Torsional Rotation Research Articles

Exogenous hedgehog antagonist delays but does not prevent fracture healing in young mice

Fracture healing recapitulates many aspects of developmental osteogenesis. The hedgehog (Hh) signaling pathway, essential to skeletal development, is upregulated during fracture healing, although its importance is unclear. Our goal was to assess the functional importance of Hh signaling in endochondral fracture healing. We created closed, transverse diaphyseal femur fractures in mice, stabilized with an intramedullary pin, and administered a systemic Hh inhibitor or vehicle. Because Hh pathway activation is mediated by the receptor Smoothened (Smo), we used the Smo antagonist GDC-0449 (GDC, 50mg/kg, twice daily) to target the pathway. First, in vehicle-treated 10-wk. female C57BL/6 mice we confirmed that Hh signaling was increased in fracture callus compared to intact bone, with >5-fold upregulation of target genes Ptch1 and Gli1. Additionally, using 10-wk. male and female Gli1 reporter mice, we saw a strong activation of the reporter in the osseous regions of the fracture callus 7–10days after fracture. GDC treatment significantly blunted these responses, indicating effective inhibition of fracture-induced Hh signaling in bone. Moreover, microCT analysis revealed that GDC treatment significantly reduced cancellous and cortical bone volume at non-fracture sites (tibial metaphysis and diaphysis), suggesting that the drug inhibited normal bone formation. GDC treatment had a modest effect on fracture healing, with evidence of delayed callus mineralization radiographically (significantly lower Goldberg score at day 14) and by microCT (reduced callus vBMD at 14days), and a delay in the recovery of torsional rotation to normal (elevated rotation-at-peak torque at 21days). On the other hand, GDC treatment did not inhibit qPCR or morphological measures of chondrogenesis or angiogenesis, and did not impair the recovery of failure torque (at day 14 or 21), a measure of biomechanical competence. In summary, GDC treatment inhibited Hh signaling, which delayed but did not prevent fracture healing in young mice. We conclude that Hh signaling is strongly induced after fracture and may play a role in early callus mineralization, although it does not appear to be required for eventual healing.

Dynamics of spinning particle pairs in a single-layer complex plasma crystal.

Spontaneous formation of spinning pairs of particles, or torsions, is studied in a single-layer complex plasma crystal by reducing the discharge power at constant neutral gas pressure. At higher gas pressures, torsions spontaneously form below a certain power threshold. Further reduction of the discharge power leads to the formation of multiple torsions. However, at lower gas pressures the torsion formation is preceded by mode-coupling instability (MCI). The crystal dynamics are studied with the help of the fluctuation spectra of crystal particles' in-plane velocities. Surprisingly, the spectra of the crystal with torsions and MCI are rather similar and contain hot spots at similar locations on the (k,ω) plane, despite very different appearances of the respective particle trajectories. The torsion rotation speed is close (slightly below) to the maximum frequency of the in-plane compressional mode. When multiple torsions form, their rotation speeds are distributed in a narrow range slightly below the maximum frequency.

Muscular Basis of Whisker Torsion in Mice and Rats.

Whisking mammals move their whiskers in the rostrocaudal and dorsoventral directions with simultaneous rolling about their long axes (torsion). Whereas muscular control of the first two types of whisker movement was already established, the anatomic muscular substrate of the whisker torsion remains unclear. Specifically, it was not clear whether torsion is induced by asymmetrical operation of known muscles or by other largely unknown muscles. Here, we report that mystacial pads of newborn and adult rats and mice contain oblique intrinsic muscles (OMs) that connect diagonally adjacent vibrissa follicles. Each of the OMs is supplied by a cluster of motor end plates. In rows A and B, OMs connect the ventral part of the rostral follicle with the dorsal part of the caudal follicle. In rows C-E, in contrast, OMs connect the dorsal part of the rostral follicle to the ventral part of the caudal follicle. This inverse architecture is consistent with previous behavioral observations [Knutsen et al.: Neuron 59 (2008) 35-42]. In newborn mice, torsion occurred in irregular single twitches. In adult anesthetized rats, microelectrode mediated electrical stimulation of an individual OM that is coupled with two adjacent whiskers was sufficient to induce a unidirectional torsion of both whiskers. Torsional movement was associated with protracting movement, indicating that in the vibrissal system, like in the ocular system, torsional movement is mechanically coupled to horizontal and vertical movements. This study shows that torsional whisker rotation is mediated by specific OMs whose morphology and attachment sites determine rotation direction and mechanical coupling, and motor innervation determines rotation dynamics. Anat Rec, 300:1643-1653, 2017. © 2017 Wiley Periodicals, Inc.

Electronic Delocalization, Vibrational Dynamics, and Energy Transfer in Organic Chromophores.

The efficiency of materials developed for solar energy and technological applications depends on the interplay between molecular architecture and light-induced electronic energy redistribution. The spatial localization of electronic excitations is very sensitive to molecular distortions. Vibrational nuclear motions can couple to electronic dynamics driving changes in localization. The electronic energy transfer among multiple chromophores arises from several distinct mechanisms that can give rise to experimentally measured signals. Atomistic simulations of coupled electron-vibrational dynamics can help uncover the nuclear motions directing energy flow. Through careful analysis of excited state wave function evolution and a useful fragmenting of multichromophore systems, through-bond transport and exciton hopping (through-space) mechanisms can be distinguished. Such insights are crucial in the interpretation of fluorescence anisotropy measurements and can aid materials design. This Perspective highlights the interconnected vibrational and electronic motions at the foundation of nonadiabatic dynamics where nuclear motions, including torsional rotations and bond vibrations, drive electronic transitions.

Tridimensional Analysis of Rotatory Subluxation and Sagittal Spinopelvic Alignment in the Setting of Adult Spinal Deformity

Study DesignRetrospective single-center. ObjectiveTo investigate rotatory subluxation (RS) in adult spinal deformity (ASD) with three-dimensional (3D) stereoradiographic images and analyze relationships between RS, transverse plane parameters, spinopelvic parameters, and clinical outcomes. BackgroundRecent research has demonstrated that sagittal plane malalignment and listhesis correlate with ASD patient-reported outcomes. However, there is still a lack of knowledge regarding the clinical impact of 3D evaluation and rotatory subluxation. Recent developments in stereoradiography allow clinicians to obtain full-body standing radiographs with low-dose radiation and 3D reconstruction. MethodsOne hundred thirty lumbar ASD patients underwent full-spine biplanar radiographs (EOS Imaging, Paris, France). Clinical outcomes were recorded. Using sterEOS software, spinopelvic parameters and lateral listhesis were measured. 3D transverse plane parameters included apical axial vertebral rotation, axial intervertebral rotation (AIR), and torsion index (sum of AIR in the curve). ASD patients were divided in three groups: AIR <5°, 5°< AIR <10°, AIR >10°. Groups were compared with respect to radiographic and clinical data. Correlations were performed between the transverse and sagittal plane parameters and clinical outcomes. ResultsPatients with AIR >10° were significantly older, with larger Cobb angle (39.5°) and greater sagittal plane deformity (pelvic incidence–lumbar lordosis mismatch 11.7° and pelvic tilt 22.6°). The AIR >10° group had significantly greater apical vertebra axial rotation apex (24.8°), torsion index (45°), and upper-level AIR (21.5°) than the two other groups. Overall, 27% of AIR patients did not have two-dimensional (2D) lateral listhesis. Patients with AIR >10° had significantly worse Oswestry Disability Index and more low back pain. ConclusionFor patients in which lateral listhesis was unreadable in 2D imaging, rotatory subluxation was revealed using stereoradiography and at an earlier disease stage. Moreover, different 3D transverse plane parameters are related to different patient-reported outcomes. Therefore, axial rotation can be considered in evaluation of lumbar degenerative scoliosis severity and prognosis. Level of EvidenceLevel III.

Left Ventricular Rotational and Twist Mechanics in the Human Fetal Heart

The authors investigated left ventricular (LV) rotational indices, twist, and torsion in a large cohort of fetuses using two-dimensional speckle-tracking echocardiography. Pregnant women (N=102) were prospectively recruited for fetal two-dimensional speckle-tracking echocardiography. Because of variable fetal position, ventricular orientation was established using the location of the liver and LV position in relation to the right ventricle. Twist measurements required correction to account for fetal position, reconciling directionality across all fetal orientations. Peak apical and basal rotations, global longitudinal strain, global circumferential strain (GCS), longitudinal strain rate, circumferential strain rate (CSR), twist, and torsion were reported and tested for associations with gestational age (GA) and estimated fetal weight (EFW). Measurement of rotational indices was feasible in 175 examinations (73%). The mean maternal age was 31±6years, the mean GA 24±6weeks, and the EFW 1.0±1.0kg. Mean peak apical rotation, basal rotation, twist, and torsion were 9.5±2.0°, -4.4±1.1°, 13.1±2.3°, and 7.9±3.4°/cm, respectively. Mean global longitudinal strain, GCS, longitudinal strain rate, and CSR were -22.3±4.3%, -25.0±6.1%, -1.4±0.5sec-1, and -1.6±0.5sec-1, respectively. Absolute GCS, CSR, apical rotation, and twist declined moderately with GA and EFW (P<.05). There were strong negative nonlinear correlations of torsion with GA and EFW: torsion=1,104×GA-1.591 (r2=0.760, P<.001); torsion=115.88×EFW-0.427 (r2=0.772, P<.001). Determination of fetal LV rotational mechanics is feasible and reproducible using two-dimensional speckle-tracking echocardiography. Basal rotation, longitudinal strain, and strain rate vary little with EFW and GA. Interpretation of LV apical rotation, twist, torsion, GCS, and CSR, however, must take GA or EFW into account. These data form the basis for comparison with findings in fetuses with abnormal cardiacanatomy and function.

Retrospective study of cranial strain pattern prevalence in a healthy population.

Research studies have associated cranial strain patterns with a variety of neurologic disorders. However, baseline data on the prevalence of such patterns in a healthy population is lacking. To determine the prevalence of cranial strain patterns in healthy subjects. A retrospective analysis of cranial strain findings from healthy subjects who participated in two previous research projects. Data were collected for the following cranial strain patterns: torsion (left or right), sidebending rotation (left or right), lateral (left or right), and vertical (superior or inferior). Data from 142 healthy subjects--119 women and 23 men with a mean age of 24.5 years--were analyzed. Torsion and sidebending rotation were the most common cranial strain patterns observed, comprising 72% of all identified patterns. The most prevalent patterns when stratified by the side of dysfunction were right torsion (31%), left sidebending rotation (23%), and left lateral (19%). Left sidebending rotation with right torsion (17%); left lateral, left sidebending rotation, and right torsion (14%); and right sidebending rotation with right torsion (11%) were the most common combinations of cranial stain patterns. Although the present study identified common cranial strain patterns in a healthy population, future studies with broader patient populations and multiple observers are needed to confirm and further define these findings.

Study on dual rotary fretting wear behavior of Ti6Al4V titanium alloy

To investigate the wear mechanism and microstructural evolution of Ti6Al4V titanium alloy under the condition of dual rotary fretting (DRF), which mainly exists in the interfaces of ball-and-socket joints with the motion combing torsional fretting with rotational fretting. Using the Ti6Al4V titanium alloy flat specimen against the 52100 steel ball to investigate the DRF and damage behavior were carried out under the normal load of 50 N with different tilt angles (10°~60°) and varying angular displacement amplitudes (0.25°~5°). The morphologies of wear surface and their cross-sections were analyzed by scanning electron microscopy, electron probe microscopy analyzer and a surface profilometer etc. The results are as followed: 1) The DRF wear behavior of Ti6Al4V is strongly dependent on the tilt angle, which decides the scale for combination of rotation component and torsion component. 2) Fx/Fn curves presents different varied trends in different fretting regimes. The fretting wear is slight in partial slip regime due to the oxidative wear, and the surface bulge is formed in mixed fretting regime probably due to the plastic-flow, and in sliding regime, plough scratches caused by the abrasive wear. 3) As the tilt angle increase, DRF wear mechanism of Ti6Al4V titanium alloy transfers from oxidative wear to the abrasive wear. 4) The DRF damage of Ti6Al4V is the result of the competition between the rotational fretting component and the torsional fretting component. When the DRF behavior is mainly controlled by the torsional fretting component, the wear mechanism is the oxidative wear with the oxygen element distributing around the micro-slip circle zone. When the DRF behavior is mainly controlled by the rotational fretting component, the severe plastic deformation can be observed.

Nucleation of recrystallized magnesium grains over quasicrystalline phase during severe plastic deformation of a Mg-Zn-Y alloy at room temperature

We show by high pressure torsion at room temperature and transmission electron microscopy that nucleation of recrystallized α-Mg grains occurs preferentially over quasicrystalline i-phase particles at an early stage of recrystallization in a Mg-3.0Zn-0.5Y (at%) alloy. α-Mg grains nucleated on i-phase surfaces by torsional rotation N=1/2 (at 5GPa pressure), and show definite orientation relationships with the i-phase. These orientation relationships are asymmetrical variations of those reported for as-cast and extruded alloys. The nucleated grains show a planar interface with the i-phase and are often faceted as they grow into a yet unrecrystallized matrix.

The Effect of Prophylactic Cerclage Wires in Primary Total Hip Arthroplasty: A Biomechanical Study

BackgroundDespite literature to support the use of various cerclage techniques to address intraoperative femoral fractures in total hip arthroplasty, there are limited data to support prophylactic cerclage wiring of the femur during cementless implant placement. This study aims to evaluate the effect of prophylactic calcar cerclage wires on the biomechanical parameters required to produce periprosthetic femoral fractures and on the morphology of these fracture patterns in stable cementless femoral implants. MethodsTen pairs of matched fresh frozen cadaveric femurs were implanted with anatomic tapered cementless implants with or without the addition of 2 monofilament calcar wires. Specimens were axially loaded and externally rotated to failure. Initial torsional stiffness, rotation and energy to failure, and torque at failure were measured. Statistical significance was set at P < .05. Fracture patterns were classified according to a well-known classification system. ResultsWired specimens required significantly more rotation (P = .039) and energy to failure (P = .048). No significant difference was detected in initial torsional stiffness (P = .63) or torque at failure (P = .10). All unwired samples developed a Vancouver B2 fracture pattern. Seven of the 8 wired specimens also developed a Vancouver B2 fracture pattern, while the eighth wired specimen developed a Vancouver B1 fracture pattern. ConclusionProphylactic cerclage wire placement increases the rotation and energy to failure in well-fixed press-fit femoral implants. The increase in torsional energy needed for failure may reduce the risk of early periprosthetic fracture. Further studies are needed to evaluate cost vs benefit and long-term outcomes of prophylactic wiring. Based on the results of our study, consideration of prophylactic wiring should be addressed on a case-to-case basis.

High-J rotational spectrum of toluene in |m| ⩽ 3 torsional states

The study of the rotational spectrum of toluene (C6H5CH3) is considerably extended to include transitions in |m|⩽3 torsional states up to the onset of the submillimeter wave region. New data involving torsion–rotation transitions up to 336GHz were combined with previously published measurements and fitted using the rho-axis-method torsion–rotation Hamiltonian. The final fit used 50 parameters to give an overall weighted root-mean-square deviation of 0.69 for a dataset consisting of 8924 transitions with J up to 94 and Ka up to 50. The new analysis allowed us to resolve all problems encountered previously for m=0 transitions beyond a certain combination of quantum numbers J and Ka when many lines of appreciable intensity and unambiguous assignment deviated from the distorted asymmetric rotor treatment. Those discrepancies are now identified to result from m=0↔m=3 and m=0↔m=−3 resonances, which have been successfully encompassed by the current fit. At the same time an analogous problem was discovered and fitted for m=2 transitions, which were found to be affected by many m=1↔m=2 resonances.

Dynamic Flexibility of Hydrogenase Active Site Models Studied with 2D-IR Spectroscopy.

Hydrogenase enzymes enable organisms to use H2 as an energy source, having evolved extremely efficient biological catalysts for the reversible oxidation of molecular hydrogen. Small-molecule mimics of these enzymes provide both simplified models of the catalysis reactions and potential artificial catalysts that might be used to facilitate a hydrogen economy. We have studied two diiron hydrogenase mimics, μ-pdt-[Fe(CO)3]2 and μ-edt-[Fe(CO)3]2 (pdt = propanedithiolate, edt = ethanedithiolate), in a series of alkane solvents and have observed significant ultrafast spectral dynamics using two-dimensional infrared (2D-IR) spectroscopy. Since solvent fluctuations in nonpolar alkanes do not lead to substantial electrostatic modulations in a solute's vibrational mode frequencies, we attribute the spectral diffusion dynamics to intramolecular flexibility. The intramolecular origin is supported by the absence of any measurable solvent viscosity dependence, indicating that the frequency fluctuations are not coupled to the solvent motional dynamics. Quantum chemical calculations reveal a pronounced coupling between the low-frequency torsional rotation of the carbonyl ligands and the terminal CO stretching vibrations. The flexibility of the CO ligands has been proposed to play a central role in the catalytic reaction mechanism, and our results highlight that the CO ligands are highly flexible on a picosecond time scale.

Symmetric fluorescent probes for the selective recognition of Ag-ion via restricted C N isomerization and on-site visual sensing applications

Naphthalene based salen type fluorescent chemosensors have been designed and synthesized for the highly selective detection of silver ions by fluorimetry. These probes 1, 2 and 3 sense Ag+ over other cations as fluorescence ‘on-off’ behaviour. A possible mechanism is proposed, where the heavy atom effect of silver ion overcomes the effect of CN isomerization and intramolecular restricted torsional rotation through the CC single bond between the naphathalene and the benzene moieties. These chemosensors are further utilized to detect Ag+ as strip tests and solid supported silica gel material. These results are further supported by the theoretical calculations.

Discussion on tangle deformation of elastic loop body induced by discrete torsional rotations

This paper investigates the tangle deformation of a loop body connected with elastic tube segments and revolute hinges. We prepared three types of segment geometry: a straight tube, a necking tube, and a bellows tube. Demonstrating the traction tests for these elastic loop structures, we observed that the bellows-type model only formed the tangle conformation induced by torsional rotations of the discrete hinges while the structures having the other types of segments shrank without torsional rotation. According to the mechanics of materials, we discuss about the relationship between bending and torsional stiffness of each segment to clarify the tangle mechanism of the proposed structures.

Advanced hallux limitus and its relationship with the internal rotational pattern and the foot progression angle

IntroductionThe aim of this study was to determine whether subjects with advanced hallux limitus show a diminished ability of internal rotation of the lower limb and increased foot progression angle compared with normal population. It was also intended to relate rotational and torsional patterns of lower limbs with the foot progression angle, and to compare three different methods of measurement of the foot progression angle. Patients and methodsInternal and external rotational pattern, internal and external hip rotation and tibial torsion were measured in 30 feet of 15 subjects with advanced hallux limitus and 103 normal feet. The foot progression angle was also obtained using a pressure platform and an inked latex carpet. ResultsThe internal rotation of the lower limb was significantly lesser and the foot progression angle was significantly greater in individuals with advanced hallux limitus (p<0.05). The Pearson correlation coefficient was −0.563 (p<0.01) for the relationship between the foot progression angle and the internal rotational pattern. The measure of the foot progression angle in the inked latex carpet was significantly greater than in the pressure platform in the left foot (p<0.05). ConclusionSubjects with advanced hallux limitus had a lesser capacity of internal rotation of the lower extremity and greater foot progression angle in comparison with normal population. Internal rotational pattern determines the greater foot progression angle. The foot progression angle values measured with the pressure platform differ from those of the inked latex carpet.

Relación del hallux limitus avanzado con el patrón rotador interno y el ángulo de la marcha

IntroductionThe aims of this study were to determine whether subjects with advanced hallux limitus show a diminished capacity of internal rotation of the lower limb and increased foot progression angle compared with normal population, to relate rotational and torsional patterns of lower limbs with the foot progression angle, and to compare methods of measurement of the foot progression angle. Patients and methodsIn 15 subjects with advanced hallux limitus, internal and external rotational pattern, internal and external hip rotation and tibial torsion were measured. The foot progression angle was obtained using a pressure platform and an inked latex carpet. ResultsThe internal rotation of the lower limb was significantly lesser and the foot progression angle was significantly greater in individuals with advanced hallux limitus (P<.05). The Pearson correlation coefficient was −0,563 (P<.01) for the relationship between the foot progression angle and the internal rotational pattern. The measure of the foot progression angle in the inked latex carpet was significantly greater than in the pressure platform in the left foot (P<.05). ConclusionSubjects with advanced hallux limitus had a lesser capacity of internal rotation of the lower extremity and greater foot progression angle in comparison with normal population. Internal rotational pattern determines the greater foot progression angle. The foot progression angle values measured with the pressure platform differ from the inked latex carpet.

Torsional behavior of triangular web profile (TRIWP) steel section by experimental study

A triangular web profile (TriWP) is a modified section where the flanges are connected to a web plate of triangular profile. This study examined the torsional behavior of TriWP steel sections and compared to that of the flat web (FW) steel sections. Three types of specimen sizes were used: 180 mm × 75 mm × 5 mm × 2 mm, 200 mm × 100 mm × 8 mm × 6 mm, and 200 mm × 100 mm × 6 mm × 5 mm. All the specimens were loaded vertically until the maximum load was achieved and then the load was released. For both types of specimens, it was observed that the torsional rotation for bigger size [200 mm × 100 mm × 8mm × 6 mm] were smaller than that of smaller size [180 mm × 75 mm × 5mm × 2 mm] of the specimens. At the maximum torsional loading, the experimental result was compared to the theoretical calculation. The comparison showed that the percentage difference ranged from 1.10% to 16.80%. From the graph of torsional load versus rotational angle, the torsional rotation for all TriWP steel sections were smaller than that of the FW steel section under the same torsional loading i.e., 0.2 kNm and 1 kNm. The range between FWand TriWP were 3.74 to 71.83 at 0.2 kNm while 14.5 to 75.1 at 1.0 kNm. The findings were shown that the TriWP steel sections had better resistance against torsion in comparison to FW steel section.

Humeral torsion and shoulder rotation range of motion parameters in elite swimmers.

Optimal shoulder rotation range of motion (ROM) for swimming is unknown. The primary aim of this study was to examine shoulder rotation ROM in elite swimmers, including the influence of humeral torsion on rotation ROM, in order to establish optimal shoulder rotation parameters for swimming. In addition, we examined the relationship between rotation ROM and shoulder pain. Descriptive cohort study. Seventy elite Australian swimmers provided shoulder pain history data prior to measurement of humeral torsion and passive and active shoulder rotation ROM. Repeated measure analyses of variance were used to investigate within and between participant differences for all variables. Associations between humeral torsion and rotation ROM were investigated using Pearson's correlation coefficient. Multiple regression analysis was utilised to examine the associations between rotation ROM and shoulder pain. Average humeral torsion angles of 27±10° (dominant side) and 31±10° (non-dominant side) were demonstrated in this elite swimming cohort. In general, increased humeral torsion was positively associated with increased internal rotation (IR) and decreased external rotation (ER) ROM. There were significant differences in both IR and ER ROM measured passively and actively (F2,136≥93.1, p<0.001) with passive ROM greater than active ROM (p<0.001) and active IR ROM measured in supine greater than measured in prone (p<0.001). There were no associations between any rotation ROM variables and current or history of shoulder pain (r2=0.058; p=0.46). Humeral torsion angle and passive shoulder IR ROM were similar while passive ER ROM was greater in elite swimmers compared to reported normal population values.

A geometrically exact Kirchhoff beam model including torsion warping

This paper presents a geometrically exact beam model that includes the Kirchhoff constraint (null shear deformation), torsion-related warping and Wagner effects, and aims at capturing the flexural-torsional behaviour of thin-walled beams undergoing large displacements. The parametrization of the cross-section rotation tensor is based on the composition of a torsional rotation and the so-called smallest rotation to the tangent vector of the beam axis, as proposed in Boyer and Primault (2004). The novel aspects of the proposed model are the following: (i) closed-form expressions for the variations of the strain measures are presented and the equilibrium equations and their linearization are completely written in terms of the independent kinematic parameters, (ii) torsion-warping is allowed, as well as Wagner effects, and (iii) arbitrary cross-sections are considered, namely cross-sections where the shear centre and centroid do not coincide. Moreover, several fundamental aspects related to the cross-section rotation parametrization are discussed. The accuracy and the computational efficiency of the finite element implementation of the proposed model is demonstrated in several numerical examples.

A closed-form model for torsion of nanobeams with an enhanced nonlocal formulation

An enhanced model of nonlocal torsion based on the Eringen theory is provided in this paper. The variational formulation is given and then the governing differential equation and boundary conditions of nonlocal nanobeams subjected to torsional loading are consistently derived. No higher-order boundary conditions are required for the enhanced model. It is assumed that the ends of nanobeams are not perfectly restrained thus focusing the attention also on the influence of elastically compliant boundary conditions on the behaviour of nonlocal models. Closed-form solutions are then provided for nanocantilevers and fully clamped nanobeams subject to distributed torsional loads. It is shown that the dimensionless small-scale parameter must fulfil a suitable inequality in order to avoid that a positive distributed torsional load provides a negative torsional rotation. The size-dependent static torsional behaviour of the proposed model in terms of torsional rotations and moments is tested. Contrary to the nonlocal Eringen model, the proposed enhanced model provides the small-scale effect also for nanobeams subjected to uniformly distributed torsional loads. Comparisons with Eringen model, gradient elasticity theory and classical (local) model are provided.