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.

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

Spatial two tissue compartment model for DCE-MRI

In the quantitative analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) compartment models allow to describe the uptake of contrast medium with biological meaningful kinetic parameters. As simple models often fail to adequately describe the observed uptake behavior, more complex compartment models have been proposed. However, the nonlinear regression problem arising from more complex compartment models often suffers from parameter redundancy. In this paper, we incorporate spatial smoothness on the kinetic parameters of a two tissue compartment model by imposing Gaussian Markov random field priors on them. We analyse to what extent this spatial regularisation helps to avoid parameter redundancy and to obtain stable parameter estimates. Choosing a full Bayesian approach, we obtain posteriors and point estimates running Markov Chain Monte Carlo simulations. The proposed approach is evaluated for simulated concentration time curves as well as for in vivo data from a breast cancer study

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

This paper aims to solve the arterial input function (AIF) determination in dynamic contrast-enhanced MRI (DCE-MRI), an important linear ill-posed inverse problem, using the maximum entropy technique (MET) and regularization functionals. In addition, estimating the pharmacokinetic parameters from a DCE-MR image investigations is an urgent need to obtain the precise information about the AIF-the concentration of the contrast agent on the left ventricular blood pool measured over time. For this reason, the main idea is to show how to find a unique solution of linear system of equations generally in the form of y = Ax + b, named an ill-conditioned linear system of equations after discretization of the integral equations, which appear in different tomographic image restoration and reconstruction issues. Here, a new algorithm is described to estimate an appropriate probability distribution function for AIF according to the MET and regularization functionals for the contrast agent concentration when applying Bayesian estimation approach to estimate two different pharmacokinetic parameters. Moreover, by using the proposed approach when analyzing simulated and real datasets of the breast tumors according to pharmacokinetic factors, it indicates that using Bayesian inference-that infer the uncertainties of the computed solutions, and specific knowledge of the noise and errors-combined with the regularization functional of the maximum entropy problem, improved the convergence behavior and led to more consistent morphological and functional statistics and results. Finally, in comparison to the proposed exponential distribution based on MET and Newton's method, or Weibull distribution via the MET and teaching-learning-based optimization (MET/TLBO) in the previous studies, the family of Gamma and Erlang distributions estimated by the new algorithm are more appropriate and robust AIFs

Bayesian pharmacokinetic modeling of dynamic contrast-enhanced magnetic resonance imaging: validation and application

Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a framework of probability distributions. In this manuscript, we use the quantitative imaging biomarkers alliance (QIBA) Tofts phantom to evaluate the Bayesian tofts model (BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how Bayesian posterior probability distributions can be employed to assess treatment response in a breast cancer DCE-MRI dataset using Cohen's d. Accuracy and precision of the BTM posterior distributions were validated and found to be in good agreement with the NLLS approaches, and assessment of therapy response with respect to uncertainty in parameter estimates was found to be excellent. In conclusion, the Bayesian modeling approach provides an elegant means to determine uncertainty via posterior distributions within a single step and provides honest information about changes in parameter estimates

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated-in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching ("method of moments"), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters

A parametric model of the brain vascular system for estimation of the arterial input function (AIF) at the tissue level

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136452/1/nbm3695.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136452/2/nbm3695_am.pd

Spatio-Temporal Modelling of Perfusion Cardiovascular MRI

Myocardial perfusion MRI provides valuable insight into how coronary artery and microvascular diseases affect myocardial tissue. Stenosis in a coronary vessel leads to reduced maximum blood flow (MBF), but collaterals may secure the blood supply of the myocardium but with altered tracer kinetics. To date, quantitative analysis of myocardial perfusion MRI has only been performed on a local level, largely ignoring the contextual information inherent in different myocardial segments. This paper proposes to quantify the spatial dependencies between the local kinetics via a Hierarchical Bayesian Model (HBM). In the proposed framework, all local systems are modelled simultaneously along with their dependencies, thus allowing more robust context-driven estimation of local kinetics. Detailed validation on both simulated and patient data is provided

A comparison of Bayesian and non-linear regression methods for robust estimation of pharmacokinetics in DCE-MRI and how it affects cancer diagnosis

The aim of this work is to compare Bayesian Inference for nonlinear models with commonly used traditional non-linear regression (NR) algorithms for estimating tracer kinetics in Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI). The algorithms are compared in terms of accuracy, and reproducibility under different initialization settings. Further it is investigated how a more robust estimation of tracer kinetics affects cancer diagnosis. The derived tracer kinetics from the Bayesian algorithm were validated against traditional NR algorithms (i.e. Levenberg-Marquardt, simplex) in terms of accuracy on a digital DCE phantom and in terms of goodness-of-fit (Kolmogorov-Smirnov test) on ROI-based concentration time courses from two different patient cohorts. The first cohort consisted of 76 men, 20 of whom had significant peripheral zone prostate cancer (any cancer-core-length (CCL) with Gleason>3+3 or any-grade with CCL>=4mm) following transperineal template prostate mapping biopsy. The second cohort consisted of 9 healthy volunteers and 24 patients with head and neck squamous cell carcinoma. The diagnostic ability of the derived tracer kinetics was assessed with receiver operating characteristic area under curve (ROC AUC) analysis. The Bayesian algorithm accurately recovered the ground-truth tracer kinetics for the digital DCE phantom consistently improving the Structural Similarity Index (SSIM) across the 50 different initializations compared to NR. For optimized initialization, Bayesian did not improve significantly the fitting accuracy on both patient cohorts, and it only significantly improved the ve ROC AUC on the HN population from ROC AUC=0.56 for the simplex to ROC AUC=0.76. For both cohorts, the values and the diagnostic ability of tracer kinetic parameters estimated with the Bayesian algorithm weren't affected by their initialization. To conclude, the Bayesian algorithm led to a more accurate and reproducible quantification of tracer kinetic parameters in DCE-MRI, improving their ROC-AUC and decreasing their dependence on initialization settings