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

Direct Comparison of Bayesian and Fermi Deconvolution Approaches for Myocardial Blood Flow Quantification: In silico and Clinical Validations

Cardiac magnetic resonance myocardial perfusion imaging can detect coronary artery disease and is an alternative to single-photon emission computed tomography or positron emission tomography. However, the complex, non-linear MR signal and the lack of robust quantification of myocardial blood flow have hindered its widespread clinical application thus far. Recently, a new Bayesian approach was developed for brain imaging and evaluation of perfusion indexes (Kudo et al., 2014). In addition to providing accurate perfusion measurements, this probabilistic approach appears more robust than previous approaches, particularly due to its insensitivity to bolus arrival delays. We assessed the performance of this approach against a well-known and commonly deployed model-independent method based on the Fermi function for cardiac magnetic resonance myocardial perfusion imaging. The methods were first evaluated for accuracy and precision using a digital phantom to test them against the ground truth; next, they were applied in a group of coronary artery disease patients. The Bayesian method can be considered an appropriate model-independent method with which to estimate myocardial blood flow and delays. The digital phantom comprised a set of synthetic time-concentration curve combinations generated with a 2-compartment exchange model and a realistic combination of perfusion indexes, arterial input dynamics, noise and delays collected from the clinical dataset. The myocardial blood flow values estimated with the two methods showed an excellent correlation coefficient (r² > 0.9) under all noise and delay conditions. The Bayesian approach showed excellent robustness to bolus arrival delays, with a similar performance to Fermi modeling when delays were considered. Delays were better estimated with the Bayesian approach than with Fermi modeling. An in vivo analysis of coronary artery disease patients revealed that the Bayesian approach had an excellent ability to distinguish between abnormal and normal myocardium. The Bayesian approach was able to discriminate not only flows but also delays with increased sensitivity by offering a clearly enlarged range of distribution for the physiologic parameters.

Hierarchical Bayesian myocardial perfusion quantification

Myocardial blood flow can be quantified from dynamic contrast-enhanced magnetic resonance (MR) images through the fitting of tracer-kinetic models to the observed imaging data. The use of multi-compartment exchange models is desirable as they are physiologically motivated and resolve directly for both blood flow and microvascular function. However, the parameter estimates obtained with such models can be unreliable. This is due to the complexity of the models relative to the observed data which is limited by the low signal-to-noise ratio, the temporal resolution, the length of the acquisitions and other complex imaging artefacts. In this work, a Bayesian inference scheme is proposed which allows the reliable estimation of the parameters of the two-compartment exchange model from myocardial perfusion MR data. The Bayesian scheme allows the incorporation of prior knowledge on the physiological ranges of the model parameters and facilitates the use of the additional information that neighbouring voxels are likely to have similar kinetic parameter values. Hierarchical priors are used to avoid making a priori assumptions on the health of the patients. We provide both a theoretical introduction to Bayesian inference for tracer-kinetic modelling and specific implementation details for this application. This approach is validated in both in silico and in vivo settings. In silico, there was a significant reduction in mean-squared error with the ground-truth parameters using Bayesian inference as compared to using the standard non-linear least squares fitting. When applied to patient data the Bayesian inference scheme returns parameter values that are in-line with those previously reported in the literature, as well as giving parameter maps that match the independant clinical diagnosis of those patients.

Voxel Forecast for Precision Oncology: Predicting Spatially Variant and Multiscale Cancer Therapy Response on Longitudinal Quantitative Molecular Imaging

PURPOSE

Prediction of spatially variant response to cancer therapies can inform risk-adaptive management within precision oncology. We developed the "Voxel Forecast" multiscale regression framework for predicting spatially variant tumor response to chemoradiotherapy on fluorodeoxyglucose (FDG) positron emission tomography/computed tomography (PET/CT) imaging.

EXPERIMENTAL DESIGN

Twenty-five patients with locally advanced non-small cell lung cancer, enrolled on the FLARE-RT phase II trial (NCT02773238), underwent FDG PET/CT imaging prior to (PETpre) and during week 3 (PETmid) of concurrent chemoradiotherapy. Voxel Forecast was designed to predict tumor voxel standardized uptake value (SUV) on PETmid from baseline patient-level and voxel-level covariates using a custom generalized least squares (GLS) algorithm. Matérn covariance matrices were fit to patient- specific empirical variograms of distance-dependent intervoxel correlation. Regression coefficients from variogram-based weights and corresponding standard errors were estimated using the jackknife technique. The framework was validated using statistical simulations of known spatially variant tumor response. Mean absolute prediction errors (MAEs) of Voxel Forecast models were calculated under leave-one-patient-out cross-validation.

RESULTS

Patient-level forecasts resulted in tumor voxel SUV MAE on PETmid of 1.5 g/mL while combined patient- and voxel-level forecasts achieved lower MAE of 1.0 g/mL (P < 0.0001). PETpre voxel SUV was the most important predictor of PETmid voxel SUV. Patients with a greater percentage of under-responding tumor voxels were classified as PETmid nonresponders (P = 0.030) with worse overall survival prognosis (P < 0.001).

CONCLUSIONS

Voxel Forecast multiscale regression provides a statistical framework to predict voxel-wise response patterns during therapy. Voxel Forecast can be extended to predict spatially variant response on multimodal quantitative imaging and may eventually guide optimized spatial-temporal dose distributions for precision cancer therapy.

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.

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.

Practical aspects of prostate MRI: hardware and software considerations, protocols, and patient preparation

The use of multiparametric MRI scans for the evaluation of men with prostate cancer has increased dramatically and is likely to continue expanding as new developments come to practice. However, it has not yet gained the same level of acceptance of other imaging tests. Partly, this is because of the use of suboptimal protocols, lack of standardization, and inadequate patient preparation. In this manuscript, we describe several practical aspects of prostate MRI that may facilitate the implementation of new prostate imaging programs or the expansion of existing ones.

Boosting in Nonlinear Regression Models with an Application to DCE-MRI Data

BACKGROUND

For the statistical analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data, compartment models are a commonly used tool. By these models, the observed uptake of contrast agent in some tissue over time is linked to physiologic properties like capillary permeability and blood flow. Up to now, models of different complexity have been used, and it is still unclear which model should be used in which situation. In previous studies, it has been found that for DCE-MRI data, the number of compartments differs for different types of tissue, and that in cancerous tissue, it might actually differ over a region of voxels of one DCE-MR image.

OBJECTIVES

To find the appropriate number of compartments and estimate the parameters of a regression model for each voxel in an DCE-MR image. With that, tumors in an DCE-MR image can be located, and for example therapy success can be assessed.

METHODS

The observed uptake of contrast agent in a voxel of an image of some tissue is described by a concentration time curve. This curve can be modeled using a nonlinear regression model. We present a boosting approach with nonlinear regression as base procedure, which allows us to estimate the number of compartments and the related parameters for each voxel of an DCE-MR image. In addition, a spatially regularized version of this approach is proposed.

RESULTS

With the proposed approach, the number of compartments - and with that the complexity of the model - per voxel is not fixed but data-driven, which allows us to fit models of adequate complexity to the concentration time curves of all voxels. The parameters of the model remain nevertheless interpretable because of the underlying compartment model.

CONCLUSIONS

The proposed boosting approaches outperform all competing methods considered in this paper regarding the correct localization of tumors in DCE-MR images as well as the spatial homogeneity of the estimated number of compartments across the image, and the definition of the tumor edge.

Estimating anatomical trajectories with Bayesian mixed-effects modeling

We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD).

DCEMRI.jl: a fast, validated, open source toolkit for dynamic contrast enhanced MRI analysis

We present a fast, validated, open-source toolkit for processing dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) data. We validate it against the Quantitative Imaging Biomarkers Alliance (QIBA) Standard and Extended Tofts-Kety phantoms and find near perfect recovery in the absence of noise, with an estimated 10-20× speedup in run time compared to existing tools. To explain the observed trends in the fitting errors, we present an argument about the conditioning of the Jacobian in the limit of small and large parameter values. We also demonstrate its use on an in vivo data set to measure performance on a realistic application. For a 192 × 192 breast image, we achieved run times of <1 s. Finally, we analyze run times scaling with problem size and find that the run time per voxel scales as O(N (1.9)), where N is the number of time points in the tissue concentration curve. DCEMRI.jl was much faster than any other analysis package tested and produced comparable accuracy, even in the presence of noise.

Mixed-effects modeling of clinical DCE-MRI data: application to colorectal liver metastases treated with bevacizumab

PURPOSE

Most dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data are evaluated for individual patients with cohorts analyzed to detect significant changes from baseline values, repeating the process at each posttreatment timepoint. Our study aimed to develop a statistically valid model for the complete time course of DCE-MRI data in a patient cohort.

MATERIALS AND METHODS

Data from 10 patients with colorectal cancer liver metastases were analyzed, including two baseline scans and four post-bevacizumab scans. Apparent changes in tumor median K(trans) were adjusted for changes in observed enhancing tumor fraction (EnF) by multiplying K(trans) by EnF (KEnF). A mixed-effects model (MEM) was defined to describe the KEnF time course for all patients simultaneously by assuming a three-parameter indirect response model with model parameters lognormally distributed across patients.

RESULTS

The typical cohort time course showed a KEnF reduction to 59% of baseline at 24 hours, returning to 65% of baseline values by day 12. Interpatient variability of model parameters ranged from 11% to 307%.

CONCLUSION

The MEM approach has potential for comparing responses at a group level in clinical trials with different doses, schedules, or combination regimens. Furthermore, the KEnF biomarker successfully resolved confounds in interpreting K(trans) arising from therapy induced changes in the volume of enhancing tumor.

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.

Spatially variant noise estimation in MRI: a homomorphic approach

The reliable estimation of noise characteristics in MRI is a task of great importance due to the influence of noise features in extensively used post-processing algorithms. Many methods have been proposed in the literature to retrieve noise features from the magnitude signal. However, most of them assume a stationary noise model, i.e., the features of noise do not vary with the position inside the image. This assumption does not hold when modern scanning techniques are considered, e.g., in the case of parallel reconstruction and intensity correction. Therefore, new noise estimators must be found to cope with non-stationary noise. Some methods have been recently proposed in the literature. However, they require multiple acquisitions or extra information which is usually not available (biophysical models, sensitivity of coils). In this work we overcome this drawback by proposing a new method that can accurately estimate the non-stationary parameters of noise from just a single magnitude image. In the derivation, we considered the noise to follow a non-stationary Rician distribution, since it is the most common model in real acquisitions (e.g., SENSE reconstruction), though it can be easily generalized to other models. The proposed approach makes use of a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is then estimated by a low pass filtering with a Rician bias correction. Results in real and synthetic experiments evidence the better performance and the lowest error variance of the proposed methodology when compared to the state-of-the-art methods.

Indexed distribution analysis for improved significance testing of spatially heterogeneous parameter maps: application to dynamic contrast-enhanced MRI biomarkers

PURPOSE

To develop significance testing methodology applicable to spatially heterogeneous parametric maps of biophysical and physiological measurements arising from imaging studies.

THEORY

Heterogeneity can confound statistical analyses. Indexed distribution analysis (IDA) transforms a reference distribution, establishing correspondences across parameter maps to which significance tests are applied.

METHODS

Well-controlled simulated and clinical K(trans) data from a dynamic contrast-enhanced magnetic resonance imaging study of bevacizumab were analyzed using conventional significance tests of parameter averages, histogram analysis, and IDA. Repeated pretreatment scans provided negative control; a post treatment scan provided positive control.

RESULTS

Histogram analysis was insensitive to simulated and known effects. Simulation: conventional analysis identified treatment effect (P ≈ 5 × 10(-4)) and direction, but underestimated magnitude (relative error 67-81%); IDA identified treatment effect (P = 0.001), magnitude, direction, and spatial extent (100% accuracy). Bevacizumab: conventional analysis was sensitive to treatment effect (P = 0.01; 95% confidence interval on K(trans) decrease: 23-37%); IDA was sensitive to treatment effect (P < 0.05; K(trans) decrease approximately 25%), inferred its spatial extent to be 94-96%, and inferred that K(trans) decrease is independent of baseline value, an inference that conventional and histogram analyses cannot make.

CONCLUSIONS

In the presence of heterogeneity, IDA can accurately infer the magnitude, direction, and spatial extent of between samples of parametric maps, which can be visualized spatially with respect to the original parameter maps.

Improved intravoxel incoherent motion analysis of diffusion weighted imaging by data driven Bayesian modeling

In addition to the diffusion coefficient, fitting the intravoxel incoherent motion model to multiple b-value diffusion-weighted MR data gives pseudo-diffusion measures associated with rapid signal attenuation at low b-values that are of use in the assessment of a number of pathologies. When summary measures are required, such as the average parameter for a region of interest, least-squares based methods give adequate estimation accuracy. However, using least-squares methods for pixel-wise fitting typically gives noisy estimates, especially for the pseudo-diffusion parameters, which limits the applicability of the approach for assessing spatial features and heterogeneity. In this article, a Bayesian approach using a shrinkage prior model is proposed and is shown to substantially reduce estimation uncertainty so that spatial features in the parameters maps are more clearly apparent. The Bayesian approach has no user-defined parameters, so measures of parameter variation (heterogeneity) over regions of interest are determined by the data alone, whereas it is shown that for the least-squares estimates, measures of variation are essentially determined by user-defined constraints on the parameters. Use of a Bayesian shrinkage prior approach is, therefore, recommended for intravoxel incoherent motion modeling.

Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods - based on a single noise level for the whole image - fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.

Models of the aging brain structure and individual decline

The aging brain's structural development constitutes a spatiotemporal process that is accessible by MR-based computational morphometry. Here we introduce basic concepts and analytical approaches to quantify age-related differences and changes in neuroanatomical images of the human brain. The presented models first address the estimation of age trajectories, then we consider inter-individual variations of structural decline, using a repeated measures design. We concentrate our overview on preprocessed neuroanatomical images of the human brain to facilitate practical applications to diverse voxel- and surface-based structural markers. Together these methods afford analysis of aging brain structure in relation to behavioral, health, or cognitive parameters.

Motion correction and parameter estimation in dceMRI sequences: application to colorectal cancer

We present a novel Bayesian framework for non-rigid motion correction and pharmacokinetic parameter estimation in dceMRI sequences which incorporates a physiological image formation model into the similarity measure used for motion correction. The similarity measure is based on the maximization of the joint posterior probability of the transformations which need to be applied to each image in the dataset to bring all images into alignment, and the physiological parameters which best explain the data. The deformation framework used to deform each image is based on the diffeomorphic logDemons algorithm. We then use this method to co-register images from simulated and real dceMRI datasets and show that the method leads to an improvement in the estimation of physiological parameters as well as improved alignment of the images.

Assessing antiangiogenic therapy response by DCE-MRI: development of a physiology driven multi-compartment model using population pharmacometrics

Dynamic contrast enhanced (DCE-) MRI is commonly applied for the monitoring of antiangiogenic therapy in oncology. Established pharmacokinetic (PK) analysis methods of DCE-MRI data do not sufficiently reflect the complex anatomical and physiological constituents of the analyzed tissue. Hence, accepted endpoints such as Ktrans reflect an unknown multitude of local and global physiological effects often rendering an understanding of specific local drug effects impossible. In this work a novel multi-compartment PK model is presented, which for the first time allows the separation of local and systemic physiological effects. DCE-MRI data sets from multiple, simultaneously acquired tissues, i.e. spinal muscle, liver and tumor tissue, of hepatocellular carcinoma (HCC) bearing rats were applied for model development. The full Markov chain Monte Carlo (MCMC) Bayesian analysis method was applied for model parameter estimation and model selection was based on histological and anatomical considerations and numerical criteria. A population PK model (MTL3 model) consisting of 3 measured and 6 latent (unobserved) compartments was selected based on Bayesian chain plots, conditional weighted residuals, objective function values, standard errors of model parameters and the deviance information criterion. Covariate model building, which was based on the histology of tumor tissue, demonstrated that the MTL3 model was able to identify and separate tumor specific, i.e. local, and systemic, i.e. global, effects in the DCE-MRI data. The findings confirm the feasibility to develop physiology driven multi-compartment PK models from DCE-MRI data. The presented MTL3 model allowed the separation of a local, tumor specific therapy effect and thus has the potential for identification and specification of effectors of vascular and tissue physiology in antiangiogenic therapy monitoring.

Non-invasive in vivo imaging of vessel calibre in orthotopic prostate tumour xenografts

Susceptibility contrast magnetic resonance imaging (MRI), utilising ultrasmall superparamagnetic iron oxide (USPIO) particles, was evaluated for the quantitation of vessel size index (Rv, μm), a weighted average measure of tumour blood vessel calibre, and fractional tumour blood volume (fBV, %), in orthotopically propagated murine PC3 prostate tumour xenografts. Tumour vascular architecture was assessed in vivo by MRI prior to and 24 hr after treatment with 200 mg/kg of the vascular disrupting agent ZD6126. A Bayesian hierarchical model (BHM) was used to reduce the uncertainty associated with quantitation of Rv and fBV. Quantitative histological analyses of the uptake of Hoechst 33342 for perfused vasculature, and haematoxylin and eosin staining for necrosis, were also performed to qualify the MRI data. A relatively large median Rv of 40.3 μm (90% confidence interval (CI90) = 37.4, 44.0 μm) and a high fBV of 5.4% (CI90 = 5.3, 5.5%) were determined in control tumours, which agreed with histologically determined vessel size index. Treatment with ZD6126 significantly (p < 0.01) reduced tumour Rv (34.2 μm, CI90 = 31.2, 38.0 μm) and fBV (3.9%, CI90 = 3.8, 4.1%), which were validated against histologically determined significant reductions in perfusion and vessel size, and increased necrosis. Together these data (i) highlight the use of a BHM to optimise the inferential power available from susceptibility contrast MRI data, (ii) provide strong evaluation and qualification of R(v) and fBV as non-invasive imaging biomarkers of tumour vascular morphology, (iii) reveal the presence of a different vascular phenotype and (iv) demonstrate that ZD6126 exhibits good anti-vascular activity against orthotopic prostate tumours.

Image analysis and statistical inference in neuroimaging with R

R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.

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.