Gait & Posture 39 (2014) 778–783
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Femoral derotational osteotomy: Surgical indications and outcomes in children with cerebral palsy Michael H. Schwartz a,b,*, Adam Rozumalski a, Tom F. Novacheck a,b a b
Gillette Children’s Specialty Healthcare, USA University of Minnesota – Twin Cities, Department of Orthopaedic Surgery, USA
A R T I C L E I N F O
A B S T R A C T
Article history: Received 4 September 2013 Received in revised form 14 October 2013 Accepted 19 October 2013
Excessive femoral anteversion is common among children with cerebral palsy, and is, frequently treated by a femoral derotational osteotomy (FDO). It is important to understand surgical, indications for FDO, and the impact of these indications on the treatment outcomes. The Random Forest algorithm was used to objectively identify historical surgical indications in a large retrospective, cohort of 1088 limbs that had previously undergone single-event multi-level surgery. Treatment, outcome was based on transverse plane kinematics obtained from three-dimensional gait analysis. The, classifier effectively identified the historic indications (accuracy = .85, sensitivity = .93, specificity = .69, positive predictive value = .86, negative predictive value = .82), and naturally divided limbs into four, clusters: two homogeneous +FDO clusters (with/without significant internal hip rotation during gait), one homogeneous FDO cluster, and a mixed cluster. Concomitant surgeries were similar among the, clusters. Limbs with excessive anteversion and internal hip rotation during gait had excellent outcomes, in the transverse plane. Limbs with excessive anteversion but only mild internal hip rotation had good, outcomes at the hip level; but a significant number of these limbs ended up with an excessive external, foot progression angle. The Random Forest algorithm was highly effective for identifying and, organizing historic surgical indications. The derived criteria can be used to give surgical decision making, guidance in a majority of limbs. The results suggest that limbs with anteversion and significant, internal hip rotation during gait benefit from an FDO, but limbs with excessive anteversion and only, mild internal hip rotation are at risk of developing an excessive external foot progression angle. ß 2013 Elsevier B.V. All rights reserved.
Keywords: Femur Anteversion Cerebral palsy Random forest Outcome
1. Introduction Excessive femoral anteversion is a common orthopedic deformity in children with cerebral palsy (CP) [1]. Excessive anteversion has many consequences. Perhaps most important of these is that children with this deformity will often adopt a gait characterized by excessive internal hip rotation. The emergence of the internal hip rotation gait pattern has been explained by Arnold as a compensation for functional weakening of the hip abductors [2]. Internal hip rotation is effective for improving functional hip abductor strength, but comes at the cost of excessive internal foot progression. Internal foot progression is problematic since it can lead to tripping and foot dragging – which in turn can cause or exacerbate foot deformity. Internal rotation gait is also a significant cosmetic issue, and can lead to stigmatization and lowered
* Corresponding author at: Gillette Children’s Specialty Healthcare, James R. Gage Center for Gait and Motion Analysis, 205 University Ave, St. Paul, MN 55101, USA. Tel.: +1 612 226 5120. E-mail address: [email protected] (M.H. Schwartz). 0966-6362/$ – see front matter ß 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.gaitpost.2013.10.016
self-esteem. It is widely believed that excessive anteversion present after the maturation of gait is unlikely to resolve spontaneously [3]. Therefore, surgical correction of excessive anteversion is common among children with CP. There have been numerous scholarly articles discussing the indications for, and outcomes of, the FDO procedure. In terms of indications, the literature is vague, subjective, and occasionally contradictory. As would be expected, excessive anteversion is central to the existing indications; though to varying degrees. Meanwhile, gait indications vary in specificity and level. Ounpuu et al. state that FDO is indicated when hip internal rotation ROM is greater than 608, external rotation is less than 258, and dynamic hip internal rotation in gait is more than one SD internal compared to normal (approximately 108) [4]. The indications described by Kim et al. call for external rotation of the hip less than 158 on physical examination, and both hip internal rotation and internal foot progression angle during gait more than 108 from normal [5]. Hoffer et al. simply state that FDO is indicated ‘‘only when internal rotation of the anteverted femur interferes with gait’’ [6]. It is important to note that the outcome studies associated with these stated indications do not report how consistently the indications
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were followed, or whether following the indications led to superior outcomes. Outcomes of FDO have been reported by a number of authors. Several authors report good long-term outcomes for both deformity correction and gait improvement [4,7]. However, questions have been raised about the quality of short-term outcomes. Dreher and colleagues found that rates of over- and under-correction are problematic in up to 59% of mildly involved limbs [8]. A conclusion of Dreher’s study was that FDO should not be performed on limbs with less than 158 internal hip rotation during gait. The goal of anteversion correction in the absence of a dynamic deformity should therefore be questioned. The purposes of our study were to derive a set of indications for FDO based on historic practice at a single center, and to propose treatment guidelines derived from the criteria that can lead to improved outcomes. 2. Methods The database in Gillette Children’s Specialty Healthcare Center for Gait and Motion Analysis was queried for candidate limbs using the following rules: Diagnosis of CP. Treatment by single-event multi-level surgery (SEMLS; defined as two or more major orthopedic procedures on a limb). Preoperative gait analysis no more than 24 months prior to SEMLS. Postoperative gait analysis between 9 and 36 months after SEMLS. Age between 4 and 18 at time of pre-operative gait analysis. Limb status was classified as +FDO or FDO based on whether or not an FDO was included as part of the SEMLS. At our center, the primary technique for FDO is the inter-trochanteric method described in 1980 [9]. There is some discussion of the relative merits and drawbacks of proximal versus distal derotations [10]. The question of proximal versus distal technique is not addressed in this study. Furthermore, the minority of limbs for which the FDO was performed primarily to correct hip subluxation/dislocation are pooled with the entire sample. It is clear that in these limbs, gait outcome is a secondary concern. Nevertheless, understanding the gait outcomes is useful in guiding the decision and educating the patient. A set of 287 variables (features) were extracted for each limb. The features included information related to birth history (e.g. weeks premature), developmental history (e.g. age of first step), treatment history (e.g. prior surgery), functional status (e.g. GMFCS level), comprehensive physical examination (e.g. joint range-ofmotion), gait efficiency (e.g. energy cost), and gait data derived from instrumented three-dimensional gait analysis (e.g. joint kinematics). Gait data had been previously collected as part of clinical care using Vicon hardware and post-processing software (Vicon Clinical Manager, Plug-in-Gait, Vicon Motion Systems, Ltd., Oxford UK). The features were then used in conjunction with the Random Forest (RF) algorithm to predict whether an FDO was performed on a limb, and identify features important to the prediction (Matlab R2011a, Mathworks, Natick MA). The RF algorithm is an ensemble learning approach that has been shown to be highly effective for solving complex classification problems [11]. The RF algorithm has been recently used to successfully predict surgical outcomes in children with CP [12]. The algorithm consists of amassing a large number of decision trees (forest) constructed using standard classification tree methods [13]. The overall predicted class of an observation is determined by the majority vote of the individual trees within the
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forest. In this study, the classes are FDO, and each limb is an observation. Further details about the method can be found elsewhere [11]. Feature importance can be measured by the decrease in classification accuracy when the values of a feature are permuted among the observations. Models containing small numbers of important features frequently outperform full models. For this study, reduced models were built by sorting features according to importance, then building models with successively larger numbers of features. A reduced model was chosen that optimized a set of typical classification performance metrics. Similarity between limbs was computed using the RF algorithm’s inherent proximity measure [11]. The proximity matrix of all limbs was found, and converted to a Euclidean distance using standard metric multidimensional scaling (MDS) methods [14]. Converting from proximity to MDS coordinates allows limbs to be viewed in a scatter-plot, with similar limbs ending up near one another. A K-means cluster analysis was performed on the MDS scores to identify homogeneous regions [15]. Differences between clusters (preoperative, postoperative, or change), or within a cluster (pre to post), were tested for significance using t-tests (paired or independent, depending on the comparison), with significance set at p < 0.05. Outcome was based on improvement in transverse plane gait parameters and anteversion as measured with the trochanteric prominence angle test [16]. The FDO is intended to improve transverse plane gait kinematics by correcting hip rotation. Associated improvements in pelvic rotation and foot progression are also expected; though clearly these depend on concomitant surgery, such as tibial derotational osteotomy (TDO) and foot deformity correction. Transverse plane outcomes at different levels were defined as mean stance-phase pelvic rotation, hip rotation, and foot progression. A good outcome for each of these was defined as a postoperative level within 1.5 standard deviations of normal, or an improvement of 1.5 standard deviations from the preoperative level. Overall transverse plane alignment was assessed using a scaled combination of the pelvis, hip, and foot angles. This measure, referred to as the Transverse Plane Deviation Index (TPDI), was derived using methods analogous to the Gait Deviation Index, and Pelvis/Hip Deviation Index described elsewhere [17,18]. A TPDI of 100 or higher indicates transverse plane kinematics within normal limits. Every 10 point decrement is one standard deviation away from normal. Anteversion outcome was considered good if the postoperative anteversion was between 58 and 208. 3. Results The query resulted in 1088 limbs. Of these 1088 limbs, 73% received FDO as part of the SEMLS. The performance of a reduced model containing 200 trees and the 17 most important features resulted in excellent performance metrics (Table 1). The features of the model were grouped using clinical reasoning into those related to anteversion, age, dynamic hip rotation in gait, and prior FDO surgery. The MDS analysis showed that over 80% of the variance in interlimb proximity was accounted for by the first two MDS coordinates. Visual inspection of the limbs plotted in MDS space showed a hub-and-spoke arrangement, suggesting four naturally occurring clusters, which can be thought of as four distinct regions of the surgical indications. The K-means cluster analysis (K = 4) resulted in two homogeneous +FDO clusters, one homogeneous FDO cluster, and a heterogeneous cluster with nearly equal numbers of +FDO and FDO limbs (Fig. 1). The two +FDO clusters differed significantly (p < 0.05) in the amount of dynamic hip rotation present during gait (full gait profiles available in supplementary material) (Table 2). The mean
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Table 1 Model performance. Confusion matrix
Predicted +FDO
Predicted
Observed +FDO Observed FDO
686 109
54 239
FDO
Diagnostic metrics Acc .85
Sens .93
Spec .69
PPV .86
NPV .82
RR 4.7
MCC .65
AUC .91
Model features by category Anteversion Anteversion Hip internal ROM
Age Age Mass
Hip external ROM
Hip rotation in gait Max stance hip rot Min stance hip rot
Prior FDO Prior FDO Prior gastrocnemius length
Mean stance hip rot Max overall hip rot Min overall hip rot Mean overall hip rot Initial contact hip rot
Prior instrumentation removal Prior foot bone surgery Prior foot soft tissue surgery
Acc – accuracy, Sens – sensitivity, Spec – specificity, PPV – positive predictive value, NPV – negative predictive value, RR – relative risk, MCC – Matthews correlation coefficient, AUC – area under the receiver operating characteristic curve.
anteversion and the internal/external hip range-of-motion by physical exam were equal between the two +FDO clusters (p > 0.05). Limbs in one +FDO cluster exhibited significant internal hip rotation, while hip rotation for limbs in the other +FDO cluster were close to neutral. The +FDO clusters were therefore labeled ‘‘Anteversion and Internal Rotation’’ and ‘‘Anteversion Only’’; the word ‘‘Only’’ referring to the lack of internal hip rotation during gait. As would be expected, the FDO cluster (‘‘No FDO’’) had nearly normal levels of both anteversion and dynamic hip rotation during gait. The mixed cluster (‘‘Mixed’’) exhibited moderate amounts of both anteversion and dynamic internal hip rotation. At the deformity correction level, excessive anteversion present prior to SEMLS was improved equally in the +FDO clusters (p > 0.05). For the Anteversion and Internal Rotation and
Anteversion Only clusters respectively, median preoperative anteversion of 608 and 558 was corrected to 208 and 158, with 59% and 71% good outcomes (Fig. 2). Anteversion was essentially unchanged in the No FDO cluster (208 pre to 158 post, 58% good outcomes). In the Mixed cluster anteversion changed from 408 pre to 158 post, with 62% good outcomes. Changes in overall transverse plane gait alignment depended on cluster (Fig. 3a and b). The superiority of outcomes in the Anteversion and Internal Rotation cluster was clear, as was the lack of improvement in the Anteversion Only cluster. The TPDI improved by more than 15 points for the Anteversion and Internal Rotation cluster, but worsened slightly in the Anteversion Only cluster (+15.3 vs. 0.4, p < 0.05). The Mixed cluster improved by 6.9 points, while the No FDO cluster improved by 3.4 points. The overall transverse plane outcomes can be related to changes at specific levels. Changes in transverse plane gait alignment at the pelvis, hip and foot depended on cluster (Fig. 3c). Of particular interest was the difference in transverse plane outcome at the foot between the Anteversion and Internal Rotation cluster (65% good outcomes), and the Anteversion Only cluster (50% good outcomes). On average, the foot progression in the Anteversion Only cluster changed from nearly normal preSEMLS to more than one standard deviation external post-SEMLS. Pre-SEMLS tibial torsion was equal between the two +FDO groups (p > 0.05), as was the rate of tibial derotational osteotomies, bony foot correction surgery and most concomitant surgeries (see Supplementary Material). 4. Discussion
Fig. 1. The first two multidimensional scaling (MDS) coordinates separate the limbs into four clusters: three branches and a central hub. The branches are the homogeneous clusters (two +FDO clusters, and one FDO cluster). The central hub is a heterogeneous transition zone. The MDS coordinates each represent linear combinations of the predictive features. For this model, over 80% of the variance in the features is accounted for with two MDS coordinates.
This study used the RF algorithm to discover and quantify historic indications for FDO as part of SEMLS at a single center. The study also examined the impact of the criteria on gait outcomes. Overall, the study results show that the RF algorithm accurately identifies historic FDO criteria at a single center. The criteria are clinically sensible. The MDS and cluster analysis provide rich insight into four clinically relevant domains of limbs requiring different treatment algorithms. The RF algorithm performed exceptionally well; with overall accuracy and predictive values in the mid-80% range, and an area under the receiver operation characteristic curve greater than 0.90. This level of performance is particularly good considering the complex nature of the problem studied. It is well known that decision-making in CP is variable, and thus the level of accuracy obtained by the classifier is unexpectedly high [19]. This suggests that not only does the RF algorithm
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Table 2 Description of clusters. Cluster
1
2
3
4
Name
Anteversion and internal rotation
Anteversion only
No FDO
Mixed
Number of limbs
315 (29%)
170 (16%)
153 (14%)
450 (41%)
Composition
100% +FDO
99% +FDO
3% +FDO
56% +FDO
85.6% 56.9% 49.7% 79.7% 49.0%
29.8% 19.8% 19.3% 34.4% 19.3%
Prior FDO
Prior Prior Prior Prior Prior
FDO foot bony surgery foot soft tissue surgery gastrocnemius lengthening instrumentation removal
0.3% 2.2% 2.9% 12.4% 1.9%
0.6% 1.2% 2.4% 7.1% 1.2%
Age
Age (yr) Mass (kg)
8.5(2.8) 25.6(9.7)
8.0(2.1) 23.9(6.6)
12.3(2.5) 41.5(12.7)
10.6(3.3) 33.8(12.9)
Anteversion
Anteversion (deg) Hip external ROM (deg) Hip internal ROM (deg)
61(9) 23(12) 74(9)
57(9) 26(10) 72(8)
18(10) 42(14) 46(11)
40(13) 33(14) 60(12)
Hip rotation in gait
Max. hip rotation (deg) Min. hip rotation (deg) Max. stance hip rotation (deg) Min. stance hip rotation (deg) Mean hip rotation (deg) Mean stance hip rotation (deg) Initial contact hip rotation (deg)
30.6(9.0) 17.8(9.6) 29.5(8.9) 19.3(9.0) 24.0(8.6) 24.4(8.5) 22.9(9.9)
11.4(7.4) 3.3(7.6) 9.9(7.0) 1.7(7.2) 4.0(6.7) 4.3(6.5) 2.9(8.3)
7.1(10.1) 7.4(9.6) 4.6(10.2) 6.5(9.5) 0.6(9.4) 1.3(9.6) 2.8(10.4)
17.0(12.5) 2.2(12.6) 15.3(12.5) 3.6(12.4) 9.5(12.0) 9.4(12.0) 7.8(12.8)
Numbers in parentheses are sample standard deviation.
accurately identify the historic criteria, but also that there has been broad intra-institutional agreement among a group of surgeons during the time period covered by the study (majority of limbs operated on by seven surgeons over more than 15 years).
The ensemble nature of the RF algorithm makes it impossible to give explicit criteria in familiar terms; such as anteversion greater than 358 or hip rotation greater than 158. The prediction of the RF incorporates complex interactions between variables to calculate
Fig. 2. Substantial corrections were seen in the Anteversion and Internal Rotation and Anteversion Only clusters, moderate correction in the Mixed cluster, and no change in the No FDO cluster.
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Fig. 3. Transverse plane outcomes depended on cluster. Among the two +FDO clusters, overall transverse plane outcomes (TPDI) were excellent in the Anteversion and Internal Rotation cluster (~TPDI > 15, 80% good outcomes). In the Anteversion Only cluster, TPDI decreased and only 40% of the limbs had a good outcome. The overall outcomes can be further understood from the level-by-level outcomes, where it is clear that detrimental changes in foot progression are problematic in the Anteversion Only cluster.
the likelihood of a limb undergoing FDO as part of a SEMLS. In lieu of specific variables and levels, it is possible to describe the relative importance of variables, to look at distributions of variables among classes, and to use clinical reasoning as a way of understanding the criteria. The indications for FDO were clearly visible in the data distributions, and included excessive femoral anteversion, the absence of a prior FDO, and age around 8.5 years. The role of dynamic internal hip rotation during gait was mixed, as will be discussed below. The cluster analysis revealed a clear pattern among the limbs. Among the +FDO and FDO clusters, the clinical presentations were distinct and the algorithm gave homogeneous guidance. The +FDO clusters were well matched in terms of most features. They differed significantly, however, in the amount of dynamic internal hip rotation present during gait. In the Anteversion and Internal Rotation cluster hip rotation was markedly internal, while in the Anteversion Only cluster it was neutral. This indicates that, unexpectedly, hip rotation during gait played only a minor role in the surgical indications; confirming that anteversion correction was a primary surgical goal. Transverse plane outcomes were dependent on cluster. The best outcomes were unquestionably in the Anteversion and Internal Rotation cluster. These limbs improved significantly in the transverse plane (TPDI, pelvis, hip, and foot). In contrast, limbs in the Anteversion Only cluster did not improve in the transverse plane overall (TPDI), and had a high rate of poor outcomes at the foot. Preoperative foot progression angle was not a feature of the criteria, indicating it was not used historically as a treatment indicator. It is also worth noting that tibial derotations and bony
foot corrections were well matched between the two +FDO clusters; ruling out either of these factors as accounting for the differences in the foot progression outcomes. Limbs in the FDO cluster improved slightly in the transverse plane, and had an intermediate rate of good outcomes from pelvis to foot. Based on preoperative anteversion levels, it would appear that other factors (tibial torsion, foot deformity) are the major factors in the FDO cluster’s outcome. The Mixed cluster is typical of ‘‘real-world’’ clinical practice. It is a region where levels of deformity are moderate, and factors other than gait and orthopedic problems may play a significant role in the surgical decision. Outcomes in the Mixed cluster were generally good, but due to the heterogeneous nature of the limb characteristics and treatments, it is not possible to generalize about this cluster. The results of this study provide guidance for future decisions regarding recommendation for FDO. 1. Limbs in the Anteversion and Internal Rotation cluster should receive FDO. The prediction accuracy was high, and the outcomes were excellent in terms of both deformity correction and gait improvement. 2. Limbs in the Anteversion Only cluster are at risk of developing an excessive external foot progression angle. While anteversion correction was achieved with FDO, excessive external foot progression was found to be a significant risk. A less aggressive surgical goal, with slightly less-correction of the anteversion, may lead to satisfactory results for deformity and hip rotation while maintaining an acceptable foot progression angle. Alternatively, this group may have an acceptable outcome without an FDO.
M.H. Schwartz et al. / Gait & Posture 39 (2014) 778–783
3. Limbs in the No FDO cluster should not receive FDO. The prediction accuracy in this cluster was high, and the outcomes of the cluster were moderate. There was nothing to suggest that an FDO would improve these outcomes. Improvements may be possible from better assessment and treatment of other transverse plane factors (tibial torsion and foot deformity). 4. Limbs in the Mixed cluster must be evaluated using traditional clinical means. Outcomes were generally good, but due to heterogeneity of limbs and treatments, and low prediction accuracy in this cluster, the RF model cannot give guidance on inclusion of an FDO. The treatment algorithm suggested by this study has limitations. It is important to note that the Mixed cluster, for which the algorithm gave no guidance, comprised 41% of all limbs. Future work will focus on identifying additional factors that influence treatment decisions and outcomes among these limbs. Additional analysis is also warranted to further understand what factors lead to poor outcomes in 20% of the Anteversion and Internal Rotation cluster. A further limitation of the current model is that it only indicates which limbs should receive an FDO, but not the amount of derotation needed. This is a critical factor to explore, given the apparent ‘‘overcorrection’’ observed in the Anteversion Only cluster. Anteversion is an important feature of the criteria; but anteversion measured by physical examination may be substantially different from what is measured intraoperatively [16]. It is possible that more accurate measures of anteversion would lead to improved guidance. A clear message from this study is that gait improvements are maximized when treatment is consistent with indications from both clinical examination and gait analysis. Postoperative transverse plane alignment was optimized when derotations were performed on limbs with significant internal hip rotation identified by gait analysis. This conclusion is consistent with other studies that have shown the impact of gait data on treatment outcome [8,20]. There may be reasons to derotate an anteverted femur even in the absence of internal hip rotation. Examples include correcting or preventing hip subluxation, or concerns about abductor weakness during the adolescent growth spurt. The important lesson of this study is that if derotational osteotomy is performed to correct anteversion on such limbs, then additional considerations are needed if good transverse plane gait alignment from pelvis-to-foot is desired. Conflict of interest The authors of this manuscript attest to the fact that we do not have any conflicts of interest to disclose.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.gaitpost.2013. 10.016. References [1] Robin J, Graham HK, Selber P, Dobson F, Smith K, Baker R. Proximal femoral geometry in cerebral palsy – a population-based cross-sectional study. J Bone Joint Surg Br 2008;90B(10):1372–9. [2] Arnold AS, Komattu AV, Delp SL. Internal rotation gait: a compensatory mechanism to restore abduction capacity decreased by bone deformity? Dev Med Child Neurol 1997;39(1):40–4. [3] Somerville EW. Persistent foetal alignment of the hip. J Bone Joint Surg Br 1957;39B(1):106–13. [4] Ounpuu S, DeLuca P, Davis R, Romness M. Long-term effects of femoral derotation osteotomies: an evaluation using three-dimensional gait analysis. J Pediatr Orthop 2002;22(2):139–45. [5] Kim H, Aiona M, Sussman M. Recurrence after femoral derotational osteotomy in cerebral palsy. J Pediatr Orthop 2005;25(6):739–43. [6] Hoffer MM, Prietto C, Koffman M. Supracondylar derotational osteotomy of the femur for internal-rotation of the thigh in the cerebral-palsied child. J Bone Joint Surg Am 1981;63(3):389–93. [7] Dreher T, Wolf SI, Heitzmann D, Swartman B, Schuster W, Gantz S, Hagmann S, Doderlein L, Braatz F. Long-term outcome of femoral derotation osteotomy in children with spastic diplegia. Gait Posture 2012;36(3):467–70. [8] Dreher T, Wolf S, Braatz F, Patikas D, Doderlein L. Internal rotation gait in spastic diplegia – critical considerations for the femoral derotation osteotomy. Gait Posture 2007;26(1):25–31. [9] Root L, Siegal T. Osteotomy of the hip in children – posterior approach. J Bone Joint Surg Am 1980;62(4):571–5. [10] Pirpiris M, Trivett A, Baker R, Rodda J, Nattrass GR, Graham HK. Femoral derotation osteotomy in spastic diplegia – proximal or distal? J Bone Joint Surg Br 2003;85B(2):265–72. [11] Breiman L. Random forests. Mach Learn 2001;45(1):5–32. [12] Schwartz MH, Rozumalski A, Truong W, Novacheck TF. Predicting the outcome of intramuscular psoas lengthening in children with cerebral palsy using preoperative gait data and the random forest algorithm. Gait Posture 2013;37(4):473–9. [13] Breiman L, Friedman JH, Olshen RA, Stone CJ. Classification and Regression Trees. Boca Raton: Chapman & Hall/CRC; 1984. [14] Torgerson WS. Multidimensional scaling: I. Theory and method. Psychometrika 1952;17(4):401–19. [15] MacQueen JB. Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; 1967. p. 281–97. [16] Ruwe PA, Gage JR, Ozonoff MB, Deluca PA. Clinical determination of femoral anteversion – a comparison with established techniques. J Bone Joint Surg Am 1992;74A(6):820–30. [17] Schwartz MH, Rozumalski A. The gait deviation index: a new comprehensive index of gait pathology. Gait Posture 2008;28(3):351–7. [18] Truong WH, Rozumalski A, Novacheck TF, Beattie C, Schwartz MH. Evaluation of conventional selection criteria for psoas lengthening for individuals with cerebral palsy: a retrospective, case-controlled study. J Pediatr Orthop 2011;534–40. [19] Skaggs DL, Rethlefsen SA, Kay RM, Dennis SW, Reynolds RAK, Tolo VT. Variability in gait analysis interpretation. J Pediatr Orthop 2000;20(6):759–64. [20] de Morais MC, Yoshida R, Carvalho WD, Stein HE, Novo NF. Are the recommendations from three-dimensional gait analysis associated with better postoperative outcomes in patients with cerebral palsy? Gait Posture 2008;28(2):316–22.
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Femoral derotational osteotomy: Surgical indications and outcomes in children with cerebral palsy Michael H. Schwartz a,b,*, Adam Rozumalski a, Tom F. Novacheck a,b a b
Gillette Children’s Specialty Healthcare, USA University of Minnesota – Twin Cities, Department of Orthopaedic Surgery, USA
A R T I C L E I N F O
A B S T R A C T
Article history: Received 4 September 2013 Received in revised form 14 October 2013 Accepted 19 October 2013
Excessive femoral anteversion is common among children with cerebral palsy, and is, frequently treated by a femoral derotational osteotomy (FDO). It is important to understand surgical, indications for FDO, and the impact of these indications on the treatment outcomes. The Random Forest algorithm was used to objectively identify historical surgical indications in a large retrospective, cohort of 1088 limbs that had previously undergone single-event multi-level surgery. Treatment, outcome was based on transverse plane kinematics obtained from three-dimensional gait analysis. The, classifier effectively identified the historic indications (accuracy = .85, sensitivity = .93, specificity = .69, positive predictive value = .86, negative predictive value = .82), and naturally divided limbs into four, clusters: two homogeneous +FDO clusters (with/without significant internal hip rotation during gait), one homogeneous FDO cluster, and a mixed cluster. Concomitant surgeries were similar among the, clusters. Limbs with excessive anteversion and internal hip rotation during gait had excellent outcomes, in the transverse plane. Limbs with excessive anteversion but only mild internal hip rotation had good, outcomes at the hip level; but a significant number of these limbs ended up with an excessive external, foot progression angle. The Random Forest algorithm was highly effective for identifying and, organizing historic surgical indications. The derived criteria can be used to give surgical decision making, guidance in a majority of limbs. The results suggest that limbs with anteversion and significant, internal hip rotation during gait benefit from an FDO, but limbs with excessive anteversion and only, mild internal hip rotation are at risk of developing an excessive external foot progression angle. ß 2013 Elsevier B.V. All rights reserved.
Keywords: Femur Anteversion Cerebral palsy Random forest Outcome
1. Introduction Excessive femoral anteversion is a common orthopedic deformity in children with cerebral palsy (CP) [1]. Excessive anteversion has many consequences. Perhaps most important of these is that children with this deformity will often adopt a gait characterized by excessive internal hip rotation. The emergence of the internal hip rotation gait pattern has been explained by Arnold as a compensation for functional weakening of the hip abductors [2]. Internal hip rotation is effective for improving functional hip abductor strength, but comes at the cost of excessive internal foot progression. Internal foot progression is problematic since it can lead to tripping and foot dragging – which in turn can cause or exacerbate foot deformity. Internal rotation gait is also a significant cosmetic issue, and can lead to stigmatization and lowered
* Corresponding author at: Gillette Children’s Specialty Healthcare, James R. Gage Center for Gait and Motion Analysis, 205 University Ave, St. Paul, MN 55101, USA. Tel.: +1 612 226 5120. E-mail address: [email protected] (M.H. Schwartz). 0966-6362/$ – see front matter ß 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.gaitpost.2013.10.016
self-esteem. It is widely believed that excessive anteversion present after the maturation of gait is unlikely to resolve spontaneously [3]. Therefore, surgical correction of excessive anteversion is common among children with CP. There have been numerous scholarly articles discussing the indications for, and outcomes of, the FDO procedure. In terms of indications, the literature is vague, subjective, and occasionally contradictory. As would be expected, excessive anteversion is central to the existing indications; though to varying degrees. Meanwhile, gait indications vary in specificity and level. Ounpuu et al. state that FDO is indicated when hip internal rotation ROM is greater than 608, external rotation is less than 258, and dynamic hip internal rotation in gait is more than one SD internal compared to normal (approximately 108) [4]. The indications described by Kim et al. call for external rotation of the hip less than 158 on physical examination, and both hip internal rotation and internal foot progression angle during gait more than 108 from normal [5]. Hoffer et al. simply state that FDO is indicated ‘‘only when internal rotation of the anteverted femur interferes with gait’’ [6]. It is important to note that the outcome studies associated with these stated indications do not report how consistently the indications
M.H. Schwartz et al. / Gait & Posture 39 (2014) 778–783
were followed, or whether following the indications led to superior outcomes. Outcomes of FDO have been reported by a number of authors. Several authors report good long-term outcomes for both deformity correction and gait improvement [4,7]. However, questions have been raised about the quality of short-term outcomes. Dreher and colleagues found that rates of over- and under-correction are problematic in up to 59% of mildly involved limbs [8]. A conclusion of Dreher’s study was that FDO should not be performed on limbs with less than 158 internal hip rotation during gait. The goal of anteversion correction in the absence of a dynamic deformity should therefore be questioned. The purposes of our study were to derive a set of indications for FDO based on historic practice at a single center, and to propose treatment guidelines derived from the criteria that can lead to improved outcomes. 2. Methods The database in Gillette Children’s Specialty Healthcare Center for Gait and Motion Analysis was queried for candidate limbs using the following rules: Diagnosis of CP. Treatment by single-event multi-level surgery (SEMLS; defined as two or more major orthopedic procedures on a limb). Preoperative gait analysis no more than 24 months prior to SEMLS. Postoperative gait analysis between 9 and 36 months after SEMLS. Age between 4 and 18 at time of pre-operative gait analysis. Limb status was classified as +FDO or FDO based on whether or not an FDO was included as part of the SEMLS. At our center, the primary technique for FDO is the inter-trochanteric method described in 1980 [9]. There is some discussion of the relative merits and drawbacks of proximal versus distal derotations [10]. The question of proximal versus distal technique is not addressed in this study. Furthermore, the minority of limbs for which the FDO was performed primarily to correct hip subluxation/dislocation are pooled with the entire sample. It is clear that in these limbs, gait outcome is a secondary concern. Nevertheless, understanding the gait outcomes is useful in guiding the decision and educating the patient. A set of 287 variables (features) were extracted for each limb. The features included information related to birth history (e.g. weeks premature), developmental history (e.g. age of first step), treatment history (e.g. prior surgery), functional status (e.g. GMFCS level), comprehensive physical examination (e.g. joint range-ofmotion), gait efficiency (e.g. energy cost), and gait data derived from instrumented three-dimensional gait analysis (e.g. joint kinematics). Gait data had been previously collected as part of clinical care using Vicon hardware and post-processing software (Vicon Clinical Manager, Plug-in-Gait, Vicon Motion Systems, Ltd., Oxford UK). The features were then used in conjunction with the Random Forest (RF) algorithm to predict whether an FDO was performed on a limb, and identify features important to the prediction (Matlab R2011a, Mathworks, Natick MA). The RF algorithm is an ensemble learning approach that has been shown to be highly effective for solving complex classification problems [11]. The RF algorithm has been recently used to successfully predict surgical outcomes in children with CP [12]. The algorithm consists of amassing a large number of decision trees (forest) constructed using standard classification tree methods [13]. The overall predicted class of an observation is determined by the majority vote of the individual trees within the
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forest. In this study, the classes are FDO, and each limb is an observation. Further details about the method can be found elsewhere [11]. Feature importance can be measured by the decrease in classification accuracy when the values of a feature are permuted among the observations. Models containing small numbers of important features frequently outperform full models. For this study, reduced models were built by sorting features according to importance, then building models with successively larger numbers of features. A reduced model was chosen that optimized a set of typical classification performance metrics. Similarity between limbs was computed using the RF algorithm’s inherent proximity measure [11]. The proximity matrix of all limbs was found, and converted to a Euclidean distance using standard metric multidimensional scaling (MDS) methods [14]. Converting from proximity to MDS coordinates allows limbs to be viewed in a scatter-plot, with similar limbs ending up near one another. A K-means cluster analysis was performed on the MDS scores to identify homogeneous regions [15]. Differences between clusters (preoperative, postoperative, or change), or within a cluster (pre to post), were tested for significance using t-tests (paired or independent, depending on the comparison), with significance set at p < 0.05. Outcome was based on improvement in transverse plane gait parameters and anteversion as measured with the trochanteric prominence angle test [16]. The FDO is intended to improve transverse plane gait kinematics by correcting hip rotation. Associated improvements in pelvic rotation and foot progression are also expected; though clearly these depend on concomitant surgery, such as tibial derotational osteotomy (TDO) and foot deformity correction. Transverse plane outcomes at different levels were defined as mean stance-phase pelvic rotation, hip rotation, and foot progression. A good outcome for each of these was defined as a postoperative level within 1.5 standard deviations of normal, or an improvement of 1.5 standard deviations from the preoperative level. Overall transverse plane alignment was assessed using a scaled combination of the pelvis, hip, and foot angles. This measure, referred to as the Transverse Plane Deviation Index (TPDI), was derived using methods analogous to the Gait Deviation Index, and Pelvis/Hip Deviation Index described elsewhere [17,18]. A TPDI of 100 or higher indicates transverse plane kinematics within normal limits. Every 10 point decrement is one standard deviation away from normal. Anteversion outcome was considered good if the postoperative anteversion was between 58 and 208. 3. Results The query resulted in 1088 limbs. Of these 1088 limbs, 73% received FDO as part of the SEMLS. The performance of a reduced model containing 200 trees and the 17 most important features resulted in excellent performance metrics (Table 1). The features of the model were grouped using clinical reasoning into those related to anteversion, age, dynamic hip rotation in gait, and prior FDO surgery. The MDS analysis showed that over 80% of the variance in interlimb proximity was accounted for by the first two MDS coordinates. Visual inspection of the limbs plotted in MDS space showed a hub-and-spoke arrangement, suggesting four naturally occurring clusters, which can be thought of as four distinct regions of the surgical indications. The K-means cluster analysis (K = 4) resulted in two homogeneous +FDO clusters, one homogeneous FDO cluster, and a heterogeneous cluster with nearly equal numbers of +FDO and FDO limbs (Fig. 1). The two +FDO clusters differed significantly (p < 0.05) in the amount of dynamic hip rotation present during gait (full gait profiles available in supplementary material) (Table 2). The mean
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Table 1 Model performance. Confusion matrix
Predicted +FDO
Predicted
Observed +FDO Observed FDO
686 109
54 239
FDO
Diagnostic metrics Acc .85
Sens .93
Spec .69
PPV .86
NPV .82
RR 4.7
MCC .65
AUC .91
Model features by category Anteversion Anteversion Hip internal ROM
Age Age Mass
Hip external ROM
Hip rotation in gait Max stance hip rot Min stance hip rot
Prior FDO Prior FDO Prior gastrocnemius length
Mean stance hip rot Max overall hip rot Min overall hip rot Mean overall hip rot Initial contact hip rot
Prior instrumentation removal Prior foot bone surgery Prior foot soft tissue surgery
Acc – accuracy, Sens – sensitivity, Spec – specificity, PPV – positive predictive value, NPV – negative predictive value, RR – relative risk, MCC – Matthews correlation coefficient, AUC – area under the receiver operating characteristic curve.
anteversion and the internal/external hip range-of-motion by physical exam were equal between the two +FDO clusters (p > 0.05). Limbs in one +FDO cluster exhibited significant internal hip rotation, while hip rotation for limbs in the other +FDO cluster were close to neutral. The +FDO clusters were therefore labeled ‘‘Anteversion and Internal Rotation’’ and ‘‘Anteversion Only’’; the word ‘‘Only’’ referring to the lack of internal hip rotation during gait. As would be expected, the FDO cluster (‘‘No FDO’’) had nearly normal levels of both anteversion and dynamic hip rotation during gait. The mixed cluster (‘‘Mixed’’) exhibited moderate amounts of both anteversion and dynamic internal hip rotation. At the deformity correction level, excessive anteversion present prior to SEMLS was improved equally in the +FDO clusters (p > 0.05). For the Anteversion and Internal Rotation and
Anteversion Only clusters respectively, median preoperative anteversion of 608 and 558 was corrected to 208 and 158, with 59% and 71% good outcomes (Fig. 2). Anteversion was essentially unchanged in the No FDO cluster (208 pre to 158 post, 58% good outcomes). In the Mixed cluster anteversion changed from 408 pre to 158 post, with 62% good outcomes. Changes in overall transverse plane gait alignment depended on cluster (Fig. 3a and b). The superiority of outcomes in the Anteversion and Internal Rotation cluster was clear, as was the lack of improvement in the Anteversion Only cluster. The TPDI improved by more than 15 points for the Anteversion and Internal Rotation cluster, but worsened slightly in the Anteversion Only cluster (+15.3 vs. 0.4, p < 0.05). The Mixed cluster improved by 6.9 points, while the No FDO cluster improved by 3.4 points. The overall transverse plane outcomes can be related to changes at specific levels. Changes in transverse plane gait alignment at the pelvis, hip and foot depended on cluster (Fig. 3c). Of particular interest was the difference in transverse plane outcome at the foot between the Anteversion and Internal Rotation cluster (65% good outcomes), and the Anteversion Only cluster (50% good outcomes). On average, the foot progression in the Anteversion Only cluster changed from nearly normal preSEMLS to more than one standard deviation external post-SEMLS. Pre-SEMLS tibial torsion was equal between the two +FDO groups (p > 0.05), as was the rate of tibial derotational osteotomies, bony foot correction surgery and most concomitant surgeries (see Supplementary Material). 4. Discussion
Fig. 1. The first two multidimensional scaling (MDS) coordinates separate the limbs into four clusters: three branches and a central hub. The branches are the homogeneous clusters (two +FDO clusters, and one FDO cluster). The central hub is a heterogeneous transition zone. The MDS coordinates each represent linear combinations of the predictive features. For this model, over 80% of the variance in the features is accounted for with two MDS coordinates.
This study used the RF algorithm to discover and quantify historic indications for FDO as part of SEMLS at a single center. The study also examined the impact of the criteria on gait outcomes. Overall, the study results show that the RF algorithm accurately identifies historic FDO criteria at a single center. The criteria are clinically sensible. The MDS and cluster analysis provide rich insight into four clinically relevant domains of limbs requiring different treatment algorithms. The RF algorithm performed exceptionally well; with overall accuracy and predictive values in the mid-80% range, and an area under the receiver operation characteristic curve greater than 0.90. This level of performance is particularly good considering the complex nature of the problem studied. It is well known that decision-making in CP is variable, and thus the level of accuracy obtained by the classifier is unexpectedly high [19]. This suggests that not only does the RF algorithm
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Table 2 Description of clusters. Cluster
1
2
3
4
Name
Anteversion and internal rotation
Anteversion only
No FDO
Mixed
Number of limbs
315 (29%)
170 (16%)
153 (14%)
450 (41%)
Composition
100% +FDO
99% +FDO
3% +FDO
56% +FDO
85.6% 56.9% 49.7% 79.7% 49.0%
29.8% 19.8% 19.3% 34.4% 19.3%
Prior FDO
Prior Prior Prior Prior Prior
FDO foot bony surgery foot soft tissue surgery gastrocnemius lengthening instrumentation removal
0.3% 2.2% 2.9% 12.4% 1.9%
0.6% 1.2% 2.4% 7.1% 1.2%
Age
Age (yr) Mass (kg)
8.5(2.8) 25.6(9.7)
8.0(2.1) 23.9(6.6)
12.3(2.5) 41.5(12.7)
10.6(3.3) 33.8(12.9)
Anteversion
Anteversion (deg) Hip external ROM (deg) Hip internal ROM (deg)
61(9) 23(12) 74(9)
57(9) 26(10) 72(8)
18(10) 42(14) 46(11)
40(13) 33(14) 60(12)
Hip rotation in gait
Max. hip rotation (deg) Min. hip rotation (deg) Max. stance hip rotation (deg) Min. stance hip rotation (deg) Mean hip rotation (deg) Mean stance hip rotation (deg) Initial contact hip rotation (deg)
30.6(9.0) 17.8(9.6) 29.5(8.9) 19.3(9.0) 24.0(8.6) 24.4(8.5) 22.9(9.9)
11.4(7.4) 3.3(7.6) 9.9(7.0) 1.7(7.2) 4.0(6.7) 4.3(6.5) 2.9(8.3)
7.1(10.1) 7.4(9.6) 4.6(10.2) 6.5(9.5) 0.6(9.4) 1.3(9.6) 2.8(10.4)
17.0(12.5) 2.2(12.6) 15.3(12.5) 3.6(12.4) 9.5(12.0) 9.4(12.0) 7.8(12.8)
Numbers in parentheses are sample standard deviation.
accurately identify the historic criteria, but also that there has been broad intra-institutional agreement among a group of surgeons during the time period covered by the study (majority of limbs operated on by seven surgeons over more than 15 years).
The ensemble nature of the RF algorithm makes it impossible to give explicit criteria in familiar terms; such as anteversion greater than 358 or hip rotation greater than 158. The prediction of the RF incorporates complex interactions between variables to calculate
Fig. 2. Substantial corrections were seen in the Anteversion and Internal Rotation and Anteversion Only clusters, moderate correction in the Mixed cluster, and no change in the No FDO cluster.
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Fig. 3. Transverse plane outcomes depended on cluster. Among the two +FDO clusters, overall transverse plane outcomes (TPDI) were excellent in the Anteversion and Internal Rotation cluster (~TPDI > 15, 80% good outcomes). In the Anteversion Only cluster, TPDI decreased and only 40% of the limbs had a good outcome. The overall outcomes can be further understood from the level-by-level outcomes, where it is clear that detrimental changes in foot progression are problematic in the Anteversion Only cluster.
the likelihood of a limb undergoing FDO as part of a SEMLS. In lieu of specific variables and levels, it is possible to describe the relative importance of variables, to look at distributions of variables among classes, and to use clinical reasoning as a way of understanding the criteria. The indications for FDO were clearly visible in the data distributions, and included excessive femoral anteversion, the absence of a prior FDO, and age around 8.5 years. The role of dynamic internal hip rotation during gait was mixed, as will be discussed below. The cluster analysis revealed a clear pattern among the limbs. Among the +FDO and FDO clusters, the clinical presentations were distinct and the algorithm gave homogeneous guidance. The +FDO clusters were well matched in terms of most features. They differed significantly, however, in the amount of dynamic internal hip rotation present during gait. In the Anteversion and Internal Rotation cluster hip rotation was markedly internal, while in the Anteversion Only cluster it was neutral. This indicates that, unexpectedly, hip rotation during gait played only a minor role in the surgical indications; confirming that anteversion correction was a primary surgical goal. Transverse plane outcomes were dependent on cluster. The best outcomes were unquestionably in the Anteversion and Internal Rotation cluster. These limbs improved significantly in the transverse plane (TPDI, pelvis, hip, and foot). In contrast, limbs in the Anteversion Only cluster did not improve in the transverse plane overall (TPDI), and had a high rate of poor outcomes at the foot. Preoperative foot progression angle was not a feature of the criteria, indicating it was not used historically as a treatment indicator. It is also worth noting that tibial derotations and bony
foot corrections were well matched between the two +FDO clusters; ruling out either of these factors as accounting for the differences in the foot progression outcomes. Limbs in the FDO cluster improved slightly in the transverse plane, and had an intermediate rate of good outcomes from pelvis to foot. Based on preoperative anteversion levels, it would appear that other factors (tibial torsion, foot deformity) are the major factors in the FDO cluster’s outcome. The Mixed cluster is typical of ‘‘real-world’’ clinical practice. It is a region where levels of deformity are moderate, and factors other than gait and orthopedic problems may play a significant role in the surgical decision. Outcomes in the Mixed cluster were generally good, but due to the heterogeneous nature of the limb characteristics and treatments, it is not possible to generalize about this cluster. The results of this study provide guidance for future decisions regarding recommendation for FDO. 1. Limbs in the Anteversion and Internal Rotation cluster should receive FDO. The prediction accuracy was high, and the outcomes were excellent in terms of both deformity correction and gait improvement. 2. Limbs in the Anteversion Only cluster are at risk of developing an excessive external foot progression angle. While anteversion correction was achieved with FDO, excessive external foot progression was found to be a significant risk. A less aggressive surgical goal, with slightly less-correction of the anteversion, may lead to satisfactory results for deformity and hip rotation while maintaining an acceptable foot progression angle. Alternatively, this group may have an acceptable outcome without an FDO.
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3. Limbs in the No FDO cluster should not receive FDO. The prediction accuracy in this cluster was high, and the outcomes of the cluster were moderate. There was nothing to suggest that an FDO would improve these outcomes. Improvements may be possible from better assessment and treatment of other transverse plane factors (tibial torsion and foot deformity). 4. Limbs in the Mixed cluster must be evaluated using traditional clinical means. Outcomes were generally good, but due to heterogeneity of limbs and treatments, and low prediction accuracy in this cluster, the RF model cannot give guidance on inclusion of an FDO. The treatment algorithm suggested by this study has limitations. It is important to note that the Mixed cluster, for which the algorithm gave no guidance, comprised 41% of all limbs. Future work will focus on identifying additional factors that influence treatment decisions and outcomes among these limbs. Additional analysis is also warranted to further understand what factors lead to poor outcomes in 20% of the Anteversion and Internal Rotation cluster. A further limitation of the current model is that it only indicates which limbs should receive an FDO, but not the amount of derotation needed. This is a critical factor to explore, given the apparent ‘‘overcorrection’’ observed in the Anteversion Only cluster. Anteversion is an important feature of the criteria; but anteversion measured by physical examination may be substantially different from what is measured intraoperatively [16]. It is possible that more accurate measures of anteversion would lead to improved guidance. A clear message from this study is that gait improvements are maximized when treatment is consistent with indications from both clinical examination and gait analysis. Postoperative transverse plane alignment was optimized when derotations were performed on limbs with significant internal hip rotation identified by gait analysis. This conclusion is consistent with other studies that have shown the impact of gait data on treatment outcome [8,20]. There may be reasons to derotate an anteverted femur even in the absence of internal hip rotation. Examples include correcting or preventing hip subluxation, or concerns about abductor weakness during the adolescent growth spurt. The important lesson of this study is that if derotational osteotomy is performed to correct anteversion on such limbs, then additional considerations are needed if good transverse plane gait alignment from pelvis-to-foot is desired. Conflict of interest The authors of this manuscript attest to the fact that we do not have any conflicts of interest to disclose.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.gaitpost.2013. 10.016. References [1] Robin J, Graham HK, Selber P, Dobson F, Smith K, Baker R. Proximal femoral geometry in cerebral palsy – a population-based cross-sectional study. J Bone Joint Surg Br 2008;90B(10):1372–9. [2] Arnold AS, Komattu AV, Delp SL. Internal rotation gait: a compensatory mechanism to restore abduction capacity decreased by bone deformity? Dev Med Child Neurol 1997;39(1):40–4. [3] Somerville EW. Persistent foetal alignment of the hip. J Bone Joint Surg Br 1957;39B(1):106–13. [4] Ounpuu S, DeLuca P, Davis R, Romness M. Long-term effects of femoral derotation osteotomies: an evaluation using three-dimensional gait analysis. J Pediatr Orthop 2002;22(2):139–45. [5] Kim H, Aiona M, Sussman M. Recurrence after femoral derotational osteotomy in cerebral palsy. J Pediatr Orthop 2005;25(6):739–43. [6] Hoffer MM, Prietto C, Koffman M. Supracondylar derotational osteotomy of the femur for internal-rotation of the thigh in the cerebral-palsied child. J Bone Joint Surg Am 1981;63(3):389–93. [7] Dreher T, Wolf SI, Heitzmann D, Swartman B, Schuster W, Gantz S, Hagmann S, Doderlein L, Braatz F. Long-term outcome of femoral derotation osteotomy in children with spastic diplegia. Gait Posture 2012;36(3):467–70. [8] Dreher T, Wolf S, Braatz F, Patikas D, Doderlein L. Internal rotation gait in spastic diplegia – critical considerations for the femoral derotation osteotomy. Gait Posture 2007;26(1):25–31. [9] Root L, Siegal T. Osteotomy of the hip in children – posterior approach. J Bone Joint Surg Am 1980;62(4):571–5. [10] Pirpiris M, Trivett A, Baker R, Rodda J, Nattrass GR, Graham HK. Femoral derotation osteotomy in spastic diplegia – proximal or distal? J Bone Joint Surg Br 2003;85B(2):265–72. [11] Breiman L. Random forests. Mach Learn 2001;45(1):5–32. [12] Schwartz MH, Rozumalski A, Truong W, Novacheck TF. Predicting the outcome of intramuscular psoas lengthening in children with cerebral palsy using preoperative gait data and the random forest algorithm. Gait Posture 2013;37(4):473–9. [13] Breiman L, Friedman JH, Olshen RA, Stone CJ. Classification and Regression Trees. Boca Raton: Chapman & Hall/CRC; 1984. [14] Torgerson WS. Multidimensional scaling: I. Theory and method. Psychometrika 1952;17(4):401–19. [15] MacQueen JB. Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; 1967. p. 281–97. [16] Ruwe PA, Gage JR, Ozonoff MB, Deluca PA. Clinical determination of femoral anteversion – a comparison with established techniques. J Bone Joint Surg Am 1992;74A(6):820–30. [17] Schwartz MH, Rozumalski A. The gait deviation index: a new comprehensive index of gait pathology. Gait Posture 2008;28(3):351–7. [18] Truong WH, Rozumalski A, Novacheck TF, Beattie C, Schwartz MH. Evaluation of conventional selection criteria for psoas lengthening for individuals with cerebral palsy: a retrospective, case-controlled study. J Pediatr Orthop 2011;534–40. [19] Skaggs DL, Rethlefsen SA, Kay RM, Dennis SW, Reynolds RAK, Tolo VT. Variability in gait analysis interpretation. J Pediatr Orthop 2000;20(6):759–64. [20] de Morais MC, Yoshida R, Carvalho WD, Stein HE, Novo NF. Are the recommendations from three-dimensional gait analysis associated with better postoperative outcomes in patients with cerebral palsy? Gait Posture 2008;28(2):316–22.
