THE IMPROVEMENT OF
STRABISMUS
SURGERY
THE ROLE OF THE SUSPENSION OF
THE HUMAN EYE
Y
The Improvement of Strabismus Surgery
The Role of the Suspension of the Human Eye
The Improvement of Strabismus Surgery
The Role of the Suspension of the Human Eye
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op vrijdag 1 november 2013 om 12.30 uur
door
Sander SCHUTTE
Master of Science in Biomedical Engineering geboren te Harderwijk.
Dit proefschrift is goedgekeurd door de promotoren:
Prof. dr. F.C.T. van der Helm, Technische Universiteit Delft
Prof. dr. H.J. Simonsz, Erasmus MC Rotterdam
Samenstelling promotiecommisie:
Rector Magnificus, voorzitter
Prof. dr. F.C.T. van der Helm, Technische Universiteit Delft, promotor
Prof. dr. H.J. Simonsz, Erasmus Universiteit Rotterdam, promotor
Prof. dr. ir. F. van Keulen, Technische Universiteit Delft
Prof. L. Tychsen, Washington University School of Medicine, St. Louis, Missouri
Prof. dr. J.R. Vingerling, Erasmus Universiteit Rotterdam
Prof. dr. H. Kingma, Universiteit Maastricht
dr. ir. C.W.J. Oomens, Technische Universiteit Eindhoven
Prof. dr. ir. P.P. Jonker, Technische Universiteit Delft, reservelid
ISBN: 978-94-6203-464-8
Copyright c 2013 Sander Schutte.
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without writ-ten permission from the copyright owner. Printed by CPI Wöhrmann Print Service.
Contents
Chapter 1General Introduction 1
Chapter 2
Human Error in Strabismus Surgery: Quantification with a Sensitivity Analysis 7
Chapter 3
Inaccuracy in the surgical procedures for strabismus and avenues for improvement 29
Chapter 4
Orbital Soft Tissue Biomechanics 67
Chapter 5
A Finite-element Analysis Model of Orbital Biomechanics 85
Chapter 6
Chapter 7
Mechanical properties and functional importance of pulley bands or ‘faisseaux
tendineux’ 117
Chapter 8
Mechanical Behavior of Orbital Fat Derived from Imaging Data 133
Chapter 9
Discussion and future directions 153
Bibliography 163
Summary 177
Samenvatting 181
Dankwoord 185
1
General Introduction
General Introduction
The goal of this thesis is to investigate the causes of the large number of reoperations in strabismus surgery, and to investigate avenues for improving its treatment.
Strabismus (cross-eyedness) is a condition in which the patients’ two eyes do not fixate at the same point. Only one eye fixates at a target and the other eye has either a systematic deviation in all directions of gaze, or a deviation that varies with the direction of gaze and with the fixation distance.
The reported prevalence of strabismus ranges from 2% to 5% (Abrahamsson et al. 1999; Greenberg et al. 2007) in children. Young children with strabismus often develop amblyopia (lazy eye) and impaired stereopsis (binocular depth perception).
In healthy subjects, the retinal images of both eyes are projected into the same area in the visual cortex. The difference between the images of the eyes (binocular disparity) results in one of the control signals that determines the position of the eyes. Strabismus has causes at several levels in this control system. The most common cause is a deficit in the brain, for example when the brain lacks the ability to develop binocular vision and stereopsis from birth (e.g. congenital esotropia). Refractive errors can also cause strabismus at this level (accommodative esotropia): the patient is accommodating to correct the refraction of the eye to get a sharp image, inducing strabismus. Strabismus can also be caused at a neurological level. E.g. a lesion of one of the cranial nerves III, IV or VI can hamper one eye to make specific eye movements. Finally, strabismus can also have a mechanical cause, a tumor that grows inside the orbit, for instance, can change the biomechanics of the eye-muscles.
1.1
The surgical treatment of strabismus
Strabismus is usually treated surgically and the increase in quality of life after successful surgery is generally considerable (Durnian et al. 2011). Although the root cause of many cases of strabismus lies in the neural control, its surgical treatment is aimed at altering the biomechanics. In the Netherlands, this procedure is carried out approximately 150 times per week. The treatment goals for strabismus surgery in adult patients are to alleviate double vision (diplopia) and to improve cosmetics. In children, the treatment goals are to preserve binocular vision in worsening or recent-onset strabismus and to improve cosmetics. Binocular vision may be preserved if the eyes are aligned, which can result in better stereopsis (Simonsz et al. 2005).
Most strabismus operations are corrections of horizontal eye position by relocating the insertion of one eye muscle on the eye a few millimeters backwards (recession) and resecting
the tendon of its antagonist (resection). The amount of recession and resection depends on the angle of strabismus: Larger angles need more muscle displacement. Binocular vision may be preserved or enhanced if the eyes are aligned. If a patient has good binocular vision, he may be able to correct an undercorrection after surgery. As the chance of diplopia is larger after an overcorrection, patients are systematically undercorrected (Donahue 2007).
1.2
Variability in the surgical outcome
Patients who are overcorrected or severely undercorrected are usually operated upon a second time. Due to scar tissue and wound healing, the result of a second or third operation is more difficult to predict. The number of reoperations within a group of patients primarily depends on the variance of the postoperative angle of strabismus within that group. The re-operation rate for infantile esotropia, a common type of strabismus, is approximately 20% (Simonsz et al. 2009, Fig. 11.5) when the child is first operated at age of four, but higher when the child is first operated at an earlier age. The variances in each consecutive step of the procedure add up to the overall error, represented by a deviation of the intended angle of strabismus. The overall variance is represented by a variance of the postoperative angle of strabismus (for a group of patients). The size of the variance of the postoperative angle of strabismus primarily determines the percentage of reoperations.
1.3
Challenges in the current surgical treatment
Although many technical improvements have been made the last century in healthcare e.g. in the quality of procedures, training of surgeons and improvements in equipment, little has changed in strabismus surgery. The main two developments that have made it to clinical practice since the introduction of eye muscle surgery in 1839 are adjustable suture surgery and use of botulinum toxin to weaken the muscles. The results of these new treatments are similar to those of conventional surgery (Rowe and Noonan 2012; Sundaram and Haridas 2005).
Most studies that target improving the treatment of strabismus target only one or two effects in the procedure. For instance, the effect of placing a third suture between the two others (Roth and Speeg-Schatz 2001), a more accurate surgical measurement procedure (Clark and Rosenbaum 1999) or taking the influence of the length of the globe into account (Kushner et al. 1989). As errors occur in all of the steps that comprise a surgical procedure, and these together determine the variation in its outcome, statistical power for analysis in these studies is often insufficient. Also, a quantitative comparison between surgical procedures is difficult due to the many confounding factors. Variability is introduced in the following four stages in the surgical trajectory. The focus of this thesis was on asses the problems in each of these steps and to investigate avenues for improvement.
Figure 1.1: A box of prisms that is used to carry out a prism cover test. This test is the current golden standard for assessing the angle of strabismus.
1. Preoperative assessment In the preoperative assessment, orthoptists and ophthal-mologists diagnose the patient and decide for a surgical plan. An important mea-surement is that of the angle of strabismus in different directions of gaze in near and distant fixation. This is usually carried out with a prism cover test (Fig. 1.1). The accuracy of this test and how it affects the surgical outcome is unknown. In addition, there is variability between ophthalmologists and orthoptists in deciding what eye muscles to operate upon, and how much surgery is required. These factors and their effect have never been quantified.
2. Eye muscle surgery The surgical procedures for strabismus are carried out with varying degrees of accuracy. Variability in recession and resection surgery may exists within a surgeon, and between surgeons (Lipton and Willshaw 1995). A surgeon may have developed the habit of always putting a third suture between the two other sutures, for example. In planning for surgery, these idiosyncrasies are taken into account, consciously or unconsciously, and the planned amount of recession may be tailored to a particular surgeon. During surgery also random errors occur, due to measurement accuracy, tightening of the sutures etcetera. It is unknown how surgical accuracy affects the reoperation rate and how the surgical accuracy could be improved.
3. Variability in anatomy and physiology Strabismus surgery aims at changing the equilibrium position of an eye by adjusting the location of the insertion of eye muscles. The effect (the angular change of the eye per millimeter of eye muscle relocation)
depends on the individual biomechanics of the patient. If, for instance, the passive rotational stiffness of the eye of a patient is above average, the patient would need an above average displacement of the eye muscles to achieve a similar effect. Orbital biomechanics depends on many of the factors like the geometrical shapes of the tissues, their material properties and their mechanical interactions. The role of these factors in strabismus surgery is largely unknown. For improving strabismus surgery, understanding of the soft tissue biomechanics and the suspension of the eye in the orbit is paramount.
4. The postoperative phase Variability can also be introduced in the postoperative phase. In patients with binocular vision, it could improve the postoperative align-ment. Also, wound healing and the development of scar tissue might be different in patients.
In this thesis we will investigate error sources in the first three categories. The goal is to investigate the causes of the large number of reoperations in strabismus surgery, and to investigate avenues for improving its treatment. The research questions that were studied:
• What are the important anatomical and physiological determinants in the suspension of the human eye and how do they affect strabismus surgery?
• What are the causes of the high re-operation rate in strabismus?
• How can we improve the predictability of the surgical outcome for strabismus?
1.4
Approach and outline of this thesis
To quantify the influence of error sources in the surgical trajectory we made a statistical model of the trajectory, including preoperative and postoperative examinations (Chap-ter Two). Each of the errors in the trajectory was quantified with clinical assessments: measurement of the angle of strabismus, surgical strategy and surgical accuracy. A sen-sitivity analysis of the model identified the primary factors that influence the outcome of strabismus surgery. In Chapter Three, we investigated accuracy of common surgical techniques and procedures for strabismus. Our goal was to provide a framework for the analysis of surgical procedures and methods, and to get insight in the effect of changing certain tasks or methods within the procedures. In Chapter Four we present an overview of the main determinants of the soft-tissue biomechanics in the human orbit. To investigate the mechanical factors, we employed a continuum mechanics simulation approach using the finite-element method. Chapter Five describes this model in detail. In contrast to
previous (lumped) models, this model enables simulation of complex three-dimensional ge-ometries, anisotropic and inhomogeneous material properties, tissue interactions and load cases. This does, however require detailed data on the material properties of the orbital structures. In Chapter Six we describe our measurements of the elasticity and viscosity of orbital fat of both orbits of four calves and one rhesus monkey. A slightly controversial subject in the field of orbital biomechanics is that of the ‘pulley bands’ (Demer 2002; Tenon 1816). The pulley bands are connective tissue bands between the muscle belly and the orbital wall. To decide if we needed to consider these bands in modeling, we studied their mechanical properties (Chapter Seven). One of the biomechanical determinants of the effect of strabismus surgery is the passive rotational stiffness of the eye. If this stiff-ness is higher, the required amount of recession and resection is larger. In Chapter Eight we present a non-invasive method to assess the passive rotational stiffness from imaging data. Finally, in Chapter Nine we present a general discussion and future directions for strabismus surgery.
2
Human Error in Strabismus Surgery:
Quantification with a Sensitivity Analysis
Sander Schutte1, Jan Roelof Polling2
, Frans C.T. van der Helm1
, Huib J. Simonsz2
1 Department of BioMechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, the Netherlands
2 Department of Ophthalmology, Erasmus Medical Center, Rotterdam, the Netherlands
Abstract
Background Reoperations are frequently necessary in strabismus surgery. The goal of this study was to analyze human-error related factors that introduce variability in the results of strabismus surgery in a systematic fashion.
Methods We identified the primary factors that influence the outcome of strabismus
surgery. For each of the human-error related factors we quantified variation with clinical assessments: measurement of the angle of strabismus, surgical strategy and surgical accu-racy. Firstly, six patients were examined by six orthoptists and accuracy of prism cover tests was assessed. Secondly, a questionnaire with sample cases (10◦
, 15◦ and 20◦
of infantile esotropia) was put to orthoptists and ophthalmologists to determine variation in current surgical strategy. Finally, photographs made during surgery were analyzed to assess surgi-cal accuracy. The influence of human-error related factors was related to the influence of inter-patient differences with a mechanical model. The relative contribution of all factors was assessed with a sensitivity analysis and results were compared to clinical studies.
Results The surgical trajectory of strabismus surgery could be modeled mathematically. Measurement of angle of strabismus, surgical technique, anatomy and physiology were considered. Variations in the human-error related factors were: (1) The latent angle at distant fixation was measured with a 90% confidence interval of 5◦and comprised 20% of the total variance of the postoperative angle (2) orthoptists decided for bilateral re-cessions of, respectively, 7.3±1.7mm (total amount of two rere-cessions), 9.1±1.2mm and 10.3±1.3mm, which comprised 15% of the total variance. (2) Surgical accuracy was estimated at ±0.5mm, which comprised 20% of the total variance.
Conclusion The human error in strabismus surgery could be quantified with a sensitivity analysis. Approximately half of the reoperations in strabismus surgery are caused by inac-curacy in the measurement of the angle of strabismus, variability in surgical strategy and imprecise surgery.
2.1
Introduction
Strabismus occurs in approximately 4 percent of the population (Abrahamsson et al. 1999; Greenberg et al. 2007) and is usually corrected by surgery. In the Netherlands, this is done approximately 150 times per week. Most of these operations are corrections of horizontal eye position by relocating the insertion of one eye muscle on the eye a few millimeters backwards (recession) and resecting the tendon of its antagonist (resection).
The treatment goals for strabismus surgery in adult patients are to alleviate double vision (diplopia) and to improve cosmesis. In children, the treatment goals are to preserve binoc-ular vision in worsening or recent-onset strabismus and to improve cosmesis. Binocbinoc-ular vision may be preserved if the eyes are aligned, which can result in better stereopsis (Si-monsz et al. 2005). In general, the practical goal of strabismus surgery is to straighten the eyes within 5◦
of perfect alignment (Donahue 2007). This, however, is often not achieved. In a recent study among children with infantile esotropia, Polling et al. (2009) found that the angle of strabismus was reduced by 1.44 degrees per millimeter of eye-muscle relo-cation (either recession of resection), with a standard deviation of 0.41, however. This means the coefficient of variation was 29% in that study. The large variance in the effect of surgery indicates that the outcome of surgery is unpredictable to some extent. The variance in the effect of surgery results in reoperations (Fig. 2.1); patients who are overcorrected or severely undercorrected are usually operated on a second time. The re-operation rate for infantile esotropia, a common type of strabismus, is approximately 20% (Simonsz et al. 2005) when the child is first operated at age of four, but may be higher when the child is first operated at an earlier age. The proportion of reoperations primarily depends on the variance of the postoperative angle of strabismus. As the chance of diplopia is larger after an overcorrection, patients are systematically undercorrected.
From a process engineering point of view, the variance in the effect of surgery is caused by a number of error sources in the surgical process. The variance propagates through the surgical process and finally becomes visible in the postoperative angle of strabismus. Additional variance is introduced by the fact that patients may respond differently to the same operation because of differences in anatomy and physiology of eye muscles or orbit. In the preoperative assessment, the patient’s angle of strabismus is measured in various directions of gaze. The horizontal, latent angle of strabismus (measured in gaze ahead and at distant fixation) is usually regarded as the most important in deciding on what eye muscles to operate on. The measurements by orthoptists are subject to intra-patient variation, variation of the angle of strabismus during the day, and by inter- and intra-observer variation. The latter two consist of systematic and random errors.
postoperative ACT at 5m. probability 0% 5% 10% 15% 20% 25% 30% -10° -5° 0° 5° 10° 15° 20° 25°
Figure 2.1: The empirical probability density of the postoperative angle of strabismus (N=112) as was found in a study comparing bilateral recession with recession-resection in infantile esotropia (Polling et al. 2009). The red line shows the chance of a reoper-ation given the postoperative angle of strabismus as was found in a retrospective study (Van de Vijver-Reenalda et al. 1999). In this study all patients that were operated during one year, in a number of clinics, were contacted to assess their reoperations. If the variability of the postoperative angles is reduced, the number of reoperations decreases. The angles smaller than -3◦
and larger than 6◦
, are responsible for over 50% of the reoperations. As the chance of diplopia is larger after an overcorrection, patients are systematically undercorrected.
After the preoperative orthoptic assessment, a surgical plan is formulated which consists of a decision for the eye muscles to be operated upon, the surgical technique to be used and the amount of muscle displacement that is needed. The surgical plan is based primarily upon the measured angles of strabismus. However, other non-deterministic factors play a role such as duration or nature of the strabismus (Von Noorden and Burian 1985). The goal of the surgical plan is to achieve the optimal postoperative result for individual patients. However, the surgical plan may be subject to variance in the surgical approach or in the planned amount of recession and/or resection. Surgeons’ approaches may vary, but also within one surgeon, an approach might be adjusted to individual patients. Accuracy of the surgical technique is limited as the actual amount of muscle displacement may well be different from the intended amount. This can be caused by measurement errors, variance in placement and tightening of the sutures and sagging of muscle tendon between the two points of attachment.
The change in the angle of strabismus by a given relocation of the eye muscle insertions may vary between patients, depending on anatomy and physiological properties. Eye muscle stiffness, for instance, varies among patients and is usually not taken into account when making the surgical plan. This factor therefore causes variability in the surgical outcome. It is unknown, however, to what extent. In the recovery phase after surgery, amorphous connective tissue develops (Ludwig and Chow 2000) because tissue is damaged during surgery. It is insufficiently known how wound healing of the eye muscles after strabismus surgery affects their mechanical properties. Possibly also the number of sarcomeres, the contractile element of the muscles, is reduced after a recession operation to adapt to the shorter muscle length (Goldspink et al. 1974; Hayat et al. 1978; Mims III et al. 1985). Both effects are likely to be subject to inter-patient variation.
Finally, the result of surgery is influenced positively by binocular vision. If a patient has good binocular vision, he is able to correct a small strabismus that may remain after surgery. Conversely, binocular vision is only possible if the eyes are aligned. In the randomized controlled trial of Polling et al. (2009) among children without binocular vision, a third had gross binocular vision after surgery. These children had better ocular alignment, which may have been either its cause or its consequence. As the exact influence of binocular vision has not yet been quantified, we restricted our analysis to the large group of patients with little or no binocular vision.
To investigate how we can improve the effectiveness of strabismus surgery, we have to study the sources of variability in the surgical trajectory and investigate their influence on the outcome of surgery. If the most influential source of variability, for instance, is surgical accuracy, devices are needed to increase surgical accuracy. If, on the other hand, muscle stiffness shows to be an important determinant for the outcome of surgery, this should be measured and taken into account when deciding on the surgical plan. Goal of this study was quantification of the human-error related factors in strabismus surgery.
2.2
Materials and Methods
We determined the relative contribution of error sources to variability in the effect of strabismus surgery. In a focal group, an assessment was made of all error sources present in strabismus surgery. To relate the error sources to the postoperative angle of strabismus, a mathematical model of the process of strabismus surgery was derived. We carried out a sensitivity analysis on this model to estimate the fraction of reoperations caused by each of the error sources.
The model required input data for each of the error sources. Three of the error sources that were related to human error were studied in detail in clinical assessments. Firstly, the variance in the measurement of the angle of strabismus with the prism cover test was determined. Secondly, the variance in the selection of the surgical plan was assessed with a questionnaire. Thirdly, the accuracy of relocating the eye muscles during surgery was estimated. Finally, a comparison was made with clinical studies in order to validate the model.
Clinical assessment of the variance in the measurement of the
angle of strabismus
We determined whether orthoptists can measure the angle of strabismus in a patient with sufficient accuracy. Six orthoptists from three university eye clinics were asked to measure angles of strabismus in six patients. All orthoptists had more than five years of experience in three of the academic clinics of the Netherlands. Oral informed consent was obtained from the participating patients. The patients were examined by all orthoptists in a predefined, randomized, order. The orthoptists were not able to exchange information in any way. None of the patients had been examined by any of the participating orthoptists before. Only general information about the patient was supplied: date of birth, glasses worn, visual acuity, refractive error, previous strabismus surgery and the use of medication. Horizontal and vertical, latent and manifest angles of strabismus were measured during fixation at near and at distance fixation using prism cover tests.
Accuracy of the measurements was quantified as standard deviation of the measurements of the orthoptists for each type of measurement. The standard deviations of the four types of measurements of horizontal and vertical angles were compared with a statistical F-test (Snedecor and Cochran 1989). We used a one-tailed test with a significance level of 5%. To be able to perform this test on all measurements of one type (e.g. the manifest angle in distant fixation) the 36 measurements of one type were grouped. To compare variance between measured angles, the average of the six measurements of one type of measurement
on a patient was subtracted from every measurement on that patient such that the mean of all measurements became zero. Next, standard deviations of the groups were compared with the other groups. We compared all four types of horizontal measurements to all four types of vertical measurements. Within the horizontal and vertical measurements we compared every type of measurement to the three other types of measurements.
Clinical assessment of the variance in surgical strategy
The measured angle of strabismus is the main determinant in deciding on the surgical plan. We investigated variability of the surgical strategy by distributing a questionnaire during the annual meeting of the society for Dutch strabismologists and orthoptists. The ques-tionnaire described three sample patients with infantile esotropia. Each sample patient was a three-year-old with infantile esotropia without binocular vision and with average glasses (S+1/S+1). Case 1 had an angle of strabismus of 10◦(measured with an alternating prism cover test at 5 m). Case 2 had an angle of strabismus of 15◦
. Case 3 has an angle of strabismus of 20◦. Orthoptists were asked to decide on the distance of relocation of the eye muscles for each of the patients. After 10 minutes the completed questionnaires were collected, also under strict supervision.
The main outcome parameter was the variance in the prescribed amount of surgery in millimeters of surgery for either bilateral recession (BR) or recession resection (RR). Note that this is the variance in the decision-making process, because all orthoptists had the same data available. Part of the variability is caused, however, by adaptation to the systematic errors during surgery by a particular surgeon. Differences in total amount of prescribed surgery between BR and RR were analyzed with the Student’s t-test with a significance level of 5%.
Clinical assessment of the variance in surgical accuracy
During strabismus surgery, the insertions of the eye muscles on the eye are altered to change the angle of strabismus in different directions of gaze. Surgical accuracy or mechanical differences between patients’ eye muscles influence the postoperative result of surgery. Surgical accuracy was estimated based upon the photographs from the Bilateral Recession vs. Recession Resection Study (Polling et al. 2009). In this study, photos were taken during two stages of the operation in either recession or resection: (1) after fitting the sutures through the muscle and (2) before closing the conjunctiva. A millimeter ruler next to the muscle was photographed with the eye. During the recession, four points were marked with methylene blue on the sclera: two points next to the suture knots in the
muscle at the insertion, and two points posterior on the sclera at the planned distance of recession on either side of the muscle. During the resection, four points were marked with methylene blue on the sclera: two points at the muscle insertion on the sclera, and two points posterior from these two on the muscle at the planned distance of recession of the muscle. In resection, the muscle was sutured at the level of these two posterior points, clamped in a Bangerter myostat and cut off from the insertion. If the central part of the resected or recessed muscle hung between the sutures, a third suture was placed to get the central part of the muscle in line. We estimated the maximum achievable accuracy based upon the photographs.
Mathematical model of the surgical trajectory
To obtain a comprehensive insight in the contributions of the three human-error related factors described above in the surgical trajectory, we derived a mathematical model of the surgical treatment trajectory for horizontal strabismus. The postoperative angle was expressed as a function of the measured preoperative angle of strabismus, surgical dosage, amount of surgery and anatomical and physiological parameters.
To compare the variance caused by human-error related factors to the variance caused by inter-patient differences in anatomy and physiology we used a straightforward mechanical model (Appendix A). The mechanical model enabled estimation the effect per millimeter of surgery for different values of anatomical and physiological parameters. The model has one degree of freedom (horizontal eye rotation), and only two eye muscles are present. The model comprised eye radius (r [mm]), linearized muscle stiffness (k [N/mm]) and linearized stiffness in passive rotation (g [mNm/rad]).
A sensitivity analysis was carried out to investigate how much influence each of the error sources has on the postoperative result of strabismus surgery. Sensitivity was analytically derived and numerical evaluations were performed. The sensitivity analysis resulted in variance of the postoperative angle of strabismus for each error source.
The sensitivity analysis enabled evaluation of the variability of the postoperative angle of strabismus for a group of patients with a normal distribution of the parameters. For estimating sensitivity, the mean value and variance of each parameter were required. For preoperative measurement accuracy, we used the variance found in our interobserver study. Mean and standard deviation of the eye radius (Larsen 1971) and muscle stiffness (Simonsz et al. 1984) were obtained from literature data. Some course measurements (Collins et al. 1969), of stiffness in passive rotation were used in the sensitivity analysis. Result of this evaluation was the variance (in degrees) of the postoperative angle of strabismus for each error source.
If a patient has good binocular vision, he is able to correct a small strabismus that may remain after surgery. Accordingly, the result of strabismus surgery is better and more stable, when binocular vision is good. This effect was neglected in our model.
2.3
Results
Error sources in the surgical trajectory of strabismus surgery were mapped out (Fig. 2.2). The trajectory starts with the preoperative measurements of the patient. Based upon these measurements, a surgical plan is determined. Surgery follows and after the recovery phase, a postoperative assessment is carried out.
We mathematically modeled the processes in the surgical trajectory and carried out a sensitivity analysis on this model to estimate the fraction of reoperations caused by each of the error sources. The input data for the model was acquired from the literature and from three clinical assessments of variance introduced by human error.
Clinical assessment of the variance in the measurement of the
angle of strabismus
Demographic data and diagnoses of the six patients are shown in Table 2.1. All patients gave their informed consent prior to participating in this study. All patients were examined by all orthoptists and an examination sheet was returned for every patient. Manifest and latent vertical angles of strabismus, at distance and at near fixation, were measured more accurately than their corresponding manifest and latent horizontal angles of strabismus, at distance and near fixation (Table 2.2). Horizontal manifest and latent angles were measured more accurately at distant fixation than at near fixation. Horizontal latent angles were measured more accurately than horizontal manifest angles. Especially the angles at near fixation showed a large variation (Fig. 2.3). At distance fixation, horizontal latent angles were measured more accurately than horizontal manifest angles. The horizontal angle of strabismus that could be assessed most reliably was the latent angle of strabismus at distance fixation with an average standard deviation of 1.72±0.45◦
.
Clinical assessment of the variance in surgical strategy
184 Dutch orthoptists filled out the questionnaire with three example cases of strabismus, in complete silence. Four orthoptists did not use the prescribed notation protocol and were excluded from the analysis. 12% of the orthoptists decided not to operate on the
1. Preoperative
measurement(s) Variance in the measurement
of the angle of strabismus
pre
Variance in surgical strategy
Variance in surgical accuracy
post *pre E* r k, g L suggested amount of surgery *post postoperative angle of strabismus measured preoperative angle of strabismus
PROCESS ERROR SOURCES PARAMETERS
measured postoperative angle of strabismus *pre L post *post
Variance in the measurement of the angle of strabismus 2. Surgical plan 3. Surgery 4. Recovery phase 5. Postoperative measurement Intra-patient variability Anatomical variation Variation muscle stiffness/
physiology
Surgical scarring
Binocular vision
Intra-patient variability Sarcomere length adaptation
Figure 2.2: A schematic representation of the surgical trajectory of strabismus. Er-ror sources that influence the outcome of surgery are depicted on the right. The error sources related to human error are marked red. The right column shows the nomenclature of the parameters in the mathematical model.
DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL DM DL NM NL -30° -20° -10° 0° 10° 20° 30° -30° -20° -10° 0° 10° 20° 30° -30° -20° -10° 0° 10° 20° 30° -30° -20° -10° 0° 10° 20° 30° -30° -20° -10° 0° 10° 20° 30° -30° -20° -10° 0° 10° 20° 30° Patient 1 Patient 5 Patient 3 Patient 2 Patient 6 Patient 4
Figure 2.3: A graphical representation of all measurements that were performed. Each frame represents measurements on one patient (N=6), each box plot represents all measurements (N=6) of one type of angle of strabismus. The following angles were measured: the manifest angle in distant fixation (DM), the latent angle in distant fixation (DL), the manifest angle in near fixation (NM) and the latent angle in near fixation (NL). Red box plots represent horizontal angles; green box plots vertical angles of strabismus.
Table 2.1: Age and diagnosis of the six patients that participated in the clinical as-sessment of the variance in the measurement of the angle of strabismus.
Patient Age (yr) Diagnosis
1 7 Infantile esotropia, dissociated vertical deviation and upshoot in adduction
2 8 Consecutive exotropia, A pattern and high AC/A ratio
3 9 Exophoria
4 14 Intermittent exotropia, upshoot in adduction and V pattern
5 76 Esotropia with V pattern
6 79 Consecutive exotropia with right hypertropia and V pattern
Table 2.2: The mean standard deviations of the examinations and their standard de-viations. All measurements were performed six times by different orthoptist in six patients. Significant differences are denoted by ‘<’ or ‘>’, a non significant difference is denoted by ‘◦’. Horizontal angles are measured less accurately than vertical angles. Horizontal angles of strabismus measured at distance fixation are measured more accu-rately than at near fixation. Horizontal latent angles are measured more accuaccu-rately at near and at distance fixation. The most reliable horizontal angle is the latent angle of strabismus measured at distance fixation. There was no significant difference between the four types of vertical measurements.
Distant fixation Near fixation
manifest latent manifest latent
Horizontal (4.19 ± 2.84◦ > 1.74 ± 0.45◦ ) < (5.44 ± 3.07◦ > 3.97 ± 1.33◦ ) Vertical (1.75 ± 0.63◦ ◦ 1.42 ± 0.57◦ ) ◦ (1.21 ± 1.02◦ ◦ 1.45 ± 0.96◦ )
patient with 10◦of esotropia at all. In all three patients, most of the orthoptists favored BR over RR. With a larger angle of strabismus, more orthoptists prescribed BR with a ‘loop’ (0%, 4% and 28% respectively). In bilateral recession, the orthoptists prescribed 7.3±1.7mm, 9.1±1.2mm and 10.3±1.3mm (mean±SD) muscle relocation for 10◦
, 15◦ and 20◦
of esotropia. (Fig. 2.4). In the patient with 20◦
of esotropia, orthoptists who suggested performing RR decided for a significantly higher dose than the orthoptists who decided for BR. In the patients with 10◦
and 15◦
of esotropia, these differences were not significant.
Clinical assessment of the variance in surgical accuracy
Deviations from the intended amount of surgery occur in measurements, in reattaching the muscle to the sclera and by sagging of the muscle between the attachment points. We analyzed 30 cases and estimated surgical accuracy at 0±0.5mm (mean±SD).
10° 15° 20° preoperative ACT at 5m. to ta l a m o u n t o f su rg e ry [m m ] 2 4 6 8 10 12 14 16
Figure 2.4: A graphical representation of the outcome of the questionnaire. The hor-izontal axis represents the preoperative angle of strabismus. The vertical axis depicts the total amount of prescribed surgery (mean±SD) for bilateral recession (BR) in red and for recession resection (RR) in blue.
Mathematical model of the surgical trajectory
A mathematical model of primary horizontal strabismus surgery was derived. The postop-erative angle of strabismus (θpost) was expressed as the preoppostop-erative angle of strabismus (θpr e) minus the amount of surgery (∆L) multiplied by the actual effect of surgery (E):
θpost= θpr e− ∆L · E (2.1)
To obtain the prescribed amount of surgery (∆L), the measured preoperative angle of strabismus (θ∗
pr e) is divided by the expected effect of surgery (E∗
). The error made during surgery (εL) is added to this intended amount of surgery:
∆L = θ ∗ pr e E∗ + εL (2.2)
The theoretical effect of surgery (E) was derived with a straightforward mechanical model (Appendix A). The mechanical model comprises eye radius (r ), muscle stiffness (k) and stiffness in passive rotation (g). The effect of surgery can be expressed as:
E= kr
Substitution of Eq. 2.2 and Eq. 2.3 in Eq. 2.1 finally yields the postoperative angle of strabismus as a function of all of the previously described parameters:
θpost= θpr e− θ ∗ pr e E∗ + εL ·(2krkr2+ g) (2.4)
Summarizing, the model derived in Eq. 2.4 provides the postoperative angle of strabismus as a function of the actual and measured preoperative angles of strabismus, the expected dose response ratio, the error made during surgery, and the patient’s mechanical characteristics: muscle stiffness, eye radius, and stiffness in passive rotation.
To make estimates of variance within the surgical trajectory we have done sensitivity analysis of the model. If we would substitute mean values of a population of strabismus patients into Eq. 2.4, we would estimate the mean postoperative angle of strabismus for that population. In addition, the model can be used to estimate how much each error source contributes to variance in the postoperative angle of strabismus if we perform a sensitivity analysis. The delta method (Oehlert 1992), a statistical method, can be used to approximate the variance of a function of one or more variables. If we assume the parameters are independent, variance (squared standard deviation) in the postoperative angle can be written as:
σ2θpost ≈ ∂θpost ∂θpr e 2 σ2θpr e+ ∂θpost ∂θ∗ pr e 2 σ2θ∗ pr e+ ∂θpost ∂E∗ 2 σ2E∗+ ∂θpost ∂εL 2 σεL2 + ∂θpost ∂r 2 σ2 r + ∂θpost ∂k 2 σ2 k+ ∂θpost ∂g 2 σ2 g (2.5)
In which the partial derivatives of Eq. 2.4 represent the sensitivities, based upon average values of the parameters. Multiplication with variance of each parameter then provides the estimated contributions to variance in the postoperative angle of strabismus. Influence of the individual error sources was quantified by evaluating the individual terms of Eq. 2.5. In order to evaluate Eq. 2.5 numerically, the mean and variance are required for each pa-rameter. The numerical values that were used are summarized in Table 2.3. We estimated the SD of intra-patient variation of the angle of strabismus (θpr e) at ±1 degree. For the measurement accuracy of the preoperative angle of strabismus (θ∗
pr e) we assumed the mean measurement value to be the actual angle of strabismus. For the SD we used the deviation found in the latent angle with distant fixation (1.72◦
), as this angle is used most often for making the surgical plan. We assumed the orthoptic measurements are repeated three times before surgery. The standard deviation then becomes 1◦
Table 2.3: Mean values and standard deviations that were used to estimate the vari-ability caused by each error source.
Parameter Mean SD
Preoperative angle of strabis-mus
θpr e 10◦, 15◦, 20◦ 1◦ Measured preoperative angle of
strabismus θ∗ pr e 10 ◦ , 15◦ , 20◦ 1◦ Surgical strategy E∗ 1.4, 1.65, 1.94 0.17, 0.08, 0.07 ◦ /mm Surgical accuracy εL 0 0.7 mm Eye radius r 11.6 0.5 mm Muscle stiffness k 35 6.1 N/m
Stiffness in passive rotation g 6 0.9 mNm/rad
the surgical strategy (E∗
), or the expected dose-response ratio, we used the values as found with our questionnaire: 1.4 ± 0.17, 1.65 ± 0.08, 1.94 ± 0.07◦
/mm for preoperative angles of 10◦
, 15◦ , 20◦
respectively. For the surgical accuracy (∆L) we used the variance as found in the clinical assessment, ± 0.5mm and we expected the mean deviation from the intended amount of surgery to be zero, i.e. we assumed that there are no systematic errors. Usually, two muscles are operated in one patient so the surgical error is made twice. Variances (squared SD) can be added, and the total standard deviation becomes √
2 × 0.52
mm ≈ 0.7mm.
To model the influence of the variance of anatomical and physiological factors, variances were derived for the size of the eye, for muscle stiffness and for stiffness in passive rotation of the eye. We used an eye radius (r ) of 11.6 ± 0.5mm (Larsen 1971). Muscle stiffness (k) has previously been measured under local anesthesia (Simonsz 1994) and was found to be 35 ± 6.1 N/m. Two attempts have been made to assess the stiffness in passive rotation of the human eye (g) in vivo (Collins et al. 1981; Simonsz et al. 1986). In both measurements, displacement of the eye in its orbit was neglected (Schutte et al. 2006). These are the only in-vivo measurements to date, however, and we used the measurement values from these studies (6 ± 0.9mNm/rad).
After substitution of numerical values, the sensitivity analysis predicted a total standard deviation of approx. 5.5◦ (Fig. 2.5). In our mathematical model, we assumed that intra-patient variability of the angle of strabismus was the same postoperatively and causes ap-prox. 18% of the total variance. The variability in the preoperative measurement caused 14%, 17% and 18% of the total variance for preoperative angles of 10◦
, 15◦ , 20◦
respec-tively. The variance in surgical strategy caused 22%,12% and 10% respecrespec-tively. The error in recession / resection (± 0.5mm) caused approx. 20% of the variance. The inter-patient differences in anatomical and physiological factors together caused approx. 25%, 33% and 38% respectively. The most influential parameter was muscle stiffness. Eye radius played only a minor role.
standard deviation of the postoperative angle of strabismus pre ope rative ang le of stra bism us pre *pre E L r k g 10° 15° 20° 0° 1° 2° 3° 4° 5° 6° *
Figure 2.5: Estimated contributions to the standard deviation of the postoperative angle of strabismus surgery for intra patient variation (θpr e), interobserver variation
(θ∗
pr e), variation in surgical strategy (E ∗
), surgical inaccuracy (∆L), variance in eye radius (r ), variance in muscle stiffness (k) and variance in stiffness in passive rotation (g). These estimates are based upon the mean values and standard deviations provided in Table 2.3.
The total human-error related factors, i.e. surgical accuracy and accuracy in measurement of the angle of strabismus, cause approx. 50% of the variability. The remaining 50% is caused by anatomical and physiological variation and by day-to-day variability of the patient.
2.4
Discussion
The human error in strabismus surgery could be quantified with a sensitivity analysis. The systematic approach led to a model of the processes constituting the trajectory of strabismus surgery, in which the relative contribution to variability of the surgical result could be estimated for several human-error related factors.
In many medical treatments, the outcome is often not satisfactory and the number of error sources that influence the outcome is large. In order to make improvements in these treatments, it should be known how much influence each of the error sources has on the treatment outcome. The approach that we have presented proved to be useful for strabismus surgery, but might also be valuable for other medical treatments. Firstly, the treatment trajectory has to be analyzed systematically to map out all processes and error sources, secondly a mathematical model has to be derived and finally a sensitivity analysis has to be performed to investigate the relative importance of the variables. This technique provides new insights and shows where improvements in the trajectory have the largest
effect. The input data that is required to perform a sensitivity analysis might be available in literature; otherwise clinical assessments are needed to obtain these data.
The standard deviation of the postoperative angle of strabismus that we predicted based upon the sensitivity analysis (5.5◦
) was comparable to the standard deviation found in a randomized clinical trial (4.8◦
) in which bilateral recession was compared to recession resec-tion surgery (Polling et al. 2009). We found that human errors caused approximately half of the variability of the postoperative angle of strabismus. Hence, they cause approximately half of the reoperations.
The firstly identified human factor in the surgical trajectory was the measurement of the angle of strabismus. Accuracy of the measurement of the angle of strabismus with prism cover tests limits the final result. The measurement of the horizontal manifest angle of strabismus measured with fixation at near was highly unreliable, with an average standard deviation of 5.44 ± 3.07◦
. This might be because of different accommodative efforts and because the influence of varying distances is larger with fixation at near than the influence with fixation at distance. The horizontal angle of strabismus that was measured most accurately was the horizontal angle of strabismus with fixation at distance, with an average standard deviation of 1.72 ± 0.45◦. If three measurements are carried out preoperatively, and the average angle is used for surgical planning, measurement inaccuracy causes one fifth of the overall variability. Measurement variability in the manifest angles of strabismus might be larger than variability in the latent angles because of the influence of binocular vision and because of the more difficult way of measuring manifest angles.
In addition to the measurement variability, the angle of strabismus itself may vary over time. By taking a number of measurements, the estimate of the average angle becomes more accurate. Automated measurements, for instance by employing Purkinje imaging (Barry et al. 1994), may improve the measurement accuracy and decrease the influence of this error.
The second human factor in the surgical trajectory is the surgical strategy, primarily based upon the dose response relation. We found that the variability of the prescribed amount of surgery is relatively large. The variability in the surgical strategy causes approx. one fifth of the overall variance in the postoperative angle for patients with a preoperative angle of 10◦
. Part of this variability may reflect a compensation for systematic errors made, for instance, in the measurement of the angle of strabismus or during surgery: If the recessions of a particular surgeon are systematically slightly larger than those of other surgeons, the orthoptists may, consciously or not, compensate for that systematic error by systematically suggesting less muscle displacement during surgery.
It is important to realize that the surgical plan is not equal to the expected average effect. Polling et al. (2009) found 1.44◦
most guidelines (von Pflugk 1906; Scott et al. 1975; Saggau 1976; Lang 1981; Parks 1984; Mims III et al. 1985; Kushner and Morton 1987) and our assessment amongst Dutch orthoptists employ higher dose response ratios (1.4 − 1.9◦
/mm). This discrepancy is the result of a systematic undercorrection because an overcorrection of strabismus is more likely to cause diplopia and loss of binocular vision. There are a large number of guidelines in the literature for the amount of recession/ resection per angle of strabismus. The guidelines vary and there is little agreement. Validated guidelines, if broadly adopted, would decrease the variability and reduce the number of reoperations.
The effect of surgery is usually expressed in ◦/mm and is calculated by subtracting the preoperative angle from the postoperative angle and dividing by the total amount of muscle surgery. In some of the studies about the dose-response relation in strabismus surgery, the effect of surgery is related to the preoperative angle. This should be discouraged. As the preoperative angle of strabismus is used to calculate the effect of surgery, measurement errors in the preoperative angle of strabismus cause an artifact: The effect of surgery seems larger for larger preoperative angles, and smaller for smaller preoperative angles of strabismus, as compared to the actual effect.
Surgical accuracy proved to be the third important human factor in the surgical trajectory. Surgical accuracy probably varies between individual surgeons (Lipton and Willshaw 1995). It is, however, unlikely that the accuracy is better than ±0.5mm. Based upon this accuracy we estimated that approximately one fifth of the reoperations are caused by imprecise surgery. New surgical instruments or use of adhesives (Mulet et al. 2006) might reduce this variability.
Adjustable sutures (Jampolsky 1975) are used in an effort to overcome the influence of variability in strabismus surgery. During surgery the muscle tendon is secured with sutures that can be adjusted, either with the ’bow tie’ or with the ’sliding knot’ technique. When the patient is sufficiently alert after surgery, adjustments can be made to the muscle relo-cation under local anesthesia. A disadvantage is that it requires considerable cooperation from the patient and therefore is not usable in young patients. A recent Cochrane review (Sundaram and Haridas 2005) concluded that it could not be concluded from current lit-erature that adjustable sutures produces a more accurate long-term ocular alignment than conventional surgery.
Finally, the relative contribution of anatomical and physiological variation was assessed, in comparison to human-error related variability. With a straightforward mechanical model and literature data, we estimated that up to one third of the overall variability in strabis-mus surgery could be caused by inter-individual variation in anatomy and physiology. The stiffness of the muscles and the stiffness of the eye in passive rotation can be assessed with a forced duction test in an effort to reduce variability, especially in reoperations. Our
k r g ilr imr k Lmr L lr
Figure 2.6: A schematic representation of the mechanical model that was used to derive the influence of surgical inaccuracy. The model comprised eye radius (r [mm]), linearized muscle stiffness (k [N/mm]) and linearized stiffness in passive rotation (g [mNm/rad]).
model predicted that the size of the eye plays only a minor role in average patients. This agrees with the clinical data from Kushner et al. (1989, 1991). To decrease the influence of anatomy and physiology new devices should be aimed at measuring the individual me-chanical properties of patients and relating these parameters to the effect of surgery. If these relations are known, the optimal surgical strategy can be determined after individual measurements pre- or intraoperatively.
A weakness of our study was that we neglected the influence of binocular vision. As the exact influence of binocular vision has not yet been quantified we restricted our analysis to the large group of patients with little or no binocular vision. If binocular vision develops postoperatively, the outcome of surgery is better.
Appendix A: A Mechanical Model of Strabismus Surgery
This appendix describes a straightforward model of the mechanics of strabismus surgery. The model comprises eye radius, linearized muscle stiffness and linearized stiffness in passive rotation (Fig. 2.6). The model is based upon the first strabismus model by Robinson (1975) as it was assumed that activation to the strabismic eye does not change after surgery. Regarding muscle stiffness, Robinson et al. (1969), Collins et al. (1981) and Simonsz et al. (1986) found that the relation between length and force of a contracting eye muscle is approximately linear, whether it contracts moderately or strongly. Force development by the muscles is therefore only dependent on elongation and activation in the static gaze.The force in a non-contracting eye muscle during passive elongation rises exponentially with length. In our model, we assumed a pretension in the muscles high enough, such that passive elongation is never reached. Forces that act on the eye by the medial rectus muscle (Fmr) and the lateral rectus muscle (Fl r) were reduced to linear relations. In these relations, stiffness of the muscle (k) is multiplied by its elongation due to activation (imr and il r), rotation of the eye (θ) in radians times the eye radius (r ) and surgery (∆Lmr and ∆Ll r):
Fmr = k(imr− θr + ∆Lmr) (2.6)
Fl r = k(il r+ θr + ∆Ll r) (2.7)
Stiffness in passive rotation was modeled as a linear torsional spring. This parameter represents stiffness that is caused by deformation of orbital fat by the muscles and the optic nerve. The passive moment (M) is always counteracting rotation and linearly dependant on torsional stiffness (g):
Mg= −θg (2.8)
In any static position of the eye the sum of moments acting on the eye has to be zero. The moment balance around the center of the eye is given by:
ΣM = r Fmr− r Fl r+ Mg= 0 (2.9)
Substitution of Eq. 2.6,2.7 and Eq. 2.8 in Eq. 2.9 and solving for θ gives the rotation of the eye as a function of surgery and activation:
θ= E(imr− il r) + E(∆Lmr− ∆Ll r) (2.10)
in which:
E= kr
For strabismus surgery, we assume the angle of rotation is the preoperative angle of strabis-mus (θ = θpr e) that has to be compensated. Activation remains the same after surgery and therefore has no influence in the change in angle of strabismus and the first term in Eq. 2.10 diminishes. If we perform the same amount of surgery on both muscles, ∆Ll r = −∆Lmr, the total amount of surgery for preoperative angle θpr ebecomes ∆L = 2∆Lmr, substitution in Eq. 2.10 and rewriting gives:
E=θpr e
∆L (2.12)
In which (E) proves to be the actual effect per amount of surgery, which defined as the change in angle of strabismus divided by the total amount of surgery. Summarizing, we derived the effect of surgery as a function of muscle stiffness, eye radius and stiffness in passive rotation.
3
Inaccuracy in the surgical procedures for
strabismus and avenues for improvement
Sander Schutte1, Frans C.T. van der Helm1
, Sjoukje E. Loudon2
, Huib J. Simonsz2
1 Department of Biomechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, the Netherlands
2 Department of Ophthalmology, Erasmus Medical Center, Rotterdam, the Netherlands
Abstract
The limited accuracy in recession and resection surgery is responsible for approx. 20% of the reoperations. The surgical procedure for strabismus has changed little since 1905, how-ever. The overall variability in strabismus surgery is caused by multiple errors throughout the surgical trajectory. This study focusses on errors that are introduced during strabismus surgery. We provide a framework to analyze different surgical techniques, and their alter-natives, with respect to the variances that are introduced during the surgical procedure itself. The goal is to analyze the conditions that impede the development of improved surgical devices and procedures for strabismus surgery.
We estimated the errors in the most common surgical procedures by subdividing their surgical workflow into tasks. We analyzed recessions, resections, adjustable sutures, partial tenotomies, faden surgery and injection of botulinum toxin. Subsequently, we investigated literature and patent databases for alternative solutions that could improve certain tasks within the surgical procedure. We identified the boundary conditions that have to be met for new instruments and surgical methods regarding safety, geometry, and legal. The solutions found were rated based upon maximum accuracy, safety, costs and time required. We found that all variances in each consecutive task of the surgical procedure, can be added up to an overall error. This surgical variance is reflected by a variance in the postoperative angle of strabismus, which primarily determines the percentage of reoperations. As a consequence, any improvement of a method for a task in the surgical method can be converted into a reduction of the variance of the postoperative angle and, hence, into a reduction of the percentage of reoperations. By doing this, a comprehensive insight in the tasks that constitute a surgical procedure is possible and a quantitative comparison between surgical methods became possible.
To compete with a conventional recession/resection procedure, the overall accuracy should be improved without increasing complexity and costs. To significantly reduce the reopera-tion rate, the accuracy of each of the individual tasks needs to improve. This is technically challenging within the boundary conditions (i.e. cost effectiveness).
3.1
Introduction
Strabismus occurs in approximately 4 percent of the population (Abrahamsson et al. 1999; Greenberg et al. 2007) and is usually corrected surgically. The treatment goals for stra-bismus surgery in adult patients are to alleviate double vision (diplopia) and to improve appearance. In children, the treatment goals are to preserve binocular vision in worsening or recent-onset strabismus and to improve appearance. Most strabismus operations are corrections of horizontal eye position by relocating the insertion of one muscle on the eye a few millimeters backwards (recession) and resecting the tendon of its antagonist (resec-tion). Binocular vision may be preserved or enhanced if the eyes are aligned. Contrarily, if a patient has good binocular vision, he may therefore be able to correct an undercorrec-tion after surgery. As the chance of diplopia is larger after an overcorrecundercorrec-tion, patients are systematically undercorrected (Donahue 2007). The number of children operated for stra-bismus is large (over 150 operations per week in the Netherlands alone) and the increase in quality of life due to surgery is considerable (Durnian et al. 2011).
Patients who are overcorrected or severely undercorrected are usually operated upon a second time. Due to scar tissue and wound healing the result of a second or third operation will be more difficult to predict. The number of reoperations primarily depends on the variance of the postoperative angle of strabismus. The re-operation rate for infantile esotropia, a common type of strabismus, is approximately 20% (Simonsz et al. 2009, Fig. 11.5) when the child is first operated on at the age of four, but higher when the child is first operated at an earlier age.
The variability of the result of strabismus surgery can be described in terms of error sources in the phases of the entire surgical trajectory (Schutte et al. 2009). Firstly, errors can be made during measurement of the angle of strabismus, e.g. the head position may vary between the measurements. Secondly, there may be differences between patients, stiffness of the eye muscles may differ, for instance. Thirdly, differences between ophthalmologists and orthoptists in deciding what eye muscles to operate upon, and how much surgery is required, might show variability. Finally, current surgical procedures for strabismus are carried out with varying degrees of accuracy. In the postoperative phase, also wound healing and stereopsis influence the outcome.
The variances in each consecutive step of the procedure add up to the overall error, represented by a deviation of the intended angle of strabismus. Statistically, this means that -assuming that the errors have a gaussian distribution, and that they are independent of each other- the variances can be added. The overall variance is represented by a variance of the postoperative angle of strabismus (for a group of patients). The size of the variance of the postoperative angle of strabismus primarily determines the percentage of reoperations.
A sensitivity analysis of the overall surgical trajectory including pre- and postoperative measurements (Schutte et al. 2009), weighing all of these categories of error sources, showed that approximately 30% of the variability in the surgical trajectory is caused by inter-patient differences in anatomy and physiology, i.e. variability in eye-radius, muscle stiffness and passive rotational stiffness of the eye. In that study, we estimated that the surgical accuracy is ±0.5mm. Based on that accuracy, the contribution of surgical inaccuracy is approx. 20% to the overall variability. If surgical accuracy is worse, the relative contribution to variability is larger. The remaining variability is caused by day-to-day variability of the angle of strabismus of the patient. The total human-error related factors, i.e. accuracy in measurement of the angle of strabismus, differences between ophthalmologists and orthoptists in deciding what eye muscles to operate upon, and by what distance, and surgical accuracy itself causes approximately 50% of the total variance. Variability in recession and resection surgery may exist within a surgeon, and between surgeons (Lipton and Willshaw 1995). Variability within surgeons can be expected to be random, i.e. no systematic error. Variability between surgeons has a systematic compo-nent as well, for instance, one surgeon may have developed the habit of always putting a third suture between the two other sutures when, after a recession, the muscle is sag-ging. In planning for surgery, these idiosyncrasies are taken into account, consciously or unconsciously, and the planned amount of recession may be tailored to a particular surgeon (Schutte et al. 2009). If the systematical error could be reduced, the amount of surgery could be standardized to some extent.
Most operations for strabismus are recessions of an eye muscle: cutting the tendon of the muscle off the globe and reattaching the tendon a few millimeters posteriorly to the globe. Less often, eye muscles are shortened by removing part of the muscle tendon: resection surgery. The procedure has changed little since von Pflugk (1906) first introduced recession surgery with sutures. Some of the instruments have changed, like calipers with improved accuracy (Clark and Rosenbaum 1999), but the basic procedure has remained the same: the effective length of the extraocular muscles is adjusted to change the relative position of the eyes.
The goal of strabismus surgery is generally a small undercorrection, as overcorrection could lead to diplopia. An increased surgical accuracy will reduce variability in the postoperative outcome, which will lead to more undercorrections and less overcorrections. This will lead to a shift of the target postoperative angle towards perfect alignment i.e. the surgical dosage is increased. Due to this effect, the number of reoperations will not decrease pro-portionally with the increase in accuracy. However, if surgical accuracy would be ±0.1mm, the fraction of patients with a -relatively- large postoperative angle or an overcorrection will decrease and the number of reoperations due to surgical inaccuracy will decrease from 20% to approximately 4%.
Although many technical improvements have been made the last century in healthcare e.g. in the quality of procedures, training of surgeons and improvements in equipment, little has changed in strabismus surgery. For instance in vitrectomy (Lincoff and Kreissig 2000), several innovations were introduced in clinical practice and the quality of treatments has improved considerably. New surgical instrumentation could improve accuracy of the surgical method and thereby increase the predictability of strabismus surgery. This would reduce the number of reoperations and thereby the related costs.
It is unclear why developments in strabismus surgery have gone slowly. Due to the large number of uncertainties in the surgical-treatment trajectory, it is difficult see effect of different methods for individual surgical tasks. As the experiences of surgeons might vary, the door is opened for many different viewpoints and experiences. As a result many, varying, surgical guidelines are published.
The goal of this paper is to analyze inaccuracies in surgical procedures for strabismus and to explore avenues for their improvement. We provide an analysis of different surgical techniques and other interventions to treat strabismus. By dividing a surgical procedure into tasks, and estimating the variance in each consecutive step of the procedure, we intend to provide a framework for the analysis of surgical procedures, that allows insight into the effect of changing a single task within the entire surgical procedure. In the Methods section we describe current surgical procedures, boundary conditions and constraints. Innovations and explored avenues for improvement are presented in the Results section.
3.2
Methods: Description of current procedures,
bound-ary conditions and constraints
In this section, the various tasks in the common procedures in strabismus surgery are identified. For each task within each surgical procedure, errors and potential risks were identified. We investigated if alternative surgical techniques and methods could reduce error in a task. Finally, we identified the boundary conditions that have to be met when improving the surgical procedure.
Tasks and errors in the current procedures
To investigate the errors in the current procedures for strabismus, we firstly evaluated which tasks are performed in the most common surgical treatments. By structured analysis of video recordings of the procedures, we were able to divide the workflow into tasks. We identified tasks in the following procedures: (1) changing the location of a muscle insertion
on the sclera (i.e. recessions, resections, partial tenotomies, transpositions), (2) adjusting the location of a muscle insertion postoperatively (i.e. adjustable sutures), (3) changing force-length relation of the muscle (e.g. injection of botulinum toxin).
For each task that was identified, we made an inventory of the errors that are introduced. We attempted to quantify the errors and to estimate the overall accuracy to compare different procedures. The goal of this step was to introduce a framework to compare different procedures.
Changing the location of a muscle insertion on the sclera
The procedures that were analyzed in this section relate to changing the location of the in-sertion of an eye muscle on the sclera. This is done in recession surgery, resection surgery, (partial) tenotomies and transpositions. The goal of recession and resection surgery is to move the muscle insertion from a reference position to a new position with the targeted recession distance, as accurately as possible. By structured analysis of video recordings of recession, resection, tenotomies, and transposition procedures we were able to iden-tify tasks that occur in the workflow of these procedures. The following tasks could be identified.
• Task 1 determining a reference position on the eye and on the muscle • Task 2 holding the muscle
• Task 3 cutting the muscle off the eye
• Task 4 moving the cut-off muscle to the marked position • Task 5 attaching the muscle to the sclera
Assuming that the variances that are introduced in these tasks are independent (i.e. the covariances are zero) and random, the variances in each of the tasks can be added to obtain the overall variance of the procedure as follows. The error can be expressed in terms of standard deviations. For the overall error this leads to the following equation.
σT21+T2+...= σ
2 T1+ σ
2
T2+ . . . (3.1)
In each of the tasks we analyzed possible errors, and we observed and estimated difficulties and the inaccuracies. Figures 3.1 and 3.2 show the errors that were identified in each task. In the following, a detailed description will be given of each task and the errors, inaccuracies and risks that were identified.
Figure 3.1: Two schematic views on a horizontal rectus muscle in a recession proce-dure. The close-ups show the errors that occur in the subsequent tasks of recession surgery. Figure 3.2 describes the errors in more detail.
Figure 3.2: A schematic representation of the tasks in recession surgery, and how the errors made in the subsequent tasks (See also Fig. 3.1) add up.
