Numerous applications in diffusion MRI involve computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or shell), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres. To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its isotropic part. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.

Existing Bayesian spatial priors for functional magnetic resonance imaging (fMRI) data correspond to stationary isotropic smoothing filters that may oversmooth at anatomical boundaries. We propose two anatomically informed Bayesian spatial models for fMRI data with local smoothing in each voxel based on a tensor field estimated from a T1-weighted anatomical image. We show that our anatomically informed Bayesian spatial models results in posterior probability maps that follow the anatomical structure.

Methodological research rarely generates a broad interest, yet our work on the validity of cluster inference methods for functional magnetic resonance imaging (fMRI) created intense discussion on both the minutia of our approach and its implications for the discipline. In the present work, we take on various critiques of our work and further explore the limitations of our original work. We address issues about the particular event‐related designs we used, considering multiple event types and randomization of events between subjects. We consider the lack of validity found with one‐sample permutation (sign flipping) tests, investigating a number of approaches to improve the false positive control of this widely used procedure. We found that the combination of a two‐sided test and cleaning the data using ICA FIX resulted in nominal false positive rates for all data sets, meaning that data cleaning is not only important for resting state fMRI, but also for task fMRI. Finally, we discuss the implications of our work on the fMRI literature as a whole, estimating that at least 10% of the fMRI studies have used the most problematic cluster inference method (p = .01 cluster defining threshold), and how individual studies can be interpreted in light of our findings. These additional results underscore our original conclusions, on the importance of data sharing and thorough evaluation of statistical methods on realistic null data.

Time constraints placed on magnetic resonance imaging often restrict the application of advanced diffusion MRI (dMRI) protocols in clinical practice and in high throughput research studies. Therefore, acquisition strategies for accelerated dMRI have been investigated to allow for the collection of versatile and high quality imaging data, even if stringent scan time limits are imposed. Diffusion spectrum imaging (DSI), an advanced acquisition strategy that allows for a high resolution of intra-voxel microstructure, can be sufficiently accelerated by means of compressed sensing (CS) theory. CS theory describes a framework for the efficient collection of fewer samples of a data set than conventionally required followed by robust reconstruction to recover the full data set from sparse measurements. For an accurate recovery of DSI data, a suitable acquisition scheme for sparse q-space sampling and the sensing and sparsifying bases for CS reconstruction need to be selected. In this work we explore three different types of q-space undersampling schemes and two frameworks for CS reconstruction based on either Fourier or SHORE basis functions. After CS recovery, diffusion and microstructural parameters and orientational information are estimated from the reconstructed data by means of state-of-the-art processing techniques for dMRI analysis. By means of simulation, diffusion phantom and in vivo DSI data, an isotropic distribution of q-space samples was found to be optimal for sparse DSI. The CS reconstruction results indicate superior performance of Fourier-based CS-DSI compared to the SHORE-based approach. Based on these findings we outline an experimental design for accelerated DSI and robust CS reconstruction of the sparse measurements that is suitable for the application within time-limited studies.

The orientationally-averaged diffusion magnetic resonance (MR) signal acquired at high diffusion weighting shows great potential for answering fundamental questions about neural tissue microstructure[1]. The noise-induced bias in the magnitude-valued signal and angular resolution limitations in diffusion encoding are among the challenges in obtaining an accurate estimate. Here, we present a data processing framework for computing the orientationally-averaged diffusion signal that corrects the noise induced bias and accounts for the low angular resolution of the acquisition. Noise correction is performed using a statistical transformation framework [2] that converts the noisy MR signal from a noncentralChi distribution to a noisy Gaussian one. Weights for each of the probing directions are computed to improve the rotationally invariant representation of the sample. Synthetic data, generated to mimic diffusion acquisitions with different noise levels and number of acquisition directions, were used to test the data processing framework. The performance of the framework was evaluated by comparing the processed data with the analytical solution of the orientationally-averaged signal. Results show that the computation of the orientationally-averaged signal benefits from both the noise correction and the weighted averaging, especially in the low signal regime. This work provides a tool for processing high diffusion-weighted MR signals whose interpretation could improve our knowledge about neural tissue microstructure.

[1] Özarslan E, Yolcu C, Herberthson M, Knutsson H, Westin CF. Influence of the size and curvedness ofneural projections on the orientationally averaged diffusion MR signal. Front Phys, 2018; 6:17.

[2] Koay CG, Özarslan E, Basser PJ. A signal transformational framework for breaking the noise floorand its applications in MRI. J Magn Reson 2009; 197(2):108–119.

Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive microstructure assessment technique. Scalar measures, such as FA (fractional anisotropy) and MD (mean diffusivity), quantifying micro-structural tissue properties can be obtained using diffusion models and data processing pipelines. However, it is costly and time consuming to collect high quality diffusion data. Here, we therefore demonstrate how Generative Adversarial Networks (GANs) can be used to generate synthetic diffusion scalar measures from structural T1-weighted images in a single optimized step. Specifically, we train the popular CycleGAN model to learn to map a T1 image to FA or MD, and vice versa. As an application, we show that synthetic FA images can be used as a target for non-linear registration, to correct for geometric distortions common in diffusion MRI.

Diffusion-attenuated MR signal for heterogeneous media has been represented as a sum of signals from anisotropic Gaussian sub-domains to the extent that this approximation is permissible. Any effect of macroscopic (global or ensemble) anisotropy in the signal can be removed by averaging the signal values obtained by differently oriented experimental schemes. The resulting average signal is identical to what one would get if the micro-domains are isotropically (e.g., randomly) distributed with respect to orientation, which is the case for "powdered" specimens. We provide exact expressions for the orientationally-averaged signal obtained via general gradient waveforms when the microdomains are characterized by a general diffusion tensor possibly featuring three distinct eigenvalues. This extends earlier results which covered only axisymmetric diffusion as well as measurement tensors. Our results are expected to be useful in not only multidimensional diffusion MR but also solid-state NMR spectroscopy due to the mathematical similarities in the two fields.

One‐sided t‐tests are commonly used in the neuroimaging field, but two‐sided tests should be the default unless a researcher has a strong reason for using a one‐sided test. Here we extend our previous work on cluster false positive rates, which used one‐sided tests, to two‐sided tests. Briefly, we found that parametric methods perform worse for two‐sided t‐tests, and that nonparametric methods perform equally well for one‐sided and two‐sided tests.

The methodology outlined in this chapter is intended to provide a tool for the generation of sets of MRI diffusion encoding waveforms that are optimal for tissue micro-structure estimation. The methodology presented has five distinct components: 1. Defining the class of waveforms allowed, i.e. defining the measurement space. 2. Specifying the expected distribution of microstructure features present in the targeted tissue. 3. Learning the metric in the chosen measurement space. 4. Designing a continuous parametric functional suitable for approximation of the estimated metric. 5. Finding a distribution of a chosen number of waveforms that is optimal given the continuous metric. The tissue is modeled as a collection of simple elliptical compartments with varying size and shape. Two waveform classes are tested: The classical Stejskal-Tanner waveform and an idealized Laun long-short waveform. The estimation of the metric is based on correlations between measurements obtained at given points in the measurement space using an information theoretical approach. Optimal sets of waveforms are found using a simulated annealing inspired energy minimizing approach. The superior performance of the methodology is demonstrated for a number of different cases by means of simulations.

Purpose: Estimation of uncertainty of MAP-MRI metricsis an important topic, for several reasons. Bootstrap deriveduncertainty, such as the standard deviation, providesvaluable information, and can be incorporated in MAP-MRIstudies to provide more extensive insight.

Methods: In this paper, the uncertainty of different MAPMRImetrics was quantified by estimating the empirical distributionsusing the wild bootstrap. We applied the wildbootstrap to both phantom data and human brain data, andobtain empirical distributions for theMAP-MRImetrics returnto-origin probability (RTOP), non-Gaussianity (NG) and propagatoranisotropy (PA).

Results: We demonstrated the impact of diffusion acquisitionscheme (number of shells and number of measurementsper shell) on the uncertainty of MAP-MRI metrics.We demonstrated how the uncertainty of these metrics canbe used to improve group analyses, and to compare differentpreprocessing pipelines. We demonstrated that withuncertainty considered, the results for a group analysis canbe different.

Conclusion: Bootstrap derived uncertain measures provideadditional information to the MAP-MRI derived metrics, andshould be incorporated in ongoing and future MAP-MRIstudies to provide more extensive insight.

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.

A recent Editorial by Slotnick (2017) reconsiders the findings of our paper on the accuracy of false positive rate control with cluster inference in fMRI (Eklund et al, 2016), in particular criticising our use of resting state fMRI data as a source for null data in the evaluation of task fMRI methods. We defend this use of resting fMRI data, as while there is much structure in this data, we argue it is representative of task data noise and such analysis software should be able to accommodate this noise. We also discuss a potential problem with Slotnick’s own method.

We consider diffusion within pores with general shapes in the presence of spatially linear magnetic field profiles. The evolution of local magnetization of the spin bearing particles can be described by the Bloch-Torrey equation. We study the diffusive process in the eigenbasis of the non-Hermitian Bloch-Torrey operator. It is possible to find expressions for some special temporal gradient waveforms employed to sensitize the nuclear magnetic resonance (NMR) signal to diffusion. For more general gradient waveforms, we derive an efficient numerical solution by introducing a novel matrix formalism. Compared to previous methods, this new approach requires a fewer number of eigenfunctions to achieve the same accuracy. This shows that these basis functions are better suited to the problem studied. The new framework could provide new important insights into the fundamentals of diffusion sensitization, which could further the development of the field of NMR. Published by AIP Publishing.

The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in qspace. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on nonuniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited.

Multi-compartmental models are popular to resolve intra-voxel fiber heterogeneity. One such model is the mixture of central Wishart distributions. In this paper, we use our recently proposed model to estimate the orientations of crossing fibers within a voxel based on mixture of non-central Wishart distributions. We present a thorough comparison of the results from other fiber reconstruction methods with this model. The comparative study includes experiments on a range of separation angles between crossing fibers, with different noise levels, and on real human brain diffusion MRI data. Furthermore, we present multi-fiber visualization results using tractography. Results on synthetic and real data as well as tractography visualization highlight the superior performance of the model specifically for small and middle ranges of separation angles among crossing fibers.

In the field of MRI brain image analysis, Diffusion tensor imaging (DTI) provides a description of the diffusion of water through tissue and makes it possible to trace fiber connectivity in the brain, yielding a map of how the brain is wired. DTI employs a second order diffusion tensor model based on the assumption of Gaussian diffusion. The Gaussian assumption, however, limits the use ofDTI in solving intra-voxel fiber heterogeneity as the diffusion can be non-Gaussian in several biological tissues including human brain. Several approaches to modeling the non-Gaussian diffusion and intra-voxel fiber heterogeneity reconstruction have been proposed in the last decades. Among such approaches are the multi-compartmental probabilistic mixture models. These models include the discrete or continuous mixtures of probability distributions such as Gaussian, Wishart or von Mises-Fisher distributions. Given the diffusion weighted MRI data, the problem of resolving multiple fibers within a single voxel boils down to estimating the parameters of such models.

In this chapter, we focus on such multi-compartmental probabilistic mixture models. First we present a review including mathematical formulations of the most commonly applied mixture models. Then, we present a novel method based on the mixture of non-central Wishart distributions. A mixture model of central Wishart distributions has already been proposed earlier to resolve intra-voxel heterogeneity. However, we show with detailed experiments that our proposed model outperforms the previously proposed probabilistic models specifically for the challenging scenario when the separation angles between crossing fibers (two or three) are small. We compare our results with the recently proposed probabilistic models of mixture of central Wishart distributions and mixture of hyper-spherical von Mises-Fisher distributions. We validate our approach with several simulations including fiber orientations in two and three directions and with real data. Resistivity to noise is also demonstrated by increasing levels of Rician noise in simulated data. The experiments demonstrate the superior performance of our proposed model over the prior probabilistic mixture models.

We have investigated the test-retest reliability of diffusion tractography, using 32 diffusion datasets from a single healthy subject. Preprocessing was carried out using functions in FSL (FMRIB Software Library), and tractography was carried out using FSL and Dipy. The tractography was performed in diffusion space, using two seed masks (corticospinal and cingulum gyrus tracts) created from the JHU White-Matter Tractography atlas. The tractography results were then warped into MNI standard space by a linear transformation. The reproducibility of tract metrics was examined using the standard deviation, the coefficient of variation (CV) and the Dice similarity coefficient (DSC), which all indicated a high reproducibility. Our results show that the multi-fiber model in FSL is able to reveal more connections between brain areas, compared to the single fiber model, and that distortion correction increases the reproducibility.

We are glad that our paper (1) has generated intense discussions in the fMRI field (2⇓–4), on how to analyze fMRI data, and how to correct for multiple comparisons. The goal of the paper was not to disparage any specific fMRI software, but to point out that parametric statistical methods are based on a number of assumptions that are not always valid for fMRI data, and that nonparametric statistical methods (5) are a good alternative. Through AFNI’s introduction of nonparametric statistics in the function 3dttest++ (3, 6), the three most common fMRI softwares now all support nonparametric group inference [SPM through the toolbox SnPM (www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/nichols/software/snpm), and FSL through the function randomise].

Cox et al. (3) correctly point out that the bug in the AFNI function 3dClustSim only had a minor impact on the false-positive rate (FPR). This was also covered in our original paper (1): “We note that FWE [familywise error] rates are lower with the bug-fixed 3dClustSim function. As an example, the updated function reduces the degree of false …

The mastoid of human temporal bone contains numerous air cells connected to each others. In order to gain further knowledge about these air cells, a more compact representation is needed to obtain an estimate of the size distribution of these cells. Already existing skeletonization methods often fail in producing a faithful skeleton mostly due to noise hampering the binary representation of the data. This paper proposes a different approach by extracting geometrical information embedded in the Euclidean distance transform of a volume via a structure tensor analysis based on quadrature filters, from which a secondary structure tensor allows the extraction of surface skeleton along with a curve skeleton from its eigenvalues. Preliminary results obtained on a X-ray micro-CT scans of a human temporal bone show very promising results.

The most widely used task functional magnetic resonance imaging (fMRI) analyses use parametric statistical methods that depend on a variety of assumptions. In this work, we use real resting-state data and a total of 3 million random task group analyses to compute empirical familywise error rates for the fMRI software packages SPM, FSL, and AFNI, as well as a nonparametric permutation method. For a nominal familywise error rate of 5%, the parametric statistical methods are shown to be conservative for voxelwise inference and invalid for clusterwise inference. Our results suggest that the principal cause of the invalid cluster inferences is spatial autocorrelation functions that do not follow the assumed Gaussian shape. By comparison, the nonparametric permutation test is found to produce nominal results for voxelwise as well as clusterwise inference. These findings speak to the need of validating the statistical methods being used in the field of neuroimaging.

The mastoid air cell system (MACS) with its large complex of interconnected air cells reflects an enhanced surface area (SA) relative to its volume (V), which may indicate that the MACS is adapted to gas exchange and has a potential role in middle ear pressure regulation. Thus, these geometric parameters of the MACS have been studied by high resolution clinical CT scanning. However, the resolution of these scans is limited to a voxel size of around 0.6 mm in all dimensions, and so, the geometrical parameters are also limited. Small air cells may appear below the resolution and cannot be detected. Such air cells may contribute to a much higher SA than the V, and thus, also the SA/V ratio. More accurate parameters are important for analysis of the function of the MACS including physiological modeling.

Our aim was to determine the SA, V, and SA/V ratio in MACS in human temporal bones at highest resolution by using micro-CT-scanning. Further, the influence of the resolution on these parameters was investigated by downsampling the data. Eight normally aerated temporal bones were scanned at the highest possible resolution (30-60 μm). The SA was determined using a triangular mesh fitted onto the segmented MACS. The V was determined by summing all the voxels containing air. Downsampling of the original data was applied four times by a factor of 2.

The mean SA was 194 cm², the mean V was 9 cm³, and the mean SA/V amounted to 22 cm^-1. Decreasing the resolution resulted in a non-linear decrement of SA and SA/V, whereas V was mainly independent of the resolution.

The current study found significantly higher SA and SA/V compared with previous studies using clinical CT scanning at lower resolutions. These findings indicate a separate role of the MACS compared with the tympanum, and the results are important for a more accurate modeling of the middle ear physiology.

Numerous micro-channels have recently been discovered in the human temporal bone by x-ray micro-CT-scanning. After a preliminary study suggesting that these micro-channels form a separate blood supply for the mucosa of the mastoid air cells, a structural analysis of the micro-channels using a local structure tensor was carried out. Despite the high-resolution of the micro-CT scan, presence of noise within the air cells along with missing information in some micro-channels suggested the need of image enhancement. This paper proposes an adaptive enhancement of the micro-channels based on a local structure analysis while minimizing the impact of noise on the overall data. Comparison with an anisotropic diffusion PDE based scheme was also performed.

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.

We present a novel approach to investigate the properties of diffusion weighted magnetic resonance imaging (dMRI). The process of restricted diffusion of spin particles in the presence of a magnetic field is simulated by an iterated complex matrix multiplication approach. The approach is based on first principles and provides a flexible, transparent and fast simulation tool. The experiments carried out reveals fundamental features of the dMRI process. A particularly interesting observation is that the induced speed of the local spatial spin angle rate of change is highly shift variant. Hence, the encoding basis functions are not the complex exponentials associated with the Fourier transform as commonly assumed. Thus, reconstructing the signal using the inverse Fourier transform leads to large compartment estimation errors, which is demonstrated in a number of 1D and 2D examples. In accordance with previous investigations the compartment size is under-estimated. More interestingly, however, we show that the estimated shape is likely to be far from the true shape using state of the art clinical MRI scanners.

Diffusion MRI is a useful probe of tissue structure. The prototypical diffusion encoding sequence, the single pulsed field gradient, has recently been challenged with the introduction of more general gradient waveforms. Out of these, we focus on q-space trajecory imaging, which generalizes the scalar b-value to a tensor valued property. To take full advantage of its capabilities, it is imperative to respect the constraints imposed by the hardware, while at the same time maximizing the diffusion encoding strength. We formulate this as a constrained optimization problem that accomodates constraints on maximum gradient amplitude, slew rate, coil heating and positioning of radiofrequency pulses. The power of this approach is demonstrated by a comparison with previous work on optimization of isotropic diffusion sequences, showing possible gains in diffusion weighting or in heat dissipation, which in turn means increased signal or reduced scan-times.

The software packages SPM, FSL and AFNI are the most widely used packages for the analysis of functional magnetic resonance imaging (fMRI) data. Despite this fact, the validity of the statistical methods has only been tested using simulated data. By analyzing resting state fMRI data (which should not contain specific forms of brain activity) from 396 healthy con- trols, we here show that all three software packages give in- flated false positive rates (4%-96% compared to the expected 5%). We isolate the sources of these problems and find that SPM mainly suffers from a too simple noise model, while FSL underestimates the spatial smoothness. These results highlight the need of validating the statistical methods being used for fMRI. 

Radiotherapy planning and attenuation correction of PET images require simulation of radiation transport. The necessary physical properties are typically derived from computed tomography (CT) images, but in some cases, including stereotactic neurosurgery and combined PET/MR imaging, only magnetic resonance (MR) images are available. With these applications in mind, we describe how a realistic, patient-specific, pseudo-CT of the head can be derived from anatomical MR images. We refer to the method as atlas-based regression, because of its similarity to atlas-based segmentation. Given a target MR and an atlas database comprising MR and CT pairs, atlas-based regression works by registering each atlas MR to the target MR, applying the resulting displacement fields to the corresponding atlas CTs and, finally, fusing the deformed atlas CTs into a single pseudo-CT. We use a deformable registration algorithm known as the Morphon and augment it with a certainty mask that allows a tailoring of the influence certain regions are allowed to have on the registration. Moreover, we propose a novel method of fusion, wherein the collection of deformed CTs is iteratively registered to their joint mean and find that the resulting mean CT becomes more similar to the target CT. However, the voxelwise median provided even better results; at least as good as earlier work that required special MR imaging techniques. This makes atlas-based regression a good candidate for clinical use.

In image registration it is often necessary to employ regularization in one form or another to be able to find a plausible displacement field. In medical applications, it is useful to define different constraints for different areas of the data. For instance to measure if organs have moved as expected after a finished treatment. One common problem is how to find plausible motion vectors far away from known motion. This paper introduces a new method to build and solve a Global Linear Optimizations (GLO) problem with a novel set of terms which enable specification of border areas to allow a sliding motion. The GLO approach is important especially because it allows simultaneous incorporation of several different constraints using information from medical atlases such as localization and properties of organs. The power and validity of the method is demonstrated using two simple, but relevant 2D test images. Conceptual comparisons with previous methods are also made to highlight the contributions made in this paper. The discussion explains important future work and experiments as well as exciting future improvements to the GLO framework.

Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

Recently, numerous micro-channels have been discovered in the human temporal bone by micro-CT-scanning. Preliminary structure of these channels has suggested they contain a new separate blood supply for the mucosa of the mastoid air cells, which may have important functional implications. This paper proposes a structural analysis of the microchannels to corroborate this role. A local structure tensor is first estimated. The eigenvalues obtained from the estimated local structure tensor were then used to build probability maps representing planar, tubular, and isotropic tensor types. Each tensor type was assigned a respective RGB color and the full structure tensor was rendered along with the original data. Such structural analysis provides new and relevant information about the micro-channels but also their connections to mastoid air cells. Before carrying a future statistical analysis, a more accurate representation of the micro-channels in terms of local structure tensor analysis using adaptive filtering is needed.

This paper describes the concept of eigenspine, a concept applicable for determining the correlation between pair-wise combinationsof measures useful for describing the three-dimensional spinal deformities associated with adolescent idiopathic scoliosis. Theproposed data analysis scheme is based upon the use of principal component analysis (PCA) and canonical correlation analysis(CCA). PCA is employed to reduce the dimensionality of the data space, thereby providing a regularization of the measurements,and CCA is employed to determine the linear dependence between pair-wise combinations of different measures. The usefulness ofthe eigenspine concept is demonstrated by analyzing the position and the rotation of all lumbar and thoracic vertebrae as obtainedfrom 46 patients suffering from adolescent idiopathic scoliosis. The analysis showed that the strongest linear relationship is foundbetween the lateral displacement and the coronal rotation of the vertebrae, and that a somewhat weaker but still strong correlationis found between the coronal rotation and the axial rotation of the vertebrae. These results are well in-line with the generalunderstanding of idiopathic scoliosis. Noteworthy though is that the correlation between the anterior-posterior displacement and thesagittal rotation was not as strong as expected and that the obtained results further indicate the need for including the axial vertebralrotation as a measure when characterizing different types of idiopathic scoliosis. Apart from analyzing pair-wise correlationsbetween different measures, the method is believed to be suitable for finding a maximally descriptive low-dimensional combinationof measures describing spinal deformities in idiopathic scoliosis.

In this paper, we propose the concept of eigenspine, a data analysis schemeuseful for quantifying the linear correlation between different measures relevant fordescribing spinal deformities associated with spinal diseases, such as idiopathic scoliosis.The proposed concept builds upon the use of principal component analysis(PCA) and canonical correlation analysis (CCA), where PCA is used to reduce thenumber of dimensions in the measurement space, thereby providing a regularizationof the measurements, and where CCA is used to determine the linear dependence betweenpair-wise combinations of the different measures. To demonstrate the usefulnessof the eigenspine concept, the measures describing position and rotation of thelumbar and the thoracic vertebrae of 22 patients suffering from idiopathic scoliosiswere analyzed. The analysis showed that the strongest linear relationship is foundbetween the anterior-posterior displacement and the sagittal rotation of the vertebrae,and that a somewhat weaker but still strong correlation is found between thelateral displacement and the frontal rotation of the vertebrae. These results are wellin-line with the general understanding of idiopathic scoliosis. Noteworthy though isthat the obtained results from the analysis further proposes axial vertebral rotationas a differentiating measure when characterizing idiopathic scoliosis. Apart fromanalyzing pair-wise linear correlations between different measures, the method isbelieved to be suitable for finding a maximally descriptive low-dimensional combinationof measures describing spinal deformities in idiopathic scoliosis.

We present a novel approach to determine a local q-space metric that is optimal from an information theoretic perspective with respect to the expected signal statistics. It should be noted that the approach does not attempt to optimize the quality of a pre-defined mathematical representation, the estimator. In contrast, our suggestion aims at obtaining the maximum amount of information without enforcing a particular feature representation.

Results for three significantly different average propagator distributions are presented. The results show that the optimal q-space metric has a strong dependence on the assumed distribution in the targeted tissue. In many practical cases educated guesses can be made regarding the average propagator distribution present. In such cases the presented analysis can produce a metric that is optimal with respect to this distribution. The metric will be different at different q-space locations and is defined by the amount of additional information that is obtained when adding a second sample at a given offset from a first sample. The intention is to use the obtained metric as a guide for the generation of specific efficient q-space sample distributions for the targeted tissue.

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor). © 2014 Springer International Publishing.

Detailed analysis of spinal deformity is important within orthopaedic healthcare, in particular for assessment of idiopathic scoliosis. This paper addresses this challenge by proposing an image analysis method, capable of providing a full three-dimensional spine characterization. The proposed method is based on the registration of a highly detailed spine model to image data from computed tomography. The registration process provides an accurate segmentation of each individual vertebra and the ability to derive various measures describing the spinal deformity. The derived measures are estimated from landmarks attached to the spine model and transferred to the patient data according to the registration result. Evaluation of the method provides an average point-to-surface error of 0.9 mm ± 0.9 (comparing segmentations), and an average target registration error of 2.3 mm ± 1.7 (comparing landmarks). Comparing automatic and manual measurements of axial vertebral rotation provides a mean absolute difference of 2.5° ± 1.8, which is on a par with other computerized methods for assessing axial vertebral rotation. A significant advantage of our method, compared to other computerized methods for rotational measurements, is that it does not rely on vertebral symmetry for computing the rotational measures. The proposed method is fully automatic and computationally efficient, only requiring three to four minutes to process an entire image volume covering vertebrae L5 to T1. Given the use of landmarks, the method can be readily adapted to estimate other measures describing a spinal deformity by changing the set of employed landmarks. In addition, the method has the potential to be utilized for accurate segmentations of the vertebrae in routine computed tomography examinations, given the relatively low point-to-surface error.

Local phase is a powerful concept which has been successfully used in many image processing applications. For multidimensional signals the concept of phase is complex and there is no consensus on the precise meaning of phase. It is, however, accepted by all that a measure of phase implicitly carries a directional reference. We present a novel matrix representation of multidimensional phase that has a number of advantages. In contrast to previously suggested phase representations it is shown to be globally isometric for the simple signal class. The proposed phase estimation approach uses spherically separable monomial filter of orders 0, 1 and 2 which extends naturally to N dimensions. For 2-dimensional simple signals the representation has the topology of a Klein bottle. For 1-dimensional signals the new phase representation reduces to the original definition of amplitude and phase for analytic signals. Traditional phase estimation using quadrature filter pairs is based on the analytic signal concept and requires a pre-defined filter direction. The new monomial local phase representation removes this requirement by implicitly incorporating local orientation. We continue to define a phase matrix product which retains the structure of the phase matrix representation. The conjugate product gives a phase difference matrix in a manner similar to the complex conjugate product of complex numbers. Two motion estimation examples are given to demonstrate the advantages of this approach.

Magnetic resonance (MR) images lack information about radiation transport-a fact which is problematic in applications such as radiotherapy planning and attenuation correction in combined PET/MR imaging. To remedy this, a crude but common approach is to approximate all tissue properties as equivalent to those of water. We improve upon this using an algorithm that automatically identifies bone tissue in MR. More specifically, we focus on segmenting the skull prior to stereotactic neurosurgery, where it is common that only MR images are available. In the proposed approach, a machine learning algorithm known as a support vector machine is trained on patients for which both a CT and an MR scan are available. As input, a combination of local and global information is used. The latter is needed to distinguish between bone and air as this is not possible based only on the local image intensity. A whole skull segmentation is achievable in minutes. In a comparison with two other methods, one based on mathematical morphology and the other on deformable registration, the proposed method was found to yield consistently better segmentations.

The Compressed Sensing (CS) technique accelerates Diffusion Spectrum Imaging (DSI) through sub-Nyquist sampling in q-space and subsequent nonlinear reconstruction of the diffusion propagator. State-of-the-art DSI approaches that exploit CS apply Cartesian undersampling patterns. Recently, a method was proposed to generate 3D non-Cartesian sample distributions that aim for isotropic sampling of q-space. This work compares the new scheme to standard Cartesian undersampling patterns in sparse reconstruction of simulated diffusion signals. The diffusion propagator and the corresponding orientation distribution function of the reconstruction are found to deviate less from the ground truth when using an isotropic q-space sample distribution.

The purpose of this work is to investigate, and improve, the feasibility of advanced Region Of Interest (ROI) selection schemes in clinical volume rendering. In particular, this work implements and evaluates an Automated Anatomical ROI (AA-ROI) approach based on the combination of automatic image registration (AIR) and Distance-Based Transfer Functions (DBTFs), designed for automatic selection of complex anatomical shapes without relying on prohibitive amounts of interaction. Domain knowledge and clinical experience has been included in the project through participation of practicing radiologists in all phases of the project. This has resulted in a set of requirements that are critical for Direct Volume Rendering applications to be utilized in clinical practice and a prototype AA-ROI implementation that was developed to addresses critical points in existing solutions. The feasibility of the developed approach was assessed through a study where five radiologists investigated three medical data sets with complex ROIs, using both traditional tools and the developed prototype software. Our analysis indicate that advanced, registration based ROI schemes could increase clinical efficiency in time-critical settings for cases with complex ROIs, but also that their clinical feasibility is conditional with respect to the radiologists trust in the registration process and its application to the data.

The aim of this project is to keep the x-ray exposure of the patient as low as reasonably achievable while improving the diagnostic image quality for the radiologist. The means to achieve these goals is to develop and evaluate an efficient adaptive filtering (denoising/image enhancement) method that fully explores true 4D image acquisition modes.

The proposed prototype system uses a novel filter set having directional filter responses being monomials. The monomial filter concept is used both for estimation of local structure and for the anisotropic adaptive filtering. Initial tests on clinical 4D CT-heart data with ECG-gated exposure has resulted in a significant reduction of the noise level and an increased detail compared to 2D and 3D methods. Another promising feature is that the reconstruction induced streak artifacts which generally occur in low dose CT are remarkably reduced in 4D.

Conclusions: We have presented a novel method for generating evenly distributed samples in a part of q-space that can be pre- specified in a general way. We have demonstrated the feasibility for two shapes, a sphere and a cube. The results are interesting from several points of view. There is a market tendency for the samples to group in shells indicating that the present work may provide a preferable alternative to recently proposed shell-interaction schemes [9]. The distributions attained for the cube case are far from Cartesian, this may be an advantage in a sparse reconstruction, e.g. compressed sensing, setting.

Reliable measurements of spinal deformities in idiopathic scoliosis are vital, since they are used for assessing the degree of scoliosis, deciding upon treatment and monitoring the progression of the disease. However, commonly used two dimensional methods (e.g. the Cobb angle) do not fully capture the three dimensional deformity at hand in scoliosis, of which axial vertebral rotation (AVR) is considered to be of great importance. There are manual methods for measuring the AVR, but they are often time-consuming and related with a high intra- and inter-observer variability. In this paper, we present a fully automatic method for estimating the AVR in images from computed tomography. The proposed method is evaluated on four scoliotic patients with 17 vertebrae each and compared with manual measurements performed by three observers using the standard method by Aaro-Dahlborn. The comparison shows that the difference in measured AVR between automatic and manual measurements are on the same level as the inter-observer difference. This is further supported by a high intraclass correlation coefficient (0.971-0.979), obtained when comparing the automatic measurements with the manual measurements of each observer. Hence, the provided results and the computational performance, only requiring approximately 10 to 15 s for processing an entire volume, demonstrate the potential clinical value of the proposed method.

Multivariate pattern analysis (MVPA) is a popular method for making inference about functional magnetic resonance imaging (fMRI) data. One approach is to train a classifier with voxels within a certain radius from the center voxel, to classify between different brain states. This approach is commonly known as the searchlight algorithm. As recently pointed out by Todd and colleagues, inference at the group level can however be confounded by the fact that the direction of the effect is lost if the per subject classification performance is used to generate group results. Here we show that canonical correlation analysis (CCA) can in some aspects be a better approach to multivariate fMRI analysis, than classification based analysis (CBA).

Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.