Biomechanics Explains Variability of Response of Small Hypertropia to Graded Vertical Rectus Tenotomy

Abstract

Purpose:

Small angle hypertropia in sagging eye syndrome is conveniently treated by graded vertical rectus tenotomy, yet adjustable technique under topical anesthesia has been recommended due to variability of effect. We performed graded tenotomy in an experimental model to elucidate the effect reason for variability of response to this surgical procedure.

Design:

Experimental study.

Methods:

32 fresh bovine rectus musculotendon specimens were prepared including continuity with insertional sclera, and extending for a total 40mm length to the proximal muscle bellies, and trimmed to 16mm width. Specimens were anchored by the clamps at the scleral insertion and muscle belly ends within a physiological chamber. After preconditioning and elongation to 10% strain was imposed by a linear motor, tensile force was allowed to stabilize at a plateau state. Then 25, 50, 75, 90, 100% marginal tenotomies were performed progressively as remnant forces were measured.

Results:

Tendon thickness averaged 0.29±0.05mm and width 19.71±2.25mm. On average, remnant force decreased linearly (R²=0.985) from 4.23±1.34, 2.76±0.88, 1.70±0.73, 1.01±0.49, 0.39±0.10, and 0 N, at 0, 25, 50, 75, 90, 100% tenotomy. However, there was marked individual variability in effect among specimens, with coefficient of variation 32, 32, 43, 49, and 27%, respectively.

Conclusion:

On average there is a linear relationship between graded rectus tenotomy and percentage force reduction, but the effect among individual tendons is large, paralleling the reported variation in surgical effect. This explains and implies continued advisability of adjustable technique in this procedure.

Precis:

On average, there is linear relationship between graded rectus tenotomy and percentage of force reduction, but significant individual variation in effect is explains the clinical advantage of adjustable technique for this procedure.

The sagging eye syndrome (SES) is an age-related connective tissue degeneration of the ligaments supporting the pulleys of the rectus extraocular muscles, particularly the lateral rectus (LR) pulley^{1, 2}. When inferior displacement (“sag”) of the LR pulley occurs asymmetrically, the eye having greater LR sag often exhibits a small hypotropia sufficient to produce vertical diplopia¹. Some degree of LR sag is the ubiquitous consequence of normal aging¹, but a large North American series reported that SES is the most common cause of new complaints of diplopia in people over age 50 years, and that about two-thirds of such diplopia involves vertical strabismus³. SES also occurs in Japanese ^{4, 5} and Korean populations^{4, 6}. While the small angle vertical strabismus in SES can be managed using spectacle prisms, the effectiveness of modern cataract surgery and intraocular lens implantation motivates many patients to strive for complete spectacle independence after undergoing these procedures by undergoing surgical correction of vertical strabismus as well. But, strabismus surgery for diplopia caused by vertical strabismus is unforgiving of even small under- or overcorrections. This discourages application of conventional vertical rectus recessions or resections for vertical strabismus that typically measures only a few prism diopters.

Graded vertical rectus tenotomy (GVRT) has recently emerged as a surgical technique useful to correct the small angle vertical strabismus typical of SES^7–9. This technique is performed by sharply dividing a fraction of the horizontal extent of a rectus tendon at its scleral insertion, and allowing the severed portion of the tendon to retract freely. While a rough quantitative relationship exists between the percent of the tendon divided, and the effect in prism diopters on vertical binocular alignment, the effect of the same amount of tenotomy cases can vary so widely in individual cases that it has been recommended that the procedure be performed under topical anesthesia with intraoperative monitoring of immediate effect⁷. But even though it is minimally invasive, not every patient with vertical strabismus caused by SES will tolerate strabismus surgery under topical anesthesia. Partial medial rectus tenotomy has also been employed for treatment of A and V pattern strabismus, but also produced variable responses to identical 75% dosing¹⁰.

Ideally, an understanding of the detailed biomechanical effects of GVRT might improve predictability of surgical outcomes. Despite the apparent simplicity of the GVRT procedure itself, attempts to understand it have been clouded by controversy about the fine structure and function of extraocular muscle and tendon fibers. It is recognized that extraocular tendons are comprised of parallel arrays of very stiff fibers¹¹. In theory, each of these fibers could independently transmit tensile force to the eye, with this independence limited only to the extent that other tissues bridging between the fibers might transmit a portion of force among neighboring tendon fibers. Ex vivo experiments in bovine tissues have indeed demonstrated that this transverse force coupling between parallel regions of extraocular tendon and muscle fibers is minimal during both passive application of external tension¹², and internally generated tension during muscle contraction¹³. Moreover, Z-tenotomy that divides all continuous extraocular tendon fibers demonstrates nearly zero residual strength attributable to transverse coupling among parallel tendon fibers¹⁴. These situations would appear directly applicable to GVRT, and if so, indicate that the tenotomy eliminates essentially all force application to the eye by the tendon fibers surgically divided, and leaving the force of the intact fibers essentially unchanged. This mechanical behavior is like that of isotropic rubber that was employed as a control material in experimental study of extraocular tenotomy¹⁴.

But some authors have argued that the foregoing locally independent observed behavior of extraocular muscle and tendon is impossible, or at least can only be minimal, mainly on the basis of microanatomical demonstration of connective tissues within and surrounding the muscles^{15, 16}. McLoon et al. also performed electrical stimulation of rabbit superior rectus muscles, demonstrating generation of detectable lateral force as much as 5-10% of the evoked longitudinal force¹⁵. If the mechanical coupling among adjacent extraocular muscle and tendon fibers is as significant in humans as contended by Miller, and McLoon et al., then the transverse force coupling might be an important contributor to the variability of GVRT.

The present biomechanical study aimed to resolve, at least in part, practical aspects of the foregoing controversy by determining in vitro determine the effect of graded rectus tenotomy in a large mammal having extraocular muscle and tendon anatomy comparable to human. The experiment consisted of application of fixed mechanical elongation (strain) to the extraocular muscle and tendon complex while performing incremental graded tenotomy analogous to the performance of GVRT for correction of vertical strabismus in human patients.

Materials and Methods

Specimen Preparation.

Shortly after slaughter at an abattoir (Sattar Farm, Bakersfield, CA, USA), we obtained 2 fresh and 2 frozen bovine heads aged 20 to 30 months that were transported to the laboratory while chilled on ice. Further preparation of specimens was done in the laboratory. First the globes and adnexa were exenterated and maintained hydrated using lactated Ringer’s solution. Each rectus muscle specimen consisted at the anterior end of a patch of sclera in continuity with the tendon insertion, and at the posterior end of the anterior muscle belly with overall length at least 40 mm, and width 16 mm, with long dimension size paralleling tendon fiber direction (Fig. 1). As illustrated in Figure 1 that shows every specimen tested, insertional ends of each tendon appeared quite similar among the four rectus muscles, although specimen lengths varied modestly according to the maximum length of contiguous muscle belly removed from the orbits. The 16 mm maximum widths of the load cell clamps exceeded the maximum widths of the insertional tendons and muscle bellies, so the anatomical dimensions of both were maintained intact.

Figure 1.

Specimen preparation. A. Exenteration site. B. Exenterated globe and adnexa. C. Rectus musculotendons in continuity with sclera. D. Six specimens of each anatomical musculotendon, with attached scleral patch incorporating the insertion of each. A total of 32 such specimens was tested.

Experimental Procedure.

Specimen dimensions were measured using a digital caliper (Mitutoyo Co., Kawasaki, Japan). As previously described^17–19, the load cell containing the specimen included in a humidified chamber maintained at about 37° C, over a heated water bath by thermocouple feedback control. The terminal end of the muscle belly of each specimen was placed in a custom machined compression clamp that was fixed structurally to the load cell. The sclera of the tendon end of the specimen was similarly clamped to a moving rod that passed out of the environmental chamber via a frictionless air bearing to sensitive force sensor with 0.1% error in-line with a linear motor incorporating a precise digital position sensor (Ibex Engineering, Newbury Park, CA, USA). Specimens were continuously moistened during the experiment by drip application of warmed Ringer’s lactate (Fig. 2). Using closed digital feedback control, tissues were elongated until the force sensor indicated 0.02 N as the preloading condition. Then, 6 cycles of 5% preconditioning were performed, followed by elongation to 10% strain, after which the elongation was maintained during continuous monitoring of resulting tensile force decline during stress relaxation. After stress relaxation to an approximately asymptotic value, graded tenotomy was sequentially and incrementally performed using a scalpel beginning at one tendon margin, in cumulative amounts of 25%, 50%, 75%, and 90%. The extent of each tenotomy was determined by caliper measurement. After each tenotomy, force was permitted to relax to an approximately asymptotic value before performance of the next increment of tenotomy. This approximates the surgical performance of GVRT.

Figure 2.

Rectus musculotendon specimen clamped in the load cell, as it was subjected to graded tenotomy from the bottom margin from zero to 100%. The muscle belly was fixed in the clamp at right, while tension was applied by the moving clamp at left that also measured tension. The plastic tube provided a constant drip of warmed Ringer’s lactate solution to maintain hydration.

Statistical Analysis was performed using GraphPad Prism version 9.4.1 (GraphPad Software, San Diego, CA, USA). The experiment was not designed or powered to investigate possible quantitative differences among the four anatomical rectus muscles.

Results

A total of 32 tendons were tested, including all of the rectus muscles in both orbits of each of the 4 bovine heads. Tendon thickness averaged over all specimens was 0.29 ± 0.05 mm and width was 19.7 ± 2.2 mm (Table 1). The inferior rectus tendon was thickest and the lateral rectus tendon thinnest. The widths are also the widest in inferior rectus tendon. However, analysis of variance demonstrated no significant differences in thickness or width among the groups (P=0.55, P=0.93, respectively).

Table 1.

Average Rectus Tendon Dimensions

Tendon	Inferior	Superior	Medial	Lateral	All
Thickness mm	0.31 ± 0.06	0.29 ± 0.07	0.29 ± 0.04	0.27 ± 0.01	0.29 ± 0.05
Width mm	20.2 ± 2.7	19.6 ± 1.8	19.5± 2.3	19.6 ± 2.0	19.7 ± 2.2

Progressive tenotomy caused the divided tendon fibers to retract towards the fixed clamp (Fig. 2B-E), although this reraction was greatest for fibers at the tendon margin, and least for fibers at the most central end of the incision. Tensile force data from a representative experiment are illustrated in Figure 3. Initial tensile force was cyclically increased and decreased 6 times to perform preconditioning, the process of releasing residual stress that remains in an unloaded organ following specimen preparation.^{20, 21} After preconditioning, the linear motor elongated the specimen an additional 10% of its initial length, causing tensile force in the specimen to incrase abruptly (Fig. 4). However, due to stress relaxation in the muscle belly, this force declined in approximately exponential fashion over tens of seconds. When tensile force decreased to approximately equilibrium value (Fig. 4), the first tenotomy, 25% of tendon width, was performed using a scalpel at the muscle margin (Fig. 2B). Tensile force again declined in approximately exponential fashion until reaching a new equilibrium value (Fig. 3), after which the tenotomy was increased to a total of 50% of tendon width (Fig. 2C). This process was repeated to reach 75% (Fig. 2D) and 90% tenotomy (Fig. 2E), and finally 100% tenotomy (Fig. 2F) as a control to verify return of tensile force to zero when the tendon was completely divided (Fig. 4).

Figure 3.

Time series of tensile force in inferior rectus musculotendon specimen 7 during graded tenotomy, representative of all specimens. Six cycles of preconditioning were performed to release residual stress from specimen preparation. The specimen was then rapidly elongated by 10% strain, causing a rapid increase in tensile force that gradually declined over about 400 s to reach a relatively stable equilibrium level. Marginal tenotomies were then incrementally performed from one tendon edge, and new equilibrium tension was recorded for each tenotomy. Application of the scalpel blade caused a transient increase in tension during each tenotomy.

Figure 4.

Relative remnant force following graded rectus tenotomy Average values are shown in black, and individual tendon data in gray. A. Data for all 24 musculotendons demonstrated a highly linear reduction in relative remnant force with progressive tenotomy (black line), with coefficient of determination R²=0.985. However, responses of individual musculotendons were often highly nonlinear (gray lines). Date for each anatomical musculotendon are illustrated in panels B – E.

For the same 10% initial strain, tensile force varied among anatomical rectus muscles, as well as among individual specmens of the same muscles, as listed in Table 2. Also variable was the relative response to the same tenotomy. A striking example of the variability is seen in Fig. 4 for 25% tenotomy, where one specimen maintained 90% residual force, and another less than 10%. The coefficient of variation (CV), defined as mean divided by standard deviation, of initial tensile force was about 0.32. In order to avoid confounding by this variability, statistical analysis was performed based on the percentage of remnant tensile force at equilibrium following each incremental tenotomy. As seen in Fig. 4A, this percentage remnant force was by definition 100% with zero tenotomy, and decreased monotomically with increasing cumulative tenotomy. However, for individual specimens, the decrease in remnant force typically declined in highly nonlinear fashion, for example in some cases hardly at all for the first 25% tenotomy, and in other cases nearly to zero remnant force (Fig. 4A). However, on average, remnant force declined quite lineraly with percent tenotomy, with a slope of −0.0095 (95% CI, −0.0111 to −0.0079) and 0.985 coefficient of determination for linear regression fit (P<0.001). This average slope does not differ significantly from the ideal value of −1% (P>0.91). Figure 4B illustrates the same behavior for each of the four rectus tendons.

Table 2.

Initial and Maintenance Forces After Tenotomy (Newtons)

Specimen	Tenotomy	1	2	3	4	5	6	7	8	Average	SD	CV (%)
Inferior	0%	2.47	0.32	0.82	2.33	1.23	1.04	5.93	3.18	2.16	1.68	78
	25%	1.88	0.16	0.60	1.55	0.69	0.83	4.47	2.46	1.58	1.30	82
	50%	1.70	0.12	0.36	1.21	0.52	0.45	1.89	0.71	0.87	0.61	70
	75%	1.29	0.08	0.07	1.04	0.43	0.18	0.54	0.36	0.50	0.42	84
	90%	0.66	0.06	0.04	0.48	0.34	0.07	0.12	0.27	0.25	0.21	84
	100%	0	0	0	0	0	0	0	0	0	---	---
Lateral	0%	5.84	2.60	5.68	3.13	2.58	7.57	2.95	16.83	5.90	4.48	76
	25%	0.62	0.82	4.94	1.24	1.73	5.84	2.41	13.76	3.92	4.13	105
	50%	0.37	0.44	4.73	0.44	1.18	4.00	1.80	8.84	2.73	2.79	102
	75%	0.19	0.29	3.08	0.40	0.51	2.85	1.21	5.19	1.71	1.70	99
	90%	0.06	0.24	0.89	0.27	0.32	0.04	0.47	2.03	0.54	0.62	114
	100%	0	0	0	0	0	0	0	0	0	---	---
Superior	0%	1.75	1.96	4.09	4.45	8.83	3.28	10.62	1.31	4.54	3.20	71
	25%	1.08	1.51	2.90	1.99	2.98	0.89	6.73	0.68	2.34	1.85	79
	50%	0.26	1.31	1.89	0.90	1.05	0.67	3.11	0.25	1.18	0.89	75
	75%	0.15	1.29	0.89	0.71	0.69	0.56	0.45	0.13	0.61	0.36	59
	90%	0.09	1.21	0.30	0.22	0.44	0.37	0.12	0.09	0.36	0.34	96
	100%	0	0	0	0	0	0	0	0	0	---	---
Medial	0%	1.23	6.29	3.05	1.25	0.33	9.11	8.59	4.72	4.32	3.19	74
	25%	0.98	3.94	2.13	0.81	0.24	8.80	5.24	3.42	3.19	2.66	83
	50%	0.75	2.03	1.50	0.30	0.18	6.85	2.27	2.34	2.03	1.99	98
	75%	0.64	0.87	1.18	0.13	0.12	5.20	1.01	0.66	1.23	1.54	126
	90%	0.46	0.48	0.12	0.04	0.08	1.34	0.65	0.22	0.43	0.40	95
	100%	0	0	0	0	0	0	0	0	0	---	---

SD: standard deviation, CV: coefficient variation

Discussion

The biomechanical findings of this experimental study were consistent for each of the four anatomical of bovine rectus extraocular musculotendons: graded marginal tenotomy near the scleral insertion produces, on average, a linearly proportionate reduction in tensile force applied to the sclera. This is the effect that occurs when a linearly elastic material, such as rubber, is subjected to progressive cutting in the identical manner¹⁴, and would occur if there were complete lateral coupling among all adjacent fibers of extraocular tendon, an extreme extrapolation of the effect much more modestly demonstrated by McLoon et al¹⁵. In contrast to the average results based on testing of dozens of specimens, however, there was marked variability among individual specimens in the proportionate effect of graded tenotomy. In some specimens, as little as 25% tenotomy reduced remaining tendon force by only around 10%, while in others, force was reduced by as much as 90%. The large individual variability in the effect of graded tenotomy confirms that individual regions of extraocular tendons and muscles can transmit widely different forces to the sclera, and that this wide variation seems consistent with the clinically-observed wide variation in surgical effect of GVRT in treatment of vertical strabismus⁷. Whatever connective tissues may exist to bridge adjacent extraocular muscle and tendon fibers, as we have pointed out in other contexts^{22, 23}, these tissues functionally do not preclude substantial mechanical independence of the fibers.

While the current study does not identify the origin of the wide variation in effect of graded tenotomy, several causes seem possible. One likely cause in the in vitro situation is local differences in preloading of fibers by initial tension, such that some fibers may be initially more taut, and others more slack as the initial condition. While rectus tendons remain flat in the load cell clamp, their connected myofibers fibers in the contiguous muscle curve as the muscle progressively thickens posteriorly. This means that many fibers inevitably have different lengths after exenteration and clamping in the load cell. Although the overall specimen was elongated to 10% strain, the local strain in shorter parallel fibers in the muscle would have been bearing more of the load and generating greater tension, while longer parallel fibers would have been bearing less of the load and generating less tension. Tenotomy of the slacker fibers would produce less effect on overall muscle tension than tenotomy of shorter, tight fibers; such a phenomenon could occur both experimentally and physiologically. In this experiment, the curved sclera was flattened in the load cell clamp, which would tend to tighten tendon fibers at the lateral specimen edges relative to the center. The resulting effect would tend to increase the relative contribution of lateral tendon fibers to overall tension, but the overall data of Fig. 4 do not demonstrate a greater effect of the initial 25% tenotomy that would be expected if scleral flattening were a significant factor.

The current ex vivo experiment captures only passive biomechanical behavior of extraocular muscle and tendon. In the living situation, regional differences in tension across the tendons are also anticipated due to compartmental differences in extraocular muscle tension. In particular, differential compartmental contractility in the medial compartment of the inferior rectus muscle has been demonstrated by magnetic resonance imaging to contribute to vertical fusional vergence ²⁴. In patients with large vertical heterophoria, this differential compartmental contractility in the selectively innervated lateral compartment of the inferior rectus muscle drives vertical fusional vergence that prevents strabismus²⁵. It is possible that additional physiological or pathological variations in rectus muscle tensions might also contribute to the variability of clinical response to GVRT.

This in vitro study has limitations. It was performed in post-mortem animal tissue, which cannot reflect all of the properties of living human tissue; however, there is no practical alternative way to study the biomechanical properties. Bovine extraocular muscle and tendon are structurally similar to human in nearly all respects. Temperature and humidity may have varied modestly from physiologic despite our efforts to control both. The behavior of some specimens may have been altered by temperature conditions during slaughter and transportation, including possible freezing of some heads; however, the findings supporting our conclusions were similar in fresh and frozen specimens.

The clinical implication of this study is nevertheless clear: the quantitative effect on extraocular force applied to the eye, and thus the effect on binocular alignment, can only be roughly approximated by the proportionate amount of GVRT. This means that surgeons performing fixed doses of GVRT for treatment of small angle vertical strabismus in SES must accept relatively unpredictable alignment results. A better approach remains the technique of adjustable dosing of GVRT to effect under topical anesthesia⁷. This method can effectively compensate for the inherent variation in force distribution across extraocular tendons, and provide satisfactory clinical results.

Biographies

Joseph L. Demer, M.D., Ph.D.

Leonard Apt Professor of Ophthalmology, Stein Eye Institute, Professor of Neurology, University of California, Los Angeles

Joseph L. Demer, M.D., Ph.D. is Division Chief and holds the Arthur L. Rosenbaum Professorship of Pediatric Ophthalmology and Strabismus at the Stein Eye Institute, David Geffen School of Medicine at UCLA. He is Professor of Neurology and chairs the EyeSTAR Residency-PhD Program. In 2003, Dr. Demer received the Friedenwald Award from ARVO, and a Recognition Award from the Alcon Research Institute in 2004, for his work on the extraocular muscles and orbital connective tissues.

Changzoo Kim - Biosketch

Changzoo Kim, MD, Ph.D. is assistant professor at department of Ophthalmology, College of Medicine, Kosin University, South Korea. His subspecialty is strabismus and pediatric ophthalmology. Now at the University of California, Los Angeles the Ocular Motility Laboratory, he studies eye movement and biomechanics of ocular tissue.