Temporal Margins Research Articles

A new QRS detector stress test combining temporal jitter and F-score (JF) reveals significant performance differences amongst popular detectors.

QRS detection within an electrocardiogram (ECG) is the basis of virtually any further processing and any error caused by this detection will propagate to further processing stages. However, standard benchmarking procedures of QRS detectors are seriously flawed because they report almost always close to 100% accuracy for any QRS detection algorithm. This is due to the use of large temporal error margins and noise-free ECG databases which grossly overestimate their performance. The use of a large fixed error margin masks temporal jitter between detection and ground truth measurements. Here, we present a new performance measure (JF) which combines temporal jitter with the F-score, and also an ECG database with decreasing levels of signal to noise ratios based on noise generated from different tasks. Our new performance measure JF fully encompasses all the types of errors that can occur, equally weights them and provides a percentage value which allows direct comparison between QRS detection algorithms. In combination with the new noisy ECG database, the JF performance measure now varies between 50% and 100% for different detectors and signal to noise conditions thereby making it possible to find the best detector for an application.

Extending the Gneiting class for modeling spatially isotropic and temporally symmetric vector random fields

We provide new classes of nonseparable univariate and multivariate space-time covariance functions that extend the Gneiting class. In particular, we prove that the spatial generator of the Gneiting class does not need to be completely monotone and can be replaced with the radial profile of a continuous positive semidefinite function in a finite dimensional Euclidean space, and we weaken the assumptions on the temporal margins so as to include more general behaviors than that of the original Gneiting construction. Our findings allow for covariance functions that are compactly-supported in space and/or nonmonotone in time, i.e., they offer versatility to model complex features commonly observed on data indexed with space-time coordinates.

Effective sample size for georeferenced and temporally evolving data

The effective sample size (ESS) measures the number of independent observations within a sample. This quantity has been studied and applied in many branches of statistics in recent years. In particular, it is used in the statistical analysis of spatial data for detecting duplicated observations as a consequence of the spatial correlation that is typically encountered in practice, allowing for subsequent model-informed data reduction procedures. The primary goal of this article is to introduce a space–time ESS, extending the current literature from the purely spatial to the space–time setting. The proposed ESS can be broken down into spatial and temporal margins. Thus, a statistician could perform purely spatial, purely temporal or joint space–time data reductions in such a way that the simultaneous space–time dependency structure is honored. We show that several elementary attributes that have been widely studied for the purely spatial ESS can translate naturally to the space–time context. We also present some results that connect the proposed ESS with the property of non-separability between space and time. After presenting our results, we apply them to a real data set consisting of daily averages of wind speeds in Ireland during 1961–1978. We obtain that, at each meteorological station, the sample size could be reduced by 80%, while maintaining critical statistical information of the data, demonstrating the effectiveness of our proposal.

Time Borrowing Flip-Flop architecture for error masking in near threshold voltage regime

This As dynamic delay variability increases with near-threshold voltage operation, wide timing margins need to be integrated in DVFS (Dynamic Voltage and Frequency Scaling) when deciding the frequency of operation to ensure reliable and error-free operation. Hence the maximum frequency (which is already low) in near-threshold operation is limited by these timing margins. Online methodologies for the resilience of temporal arrangement errors facilitate the recovery of temporal arrangement margins, increasing efficiency and/or energy consumption. This study presents a method for the resilience of online temporal arrangement errors that masks temporal arrangement errors by borrowing time from the phases of serial pipelines. Planned style, while not instruction replay or roll-back support, will recover temporal arrangement margins.

Taming Time: Configuring Cancer Patients as Research Subjects.

This article explores how incurable cancer patients in the affluent Danish welfare state are recruited to clinical trials. We show that patients' impending death constitutes their potential for being configured as research subjects. To produce valuable data, patients who enroll in trials and health care professionals must engage in daily "time practices" that prolong the threshold between life and death. When death becomes inevitable, the limit of configuring dying cancer patients as research subjects is reached. Navigating this temporal logic, health care professionals balance the boundary between patients' instrumental worth as research subjects and their intrinsic worth as dying cancer patients. Whereas previous studies have critically uncovered how clinical trials operate at socioeconomic margins, we point to the ways in which clinical trials operate through temporal margins. We argue that clinical trials are dependent on configuring marginal societal spaces and marginal bodies from which to produce knowledge.

Deciphering interactions between white-tailed deer and approaching vehicles

Deer-vehicle collisions are a major transportation hazard, but factors affecting deer escape decision-making in response to vehicle approach remain poorly characterized. We made opportunistic observations of deer response to vehicle approach during daylight hours on a restricted-access facility in Ohio, USA (vehicle speeds were ≤64 km/h). We hypothesized that animal proximity to the road, group size, vehicle approach, and ambient conditions would affect perceived risk by white-tailed deer (Odocoileus virginianus) to vehicle approach, as measured by flight-initiation distance (FID). We constructed a priori models for FID, as well as road-crossing behavior. Deer responses were variable and did not demonstrate spatial or temporal margins of safety. Road-crossing behavior was slightly and positively influenced by group size during winter. Deer showed greater FIDs and likelihood of crossing when approached in the road; directionality of approach likely increased the perceived risk. These findings are consistent with antipredator theory relative to predator approach direction.

Choroidal Neovascularization Associated with Morning Glory Syndrome: A Case Report

Morning glory syndrome (MGS) is a congenital optic disc anomaly caused by abnormal closure of the embryonic fissure. Retinal detachment is commonly associated with MGS, though the association of choroidal neovascularization (CNV) with MGS is rare. Herein, we report a case of CNV associated with MGS, which was successfully treated with a single intravitreal injection of bevacizumab. A 32-year-old Japanese woman consulted at our clinic for blurred vision in her left eye for five days. Her best-corrected decimal visual acuity (BCVA) was 1.5 (S-1.0) OS. The fundus examination revealed subretinal hemorrhage associated with MGS in the temporal margin of the optic disc. As she was pregnant, we planned to continue follow-up without further invasive testing and treatment; however, her visit to the hospital was interrupted. Ten months later, she returned with complaints of poor vision and central scotoma in her left eye for six months. The BCVA was 0.5 (S-1.0/C-1.0/45°) OS. The fundus examination showed that subretinal hemorrhage increased, and the subretinal fluid extended below the fovea. Multimodal imaging revealed type 2 CNV on the temporal and nasal disc margins. After she received an intravitreal injection of bevacizumab (1.25 mg), rapid absorption of subretinal fluid and regression of CNV were observed. The BCVA improved to 1.5 (S-0.5/C-0.75/35°) OS. No recurrence of CNV was observed for 26 months after the injection. During the follow-up of MGS cases, we should pay attention, not only to retinal detachment, but also to the occurrence of CNV around the disc margins.

Association of Seizure Spread With Surgical Failure in Epilepsy

Seizures recur in as many as half of patients who undergo surgery for drug-resistant temporal lobe epilepsy (TLE). Understanding why TLE is resistant to surgery in some patients may reveal insights into epileptogenic networks and direct new therapies to improve outcomes. To characterize features of surgically refractory TLE. Medical records from a comprehensive epilepsy center were retrospectively reviewed for 131 patients who received a standard anteromedial temporal resection by a single surgeon from January 1, 2000, to December 31, 2015. Thirteen patients were excluded for having less than 1 year of follow-up. Patients at the highest risk for seizure recurrence were identified. Intracranial electroencephalogram (iEEG) analyses generated 3-dimensional seizure spread representations and quantified rapid seizure spread. The final analyses of seizure outcome and follow-up data were performed in June 2017. The Engel class seizure outcome following surgery was evaluated for all patients, defining seizure recurrence as Engel class II or greater. Intracranial recordings of neocortical grids/strips and depth electrodes were analyzed visually for seizure spread. Fast β power was projected onto reconstructions of patients' brain magnetic resonance imaging scans to visualize spread patterns and was quantified to compare power within vs outside resective margins. Of 118 patients with 1 year of follow-up or more (mean [SD], 6.5 [4.6] years), 66 (55.9%) were women and 52 (44.1%) were men (median age, 39 years [range, 4-66 years]). The cumulative probability of continuous Engel class I seizure freedom since surgery at postoperative year 10 and afterward was 65.6%, with 92% of recurrences in years 1 to 3. Multivariable statistical analyses found that the selection for iEEG study was the most reliable predictor of seizure recurrence, with a mixed-effects model estimating that the Engel score in the iEEG cohort was higher by a mean (SD) of 1.1 (0.33) (P = .001). In patients with iEEG results, rapid seizure spread in less than 10 seconds was associated with recurrence (hazard ratio, 5.99; 95% CI, 1.7-21.1; P < .01). In the first 10 seconds of seizures, fast β power activity outside the resective margins in the lateral temporal cortex was significantly greater in patients whose seizures recurred compared with patients who were seizure-free (mean [SEM], 137.5% [16.8%] vs 93.4% [4.6%]; P < .05). Rapid seizure spread outside anteromedial temporal resection resective margins plays a significant role in the surgical failure of drug-resistant TLE. Seizure control after epilepsy surgery might be improved by investigating areas of early spread as candidates for resection or neuromodulation.

Rajeunissement temporal

The temporal region has imprecise limits in the young patient. During the aging process, it becomes individualized with the appearance of a temporal fossa, the temporal, orbital and zygomatic bone margins, the ptosis of the lateral part of the brow and the appearance of the wrinkles of the crow's foot. As this area frame the look, it should be taken into consideration during the clinical examination as well as the facial and cervical stages. The rejuvenation techniques are numerous, nuanced and gradual. As long as the eyebrow ptosis is not evident and the distance of the eyebrows unaltered, the volumizing techniques and the botulinum toxin can respond effectively and harmoniously to the patients' demand. Then the surgical techniques of temporal and brow liftings must be considered and coupled with the techniques of lipostructure that are more and more practiced. It should be noted that the demand for temporal rejuvenation is increasing and precedes the demand of cervicofacial rejuvenation. This underlines the importance of this region both in terms of preventing or at least slowing down the process than in terms of curing the stigma of aging.

Quantitative Association Between Peripapillary Bruch's Membrane Shape and Intracranial Pressure.

PurposeThe purpose of this study was to determine if there is a quantitative relationship between chronic intracranial pressure (ICP) and peripapillary Bruch's membrane (pp-BM) shape and to determine whether change in pp-BM shape can be detected within 1 hour after ICP lowering by lumbar puncture (LP).MethodsIn this study, 30° nasal-temporal optical coherence tomography B-scans were obtained within 1 hour before and after LP in 39 eyes from 20 patients (age = 23–86 years, 75% female, ICP [opening pressure] = 10–55 cm H2O). A total of 16 semi-landmarks defined pp-BM on each image. Geometric morphometric analysis identified principal components of shape in the image set. Generalized estimating equation models, accounting for within-subject correlation, were used to identify principal components that were associated with chronic ICP (comparing pre-LP images between eyes) and/or acute ICP changes (comparing pre- and post-LP images within eyes). The pp-BM width and anterior pp-BM location were calculated directly from each image and were studied in the same manner.ResultsPrincipal component 1 scalar variable on pre-LP images was associated with ICP (P < 0.0005). Principal component 4 magnitude changed within eyes after LP (P = 0.003). For both principal components 1 and 4, lower ICP corresponded with a more posterior position of pp-BM. Chronic ICP was associated with both pp-BM width (6.81 μm/cm H2O; P = 0.002) and more anterior location of temporal and nasal pp-BM margins (3.41, 3.49 μm/cm H2O; P < 0.0005, 0.002).ConclusionsThis study demonstrates a quantitative association between pp-BM shape and chronic ICP level. Changes in pp-BM shape are detectable within 1 hour of lowering ICP. pp-BM shape may be a useful marker for chronic ICP level and acute ICP changes. Further study is needed to determine how pp-BM shape changes relate to clinical markers of papilledema.

Adjusting for population shifts and covariates in space-time interaction tests.

Statistical tests for epidemic patterns use measures of space-time event clustering, and look for high levels of clustering that are unlikely to appear randomly if events are independent. Standard approaches, such as Knox's (1964, Applied Statistics 13, 25-29) test, are biased when the spatial distribution of population changes over time, or when there is space-time interaction in important background variables. In particular, the Knox test is too sensitive to coincidental event clusters in such circumstances, and too likely to raise false alarms. Kulldorff and Hjalmars (1999, Biometrics 55, 544-552) proposed a variant of Knox's test to control for bias caused by population shifts. In this article, I demonstrate that their test is also generally biased, in an unknown direction. I suggest an alternative approach that accounts for exposure shifts while also conditioning on the observed spatial and temporal margins of event counts, as in the original Knox test. The new approach uses Metropolis sampling of permutations, and is unbiased under more general conditions. I demonstrate how the new method can also include controls for the clustering effects of covariates.

Biometric Features of Peripapillary Atrophy Beta in Eyes with High Myopia

To evaluate peripapillary atrophy β (PPA-β) characteristics in highly myopic eyes, using simultaneous confocal scanning laser ophthalmoscopy (cSLO) and enhanced spectral-domain optical coherence tomography (SD-OCT). The authors retrospectively analyzed 61 highly myopic (≥ -6.0 D) eyes without myopic retinopathy. cSLO fundus images were used to measure the distances from the foveal center to the temporal and nasal margins of the PPA-β zone; horizontal cross-sectional SD-OCT images, to determine the position where the inner plexiform layer (IPL) terminates within the PPA-β zone; and A-mode ultrasonography, to measure axial length. The distance from the foveal center to the PPA-β zone temporal margin (2.68-4.39 mm) correlated with the circumferential extent of PPA-β (P <0.001, r = -0.49). The distance from the foveal center to the nasal margin (3.41-5.60 mm) correlated with the ovality index of the optic disc (P <0.001, r = -0.51) and with the axial length (P <0.05, r = 0.26). PPA-β zone width (0.20-2.05 mm) correlated with the circumferential extent of PPA-β (P <0.001, r = 0.42), ovality index of the optic disc (P <0.001, r = -0.68), and axial length (P <0.05, r = 0.32). The IPL termination within the PPA-β zone was significantly closer to the optic disc when the circumferential extent of PPA-β was large (P <0.01, r = 0.36). Interindividual variations in biometric features of PPA-β in highly myopic eyes showed different associations with axial length, degree of disc ovality, and circumferential extent of PPA-β.

SPATIO-TEMPORAL COVARIANCE MODELING WITH SOME ARMA TEMPORAL MARGINS

A valid covariance structure is needed to model spatio-temporal data in various disciplines, such as environmental science, climatology and agriculture. In this work we propose a collection of spatio-temporal functions whose discrete temporal margins are some autoregressive and moving average (ARMA) models, obtain a necessary and sufficient condition for them to be covariance functions. An asymmetric version of this model is also provided to account for space-time irreversibility property in practice. Finally, a spatio-temporal model with AR(2) discrete margin is fitted to wind data from Ireland for estimation and prediction, which are compared with some general existing parametric models in terms of likelihood and mean squared prediction error.

Quasi-arithmetic means of covariance functions with potential applications to space–time data

The theory of quasi-arithmetic means represents a powerful tool in the study of covariance functions across space–time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility criteria. Also, some important inequalities involving covariance functions and preference relations as well as algebraic properties can be derived by means of the proposed approach. In particular, quasi-arithmetic covariances allow for ordering and preference relations, for a Jensen-type inequality and for a minimal and maximal element of their class. The general results shown in this paper are then applied to the study of spatial and spatio-temporal random fields. In particular, we discuss the representation and smoothness properties of a weakly stationary random field with a quasi-arithmetic covariance function. Also, we show that the generator of the quasi-arithmetic means can be used as a link function in order to build a space–time nonseparable structure starting from the spatial and temporal margins, a procedure that is technically sound for those working with copulas. Several examples of new families of stationary covariances obtainable with this procedure are shown. Finally, we use quasi-arithmetic functionals to generalise existing results concerning the construction of nonstationary spatial covariances, and discuss the applicability and limits of this generalisation.

Multiple brown tumors of the orbital walls: case report

We report the case of a 40-year-old woman with chronic renal failure and secondary hyperparathyroidism that presented with slowly progressive proptosis of the right eye and mass sensation in the temporal and frontal orbital margins. Computerized tomography scan revealed two separate hyperdense and well-circumscribed lesions in the right orbital walls. A biopsy followed by histopathologic study revealed a dense lesion, with fibrous proliferation associated with osseous metaplasia and osteoclastic activity in the tumor, compatible with the diagnosis of brown tumor. The patient was submitted to surgical removal of the parathyroid glands that resulted in marked improvement in her condition and regression of the orbital tumors. Although the occurrence of more than one separate bone lesion in the orbit usually suggests metastasis, our case shows that brown tumors should also be included in the differential diagnosis of such lesions, particularly in patients with hyperparathyroidism.

Gait Initiation in Multiple Sclerosis

Individuals with multiple sclerosis (MS) often have poor balance control that is especially apparent during dynamic tasks such as gait initiation (GI). The purpose of this study was to investigate how balance symptoms due to MS alter spatiotemporal variables, coordination, and temporal margins within the stability boundary during gait initiation. Twelve women with MS (Expanded Disability Status Scale [EDSS] mean = 4.0, SD = 1.4) and 12 women without MS (control group) initiated gait at their preferred speed. MS participants attained a slower anterior velocity because of smaller anterior center of mass displacements and took longer to complete the initiation of gait than the control group. MS participants exhibited a smaller posterior shift in center of pressure during GI and stepped with a longer dual support time than the control group. However, these changes may be due to differences in initiation velocity. Relative timing analysis showed invariance in postural and locomotor phases of gait initiation between groups. The MS group showed different coordination between anterior-posterior and medio-lateral center of pressure components while increasing temporal margins to the posterior and lateral stability boundaries in comparison with the control group. Overall, during gait initiation at their preferred speed the MS participants adopted a functional strategy that produces lower speed and reduced proximity to the stability boundaries prior to stepping.

Choroidal and optic disc metastases in a man with metachronous and metastatic breast carcinoma

Editor, We read with interest the article by Wickremasinghe et al. (2007) on ocular presentations of breast cancer. We agree with the authors that male breast carcinoma is a rare disease accounting for 1% of all breast cancer diagnosis and less than 1.5% of all malignant tumours in men (Fowble 1991). We report an unusual and interesting case of bilateral simultaneous choroidal metastases and unilateral optic disc metastasis from metachronous breast cancer in a man. A 65-year-old man presented with a history of gradual painless blurring of vision in his left eye. There was nothing notable in his past ophthalmic history. His best corrected visual acuity was 6/6 in the right eye and hand movements in the left eye. A left relative afferent pupillary defect was noted on examination. Fundus examination of the right eye revealed two flat choroidal lesions of one disc diameter size inferotemporally within the vascular arcade (Fig. 1A). In the left eye, multiple ill-defined elevated creamy white lesions were noted in the posterior pole with serous retinal detachment. There was also diffuse yellowish thickening of the optic disc with surrounding venous congestion and juxtapapillary choroidal metastasis at the temporal and inferior margins in the left eye (Fig. 1B). Standardized B-scan ultrasonography of the left eye demonstrated mild elevation of optic disc with high internal reflectivity, and echogenic subretinal mass with overlying serous retinal detachment (Fig. 2A, B). Ocular metastasis was diagnosed and the patient was referred for radiotherapy (Fig. 1C). Fundus photographs. (A) Right eye showing flat multifocal choroidal metastasis inferotemporally within the vascular arcade. (B) Left eye showing optic disc metastasis, juxtapapillary choroidal metastasis and inferior serous retinal detachment. (C) Left eye after radiotherapy showing diffuse enlargement of optic disc and mottling of retinal pigment epithelium. Ultrasonography of the left eye, showing (A) echogenic choroidal metastasis and (B) elevation of optic disc with high internal reflectivity. His past medical history was significant: breast carcinoma was diagnosed 6 years ago. He presented with incidental finding of a swelling in his left breast and nipple inversion. He was treated by mastectomy and axillary clearance. The surgery was followed by chemotherapy, radiotherapy and a 5 year course of tamoxifen. Histological examination showed invasive ductal carcinoma. The tumour was highly positive for oestrogen and progesterone receptors. He was monitored in clinic by periodical mammography for recurrence. The patient failed chemotherapy and tamoxifen treatment; 6 years after his initial presentation, he developed recurrence on the other side. He subsequently underwent right mastectomy with axillary clearance. The surgery was again followed by chemotherapy and radiotherapy. The histology demonstrated multifocal ductal carcinoma with extensive vascular invasion. By this time, the breast carcinoma also disseminated to liver and bone. Uveal metastasis is the most common malignancy of adult eyes (Shields & Shields 1992). Among uveal metastases, choroid is the most frequent site. The most common primary source is breast carcinoma in females and lung cancer in males. Metastasis to the optic disc is very uncommon and accounts for 4.5% of all intraocular metastases. The systemic prognosis for patients with optic disc metastasis is generally poor (Shields et al. 2000). Carcinoma of the breast is rare in men. Physicians and patients have a low index of suspicion for the disease; in addition, it tends to be diagnosed late in men leading to increased morbidity and mortality. Bilateral breast carcinoma is more common in women than in men. In a large case series, the prevalence of bilaterality was found to be only 1.4% in men (Crichlow 1972). Men are also more likely to develop a second type of cancer than to have a recurrence of the same type in the opposite breast as compared to women. This patient developed recurrence of the same type of carcinoma in the contralateral breast with widespread systemic and ocular metastases 6 years after his initial presentation despite adequate treatment. This case highlights the increased risk of ocular metastases and the presence of advanced disease at the time of presentation in male patients with breast carcinoma.

Evaluating temporal and spatial margins of safety in galahs

When approached by a potential predator, individuals must decide when to flee. Individuals could assess risk by monitoring their distance from an approaching threat or by monitoring the expected time that the predator would take to reach them. Theory predicts, and empirical studies support the hypothesis, that some species may maintain a temporal margin of safety and therefore monitor the expected time a predator would take to reach them. We systematically walked towards galahs, Cacatua roseicapilla, an Australian parrot, and varied our approach speed. If galahs maintain a temporal margin of safety, we expected them to flush at a greater distance in response to the fast approach. We found, however, no support for the temporal margin of safety hypothesis. Rather, we found evidence that galahs are sensitive to distance in a novel way: after being alerted, they flushed when humans approached to within 44% of the alert distance. Our result differs from traditional models of spatial margins of safety because it suggests that animals will take flight after being approached to within about half the alert distance. By doing so, individuals maintain a dynamic spatial margin of safety and may reduce costs associated with ongoing monitoring of predation risk.

Relative stability improves with experience in a dynamic standing task.

This study tested the hypothesis that subjects improve their relative stability as they learn a dynamic pulling task. Healthy adult subjects practiced making brief horizontal pulls (<300 ms) on a handle to a range of target forces ranging from 20 to 80% of their estimated maximum for 5 days. They were instructed to always keep their feet flat and begin and end their motion in an upright posture. In order to do this, subjects had to develop the appropriate body momentum prior to the pull and then recover their balance following the pull. We analyzed relative stability during balance recovery, using two measures: spatial safety margin (minimum distance of the center of pressure, COP, to the edges of the feet) and temporal safety margin (minimum extrapolated time for the COP to reach the edges of the feet). We hypothesized that: (1) spatial and temporal safety margins would be uncorrelated; (2) safety-margin means would increase with practice; and (3) safety-margin standard deviations would decrease with practice. Two experiments were conducted: one where subjects practiced three force targets and positioned their initial COP in a small window, and one where subjects practiced two force targets with no initial COP constraint. Results showed that spatial and temporal safety margins were correlated but shared less than 6% variance, indicating that they reflected different aspects of control. Safety-margin averages increased with practice and standard deviations decreased with practice, indicating that the stability of balance control in the execution of this task became more robust. We suggest that the nervous system could use safety margins in both feedback and feedforward control of balance.

Magnetic resonance imaging after surgical transposition defines the anteroposterior location of the rectus muscle pulleys

Introduction: Connective tissue pulleys serve as the functional origins of the rectus extraocular muscles (EOMs) and constrain the sideslip of the posterior EOM bellies after transposition surgery. Anterior to the pulleys, EOM paths appreciably displace to reach their transposed insertions. The inflection points in the EOM paths from minimal posterior displacement to maximal anterior displacement should define the anteroposterior location of the EOM pulleys after transposition. Methods: Contiguous cross-sectional magnetic resonance images were obtained in planes perpendicular to the long axis of the orbit over its entire anteroposterior extent before and after operation in 6 patients who underwent rectus muscle transposition surgery. Four patients underwent full tendon width transposition of the vertical rectus muscles laterally for lateral rectus palsy. Two of these patients had augmentation of the transposition with sutures that fixated the temporal margins of the transposed muscles posteriorly to the sclera adjacent to the borders of the lateral rectus muscle. One patient underwent full tendon width transposition of the horizontal rectus muscles superiorly for superior rectus palsy. One patient underwent full tendon width transposition of both lateral rectus muscles inferiorly for “A” pattern esotropia. Paths of EOMs were defined relative to the area centroid of the orbit. Pulley locations were inferred from EOM paths. The postoperative change in EOM pulley location was obtained by subtracting the preoperative pulley location from the postoperative pulley location for each image plane. Results: For all patients, the postoperative change in EOM belly location was relatively small posterior to the globe-optic nerve junction. The 2 patients with abducens palsy who underwent placement of posterior augmentation sutures, however, demonstrated a significantly larger displacement of the posterior vertical rectus paths compared with similar patients who did not receive augmentation sutures. For all horizontally transposed vertical rectus muscles and inferiorly transposed lateral rectus muscles, the inflection of the EOM path began 3 mm anterior to the globe-optic nerve junction. For the superiorly transposed medial rectus muscle and lateral rectus muscle, the inflection began 6 mm anterior to the globe-optic nerve junction. Conclusions: The anteroposterior locations of the EOM pulleys can be defined by analysis of EOM displacement after transposition surgery. Augmentation of transpositions by posterior suturing displaces the EOM pulleys substantially more than nonaugmented transpositions. (J AAPOS 1999;3:9-14)