Michael A. Chappell

Bayesian analysis of neuroimaging data in FSL.

Typically in neuroimaging we are looking to extract some pertinent information from imperfect, noisy images of the brain. This might be the inference of percent changes in blood flow in perfusion FMRI data, segmentation of subcortical structures from structural MRI, or inference of the probability of an anatomical connection between an area of cortex and a subthalamic nucleus using diffusion MRI. In this article we will describe how Bayesian techniques have made a significant impact in tackling problems such as these, particularly in regards to the analysis tools in the FMRIB Software Library (FSL). We shall see how Bayes provides a framework within which we can attempt to infer on models of neuroimaging data, while allowing us to incorporate our prior belief about the brain and the neuroimaging equipment in the form of biophysically informed or regularising priors. It allows us to extract probabilistic information from the data, and to probabilistically combine information from multiple modalities. Bayes can also be used to not only compare and select between models of different complexity, but also to infer on data using committees of models. Finally, we mention some analysis scenarios where Bayesian methods are impractical, and briefly discuss some practical approaches that we have taken in these cases.

Quantitative measurement of cerebral physiology using respiratory-calibrated MRI.

Functional magnetic resonance imaging typically measures signal increases arising from changes in the transverse relaxation rate over small regions of the brain and associates these with local changes in cerebral blood flow, blood volume and oxygen metabolism. Recent developments in pulse sequences and image analysis methods have improved the specificity of the measurements by focussing on changes in blood flow or changes in blood volume alone. However, FMRI is still unable to match the physiological information obtainable from positron emission tomography (PET), which is capable of quantitative measurements of blood flow and volume, and can indirectly measure resting metabolism. The disadvantages of PET are its cost, its availability, its poor spatial resolution and its use of ionising radiation. The MRI techniques introduced here address some of these limitations and provide physiological data comparable with PET measurements. We present an 18-minute MRI protocol that produces multi-slice whole-brain coverage and yields quantitative images of resting cerebral blood flow, cerebral blood volume, oxygen extraction fraction, CMRO(2), arterial arrival time and cerebrovascular reactivity of the human brain in the absence of any specific functional task. The technique uses a combined hyperoxia and hypercapnia paradigm with a modified arterial spin labelling sequence.

Variational Bayesian Inference for a Nonlinear Forward Model

Variational Bayes (VB) has been proposed as a method to facilitate calculations of the posterior distributions for linear models, by providing a fast method for Bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution. Here a VB method for nonlinear forward models with Gaussian additive noise is presented. In the case of noninformative priors the parameter estimates obtained from this VB approach are identical to those found via nonlinear least squares. However, the advantage of the VB method lies in its Bayesian formulation, which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution. Unlike other Bayesian methods VB is only approximate in comparison with the sampling method of MCMC. However, the VB method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable. Practically, the VB approach is substantially faster than MCMC as fewer calculations are required. Some of the advantages of the fully Bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of automatic relevance determination (ARD) within the VB algorithm.

Assessment of arterial arrival times derived from multiple inversion time pulsed arterial spin labeling MRI

The purpose of this study was to establish a normal range for the arterial arrival time (AAT) in whole‐brain pulsed arterial spin labeling (PASL) cerebral perfusion MRI. Healthy volunteers (N = 36, range: 20 to 35 years) provided informed consent to participate in this study. AAT was assessed in multiple brain regions, using three‐dimensional gradient and spin echo (GRASE) pulsed arterial spin labeling at 3.0 T, and found to be 641 ± 95, 804 ± 91, 802 ± 126, and 935 ± 108 ms in the temporal, parietal, frontal, and occipital lobes, respectively. Mean gray matter AAT was found to be 694 ± 89 ms for females (N = 15), which was significantly shorter than for men, 814 ± 192 ms (N = 21; P < 0.0003), and significant after correcting for brain volume (P < 0.001). Significant AAT sex differences were also found using voxelwise permutation testing. An atlas of AAT values across the healthy brain is presented here and may be useful for future experiments that aim to quantify cerebral blood flow from ASL data, as well as for clinical comparisons where disease pathology may lead to altered AAT. Pulsed arterial spin labeling signals were simulated using an identical sampling scheme as the empiric study and revealed AAT can be estimated robustly when simulated arrival times are well beyond the normal range. Magn Reson Med, 2010.

Separation of macrovascular signal in multi-inversion time arterial spin labelling MRI.

Arterial spin labeling (ASL) provides a noninvasive method to measure brain perfusion and is becoming an increasingly viable alternative to more invasive MR methods due to improvements in acquisition, such as the use of a three‐dimensional GRASE readout. A potential source of error in ASL measurements is signal arising from intravascular blood that is destined for more distal tissue. This is typically suppressed using diffusion gradients in many ASL sequences. However, several problems exist with this approach, such as the choice of cutoff velocity and gradient direction and incompatibility with certain readout modules. An alternative approach is to explicitly model the intravascular signal. This study exploits this approach by using multi‐inversion time ASL data with a recently developed model‐fitting method. The method employed permits the intravascular contribution to be discarded in voxels where there is no support in the data for its inclusion, thereby addressing the issue of overfitting. It is shown by comparing data with and without flow suppression, and by comparing the intravascular contribution in GRASE ASL data to MR angiographic images, that the model‐fitting approach can provide a viable alternative to flow suppression in ASL where suppression is either not feasible or not desirable. Magn Reson Med 63:1357–1365, 2010.

Identifying the ischaemic penumbra using pH-weighted magnetic resonance imaging

Harston et al. establish proof of principle for clinical use of pH-weighted MRI in patients with acute ischaemic stroke. Detailed tissue-level analysis reveals that cerebral intracellular pH, a marker of metabolic stress, is associated with eventual tissue outcome, and complements established imaging modalities.

Bolus arrival time and cerebral blood flow responses to hypercarbia

The purpose of this study was to evaluate how cerebral blood flow and bolus arrival time (BAT) measures derived from arterial spin labeling (ASL) MRI data change for different hypercarbic gas stimuli. Pseudocontinuous ASL (pCASL) was applied (3.0T; spatial resolution = 4 × 4 × 7 mm 3 ; repetition time/echo time (TR/TE) = 3,600/11 ms) sequentially in healthy volunteers (n = 12; age = 30±4 years) for separate experiments in which (i) normocarbic normoxia (i.e., room air), hypercarbic normoxia (i.e., 5% CO2/21% O2/74% N2), and hypercarbic hyperoxia (i.e., carbogen: 5% CO2/95% O2) gas was administered (12 L/minute). Cerebral blood flow and BAT changes were quantified using models that account for macrovascular signal and partial volume effects in all gray matter and regionally in cerebellar, temporal, occipital, frontal, and parietal lobes. Regional reductions in BAT of 4.6% to 7.7% and 3.3% to 6.6% were found in response to hypercarbic normoxia and hypercarbic hyperoxia, respectively. Cerebral blood flow increased by 8.2% to 27.8% and 3.5% to 19.8% for hypercarbic normoxia and hypercarbic hyperoxia, respectively. These findings indicate that changes in BAT values may bias functional ASL data and thus should be considered when choosing appropriate experimental parameters in calibrated functional magnetic resonance imaging or ASL cerebrovascular reactivity experiments that use hypercarbic gas stimuli.

Combined spatial and non-spatial prior for inference on MRI time-series.

When modelling FMRI and other MRI time-series data, a Bayesian approach based on adaptive spatial smoothness priors is a compelling alternative to using a standard generalized linear model (GLM) on presmoothed data. Another benefit of the Bayesian approach is that biophysical prior information can be incorporated in a principled manner; however, this requirement for a fixed non-spatial prior on a parameter would normally preclude using spatial regularization on that same parameter. We have developed a Gaussian-process-based prior to apply adaptive spatial regularization while still ensuring that the fixed biophysical prior is correctly applied on each voxel. A parameterized covariance matrix provides separate control over the variance (the diagonal elements) and the between-voxel correlation (due to off-diagonal elements). Analysis proceeds using evidence optimization (EO), with variational Bayes (VB) updates used for some parameters. The method can also be applied to non-linear forward models by using a linear Taylor expansion centred on the latest parameter estimates. Applying the method to FMRI with a constrained haemodynamic response function (HRF) shape model shows improved fits in simulations, compared to using either the non-spatial or spatial-smoothness prior alone. We also analyse multi-inversion arterial spin labelling data using a non-linear perfusion model to estimate cerebral blood flow and bolus arrival time. By combining both types of prior information, this new prior performs consistently well across a wider range of situations than either prior alone, and provides better estimates when both types of prior information are relevant.

Comparing different analysis methods for quantifying the MRI amide proton transfer (APT) effect in hyperacute stroke patients.

Amide proton transfer (APT) imaging is a pH mapping method based on the chemical exchange saturation transfer phenomenon that has potential for penumbra identification following stroke. The majority of the literature thus far has focused on generating pH‐weighted contrast using magnetization transfer ratio asymmetry analysis instead of quantitative pH mapping. In this study, the widely used asymmetry analysis and a model‐based analysis were both assessed on APT data collected from healthy subjects (n = 2) and hyperacute stroke patients (n = 6, median imaging time after onset = 2 hours 59 minutes). It was found that the model‐based approach was able to quantify the APT effect with the lowest variation in grey and white matter (≤ 13.8 %) and the smallest average contrast between these two tissue types (3.48 %) in the healthy volunteers. The model‐based approach also performed quantitatively better than the other measures in the hyperacute stroke patient APT data, where the quantified APT effect in the infarct core was consistently lower than in the contralateral normal appearing tissue for all the patients recruited, with the group average of the quantified APT effect being 1.5 ± 0.3 % (infarct core) and 1.9 ± 0.4 % (contralateral). Based on the fitted parameters from the model‐based analysis and a previously published pH and amide proton exchange rate relationship, quantitative pH maps for hyperacute stroke patients were generated, for the first time, using APT imaging.

Vessel-encoded dynamic magnetic resonance angiography using arterial spin labeling.

A new noninvasive MRI method for vessel‐selective angiography is presented. The technique combines vessel‐encoded pseudocontinuous arterial spin labeling with a two‐dimensional dynamic angiographic readout and was used to image the cerebral arteries in healthy volunteers. Time‐of‐flight angiograms were also acquired prior to vessel‐selective dynamic angiography acquisitions in axial, coronal, and/or sagittal planes, using a 3‐T MRI scanner. The latter consisted of a vessel‐encoded pseudocontinuous arterial spin labeling pulse train of 300 or 1000 ms followed by a two‐dimensional thick‐slab flow‐compensated fast low‐angle shot readout combined with a segmented Look‐Locker sampling strategy (temporal resolution = 55 ms). Selective labeling was performed at the level of the neck to generate individual angiograms for both right and left internal carotid and vertebral arteries. Individual vessel angiograms were reconstructed using a bayesian inference method. The vessel‐selective dynamic angiograms obtained were consistent with the time‐of‐flight images, and the longer of the two vessel‐encoded pseudocontinuous arterial spin labeling pulse train durations tested (1000 ms) was found to give better distal vessel visibility. This technique provides highly selective angiograms quickly and noninvasively that could potentially be used in place of intra‐arterial x‐ray angiography for larger vessels. Magn Reson Med, 2010.