Three-dimensional ocular kinematics underlying binocular single vision

Functional anatomy of extraocular muscles during human vergence compensation of horizontal heterophoria

We employed magnetic resonance imaging to quantify human extraocular muscle (EOM) contractility during intermittent convergent and divergent strabismus with each eye viewing monocularly at 20 cm compared with centered target fusion. Contractility, indicated by posterior partial volume change, was analyzed in transverse rectus and in medial and lateral superior oblique (SO) muscle compartments. In five subjects with intermittent esotropia, abduction of the deviated eye to monocular target fixation was associated with significant whole lateral rectus (LR) contraction, but with medial rectus (MR) relaxation that was significantly greater in the superior than inferior compartment. Esotropic eye abduction to binocular fusion was associated with similar relaxation in the two MR compartments, but with greater contraction in the LR's superior than inferior compartment. The whole diverging eye SO muscle relaxed. In three subjects with intermittent exotropia, converging eye fusional adduction was associated with significant whole LR relaxation and with MR contraction attributable to significantly greater contraction in the superior than inferior compartment. In adduction of the exotropic eye to monocular target fixation but not fusional adduction, the whole SO exhibited significant relaxation. Rectus pulley positions were not significantly altered by fusion of either form of intermittent strabismus. Globe rotational axis was eccentric in intermittent strabismus, rolling the eye so that rectus EOM lever arms facilitated vergence. These results confirm, and extend to fusion of intermittent horizontal strabismus, differential compartmental function in horizontal rectus EOMs and suggest a novel role for the SO in compensation of both intermittent esotropia and exotropia. NEW & NOTEWORTHY Disjunctive eye movements normally permit binocular fixation in near visual space but also compensate for mechanical imbalances in binocular alignment developing over the life span. Magnetic resonance imaging of the extraocular muscles demonstrates important differential function in muscle compartments during compensation of large-angle intermittent convergent and divergent strabismus in humans. Eye translation during rotation also enhances vergence compensation of intermittent strabismus.

An alignment maximization method for the kinematics of the eye and eye-head fixations

The orientation of human eyes is uniquely defined with respect to their gaze direction, known as Donders' law. Further, the manner in which the eyes follow Donders' law varies as a function of the situation. When the head is stationary, the Donders' surfaces are flat planes but they tilt when eye fixation distance changes. These planes also shift and rotate when head orientation changes with respect to the direction of gravito-inertial acceleration. When the head is free to rotate, the Donders' surfaces are twisted. In this paper, we present a systematic method to analyze the kinematics of the eye under different gaze situations utilizing the measurement of alignment between various coordinate frames. Kinematic equations are presented for various eye movements ranging from simple head-fixed monocular shifts of eye gaze to complex eye-head shifts of gaze. At each stage, we show that simulated eye orientations that derived from our equations are able to capture the variations of Donders' surfaces and they are comparable with experimental results in the literature. The final equations we propose provide the unified kinematics of head-upright far gaze, head-upright binocular fixation, head static tilted monocular gaze and head-free monocular gaze.

Functional anatomy of human extraocular muscles during fusional divergence

We employed magnetic resonance imaging to quantify human extraocular muscle contractility during centered target fusion and fusional divergence repeated with each eye viewing monocularly at 20 cm through 8Δ and at 400 cm through 4Δ base in prism. Contractility, indicated by posterior partial volume (PPV) change, was analyzed in transverse rectus and in medial and lateral superior oblique (SO) muscle compartments and by cross-sectional area change in the inferior oblique (IO). At 20 cm, 3.1 ± 0.5° (SE) diverging eye abduction in 10 subjects was associated with 4.2 ± 1.5% whole lateral rectus (LR) PPV increase ( P < 0.05) and 1.7 ± 1.1% overall medial rectus (MR) PPV decrease attributable to 3.1 ± 1.8% reduction in the superior compartment ( P < 0.025), without change in its inferior compartment or in muscles of the aligned eye. At 400 cm, 2.2 ± 0.5° diverging eye abduction in nine subjects was associated with 6.1 ± 1.3% whole LR PPV increase ( P < 10^-5) but no change in MR, with compartmentally similar relaxation in the LR and MR of the aligned eye. Unlike convergence, there were no IO or SO contractile changes for divergence to either target nor any change in rectus pulley positions. Results confirm and extend to proximal divergence the unique role of the superior MR compartment, yet no MR role for far divergence. Corelaxation of aligned eye LR and MR combined with failure of MR relaxation during divergence is consistent with the limited behavioral range of divergence. NEW & NOTEWORTHY Magnetic resonance imaging shows that the lateral rectus muscle must overcome continued contraction by its opponent the medial rectus when humans diverge their visual axes to achieve single, binocular vision. While the upper but not lower compartment of the medial rectus assists by relaxing for near targets, it does not do so when targets are far away. This behavior violates Sherrington's law of reciprocal action of antagonists and conventional assumptions about the ocular motor system.

On the role of ocular torsion in binocular visual matching

When an observer scans the visual surround, the images cast on the two retinae are slightly different due to the different viewpoints of the two eyes. Objects in the horizontal plane of regard can be seen single by aligning the lines of sight without changing the torsional stance of the eyes. Due to the peculiar ocular kinematics this is not possible for objects above or below the horizontal plane of regard. We provide evidence that binocular fusion can be achieved independently of viewing direction by adjusting the mutual torsional orientation of the eyes in the frontal plane. We characterize the fusion positions of the eyes across the oculomotor range by deriving simple trigonometric equations for the required torsion as a function of gaze direction and compute the iso-torsion contours yielding binocular fusion. Finally, we provide experimental evidence that eye positions in far-to-near re-fixation saccades indeed converge towards the predicted positions by adjusting the torsion of the eyes. This is the first report that describes the three-dimensional orientation of the eyes at binocular fusion positions based on the three-dimensional ocular kinematics. It closes a gap between the sensory and the motor side of binocular vision and stereoscopy.