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 [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.

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.

The impact of model assumptions in scalar-on-image regression.

Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of nonidentifiability. While in theory, it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. This article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice based on the new measures and simulations using hypothetic coefficient images and the observed data.

Quantitative analyses of the 3D nuclear landscape recorded with super-resolved fluorescence microscopy.

Recent advancements of super-resolved fluorescence microscopy have revolutionized microscopic studies of cells, including the exceedingly complex structural organization of cell nuclei in space and time. In this paper we describe and discuss tools for (semi-) automated, quantitative 3D analyses of the spatial nuclear organization. These tools allow the quantitative assessment of highly resolved different chromatin compaction levels in individual cell nuclei, which reflect functionally different regions or sub-compartments of the 3D nuclear landscape, and measurements of absolute distances between sites of different chromatin compaction. In addition, these tools allow 3D mapping of specific DNA/RNA sequences and nuclear proteins relative to the 3D chromatin compaction maps and comparisons of multiple cell nuclei. The tools are available in the free and open source R packages nucim and bioimagetools. We discuss the use of masks for the segmentation of nuclei and the use of DNA stains, such as DAPI, as a proxy for local differences in chromatin compaction. We further discuss the limitations of 3D maps of the nuclear landscape as well as problems of the biological interpretation of such data.

Bayesian mixed-effects model for the analysis of a series of FRAP images.

The binding behavior of molecules in nuclei of living cells can be studied through the analysis of images from fluorescence recovery after photobleaching experiments. However, there is still a lack of methodology for the statistical evaluation of FRAP data, especially for the joint analysis of multiple dynamic images. We propose a hierarchical Bayesian nonlinear model with mixed-effect priors based on local compartment models in order to obtain joint parameter estimates for all nuclei as well as to account for the heterogeneity of the nuclei population. We apply our method to a series of FRAP experiments of DNA methyltransferase 1 tagged to green fluorescent protein expressed in a somatic mouse cell line and compare the results to the application of three different fixed-effects models to the same series of FRAP experiments. With the proposed model, we get estimates of the off-rates of the interactions of the molecules under study together with credible intervals, and additionally gain information about the variability between nuclei. The proposed model is superior to and more robust than the tested fixed-effects models. Therefore, it can be used for the joint analysis of data from FRAP experiments on various similar nuclei.

Stage-dependent remodeling of the nuclear envelope and lamina during rabbit early embryonic development.

Utilizing 3D structured illumination microscopy, we investigated the quality and quantity of nuclear invaginations and the distribution of nuclear pores during rabbit early embryonic development and identified the exact time point of nucleoporin 153 (NUP153) association with chromatin during mitosis. Contrary to bovine early embryonic nuclei, featuring almost exclusively nuclear invaginations containing a small volume of cytoplasm, nuclei in rabbit early embryonic stages show additionally numerous invaginations containing a large volume of cytoplasm. Small-volume invaginations frequently emanated from large-volume nuclear invaginations but not vice versa, indicating a different underlying mechanism. Large- and small-volume nuclear envelope invaginations required the presence of chromatin, as they were restricted to chromatin-positive areas. The chromatin-free contact areas between nucleolar precursor bodies (NPBs) and large-volume invaginations were free of nuclear pores. Small-volume invaginations were not in contact with NPBs. The number of invaginations and isolated intranuclear vesicles per nucleus peaked at the 4-cell stage. At this stage, the nuclear surface showed highly concentrated clusters of nuclear pores surrounded by areas free of nuclear pores. Isolated intranuclear lamina vesicles were usually NUP153 negative. Cytoplasmic, randomly distributed NUP153-positive clusters were highly abundant at the zygote stage and decreased in number until they were almost absent at the 8-cell stage and later. These large NUP153 clusters may represent a maternally provided NUP153 deposit, but they were not visible as clusters during mitosis. Major genome activation at the 8- to 16-cell stage may mark the switch from a necessity for a deposit to on-demand production. NUP153 association with chromatin is initiated during metaphase before the initiation of the regeneration of the lamina. To our knowledge, the present study demonstrates for the first time major remodeling of the nuclear envelope and its underlying lamina during rabbit preimplantation development.

Spatially regularized estimation for the analysis of dynamic contrast-enhanced magnetic resonance imaging data.

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.

Sensitivity to prior specification in Bayesian genome-based prediction models.

Different statistical models have been proposed for maximizing prediction accuracy in genome-based prediction of breeding values in plant and animal breeding. However, little is known about the sensitivity of these models with respect to prior and hyperparameter specification, because comparisons of prediction performance are mainly based on a single set of hyperparameters. In this study, we focused on Bayesian prediction methods using a standard linear regression model with marker covariates coding additive effects at a large number of marker loci. By comparing different hyperparameter settings, we investigated the sensitivity of four methods frequently used in genome-based prediction (Bayesian Ridge, Bayesian Lasso, BayesA and BayesB) to specification of the prior distribution of marker effects. We used datasets simulated according to a typical maize breeding program differing in the number of markers and the number of simulated quantitative trait loci affecting the trait. Furthermore, we used an experimental maize dataset, comprising 698 doubled haploid lines, each genotyped with 56110 single nucleotide polymorphism markers and phenotyped as testcrosses for the two quantitative traits grain dry matter yield and grain dry matter content. The predictive ability of the different models was assessed by five-fold cross-validation. The extent of Bayesian learning was quantified by calculation of the Hellinger distance between the prior and posterior densities of marker effects. Our results indicate that similar predictive abilities can be achieved with all methods, but with BayesA and BayesB hyperparameter settings had a stronger effect on prediction performance than with the other two methods. Prediction performance of BayesA and BayesB suffered substantially from a non-optimal choice of hyperparameters.

The potential of 3D-FISH and super-resolution structured illumination microscopy for studies of 3D nuclear architecture: 3D structured illumination microscopy of defined chromosomal structures visualized by 3D (immuno)-FISH opens new perspectives for studies of nuclear architecture.

Three-dimensional structured illumination microscopy (3D-SIM) has opened up new possibilities to study nuclear architecture at the ultrastructural level down to the ~100 nm range. We present first results and assess the potential using 3D-SIM in combination with 3D fluorescence in situ hybridization (3D-FISH) for the topographical analysis of defined nuclear targets. Our study also deals with the concern that artifacts produced by FISH may counteract the gain in resolution. We address the topography of DAPI-stained DNA in nuclei before and after 3D-FISH, nuclear pores and the lamina, chromosome territories, chromatin domains, and individual gene loci. We also look at the replication patterns of chromocenters and the topographical relationship of Xist-RNA within the inactive X-territory. These examples demonstrate that an appropriately adapted 3D-FISH/3D-SIM approach preserves key characteristics of the nuclear ultrastructure and that the gain in information obtained by 3D-SIM yields new insights into the functional nuclear organization.

Automatic post-picking using MAPPOS improves particle image detection from cryo-EM micrographs.

Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are detected on and boxed out from each micrograph using fully- or semi-automated approaches. However, the obtained particles still require laborious manual post-picking classification, which is one major bottleneck for single particle analysis of large datasets. We introduce MAPPOS, a supervised post-picking strategy for the classification of boxed particle images, as additional strategy adding to the already efficient automated particle picking routines. MAPPOS employs machine learning techniques to train a robust classifier from a small number of characteristic image features. In order to accurately quantify the performance of MAPPOS we used simulated particle and non-particle images. In addition, we verified our method by applying it to an experimental cryo-EM dataset and comparing the results to the manual classification of the same dataset. Comparisons between MAPPOS and manual post-picking classification by several human experts demonstrated that merely a few hundred sample images are sufficient for MAPPOS to classify an entire dataset with a human-like performance. MAPPOS was shown to greatly accelerate the throughput of large datasets by reducing the manual workload by orders of magnitude while maintaining a reliable identification of non-particle images.

An automated tool for detection of FLAIR-hyperintense white-matter lesions in Multiple Sclerosis.

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.

Double-strand break-induced transcriptional silencing is associated with loss of tri-methylation at H3K4.

Epigenetic alterations induced by ionizing radiation may contribute to radiation carcinogenesis. To detect relative accumulations or losses of constitutive post-translational histone modifications in chromatin regions surrounding DNA double-strand breaks (DSB), we developed a method based on ion microirradiation and correlation of the signal intensities after immunofluorescence detection of the histone modification in question and the DSB marker γ-H2AX. We observed after ionizing irradiation markers for transcriptional silencing, such as accumulation of H3K27me3 and loss of active RNA polymerase II, at chromatin regions labeled by γ-H2AX. Confocal microscopy of whole nuclei and of ultrathin nuclear sections revealed that the histone modification H3K4me3, which labels transcriptionally active regions, is underrepresented in γ-H2AX foci. While some exclusion of H3K4me3 is already evident at the earliest time amenable to this kind of analysis, the anti-correlation apparently increases with time after irradiation, suggesting an active removal process. Focal accumulation of the H3K4me3 demethylase, JARID1A, was observed at damaged regions inflicted by laser irradiation, suggesting involvement of this enzyme in the DNA damage response. Since no accumulation of the repressive mark H3K9me2 was found at damaged sites, we suggest that DSB-induced transcriptional silencing resembles polycomb-mediated silencing rather than heterochromatic silencing.

A Bayesian hierarchical model for DCE-MRI to evaluate treatment response in a phase II study in advanced squamous cell carcinoma of the head and neck.

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.

Co-localization analysis in fluorescence microscopy via maximum entropy copula.

Co-localization analysis is a popular method for quantitative analysis in fluorescence microscopy imaging. The localization of marked proteins in the cell nucleus allows a deep insight into biological processes in the nucleus. Several metrics have been developed for measuring the co-localization of two markers, however, they depend on subjective thresholding of background and the assumption of linearity. We propose a robust method to estimate the bivariate distribution function of two color channels. From this, we can quantify their co- or anti-colocalization. The proposed method is a combination of the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This new method can measure the spatial and nonlinear correlation of signals to determine the marker colocalization in fluorescence microscopy images. The proposed method is compared with MEM for bivariate probability distributions. The new colocalization metric is validated on simulated and real data. The results show that MEC can determine co- and anti-colocalization even in high background settings. MEC can, therefore, be used as a robust tool for colocalization analysis.

Cohesin depleted cells rebuild functional nuclear compartments after endomitosis.

Cohesin plays an essential role in chromatin loop extrusion, but its impact on a compartmentalized nuclear architecture, linked to nuclear functions, is less well understood. Using live-cell and super-resolved 3D microscopy, here we find that cohesin depletion in a human colon cancer derived cell line results in endomitosis and a single multilobulated nucleus with chromosome territories pervaded by interchromatin channels. Chromosome territories contain chromatin domain clusters with a zonal organization of repressed chromatin domains in the interior and transcriptionally competent domains located at the periphery. These clusters form microscopically defined, active and inactive compartments, which likely correspond to A/B compartments, which are detected with ensemble Hi-C. Splicing speckles are observed nearby within the lining channel system. We further observe that the multilobulated nuclei, despite continuous absence of cohesin, pass through S-phase with typical spatio-temporal patterns of replication domains. Evidence for structural changes of these domains compared to controls suggests that cohesin is required for their full integrity.

A Bayesian hierarchical model for the analysis of a longitudinal dynamic contrast-enhanced MRI oncology study.

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.

Joint Spatio-Temporal Shared Component Model with an Application in Iran Cancer Data

Background: Among the proposals for joint disease mapping, the shared component model has become more popular. Another advance to strengthen inference of disease data is the extension of purely spatial models to include time aspect. We aim to combine the idea of multivariate shared components with spatio-temporal modelling in a joint disease mapping model and apply it for incidence rates of seven prevalent cancers in Iran which together account for approximately 50% of all cancers. Methods: In the proposed model, each component is shared by different subsets of diseases, spatial and temporal trends are considered for each component, and the relative weight of these trends for each component for each relevant disease can be estimated. Results: For esophagus and stomach cancers the Northern provinces was the area of high risk. For colorectal cancer Gilan, Semnan, Fars, Isfahan, Yazd and East-Azerbaijan were the highest risk provinces. For bladder and lung cancer, the northwest were the highest risk area. For prostate and breast cancers, Isfahan, Yazd, Fars, Tehran, Semnan, Mazandaran and Khorasane-Razavi were the highest risk part. The smoking component, shared by esophagus, stomach, bladder and lung, had more effect in Gilan, Mazandaran, Chaharmahal and Bakhtiari, Kohgilouyeh and Boyerahmad, Ardebil and Tehran provinces, in turn. For overweight and obesity component, shared by esophagus, colorectal, prostate and breast cancers the largest effect was found for Tehran, Khorasane-Razavi, Semnan, Yazd, Isfahan, Fars, Mazandaran and Gilan, in turn. For low physical activity component, shared by colorectal and breast cancers North-Khorasan, Ardebil, Golestan, Ilam, Khorasane-Razavi and South-Khorasan had the largest effects, in turn. The smoking component is significantly more important for stomach than for esophagus, bladder and lung. The overweight and obesity had significantly more effect for colorectal than of esophagus cancer. Conclusions: The presented model is a valuable model to model geographical and temporal variation among diseases and has some interesting potential features and benefits over other joint models.

Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

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.

Initial high-resolution microscopic mapping of active and inactive regulatory sequences proves non-random 3D arrangements in chromatin domain clusters.

BACKGROUND: The association of active transcription regulatory elements (TREs) with DNAse I hypersensitivity (DHS[+]) and an 'open' local chromatin configuration has long been known. However, the 3D topography of TREs within the nuclear landscape of individual cells in relation to their active or inactive status has remained elusive. Here, we explored the 3D nuclear topography of active and inactive TREs in the context of a recently proposed model for a functionally defined nuclear architecture, where an active and an inactive nuclear compartment (ANC-INC) form two spatially co-aligned and functionally interacting networks. RESULTS: Using 3D structured illumination microscopy, we performed 3D FISH with differently labeled DNA probe sets targeting either sites with DHS[+], apparently active TREs, or DHS[-] sites harboring inactive TREs. Using an in-house image analysis tool, DNA targets were quantitatively mapped on chromatin compaction shaped 3D nuclear landscapes. Our analyses present evidence for a radial 3D organization of chromatin domain clusters (CDCs) with layers of increasing chromatin compaction from the periphery to the CDC core. Segments harboring active TREs are significantly enriched at the decondensed periphery of CDCs with loops penetrating into interchromatin compartment channels, constituting the ANC. In contrast, segments lacking active TREs (DHS[-]) are enriched toward the compacted interior of CDCs (INC). CONCLUSIONS: Our results add further evidence in support of the ANC-INC network model. The different 3D topographies of DHS[+] and DHS[-] sites suggest positional changes of TREs between the ANC and INC depending on their functional state, which might provide additional protection against an inappropriate activation. Our finding of a structural organization of CDCs based on radially arranged layers of different chromatin compaction levels indicates a complex higher-order chromatin organization beyond a dichotomic classification of chromatin into an 'open,' active and 'closed,' inactive state.

Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging.

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.