Muscle Capacity to Accelerate the Body During Gait Varies with Foot Position in Cerebral Palsy

Journal Pre-proof Muscle Capacity to Accelerate the Body During Gait Varies with Foot Position in Cerebral Palsy Amy K. Hegarty, Max J. Kurz, Wayne Stuberg, Anne K. Silverman

PII:

S0966-6362(20)30075-8

DOI:

https://doi.org/10.1016/j.gaitpost.2020.02.014

Reference:

GAIPOS 7474

To appear in:

Gait & Posture

Received Date:

1 March 2019

Revised Date:

4 February 2020

Accepted Date:

18 February 2020

Please cite this article as: Hegarty AK, Kurz MJ, Stuberg W, Silverman AK, Muscle Capacity to Accelerate the Body During Gait Varies with Foot Position in Cerebral Palsy, Gait and amp; Posture (2020), doi: https://doi.org/10.1016/j.gaitpost.2020.02.014

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Muscle Capacity to Accelerate the Body During Gait Varies with Foot Position in Cerebral Palsy

Amy K. Hegartya, Max J. Kurzb, Wayne Stubergb, and Anne K. Silvermana

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Department of Mechanical Engineering

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Colorado School of Mines

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Golden, CO 80401

Department of Physical Therapy

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Munroe-Meyer Institute for Genetics and Rehabilitation, University of Nebraska Medical Center

Anne K. Silverman, Ph.D. Department of Mechanical Engineering Colorado School of Mines 1500 Illinois Street Golden, CO 80401 [email protected] Tel: 303-384-2162 Fax: 303-273-3602

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Address correspondence to:

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Omaha, NE 68198

Abstract Word Count: 203

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Text Word Count: 2818

Research Highlights:

1. Reduced muscle capacity to accelerate the body is associated with external FPAs 2. Transverse plane kinematics and skeletal alignment affect muscle acceleration capacity 3. Skeletal alignment and posture consideration are needed for cerebral palsy treatment

Abstract Background: Children with cerebral palsy (CP) often have altered gait patterns compared to their typically developing peers. These gait patterns are characterized based on sagittal plane

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kinematic deviations; however, many children with CP also walk with altered transverse plane

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kinematics.

muscles’ capacity to accelerate the body during gait?

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Research Question: How do both altered skeletal alignment and kinematic deviations affect

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Methods: A three-dimensional gait analysis was completed for 18 children with spastic CP (12.5 ± 2.9 years; GMFCS level II). Musculoskeletal models were developed for each participant, and

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tibial torsion, measured during a static standing trial and assessed using motion capture, was incorporated. An induced acceleration analysis was performed to evaluate the capacity of

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muscles to accelerate the body center of mass throughout stance. Differences between the rootmean-square muscle capacity for children with CP walking with internally rotated, standard, and externally rotated postures were evaluated. Results: Externally rotated postures resulted in a lower capacity to accelerate the body center of

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mass compared with internally rotated postures. Both changes in skeletal alignment and kinematics contributed to changes in muscle capacity to accelerate the body. Significance: Altered transverse plane skeletal alignment and compensatory kinematics should both be considered in surgical treatment of children with CP.

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Keywords: Musculoskeletal modeling, biomechanics, gait, children, foot progression angle

1.

Introduction Cerebral palsy (CP) is a neuromuscular disorder resulting from damage to the central

nervous system at or near the time of birth [1]. Children with CP often have altered gait patterns resulting in reduced walking ability [2]. These altered gait patterns can result from numerous altered musculoskeletal and neurological properties such as spastic muscles, skeletal deformities,

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and impaired muscle coordination [e.g., 3,4]. Specifically, torsional deformities in the long bones of the legs (i.e., femoral anteversion and excessive internal or external tibial torsion) are

interventions are often used to correct these deformities [7].

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commonly seen in children with CP as their skeletal system matures [5,6], and surgical

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Ninety-eight percent of children with CP have kinematic rotational deviation during gait

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[5]. However, only 25% of lower-limb torsion measured during gait can be explained by skeletal deformities [8]. Lower-limb transverse plane kinematic profiles during gait are often

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characterized by the foot progression angle (FPA), which quantifies the orientation of the foot relative to the direction of walking. Internally rotated FPAs are observed in 61% of children with

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CP, and externally rotated FPAs are observed in 21% of children with CP [5]. These altered FPAs can arise from skeletal malalignment, kinematic deviations during gait, or a combination of both. Often, children with CP have internal or external skeletal alignment yet walk within a normal range of FPAs due to transverse plane kinematic angles that alter the overall alignment of

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the lower-limbs during gait [5]. For example, compensatory internal rotation of the hips during gait is thought to restore the critical function of the hip abduction moment arm of the gluteus medius for individuals with excessive femoral anteversion [9]. To appropriately treat patients with rotational deficits, we must understand how altered skeletal alignments and kinematics affect the functional roles of muscles during daily activities.

Musculoskeletal modeling and simulation provide a platform to investigate this question noninvasively. Musculoskeletal modeling and simulation have been used to understand muscle coordination and the function of muscles in typically developing gait [e.g., 10] and in children with CP [e.g., 11–13]. Implications of altered skeletal alignment have also been investigated for idiopathic skeletal torsion of the femur and tibia, revealing greater estimates of joint contact forces in the hip and patellofemoral joint relative to typical skeletal alignment [14].

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The capacity of a muscle to accelerate the body, or muscle “potential”, is dependent

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primarily on the orientation of body segments, and explains how a muscle, when activated, can accelerate the body. Evaluating the capacity of muscles to accelerate the body can provide

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critical insight into the functional roles of muscles and is separately quantified from muscle

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coordination. Prior work suggests that excessive external tibial torsion substantially reduces the capacity of muscles to extend lower-limb joints and support the body [15,16]. The mechanism

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behind these functional deficits of lower-limb muscles is based on the position of the center of pressure (COP) in relation to the knee joint center, often referred to as lever arm dysfunction

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[16]. Reduced capacity to accomplish the critical functions of limb extension and body support may be one contributing factor to the development of crouch gait [15,16]. Previous work has established possible implications of external tibial torsion for children with CP; however, these studies evaluated the altered skeletal alignment within a single pose

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consistent with mid-stance of typically developing gait [15,16]. In this work, we explore the implications of both altered transverse plane skeletal alignment and kinematic deviations in the gait of children with CP. Therefore, the purpose of this study was to evaluate the effects of both internally rotated and externally rotated lower-limb postures incorporating both kinematic and skeletal sources of transverse plane deviations on the capacity of muscles to accelerate the body

center of mass (COM) during gait for children with CP. We further explore possible sources of altered muscle capacity by evaluating the COP and muscle moment arms for children with CP. 2.

Methods A three-dimensional gait analysis was completed for 18 children with spastic CP (Gross

Motor Function Classification System: level II, age: 12.5 ± 2.9 yrs., leg length: 0.81 ± 0.09 m,

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mass: 45.5 ± 14.9 kg, Males: 10) and approved by the University’s Committee for the Protection of Human Subjects. Children were excluded if they had undergone a tendon transfer surgery

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prior to participating or had undergone surgery or botulinum toxin-A injections within the last six months. All participants’ legal guardians provided written consent and all children gave their

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assent to participate.

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Lower body kinematics (Vicon Nexus, Oxford Metrics Group, Oxford, UK, 120 Hz) and ground reaction forces (AMTI, Watertown, MA, USA, 1200 Hz) were collected for each child

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walking overground and barefoot without any assistive devices at their self-selected walking speed. Sixteen lower body markers tracked the leg and pelvis kinematics. Marker trajectories and

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ground reaction forces were low-pass filtered using a bidirectional Butterworth filter with a cutoff frequency of 6 Hz in Visual3D (C-Motion, Inc., Germantown, MD). A generic musculoskeletal model with 14 rigid body segments, 21 degrees of freedom (DOF), and 92 musculotendon actuators with force-length-velocity properties [17–21] in

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OpenSim 3.2 (simtk.org) was used to represent each child. Body segments were scaled in size and mass. Tibial torsion for each participant was measured from the static trial as the rotation between the knee and ankle joint flexion–extension axes in the transverse plane defined by a 6 DOF kinematic model in Visual3D. Tibial torsion was incorporated into the musculoskeletal model based on [16], where the relative angle between the knee and ankle flexion axis was

applied linearly along the shank. Muscle paths for muscles attached to the shank were also transformed based on this linear function. Craig’s test was performed by a licensed physical therapist (WS) on all participants to measure femoral anteversion. We have previously validated the clinical measures of femoral anteversion performed by the same pediatric physical therapist against a gold standard of computed tomography scans [22], and are therefore confident in the

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accuracy of femoral anteversion measurements acquired in this study. Participants had normal ranges of femoral anteversion except for two participants who were within 5 degrees of normal

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(mean: 19° [range: 10°-30°] femoral anteversion) [23]. Therefore, the axis alignment and muscle paths for the hip and femur were unchanged from the generic model.

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Three overground walking trials with consecutive force plate hits were selected for each

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child. Joint kinematics were calculated using a least-squares optimization algorithm in Visual3D [24]. A residual reduction algorithm was used to resolve dynamic inconsistencies between

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ground reaction forces and the inverse kinematics solution and to approximate trunk-pelvis angles. An induced acceleration analysis was used to determine the capacity of each muscle

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within the model to accelerate the body COM at each instant in time during the stance phase of gait, by applying 1 Newton of force from each muscle and evaluating the resulting body COM acceleration. A hard kinematic constraint of rolling without slipping was used to model footground contact [25]. Muscle moment arms for each model DOF were calculated as the

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perpendicular distance between the joint center and muscle line of action. COP was evaluated relative to the body COM during stance. INSERT TABLE 1 HERE

Foot progression angle (FPA) averaged across the walking trials was quantified as the average value when the foot was flat on the ground. Each leg was characterized as internally

rotated (FPA greater than 4° internal rotation), externally rotated (FPA greater than 10° external rotation), or standard (FPA 4° internal rotation to 10° external rotation). TABLE 2 ABOUT HERE The root-mean-square (RMS) average muscle capacity to accelerate the body COM during stance was evaluated for eight lower-limb muscle groups (Table 1) in the 1)

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anterior/posterior (propulsion), 2) superior/inferior (body support), and 3) medial/lateral (mediolateral balance) directions. A single RMS value was established for each child for both the

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right and left leg muscles and averaged across three walking trials.

The effect of FPA on muscle capacity to accelerate the body COM was evaluated using

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the Kruskal-Wallis test by ranks. Pairwise comparisons were completed using Nemenyi-test with

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Tukey multiple comparison corrections when significant Kruskal-Wallis test results were indicated. Effect size was computed for each pairwise comparison using Hedge’s G. Group

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effects for participant characteristics (Table 2) and average relative COP in the medio-lateral direction were evaluated using Kruskal-Wallis test by ranks. Similarly, pairwise comparisons

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were completed using Nemenyi-test with Tukey multiple comparisons when indicated (α=0.05). To interpret changes in muscle capacity to accelerate the COM, muscle moment arms during the gait trials were also calculated. Ankle plantarflexor moment arms as a function of tibial torsion were extracted from the model, and moment arms from all lower-limb joints were evaluated for

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representative participants. 3.

Results

Peak and RMS residual forces and moments, averaged across all participants, were low.

Peak residual forces < 3.0% net ground reaction force (GRF) and RMS < 1.5% net GRF; and peak reserve moments < 10% net GRF-%COM height and RMS < 4.1% net GRF-%COM height

were found across all residual actuators. Peak kinematic error between IK and RRA solutions averaged across participants was less than 2.2 degrees for all lower-limb joints. Altered FPAs significantly affected muscles’ capacity to accelerate the COM (Figure 1). The vasti, hamstrings, and soleus muscles’ capacity to propel and brake the body were significantly different between the internally and externally rotated FPA groups (Table 3, Figure 1). The hamstrings, gastrocnemius, and soleus muscles’ capacity to support the body were also

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different between the internally and externally rotated FPA groups (Table 3, Figure 1). Muscles’

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capacity to accelerate the body COM mediolaterally were significantly different between the internally and externally rotated groups for the iliopsoas and gluteus maximus (Table 3, Figure

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1), and significantly different between internally rotated and standard FPA groups for the vasti

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(Table 3, Figure 1).

Externally rotated FPAs had COPs that were more lateral to the body COM relative to

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internally rotated FPAs (p=0.035, Figure 2) and standard FPAs (p=0.046, Figure 2). Extracted from the model, the ankle plantarflexor moment arms had a 1.1mm (2.4%) change at max

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external rotation, and 1.4mm (3.0%) change at max internal rotation over the range of tibial torsion angles evaluated in a static, standing pose (Figure 3). INSERT FIGURE 1 & TABLE 3 ABOUT HERE

4.

Discussion

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This study characterized the effects of different torsional kinematic gait patterns for

individuals with CP on muscles’ capacity to accelerate the body COM. Similar to previous work, we found externally rotated FPAs led to lower muscle capacity to accelerate the COM [15,16]. In addition, we found muscle capacity to accelerate the COM for internally rotated FPAs was similar to standard FPAs.

Previous work has established flexed postures, such as in crouch gait, substantially reduce extensor muscles’ capacity to accelerate the hip and knee joints [26]. To establish if smaller capacity to accelerate the body COM found in the vasti, hamstrings, gastrocnemius, and soleus was a result of joint flexion observed in the externally rotated FPA group, a result of the altered transverse plane joint angles, or a combination of both flexion and rotation, we evaluated muscle moment arms for a single participant. Muscle moment arms derived from the inverse

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kinematics solution were decomposed into the altered muscle moment arm from the participant’s

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flexed posture alone (by setting internal/external rotation to zero at the hip and ankle), and from the combined effect of both flexed and rotated posture (inverse kinematics solution). At the hip,

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large reductions in muscle moment arm for both the hamstrings and gluteus maximus occurred

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from increases in hip flexion during stance. The hamstrings’ hip extension moment arm was insensitive to changes in hip rotation (Figure 4), which indicates a reduction in the hamstrings’

COP location.

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capacity to accelerate the COM in the sagittal plane primarily results from hip flexion and the

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The capacity to accelerate the body COM mediolaterally was also smaller for the externally rotated FPA group for the gluteus maximus and iliopsoas. Reduced capacity to accelerate the body mediolaterally from the gluteus maximus likely results from altered transverse plane hip kinematics, especially for individuals walking with external hip rotation.

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This hypothesis is supported by analysis of the hip abduction moment arm for both the gluteus maximus and medius muscles. Superior portion of the gluteus maximus and all compartments of the gluteus medius hip abduction moment arms are reduced by 66% and 31% respectively for moderate (30°) external rotation of the hip, while these moment arms are 25% increased for moderate (30°) internal hip rotation. The analyses of hip muscle moment arms provide insight

into how compensatory strategies of internal and external hip rotation can influence gait mechanics. It is worth noting, in a secondary analysis (Supplemental Material A) we identified estimates of mediolateral acceleration capacity, especially those from the gluteus maximus, were moderately sensitive to uncertainty within bony alignment measurement techniques. However, mean differences between the externally and internally rotated FPA groups in this study were

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approximately one order of magnitude larger than estimates of model uncertainty, suggesting findings in this study are robust to possible sources of model uncertainty related to estimating

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bony alignment from clinical and motion capture measurements.

The capacity of the ankle plantarflexors to accelerate the body COM in the sagittal plane

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was substantially smaller for individuals with external FPAs, which could arise from altered

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kinematics and/or skeletal alignment of the tibia. The moment arms of the plantarflexors were insensitive to changes in skeletal rotation both for internally and externally rotated torsion

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(Figure 3), consistent with previous work [15,16]. Changes in ankle and subtalar kinematics during walking resulted in much larger changes in the plantarflexion moment arm (Figure 4).

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Therefore, loss of ankle plantarflexion propulsion and support capacity is likely a result of altered sagittal and transverse plane kinematics, rather than skeletal malalignment alone. The capacity of muscles to accelerate the COM also relies on the relative lever arm between the muscles’ line of action and the location of the COP. For individuals with external

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FPAs, the average COP, relative to the COM, was more lateral compared to standard or internal FPAs, reducing the ability of the muscles to accelerate the body COM. COP trajectories for the external FPA group were similar to those reviewed previously [15,16], finding reduced muscle capacity to extend lower-limb joints and support the body COM.

The externally rotated group tended to walk at slower walking speeds, though not statistically different (Table 2). Analyses of healthy gait have shown muscle function is unchanged while muscle contributions to COM acceleration increase with walking speed driven by greater muscle forces necessary to walk faster [10,27]. In this study, we evaluated muscles’ capacity to accelerate the body COM, which depends on kinematics and does not incorporate

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muscle force magnitudes or coordination. The smaller IAA muscle capacity observed in the externally rotated group may explain in part why these individuals have a slower self-selected

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walking speed.

The results of this study provide useful information when considering the surgical and

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non-surgical treatments for transverse plane skeletal deformities. We found hip rotation and

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overall foot position to be two potential sources of altered muscle capacity, in addition to previously observed flexed lower-limb joints [3,15]. Despite finding similar or greater muscle

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capacity to accelerate the COM for internal FPAs, these postures can lead to greater loading in the knee [28] and long term skeletal damage, and therefore are often corrected using surgical

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techniques or orthoses.

Muscle capacity is useful to understand the implications of altered kinematic and musculoskeletal deviations on muscle function but should be considered in combination with muscle coordination during gait. A limitation to this study is the lack of imaging data to

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characterize bone deformity in the lower-limb. Clinical measures of femoral anteversion and tibial torsion provide a cost-effective method to implement altered skeletal alignment within musculoskeletal models but are not as accurate as image-based approaches, which should be considered in future work. To help address this limitation, uncertainty in skeletal alignment and the tibial torsion path were quantified in a sensitivity analysis, finding that group differences

reported in this study (internally, standard, or externally rotated FPA) substantially exceeded uncertainty related to potential measurement error (Supplementary Material A). Clinical and motion capture measurements of bony alignment were therefore sufficient to model the different groups in this study related to muscle capacity, but may not be detailed enough for patientspecific analyses. Future studies should consider image-based patient-specific customization in

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musculoskeletal modeling for detailed patient-specific analyses that guide individual treatment. Conclusion

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Children with externally rotated FPAs had the lowest capacity to accelerate the body

COM relative to those with standard FPAs. This lower capacity resulted from a combination of

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smaller muscle moment arms based on the flexed hip, knee and ankle posture, as well as altered

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hip rotation and subtalar angles observed in this group, and a lateral shift of the COP throughout stance. Correcting both the underlying skeletal deformity and the altered kinematic posture has

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potential to help the child take full advantage of their lower-limb strength.

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There was no conflict of interest in the preparation or publication of this work.

Acknowledgements

This work was partially supported by the National Science Foundation Graduate

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Research Fellowship (DGE-1057607).

References [1]

J. Zhou, E.E. Butler, J. Rose, Neurologic Correlates of Gait Abnormalities in Cerebral Palsy: Implications for Treatment, Front. Hum. Neurosci. 11 (2017) 1–20.

doi:10.3389/fnhum.2017.00103. [2]

C.J. Kim, S.M. Son, Comparison of Spatiotemporal Gait Parameters between Children with Normal Development and Children with Diplegic Cerebral Palsy, J. Phys. Ther. Sci. 26 (2014) 1317–1319. doi:10.1589/jpts.26.1317.

[3]

S. Law, Risk factors contributing to crouch gait in children with spastic cerebral palsy,

[4]

of

Phys. Ther. Rev. 19 (2014) 114–123. doi:10.1179/1743288X13Y.0000000119. M.H. Schwartz, A. Rozumalski, K.M. Steele, Dynamic motor control is associated with

ro

treatment outcomes for children with cerebral palsy, Dev. Med. Child Neurol. (2016) 1139–1145. doi:10.1111/dmcn.13126.

A.-L. Simon, B. Ilharreborde, F. Megrot, C. Mallet, R. Azarpira, K. Mazda, A. Presedo,

-p

[5]

re

G.F. Penneçot, A Descriptive Study of Lower Limb Torsional Kinematic Profiles in Children With Spastic Diplegia, J. Pediatr. Orthop. 35 (2015) 576–582.

[6]

lP

doi:10.1097/BPO.0000000000000331.

T.A.L. Wren, S.A. Rethlefsen, R.M. Kay, Prevalence of specific gait abnormalities in

ur na

children with cerebral palsy: influence of cerebral palsy subtype, age, and previous surgery., J. Pediatr. Orthop. 25 (2005) 79–83. [7]

M. Aiona, K. Calligeros, R. Pierce, Coronal plane knee moments improve after correcting external tibial torsion in patients with cerebral palsy, Clin. Orthop. Relat. Res. 470 (2012)

Jo

1327–1333. doi:10.1007/s11999-011-2219-x.

[8]

K.M. Lee, C.Y. Chung, K.H. Sung, T.W. Kim, S.Y. Lee, M.S. Park, Femoral anteversion and tibial torsion only explain 25% of variance in regression analysis of foot progression angle in children with diplegic cerebral palsy, J. Neuroeng. Rehabil. 10 (2013) 1. doi:10.1186/1743-0003-10-56.

[9]

A.S. Arnold, A.V. Komattu, S.L. Delp, Internal rotation gait: A compensatory mechanism to restore abduction capacity decreased by bone deformity?, Dev. Med. Child Neurol. 39 (1997) 40–44.

[10]

R.R. Neptune, K. Sasaki, S.A. Kautz, The effect of walking speed on muscle function and mechanical energetics, Gait Posture. 28 (2008) 135–143.

[11]

of

doi:10.1016/j.gaitpost.2007.11.004. A.K. Hegarty, M.J. Kurz, W. Stuberg, A.K. Silverman, Changes in Mobility and Muscle

ro

Function of Children with Cerebral Palsy after Gait Training: A Pilot Study, J. Appl. Biomech. 32 (2016) 469–86.

A.K. Hegarty, M.J. Kurz, W.A. Stuberg, A.K. Silverman, Strength Training Effects on

-p

[12]

re

Muscle Forces and Contributions to Whole-Body Movement in Cerebral Palsy, J. Mot. Behav. (2018) 1:15.

T.A. Correa, A.G. Schache, H.K. Graham, R.J. Baker, P. Thomason, M.G. Pandy,

lP

[13]

Potential of lower-limb muscles to accelerate the body during cerebral palsy gait, Gait

[14]

ur na

Posture. 36 (2012) 194–200. doi:10.1016/j.gaitpost.2012.02.014. E. Passmore, H.K. Graham, M.G. Pandy, M. Sangeux, Hip- and patellofemoral-joint loading during gait are increased in children with idiopathic torsional deformities, Gait Posture. 63 (2018) 228–235. doi:10.1016/j.gaitpost.2018.05.003. J. Hicks, A.S. Arnold, F.C. Anderson, M.H. Schwartz, S.L. Delp, The effect of excessive

Jo

[15]

tibial torsion on the capacity of muscles to extend the hip and knee during single-limb stance, Gait Posture. 26 (2007) 546–52. doi:10.1016/j.gaitpost.2006.12.003.

[16]

M.H. Schwartz, G. Lakin, The effect of tibial torsion on the dynamic function of the soleus during gait, Gait Posture. 17 (2003) 113–8.

[17]

S.L. Delp, P.J. Loan, M.G. Hoy, F.E. Zajac, E.L. Topp, J.M. Rosen, An Interactive Graphics-Based Model of the Lower Extremity to Study Orthopaedic Surgical Procedures, IEEE Trans. Biomed. Eng. 37 (1990) 757–767. doi:10.1109/10.102791.

[18]

G.T. Yamaguchi, F.E. Zajac, A planar model of the knee joint to characterize the knee externsor mechanism, J. Biomech. 22 (1989) 1–10. doi:10.1016/0021-9290(89)90179-6. F.C. Anderson, M.G. Pandy, A dynamic optimization solution for vertical jumping in

of

[19]

three dimensions, Comput. Methods Biomech. Biomed. Engin. 2 (1999) 201–231.

F.C. Anderson, M.G. Pandy, Dynamic Optimization of Human Walking, J. Biomech. Eng. 123 (2001) 381–90. doi:10.1115/1.1392310.

F.E. Zajac, Muscle and tendon: properties, models, scaling, and application to

re

[21]

-p

[20]

ro

doi:10.1080/10255849908907988.

biomechanics and motor control, Crit. Rev. Biomed. Eng. 17 (1989) 359–411. W. Stuberg, J. Temme, P. Kaplan, A. Clarke, R. Fuchs, Measurement of tibial torsion and

lP

[22]

thigh-foot angle using goniometry and computed tomography, Clin. Orthop. Relat. Res.

[23]

ur na

(1991) 208–212. http://europepmc.org/abstract/MED/1934735. D. Neumann, Kinesiology of the Musculoskeletal System: Foundations for Rehabilitation, 2nd ed., Mosby Elsevier, St. Louis, MO, 2010. [24]

T.-W. Lu, J.J. O’Connor, Bone position estimation from skin marker co-ordinates using

Jo

global optimisation with joint constraints., J. Biomech. 32 (1999) 129–34. doi:10.1016/S0021-9290(98)00158-4.

[25]

S.R. Hamner, A. Seth, S.L. Delp, Muscle contributions to propulsion and support during running, J. Biomech. 43 (2010) 2709–16. doi:10.1016/j.jbiomech.2010.06.025.

[26]

J. Hicks, M.H. Schwartz, A.S. Arnold, S.L. Delp, Crouched postures reduce the capacity

of muscles to extend the hip and knee during the single-limb stance phase of gait, J. Biomech. 41 (2008) 960–967. doi:10.1016/j.jbiomech.2008.01.002. [27]

M.Q. Liu, F.C. Anderson, M.H. Schwartz, S.L. Delp, Muscle contributions to support and progression over a range of walking speeds, J. Biomech. 41 (2008) 3243–3252. doi:10.1016/j.jbiomech.2008.07.031. J.R. Davids, R.B. Davis, L.C. Jameson, D.E. Westberry, J.W. Hardin, Surgical

of

[28]

management of persistent intoeing gait due to increased internal tibial torsion in children,

[29]

ro

J. Pediatr. Orthop. 34 (2014) 467–473. doi:10.1097/BPO.0000000000000173.

M.Q. Liu, F.C. Anderson, M.G. Pandy, S.L. Delp, Muscles that support the body also

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modulate forward progression during walking, J. Biomech. 39 (2006) 2623–30.

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ur na

lP

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doi:10.1016/j.jbiomech.2005.08.017.

Table 1 Muscle groups defined for induced acceleration analysis interpretation. Muscle groups selected for analysis are critical for propulsion, support, and mediolateral balance in both typically developing and the gait of children with CP [13,29].

VAS

Gluteus Medius

GMED

Gluteus Maximus

GMAX

Hamstrings

HAM

Gastrocnemius

GAS

Soleus

SOL

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Vasti

Iliacus Psoas Vastus Medialis Vastus Intermedius Vastus Lateralis Gluteus Medius (Anterior, Middle, and Posterior) Gluteus Minimus (Anterior, Middle, and Posterior) Gemellus Piriformis Gluteus Maximus (Superior, Middle, and Inferior) Semimembranosus Semitendinosus Gracilis Biceps Femoris Long Head Gastrocnemius: Medial and Lateral Heads Soleus Tibialis Posterior Flexor Digitorum Longus

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IL

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Illiopsoas

Individual Muscles in Model

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Muscle Group Abbreviation

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Muscle Group

Table 2 Participant characteristics for each foot progression angle (FPA) group. Skeletal rotation of the femur, femoral anteversion, was measured using Craig’s test for femoral anteversion, and skeletal rotation of the tibia, tibial torsion, was measured using joint alignment during 3D kinematic static standing trials (negative values indicate external rotation). Mean values ± standard deviation are reported within each group. Significantly different group means are indicated as: *-pairwise contrast between internal and external FPA (p<0.05), §-pairwise contrast between internal and standard FPA (p<0.05). External FPA 5

11.3 ± 3.2*

13.6 ± 2.9

15.3 ± 2.4*

1.17 ± 0.12

1.17 ± 0.17

21.33 ± 4.4

17.5 ± 4.2

3.2 ± 11.9*§

-9.6 ± 14.4§

0.99 ± 0.03

18.33 ± 2.9

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Standard FPA 15

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Number of Observations Age of participants (yrs.) Walking Speed (m/s) Femoral Anteversion (°) Tibial Torsion (°)

Internal FPA 16

-20 ± 20.7*

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Table 3. Root-mean-square (RMS) capacity for each listed muscle group to accelerate the body COM each direction of motion. Results are grouped according to foot progression angle (FPA), identified as externally rotated FPA (Ext. Rot.), standard FPA (Int. Rot.), and internally rotated FPA (Int. Rot.). All muscle acceleration capacity values were normalized by participant mass. Mean differences between FPA groups (𝑋̅), group difference effect size calculated using Hedge’s G (G), and p-value statistic (p) are shown for each group contrast. Non-significant results are indicated as n.s. ANTERIOR / POSTERIOR COM ACCELERATION CAPACITY Int. Rot. x 10-4 (1/kg2) 0.40 0.87 0.67 4.11 2.44 2.00 1.24

Internal – External Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.27 1.00 n.s. 0.63 0.79 n.s. 0.40 0.95 n.s. 2.90 1.14 0.011 1.63 1.23 0.019 1.24 1.07 n.s. 0.89 1.08 0.010

Int. Rot. x 10-4 (1/kg2) 1.00 1.37 1.77 4.15 2.15 6.84 5.43

Internal – External Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.52 0.62 n.s. 0.52 0.45 n.s. 0.99 0.66 n.s. 2.58 1.04 n.s. 1.50 1.15 0.010 4.82 1.14 0.011 4.09 1.15 0.008

Standard – External Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.18 0.92 n.s. 0.27 0.82 n.s. 0.33 0.92 n.s. 1.32 0.97 n.s. 0.61 0.83 n.s. 0.53 0.64 n.s. 0.37 0.72 n.s.

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Std. Rot. x 10-4 (1/kg2) 0.31 0.51 0.60 2.53 1.42 1.29 0.72

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IL GMED GMAX VAS HAM GAS SOL

Ext. Rot. x 10-4 (1/kg2) 0.13 0.24 0.27 1.21 0.81 0.76 0.35

Internal - Standard Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.09 0.33 n.s. 0.36 0.52 n.s. 0.07 0.16 n.s. 1.58 0.68 n.s. 1.02 0.84 n.s. 0.71 0.63 n.s. 0.52 0.68 n.s.

Std. Rot. x 10-4 (1/kg2) 0.88 1.28 1.46 2.82 1.28 4.39 3.39

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IL GMED GMAX VAS HAM GAS SOL

Ext. Rot. x 10-4 (1/kg2) 0.48 0.84 0.77 1.57 0.65 2.02 1.33

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VERTICAL COM ACCELERATION CAPACITY Standard – External Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.40 0.61 n.s. 0.44 0.44 n.s. 0.68 0.68 n.s. 1.25 0.75 n.s. 0.63 0.90 n.s. 2.37 0.85 n.s. 2.06 0.87 n.s.

Internal - Standard Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.12 0.15 n.s. 0.09 0.07 n.s. 0.31 0.22 n.s. 1.33 0.56 n.s. 0.87 0.74 n.s. 2.44 0.60 n.s. 2.03 0.60 n.s.

Std. Rot. x 10-4 (1/kg2) 0.14 1.18 0.75 0.35 0.33 0.76 1.27

Int. Rot. x 10-4 (1/kg2) 0.26 2.11 1.29 0.83 0.62 1.03 1.76

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IL GMED GMAX VAS HAM GAS SOL

Ext. Rot. x 10-4 (1/kg2) 0.05 0.72 0.24 0.42 0.30 0.57 0.81

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MEDIOLATERAL COM ACCELERATION CAPACITY

Internal – External Rotation G 𝑋̅ p x 10-4 (1/kg2) 0.21 1.08 0.001 1.39 0.87 n.s. 1.05 1.10 0.005 0.41 0.61 n.s. 0.32 0.57 n.s. 0.46 0.66 n.s. 0.95 0.85 n.s.

Standard – External Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.09 1.03 n.s. 0.46 0.64 n.s. 0.51 0.98 n.s. -0.07 0.31 n.s. 0.03 0.10 n.s. 0.19 0.37 n.s. 0.46 0.67 n.s.

Internal - Standard Rotation 𝑋̅ G p x 10-4 (1/kg2) 0.12 0.69 n.s. 0.94 0.66 n.s. 0.55 0.62 n.s. 0.48 0.87 0.010 0.29 0.59 n.s. 0.27 0.40 n.s. 0.49 0.47 n.s.

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Figure Captions

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Figure 1. Root-mean-square (RMS) capacity for each listed muscle group to accelerate the body COM in the anterior/posterior (A/P) direction (top), vertical direction (middle), and

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medial/lateral (M/L) direction (bottom) during stance is shown. Results are grouped according to foot progression angle (FPA) and were normalized by participant mass. Statistically significant

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differences between groups are indicated (*).

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Figure 2. Average center of pressure throughout stance grouped based on foot progression angle

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(FPA). Center of pressure (COP) was measured relative to the location of the body center of mass (COM) and reported in the anterior/posterior (A/P) direction and medial/lateral (M/L)

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directions.

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Figure 3. Plantarflexion moment arm determined during a default static standing pose, evaluated based on degree of tibial torsion introduced into the musculoskeletal model. Both internal tibial torsion (top) and external tibial torsion (bottom) are evaluated.

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Figure 4. Moment arms shown are representative of a single participant in the externally rotated FPA group. This participant walked with everted subtalar kinematics, internally rotated hip

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kinematics, and flexed hip, knee, and ankle joints during stance, and 10° externally rotated tibial torsion. Muscle moment arms based on the flexed posture alone (with transverse plane

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kinematics set to zero) and based on both the flexed and rotated posture (inverse kinematics

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solution) are shown over the gait cycle.