient DCE-MRI scans under IRB-approval, the clinically obtained image data was selected as reference data, and the simulated accelerated k-space acquisition was generated via undersampling the reference image full k-space with designed sampling grids. Two undersampling strategies were proposed: 1) a radial multi-ray grid with a special angular distribution was adopted to sample each slice of the full k-space; 2) a Cartesian random sampling grid series with spatiotemporal constraints from adjacent frames was adopted to sample the dynamic k-space series at a slice location. Two sets of PK parameters’ maps were generated from the undersampled data and from the fully-sampled data, respectively. Multiple quantitative measurements and statistical studies were performed to evaluate the accuracy of PK maps generated from the undersampled data in reference to the PK maps generated from the fully-sampled data. Results showed that at a simulated acceleration factor of four, PK maps could be faithfully calculated from the DCE images that were reconstructed using undersampled data, and no statistically significant differences were found between the regional PK mean values from undersampled and fully-sampled data sets. DCE-MRI acceleration using the investigated image reconstruction method has been suggested as feasible and promising.

Second, for high temporal resolution DCE-MRI, a new PK model fitting method was developed to solve PK parameters for better calculation accuracy and efficiency. This method is based on a derivative-based deformation of the commonly used Tofts PK model, which is presented as an integrative expression. This method also includes an advanced Kolmogorov-Zurbenko (KZ) filter to remove the potential noise effect in data and solve the PK parameter as a linear problem in matrix format. In the computer simulation study, PK parameters representing typical intracranial values were selected as references to simulated DCE-MRI data for different temporal resolution and different data noise level. Results showed that at both high temporal resolutions (<1s) and clinically feasible temporal resolution (~5s), this new method was able to calculate PK parameters more accurate than the current calculation methods at clinically relevant noise levels; at high temporal resolutions, the calculation efficiency of this new method was superior to current methods in an order of 102. In a retrospective of clinical brain DCE-MRI scans, the PK maps derived from the proposed method were comparable with the results from current methods. Based on these results, it can be concluded that this new method can be used for accurate and efficient PK model fitting for high temporal resolution DCE-MRI.

II. Development of DCE-MRI analysis methods for therapeutic response assessment. This part aims at methodology developments in two approaches. The first one is to develop model-free analysis method for DCE-MRI functional heterogeneity evaluation. This approach is inspired by the rationale that radiotherapy-induced functional change could be heterogeneous across the treatment area. The first effort was spent on a translational investigation of classic fractal dimension theory for DCE-MRI therapeutic response assessment. In a small-animal anti-angiogenesis drug therapy experiment, the randomly assigned treatment/control groups received multiple fraction treatments with one pre-treatment and multiple post-treatment high spatiotemporal DCE-MRI scans. In the post-treatment scan two weeks after the start, the investigated Rényi dimensions of the classic PK rate constant map demonstrated significant differences between the treatment and the control groups; when Rényi dimensions were adopted for treatment/control group classification, the achieved accuracy was higher than the accuracy from using conventional PK parameter statistics. Following this pilot work, two novel texture analysis methods were proposed. First, a new technique called Gray Level Local Power Matrix (GLLPM) was developed. It intends to solve the lack of temporal information and poor calculation efficiency of the commonly used Gray Level Co-Occurrence Matrix (GLCOM) techniques. In the same small animal experiment, the dynamic curves of Haralick texture features derived from the GLLPM had an overall better performance than the corresponding curves derived from current GLCOM techniques in treatment/control separation and classification. The second developed method is dynamic Fractal Signature Dissimilarity (FSD) analysis. Inspired by the classic fractal dimension theory, this method measures the dynamics of tumor heterogeneity during the contrast agent uptake in a quantitative fashion on DCE images. In the small animal experiment mentioned before, the selected parameters from dynamic FSD analysis showed significant differences between treatment/control groups as early as after 1 treatment fraction; in contrast, metrics from conventional PK analysis showed significant differences only after 3 treatment fractions. When using dynamic FSD parameters, the treatment/control group classification after 1st treatment fraction was improved than using conventional PK statistics. These results suggest the promising application of this novel method for capturing early therapeutic response.

The second approach of developing novel DCE-MRI methods is to combine PK information from multiple PK models. Currently, the classic Tofts model or its alternative version has been widely adopted for DCE-MRI analysis as a gold-standard approach for therapeutic response assessment. Previously, a shutter-speed (SS) model was proposed to incorporate transcytolemmal water exchange effect into contrast agent concentration quantification. In spite of richer biological assumption, its application in therapeutic response assessment is limited. It might be intriguing to combine the information from the SS model and from the classic Tofts model to explore potential new biological information for treatment assessment. The feasibility of this idea was investigated in the same small animal experiment. The SS model was compared against the Tofts model for therapeutic response assessment using PK parameter regional mean value comparison. Based on the modeled transcytolemmal water exchange rate, a biological subvolume was proposed and was automatically identified using histogram analysis. Within the biological subvolume, the PK rate constant derived from the SS model were proved to be superior to the one from Tofts model in treatment/control separation and classification. Furthermore, novel biomarkers were designed to integrate PK rate constants from these two models. When being evaluated in the biological subvolume, this biomarker was able to reflect significant treatment/control difference in both post-treatment evaluation. These results confirm the potential value of SS model as well as its combination with Tofts model for therapeutic response assessment.

In summary, this study addressed two problems of DCE-MRI application in radiotherapy assessment. In the first part, a method of accelerating DCE-MRI acquisition for better temporal resolution was investigated, and a novel PK model fitting algorithm was proposed for high temporal resolution DCE-MRI. In the second part, two model-free texture analysis methods and a multiple-model analysis method were developed for DCE-MRI therapeutic response assessment. The presented works could benefit the future DCE-MRI routine clinical application in radiotherapy assessment.

Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Application of computer-aided tomography techniques to visualize kelp holdfast structure reveals the importance of habitat complexity for supporting marine biodiversity

Ecosystem engineers that increase habitat complexity are keystone species in marine systems, increasing shelter and niche availability, and therefore biodiversity. For example, kelp holdfasts form intricate structures and host the largest number of organisms in kelp ecosystems. However, methods that quantify 3D habitat complexity have only seldom been used in marine habitats, and never in kelp holdfast communities. This study investigated the role of kelp holdfasts (Laminaria hyperborea) in supporting benthic faunal biodiversity. Computer-aided tomography (CT-) scanning was used to quantify the three-dimensional geometrical complexity of holdfasts, including volume, surface area and surface fractal dimension (FD). Additionally, the number of haptera, number of haptera per unit of volume, and age of kelps were estimated. These measurements were compared to faunal biodiversity and community structure, using partial least-squares regression and multivariate ordination. Holdfast volume explained most of the variance observed in biodiversity indices, however all other complexity measures also strongly contributed to the variance observed. Multivariate ordinations further revealed that surface area and haptera per unit of volume accounted for the patterns observed in faunal community structure. Using 3D image analysis, this study makes a strong contribution to elucidate quantitative mechanisms underlying the observed relationship between biodiversity and habitat complexity. Furthermore, the potential of CT-scanning as an ecological tool is demonstrated, and a methodology for its use in future similar studies is established. Such spatially resolved imager analysis could help identify structurally complex areas as biodiversity hotspots, and may support the prioritization of areas for conservation.

Application of computer-aided tomography techniques to visualize kelp holdfast structure reveals the importance of habitat complexity for supporting marine biodiversity

Ecosystem engineers that increase habitat complexity are keystone species in marine systems, increasing shelter and niche availability, and therefore biodiversity. For example, kelp holdfasts form intricate structures and host the largest number of organisms in kelp ecosystems. However, methods that quantify 3D habitat complexity have only seldom been used in marine habitats, and never in kelp holdfast communities. This study investigated the role of kelp holdfasts (Laminaria hyperborea) in supporting benthic faunal biodiversity. Computer-aided tomography (CT-) scanning was used to quantify the three-dimensional geometrical complexity of holdfasts, including volume, surface area and surface fractal dimension (FD). Additionally, the number of haptera, number of haptera per unit of volume, and age of kelps were estimated. These measurements were compared to faunal biodiversity and community structure, using partial least-squares regression and multivariate ordination. Holdfast volume explained most of the variance observed in biodiversity indices, however all other complexity measures also strongly contributed to the variance observed. Multivariate ordinations further revealed that surface area and haptera per unit of volume accounted for the patterns observed in faunal community structure. Using 3D image analysis, this study makes a strong contribution to elucidate quantitative mechanisms underlying the observed relationship between biodiversity and habitat complexity. Furthermore, the potential of CT-scanning as an ecological tool is demonstrated, and a methodology for its use in future similar studies is established. Such spatially resolved imager analysis could help identify structurally complex areas as biodiversity hotspots, and may support the prioritization of areas for conservation.

El surgimiento de HTML5; un nuevo paradigma en los estándares Web

Gracias al crecimiento, expansión y popularización de la World Wide Web, su desarrollo tecnológico tiene una creciente importancia en la sociedad. La simbiosis que protagonizan estos dos entornos ha propiciado una mayor influencia social en las innovaciones de la plataforma y un enfoque mucho más práctico. Nuestro objetivo en este artículo es describir, caracterizar y analizar el surgimiento y difusión del nuevo estándar de hipertexto que rige la Web; HTML5. Al mismo tiempo exploramos este proceso a la luz de varias teorías que aúnan tecnología y sociedad. Dedicamos especial atención a los usuarios de la World Wide Web y al uso genérico que realizan de los Medios Sociales o "Social Media". Sugerimos que el desarrollo de los estándares web está influenciado por el uso cotidiano de este nuevo tipo de tecnologías y aplicaciones. 

Pulling Back the Veil: The Characterization and Habitability of Enshrouded Worlds

Thesis (Ph.D.)--University of Washington, 2016-08

Prediction of Sudden Cardiac Arrest for Patients with Congestive Heart Failure

Thesis (Ph.D.)--University of Washington, 2016-07

Human traces in urban places.

Over the last two centuries many major cities have undergone large-scale modernisation that has led to the growing sense of homogenisation associated with such locales across the globe. The fractal logic that is at the heart of so many urban settings, where the whole system is made up of parts that are identical to the whole, seems to serve in making anonymous everyday experiences. Public transport and its corresponding street furniture, if thoughtfully designed and planned, has the potential to form an integral element in the promotion of a sense of identity, interconnectedness and flow within a city. Furthermore, bus stops, benches, litter bins, curb-sides, posts and pavements, to mention a few, offer interesting cases to consider how people truly engage with contemporary urban spaces. These objects—part of routine and made familiar—are elements of daily lives that are ingredients towards visual and multi-modal experiences. In addition, these are places where individuals encounter sociality and materiality in ordinary and sometimes extraordinary ways. This paper uses a visual ethnographic approach towards exploring the human traces of routine activities that have an impact on the cityscape. An Investigation of these details found within the urban landscape lead us towards understanding how we engage with and navigate cities. This is essentially an urban archaeological study that looks to reveal how non-designed phenomenon in urban places can contribute to our image of a city, providing a reflection on homogeneity within the built environment. Our visual ethnography focuses on six major cities: two each in Britain, Europe and North America. The findings of this work illustrate through visual analyses three key characteristics: first, how urban spaces are transformed intentionally and unintentionally; second, how transformations are practical, functional, beautiful and sometimes ridiculous; third, how transformations reveal values around visual and multi-modal experiences inherent to people.

Padrões de organização das assembleias de aves florestais em uma paisagem fragmentada de Floresta Atlântica

Brazil is home to one of the richest avifaunas the world, which is subject to high levels of environmental degradation, in particular forest fragmentation. The Atlantic Forest biome depicts this history of devastation and today remains as small isolated fragments on highly degraded landscapes. This project aimed to evaluate the effects of forest fragmentation in an area with Atlantic Forest remnants in northern Paraná (Brazil) on the distribution and the organization of assemblage of forest birds and tested the hypothesis that the structure of the assembly in the fragments is different than expected by chance. We did four qualitative samplings of birds in three sets of forest fragments in the landscape, each with three fragments: large, medium and small. The method applied in the sampling was point counts along transects, traveled randomly for four hours in each fragment. Samples were taken in two periods: from September to November / 2013, and between March and May / 2014. The structure of the meeting was assessed by rates of co-occurring species (Checkerboard and CScore) and α diversity patterns (wealth) and β (turnover of species), while the landscape structure was analyzed from the parameters: area, distance between fragments, fractal dimension, edge density, fragment shape index and nuclear area index. The null hypothesis of no structure in the assembly of birds in the landscape was tested with null models from the co-occurrence indexes. The effects of landscape structure on the assembly of the structure were analyzed by the Mantel test and principal component analysis (PCA). The assembly of the structure in the landscape showed a pattern of spatiotemporal organization significantly different from that expected by chance, revealing a structure most influenced by segregation of the species. The fragments showed significant differences in richness, unlike sets of fragments, indicating relative homogeneity in the landscape structure. The differences between the size and the distance between the fragments significantly influenced the patterns of organization of the meeting of forest birds in the landscape and patterns of α and β diversity, indicating that the higher the fragment and smaller distances between them, more the standard of species cooccurrence is different than expected by chance. Thus, the fragmented landscape of remnants of the northern Paraná Atlantic Forest still has availability of environmental resources and physical characteristics that allow a persistent organizational structure of the assembly of forest birds in space over time.

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in R3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

Biomonitoramento da comunidade de macroinvertebrados de um reservatório de abastecimento público no sul do Brasil

The faunal inventory of the macroinvertebrate community is important to the environmental assessment, since this biota is sensitive to human disturbance. The reservoir of Rio Verde, located on the first plateau of Paraná, is inserted into an agricultural region with several forest fragments Araucaria. The aim of this study was to evaluate the environmental integrity of the reservoir through ecological indexes of macroinvertebrate community benthic and associated with macrophytes. Five sampling points were defined in the study area, which comprise distinct microhabitats in the basin. There were four sampling campaigns, each by weather station: Spring (2014); Summer (2015); Autumn (2015) and Winter (2015). In each sample were measured abiotic various parameters in the field and be collected water samples for nutrient analysis in the laboratory. The macroinvertebrates were collected in triplicate at adapted Macan method using mesh sieve 1 mm and CPUE (catch per unit effort) for 20 minutes. In order to pellet sample was used a dredger model Petersen 2L. Still in the field, by season, samples were collected from macrophytes Myriophyllum aquaticum (Vell) Verdc. and Potamogeton montevidensis A. Benn. in triplicates in the fluvial region of the reservoir, to analyze the associated fractal dimension and macrofauna. For this we used a PVC sampler specific volume 0.025 m3. the following ecological descriptors were calculated in each case: abundance, wealth tax, wealth Margalef, Shannon-Wiener diversity, evenness evenness through the Past software. The index Biological Monitoring Working Party (BMWP) for monitoring sampling points was also calculated. Regarding the statistical analysis, we used the analysis of PERMANOVA to compare points and seasons and canonical correspondence analysis (CCoA) for variables. Regarding M. aquaticum and P. montevidensis it was not verified difference to the average associated macroinvertebrates. However there was a difference for abundance of organisms in the fractal dimension and biomass of specimens. M. aquaticum is more complex and took more macrofauna in relation to P. montevidensis. Regarding the monitoring of the reservoir, it showed up mesotrophic with moderate nutrient concentrations and within the regulatory limits. Benthic macrofauna showed statistical differences in relation to the reservoir region, sample point and temporal variation. The BMWP index showed that the river region has the highest biotic integrity (in all samples above 70 points), and the ecological descriptors of wealth and Margalef diversity of Shannon- Wiener higher. In point 4 (dam downstream) were recorded evidence of possible impacts due to lower wealth and BMWP index which resulted in a questionable quality water. New approaches are needed to focus on the aquatic community in the best understanding of this ecosystem and also with a view to environmental preservation of the Green River Basin.

Characterization of the effect of nitrogen deficiency on above-ground plant phenotypes in relation to root complexity in maize

Nitrogen (N) is an essential plant nutrient in maize production, and if considering only natural sources, is often the limiting factor world-wide in terms of a plant’s grain yield. For this reason, many farmers around the world supplement available soil N with synthetic man-made forms. Years of over-application of N fertilizer have led to increased N in groundwater and streams due to leaching and run-off from agricultural sites. In the Midwest Corn Belt much of this excess N eventually makes its way to the Gulf of Mexico leading to eutrophication (increase of phytoplankton) and a hypoxic (reduced oxygen) dead zone. Growing concerns about these types of problems and desire for greater input use efficiency have led to demand for crops with improved N use efficiency (NUE) to allow reduced N fertilizer application rates and subsequently lower N pollution. It is well known that roots are responsible for N uptake by plants, but it is relatively unknown how root architecture affects this ability. This research was conducted to better understand the influence of root complexity (RC) in maize on a plant’s response to N stress as well as the influence of RC on other above-ground plant traits. Thirty-one above-ground plant traits were measured for 64 recombinant inbred lines (RILs) from the intermated B73 & Mo17 (IBM) population and their backcrosses (BCs) to either parent, B73 and Mo17, under normal (182 kg N ha-1) and N deficient (0 kg N ha-1) conditions. The RILs were selected based on results from an earlier experiment by Novais et al. (2011) which screened 232 RILs from the IBM to obtain their root complexity measurements. The 64 selected RILs were comprised of 31 of the lowest complexity RILs (RC1) and 33 of the highest complexity RILs (RC2) in terms of root architecture (characterized as fractal dimensions). The use of the parental BCs classifies the experiment as Design III, an experimental design developed by Comstock and Robinson (1952) which allows for estimation of dominance significance and level. Of the 31 traits measured, 12 were whole plant traits chosen due to their documented response to N stress. The other 19 traits were ear traits commonly measured for their influence on yield. Results showed that genotypes from RC1 and RC2 significantly differ for several above-ground phenotypes. We also observed a difference in the number and magnitude of N treatment responses between the two RC classes. Differences in phenotypic trait correlations and their change in response to N were also observed between the RC classes. RC did not seem to have a strong correlation with calculated NUE (ΔYield/ΔN). Quantitative genetic analysis utilizing the Design III experimental design revealed significant dominance effects acting on several traits as well as changes in significance and dominance level between N treatments. Several QTL were mapped for 26 of the 31 traits and significant N effects were observed across the majority of the genome for some N stress indicative traits (e.g. stay-green). This research and related projects are essential to a better understanding of plant N uptake and metabolism. Understanding these processes is a necessary step in the progress towards the goal of breeding for better NUE crops.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Geometría diferencial de superficies

Este texto abarca temas como: superficies diferenciales, diferenciación e integración en superficies, formas fundamentales, Curvatura Gaussiana, teorema Egregio y teorema de Gauss-Bonnet. La colección de textos lecciones de matemáticas, iniciativa del departamento de Ciencias Básicas de la Universidad de Medellín (Medellín, Colombia) y su grupo de investigación SUMMA, incluye en cada número la exposición detallada de un tema matemático en particular, tratado con el rigor que muchas veces no es posible lograr en un curso regular de la disciplina. Las matemáticas incluyen diferentes áreas del saber matemático como: álgebra, trigonometría, cálculo, estadística y probabilidades, álgebra lineal, métodos lineales y numéricos, historia de las matemáticas, geometría, matemáticas puras y aplicadas, ecuaciones diferenciales y empelo de softwares matemáticos. Todas las carátulas de la colección vienen ilustradas, a manera de identificación, con diseños de la geometría fractal cuya fuente u origen se encuentra referenciada en las páginas interiores de los textos.

3D Porous Architecture of Stacks of β-TCP Granules Compared with That of Trabecular Bone: A microCT, Vector Analysis, and Compression Study

International audience