Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data

Diffusion-weighted imaging can potentially be used to infer the connectivity of the human brain in vivo using fibre-tracking techniques, and is therefore of great interest to neuroscientists and clinicians. A key requirement for fibre tracking is the accurate estimation of white matter fibre orientations within each imaging voxel. The diffusion tensor model, which is widely used for this purpose, has been shown to be inadequate in crossing fibre regions. A number of approaches have recently been proposed to address this issue, based on high angular resolution diffusion-weighted imaging (HARDI) data. In this study, an experimental model of crossing fibres, consisting of water-filled plastic capillaries, is used to thoroughly assess three such techniques: constrained spherical deconvolution (CSD), super-resolved CSD (super-CSD) and Q-ball imaging (QBI). HARDI data were acquired over a range of crossing angles and b-values, from which fibre orientations were computed using each technique. All techniques were capable of resolving the two fibre populations down to a crossing angle of 45 degrees , and down to 30 degrees for super-CSD. A bias was observed in the fibre orientations estimated by QBI for crossing angles other than 90 degrees, consistent with previous simulation results. Finally, for a 45 degrees crossing, the minimum b-value required to resolve the fibre orientations was 4000 s/mm(2) for QBI, 2000 s/mm(2) for CSD, and 1000 s/mm(2) for super-CSD. The quality of estimation of fibre orientations may profoundly affect fibre tracking attempts, and the results presented provide important additional information regarding performance characteristics of well-known methods.     

An objective method for regularization of fiber orientation distributions derived from diffusion-weighted MRI

Spherical deconvolution is an elegant method by which the orientation of crossing fibers in the brain can be estimated from a diffusion-weighted MRI measurement. However, higher resolution of fiber directions comes at the cost of higher susceptibility to noise. In this study, we describe the use of linear regularization of the fiber orientation distribution function by Damped Singular Value Decomposition. Furthermore, the degree of regularization is optimized on a voxel-by-voxel basis with no user interaction using Generalized Cross Validation. We find, by simulations, that regularization can improve the reliability of fiber orientation determination when the signal-to-noise ratio is low. Simulations and in vivo measurements indicate that spurious peaks of the fiber orientation distribution function in regions with low anisotropy largely disappear when regularization is introduced. The methods examined are fast enough to be used on a routine basis with diffusion MRI data sets and may improve estimation of water diffusion properties in heterogeneous white matter and boost reliability of fiber tracking through regions of brain with complex fiber geometry.     

Estimation of fiber orientation and spin density distribution by diffusion deconvolution

A diffusion deconvolution method is proposed to apply deconvolution to the diffusion orientation distribution function (dODF) and calculate the fiber orientation distribution function (fODF), which is defined as the orientation distribution of the fiber spin density. The dODF can be obtained from q-space imaging methods such as q-ball imaging (QBI), diffusion spectrum imaging (DSI), and generalized q-sampling imaging (GQI), and thus the method can be applied to various diffusion sampling schemes. A phantom study was conducted to compare the angular resolution of the fODF with the dODF, and the in vivo datasets were acquired using single-shell, two-shell, and grid sampling schemes, which were then reconstructed by QBI, GQI, and DSI, respectively. The phantom study showed that the fODF significantly improved the angular resolution over the dODF at 45- and 60-degree crossing angles. The in vivo study showed consistent fODF regardless of the applied sampling schemes and reconstruction methods, and the ability to resolve crossing fibers was improved in reduced sampling condition. The fiber spin density obtained from deconvolution showed a higher contrast-to-noise ratio than the fractional anisotropy (FA) mapping, and further application on tractography showed that the fiber spin density can be used to determine the termination of fiber tracts. In conclusion, the proposed deconvolution method is generally applicable to different q-space imaging methods. The calculated fODF improves the angular resolution and also provides a quantitative index of fiber spin density to refine fiber tracking.     

Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution

Diffusion-weighted (DW) MR images contain information about the orientation of brain white matter fibres that potentially can be used to study human brain connectivity in vivo using tractography techniques. Currently, the diffusion tensor model is widely used to extract fibre directions from DW-MRI data, but fails in regions containing multiple fibre orientations. The spherical deconvolution technique has recently been proposed to address this limitation. It provides an estimate of the fibre orientation distribution (FOD) by assuming the DW signal measured from any fibre bundle is adequately described by a single response function. However, the deconvolution is ill-conditioned and susceptible to noise contamination. This tends to introduce artefactual negative regions in the FOD, which are clearly physically impossible. In this study, the introduction of a constraint on such negative regions is proposed to improve the conditioning of the spherical deconvolution. This approach is shown to provide FOD estimates that are robust to noise whilst preserving angular resolution. The approach also permits the use of super-resolution, whereby more FOD parameters are estimated than were actually measured, improving the angular resolution of the results. The method provides much better defined fibre orientation estimates, and allows orientations to be resolved that are separated by smaller angles than previously possible. This should allow tractography algorithms to be designed that are able to track reliably through crossing fibre regions.     

Reliable estimation of incoherent motion parametric maps from diffusion-weighted MRI using fusion bootstrap moves

Diffusion-weighted MRI has the potential to provide important new insights into physiological and microstructural properties of the body. The Intra-Voxel Incoherent Motion (IVIM) model relates the observed DW-MRI signal decay to parameters that reflect blood flow in the capillaries (D¹), capillaries volume fraction (f), and diffusivity (D). However, the commonly used, independent voxel-wise fitting of the IVIM model leads to imprecise parameter estimates, which has hampered their practical usage.In this work, we improve the precision of estimates by introducing a spatially-constrained Incoherent Motion (IM) model of DW-MRI signal decay. We also introduce an efficient iterative “fusion bootstrap moves” (FBM) solver that enables precise parameter estimates with this new IM model. This solver updates parameter estimates by applying a binary graph-cut solver to fuse the current estimate of parameter values with a new proposal of the parameter values into a new estimate of parameter values that better fits the observed DW-MRI data. The proposals of parameter values are sampled from the independent voxel-wise distributions of the parameter values with a model-based bootstrap resampling of the residuals.We assessed both the improvement in the precision of the incoherent motion parameter estimates and the characterization of heterogeneous tumor environments by analyzing simulated and in vivo abdominal DW-MRI data of 30 patients, and in vivo DW-MRI data of three patients with musculoskeletal lesions. We found our IM-FBM reduces the relative root mean square error of the D¹ parameter estimates by 80%, and of the f and D parameter estimates by 50% compared to the IVIM model with the simulated data. Similarly, we observed that our IM-FBM method significantly reduces the coefficient of variation of parameter estimates of the D¹ parameter by 43%, the f parameter by 37%, and the D parameter by 17% compared to the IVIM model (paired Student’s t-test, p < 0.0001). In addition, we found our IM-FBM method improved the characterization of heterogeneous musculoskeletal lesions by means of increased contrast-to-noise ratio of 19.3%.The IM model and FBM solver combined, provide more precise estimate of the physiological model parameter values that describing the DW-MRI signal decay and a better mechanism for characterizing heterogeneous lesions than does the independent voxel-wise IVIM model.     

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.     

Ball and rackets: Inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions.     

Variational inference of the fiber orientation density using diffusion MR imaging

Diffusion MR imaging has enabled the in vivo exploration of the connectional architecture in human brain. This method particularly reveals the complex system of long-range nerve fibers that integrate the functionally distinct areas of the cerebral cortex. Since the fibers are not directly observed but the diffusion process of water molecules in the underlying material, a forward model is established that maps the microgeometry of nervous tissue onto the diffusion-weighted signals. This article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel Hilbert space, thereby generalizing previous approaches that perform a truncated Fourier analysis on the sphere. The specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function, namely its normalization and non-negativity. A Gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters, here the high-frequency content in the density function and the noise variance of the MR observations. In addition, we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology. The novel approach, which uncovers the fiber orientation field of white matter, is demonstrated with diffusion-weighted data sets featuring high angular resolution.     

Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.     

Multilook polarimetric SAR data probability density function estimation using a generalized form of multivariate K-distribution

In our previous work, the probability density function (pdf) of single-channel synthetic aperture radar (SAR) data was modelled as a generalized form of the univariate K-distribution in order to incorporate higher order moments in the pdf estimation. In this paper, we extend this univariate model to the multivariate case, the objective being the sample covariance matrix pdf estimation of multilook polarimetric SAR data. Applying the product model, and assuming the texture distribution as the Laguerre expansion of the gamma distribution, we derive this pdf, which is a generalized form of the well-known multivariate K-distribution. The resulting distributions are assessed quantitatively with respect to multilook fully polarimetric L-band SAR image data from which we conclude that the proposed pdf demonstrates an improved goodness of fit.     

Atlas-based fiber reconstruction from diffusion tensor MRI data

Purpose

Develop a neural fiber reconstruction method based on diffusion tensor imaging, which is not as sensitive to user-defined regions of interest as streamline tractography.

Methods

A simulated annealing approach is employed to find a non-rigid transformation to map a fiber bundle from a fiber atlas to another fiber bundle, which minimizes a specific energy functional. The energy functional describes how well the transformed fiber bundle fits the patient??s diffusion tensor data.

Results

The feasibility of the method is demonstrated on a diffusion tensor software phantom. We analyze the behavior of the algorithm with respect to image noise and number of iterations. First results on the datasets of patients are presented.

Conclusions

The described method maps fiber bundles based on diffusion tensor data and shows high robustness to image noise. Future developments of the method should help simplify inter-subject comparisons of fiber bundles.     

Direct estimation of biofilm density on different pipe material coupons using a specific DNA-probe

A variety of approaches to quantify biomass in biofilms without disruption due to detachment have been developed over the years. One basic approach is the combination of advanced microscopy with molecular staining. However, many stains (e.g. 4',6-diamino-2-phenylindole, acridine orange or live-dead stains) can be non-specific when corrosion products, precipitates, and pipe material are present. In addition, some pipe materials cause high background when using epifluorescent microscopy. The new refinement discussed in this presentation used fluorescence spectroscopy to obtain the spectra from four common distribution system pipe materials: PVC, 'concrete' lined cast iron, cast iron, and galvanized steel. The emission maximum for all four materials was between 500 and 550 nm, but emissions radically decreased around 575-600 nm. A molecular probe, BO-PRO-3 (Molecular Probes, Inc., Eugene, OR, USA) was identified which has an emission intensity maximum at 599 nm (red), with emission intensity 200 times greater when it is bound to DNA. The BO-PRO-3 has greatly reduced non-specific staining and background problems. In the preliminary experiment, using diluted waste water, a significant exponential relationship was found between stained surface area/total area ratio and fixed biofilm inventory measurements from scraping heterotrophic plate counts (SHPC) on R2A medium. In addition, the biofilm inventory on different pipe material coupons from pilot distribution systems was also correlated to the stained surface area fraction and SHPC.     

Bayesian deconvolution of [corrected] fMRI data using bilinear dynamical systems

In Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983–993], a particular case of the Linear Dynamical Systems (LDSs) was used to model the dynamic behavior of the BOLD response in functional MRI. This state-space model, called bilinear dynamical system (BDS), is used to deconvolve the fMRI time series in order to estimate the neuronal response induced by the different stimuli of the experimental paradigm. The BDS model parameters are estimated using an expectation–maximization (EM) algorithm proposed by Ghahramani and Hinton [Ghahramani, Z., Hinton, G.E. 1996. Parameter Estimation for Linear Dynamical Systems. Technical Report, Department of Computer Science, University of Toronto]. In this paper we introduce modifications to the BDS model in order to explicitly model the spatial variations of the haemodynamic response function (HRF) in the brain using a non-parametric approach. While in Penny et al. [Penny, W., Ghahramani, Z., Friston, K.J. 2005. Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360(1457) 983–993] the relationship between neuronal activation and fMRI signals is formulated as a first-order convolution with a kernel expansion using basis functions (typically two or three), in this paper, we argue in favor of a spatially adaptive GLM in which a local non-parametric estimation of the HRF is performed. Furthermore, in order to overcome the overfitting problem typically associated with simple EM estimates, we propose a full Variational Bayes (VB) solution to infer the BDS model parameters. We demonstrate the usefulness of our model which is able to estimate both the neuronal activity and the haemodynamic response function in every voxel of the brain. We first examine the behavior of this approach when applied to simulated data with different temporal and noise features. As an example we will show how this method can be used to improve interpretability of estimates from an independent component analysis (ICA) analysis of fMRI data. We finally demonstrate its use on real fMRI data in one slice of the brain.     

Local estimation of the noise level in MRI using structural adaptation

We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results were compared with a recently proposed estimate. The method was also applied to a high-resolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data.     

Role of MRI and added value of diffusion-weighted and gadolinium-enhanced MRI for the diagnosis of local recurrence from rectal cancer

Abdominal Radiology - To evaluate whether the addition of gadolinium-enhanced MRI and diffusion-weighted imaging (DWI) improves T2 sequence performance for the diagnosis of local recurrence (LR)...     

扩散加权成像对宫颈癌分期与疗效预测的价值

目的：探讨扩散加权成像(DWI)表现及表观扩散系数(ADC)值在宫颈癌分期、放化疗短期疗效预测中的应用价值。材料与方法对68例治疗前的宫颈癌患者,行常规MRI及DWI检查,将常规MRI分期、常规MRI结合DWI分期与病理分期进行对照,比较两种方法对宫颈癌分期准确性的差异。测量宫颈癌各期的ADC值,分析ADC值与宫颈癌分期的相关性。对38例行放化疗的宫颈癌患者进行追踪复查,将疗效分为完全缓解组(CR)组和部分缓解组(PR)组,比较两组患者放化疗前的ADC值的差异。结果(1)常规MRI序列漏诊1例Ib期,常规MRI结合DWI检出全部病例,常规MRI对IIa期分期符合率85%,而与DWI联合应用符合率达95%,但两种方法无统计学意义。(2)对宫颈癌各期的ADC值进行比较,P＞0.05,无统计学意义,宫颈癌的分期与ADC值无相关性。(3)38例行放化疗的宫颈癌患者,25例CR组治疗前ADC均值1.02×10-3 mm2/s,13例PR组治疗前ADC均值1.14×10-3 mm2/s,采用t检验法比较两组ADC值,P<0.05,具有统计学意义,CR组ADC值低于PR组。结论常规MRI序列联合DWI对于宫颈癌的检出及分期更准确,ADC值对放化疗短期疗效有一定的预测价值。