Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

The Blood-Brain Barrier in Health and Chronic Neurodegenerative Disorders

The neurovascular unit (NVU) comprises brain endothelial cells, pericytes or vascular smooth muscle cells, glia and neurons. The NVU controls blood-brain barrier (BBB) permeability and cerebral blood flow, and maintains the chemical composition of the neuronal 'milieu', which is required for proper functioning of neuronal circuits. Recent evidence indicates that BBB dysfunction is associated with the accumulation of several vasculotoxic and neurotoxic molecules within brain parenchyma, a reduction in cerebral blood flow, and hypoxia. Together, these vascular-derived insults might initiate and/or contribute to neuronal degeneration. This article examines mechanisms of BBB dysfunction in neurodegenerative disorders, notably Alzheimer's disease, and highlights therapeutic opportunities relating to these neurovascular deficits.

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Neurovascular pathways to neurodegeneration in Alzheimer's disease and other disorders.

Mr M, a patient with semantic dementia - a neurodegenerative disease that is characterized by the gradual deterioration of semantic memory - was being driven through the countryside to visit a friend and was able to remind his wife where to turn along the not-recently-travelled route. Then, pointing at the sheep in the field, he asked her "What are those things?" Prior to the onset of symptoms in his late 40s, this man had normal semantic memory. What has gone wrong in his brain to produce this dramatic and selective erosion of conceptual knowledge?

Where do you know what you know? The representation of semantic knowledge in the human brain.

Volume losses in the medial temporal lobe, posterior cingulated, and orbitofrontal region have been observed in Alzheimer's disease (AD). Smaller reductions in similar regions have also been reported in amnestic mild cognitive impairment (aMCI), a canonical precursor to AD. We previously demonstrated that volume loss in bilateral anteromedial temporal lobe is present at baseline in longitudinally followed normal subjects who later developed MCI or AD. In this study we compared grey matter volumes within this predefined anteromedial temporal region (AMTR) at baseline between: 1) normal subjects enrolled in the Alzheimer's Disease Neuroimaging Initiative (ADNI) who subsequently developed cognitive complaints as reflected in a CDR memory box score of 0.5; and 2) normal subjects who remained normal over a median of 48 months of follow-up (CDR sum of boxes 0). We found significantly decreased volume within AMTR in the ADNI memory complainers. To relate AMTR results to those from conventional anatomy, we demonstrate that volumes extracted with the ICBM amygdala region had the best correspondence with AMTR volumes. In contrast, regions that have demonstrated volume loss in frank MCI and AD in ADNI, e.g., the posterior cingulate, did not show volume loss. These findings provide independent confirmation that volume changes preceding MCI occur in AMTR, a region of overlap between amygdala and anterior hippocampus.

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Structural brain alterations before mild cognitive impairment in ADNI: validation of volume loss in a predefined antero-temporal region.

Geometrical optics is applied in a modeling of the forward-propagation process for transmission tomography with diffracting sources. The forward process is described mathematically as an optical tomography transform of an object function into a set of measured projection data representing line integrals of that parameter function. A recursive scheme is devised for the inverse process of reconstruction of the object parameter function from its forward projections. Ultimately, a new computational scheme is presented for the fast and accurate reconstruction of the object function. Ray-tracing methods lead to a representation of the forward-propagation process as a system of linear equations. Simultaneous algebraic reconstruction methods are applied in the discretized inverse process.

Tomography transform and inverse in geometrical optics

Assessing nigrostriatal dysfunctions by pharmacological MRI in parkinsonian rhesus macaques.

Diffusion tensor imaging (DTI) has been used extensively both clinically [1] and for research [2] to map white matter fiber tracts in the central nervous system (CNS). In this application DTI takes advantage of the anisotropic structure of axons, which permits faster diffusion of water molecules parallel to and slower diffusion perpendicular to the axon. DTI has also been applied, although to a much lesser extent, for defining the micro structure of other tissues which also have an inherent structural anisotropy [3]. For example, skeletal muscles consist of bundles of individual muscle fibers, which are in turn comprised of multiple parallel protein bands called myofibrils. This protein configuration and the overall cellular geometry give muscle fibers a highly anisotropic structure. Consequently, DTI can be used to reveal the orientation of muscle fibers [4, 5].

The value of these analyses is derived partly from the observation that the spatial arrangement of muscle fibers with respect to the muscle's line of action is directly related to the muscle's ability to produce force [6, 7]. In particular, two structural phenomena, the pennation angle and muscle fiber length, are integral for assessing the ability of a muscle to generate force. Estimating muscle fiber structure through DTI in fact may be easier than deriving aspects of axonal structure because the muscle fiber diameters, which are approximately 10-90 μm, match the diffusion length within the typical diffusion time of between 10- 50 ms [8, 9]. This could be particularly helpful when assessing changes in muscle fibers as a result of injury or training, where measurements cannot currently be readily made non-invasively over the whole muscle. While there is growing interest in applying these techniques to muscle, data are still lacking regarding the effect of different DTI pulse sequences on the derived muscle fiber length and pennation angle.

The application of DTI to muscle presents a number of unique challenges that require adaptation of the twice refocused spin echo (TRSE) MR pulse sequences commonly used in the brain. One factor is the smaller T2 to T1 ratio in muscle versus the white matter in the CNS [10]. One consequence of this is that the signal-to-noise ratio (SNR) in diffusion weighted images is poorer in muscle compared to the brain [11]. An additional challenge, more important to imaging muscle than the CNS, is minimizing the contribution to the image of adipose tissue that surrounds and infiltrates the muscle. Because diffusion weighted images are typically acquired with echo planar imaging (EPI) techniques, the off-resonance protons in fat lead to displacement of the fat in the image so that it overlaps the muscle of interest [5]. The result will be a bias in the estimates of the diffusion coefficients and added variability to the estimates of the eigenvector directions [12, 13]. Because of the much smaller amount of fat in the scalp, this problem is not nearly as significant for imaging the brain. Lastly, localized eddy current-induced fields which result from the prolonged high gradient pulses to encode diffusion can further degrade the geometric fidelity and general image quality [11, 14]. These well recognized challenges have encouraged the exploration of alternative diffusion encoding strategies from the more commonly used TRSE, echo planar acquisitions typically used with DTI.

To deal with these challenges some investigators have explored using a single-echo spin echo acquisition similar to the original Stejskal-Tanner technique but with a modified gradient design to reduce eddy current generation [14-16]. Within a TRSE technique alternative bipolar gradient encoding schemes have been investigated to minimize the compromise in image quality and SNR [17]. Bipolar gradient schemes have reduced geometric distortion but at the expense of slightly longer TE than monopolar encoding schemes [18] [14]. A few groups have used a Stimulated Echo Acquisition Mode (STEAM) sequence, wherein the diffusion encoding occurs during the mixing time (TM) [8, 19]. As only T1 recovery occurs during TM, it is possible to increase TM to achieve an adequate b value while simultaneously reducing TE. The lengthened diffusion encoding time also reduces the need for high amplitude gradients, thus reducing the induced eddy currents that spatially distort the images. While in limited studies both techniques have been shown to work in muscle, a comparison between the two pulse sequences, particularly for quantitative fiber tracking applications, is lacking in the literature. Such a comparison will be of value to clinicians and researchers alike to help them optimize or choose the sequence that would work best for their particular application.

Previous studies that have evaluated either a STEAM or a TRSE sequence for imaging muscle have used different field strengths (1.5 T and 3.0T), have compared the sequences in-vivo in human muscle, run simulations, or used excised brain tissue [5, 11, 14]. Thus, the purpose of this study was to compare a TRSE DTI sequence to a STEAM DTI sequence on the Vastus Lateralis (VL) of healthy human participants.

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Comparison of twice refocused spin echo versus stimulated echo diffusion tensor imaging for tracking muscle fibers

Functional magnetic resonance imaging was used to detect cortical activation in the right and left perisylvian cortex of seven young adult right-handed volunteers in response to a letter fluency task and to a visual naming task using standardized line drawings. Both letter fluency and visual naming activated left dorsolateral prefrontal cortex (Brodmann's areas 6, 9, 44 and 45). Only visual naming activated area 37 (a cortical region with strong connections to visual association areas), visual association area 19, and areas 39 and 21 previously shown to activate with auditory semantic tasks. This study supports a role for area 37 as participant in a visual lexicosemantic processing network which may otherwise overlap the auditorysemantic network.

Anders H. Andersen

Papers

Structural brain alterations before mild cognitive impairment in ADNI: validation of volume loss in a predefined antero-temporal region.

Tomography transform and inverse in geometrical optics

Assessing nigrostriatal dysfunctions by pharmacological MRI in parkinsonian rhesus macaques.

Comparison of twice refocused spin echo versus stimulated echo diffusion tensor imaging for tracking muscle fibers

Cortical activation in confrontation naming.