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.

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.

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.

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.

Morphological traits of surveillant/activated microglia during an experimentally induced acute neuroinflammatory process

Several studies show that morphological changes of microglia over the course of inflammation are tightly coupled to function. However the progressive transformation into activated microglia is poorly characterized. AIMS: This study aimed to establish a spatiotemporal correlation between quantifiable morphological parameters of microglia and the spread of an acute ventricular inflammatory process. METHODS: Inflammation was induced by a single injection of the enzyme neuraminidase within the lateral ventricle of rats. Animals were sacrificed 2, 4 and 12 hours after injection. Coronal slices were immunostained with Iba1 to label microglia and with IL1β to delimit the spread of inflammation. Digital images were obtained by scanning the labelled sections. Single microglia images were randomly selected from periventricular areas of caudate putamen, hippocampus and hypothalamus. FracLac for ImageJ software was used to measure the following morphological parameters: fractal dimension, lacunarity, area, perimeter and density. RESULTS: Significant differences were found in fractal dimension, lacunarity, perimeter and density of microglia cells of neuraminidase injected rats compared to sham animals. However no differences were found in the parameter “area”. In hipoccampus there was a delay in the significant change of the measured parameters. These morphological changes correlated with IL1β-expression in the same areas. CONCLUSIONS: Ventricular inflammation induced by neuraminidase provokes quantifiable morphological changes in microglia restricted to areas labelled with IL1β. Morphological parameters of microglia such as fractal dimension, lacunarity, perimeter and density are sensitive and valuable tools to quantify activation. However, the extensively used parameter “area” did not change upon microglia activation.

Os fractais no urbanismo

Dissertação para obtenção do grau de Mestre em Arquitectura com Especialização em Urbanismo, apresentada na Universidade de Lisboa - Faculdade de Arquitectura.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Análise não linear de séries temporais e aplicações à Psicologia

Nesta dissertação estudámos as séries temporais que representam a complexa dinâmica do comportamento. Demos especial atenção às técnicas de dinâmica não linear. As técnicas fornecem-nos uma quantidade de índices quantitativos que servem para descrever as propriedades dinâmicas do sistema. Estes índices têm sido intensivamente usados nos últimos anos em aplicações práticas em Psicologia. Estudámos alguns conceitos básicos de dinâmica não linear, as características dos sistemas caóticos e algumas grandezas que caracterizam os sistemas dinâmicos, que incluem a dimensão fractal, que indica a complexidade de informação contida na série temporal, os expoentes de Lyapunov, que indicam a taxa com que pontos arbitrariamente próximos no espaço de fases da representação do espaço dinâmico, divergem ao longo do tempo, ou a entropia aproximada, que mede o grau de imprevisibilidade de uma série temporal. Esta informação pode então ser usada para compreender, e possivelmente prever, o comportamento. ABSTRACT: ln this thesis we studied the time series that represent the complex dynamic behavior. We focused on techniques of nonlinear dynamics. The techniques provide us a number of quantitative indices used to describe the dynamic properties of the system. These indices have been extensively used in recent years in practical applications in psychology. We studied some basic concepts of nonlinear dynamics, the characteristics of chaotic systems and some quantities that characterize the dynamic systems, including fractal dimension, indicating the complexity of information in the series, the Lyapunov exponents, which indicate the rate at that arbitrarily dose points in phase space representation of a dynamic, vary over time, or the approximate entropy, which measures the degree of unpredictability of a series. This information can then be used to understand and possibly predict the behavior.

Improving multivariate data streams clustering.

Clustering data streams is an important task in data mining research. Recently, some algorithms have been proposed to cluster data streams as a whole, but just few of them deal with multivariate data streams. Even so, these algorithms merely aggregate the attributes without touching upon the correlation among them. In order to overcome this issue, we propose a new framework to cluster multivariate data streams based on their evolving behavior over time, exploring the correlations among their attributes by computing the fractal dimension. Experimental results with climate data streams show that the clusters' quality and compactness can be improved compared to the competing method, leading to the thoughtfulness that attributes correlations cannot be put aside. In fact, the clusters' compactness are 7 to 25 times better using our method. Our framework also proves to be an useful tool to assist meteorologists in understanding the climate behavior along a period of time.

The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.

Mechanics of metallic foams: A fractal approach

A fractal approach was proposed to investigate the meso structures and size effect of metallic foams: For a series At foams of different relative densities, the information dimension method was applied to measure meso structures. The generalized sierpinski carpet was introduced to map the meso structures of the foam according to specific dimension. The results show that the fractal-based model can not only reveal the variation of yield strength with specimen size, but also bridge the meso structures and mechanical proper-ties of Al foams directly. Key words: metallic foams; fractal; size effect; meso structures

Slip flow and heat transfer in microbearings with fractal surface topographies

The effects of random surface roughness on slip flow and heat transfer in microbearings are investigated. A three-dimensional random surface roughness model characterized by fractal geometry is used to describe the multiscale self-affine roughness, which is represented by the modified two-variable Weierstrass- Mandelbrot (W-M) functions, at micro-scale. Based on this fractal characterization, the roles of rarefaction and roughness on the thermal and flow properties in microbearings are predicted and evaluated using numerical analyses and simulations. The results show that the boundary conditions of velocity slip and temperature jump depend not only on the Knudsen number but also on the surface roughness. It is found that the effects of the gas rarefaction and surface roughness on flow behavior and heat transfer in the microbearing are strongly coupled. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. In addition, the effects of temperature difference and relative roughness on the heat transfer in the bearing are also analyzed and discussed. © 2012 Elsevier Ltd. All rights reserved.

Optical determination of fractal dimensions using Fourier transforms

R. Zwiggelaar and C.R. Bull, 'Optical determination of fractal dimensions using Fourier transforms', Optical Engineering 34 (5), 1325-1332 (1995)