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.

In this paper we describe the enormous potential that multilinear models hold for the analysis of data from neuroimaging experiments that rely on functional magnetic resonance imaging (MRI) or other imaging modalities. A case is made for why one might fully expect that the successful introduction of these models to the neuroscience community could define the next generation of structure-seeking paradigms in the area. In spite of the potential for immediate application, there is much to do from the perspective of statistical science. That is, although multilinear models have already been particularly successful in chemistry and psychology, relatively little is known about their statistical properties. To that end, our research group at the University of Kentucky has made significant progress. In particular, we are in the process of developing formal influence measures for multilinear methods as well as associated classification models and effective implementations. We believe that these problems will be among the most important and useful to the scientific community. Details are presented herein and an application is given in the context of facial emotion processing experiments.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Mathematical problems in the application of multilinear models to facial emotion processing experiments

/pdf/validations-of-apomorphine-induced-bold-activation-2soc8reg2s.pdf

Validations of apomorphine-induced BOLD activation correlations in hemiparkinsonian rhesus macaques.

Following an anterior cruciate ligament (ACL) reconstruction, the quadriceps muscles experience 3 times greater reduction in strength as compared to the hamstring muscles. The causes of this imbalance include both neurological and local muscular factors. Among local muscular factors, we have recently shown that the vastus lateralis (VL) muscle has a dysregulated extracellular matrix (ECM) after injury. However, evaluating the ECM via muscle biopsy in other thigh muscles to determine if regional differences exist is not practical due to depth and location. Utilizing new techniques in magnetic resonance imaging, it is possible to measure the dysregulation of the ECM for muscles that cannot be biopsied. Measuring the T1Rho relaxation time of the quadriceps and hamstrings may provide new insight on regional differences between the muscles of the thigh after an ACL tear. PURPOSE: To compare the T1Rho relaxation time for the VL, vastus intermedius (VI), vastus medialis (VM), rectus femoris (RF), biceps femoris (BF), semitendinosus (ST), and semimembranosus (SM) of the injured and non-injured limbs following an ACL tear. METHODS: 11 individuals (age: 20.5 ± 4.8 years) with ACL tears underwent a T1rho MRI scan of both limbs. T1Rho relaxation time per muscle was determined using a custom MATLAB code. Relaxation times were compared between limbs with a paired t-test. RESULTS: Mean T1Rho relaxation times (in s) for injured and non-injured limbs are given in Table 1. Differences between the injured and non-injured limbs were significant for the all quadricep muscles, but were not significant for the BF, ST, and SM. CONCLUSION: Regional differences in T1Rho relaxation time suggest that dysregulation of ECM is limited to just the quadricep muscles following ACL injury. Potentially, this dysregulation is an adaptation that weakens the quadriceps but maintains hamstring strength to limit anterior translation of the tibia causing knee buckling. Supported by: NIH Grant RO1AR071398 

Anders H. Andersen

Papers

Mathematical problems in the application of multilinear models to facial emotion processing experiments

Validations of apomorphine-induced BOLD activation correlations in hemiparkinsonian rhesus macaques.

Regional Differences In T1 Rho Relaxation Times Between Healthy And Acl-deficient Limbs