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Using the axis of rotation of polar navigator echoes to rapidly measure 3D rigid-body motion.

An improved technique to prospectively correct three-dimensional rigid-body motion using polar spherical navigator (pNAV) echoes is presented. The technique is based on acquiring pNAVs of an object in a baseline and rotated position and determining the axis of rotation (AOR) between data sets, thereby reducing 3D rotations to a 2D, planar rotation. Finding the AOR is simplified by prerotating the baseline trajectory, which forces the axis to lie within a specific polar region of a spherical shell in k-space. Orbital navigator echoes are interpolated from the pNAV data in planes orthogonal to the AOR and cross-correlated to determine the 2D rotation. The rotation about the AOR is used in conjunction with its orientation to calculate the overall 3D rotation. The pNAV-AOR technique was tested for its precision, accuracy, and processing speed in detecting compound rotations and translations of varying magnitude. In comparison to the spherical navigator echo technique, the pNAV-AOR technique is noniterative, fast, and independent of rotation magnitude and direction. At low SNR, the technique can detect compound rotations to 0.5 degrees accuracy in an estimated 100 msec, indicating that prospective 3D rigid-body motion correction may be feasible with this technique.

Humans↗

Real-time rigid body motion correction and shimming using cloverleaf navigators.

Subject motion during scanning can greatly reduce MRI image quality and is a major reason for discarding data in both clinical and research scanning. The quality of the high-resolution structural data used for morphometric analysis is especially compromised by subject movement because high-resolution scans are of longer duration. A method is presented that measures and corrects rigid body motion and associated first-order shim changes in real time, using a pulse sequence with embedded cloverleaf navigators and a feedback control mechanism. The procedure requires a 12-s preliminary mapping scan. A single-path, 4.2-ms cloverleaf navigator is inserted every repetition time (TR) after the readout of a 3D fast low-angle shot (FLASH) sequence, requiring no additional RF pulses and minimally impacting scan duration. Every TR, a rigid body motion estimate is made and a correction is fed back to adjust the gradients and shim offsets. Images are corrected and reconstructed on the scanner computer for immediate access. Correction for between-scan motion can be accomplished by using the same reference map for each scan repetition. Human and phantom tests demonstrated a consistent improvement in image quality if motion occurred during the acquisition.

Algorithms↗

Protein flexibility and rigidity predicted from sequence.

Structural flexibility has been associated with various biological processes such as molecular recognition and catalytic activity. In silico studies of protein flexibility have attempted to characterize and predict flexible regions based on simple principles. B-values derived from experimental data are widely used to measure residue flexibility. Here, we present the most comprehensive large-scale analysis of B-values. We used this analysis to develop a neural network-based method that predicts flexible-rigid residues from amino acid sequence. The system uses both global and local information (i.e., features from the entire protein such as secondary structure composition, protein length, and fraction of surface residues, and features from a local window of sequence-consecutive residues). The most important local feature was the evolutionary exchange profile reflecting sequence conservation in a family of related proteins. To illustrate its potential, we applied our method to 4 different case studies, each of which related our predictions to aspects of function. The first 2 were the prediction of regions that undergo conformational switches upon environmental changes (switch II region in Ras) and the prediction of surface regions, the rigidity of which is crucial for their function (tunnel in propeller folds). Both were correctly captured by our method. The third study established that residues in active sites of enzymes are predicted by our method to have unexpectedly low B-values. The final study demonstrated how well our predictions correlated with NMR order parameters to reflect motion. Our method had not been set up to address any of the tasks in those 4 case studies. Therefore, we expect that this method will assist in many attempts at inferring aspects of function.

Amino Acid Sequence↗

Differences in the specificities of the highly alkalophilic proteinases Savinase and Esperase imposed by changes in the rigidity and geometry of the substrate binding sites.

Savinase and Esperase are closely related highly alkalophilic proteinases produced by Bacillus lentus. They are suitable couple for investigating the structural basis of proteinase specificity due to the identity of the catalytic and the differences in the substrate binding sites. Two of the substitutions in these sites are very important: T129P and G131P. The two prolines provide an extra rigidity of the Savinase-binding site. The substitutions S166N and Q191T in the S1 recognition loop change the binding geometry of the substrate P1 residue. The geometry of S1 in Esperase is more favorable for binding and catalysis in comparison to that in Savinase. Differences in P3 specificity are probably created by the substitution V104L, which influences the conformation of S3. Leu in position 104 is more favorable for the binding of Phe to S4 than Val. The lower affinity and catalytic efficiency as well as more narrow proteolytic specificity of Savinase in comparison to those of Esperase are explained with the extra rigidity and unfavorable changes in geometry of the substrate binding site of the first enzyme.

Alkalies↗

Effect of Coupling between Rotational and Translational Brownian Motions on NMR Spin Relaxation: Consideration Using Green Function of Rigid Body Diffusion.

Using the Green function of arbitrary rigid Brownian diffusion (Goldstein, Biopolymers 33, 409-436, 1993), it was analytically shown that coupling between translation and rotation diffusion degrees of freedom does not affect the correlation functions relevant to the NMR intramolecular relaxation. It follows that spectral densities usually used for the anisotropic rotation diffusion (Woessner, J. Chem. Phys. 37, 647-654, 1962) can be regarded as exact in respect to the rotation-translation coupling for the spin system connected with a rigid body. Copyright 1998 Academic Press.

Journal Article↗

A close look at 13C CPMAS linewidths in solids for rigid, strongly coupled carbons under CW proton decoupling

Ambient-temperature 13C linewidth (LW) and transverse relaxation (TC2) data are presented for the natural-abundance crystalline carbons of linear polyethylene (LPE) under CW proton decoupling conditions and magic angle spinning (MAS). This linewidth behavior typifies that seen for rigid methylene carbons whose attached protons are also strongly coupled to other protons. These data are presented for two LPE samples (unoriented, melt-crystallized and uniaxially oriented, extruded) as a function of several parameters including static field (1.4 T < B0 < 9.4 T), proton decoupling field strength (38 kHz < nuH1 < 90 kHz), MAS frequency (0.5 kHz < nur < 8 kHz) and RF frequency offsets from resonance (-4 kHz < Deltanuoff < 4 kHz). It is the ubiquitous nature of off-resonance proton irradiation (ORPI) (arising from fixed or rotationally dependent deviations from the true proton resonance condition) which provides the focus for this work. Corresponding contributions, LW(ORPI), to the total LW are treated within the general framework of the effective-field picture of CW decoupling. Then, considering the presence of spin fluctuations characteristic of the strongly-dipolar-coupled protons of LPE, LW(ORPI) can be traced to orbit-dependent TC2 contributions to LW. Important dependences demonstrated and discussed include: (1) For "off-resonance" decoupling, there is a quadratic dependence of LW(ORPI) on (Deltanuoff/nuH1) and there is a strong dependence of the corresponding parabolic coefficient on nur. From the latter dependence, characteristic times for spin fluctuations are also estimated. (2) For "on-resonance" decoupling, LW(ORPI) is proportional to (nuH1)-2 and shows very little sensitivity to nur. These LW(ORPI) contributions become more important at higher B0 since the principle reason for ORPI is the chemical shift anisotropy (CSA) of the 13C-bonded protons. The difference in sensitivities of LW(ORPI) to nur for the off-resonance and the on-resonance cases is traced back, respectively, to the scalar property of Deltanuoff for RF frequency offsets and to the tensorial character of the proton CSA. Contributions from LW(ORPI), possibly much larger than those seen in LPE, can be expected when protons near 13C nuclei sense any non-scalar, rotor-position-dependent magnetic fields, e.g., (a) local dipolar fields associated with third, magnetic nuclei or (b) perturbing magnetic-susceptibility fields arising from paramagnetic or ferromagnetic inclusions in a sample. By understanding the contributions to LW in LPE, one can forecast much more precisely what the potential benefits will be from new decoupling schemes like the recently reported "two-pulse phase modulation" (TPPM) since TPPM is designed to reduce LW(ORPI). Aside from LW(ORPI) contributions, the experimental LW data cover parameter space where another broadening mechanism, namely, MAS-assisted dipolar fluctuations (MADF), is seen. This mechanism, also recognized by others, creates a TC2-type linewidth contribution which increases rapidly as nuH1 decreases and which additionally has some orbit dependence. If the current trend in 13CCPMAS is toward higher B0 and nur, the nur-dependent MADF contributions can easily dominate LW relative to the B0-dependent LW(ORPI) contributions. One can avoid serious MADF broadening; however, the minimum acceptable values of nuH1 for good decoupling rise rapidly with B0. Finally, a few LW measurements are made on methyl-alpha-d-glucopyranoside tetraacetate (MGT), a rigid, polycrystalline material containing carbons with 0, 1, 2, and 3 attached protons. The behaviors of the methylene, methine, and methyl carbons at 9.4 T are compared with the behavior of LPE. Copyright 1998 Academic Press.

Journal Article↗

Using conjoined rigid body/torsion angle simulated annealing to determine the relative orientation of covalently linked protein domains from dipolar couplings.

A simple and robust method for determining the relative orientations of covalently linked protein domains using conjoined rigid body/torsion angle dynamics simulated annealing on the basis of residual dipolar couplings is presented. In this approach each domain is treated as a rigid body and the relevant degrees of conformational freedom are restricted to the backbone torsion angles (phi, psi) of the linker between the domains. By this means translational information afforded by the presence of an intact linker is preserved. We illustrate this approach using the domain-swapped dimer of the HIV-inactivating protein cyanovirin-N as an example.

Anti-HIV Agents↗

Articulated rigid registration for serial lower-limb mouse imaging.

This paper describes a new piecewise rotational transformation model for capturing the articulation of joints such as the hip and the knee. While a simple piecewise rigid model can be applied, such models suffer from discontinuities at the motion boundary leading to both folding and stretching. Our model avoids both of these problems by constructing a provably continuous transformation along the motion interface. We embed this transformation model within the robust point matching framework and demonstrate its successful application to both synthetic data, and to serial x-ray CT mouse images. In the later case, our model captures the articulation of six joints, namely the left/right hip, the left/right knee and the left/right ankle. In the future such a model could be used to initialize non-rigid registrations of images from different subjects, as well as, be embedded in intensity-based and integrated registration algorithms. It could also be applied to human data in cases where articulated motion is an issue (e.g. image guided prostate radiotherapy, lower extremity CT angiography).

Algorithms↗

Interpolation artefacts in non-rigid registration.

Voxel based non-rigid registration of images involves finding a similarity maximising transformation that deforms a source image to the coordinate system of a target image. In order to do this, interpolation is required to estimate the source intensity values corresponding to transformed target voxels. These interpolated source intensities are used when calculating the similarity measure being optimised. In this work, we compare the extent and nature of artefactual displacements produced by voxel based non-rigid registration techniques for different interpolators and investigate their relationship to image noise and global transformation error. A per-voxel similarity gradient is calculated and the resulting vector field is used to characterise registration artefacts for each interpolator. Finally, we show that the resulting registration artefacts can generate spurious volume changes for image pairs with no expected volume change.

Algorithms↗

Learning based non-rigid multi-modal image registration using Kullback-Leibler divergence.

The need for non-rigid multi-modal registration is becoming increasingly common for many clinical applications. To date, however, existing proposed techniques remain as largely academic research effort with very few methods being validated for clinical product use. It has been suggested by Crum et al. that the context-free nature of these methods is one of the main limitations and that moving towards context-specific methods by incorporating prior knowledge of the underlying registration problem is necessary to achieve registration results that are accurate and robust enough for clinical applications. In this paper, we propose a novel non-rigid multi-modal registration method using a variational formulation that incorporates a prior learned joint intensity distribution. The registration is achieved by simultaneously minimizing the Kullback-Leibler divergence between an observed and a learned joint intensity distribution and maximizing the mutual information between reference and alignment images. We have applied our proposed method on both synthetic and real images with encouraging results.

Algorithms↗

Myocardial motion estimation in tagged MR sequences by using alphaMI-based non rigid registration.

Tagged Magnetic Resonance Imaging (MRI) is currently the reference MR modality for myocardial motion and strain analysis. NMI-based non rigid registration has proven to be an accurate method to retrieve cardiac deformation fields. The use of alphaMI permits higher dimensional features to be implemented in myocardial deformation estimation through image registration. This paper demonstrates that this is feasible with a set of Haar wavelet features of high dimension. While we do not demonstrate performance improvement for this set of features, there is no significant degradation as compared to implementing the registration method with the traditional NMI metric. We use Entropic Spanning Graphs (ESGs) to estimate the alphaMI of the wavelet feature vectors WFVs since this is not possible with histograms. To the best of our knowledge, this is the first time that ESGs are used for non rigid registration.

Algorithms↗

Non-rigid image registration using a statistical spline deformation model.

We propose a statistical spline deformation model (SSDM) as a method to solve non-rigid image registration. Within this model, the deformation is expressed using a statistically trained B-spline deformation mesh. The model is trained by principal component analysis of a training set. This approach allows to reduce the number of degrees of freedom needed for non-rigid registration by only retaining the most significant modes of variation observed in the training set. User-defined transformation components, like affine modes, are merged with the principal components into a unified framework. Optimization proceeds along the transformation components rather then along the individual spline coefficients. The concept of SSDM's is applied to the temporal registration of thorax CR-images using pattern intensity as the registration measure. Our results show that, using 30 training pairs, a reduction of 33% is possible in the number of degrees of freedom without deterioration of the result. The same accuracy as without SSDM's is still achieved after a reduction up to 66% of the degrees of freedom.

Algorithms↗

Semi-rigid analogues of the calcium antagonist verapamil: a molecular modelling study.

In this work the rigid-analogue approach has been used to obtain information on the active conformation(s) of the calcium antagonist verapamil. A series of semi-rigid analogues of verapamil were synthesized and their biological activities evaluated on guinea-pig heart and aorta. These molecules were analysed by means of molecular modelling techniques. On the basis of the pharmacological profile and conformational analysis of these compounds, two different models for negative inotropic and negative chronotropic activity are proposed. The two actions seem to be due to conformations of the molecules which differ in the orientation of their phenylethylamino groups.

Animals↗

Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption.

When a flat figure of uniform color and with an elliptic contour is slowly rotated around an axis orthogonal to the plane of the image, an observer set in the frontal position will perceive it first as a rotating ellipse. After a few seconds of inspection, the ellipse appears to deform with an amoeba-like movement until it appears as a rigid, circular disk tilting back and forth in 3-D space; finally it is seen as a rotating ellipsoid tilted in depth at a constant inclination angle with respect to the rotating platform. In an attempt to provide an explanation for the apparent ellipsoid, the authors present a mathematical model based on an hypothesis of velocity differences minimization, successfully used to describe other stereokinetic phenomena, such as "the rotating cone" and the "tilted bar". This technique does not make use of Ullman's "rigidity hypothesis" for extracting depth from 2-D moving stimuli. A comparison with experimental results supports the validity of the model.

Depth Perception↗

The nucleus accumbens and forelimb muscular rigidity in rats.

The present set of experiments were performed to evaluate the role of the nucleus accumbens in the regulation of forelimb muscle tone. Rats were chronically implanted with cannulae aimed at the nucleus accumbens or the neostriatum and with EMG electrodes in the triceps or the gastrocnemius soleus muscle. The experiments were all performed in non-anaesthetised freely moving animals. The results show that haloperidol induced an increase in triceps muscle tone when injected into the nucleus accumbens but not when injected into the neostriatum. Likewise it was found that haloperidol induced an increase in gastrocnemius soleus muscle tone when injected into the neostriatum but not when injected into the nucleus accumbens. The increase in triceps muscle tone seen after intra-accumbens haloperidol was only briefly attenuated by apomorphine, whereas phenylephrine produced a more long lasting antagonism. The present data show that in addition to the cortex, subcortical structures also appear to possess a certain topography, with forelimb rigidity being mediated, at least in part, by the nucleus accumbens, and hindlimb rigidity, at least in part by the neostriatum. In addition it appears that the effects of haloperidol in the nucleus accumbens on triceps muscle tone are primarily mediated by alpha 1 adrenergic receptors, although a minor role of dopamine D2 receptors cannot be fully excluded.

Animals↗

Familial myopathy with scapulohumeral distribution, rigid spine, cardiopathy and mitochondrial abnormality.

A 37-year-old woman with scapulohumeral muscular atrophy, rigid spine and cardiopathy is reported. Muscle weakness, advanced atrioventricular block and contractures at the neck, elbows and ankles had occurred during her childhood. An autosomal dominant mode of inheritance was suggested because her mother, sister and brother had the same disorder. Pleomorphic mitochondria had accumulated in the subsarcolemmal space of the skeletal muscle. There was no evident enzyme defect in the mitochondrial electron transport system. Although the clinical features had some similarity with those of Emery-Dreifuss muscular dystrophy or rigid spine syndrome, the pattern of inheritance and the muscle pathology differed.

Adult↗

Antagonism of reserpine rigidity without inducing sedation.

The effects of pretreatment with chlorpromazine, promethazine or SKF 7265 on the severity of reserpine-induced rigidity were evaluated using a series of behavioral responses. Chlorpromazine (10 mg/kg) reduced the severity of the syndrome, particularly the tremor, but only at doses that also produced marked sedation. SKF 7265 was more effective than chlorpromazine and produced no detectable sedation or other motor impairment. Promethazine was ineffective in protecting against the effects of reserpine. These studies demonstrate that motor and behavioral abnormalities induced by high doses of reserpine can be blocked without inducing generalized sedation. This would suggest that it is possible to separate pharmacologically the motor pathways responsible for reserpine rigidity and those responsible for sedation.

Acridines↗

The role of rigidity in fracture fixation. An overview.

UNLABELLED: The optimal degree of rigidity of internal fixation of fractures is still a matter of controversy. Since any attempt to clarify this situation must rest on a clear terminology, we propose terms relating to different degrees of rigidity. They are based on the material and the design of implants as well as the morphologic features of repair. From our morphologic findings it is obvious that the healing response and the subsequent structural remodelling depend on bone deformation and gap motion. CLINICAL SIGNIFICANCE: For sound patient care, the most ideal mode of internal fixation by plates, yielding rapid and efficient fracture healing, has to be established scientifically in a comparative study.

Animals↗