Oblique Component Research Articles

Medial patellofemoral ligament MRI abnormalities in the setting of MCL injuries: are they clinically relevant?

To assess MRI abnormalities of the medial patellofemoral ligament (MPFL) in patients with clinically and MRI-proven superficial medial collateral ligament (sMCL) injuries and determine the clinical significance. High-field strength knee MRI examinations were selected which demonstrated sMCL injuries. These cases were retrospectively reviewed for the presence, location, and severity of MPFL abnormality. The MPFL was divided into a more superior transverse component arising from a femoral attachment (tMPFL), and a broader more inferior oblique decussation component (odMPFL) arising from the anterior margin of the upper sMCL. Chart review was performed to determine the clinical relevance of any MPFL findings. One hundred patients with MCL injury were identified. These included 37 grade I sprains, 33 partial tears, 20 high-grade partial tears, and 10 full thickness tears. Abnormal edema was present at the femoral attachment of the tMPFL in 83%. The odMPFL was abnormal in 90%, most commonly involving the femoral third. No patients had imaging evidence of concurrent lateral patellar dislocation on the initial MRI study. No patients had documented patellofemoral instability at the time of original injury or upon follow-up. No patients required MPFL reconstruction. The MRI appearance of the MPFL is abnormal in the majority of patients with clinically and MRI-documented sMCL sprains and tears. These cases had no evidence of concurrent lateral patellar dislocation on the initial MRI and did not develop patellar instability symptoms.

Astigmatic Vectorial Analysis in Pediatric Keratoconus After Unilateral Cross-Linking Treatment.

The aims of this study were to evaluate the treatment response of pediatric keratoconus (KC) patients to unilateral corneal collagen cross-linking (CXL) in treated eyes, disease progression in untreated eyes, and define the predictive value of astigmatic parameters by astigmatic vectorial analysis. Pediatric patients with KC with CXL-treated progressive eye and untreated fellow eye were included. Patients with other ocular conditions and a history of previous ocular surgery were excluded. Astigmatic changes in anterior and posterior corneal surfaces were evaluated with vectorial analysis. The receiver operating characteristic curves were analyzed to detect the best parameter that discriminates treated and untreated groups. Thirty-two eyes of 16 patients with at least 2-year follow-up were analyzed. The maximum keratometry (K) in CXL-treated eyes remained stable (from 53.51 ± 2.86-53.41 ± 2.84 diopter (D), P = 0.84) while the steepest K increased in untreated eyes (from 47.82 ± 1.71-49.59 ± 3.32 D, P = 0.03). The oblique components of corneal astigmatism in CXL-treated eyes were higher than those of fellow eyes (all P < 0.05), which significantly decreased in the anterior 3-mm zone after treatment (P = 0.048). The mean differential astigmatism magnitudes were significantly higher in treated eyes (all P < 0.05). The refractive centroid remained unchanged in treated eyes (P = 0.553) and shifted in the oblique direction in untreated eyes (P = 0.04). The oblique differential astigmatism in the anterior 7-mm zone showed the highest area under the curve value in predicting treatment efficacy (0.813, 95% confidence interval: 0.646-0.981, P < 0.001). Astigmatic vectorial analysis is an objective tool for longitudinal assessment of clinical outcomes in KC. Changes in the oblique components of corneal astigmatism might predict progression and treatment efficacy.

Post‐20 ka Earthquake Scarps Along NE‐Tibet's Qilian Shan Frontal Thrust: Multi‐Millennial Return, ∼Characteristic Co‐Seismic Slip, and Geological Rupture Control

AbstractEarthquake slip distributions help constrain rupture behavior and return times. Here, by combining 0.5‐m‐resolution image and topographic data interpretation with fieldwork, we quantify the co‐seismic throw distribution and rupture geometry of the 1609 Hongyazi earthquake along the Qilian Shan Fodongmiao fontal thrust (NE Tibet). We measured 396 vertical offsets across mapped geomorphic units along the thrust trace. The 1609 rupture was ∼118‐km long, with average co‐seismic throw and slip amounts of ∼1.8 ± 1.0 and ∼2.9 ± 1.4 m, respectively, consistent with a magnitude Mw of 7.4 ± 0.3. Along the ∼88‐km‐long western stretch of the thrust, our data also reveal five distinct clusters with peak cumulative throws (∼4.9, 9.3, 13.8, 18.0, and 22.2 m), implying older ruptures with nearly characteristic slip during five Mw ∼ 7.6–7.8 events, three of which were also identified in trenches. Two of these earthquakes ruptured the entire thrust, while three mainly broke the western and middle segments. The thrust geometry and segmentation are influenced by geological inheritance. The middle segment emplaces Silurian granites atop Quaternary alluvium, which may account for its irregularly cusped trace, and favor rupturing during large, Mw ∼7.8 events with multi‐millennium (∼3.7 +0.5/−2.2 ka) return times. Since ∼20 ka, the Fodongmiao Thrust has kept shortening and uplifting Tibet's northeastern boundary at steady rates of ∼1.4 and 1.1 mm/a, respectively. The remaining oblique component of convergence across the ∼800‐km‐long pushup between the Altyn Tagh and Haiyuan faults is absorbed by slip partitioning along the left‐lateral Changma and Lenglongling faults.

The posterior oblique ligament in MRI of acute knee trauma

To identify the posterior oblique ligament and assess incidence and patterns of injury to the ligament on MRI of acute knee trauma. One hundred twenty-three MRI studies met the study criteria. For each case, the posterior oblique ligament was identified and scored as injured or normal. Incidence of proximal and distal posterior oblique ligament tears was calculated. Fisher's tests were employed to determine significance of association between tears of the posterior oblique ligament and components of the posteromedial corner and other capsuloligamentous structures of the knee. The posterior oblique ligament was reliably identified as a distinct structure in 123 MRI scans that met the criteria and was consistently labeled as intact or torn. Posterior oblique ligament tear was seen in 61.7% of knee trauma with proximal injury in 56.5% and distal injury in 97.3% of positive cases. Posterior oblique ligament disruption was a part of multiligamentous injury in 94.7% of positive cases. Posterior oblique ligament injuries (n = 76) had an extremely significant relationship with oblique popliteal ligament tears (n = 27) (p = 0.0001), semimembranosus tendon insertion tears (n = 15) (p = 0.0005), and medial collateral ligament tears (n = 15) (p = 0.0005) and a highly significant association with medial meniscus tears (n = 68) (p = 0.0049) and posterior cruciate ligament tears (n = 12) (p = 0.0033). The association with anterior cruciate ligament tears (n = 53) was not significant. The posterior oblique ligament is a distinct radiological entity consistently identified in acute trauma MRI. Disruptions of the distal posterior oblique ligament are frequent in complex knee injury, notably in association with oblique popliteal ligament, medial collateral ligament, and semimembranosus tendon tears.

Long-term changes in the refractive effect of a toric intraocular lens on astigmatism correction

PurposeTo examine the long-term changes in the astigmatism-correcting effect of a toric intraocular lens (IOL) after stabilization of surgically induced astigmatic changes due to cataract surgery.MethodsUnilateral eyes of 120 patients that received a toric IOL for against-the-rule (ATR) or with-the-rule (WTR) astigmatism were enrolled. Manifest refractive and anterior corneal astigmatism, and ocular residual astigmatism which is mainly derived from internal optics were examined preoperatively, at approximately 2 months postoperatively (baseline) and at 5 ~ 10 years postbaseline. The astigmatism was decomposed to vertical/horizontal (Rx) and oblique components (Ry), which was compared between baseline and 5 ~ 10 years postbaseline.ResultsIn the eyes having ATR astigmatism, the mean Rx and Ry of the manifest refractive and corneal astigmatism significantly changed toward ATR astigmatism between the baseline and 5 ~ 10 years postbaseline (p ≤ 0.0304), but those of ocular residual astigmatism did not change significantly between the 2 time points. In the eyes having WTR astigmatism, the Rx and Ry of refractive, corneal, and ocular residual astigmatism did not change significantly between the 2 time points. Double-angle plots revealed an ATR shift in refractive and corneal astigmatism and no marked change in the ocular residual astigmatism in the eyes with ATR astigmatism, and there is no change in this astigmatism in the eyes with WTR astigmatism.ConclusionThe long-term changes with age in the effect of a toric IOL significantly deteriorated due to an ATR shift of corneal astigmatism in the eyes having ATR astigmatism, while it was maintained in eyes having WTR astigmatism, suggesting that ATR astigmatism should be overcorrected.

Insolation-paced sea level and sediment flux during the early Pleistocene in Southeast Asia

Global marine archives from the early Pleistocene indicate that glacial-interglacial cycles, and their corresponding sea-level cycles, have predominantly a periodicity of ~ 41 kyrs driven by Earth’s obliquity. Here, we present a clastic shallow-marine record from the early Pleistocene in Southeast Asia (Cholan Formation, Taiwan). The studied strata comprise stacked cyclic successions deposited in offshore to nearshore environments in the paleo-Taiwan Strait. The stratigraphy was compared to both a δ18O isotope record of benthic foraminifera and orbital parameters driving insolation at the time of deposition. Analyses indicate a strong correlation between depositional cycles and Northern Hemisphere summer insolation, which is precession-dominated with an obliquity component. Our results represent geological evidence of precession-dominated sea-level fluctuations during the early Pleistocene, independent of a global ice-volume proxy. Preservation of this signal is possible due to the high-accommodation creation and high-sedimentation rate in the basin enhancing the completeness of the stratigraphic record.

Limiting Behavior of Asteroid Obliquity and Spin Using a Semi-analytic Thermal Model of the YORP Effect

Abstract The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect governs the spin evolution of small asteroids. The axial component of YORP, which alters the rotation rate of the asteroid, is mostly independent of its thermal inertia, while the obliquity component is very sensitive to the thermal model of the asteroid. Here, we develop a semi-analytic theory for the obliquity component of YORP. We integrate an approximate thermal model over the surface of an asteroid, and find an analytic expression for the obliquity component in terms of two YORP coefficients. This approach allows us to investigate the overall evolution of asteroid rotation state, and to generalize the results previously obtained in the case of zero thermal inertia. The proposed theory also explains how a nonzero obliquity component of YORP originates even for a symmetric asteroid, due to its finite thermal inertia. In many cases, this causes equatorial planes of asteroids to align with their orbital planes. The studied nontrivial behavior of YORP as a function of thermal model allows for a new kind of rotational equilibria, which can have important evolutionary consequences for asteroids.

On the Rootless Nature of a Devonian Suture in SW Iberia (Ossa‐Morena Complex, Variscan Orogen): Geometry and Kinematics of the Azuaga Fault

AbstractSuture zones are key to understand collisional orogens, but not all the remains of subduction leading to collision occur in the root of the suture. The Azuaga Fault bounds a Devonian suture zone known as Central Unit. This fault is a steeply NE‐dipping, Variscan strike‐slip fault with left‐lateral and reverse oblique slip components formed during sinistral transpression in the Pennsylvanian. Motion along this fault was coeval with folding and fabric development in both its hanging wall and footwall, and also with the Matachel Fault. Tectonic flow associated with the Azuaga Fault shows high‐vorticity, explaining the exhumation of a flat‐lying Devonian suture zone via WNW‐plunging extrusion from the upper‐middle crust under inclined triclinic transpression during ENE‐WSW convergence. The exposed basal contact of the Central Unit is not the root zone of a Variscan suture zone, but instead is a NE‐dipping breaching fault that cuts across the suture zone that is contiguous to the SW under the upper section of the footwall. The peri‐Gondwanan terrane between the Central Unit and the South‐Portuguese Zone of the Iberian Massif (most of the Ossa‐Morena Zone) is underlain by a Devonian suture, implying it is a continental allochthon. Variscan suture zones in Europe are affected by strike‐slip faults. In our case, this pattern implies the location of suture zone exposures and location of its root are different. Suture zones and strike‐slip faults are common in orogens and analysis of their relationships may lead to relocation of suture zone roots and re‐thinking of upper and lower plates.

Resonant Damping of Kink Modes in Solar Coronal Slabs

We examine resonantly damped kink modes in straight coronal slabs, paying special attention to the effects of the formulation for the transverse density distribution (“profile”). We work in the framework of pressure-less, gravity-free, resistive magnetohydrodynamics, and we adopt the dissipative-eigenmode perspective. The density profile is restricted to be one-dimensional, but nonetheless allowed to take a generic form characterized by a continuous transition layer connecting a uniform interior to a uniform exterior. A dispersion relation (DR) is derived in the thin-boundary limit, yielding analytical expressions for the eigenfrequencies that generalize known results in various aspects. We find that the analytical rather than the numerical solutions to the thin-boundary DR serve better the purpose for validating our self-consistent resistive solutions. More importantly, the eigenfrequencies are found to be sensitive to profile specifications, the ratio of the imaginary to the real part readily varying by a factor of two when one profile is used in place of another. Our eigenmode computations are also examined in the context of impulsively excited kink waves, suggesting the importance of resonant absorption for sufficiently oblique components when the spatial scale of the exciter is comparable to the slab half-width.

Prediction of postoperative refractive astigmatism before toric intraocular lens implantation

BackgroundTo determine the preoperative factors influencing refractive astigmatism after cataract surgery for astigmatism correction by toric intraocular lens (IOL) implantation and to evaluate the prediction model using these factors.MethodsProspective, observational case series. The right eyes of forty consecutive patients with preoperative corneal astigmatism of the total cornea of 1.5 diopters (D) or more in magnitude and scheduled for implantation of a non-toric IOL during cataract surgery with a 2.4-mm temporal clear corneal incision were examined prospectively. The vertical/horizontal astigmatism component (J0) and oblique astigmatism component (J45) of refractive and corneal astigmatism were converted using power vector analysis. Multivariate regression analysis was performed with refractive astigmatism at three months postoperatively as the dependent variable, and preoperative parameters including age, sex, refractive astigmatism, corneal astigmatism, sphere, spherical equivalent, intraocular pressure, corneal thickness, anterior chamber depth, lens thickness, lens positions (tilt and decentration), axial length, and corneal higher order aberrations as independent variables. The root mean square (RMS) errors were calculated to express the regression model fit.ResultsThe regression model for the J0 component was Postoperativekern0.34em refractivekern0.2em J0=1.05times Conealkern0.2em J0-0.14 (R2 = 0.96, P < 0.001). The model for the J45 component was Postoperativekern0.34em refractivekern0.2em J45=0.68times Conealkern0.2em J45+0.19times Preoperativekern0.34em refractivekern0.2em J45-0.06 (R2 = 0.72, P < 0.001). The mean RMS errors for preoperative corneal astigmatism alone and the multivariate model were 0.58 D and 0.46 D, respectively. There was a statistically significant difference between them (P = 0.02).ConclusionsRefractive astigmatism after implantation of a toric IOL can be predicted by the regression model more accurately than by corneal astigmatism alone. However, the prediction of oblique astigmatism remains a challenge.

Further Empirical Evidence on Patrick Hughes' Reverspectives: A Pilot Study.

Reverspectives are paintings created by the English artist Patrick Hughes. They are 3D structures, for example, pyramids or prisms, which elicit an illusory depth perception that corresponds to the reverse of the physical depth layout. Rogers and Gyani state that “the perspective information provided by a simple grid of vertical and horizontal lines on a slanting surface can be just as powerful as the information provided by a rich, naturalistic scene”. The present experiment was aimed to further investigate this perspective reversal. Three independent variables were manipulated: (1) texture components (i.e., vertical, horizontal, and oblique lines components), (2) texture spatial arrangement (i.e., Hughes-type “perspective” grid vs. equidistant “no perspective” grid), and (3) illumination direction (i.e., homogeneous illumination, light from above, and light from below). The dependent variable was the “critical distance”, namely, the distance between an approaching observer and the stimulus at which the illusory depth perception of concavity/convexity switched to the actual perception of convexity/concavity. The results showed that a stronger illusion is elicited by: (a) a Hughes-type texture spatial arrangement; (b) a complete grid texture composition, having both vertical and horizontal, and oblique components; and (c) illumination from below, as opposed to the condition in which light is coming from above.

The Eocene‐Oligocene Transition in the South‐Western Neo‐Tethys (Tunisia): Astronomical Calibration and Paleoenvironmental Changes

AbstractA detailed biostratigraphic, chemostratigraphic, and chronostratigraphic study was carried out in the South‐Western margin of the Neo‐Tethys ocean (Tunisia) covering the Eocene‐Oligocene interval to report potential paleoenvironmental and paleoclimatic changes associated with the growth of the Antarctic ice sheet (AIS). The studied section consists of marls and limestones extending from the Helicosphaera compacta nannofossil Zone (CNE21) to the Reticulofenestra umbilicus Zone (CNO2). The Bc of Clausicoccus subdistichus coincides in northeastern Tunisia with the extinction of hantkeninids and is thus used here to define the Eocene/Oligocene boundary (EOB) at 34.03 Ma. Calcareous nannofossil assemblages suggest a significant change from oligotrophic/warm surface waters during the late Eocene to eutrophic/cool waters during the early Oligocene. The observed changes in trophic conditions are synchronous with a shallowing trend testified by an increase in nearshore species and enhanced terrigenous input. Major environmental changes occurred at the EOB and across glaciation event Oi‐1a whereas we record a poor imprint of glaciation event Oi‐1. Three orbital configurations have been distinguished: (1) The late Eocene is characterized by a prominent 405‐kyr cycle and a weak obliquity component; (2) the onset of cooling at 34.35 Ma coincides with the rosette‐shaped discoaster extinction and is reflected by a shift toward enhanced obliquity and short‐eccentricity cycles. The installation of a fully developed AIS (event Oi‐1a, 32.75 Ma) shows the most pronounced obliquity imprint reflecting an increased influence of high‐latitude climate processes; (3) after 31.75 Ma, the obliquity decreases in coincidence with the return to a dominant long‐eccentricity cycle.

Proteomic Signatures During Treatment in Different Stages of Heart Failure.

Proteomics have already provided novel insights into the pathophysiology of heart failure (HF) with reduced ejection fraction. Previous studies have evaluated cross-sectional protein signatures of HF, but few have characterized proteomic changes following HF with reduced ejection fraction treatment with ARNI (angiotensin receptor/neprilysin inhibitor) therapy or left ventricular assist devices. In this retrospective omics study, we performed targeted proteomics (N=625) of whole blood sera from patients with American College of Cardiology/American Heart Association stage D (N=29) and stage C (N=12) HF using proximity extension assays. Samples were obtained before and after (median=82 days) left ventricular assist device implantation (stage D; primary analysis) and ARNI therapy initiation (stage C; matched reference). Oblique principal component analysis and point biserial correlations were used for feature extraction and selection; standardized mean differences were used to assess within and between-group differences; and enrichment analysis was used to generate and cluster Gene Ontology terms. Core sets of proteins were identified for stage C (N=9 proteins) and stage D (N=18) HF; additionally, a core set of 5 shared HF proteins (NT-proBNP [N-terminal pro-B type natriuretic peptide], ESM [endothelial cell-specific molecule]-1, cathepsin L1, osteopontin, and MCSF-1) was also identified. For patients with stage D HF, moderate (δ, 0.40-0.60) and moderate-to-large (δ, 0.60-0.80) sized differences were observed in 8 of their 18 core proteins after left ventricular assist devices implantation. Additionally, specific protein groups reached concentration levels equivalent (g<0.10) to stage C HF after initiation on ARNI therapy. HF with reduced ejection fraction severity associates with distinct proteomic signatures that reflect underlying disease attributes; these core signatures may be useful for monitoring changes in cardiac function following initiation on ARNI or left ventricular assist device implantation.

Active 650-km Long Fault System and Xolapa Sliver in Southern Mexico

New estimates of long-term velocities of permanent GPS stations in Southern Mexico reveal that the geologically discernible ~650 km long shear zone, which strikes parallel to the Middle America trench, is active. This left-lateral strike-slip La Venta-Chacalapa (LVC) fault system is apparently associated with a motion of the Xolapa terrain, and at the present time is the northern boundary of a ~110 – 160 km wide forearc sliver with a sinistral motion of 3 – 6 mm/yr with respect to the North America plate. This sliver is the major tectonic feature in the Guerrero and Oaxaca regions, which accommodates most of the oblique component of the convergence between the Cocos and North America plates. Previous studies based purely on the moment tensor coseismic slips exceedingly overestimated the sliver inland extent and allocated its northern margin on or to the north of the Trans-Mexican Volcanic Belt. While the LVC fault system probably slips slowly over geologic scale time, and there is not any historic evidence of large earthquakes on the fault so far, its seismic potential could be very high assuming a feasible order of ~103 years recurrence cycle. A detailed analysis of long-term position time series of permanent GPS stations in the Guerrero and Oaxaca states, Southern Mexico discards previous models and provides clear evidence of an active LVC fault zone bounding the Xolapa forearc sliver. The southeastward motion of this sliver may have persisted for the last ~8-10 Myr and played an important role in the tectonic evolution of the region.

An overview of the current seismicity of the Sultandağı Fault Zone (Afyonkarahisar-Konya, Western Anatolia)

Western Anatolia is one of the most seismically active regions in Turkey. The high seismic activity is a result of a complex tectonic deformation dominated by the N-S extensional tectonic regime in Western Anatolia. This tectonic deformation is also a result of the relative movement of the African- Arabian plates towards the north, which causes the Anatolian plate to shift 2.5 cm per year towards W-SW. One of the largest fault zones in the Western Anatolia, Sultandağı Fault Zone (SFZ) has a northwest-southeast trend. SFZ, approximately 120 km long, is an important tectonic structure, which produced three major earthquakes (Mw> 6.0) between the years of 2000 -2002. Therefore, the most significant goals of this study were to monitor the micro-earthquakes along SFZ, to enrich the current seismic network and to increase the earthquake detection threshold in the region (Mc <2.5). Within the scope of the study, 3 digital broadband earthquake stations were installed in the region. The analysis of the data obtained in the research indicated that the central and western parts of SFZ are active and there is intense seismic activity especially in the vicinity of Sultandağı, Çay, Çobanlar, and Afyonkarahisar. Fault plane solutions revealed that the earthquakes in the region generally occur with normal faulting with oblique components. Seismic stations installed within the scope of the study contributed positively to the increase of the sensitivity (Mc = 1.3) of the earthquake detection threshold (Mc) in the region and increased the detection capacity.

Corneal Astigmatism Measurements Comparison among Ray-Tracing Aberrometry, Partial Coherence Interferometry, and Scheimpflug Imaging System.

Purpose To investigate interdevice agreement among corneal topography/ray-tracing aberrometry (iTrace), partial coherence interferometry (IOLMaster), and Scheimpflug imaging (Pentacam) for the measurement of corneal astigmatism. Methods The analysis included 90 eyes of 90 subjects without ocular disease. The main outcome measures were corneal cylinder power and axis of astigmatism. All corneal astigmatism measurements were converted to two perpendicular components by using vector analysis. Interdevice agreement was assessed using Bland–Altman analysis, paired sample t-test, and one-way analysis of variance. Results No significant interdevice difference existed in the astigmatism magnitude, cardinal component, and oblique component (all P > 0.05). On comparing iTrace wavefront and simulated keratometry (SimK) astigmatism, significant differences were observed in the astigmatism magnitude and oblique component (both P < 0.01), but not in the cardinal component (P=0.687). On comparing Pentacam pupil 3 mm and corneal vertex 3 mm axial astigmatism, significant difference was observed in the astigmatism magnitude (P < 0.001), but not in the cardinal and oblique components (both P > 0.05). Conclusions The iTrace, IOLMaster, and Pentacam devices could be used interchangeably for corneal astigmatism measurement. However, the measurement difference in iTrace wavefront and SimK astigmatism and Pentacam pupil 3 mm and vertex 3 mm axial astigmatism should be considered in clinic practice.

Siacci's Theorem for Frenet Curves in Minkowski 3-Space

For motion of a material point along a space curve, due to Siacci [1], a resolution of the acceleration vector is well known. In this resolution, the acceleration vector is stated as the sum of two special oblique components in the osculating plane to the curve. In this paper, we have studied the Siacci’s theorem for non-relativistic particles moving along the Frenet curves at very low speeds relative to the speed of light in Minkowski 3-space. Moreover, an illustrative example is given to show how the aforesaid theorem works. This theorem is a new contribution to the field and it may be useful for some specific applications in mathematical and computational physics.

A Note on the Acceleration and Jerk in Motion Along a Space Curve

Abstract The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.

Agreement of ocular biometric measurements in young healthy eyes between IOLMaster 700 and OA-2000

This prospective cross-sectional study aimed to evaluate the agreement of two new biometers for measuring ocular biometric parameters in young healthy eyes. Ocular biometric parameters were measured using IOLMaster 700 and OA-2000. Power vector analyses of Cartesian (J0) and oblique (J45) components of corneal astigmatism were performed. The right eyes of 103 healthy volunteers were analyzed. The 95% limits of agreement ranged from −0.03 to 0.03 mm, −0.08 to 0.07 mm, −0.18 to 0.18 diopters (D), −1.09 to 1.16 D, −1.18 to 1.15 D for axial length (AL), anterior chamber depth (ACD), mean keratometry, J0 and J45 respectively, which were all comparable between the two biometers, while significant differences were detected in lens thickness (LT), central corneal thickness (CCT), white-to-white (WTW) and pupil diameter (PD). Predicted intraocular lens (IOL) powers were comparable between the two biometers by Haigis and Barrett Universal II formulas, while not by SRK/T, Hoffer Q and Holladay 2. Excepting CCT, WTW and PD meaurements, IOLMaster 700 and OA-2000 have excellent agreement on ocular biometric measurements and astigmatism power vectors, which provides more options for ocular biometric measurements and enables constant optimization for IOL power calculation.

Multivariate Regression Analysis to Predict Postoperative Refractive Astigmatism in Cataract Surgery.

Purpose To assess the correlation between postoperative refractive astigmatism and preoperative parameters in cataract surgery. Methods Left eyes of 100 consecutive patients scheduled for cataract surgery with a 2.4 mm clear corneal incision were examined prospectively. Refractive astigmatism was measured using an autokerato/refractometer. Corneal astigmatism of the total cornea was calculated using a Scheimpflug camera. The vertical/horizontal component (J0) and oblique component (J45) of refractive and total corneal astigmatism were determined using power vector analysis. Refractive astigmatism at 8 weeks postoperatively was estimated using multivariate linear regression analysis. Independent variables analyzed included age, sex, refractive astigmatism, total corneal astigmatism, sphere, intraocular pressure, corneal thickness, anterior chamber depth, lens thickness, axial length, and pupil diameter. Results Multivariate regression analysis identified total corneal J0 and age as significant contributors to postoperative refractive J0 (P < 0.001 and P=0.029, respectively). The standard partial regression coefficients in the multiple regression analysis were 0.59 and −0.16 for total corneal J0 and age, respectively. Significant contributors to postoperative refractive J45 were total corneal J45 and lens thickness (P < 0.001 and P=0.015, respectively). The standard partial regression coefficients were 0.79 and −0.15 for total corneal J45 and lens thickness, respectively. Conclusion These results suggest that preoperative total corneal astigmatism is the most significant predictor of postoperative refractive astigmatism when performing astigmatism correction in cataract surgery.