Urist^5,6 suggests weakening or strengthening the horizontal rectus muscles, claiming that the medial rectus muscles are most effective in midline downgaze because this is the usual position for convergence. He further claims that the lateral rectus muscles are most effective in midline upgaze because divergence is usually accomplished by looking upward from the downturned near-seeing position to see something at distance. By appropriately recessing or resecting these muscles to alter their power, not only is the horizontal measurement in the primary position improved, but also, theoretically, the A and V patterns are improved. For example, an ET-V pattern is improved with recessions of the medial rectus muscles, an ET-A pattern with resections of the lateral rectus muscles, an XT-V pattern with recession of the lateral rectus muscles, and an XT-A pattern with resections of the medial rectus muscles.

Knapp²³ conceived the idea of vertical transposition of the insertions of the horizontal rectus muscles, proved its effectiveness, and popularized its usefulness in treating A and V patterns. He reasoned that vertical transposition of the insertions of the horizontal rectus muscles alters their scleral attachment relative to the rotation center of the globe, thus increasing the arc of contact of the transpositioned muscle in one vertical gaze position and decreasing it in the opposite vertical gaze position. Because the pull power of the muscle is related to the stretch put on it by the arc of contact, the horizontal pull power is enhanced and diminished in opposite vertical gaze positions, as compared with the unoperated horizontal rectus muscle. Hence, the horizontal rectus muscles become more effective abductors or adductors in the vertical gaze position opposite the direction in which their insertions are moved. Stated differently, the transpositioned horizontal rectus muscles become less effective horizontal rotators in the same vertical gaze position as the direction in which they are moved. For example, the infraplaced medial rectus muscles are more effective adductors in upgaze than in downgaze, or the supraplaced lateral rectus muscles are less effective abductors in upgaze than in downgaze. Therefore, an ET-V pattern is improved with either recessions and infraplacement of the medial rectus muscles or recession-resection on one eye, which also infraplaces the medial rectus muscle and supraplaces the lateral rectus muscle.

The directions in which the horizontal rectus muscle are transpositioned for A or V patterns associated with horizontal tropia are summarized in Table 1. The consensus seems to be that the usual quantity of transposition is half the width of the tendon. Although some surgeons perform total-width transplants, they experience greater unpredictable results in horizontal alignment in the primary position. Half-width tendon transpositions yield 15Δ to 20Δ change in the A or V pattern between upgaze and downgaze. Full-width transpositions produce more improvement, but the unpredictability of the horizontal correction in the primary position plus frequent limitation of duction in the field of action of the transpositioned muscle limits the usefulness of this quantity of surgery. Sharma and colleagues²⁴ concluded that a 5-mm shift was as effective as an 8-mm shift in monocular vertical displacement of horizontal rectus muscles in A and V patterns, even when mild or moderate cyclovertical muscle imbalance was present. However, in all cases with oblique muscle dysfunction, residual vertical incomitance was observed, and therefore, the authors recommended vertical shifting only when there was no associated cyclovertical muscle imbalance.

Vertical transposition of the horizontal rectus muscles may be performed symmetrically and bilaterally, or surgery may be confined to one eye, with appropriate vertical displacement of the medial and lateral rectus muscles.^1,25,26 The determination of the amount of horizontal surgery is the same whether or not monocular vertical displacement is performed,²⁷ even though Knapp²³ has suggested increasing the usual amount of horizontal surgery when vertically displacing the horizontal muscles. Postoperative torsional symptoms or significant torsional measurements have not been produced. Oblique muscle dysfunction associated with the A or V pattern is not changed by vertically offsetting the horizontal rectus muscles.

In a retrospective study of 67 patients, Scott and colleagues²⁸ reported an initial correction of 96%, within ± 10Δ of pattern. The standard horizontal rectus muscle surgery combined with half-width tendon offsetting surgery of the horizontal rectus muscles was shown to be an effective operation for collapsing all subgroups of the A- and V-pattern strabismus with appropriate indications. With A and V patterns without significant oblique dysfunction requiring surgery, the authors advocated standard horizontal surgery with half-width tendon offsets in A and V patterns from 10Δ to 30Δ. If the pattern exceeded 30Δ, they recommended three-fourths to full-tendon–width offsets combined with the standard horizontal rectus muscle surgery. When oblique muscle dysfunction was present, they recommended appropriate oblique muscle strengthening or weakening procedures along with appropriate horizontal or vertical rectus muscle surgery.