A fast schema for parameter estimation in diffusion kurtosis imaging

Diffusion kurtosis imaging (DKI) is a new model in magnetic resonance imaging (MRI) characterizing restricted diffusion of water molecules in living tissues. We propose a method for fast estimation of the DKI parameters. These parameters – apparent diffusion coefficient (ADC) and apparent kurtosis coefficient (AKC) – are evaluated using an alternative iteration schema (AIS). This schema first roughly estimates a pair of ADC and AKC values from a subset of the DKI data acquired at 3 b-values. It then iteratively and alternately updates the ADC and AKC until they are converged. This approach employs the technique of linear least square fitting to minimize estimation error in each iteration. In addition to the common physical and biological constrains that set the upper and lower boundaries of the ADC and AKC values, we use a smoothing procedure to ensure that estimation is robust. Quantitative comparisons between our AIS methods and the conventional methods of unconstrained nonlinear least square (UNLS) using both synthetic and real data showed that our unconstrained AIS method can significantly accelerate the estimation procedure without compromising its accuracy, with the computational time for a DKI dataset successfully reduced to only 1 or 2 min. Moreover, the incorporation of the smoothing procedure using one of our AIS methods can significantly enhance the contrast of AKC maps and greatly improve the visibility of details in fine structures.     

Evaluation of optimized b-value sampling schemas for diffusion kurtosis imaging with an application to stroke patient data

Diffusion kurtosis imaging (DKI) is a new method of magnetic resonance imaging (MRI) that provides non-Gaussian information that is not available in conventional diffusion tensor imaging (DTI). DKI requires data acquisition at multiple b-values for parameter estimation; this process is usually time-consuming. Therefore, fewer b-values are preferable to expedite acquisition. In this study, we carefully evaluated various acquisition schemas using different numbers and combinations of b-values. Acquisition schemas that sampled b-values that were distributed to two ends were optimized. Compared to conventional schemas using equally spaced b-values (ESB), optimized schemas require fewer b-values to minimize fitting errors in parameter estimation and may thus significantly reduce scanning time. Following a ranked list of optimized schemas resulted from the evaluation, we recommend the 3b schema based on its estimation accuracy and time efficiency, which needs data from only 3 b-values at 0, around 800 and around 2600 s/mm², respectively. Analyses using voxel-based analysis (VBA) and region-of-interest (ROI) analysis with human DKI datasets support the use of the optimized 3b (0, 1000, 2500 s/mm²) DKI schema in practical clinical applications.     

Constrained maximum likelihood estimation of the diffusion kurtosis tensor using a Rician noise model

A computational framework to obtain an accurate quantification of the Gaussian and non‐Gaussian component of water molecules' diffusion through brain tissues with diffusion kurtosis imaging, is presented. The diffusion kurtosis imaging model quantifies the kurtosis, the degree of non‐Gaussianity, on a direction dependent basis, constituting a higher order diffusion kurtosis tensor, which is estimated in addition to the well‐known diffusion tensor. To reconcile with the physical phenomenon of molecular diffusion, both tensor estimates should lie within a physically acceptable range. Otherwise, clinically and artificially significant changes in diffusion (kurtosis) parameters might be confounded. To guarantee physical relevance, we here suggest to estimate both diffusional tensors by maximizing the joint likelihood function of all Rician distributed diffusion weighted images given the diffusion kurtosis imaging model while imposing a set of nonlinear constraints. As shown in this study, correctly accounting for the Rician noise structure is necessary to avoid significant overestimation of the kurtosis values. The performance of the constrained estimator was evaluated and compared to more commonly used strategies during simulations. Human brain data were used to emphasize the need for constrained estimators as not imposing the constraints give rise to constraint violations in about 70% of the brain voxels. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

More accurate estimation of diffusion tensor parameters using diffusion kurtosis imaging

With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion‐weighted signal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b‐value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model provides a more accurate parameterization of both the Gaussian and non‐Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b‐value‐independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusion‐weighted rat data, which was acquired with eight different b‐values, uniformly distributed in a range of [0,2800 sec/mm²]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the diffusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusion‐weighted data will result in an overestimated degree of non‐Gaussian diffusion and a b‐value‐dependent underestimation of diffusivity measures, a Rician noise model was used in this study. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Robust estimation of spatially variable noise fields

Consideration of spatially variable noise fields is becoming increasingly necessary in MRI given recent innovations in artifact identification and statistically driven image processing. Fast imaging methods enable study of difficult anatomical targets and improve image quality but also increase the spatial variability in the noise field. Traditional analysis techniques have either assumed that the noise is constant across the field of view (or region of interest) or have relied on separate MRI acquisitions to measure the noise field. These methods are either inappropriate for many modern scanning protocols or are overly time‐consuming for already lengthy scanning sessions. We propose a new, general framework for estimating spatially variable noise fields from related, but independent MR scans that we call noise field equivalent scans. These heuristic analyses enable robust noise field estimation in the presence of artifacts. Generalization of noise estimators based on uniform regions, difference images, and maximum likelihood are presented and compared with the estimators derived from the proposed framework. Simulations of diffusion tensor imaging and T₂‐relaxometry demonstrate a 10‐fold reduction in mean squared error in noise field estimation, and these improvements are shown to be robust to artifact contamination. In vivo studies show that spatially variable noise fields can be readily estimated with typical data acquired at 1.5T. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements

PURPOSE: To establish a general methodology for quantifying streamline-based diffusion fiber tracking methods in terms of probability of connection between points and/or regions. MATERIALS AND METHODS: The commonly used streamline approach is adapted to exploit the uncertainty in the orientation of the principal direction of diffusion defined for each image voxel. Running the streamline process repeatedly using Monte Carlo methods to exploit this inherent uncertainty generates maps of connection probability. Uncertainty is defined by interpreting the shape of the diffusion orientation profile provided by the diffusion tensor in terms of the underlying microstructure. RESULTS: Two candidates for describing the uncertainty in the diffusion tensor are proposed and maps of probability of connection to chosen start points or regions are generated in a number of major tracts. CONCLUSION: The methods presented provide a generic framework for utilizing streamline methods to generate probabilistic maps of connectivity.     

Utilizing the diffusion-to-noise ratio to optimize magnetic resonance diffusion tensor acquisition strategies for improving measurements of diffusion anisotropy.

It is well known that quantitative anisotropy measurements derived from the diffusion tensor are extremely sensitive to noise contamination. The level of noise in the diffusion tensor imaging (DTI) experiment is usually measured from some estimate of the signal-to-noise ratio (SNR) in the component diffusion-weighted (DW) images. This measure is, however, highly dependent on experimental parameters, such as the diffusion attenuation b-value and the diffusion coefficient of the subject. Conversely, the diffusion-to-noise ratio (DNR), defined as the SNR of the calculated diffusion tensor trace map, provides a reliable estimate of noise contamination, which is largely independent of such parameters. In this work it is demonstrated how reliable anisotropy measurements can be obtained using an image acquisition strategy that optimizes the DNR of the DTI experiment. This acquisition scheme is shown to provide noise-independent measurements of typical diffusion anisotropy values found in the human brain.     

Classification and quantification of neuronal fiber pathways using diffusion tensor MRI.

Quantitative characterization of neuronal fiber pathways in vivo is of significant neurological and clinical interest. Using the capability of MR diffusion tensor imaging to determine the local orientations of neuronal fibers, novel algorithms were developed to bundle neuronal fiber pathways reconstructed in vivo with diffusion tensor images and to quantify various physical and geometric properties of fiber bundles. The reliability of the algorithms was examined with reproducibility tests. Illustrative results show that consistent physical and geometric measurements of novel properties of neuronal tissue can be obtained, which offer considerable potential for the quantitative study of fiber pathways in vivo.     

Investigation of anomalous estimates of tensor-derived quantities in diffusion tensor imaging.

The diffusion tensor is typically assumed to be positive definite. However, noise in the measurements may cause the eigenvalues of the tensor estimate to be negative, thereby violating this assumption. Negative eigenvalues in diffusion tensor imaging (DTI) data occur predominately in regions of high anisotropy and may cause the fractional anisotropy (FA) to exceed unity. Two constrained least squares methods for eliminating negative eigenvalues are explored. These methods, the constrained linear least squares method (CLLS) and the constrained nonlinear least squares method (CNLS), are compared with other commonly used algebraic constrained methods. The CLLS tensor estimator can be shown to be equivalent to the linear least squares (LLS) tensor estimator when the LLS tensor estimate is positive definite. Similarly, the CNLS tensor estimator can be shown to be equivalent to the nonlinear least squares (NLS) tensor estimator when the NLS tensor estimate is positive definite. The constrained least squares methods for eliminating negative eigenvalues are evaluated with both simulations and in vivo human brain DTI data. Simulation results show that the CNLS method is, in terms of mean squared error for estimating trace and FA, the most effective method for correcting negative eigenvalues.