Biomechanical Analysis of X-Pattern Exotropia


To simulate and check the plausibility of the proposed mechanisms of X-pattern exotropia and to determine the least invasive surgical method that can be used to treat the disorder.


Computational supported analysis and retrospective study.


The oculomotor model SEE++ was used to simulate the effects of the different causes that have been proposed for the X-phenomenon. In addition, a retrospective study was conducted using preoperative and postoperative measurements of 10 patients with X-pattern exotropia. Eye movements and surgery of these patients were simulated and analyzed statistically.


Our computer-based simulations showed that only 1 of the 4 proposed theories can account successfully for the observed X-patterns: an overaction of all 4 oblique muscles can induce divergent exotropia in upgaze and downgaze, and an alteration of horizontal muscles can cause the additional divergence in all gaze positions. The simulation of eye muscle surgery confirmed that a sufficient correction of the divergent deviation in all gazes already can be achieved by a recession and resection of 2 horizontal eye muscles.


In case of X-pattern exotropia, recession and resection of 2 horizontal muscles can be used as a first-line therapy, leading to a simplification of the therapy.

Alphabet-pattern strabismus, also known as A-pattern, V-pattern, X-phenomenon, or diamond-phenomenon strabismus, is characterized by a differing horizontal deviation in upgaze and downgaze. In case of exotropia, A-pattern strabismus shows an increase of the strabismus angle in downgaze, whereas V-pattern strabismus is characterized by an increased angle in upgaze. The combination of the 2, that is, exotropia with an increasing divergent angle in upgaze and downgaze, consequently is referred to as X-pattern exotropia or X-phenomenon . Because only a few patients have X-pattern exotropia, it is difficult to investigate what causes these symptoms and how such patients can be treated most effectively.

Regarding possible causes of X-pattern exotropia, 4 different explanations have been proposed. Jampolsky postulated an ipsilateral overaction of the oblique muscles as a possible reason for the X-phenomenon in unilateral large-degree exotropia. He suggested that overaction of all 4 oblique muscles may produce the increase of exodeviation in upgaze and downgaze. A different cause was suggested by Wright: he proposed that a tightly contracted lateral rectus muscle could produce a leash effect, causing the observed X-pattern exotropia. The third mechanism was suggested by de Decker: in patients with long-standing exotropia, he observed a slip of all 4 oblique muscles to the polar cap. This dislocation may amplify the abductional effect of the oblique muscles, and therefore may induce an increase of exotropia. In addition, in upgaze and downgaze, the lateral rectus muscle may slip above or below the eye and pull the eye up and out or down and out, thereby contributing to the X-shaped exotropia. A fourth possible explanation comes from observations by von Noorden: he reported that patients with X-pattern exotropia show a combination of oblique dysfunction together with horizontal deviations.

The complex interactions of eye positions, pulling directions, and mechanical and neural contributions render purely intuitive interpretations of strabismus patterns highly complex and speculative. For example, the effect of an increase in stiffness of the lateral rectus muscle depends on the gaze position, on the relation of the center of eye rotation to the location of the muscle insertion, on the location and behavior of the corresponding muscle pulleys, and on the insertion width of the lateral rectus. To gain a better understanding of possible biomechanical causes of the X-phenomenon, we therefore decided to look at the predictions of computer-based simulations of the oculomotor plant for the 4 suggested causes of X-pattern exotropia. An overview of these hypotheses and the corresponding suggested treatments, as well as the results of our computer simulation of the mechanisms proposed by these hypotheses, is provided ( Table ).


Comparison of Hypothetical X-Pattern Exotropia Mechanisms with Simulation Results and Suggested Therapies

X-Pattern Exotropia Hypothesis Author Pathologic Mechanisms Suggested Therapies Simulation Results
Jampolsky Bilateral overaction of all 4 oblique muscles Surgical treatment of all 4 oblique muscles Little exotropia in primary position
Wright Contracted lateral rectus muscle(s) Recession of lateral rectus muscle(s) No change in upgaze or downgaze
de Decker Slip of all 4 oblique muscles to polar cap No general treatment suggestions Not simulated, for lack of specific information
van Noorden Cumulative oblique-dysfunction and horizontal deviations Surgical treatment of all 4 oblique muscles, or surgical treatment of horizontal rectus muscles X-pattern can be reproduced, with different options for horizontal deviation

Computer-based simulations of 3-dimensional eye movements have many adjustable parameters, so results based only on such simulations have to be treated with caution. We therefore combined our computer-based simulations with a retrospective pilot study of all X-pattern exotropia patients who sought treatment at our clinics over the last 20 years and the effects of the horizontal rectus surgeries that have been used to treat those patients. Our simulations of the oculomotor mechanics allow us for the first time to simulate the effects of the suggested causes of X-pattern exotropia and to analyze the mechanics behind the X-phenomenon.



In the last decade, 2 computer-based models of the oculomotor system have been commercially available. The first one was Orbit (Eidactics, San Francisco, California, USA), which has been developed for the Mac (Apple, Inc, Cupertino, California, USA). An updated, Java-based version is under development, but currently is not available. The second commercial oculomotor model, SEE++, has been developed for PCs (RISC Software GmbH, Hagenberg, Austria). The simulation results of SEE++ have reproduced successfully the effects of surgeries for simple operations, as well as for biomechanically complex pathologic conditions. Our simulations of the suggested biomechanical causes of X-pattern exotropia were carried out with SEE++ release 7.4.


Strabismus patients with X-pattern exotropia are very rare. Over a period of 20 years, only 10 patients with X-pattern exotropia qualified for inclusion in our study. The mean age ± standard deviation of these patients was 31.7 ± 15.2 years. The best-corrected logarithm of the minimal angle of resolution visual acuity on the better eye was 1.0 ± 0.1, and that of the weaker eye 0.4 ± 0.4. Five of these patients previously had undergone squint surgery. A statistical comparison of strabismus angles between the 2 groups showed no significant difference between patients with and without squint surgery. We therefore pooled the 10 cases and treated them as 1 homogenous sample.

The strabismus angle was measured using the prism cover test under optimal refractive correction. Measurements were performed before surgery, 2 days after surgery, and 4 months after surgery. Patients with additional ocular pathologic features were excluded. For achieving the best results when comparing simulations with field data, the preoperative and postoperative measurements were obtained directly as input parameters for the computer simulations.

Surgical Treatment

The goal of the surgical treatment of these patients was to reduce the horizontal deviations to a level acceptable to the patients, not to eliminate the X-pattern exotropia. To achieve this goal, only the horizontal extraocular muscles were operated on.

In 9 patients, common recession and resection was performed for divergent deviation. In 1 case, a bilateral recession was performed. The dosage of recession was 5.1 ± 1.3 mm, and that of resection was 4.8 ± 3.0 mm. The dosage of bilateral recession of the lateral rectus muscle was 7 mm. The expected effect of muscle displacement by 1 mm was calculated with 2.1 ± 0.4 degrees (4 ± 0.7 prism diopters).

Statistical Analysis

Because of the small sample size of 10 patients, our statistical analysis focused on a comparison between the results of surgery and of the simulation on the mean and median levels of the strabismus in all gaze positions. The statistical tests included the 2-sided t test for paired data as well as the Wilcoxon rank-sum test (Mann–Whitney U test) for nonparametric analyses.


Computer-Based Simulation of the Biomechanical Cause of X-Pattern Exotropia

Figure 1 shows the average strabismus angles found in patients (Left), as well as the simulation results for the overaction of the oblique muscles (Middle left and Middle right) and of a tether effect of the horizontal muscles (Right). For the simulations of X-pattern exotropia, muscle forces were changed by increasing or decreasing the active and passive muscle strengths. The active muscle strength corresponds to the muscle force induced by neural activity; the passive muscle strength describes the contribution of the muscle stiffness and elasticity to the total force exerted. To simulate the hypothesis of Jampolsky of an overaction of all 4 oblique muscles as a possible cause of the X-phenomenon, we first tested the effect of an increase in passive muscle strength of all 4 oblique muscles. However, this did not result in a typical X-phenomenon ( Figure 1 , Middle left). In contrast, an increase of the active muscle strengths of all 4 oblique muscles, comparable with a muscle overaction, induced typical X-pattern exotropia ( Figure 1 , Middle right). The second mechanism suggested for the X-pattern is a tether effect, a leash effect induced by a tightly contracted lateral rectus muscle on upgaze and downgaze. We simulated this effect by increasing active and passive forces for the lateral rectus. The simulation results showed no typical signs of the X-phenomenon ( Figure 1 , Right). None of these hypotheses is able to explain the pronounced divergent deviation, which is typical for the X-phenomenon and which was present in all our patients. The hypothesis of de Decker, a “slip of all four oblique muscles to the polar cap,” could not be simulated because he provided no specific information on this proposed muscle slip.

Jan 16, 2017 | Posted by in OPHTHALMOLOGY | Comments Off on Biomechanical Analysis of X-Pattern Exotropia
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