Helical Axis Research Articles

Response of helielectric nematics under an in-plane electric field.

In traditional chiral nematic liquid crystals, the apolar cholesterics, the dielectric effect is the main driving force for responding to an electric field. The emerging polar chiral nematics, dubbed helielectric nematics, are the polar counterparts of the cholesterics. The head-to-tail symmetry breaking of the new matter state enables it to respond sensitively to the polarity of an electric field. Here, we report on the observation of a sequential polar winding/unwinding process of polarization helices under an electric field applied perpendicular to the helical axes, which behaves distinctly from the unwinding of the apolar cholesteric helices. Understanding the helix-unwinding behaviors provides insights for developing switchable devices based on helielectric nematics.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Crystal Structure of Zwitterionic (E)-9-(((3-hydroxyphenyl)iminio)methyl)-1,2,3,5,6,7- Hexahydropyrido[3,2,1-ij]Quinolin-8-Olate

The title compound (1), C19H20N2O2, crystallized with single molecule in the asymmetric unit and is present in the zwitterionic form. The compound was synthesized from the condensation reaction of 8-hydroxyjulolidine-9-carbaldehyde and 3-aminophenol. In solid state compound adopts the keto–amine tautomeric form, with the H atom attached to the N atom, which participates in an intramolecular N—H···O hydrogen bond with an S(6) ring motif. The conformation about the C=N bond is E. The aromatic ring of the julolidine moiety is inclined to the phenol ring by 13.00 (10)°. The fused non-aromatic rings of the julolidine moiety adopts a screw-boat conformations. In the crystal, the molecules are connected by N—H···O and O—H···O hydrogen bonds, with adjacent molecules related by a 21 screw axis, generating– A–B–A–B–zigzag chains extending along [010]. Furthermore, adjacent molecules are linked by pairs of C—H···O interactions, forming a ladder-like structure propagating along the a-axis direction. Density functional theory (DFT) optimized structures at the B3LYP/6–311 G(d,p) level is compared with the experimentally determined molecular structure in the solid state.

Can Magnetic Dipole Transition Moment Be Engineered?

AbstractThe development of chiral compounds with enhanced chiroptical properties is an important challenge to improve device applications. To that end, an optimization of the electric and magnetic dipole transition moments of the molecule is necessary. Nevertheless, the relationship between chemical structure and such quantum mechanical properties is not always clear. That is the case of magnetic dipole transition moment (m) for which no general trends for its optimization have been suggested. In this work we propose a general rationalization for improving the magnitude of m in different families of chiral compounds. Performing a clustering analysis of hundreds of transitions, we have been able to identify a single group in which |m| value is maximized along the helix axis. More interestingly, we have found an accurate linear relationship (up to R2=0.994) between the maximum value of this parameter and the area of the inner cavity of the helix, thus resembling classical behavior of solenoids. This research provides a tool for the rationalized synthesis of compounds with improved chiroptical responses.

Can Magnetic Dipole Transition Moment Be Engineered?

The development of chiral compounds with enhanced chiroptical properties is an important challenge to improve device applications. To that end, an optimization of the electric and magnetic dipole transition moments of the molecule is necessary. Nevertheless, the relationship between chemical structure and such quantum mechanical properties is not always clear. That is the case of magnetic dipole transition moment (m) for which no general trends for its optimization have been suggested. In this work we propose a general rationalization for improving the magnitude of m in different families of chiral compounds. Performing a clustering analysis of hundreds of transitions, we have been able to identify a single group in which |m| value is maximized along the helix axis. More interestingly, we have found an accurate linear relationship (up to R2 =0.994) between the maximum value of this parameter and the area of the inner cavity of the helix, thus resembling classical behavior of solenoids. This research provides a tool for the rationalized synthesis of compounds with improved chiroptical responses.

Growth, crystal structures, and magnetic properties of Fe–As films grown on GaAs (111)B substrates by molecular beam epitaxy

We study epitaxial growth, crystal structures, and magnetic properties of Fe–As compound thin films grown on GaAs (111)B substrates at various values of the As4:Fe flux ratio γ, using molecular beam epitaxy. The samples grown at low As4 flux (γ = 0.3, sample A) show mainly a body-centered-cubic (bcc) crystal structure, exhibiting ferromagnetic properties similar to bcc Fe. Meanwhile, the Fe–As samples grown at medium γ (2.7–4.5, sample group B) comprise regions of Ni2In-type FeAs (a hexagonal crystal with lattice constants of a = 0.399 nm and c = 0.536 nm), which are grown at the bottom and interface with the GaAs buffer layer, and a layer of non-stoichiometric FeAs with a DO3 structure (a = 0.522 nm) formed on the top. The DO3-structure FeAs phase contains partially transformed regions, which are characterized by thin stripes in a scanning transmission electron microscopy image. Furthermore, in the sample grown with high γ = 8.5 (sample C), a hexagonal Fe–As crystal with a large in-plane lattice constant (a = 0.691 nm and c = 0.542 nm) and threefold screw axes are observed. None of these crystal structures of Fe–As compounds has ever been reported. While sample C shows no ferromagnetism, the samples in group B exhibit strong ferromagnetism with high Curie temperature TC above 400 K. These new ferromagnetic Fe–As compounds are promising for spintronic device applications.

Exploration of the Character Representation of DNA Chiral Conformations and Deformations via a Curved Surface Discrete Frenet Frame.

While undergoing structural deformation, DNA experiences changes in the interactions between its internal base pairs, presenting challenges to conventional elastic methods. To address this, we propose the Discrete Critical State (DCS) model in this paper. This model combines surface discrete frame theory with gauge theory and Landau phase transition theory to investigate DNA's structural deformation, phase transitions, and chirality. Notably, the DCS model considers both the internal interactions within DNA and formulates an overall equation using unified physical and geometric parameters. By employing the discrete frame, we derive the evolution of physical quantities along the helical axis of DNA, including geodesic curvature, geodesic torsion, and others. Our findings indicate that B-DNA has a significantly lower free energy density compared to Z-DNA, which is in agreement with experimental observations. This research reveals that the direction of base pairs is primarily governed by the geodesic curve within the helical plane, aligning closely with the orientation of the base pairs. Moreover, the geodesic curve has a profound influence on the arrangement of base pairs at the microscopic level and effectively regulates the configuration and geometry of DNA through macroscopic-level free energy considerations.

All Carbon Helicenes and π‐Extended Helicene Derivatives

AbstractAtomic precise chiral molecules with all‐hydrocarbon backbones, such as helicenes and related π‐extended derivatives, attract critical interests due to their great application potential in many fields (e. g., chiral optical materials, asymmetric catalysis, and molecular machines). Herein, the main development of these molecules in the past decade was summarizes, including enantioselective synthesis of helicenes, helicene with extension along with perpendicular to the helical axis, as well as π‐extended following both directions, namely along with helix axis and perpendicular to the helical axis direction.

Non-crystallographic helices in polymers and close-packed metallic crystals determined by the four-dimensional counterpart of the icosahedron

Non-crystallographic fractional screw axes are inherent to the constructions of n-dimensional crystallography, where 3 < n ≤ 8. This fact allows one to consider experimentally obtained helices as periodic approximants of helices from the four-dimensional {3, 3, 5} polytope and its derivative constructions. For the tetrahedral Coxeter–Boerdijk helix (tetrahelix) with a 30/11 axis from the {3, 3, 5} polytope, approximants with 11/4 and 8/3 axes in three-dimensional Euclidean space {\bb E}^{3} are considered. These determine the structure of rods composed of deformed tetrahedra in close-packed crystals of α-Mn and β-Mn. In the {3, 3, 5} polytope, highlighted here for the first time, is a 40-vertex helix with a 20/9 axis composed of seven-vertex quadruples of tetrahedra (tetrablocks), whose 7/3 approximants determine in a crystal of an α-Mn rod of deformed tetrablocks with the same period as the 11/4 approximant of the tetrahelix. In the spaces of the three-dimensional sphere and {\bb E}^{3}, the parameters of 20/9, 40/9 and 40/11 helices, as well as of their 20- and 40-vertex approximants, are calculated. The parameters of the approximant of the 40/11 helix in {\bb E}^{3} correspond to experimentally determined parameters of the α-helix, which allows us to explain the versatility of the α-helix in proteins by the symmetry of the polytope. The set of fractional axes of all periodic approximants of helices with 30/11, 20/9, 40/9, 40/11 axes, as well as the powers of these axes, are combined into a tetrahedral-polytope class of 50 basic axes. The basic axes as well as composite (defined as a combination of basic ones) fractional axes of this class cover all fractional axes known to us according to literature data for polymers, biopolymers and close-packed metals.

Anterior fusion surgery with overcorrection in the treatment of adolescent idiopathic scoliosis with Lenke 1 AR curve type: how to achieve overcorrection and its effect on postoperative spinal alignment

BackgroundThe efficacy of anterior fusion with overcorrection in the instrumented vertebra for Lenke 1 AR type curves has been reported, but how to achieve overcorrection and how overcorrection affects spinal alignment are unclear. The purpose of this study was to identify the factors that cause overcorrection, and to investigate how overcorrection affects postoperative spinal alignment in the surgical treatment of Lenke 1 AR type curves.MethodsPatients who had anterior surgery for a Lenke type 1 or 2 and lumbar modifier AR (L4 vertebral tilt to the right) type scoliosis and minimum 2-year follow-up were included. The radiographic data were measured at preoperative, postoperative 1 month, and final follow-up. The UIV-LIV Cobb angle was determined as the Cobb angle between the upper instrumented vertebra (UIV) and the lower instrumented vertebra (LIV), and a negative number for this angle was considered overcorrection. The screw angle was determined to be the sum of the angle formed by the screw axis and the lower and upper endplates in the LIV and UIV, respectively. The change (Δ) in the parameters from postoperative to final follow-up was calculated. The relationships between the UIV-LIV Cobb angle and other radiographic parameters were evaluated by linear regression analyses.ResultsFourteen patients met the inclusion criteria. Their median age was 15.5 years, and the median follow-up period was 53.6 months. The median UIV-LIV Cobb angle was –1.4° at postoperative 1 month. The median screw angle was 4.7°, and overcorrection was achieved in 11 (79%) cases at postoperative 1 month. The screw angle (r2 = 0.42, p = 0.012) and Δ FDUV-CSVL (the deviation of the first distal uninstrumented vertebra from the central sacral vertical line, r2 = 0.53, p = 0.003) were significantly correlated with the UIV-LIV Cobb angle.ConclusionsScrew placement in the UIV and LIV not parallel to the endplate, but angled, was an effective method to facilitate overcorrection in the instrumented vertebrae. The results of the present study suggest that overcorrection could bring spontaneous improvement of coronal balance below the instrumented segment during the postoperative period.

Direct‐Ink‐Written Cholesteric Liquid Crystal Elastomer with Programmable Mechanochromic Response

AbstractCholesteric liquid crystal elastomers (CLCEs) are unique anisotropic rubbers that can change their structural color in response to various stimuli such as heat, chemicals, electric fields, and mechanical stress. Methods such as anisotropic deswelling and surface alignment have been adopted to prepare CLCEs; however, they have limitations in creating spatially controlled CLCE geometries. In this work, a direct ink writing (DIW)‐based 3D‐printable CLCE that can be prepared by extruding viscous CLC ink is developed through a 3D printer nozzle, followed by photopolymerization. Interestingly, the helical axis is inclined to the printing direction by ≈32° due to a combination of the shear‐induced alignment causes during extrusion and the elongational force generated during deposition onto the substrate. This unusual helical axis distortion leads to both blue and red shifts of the reflection color depending on the direction of observation relative to the printing axis. Notably, the printed CLCE exhibits anisotropic mechanochromism upon stretching, because of the stretching‐direction‐dependent variations in the slant angle of the helical axis. This anisotropic mechanochromism can be harnessed to develop a unique CLCE‐based strain sensor displaying intricate color patterns upon stretching, with significant application potential in encryption, anticounterfeiting, and structural health monitoring.

Herringbone Helical Foldamers from Aromatic Ether Derived ϵ-Amino Acid Peptides.

Oligomers based on an aromatic ether derived ϵ-amino acid peptides folded into herringbone helical structures, induced by successive NH-O-NH & O-NH-O bifurcated hydrogen bonding interactions and reinforced by π-π stacking between aryls from adjacent layers. The diaryl ether bonds -O- worked both as structural units to provide turn motifs for changing the amplitude of the slope along the axis of helix for herringbone formation, and also as acceptors for hydrogen bonding. Attachment of a single chiral carbon to the C-termini of the peptides induced excess of single-handed screw sense and amplification through the chain propagation as exemplified by chain length dependent circular dichroism (CD) investigations.

Ankle and subtalar joint axes of rotation and center of rotation during walking and running in healthy individuals measured using dynamic biplane radiography

The goal of this study was to determine how foot type and activity level affect ankle and hindfoot motion. Dynamic biplane radiography and a validated volumetric registration process was used to measure ankle and hindfoot motion of 20 healthy adults during walking and running. The helical axes of motion (HAM) during stance were calculated at the tibiotalar and subtalar joints. The intersection of each HAM and the rotation plane of interest defined the tibiotalar and subtalar centers of rotation (COR). Correlations between foot type and hindfoot kinematics were calculated using Pearson’s correlations. The effect of activity, phase of gait, and dominant vs. non-dominant limb on HAM and COR were evaluated using linear mixed effects models. Activity and phase of gait influenced the superior location of the tibiotalar (p < 0.041) and subtalar (p < 0.044) CORs. Activity and gait phase affected tibiotalar (p < 0.049) and subtalar (p < 0.044) HAM direction during gait. Both HAM orientation and COR location changed with activity and phase of gait. These ankle and hindfoot kinematics have implications for total ankle replacement design and musculoskeletal models that estimate force and moment generating capabilities of muscles.

Complete 3D Kinematics Parameters of the Temporo-Mandibular Joints Using in Vivo Data Fusion

ObjectivesThe temporo-mandibular joint (TMJ) has implications in vital functions and its disorder prevalence is between 5% and 12%. The mandible motions rely on two joints where mandibular condyles are generally asymmetric and highly individual. They rotate during jaw opening and closing and translate vertically and anteroposteriorly. Quantitative motion analysis tools are of interest to better understand normal and abnormal TMJ behavior. Previous studies have reported the asymmetrical behavior of the mandible compared to the skull as well as the synchronism of rotation and translation during its motions. But none of them has developed an experimental protocol using in vivo motion data fused with a tridimensional (3D) model. Therefore, we aim to provide the detailed kinematic parameters of the mandible compared to the skull, of the 2 condyles compared to their sockets and the instantaneous helicoidal axis (IHA) calculation through a clearly described new technology: in vivo data motion fused with virtual palpation on 3D models. We also compare the accuracy and the consistency of our results with the existing literature. Material and methodsFive healthy subjects fitted with a tailor-made dental and head clusters performed mouth opening/closing, diduction and chewing motions. 15 anatomical landmarks (ALs) were palpated on their skull and their mandible. The trajectory of the markers and ALs was recorded by opto-electronic cameras. 3D models created from magnetic resonance imaging (MRI) from the 5 subjects were processed through a segmentation procedure and imported into a musculo-skeletal data processing software. Virtual palpation was used to locate specific ALs and to build coordinate systems following the ISB recommendations. The ALs coordinates, the motion files and the morphological model were fused. Motion cycles were normalized from 1 to 100% of rotations and translations duration in coordinate systems, instantaneous helical axis (IHA) parameters were computed for the 3 motions. ResultsMedian RMSE between manually and virtually palpated ALs was 8,0 mm.During opening motion, rotation around the Z-axis (median 24,9°), translations along the X-axis and the Y-axis (median 9,7 mm and 6,3 mm respectively) were happening all at once. The IHA was obliquely orientated.During diduction motion, rotations around the Y-axis and the X-axis (median 10,7° and 3.3° respectively), translation on the Z-axis is (median −9.4 mm) occurred simultaneously. The IHA orientation was oblique and changed accordingly to the diduction side.During chewing motion, median rotation around the Z-axis was −2.2° and median translation on the Y-axis −1.0 mm. The IHA pathway high asymmetry coincided with typical movements of working and balancing condyles. ConclusionComplete 3D kinematics parameters of the TMJs, corresponding to the ISB recommendations, have been extracted with our methodology. Our values matched previous studies if available and the palpation RMSE was within the bounds of precedent experimental protocol. It is therefore efficient to study in vivo motion.Motion data have been registered in an open access data repository, allowing other researchers to exploit them and develop their own TMJ model.

Increased subtalar rotational motion in patients with symptomatic ankle instability under load and stress conditions.

Differentiating subtalar and ankle instability in the clinical setting is challenging. This study aims to analyze the rotational laxity of the subtalar joint bilaterally in patients with asymptomatic and symptomatic ankle instability under simulated load and stress-induced position of the subtalar joint. A case-control study was conducted using an adjustable load device (ALD). Patients with chronic ankle instability and healthy volunteers were included. Each subject underwent a CT scan under mechanical stress and simulated weight-bearing conditions, maintaining maximum eversion and inversion hindfoot positions. The images were obtained in a single model, allowing calculations of the motion vector as well as the helical axis. The helical axis was defined by a rotation angle and a translation distance. A total of 72 feet were included in the study. Thirty-one patients with unilateral symptoms and five healthy controls were selected, defining two groups: symptomatic (n = 31) and asymptomatic (n = 41). An absolute difference of 4.6º (95%CI 2-11.1) rotation angle was found on the helical axis of the symptomatic vs. asymptomatic group (p = 0.001). No significant differences were detected in the translation distance (n.s.) between the groups. Additionally, a significant positive correlation was found between the rotation angle and translation distance through the helical axis in the asymptomatic group (r = 0.397, p = 0.027). Patients with chronic ankle instability suspected of having subtalar joint instability showed a wider subtalar range of laxity in terms of rotation about the helical axis. Furthermore, differences in kinematics between symptomatic and asymptomatic hindfeet was demonstrated when both feet were compared. III.

Research on load distributions for ball screw feed system with assembly errors

This paper proposes a load distribution model for the ball screw feed system with the assembly errors of the guide rails, which is used to predict the variation law of the load distributions for the ball screws and carriage-guide rail systems. Firstly, under the action of the contact loads of the ball screws, the bending deformation of the screw axis corresponding to each ball is derived. Secondly, a static model of the machine tool bearing system with the assembly errors is established. Then, the load distribution model of the ball screw feed system is proposed based on the load balance and deformation compatibility equation, and the solution process of the proposed model including judging the ball-raceway contact state is given. In addition, the results are compared with those of the existing models to demonstrate the validity of the proposed model. Finally, the relation between the curve shape of the load distribution and the bending of the screw shaft axis is explored, and the variation law of the load distributions for the feed system under the effects of the axial, radial loads, and assembly errors is discussed.

Exceptional points and lines and Dirac points and lines in magnetoactive cholesteric liquid crystals

We investigated the properties of cholesteric liquid crystals (CLCs) being in external static magnetic field directed along the helix axis. We have shown that in the case of the wavelength dependence of magneto-optic activity parameter, and in the presence of absorption new features appear in the optics of CLCs. We have shown that in this case new photonic band gaps (PBGs) appear. This new PBG is sensitive to the polarization of the incident light. But if the chirality sign of the polarization of the incident diffracting light for the basic PBG (which exist also at the absence of external magnetic field) is determined only by the chirality sign of the CLC helix, then for the second one it is determined by the external magnetic field direction (i.e., on whether the directions of the external magnetic field and the incident light are parallel, or they are antiparallel). We have shown that in this case besides Dirac points there appear also Dirac lines as well as exceptional points and exceptional lines. And moreover, near some of these points and lines the narrow bands or wide bands of magnetically induced transparency, and magnetically induced absorption appear, and near the others a wide coherent perfect absorption band appears that is insensitive to incident light polarization. And finally at some wavelength the same reflection, transmission and absorption takes place for any polarization of incident light, although it is not Dirac point nor exceptional point. This system can apply as tunable narrow-band or broad-band filters and mirrors, a highly tunable broad/narrow-band coherent perfect absorber, transmitter, ideal optical diode, and other devices.

Hyper Thermostability and Liquid-Crystal-Like Properties of Designed α-Helical Peptide Nanofibers.

Structural and thermodynamic transitions of artificially designed α-helical nanofibers were investigated using eight peptide variants, including four peptides with amide-modified carboxyl termini (CB peptides) and four unmodified peptides (CF peptides). Temperature-dependent circular dichroism spectroscopy and differential scanning calorimetry showed that CB peptides exhibit thermostability up to 50 °C higher than CF peptides. As a result, one of the denaturation temperatures approached nearly 130 °C, which is exceptionally high for a biomacromolecule. Thermodynamic analysis and microscopy observations also showed that CB peptides undergo a thermal transition similar to the phase transition in liquid crystals. In addition, one of the peptides showed a sharp and highly cooperative transition with a small enthalpy change at around 25 °C, which was ascribed to a giga-bundle burst of the molecular assembly. These macroscopic changes in the thermostability and crystallinity of CB peptides may be attributed to an increased amphiphilicity of the molecule in the direction of the helix axis, originating from the microscopic modification of the carboxyl-terminus.

A structural study on chiral poly(methacrylic acid) polymerized with chitosan templates

Poly(methacrylic acid) (PMAA) with a two-fold helical axis was synthesized from sodium methacrylate in the presence of chitosans. The polymer chain formed a two-fold helix with a syndiotactic conformation, in which the sequence of the bond rotation was (TTGG)2 (T- trans, G- gauche). The PMAA was optically active to produce a negative Cotton effect in the UV region. The crystalline powder of PMAA was found to form an orthorhombic lattice with a = 7.94, b = 6.51, and c = 7.99 Å (identical period), of which the space group was determined to be P2221. The astonishing crystallinity of this compound comes from template polymerization with a chiral strand of chitosan. Electronic structures of stereoregular PMAA isomers are also discussed from the perspective of band theory and spectroscopic data. The helical sense was determined to be left-handed by circular dichroism and quantum-chemical calculations, which followed the helical rule for C2 molecules.

Comparison of finite helical axis of the knee joint before and after bi-cruciate-preserving knee arthroplasty

BackgroundDifference in the finite helical axis of the knee joints before and after anterior cruciate ligament-preserving knee arthroplasties such as unicompartmental knee arthroplasty and bi-cruciate-retaining total knee arthroplasty remains unknown. This study compared the knee finite helical axes before and after bi-cruciate-preserving knee arthroplasty. MethodsPatients undergoing medial unicompartmental knee arthroplasty and bi-cruciate-retaining total knee arthroplasty were included. Under fluoroscopy, participants performed a deep knee bend before and after surgery. A two/three-dimensional registration technique was employed to measure tibiofemoral kinematics. Femoral finite helical axis was calculated in a flexion range of 0–120° using 30° windows (early-, mid-, late-, and deep-flexion phases). FindingsIn unicompartmental knee arthroplasty, the preoperative knee vertical angle was larger than the postoperative vertical angle in mid- and deep-flexion phases. The postoperative knee vertical angle was smaller in unicompartmental knee arthroplasty than in bi-cruciate-retaining total knee arthroplasty. In unicompartmental knee arthroplasty, the preoperative horizontal angle was smaller than the postoperative horizontal angle in the early-flexion phase. However, in bi-cruciate-retaining total knee arthroplasty, the preoperative horizontal angle was larger than the postoperative horizontal angle in mid- and deep-flexion phases. The horizontal angle was smaller before unicompartmental knee arthroplasty than that before bi-cruciate-retaining total knee arthroplasty in early-, mid-, and deep-flexion phases. However, the vertical angle was larger after unicompartmental knee arthroplasty than that after bi-cruciate-retaining total knee arthroplasty in the early-flexion phase. InterpretationThe knee finite helical axes before and after unicompartmental knee arthroplasty differed from those before and after bi-cruciate-retaining total knee arthroplasty.