Showing papers on "Transverse plane published in 2014"
TL;DR: The Vertex Locator (VELO) as mentioned in this paper is a silicon microstrip detector that surrounds the proton-proton interaction region in the LHCb experiment, and the performance of the detector during the first years of its physics operation is reviewed.
Abstract: The Vertex Locator (VELO) is a silicon microstrip detector that surrounds the proton-proton interaction region in the LHCb experiment. The performance of the detector during the first years of its physics operation is reviewed. The system is operated in vacuum, uses a bi-phase CO2 cooling system, and the sensors are moved to 7 mm from the LHC beam for physics data taking. The performance and stability of these characteristic features of the detector are described, and details of the material budget are given. The calibration of the timing and the data processing algorithms that are implemented in FPGAs are described. The system performance is fully characterised. The sensors have a signal to noise ratio of approximately 20 and a best hit resolution of 4 microns is achieved at the optimal track angle. The typical detector occupancy for minimum bias events in standard operating conditions in 2011 is around 0.5%, and the detector has less than 1% of faulty strips. The proximity of the detector to the beam means that the inner regions of the n+-on-n sensors have undergone space-charge sign inversion due to radiation damage. The VELO performance parameters that drive the experiment's physics sensitivity are also given. The track finding efficiency of the VELO is typically above 98% and the modules have been aligned to a precision of 1 micron for translations in the plane transverse to the beam. A primary vertex resolution of 13 microns in the transverse plane and 71 microns along the beam axis is achieved for vertices with 25 tracks. An impact parameter resolution of less than 35 microns is achieved for particles with transverse momentum greater than 1 GeV/c.
241 citations
TL;DR: In this article, a narrow-band transmission filter is demonstrated near normal incidence that operates through relaxation of supported-mode selection rules and is explained in the context of group theory, where the transverse magnetic and transverse electric dispersion relations of a dielectric grating in the subwavelength and near-wavelength region using finite element modal analysis are determined.
Abstract: A narrow-band transmission filter is demonstrated near normal incidence that operates through relaxation of supported-mode selection rules and is explained in the context of group theory. We calculated the transverse magnetic and transverse electric dispersion relations of a dielectric grating in the subwavelength and near-wavelength region using finite element modal analysis and determine the modes' corresponding irreducible representations. Coupling to select transverse magnetic modes at normal incidence is optimized to yield broadband high reflectance that acts as the background for the transmission filter. While some modes couple at normal incidence, others are shown to remain inaccessible due to symmetry mismatch. Away from normal incidence, the reduced symmetry relaxes the selection rules, enabling weak coupling between the incident field and these symmetry-protected modes. This weak coupling produces narrow transmission bands within the opaque background. Furthermore, by choosing the plane of incidence to include or exclude the grating periodicity, we show that orthogonal mode sets can independently be selected to couple to the incident light, yielding separate transmission bands. This spectral filtering is experimentally demonstrated with a suspended silicon grating in the infrared spectrum ($7--14\ensuremath{\mu}\mathrm{m}$), which agrees well with simulated transmittance spectra and modal analysis.
184 citations
TL;DR: In this article, the size-dependent motion characteristics of a microbeam are investigated numerically, with special consideration to one-to-one internal resonances between the in-plane and out-of-plane transverse modes.
Abstract: The three-dimensional nonlinear size-dependent motion characteristics of a microbeam are investigated numerically, with special consideration to one-to-one internal resonances between the in-plane and out-of-plane transverse modes. All of the in-plane and out-of-plane displacements and inertia are taken into account and Hamilton’s principle, in conjunction with the modified couple stress theory, is employed to obtain the nonlinear partial differential equations governing the motions of the system in the in-plane and out-of-plane directions. The discretization procedure is carried out by applying the Galerkin technique to the partial differential equations of motion, yielding a set of nonlinear ordinary differential equations. A linear analysis is performed upon this set of equations so as to obtain the size-dependent natural frequencies of the system. The nonlinear analysis of the discretized equations of motion is carried out by employing the pseudo-arclength continuation technique, resulting in the resonant responses of the system. It is shown that, due to the presence of one-to-one internal resonances between the in-plane and out-of-plane transverse modes, an in-plane excitation can give rise to an out-of-plane displacement; the internal resonances also cause the occurrence of extra solution branches and new bifurcation points.
173 citations
TL;DR: Using a multiphase transport model (AMPT), the elliptic v_{2} and triangular v_{3} Fourier coefficients of the two-particle azimuthal correlation function in proton-nucleus (p-Pb) and peripheral nucleus-n nucleus (Pb-pb) collisions are calculated and predicted.
Abstract: Using a multiphase transport model (AMPT) we calculate the elliptic v_{2} and triangular v_{3} Fourier coefficients of the two-particle azimuthal correlation function in proton-nucleus (p-Pb) and peripheral nucleus-nucleus (Pb-Pb) collisions. Our results for v_{3} are in a good agreement with the CMS data collected at the Large Hadron Collider. The v_{2} coefficient is very well described in p-Pb collisions and is underestimated for higher transverse momenta in Pb-Pb interactions. The characteristic mass ordering of v_{2} in p-Pb is reproduced, whereas for v_{3}, this effect is not observed. We further predict the pseudorapidity dependence of v_{2} and v_{3} in p-Pb and observe that both are increasing when going from a proton side to a Pb-nucleus side. Predictions for the higher-order Fourier coefficients, v_{4} and v_{5}, in p-Pb are also presented.
151 citations
TL;DR: In this article, the performance of the nonlinear energy sink (NES) that composed of a small mass and essentially nonlinear coupling stiffness with a linear structure is considerably enhanced by including the negative linear and nonlinear stiffness components.
Abstract: The performance of the nonlinear energy sink (NES) that composed of a small mass and essentially nonlinear coupling stiffness with a linear structure is considerably enhanced here by including the negative linear and nonlinear coupling stiffness components. These negative linear and nonlinear stiffness components in the NES are realized here through the geometric nonlinearity of the transverse linear springs. By considering these components in the NES, very intersecting results for passive targeted energy transfer (TET) are obtained. The performance of this modified NES is found here to be much improved than that of all existing NESs studied up to date in the literature. Moreover, nearly 99 % of the input shock energy induced by impulse into the linear structures considered here has been found to be rapidly transferred and locally dissipated by the modified NES. In addition, this modified NES maintains its high performance of shock mitigation in a broadband fashion of the input initial energies where it keeps its high performance even for sever input energies. This is found to be achieved by an immediate cascade of several resonance captures at low- and high- nonlinear normal modes frequencies. The findings obtained here by including the negative linear and nonlinear stiffness components are expected to significantly enrich the application of these stiffness components in the TET field of such nonlinear oscillators.
134 citations
TL;DR: In this article, the authors explored the approach towards transverse uniformity of concentration distribution in the laminar flow of a solvent in a straight pipe and showed that the transverse variation of the concentration distribution remains near one-half of the centroid concentration of the cloud.
Abstract: Associated with Taylor’s classical analysis of scalar solute dispersion in the laminar flow of a solvent in a straight pipe, this work explores the approach towards transverse uniformity of concentration distribution. Mei’s homogenization technique is extended to find solutions for the concentration transport. Chatwin’s result for the approach to longitudinal normality is recovered in terms of the mean concentration over the cross-section. The asymmetrical structure of the concentration cloud and the transverse variation of the concentration distribution are concretely illustrated for the initial stage. The rate of approach to uniformity is shown to be much slower than that to normality. When the longitudinal normality of mean concentration is well established, the maximum transverse concentration difference remains near one-half of the centroid concentration of the cloud. A time scale up to 10R 2 =D (R is the radius of the pipe and D is the molecular diffusivity) is suggested to characterize the transition to transverse uniformity, in contrast to the time scale of 0:1R 2 =D estimated by Taylor for the initial stage of dispersion, and that of 1:0R 2 =D by Chatwin for longitudinal normality.
102 citations
TL;DR: In this paper, a nonlinear force-free field (NLFFF) model was proposed to model the coronal magnetic field of active region (AR) 11158 as a non-linear force free field.
Abstract: The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the non-potential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of active region (AR) 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around the time of major flare activity on 2011 February 15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also being subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about 1 × 1032 erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption, the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by ≈0.9 full turns about its axis.
77 citations
TL;DR: In this article, it was shown that the displacement field of the kink wave is a sum of its transverse and rotational components, both for a flux tube with a discontinuous density profile at its boundary, and one with a more realistic density continuum between the internal and external plasma.
Abstract: Magnetohydrodynamic (MHD) kink waves have now been observed to be ubiquitous throughout the solar atmosphere. With modern instruments, they have now been detected in the chromosphere, interface region, and corona. The key purpose of this paper is to show that kink waves do not only involve purely transverse motions of solar magnetic flux tubes, but the velocity field is a spatially and temporally varying sum of both transverse and rotational motion. Taking this fact into account is particularly important for the accurate interpretation of varying Doppler velocity profiles across oscillating structures such as spicules. It has now been shown that, as well as bulk transverse motions, spicules have omnipresent rotational motions. Here we emphasize that caution should be used before interpreting the particular MHD wave mode/s responsible for these rotational motions. The rotational motions are not necessarily signatures of the classic axisymmetric torsional Alfven wave alone, because kink motion itself can also contribute substantially to varying Doppler velocity profiles observed across these structures. In this paper, the displacement field of the kink wave is demonstrated to be a sum of its transverse and rotational components, both for a flux tube with a discontinuous density profile at its boundary, and one with a more realistic density continuum between the internal and external plasma. Furthermore, the Doppler velocity profile of the kink wave is forward modeled to demonstrate that, depending on the line of sight, it can either be quite distinct or very similar to that expected from a torsional Alfven wave.
74 citations
TL;DR: In this article, the flow of a liquid film sheared by high velocity gas stream in a horizontal rectangular duct was investigated using a high-speed laser-induced fluorescence technique Measurements of local film thickness were resolved in both longitudinal and transverse coordinates with high spatial and temporal resolution.
69 citations
21 Jan 2014
TL;DR: Inter-subject variance tended to be high in both models for knee abduction/adduction, but particularly so for plug-in gait, suggesting that a cluster-based model may reduce the variability.
Abstract: Gait analysis is an important clinical tool. A variety of models are used for gait analysis, each yielding different results. Errors in model outputs can occur due to inaccurate marker placement and skin motion artefacts, which may be reduced using a cluster-based model. We aimed to compare a custom-made cluster model (ClusBB) with Vicon’s plug-in gait. A total of 21 healthy subjects wore marker sets for the ClusBB and plug-in gait models simultaneously while walking on a 6-m walkway. Marker and force plate data were captured synchronously and joint angles/moments were calculated using both models. There was good correlation between the models (coefficient of multiple correlations > 0.65) and good intra-session correlation for both models (coefficient of multiple correlations > 0.80). Inter-subject variability was high, ranging from 15° to 40° in the sagittal plane and 11° to 52° in the coronal and transverse planes. Intra-subject variability was small for both ClusBB and plug-in gait models. Inter-subjec...
67 citations
TL;DR: The performance of strain imaging using plane wave compounding is investigated using simulations of an artery with a vulnerable plaque and experimental data of a two-layered vessel phantom, and the results show that planeWave compounding outperforms 0° focused strain imaging.
TL;DR: In this article, the authors used in-situ SEM micromechanical testing and acoustic damage detection techniques to determine transverse microcrack initiation loads, transverse crack density, and local micro-delamination lengths for a number of cross-ply laminates.
TL;DR: In this article, the authors present a methodology to detect transverse cracks by optical means, which does not interfere with the tensile test, and show that the in situ strength depends on the thickness of the ply and the orientation of the adjacent layers.
Abstract: Failure of a ply due to transverse loading is one of the mechanisms that was taken into account in physically-based failure criteria, used in composites design. However, experimental data are scarce and the measurement techniques used in the past are time consuming and involve a lot of specimen handling during testing. While some physical information is currently well consolidated (such as the dependence of the strength on ply thickness, or in situ strength), there still remain relevant open questions. This work presents a methodology, which does not interfere with the tensile test, to detect transverse cracks by optical means. Four different configurations of CFRP are considered. The results show that the in situ strength depends on the thickness of the ply and the orientation of the adjacent layers. In the case of thick transverse plies, the strength is controlled by full-width transverse cracks whereas, in thin plies cracking parallel to the specimen’s mid-plane occurs before transverse matrix cracking.
TL;DR: In this article, high-speed shadowgraph images show that the mechanism of core breakup and atomization differs between off-resonance and first transverse excitation conditions, with a core length reduction of up to 70% for conditions approaching those of naturally occurring high frequency combustion instabilities.
Abstract: Testing has been conducted with the BKH rocket combustor at the European Research and Technology Test Facility P8 for cryogenic rocket engines at DLR Lampoldshausen. BKH has multiple shear coaxial injectors and an exhaust modulation system for forcing excitation of acoustic resonances in the combustion chamber. Optical access windows allow the application of parallel high-speed shadowgraph and flame emission imaging of the near-injector region. This paper reports measurements of the intact liquid oxygen core during forced excitation of the first transverse acoustic mode. High-speed shadowgraph images show that the mechanism of core breakup and atomization differs between off-resonance and first transverse excitation conditions. The core length is found to decrease with increasing amplitude of acoustic pressure, or equivalently with transverse acoustic velocity, with a core length reduction of up to 70% for conditions approaching those of naturally occurring high frequency combustion instabilities. This de...
TL;DR: It is shown how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection, resolving the long-standing puzzle of why such beam shifts transverse to the incident plane tend to be an order of magnitude smaller than the related Goos-Hänchen shifts.
Abstract: We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane (Imbert-Fedorov shifts) tend to be an order of magnitude smaller than the related Goos-Hanchen shifts in the longitudinal direction, which are largest close to critical incidence. We demonstrate that with the proper initial polarization the transverse displacements can be equally large, which we confirm experimentally near Brewster incidence. In contrast to the established understanding, these polarizations are elliptical and angle dependent. We explain the magnitude of the Imbert-Fedorov shift by an analogous change of the symmetry properties for the reflection operators as compared to the Goos-Hanchen shift.
TL;DR: In this article, the influence of temperature and moisture on the hygrothermal behavior of laminated composite plates resting on elastic foundations is investigated using a refined plate theory, which enables the trial and testing of different through-the-thickness transverse shear-deformation distributions.
TL;DR: This work shows that for collisions of electrons with a high-intensity laser, discrete photon emissions introduce a transverse beam spread that is distinct from that due to classical (or beam shape) effects, and proposes it as a measurable signature of strong-field quantum electrodynamics.
Abstract: We show that for collisions of electrons with a high-intensity laser, discrete photon emissions introduce a transverse beam spread that is distinct from that due to classical (or beam shape) effects. Via numerical simulations, we show that this quantum induced transverse momentum gain of the electron is manifest in collisions with a realistic laser pulse of intensity within reach of current technology, and we propose it as a measurable signature of strong-field quantum electrodynamics.
TL;DR: In this paper, the effects of the magnetic field, electric current, pre-tension force, frequency of the applied load, surface and size effects on the maximum transverse displacements are discussed.
Abstract: Forced vibrations of current-carrying nanowires in the presence of a longitudinal magnetic field are of interest. By considering the surface energy and size effects, the coupled equations of motion describing transverse motions of the nanostructure are derived. By employing Galerkin and Newmark- β approaches, the deflections of the nanowire subjected to transverse dynamic loads are evaluated. The effects of the magnetic field, electric current, pre-tension force, frequency of the applied load, surface and size effects on the maximum transverse displacements are discussed. The obtained results display that for the frequency of the applied load lower than the nanowire׳s fundamental frequency, by increasing the magnetic field or electric current, the maximum transverse displacements would increase. However, for exciting frequencies greater than that of the nanowire, maximum transverse displacements would increase or decrease with the magnetic field strength or electric current. Additionally, the pre-tension force results in decreasing of the maximum transverse displacements. Such a reduction is more apparent for higher values of the magnetic field strength and electric current. The present study would be useful in the design of the micro- and nano-electro-mechanical systems expected to be one of the most wanted technologies in the near future.
TL;DR: In this paper, the formation of fast wave trains in a super-radially expanding coronal hole modelled by a magnetic funnel with a field-aligned density profile was investigated.
Abstract: Context. Rapidly propagating coronal EUV disturbances recently discovered in the solar corona are interpreted in terms of guided fast magnetoacoustic waves. Fast magnetoacoustic waves experience geometric dispersion in waveguides, which causes localised, impulsive perturbations to develop into quasi-periodic wave trains.
Aims. We consider the formation of fast wave trains in a super-radially expanding coronal hole modelled by a magnetic funnel with a field-aligned density profile that is rarefied in comparison to the surrounding plasma. This kind of structure is typical of coronal holes, and it forms a fast magnetoacoustic anti-waveguide as a local maximum in the Alfven speed.
Methods. We performed 2D MHD numerical simulations for impulsively generated perturbations to the system. Both sausage and kink perturbations are considered and the role of the density contrast ratio investigated.
Results. The anti-waveguide funnel geometry refracts wave energy away from the structure. However, in this geometry the quasi-periodic fast wave trains are found to appear, too, and so can be associated with the observed rapidly propagating coronal EUV disturbances. The wave trains propagate along the external edge of the coronal hole. The fast wave trains generated in coronal holes exhibit less dispersive evolution than in the case of a dense waveguide.
Conclusions. We conclude that an impulsive energy release localised in a coronal plasma inhomogeneity develops into a fast wave train for both kink and sausage disturbances and for both waveguide and anti-waveguide transverse plasma profiles.
TL;DR: In this paper, a finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study.
TL;DR: In this article, a rectangular combustor with acoustic forcing was used to study flame-acoustic interaction under injection conditions that are representative of liquid propellant rocket engines, and hot-fire tests using liquid oxygen and gaseous hydrogen were conducted at pressures of 40 and 60 bar, respectively.
Abstract: A rectangular combustor with acoustic forcing was used to study flame–acoustic interaction under injection conditions that are representative of liquid propellant rocket engines. Hot-fire tests using liquid oxygen and gaseous hydrogen were conducted at pressures of 40 and 60 bar, which are sub- and supercritical conditions, respectively, for oxygen. Examined samples of hydroxyl-radical emission imaging, collected using a high-speed camera during periods of forced acoustic resonance, showed significant response in the multi-injection element flame. Fluctuating acoustic pressure causes in-phase fluctuation of the emission intensity, producing response factor values of around 0.8. Transverse acoustic velocity causes shortening of the flame, concentrating heat release near the injection plane. The flame is also convectively displaced with transverse acoustic velocity, a process believed by many to be responsible for driving transverse mode high-frequency combustion instabilities. The analysis in this work was...
TL;DR: In this article, the biaxial strain induced phonon dispersion curves of monolayer boron pnictides (BX, X, P, As, and Sb) have been investigated.
Abstract: In the frame work of density functional theory, the biaxial strain induced phonon dispersion curves of monolayer boron pnictides (BX, X = N, P, As, and Sb) have been investigated. The electron-ion interactions have been modelled using ultrasoft pseudopotentials while exchange-correlation energies have been approximated by the method of local density approximation in the parameterization of Perdew-Zunger. The longitudinal and transverse acoustic phonon modes of boron pnictide sheets show linear dependency on wave vector k→ while out of plane mode varies as k2. The in-plane longitudinal and out of plane transverse optical modes in boron nitride displaying significant dispersion similar to graphene. We have analyzed the biaxial strain dependent behaviour of out of plane acoustic phonon mode which is linked to ripple for four BX sheets using a model equation with shell elasticity theory. The strain induces the hardening of this mode with tendency to become more linear with increase in strain percentage. The s...
TL;DR: A novel method that uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced and can be used with other types of motion.
Abstract: The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge because detection is usually done by means of an interferometric setup, which only provides an absolute value of the frequency shift. In this Letter, we present a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating microparticles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.
TL;DR: In this article, the beam dynamics in transverse deflecting structures, operating in streaking mode, are discussed concentrating on slightly nonrelativistic particle energies, and an optimized cavity design which combines minimal aberrations with a high rf efficiency is proposed.
Abstract: The beam dynamics in transverse deflecting structures, operating in streaking mode, is discussed concentrating on slightly nonrelativistic particle energies. Transverse offsets of the average trajectory, bunch lengthening, and defocusing as well as emittance growth due to nonlinearities of the cavity field are considered. The analysis of the deflecting field reveals the origin of nonlinearities and leads to proposals for their suppression. An optimized cavity design which combines minimal aberrations with a high rf efficiency is proposed.
TL;DR: In this paper, the rotational and translational velocities of particles moving in helical motion under a Laguerre-Gaussian mode illumination were determined by switching between two modes.
Abstract: We measure the rotational and translational velocity components of particles moving in helical motion under a Laguerre-Gaussian mode illumination. The moving particle reflects light that acquires an additional frequency shift proportional to the velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.
TL;DR: In this paper, the authors investigated how the shape and the magnitude of the transverse profile of the loss-gain distribution affect soliton stability and found the stability region for nonlinear wave packets via a linear stability analysis.
Abstract: Existence, stability, and dynamics of $\mathcal{PT}$-symmetric fundamental bright solitons supported by localized super-Gaussian potentials in a focusing Kerr medium are investigated theoretically. We address how the shape and the magnitude of the transverse profile of the loss-gain distribution affect soliton stability. We find the stability region for nonlinear wave packets via a linear stability analysis, interpreting the insurgence of instability as an unbalanced flow of energy on the transverse plane. We confirm our results via numerical simulations, showing that an unstable soliton first undergoes longitudinal oscillations in propagation due to the interference between the soliton and the exponentially growing perturbation modes, eventually forming a highly localized single peak in the gain region.
TL;DR: In this paper, a model for free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field is developed to investigate the problem on the basis of the surface elasticity theory, and analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained.
TL;DR: In this article, it was shown that axial asymmetrical valence quark distributions in the transverse plane of a transversely polarized proton can give rise to a spin-dependent odderon.
Abstract: We show that in the McLerran-Venugopalan model an axial asymmetrical valence quark distributions in the transverse plane of a transversely polarized proton can give rise to a spin-dependent odderon. Such polarized odderon is responsible for the transverse single spin asymmetries for jet production in the backward region of pp collisions and open charm production in the semi-inclusive deep inelastic scattering process.
TL;DR: The condyles are approximately spherical except for the inferior facet medially, which has a larger radius in the sagittal plane and has implications for understanding anterior knee pain and for the design of knee replacements.
Abstract: We scanned 25 left knees in healthy human subjects
using MRI. Multiplanar reconstruction software was used to take
measurements of the inferior and posterior facets of the femoral
condyles and the trochlea. A ‘basic circle’ can be defined which, in the sagittal plane,
fits the posterior and inferior facets of the lateral condyle, the
posterior facet of the medial condyle and the floor of the groove
of the trochlea. It also approximately fits both condyles in the
coronal plane (inferior facets) and the axial plane (posterior facets).
The circle fitting the inferior facet of the medial condyle in the
sagittal plane was consistently 35% larger than the other circles
and was termed the ‘medial inferior circle’. There were strong correlations
between the radii of the circles, the relative positions of the
centres of the condyles, the width of the condyles, the total knee
width and skeletal measurements including height. There was poor
correlation between the radii of the circles and the position of
the trochlea relative to the condyles. In summary, the condyles are approximately spherical except for
the inferior facet medially, which has a larger radius in the sagittal
plane. The size and position of the condyles are consistent and
change with the size of the person. However, the position of the
trochlea is variable even though its radius is similar to that of
the condyles. This information has implications for understanding
anterior knee pain and for the design of knee replacements. Cite this article: Bone Joint J 2014;96-B:1623–30.