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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 [Formula: see text] 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., (© 2022. The Author(s).)

Background: In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role., Objectives: This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available., Methods: In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study., Results: The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently., Conclusions: The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI., Competing Interests: Disclosure The authors report no conflicts of interest in this work., (Schattauer GmbH.)

Competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging data. We present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori. A multi-compartment approach is considered, which is translated into a restricted least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment. Using a spatial elastic net estimator, we chose a sparse set of basis functions per voxel, and hence, rate constants of compartments. The spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently. The proposed estimation method is evaluated for simulated images and applied to an in vivo dataset., (Copyright © 2013 John Wiley & Sons, Ltd.)

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

In Multiple Sclerosis (MS), detection of T2-hyperintense white matter (WM) lesions on magnetic resonance imaging (MRI) has become a crucial criterion for diagnosis and predicting prognosis in early disease. Automated lesion detection is not only desirable with regard to time and cost effectiveness but also constitutes a prerequisite to minimize user bias. Here, we developed and evaluated an algorithm for automated lesion detection requiring a three-dimensional (3D) gradient echo (GRE) T1-weighted and a FLAIR image at 3 Tesla (T). Our tool determines the three tissue classes of gray matter (GM) and WM as well as cerebrospinal fluid (CSF) from the T1-weighted image, and, then, the FLAIR intensity distribution of each tissue class in order to detect outliers, which are interpreted as lesion beliefs. Next, a conservative lesion belief is expanded toward a liberal lesion belief. To this end, neighboring voxels are analyzed and assigned to lesions under certain conditions. This is done iteratively until no further voxels are assigned to lesions. Herein, the likelihood of belonging to WM or GM is weighed against the likelihood of belonging to lesions. We evaluated our algorithm in 53 MS patients with different lesion volumes, in 10 patients with posterior fossa lesions, and 18 control subjects that were all scanned at the same 3T scanner (Achieva, Philips, Netherlands). We found good agreement with lesions determined by manual tracing (R2 values of over 0.93 independent of FLAIR slice thickness up to 6mm). These results require validation with data from other protocols based on a conventional FLAIR sequence and a 3D GRE T1-weighted sequence. Yet, we believe that our tool allows fast and reliable segmentation of FLAIR-hyperintense lesions, which might simplify the quantification of lesions in basic research and even clinical trials., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Contrast enhanced myocardial perfusion magnetic resonance imaging (MRI) is a promising technique, providing insight into how reduced coronary flow affects the myocardial tissue. Stenosis in a coronary vessel leads to reduced myocardial blood flow, but collaterals may secure the blood supply of the myocardium, with altered tracer kinetics. Due to a low signal-to-noise ratio, quantitative analysis of the signal is typically difficult to achieve at the voxel level. Hence, analysis is often performed on measurements that are aggregated in predefined myocardial segments, that ignore the variability in blood flow in each segment. The approach presented in this paper uses local spatial information that enables one to perform a robust analysis at the voxel level. The spatial dependencies between local response curves are modelled via a hierarchical Bayesian model. In the proposed framework, all local systems are analyzed simultaneously along with their dependencies, producing a more robust context-driven estimation of local kinetics. Detailed validation on both simulated and patient data is provided.

Object: Pharmacokinetic parameters from dynamic contrast-enhanced MRI (DCE-MRI) were used to assess the perfusion effects due to treatment response using a tyrosine kinase inhibitor. A Bayesian hierarchical model (BHM) is proposed, as an alternative to voxel-wise estimation procedures, to test for a treatment effect while explicitly modeling known sources of variability., Materials and Methods: Nine subjects from a randomized, blinded, placebo-controlled, multicenter, phase II study of lapatinib were examined before and after treatment. Kinetic parameters were estimated, with an extended compartmental model and subject-specific arterial input function, on a voxel-by-voxel basis., Results: The group treated with lapatinib had a decrease in median K(trans) of 0.17 min⁻¹, when averaged across all voxels in the tumor ROIs, compared with no change in the placebo group based on nonlinear regression. A hypothesis test of equality between pre- and posttreatment K (trans) could not be rejected against a one-sided alternative (P = 0.09). Equality between median K(trans) in placebo and lapatinib groups posttreatment could also not be rejected using the BHM (P = 0.32). Across all scans acquired in the study, estimates of K(trans) at one site were greater on average than those at the other site by including a site effect in the BHM. The inter-voxel variability is of similar order (within 15%) when compared to the inter-patient variability., Conclusion: Though the study contained a small number of subjects and no significant difference was found, the Bayesian hierarchical model provided estimates of variability from known sources in the study and confidence intervals for all estimated parameters. We believe the BHM provides a straightforward and thorough interrogation of the imaging data at the level of voxels, patients or sites in this multicenter clinical study.

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 nonlinear 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 these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where 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.

Imaging in clinical oncology trials provides a wealth of information that contributes to the drug development process, especially in early phase studies. This article focuses on kinetic modeling in DCE-MRI, inspired by mixed-effects models that are frequently used in the analysis of clinical trials. Instead of summarizing each scanning session as a single kinetic parameter--such as median k(trans) across all voxels in the tumor ROI-we propose to analyze all voxel time courses from all scans and across all subjects simultaneously in a single model. The kinetic parameters from the usual nonlinear regression model are decomposed into unique components associated with factors from the longitudinal study; e.g., treatment, patient, and voxel effects. A Bayesian hierarchical model provides the framework to construct a data model, a parameter model, as well as prior distributions. The posterior distribution of the kinetic parameters is estimated using Markov chain Monte Carlo (MCMC) methods. Hypothesis testing at the study level for an overall treatment effect is straightforward and the patient- and voxel-level parameters capture random effects that provide additional information at various levels of resolution to allow a thorough evaluation of the clinical trial. The proposed method is validated with a breast cancer study, where the subjects were imaged before and after two cycles of chemotherapy, demonstrating the clinical potential of this method to longitudinal oncology studies.

Non-linear attenuation of the Arterial Input Function (AIF) is a major problem in first-pass MR perfusion imaging due to the high concentration of the contrast agent in the blood pool. This paper presents a technique to reconstruct the true AIF using signal intensities in the myocardium and the attenuated AIF based on a Hierarchical Bayesian Model (HBM). With the proposed method, both the AIF and the response function are modeled as smoothed functions by using Bayesian penalty splines (P-Splines). The derived AIF is then used to estimate the impulse response of the myocardium based on deconvolution analysis. The proposed technique is validated both with simulated data using the MMID4 model and ten in vivo data sets for estimating myocardial perfusion reserve rates. The results demonstrate the ability of the proposed technique in accurately reconstructing the desired AIF for myocardial perfusion quantification. The method does not involve any MRI pulse sequence modification, and thus is expected to have wider clinical impact.

This paper proposes a new method for estimating kinetic parameters of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on adaptive Gaussian Markov random fields. Kinetic parameter estimates using neighboring voxels reduce the observed variability in local tumor regions while preserving sharp transitions between heterogeneous tissue boundaries. Asymptotic results for standard errors from likelihood-based nonlinear regression are compared with those derived from the posterior distribution using Bayesian estimation with and without neighborhood information. Application of the method to the analysis of breast tumors based on kinetic parameters has shown that the use of Bayesian analysis combined with adaptive Gaussian Markov random fields provides improved convergence behavior and more consistent morphological and functional statistics.

Current approaches to quantitative analysis of DCE-MRI with non-linear models involve the convolution of an arterial input function (AIF) with the contrast agent concentration at a voxel or regional level. Full quantification provides meaningful biological parameters but is complicated by the issues related to convergence, (de-)convolution of the AIF, and goodness of fit. To overcome these problems, this paper presents a penalized spline smoothing approach to model the data in a semi-parametric way. With this method, the AIF is convolved with a set of B-splines to produce the design matrix, and modeling of the resulting deconvolved biological parameters is obtained in a way that is similar to the parametric models. Further kinetic parameters are obtained by fitting a non-linear model to the estimated response function and detailed validation of the method, both with simulated and in vivo data is

This paper assesses the estimation of kinetic parameters from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Asymptotic results from likelihood-based nonlinear regression are compared with results derived from the posterior distribution using Bayesian estimation, along with the output from an established software package (MRIW). By using the estimated error from kinetic parameters, it is possible to produce more accurate clinical statistics, such as tumor size, for patients with breast tumors. Further analysis has also shown that Bayesian methods are more accurate and do not suffer from convergence problems, but at a higher computational cost.

Object: Pharmacokinetic parameters from dynamic contrast-enhanced MRI (DCE-MRI) were used to assess the perfusion effects due to treatment response using a tyrosine kinase inhibitor. A Bayesian hierarchical model (BHM) is proposed, as an alternative to voxel-wise estimation procedures, to test for a treatment effect while explicitly modeling known sources of variability. Materials and methods: Nine subjects from a randomized, blinded, placebo-controlled, multicenter, phase II study of lapatinib were examined before and after treatment. Kinetic parameters were estimated, with an extended compartmental model and subject-specific arterial input function, on a voxel-by-voxel basis. Results: The group treated with lapatinib had a decrease in median K of 0.17min, when averaged across all voxels in the tumor ROIs, compared with no change in the placebo group based on nonlinear regression. A hypothesis test of equality between pre- and posttreatment K could not be rejected against a one-sided alternative ( P = 0.09). Equality between median K in placebo and lapatinib groups posttreatment could also not be rejected using the BHM ( P = 0.32). Across all scans acquired in the study, estimates of K at one site were greater on average than those at the other site by including a site effect in the BHM. The inter-voxel variability is of similar order (within 15%) when compared to the inter-patient variability. Conclusion: Though the study contained a small number of subjects and no significant difference was found, the Bayesian hierarchical model provided estimates of variability from known sources in the study and confidence intervals for all estimated parameters. We believe the BHM provides a straightforward and thorough interrogation of the imaging data at the level of voxels, patients or sites in this multicenter clinical study. [ABSTRACT FROM AUTHOR]