Motion Tensor Research Articles

Integrated intravoxel incoherent motion tensor and diffusion tensor brain MRI in a single fast acquisition.

The acquisition of intravoxel incoherent motion (IVIM) data and diffusion tensor imaging (DTI) data from the brain can be integrated into a single measurement, which offers the possibility to determine orientation-dependent (tensorial) perfusion parameters in addition to established IVIM and DTI parameters. The purpose of this study was to evaluate the feasibility of such a protocol with a clinically feasible scan time below 6 min and to use a model-selection approach to find a set of DTI and IVIM tensor parameters that most adequately describes the acquired data. Diffusion-weighted images of the brain were acquired at 3 T in 20 elderly participants with cerebral small vessel disease using a multiband echoplanar imaging sequence with 15 b-values between 0 and 1000 s/mm2 and six non-collinear diffusion gradient directions for each b-value. Seven different IVIM-diffusion models with 4 to 14 parameters were implemented, which modeled diffusion and pseudo-diffusion as scalar or tensor quantities. The models were compared with respect to their fitting performance based on the goodness of fit (sum of squared fit residuals, chi2 ) and their Akaike weights (calculated from the corrected Akaike information criterion). Lowest chi2 values were found using the model with the largest number of model parameters. However, significantly highest Akaike weights indicating the most appropriate models for the acquired data were found with a nine-parameter IVIM-DTI model (with isotropic perfusion modeling) in normal-appearing white matter (NAWM), and with an 11-parameter model (IVIM-DTI with additional pseudo-diffusion anisotropy) in white matter with hyperintensities (WMH) and in gray matter (GM). The latter model allowed for the additional calculation of the fractional anisotropy of the pseudo-diffusion tensor (with a median value of 0.45 in NAWM, 0.23 in WMH, and 0.36 in GM), which is not accessible with the usually performed IVIM acquisitions based on three orthogonal diffusion-gradient directions.

Robot-world and hand–eye calibration based on motion tensor with applications in uncalibrated robot

Accurate estimation of robot-world and hand–eye transformations is crucial for robotic vision system. Although as existing methods provide accurate calibration results, which method is best for uncalibrated robot remains a challenging question. This study applied the motion tensor to the dual equations as an operator that performs coordinate frame change, resulting in the most efficient and elegant representation of dual equations. The analytical solution and the numerical solution were given, respectively. The analytical solution requires only four independent variables involving the screw axis, since the pitch and magnitude of a general screw motion are coordinate invariants. The numerical solution used the closed-form rotation solution based on the Kronecker product as an initial value, and followed the optimization with Gauss–Newton algorithm. The superiority with applications in uncalibrated robot was further tested through simulated and experimental tests compared to the existing methods.

Short‐Term Repeatability of in Vivo Cardiac Intravoxel Incoherent Motion Tensor Imaging in Healthy Human Volunteers

FA and MD/MF Maps of IVIM Tensors as well as HA Maps of D Tensor from a Typical Subject on Test and Retest. by Zhang et al. (854-865)

Temperature and humidity optimisation control of cold chain vehicle carriage based on Gray Wolf algorithm

There are some problems in the traditional temperature and humidity control of cold chain transportation vehicles, such as poor control effect, poor real-time control, etc. The paper introduces Descartes coordinate system to construct the air motion tensor model in the carriage of cold chain transportation vehicles. The influence parameters of temperature and humidity of cold chain transport vehicles are divided into different temperature and humidity parameters. The Gray Wolf algorithm is used to search for the optimal solution of humidity influence parameters, and different wolf fitness models are constructed to determine the optimal solution of parameters to realise optimal control. The comparison shows that: the control deviation of temperature and humidity of cold chain transport vehicle compartment is always lower than 0.4, and the control efficiency coefficient is higher than 0.9.

Short-Term Repeatability of in Vivo Cardiac Intravoxel Incoherent Motion Tensor Imaging in Healthy Human Volunteers.

Intravoxel incoherent motion (IVIM) tensor imaging is a promising technique for diagnosis and monitoring of cardiovascular diseases. Knowledge about measurement repeatability, however, remains limited. To evaluate short-term repeatability of IVIM tensor imaging in normal in vivo human hearts. Prospective. Ten healthy subjects without history of heart diseases. Balanced steady-state free-precession cine sequence and single-shot spin-echo echo planar IVIM tensor imaging sequence (9 b-values, 0-400 seconds/mm2 and six diffusion-encoding directions) at 3.0 T. Subjects were scanned twice with an interval of 15 minutes, leaving the scanner between studies. The signal-to-noise ratio (SNR) was evaluated in anterior, lateral, septal, and inferior segments of the left ventricle wall. Fractional anisotropy (FA), mean diffusivity (MD), mean fraction (MF), and helix angle (HA) in the four segments were independently measured by five radiologists. IVIM tensor indexes were compared between observers using a one-way analysis of variance or between scans using a paired t-test (normal data) or a Wilcoxon rank-sum test (non-normal data). Interobserver agreement and test-retest repeatability were assessed using the intraclass correlation coefficient (ICC), within-subject coefficient of variation (WCV), and Bland-Altman limits of agreements. SNR of inferior segment was significantly lower than the other three segments, and inferior segment was therefore excluded from repeatability analysis. Interobserver repeatability was excellent for all IVIM tensor indexes (ICC: 0.886-0.972; WCV: 0.62%-4.22%). Test-retest repeatability was excellent for MD of the self-diffusion tensor (D) and MF of the perfusion fraction tensor (fp ) (ICC: 0.803-0.888; WCV: 1.42%-9.51%) and moderate for FA and MD of the pseudo-diffusion tensor (D* ) (ICC: 0.487-0.532; WCV: 6.98%-10.89%). FA of D and fp and HA of D presented good test-retest repeatability (ICC: 0.732-0.788; WCV: 3.28%-8.71%). The D and fp indexes exhibited satisfactory repeatability, but further efforts were needed to improve repeatability of D* indexes. 2 TECHNICAL EFFICACY: Stage 1.

Modal reduction procedures for flexible multibody dynamics

Through a critical review of the various component mode synthesis techniques developed in the past, it is shown that both Craig–Bampton’s and Herting’s methods are particular cases of the mode-acceleration method and furthermore, Rubin’s method is equivalent to Herting’s method. Consequently, the mode-acceleration method is the approach of choice due to its simplicity and because unlike the other methods, it imposes no restriction on the selection of the modes. Next, a general approach to the modal reduction of geometrically nonlinear structures is developed within the framework of the motion formalism, based on the small deformation assumption. The floating frame of reference is defined unequivocally by imposing six linear constraints on the deformation measures, which are defined as the vectorial parameterization of the relative motion tensor that brings the fictitious rigid-body configuration to its deformed counterpart. This approach yields deformation measures that are both objective and tensorial, unlike their classical counterparts that share the first property only. Derivatives are expressed in the material frame, leading to computationally advantageous properties: tangent matrices are functions of the deformation measures only and become nearly constant during the simulation. Numerical examples demonstrate the accuracy, robustness, and numerical efficiency of the proposed approach. With a small number of modal elements, the formulation is able to capture geometrically nonlinear effects accurately, even in the presence of inherently nonlinear phenomena such as buckling.

Investigation of intravoxel incoherent motion tensor imaging for the characterization of the in vivo human heart

To investigate intravoxel incoherent motion (IVIM) tensor imaging of the in vivo human heart and elucidate whether the estimation of IVIM tensors is affected by the complexity of pseudo-diffusion components in myocardium. The cardiac IVIM data of 10 healthy subjects were acquired using a diffusion weighted spin-echo echo-planar imaging sequence along 6 gradient directions with 10 b values (0~400 s/mm2 ). The IVIM data of left ventricle myocardium were fitted to the IVIM tensor model. The complexity of myocardial pseudo-diffusion components was reduced through exclusion of low b values (0 and 5 s/mm2 ) from the IVIM curve-fitting analysis. The fractional anisotropy, mean fraction/mean diffusivity, and Westin measurements of pseudo-diffusion tensors (fp and D*) and self-diffusion tensor (D), as well as the angle between the main eigenvector of fp (or D*) and that of D, were computed and compared before and after excluding low b values. The fractional anisotropy values of fp and D* without low b value participation were significantly higher (P < .001) than those with low b value participation, but an opposite trend was found for the mean fraction/diffusivity values. Besides, after removing low b values, the angle between the main eigenvector of fp (or D*) and that of D became small, and both fp and D* tensors presented significant decrease of spherical components and significant increase of linear components. The presence of multiple pseudo-diffusion components in myocardium indeed influences the estimation of IVIM tensors. The IVIM tensor model needs to be further improved to account for the complexity of myocardial microcirculatory network and blood flow.

Construction worker's awkward posture recognition through supervised motion tensor decomposition

Abstract Awkward postures in construction activities pose substantial hazards in both instantaneous injuries and long-term work-related musculoskeletal disorders (WMSDs). Posture recognition using motion capturing systems shows promising potential in avoiding and minimizing workers' exposure to awkward postures. However, current motion capturing systems require huge computational resources and complicated processes to recognize postures in construction tasks. To address this issue, we proposed an abstract and efficient motion tensor decomposition approach to compress and reorganize the motion data. Together with a multi-classification algorithm, the proposed approach is able to efficiently and accurately differentiate various postures. To validate the approach, we employed a system based on inertial measurement units (IMUs) to examine two sample activities composed of sequencing postures. The results indicate the proposed approach is able to provide sufficient recognition accuracy with less computation power and memory. Also, the idea of tensorization and tensor decomposition in this paper is extendable to other studies in the construction industry.

Manipulation of motion via dual entities

The manipulation of motion and ancillary operations are important tasks in kinematics, robotics, and rigid and flexible multibody dynamics. Motion can be described in purely geometric terms, based on Chasles’ theorem. Representations and parameterizations of motion are also available, such as Euler motion parameters and the vectorial parameterization, respectively. Typical operations to be performed on motion involve the selection of local or global parameterizations and the derivation of the associated expressions for the motion tensor, velocity or curvature vector, composition of motions, and tangent tensors. Many of these tasks involve arduous, error-prone algebra. The use of dual entities has been shown to ease the manipulation of motion, yet this concept has received little attention outside of the fields of kinematics and robotics. This paper presents a comprehensive treatment of the topic using a notation that eliminates the bookkeeping parameter typically used in dual number algebra, thereby recasting all operations within the framework of linear algebra and streamlining the process. The manipulation of geometric entities is recast within this formalism, paving the way for the manipulation of motion. All developments are presented within the framework of dual numbers directly; the principle of transference is never invoked: The manipulation of rotation is a particular case of that of motion, as should be. The problem of interpolation of motion, a thorny issue in finite element applications, is also addressed.

Tensorial Deformation Measures for Flexible Joints

Flexible joints, sometimes called bushing elements or force elements, are found in all multibody dynamics codes. In their simplest form, flexible joints simply consist of sets of three linear and three torsional springs placed between two nodes of a multibody system. For infinitesimal deformations, the selection of the lumped spring constants is an easy task, which can be based on a numerical simulation of the joint or on experimental measurements. If the joint undergoes finite deformations, the identification of its stiffness characteristics is not so simple, especially if the joint itself is a complex system. When finite deformations occur, the definition of deformation measures becomes a critical issue. Indeed, for finite deformation, the observed nonlinear behavior of materials is partly due to material characteristics and partly due to kinematics. This paper focuses on the determination of the proper finite deformation measures for elastic bodies of finite dimension. In contrast, classical strain measures, such as the Green–Lagrange or Almansi strains, among many others, characterize finite deformations of infinitesimal elements of a body. It is argued that proper finite deformation measures must be of a tensorial nature, i.e., must present specific invariance characteristics. This requirement is satisfied if and only if the deformation measures are parallel to the eigenvector of the motion tensor.

不規則性をもつ結晶，超イオン導電体，非晶質，ガラス，融体の構造解析―不規則系・ランダム系の結晶学―１．周期系における不規則性の解析 Ｘ線回折，ラマン散乱による高温相解析，相転移の研究（シリカ系における熱振動と原子変位）

Thermal vibrational parameters of lower temperature phases of tridymite and melanophlogite, and their related quantities were used to characterize their higher temperature phases and phase transitions. The orthorhombic tridymite appearing right above the monoclinic room temperature phase and β-melanophlogite are all subject to atom disorder. Raman spectroscopic data of the orthorhombic tridymite and their simulations in lattice dynamical calculations suggested that the motions causing the disorder are triggered by a low frequency phonon mode via coupling between themselves having the same symmetry. Higher-order thermal motion tensor analysis of β-melanophlogite indicated that the probability density functions of O atoms are strongly distorted from ellipsoidal ones, directly proving atom disorder, which were further analyzed in terms of 12 α-domains.

The Vector Parameterization of Motion

This paper presents a vector parameterization of motion thatgeneralizes the vector parameterization of rotation. The Plucker coordinates of an arbitrary material line of a rigid bodysubjected to a screw motion are shown to transform by the action of amotion tensor. The proposed vector parameterization completelydescribes an arbitrary motion by means of two vectors that constitutean eigenvector of the motion tensor associated with its positive uniteigenvalue. The first vector is conveniently selected as the vectorparameterization of rotation, and the second is related to thedisplacement of a point of the rigid body. A complete description ofmotion is presented in terms of a generic vectorparameterization. Relevant formulae for specific parameterizations ofthis class can then be easily obtained. More details are given forthree parameterizations that present desirable properties: the Euler,Cayley–Gibbs–Rodrigues, and Wiener–Milenkovic motionparameters. Applications to the dynamic analysis of a rigid body arepresented as an illustration.

1,3,5-Triiodo-2,4,6-trimethylbenzene at 293 K.

In the structure of triiodomesitylene (1,3,5-triiodo-2,4,6-trimethylbenzene), C(9)H(9)I(3), at 293 K, the benzene ring is found to be significantly distorted from ideal D(6h) symmetry; the average endocyclic angles facing the I atoms and the methyl groups are 123.8 (3) and 116.2 (3) degrees, respectively. The angle between the normal to the molecular plane and the normal to the (100) plane is 5.1 degrees. No disorder was detected at 293 K. The thermal motion was investigated by a rigid-body motion tensor analysis. Intra- and intermolecular contacts are described and topological differences compared with the isomorphous compounds trichloromesitylene and tribromomesitylene are discussed.

On zero-field anisotropic static Kubo-Toyabe relaxation functions

For muons which have thermalized in the allowed stopping sites of a given crystal, zero-field static Kubo-Toyabe spin dynamics is expressed in terms of the crystal frame spherical harmonic coefficients of the local classical random magnetic field distributions associated with each stopping site. The resulting muon spin polarization involves nine observable relaxation functions which are the counter frame spherical tensor expansion coefficients of the second-rank dynamic motion tensor. These relaxation functions can be measured simultaneously using the skewed field technique for the same experimental conditions, that is, with a single apparatus and with a single crystal-counter frame orientation. The local field distributions of, in general, arbitrary symmetry are classical approximations to the magnetic field interactions between the spin of the muon and the spins of the nuclei associated with each site at which the muon has stopped. They are characterized by equating their moments with the quantal moments generated by the quantal magnetic fields. The observable consequences of the anisotropic second-order moments associated with the planar sites of hexagonal crystals are used as an illustration.

On the observables associated with zero and intermediate applied external field muon spin rotation

For zero and intermediate applied external fields, the dynamics of the static spin polarization associated with muons which have thermalized in the allowed stopping sites of a given solid is expressed in terms of counter and crystal frame spherical harmonic tensor expansions of the second-rank dynamical motion tensor. Coefficients of these expansions, usually termed relaxation functions, are related to observable longitudinal, co-planar transverse and perpendicular transverse relaxation functions which can be measured simultaneously using the skewed field technique. Since the motion tensor is of second rank then, in general, nine observable relaxation functions exist. This stands in contrast to the traditional high-field longitudinal and transverse techniques employed in muon spin rotation (ΜSR) experiments wherein only three of the nine observable relaxation functions are non-zero. These traditional experiments, usually employing different apparatus, are carried out separately. Even when the other six relaxation functions are identically zero in zero and intermediate applied field experiments, they still contain information about the stopping probabilities or the dynamical symmetries associated with the muon sites, that is, that such symmetries are not present or that the sites with these symmetries are orientated in such a way that the statistical sums of their relaxation functions are zero. Thus these relaxation functions can then be used asexperimental confirmation of expected stopping probabilities associated with one type of site for which there are different orientations or for aligned sites with appropriate dynamical symmetries.