Advanced signal processing methods in dynamic contrast enhanced magnetic resonance imaging

Tato dizertační práce představuje metodu zobrazování perfúze magnetickou rezonancí, jež je výkonným nástrojem v diagnostice, především v onkologii. Po ukončení sběru časové sekvence T1-váhovaných obrazů zaznamenávajících distribuci kontrastní látky v těle začíná fáze zpracování dat, která je předmětem této dizertace. Je zde představen teoretický základ fyziologických modelů a modelů akvizice pomocí magnetické rezonance a celý řetězec potřebný k vytvoření obrazů odhadu parametrů perfúze a mikrocirkulace v tkáni. Tato dizertační práce je souborem uveřejněných prací autora přispívajícím k rozvoji metodologie perfúzního zobrazování a zmíněného potřebného teoretického rozboru.This dissertation describes quantitative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI), which is a powerful tool in diagnostics, mainly in oncology. After a time series of T1-weighted images recording contrast-agent distribution in the body has been acquired, data processing phase follows. It is presented step by step in this dissertation. The theoretical background in physiological and MRI-acquisition modeling is described together with the estimation process leading to parametric maps describing perfusion and microcirculation properties of the investigated tissue on a voxel-by-voxel basis. The dissertation is divided into this theoretical analysis and a set of publications representing particular contributions of the author to DCE-MRI.

Laplace deconvolution on the basis of time domain data and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Due to this triangular structure, there is a common number $m$ of terms in the function expansions to control, which is realized via complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut-off at $T$ and provides an estimator with the risk within a logarithmic factor of the oracle risk. We emphasize that, in the present paper, we consider the true observational model with possibly nonequispaced observations which are available on a finite interval of length $T$ which appears in many different contexts, and account for the bias associated with this model (which is not present when $T\rightarrow\infty$). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of micro-circulation within tissues such as cancerous tumors. Presence of a tuning parameter $a$ allows to choose the most advantageous time units, so that both the kernel and the unknown right hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast, efficient, accurate, usable from a practical point of view and very competitive.Comment: 36 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1207.223

A Semi-parametric Technique for the Quantitative Analysis of Dynamic Contrast-enhanced MR Images Based on Bayesian P-splines

Dynamic Contrast-enhanced Magnetic Resonance Imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the non-linear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome this problems, this paper proposes a semi-parametric penalized spline smoothing approach, with which the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided

Laplace deconvolution and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable improvement in {evaluating} the quality of a vascular network and its permeability and is widely used in medical assessment of brain flows or cancerous tumors. Although the study is motivated by medical imaging application, we obtain a solution of a general problem of Laplace deconvolution based on noisy data which appears in many different contexts. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. The number $m$ of the terms in the expansion of the estimator is controlled via complexity penalty. The advantage of this methodology is that it leads to very fast computations, does not require exact knowledge of the kernel and produces no boundary effects due to extension at zero and cut-off at $T$. The technique leads to an estimator with the risk within a logarithmic factor of $m$ of the oracle risk under no assumptions on the model and within a constant factor of the oracle risk under mild assumptions. The methodology is illustrated by a finite sample simulation study which includes an example of the kernel obtained in the real life DCE experiments. Simulations confirm that the proposed technique is fast, efficient, accurate, usable from a practical point of view and competitive

Laplace deconvolution with noisy observations

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge, it has been given very little attention by the statistical community. Our objective is to fill this gap and provide statistical treatment of Laplace deconvolution problem with noisy discrete data. The main contribution of the paper is explicit construction of an asymptotically rate-optimal (in the minimax sense) Laplace deconvolution estimator which is adaptive to the regularity of the unknown function. We show that the original Laplace deconvolution problem can be reduced to nonparametric estimation of a regression function and its derivatives on the interval of growing length T_n. Whereas the forms of the estimators remain standard, the choices of the parameters and the minimax convergence rates, which are expressed in terms of T_n^2/n in this case, are affected by the asymptotic growth of the length of the interval. We derive an adaptive kernel estimator of the function of interest, and establish its asymptotic minimaxity over a range of Sobolev classes. We illustrate the theory by examples of construction of explicit expressions of Laplace deconvolution estimators. A simulation study shows that, in addition to providing asymptotic optimality as the number of observations turns to infinity, the proposed estimator demonstrates good performance in finite sample examples

DATforDCEMRI: An R Package for Deconvolution Analysis and Visualization of DCE-MRI Data

Numerical deconvolution is a powerful mathematical operation that can be used to extract the impulse response function of a linear, time-invariant system. We have found this method to be useful for preliminary analysis of dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) data, capable of quickly producing voxel-wise parametric maps describing the heterogeneity of contrast agent kinetics over the entire field of view, typically comprising tens of thousands of voxels. The statistical programming language R is well suited for this type of analysis and when combined with LATEX, via Sweave, allows one to perform all calculations and generate a report with a single script. The purpose of this manuscript is to describe the R package DATforDCEMRI, a Deconvolution Analysis Tool for DCE-MRI contrast agent concentration vs. time data, which allows the user to perform kinetic deconvolution analysis and visualize/explore the resulting voxel-wise parametric maps and associated data

Quantitative Magnetic Resonance Imaging of Tissue Microvasculature and Microstructure in Selected Clinical Applications

This thesis is based on four papers and aims to establish perfusion and diffusion measurements with magnetic resonance imaging (MRI) in selected clinical applications. While structural imaging provides invaluable geometric and anatomical information, new disease relevant information can be obtained from measures of physiological processes inferred from advanced modelling. This study is motivated by clinical questions pertaining to diagnosis and treatment effects in particular patient groups where inflammatory processes are involved in the disease. Paper 1 investigates acquisition parameters in dynamic contrast enhanced (DCE)-MRI of the temporomandibular joint (TMJ) with possible involvement of juvenile idiopathic arthritis. High level elastic motion correction should be applied to DCE data from the TMJ, and the DCE data should be acquired with a sample rate of at least 4 s. Paper 2 investigates choices of arterial input functions (AIFs) in dynamic susceptibility contrast (DSC)-MRI in brain metastases. AIF shapes differed across patients. Relative cerebral blood volume estimates differentiated better between perfusion in white matter and grey matter when scan-specific AIFs were used than when patient-specific AIFs and population-based AIFs were used. Paper 3 investigates DSC-MRI perfusion parameters in relation to outcome after stereotactic radiosurgery (SRS) in brain metastases. Low perfusion prior to SRS may be related to unfavourable outcome. Paper 4 applies free water (FW) corrected diffusion MRI to characterise glioma. Fractional anisotropy maps of the tumour region were significantly impacted by FW correction. The estimated FW maps may also contribute to a better description of the tumour. Although there are challenges related to post-processing of MRI data, it was shown that the advanced MRI methods applied can add to a more accurate description of the TMJ and of brain lesions.Doktorgradsavhandlin

Quantitative Dynamic Contrast Enhanced Magnetic Resonance Imaging for Evaluation of the Myocardium in Ischaemic Heart Disease

Background: Use of contrast enhanced cardiac magnetic resonance imaging (MRI) for identification of focal pathology (perfusion deficit and scar) is widespread. Quantitative analysis of dynamic contrast enhanced (DCE) MRI data may allow objective assessment of focal and diffuse disease. However it is a complex process and not widely adopted outside the research domain. For accurate quantification temporal variation in relative contrast agent concentration in the myocardium and feeding blood supply must be measured. While MRI signal intensity can be used as a probe of contrast agent concentration its response is non-linear. Aims: In this thesis non-linearity correction methods for quantitative myocardial DCE-MRI are compared, the feasibility of a novel bookend T1 based correction is tested and the method is used in clinical studies to assess myocardial characteristics in health and ischaemic disease. Methods: Signal non-linearity correction methods were compared using simulation, phantom experiments and a volunteer study. Methods compared were independent sampling strategies (dual-bolus and dual-sequence), previously proposed model based correction (native T1 or proton density weighted image based) and bookend T1 based correction which is proposed as a method to account for imperfect magnetisation preparation. The feasibility of the bookend T1 method was tested and characteristics of heathy and diseased myocardium were assessed in clinical studies of ischaemia and infarction. Conclusions: Native T1 based correction has been found to be highly sensitive to imperfect magnetisation preparation, and is thus recommended against. Model based correction using proton density weighted images or bookend T1 data have been found to be more accurate and precise than dual-sampling methods. The clinical studies have demonstrated the feasibility of the bookend T1 based method and have yielded insights into myocardial characteristics in a range of conditions

Quantitative Perfusion-Sensitive Mri Phantoms

Perfusion-sensitive MR methods are increasingly utilized in preclinical and clinical MR research studies with the promise of providing quantitative estimates of parameters that describe in vivo microvasculature. One of these techniques, dynamic contrast enhanced: DCE) MRI, has found particularly common use in oncology for the detection, staging, and monitoring of highly vascularized tumors. DCE-MRI has been qualitatively validated by various studies that show a high correlation between modeled parameters from DCE and histologically measured microvascular density: MVD). However, in the absence of a matching gold-standard technique, DCE-MRI has not yet been quantitatively validated: i.e., the accuracy of the estimated parameters is unknown). Partly because of this inability to determine the accuracy of the measured parameters, there remains debate in the literature about which DCE signal model(s) best reflect(s) experimental data. In order to address these scientific challenges, realistic DCE tissue phantoms have been constructed. These phantoms implement semi-permeable hollow fibers, found commonly in commercial hemodialysis cartridges, to simulate leaky vasculature. Their design and construction are cataloged in this thesis. In addition, the phantoms have been experimentally characterized. In conjunction with these experiments, an interesting example of diffusion driven longitudinal relaxation was observed and is described herein. Lastly, the permeability of the fiber wall with respect to Gd-based contrast agents has been measured independently and compared with values derived from a mock-DCE experiment performed on the phantoms. In general, the results of these experiments support current DCE-MRI methods