Moving muscle points provide accurate curved muscle paths in a model of the cervical spine

Journal of Biomechanics 45 (2012) 400–404

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Short communication

Moving muscle points provide accurate curved muscle paths in a model of the cervical spine Bethany L. Suderman a,c,n, Anita N. Vasavada a,b,c a

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99163, USA Gene and Linda Voiland School of Chemical and Bioengineering, Washington State University, Pullman, WA 99163, USA c Department of Veterinary and Comparative Anatomy, Pharmacology and Physiology, Washington State University, Pullman, WA 99163, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Accepted 8 October 2011

Muscle paths in musculoskeletal models have been modeled using several different methods; however, deformation of soft tissue with changes in posture is rarely accounted for, and often only the neutral posture is used to define a muscle path. The objective of this study was to model curved muscle paths in the cervical spine that take into consideration soft tissue deformation with changes in neck posture. Two subject-specific models were created from magnetic resonance images (MRI) in 5 different sagittal plane neck postures. Curved paths of flexor and extensor muscles were modeled using piecewise linear lines-of-action in two ways; (1) using fixed via points determined from muscle paths in the neutral posture and (2) using moving muscle points that moved relative to the bones determined from muscle paths in all 5 postures. Accuracy of each curved modeled muscle path was evaluated by an error metric, the distance from the anatomic (centroid) muscle path determined from the MRI. Error metric was compared among three modeled muscle path types (straight, fixed via and moving muscle point) using a repeated measures one-way ANOVA (a ¼ 0.05). Moving muscle point paths had 21% lower error metric than fixed via point paths over all 15 pairs of neck muscles examined over 5 postures (3.86 mm vs. 4.88 mm). This study highlights the importance of defining muscle paths in multiple postures in order to properly define the changing curvature of a muscle path due to soft tissue deformation with posture. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Cervical spine Curved muscle path Musculoskeletal model Moving muscle point

1. Introduction In the field of musculoskeletal modeling, researchers strive to improve existing methods to model muscle paths accurately (Arnold et al., 2000; Garner and Pandy, 2000; Kruidhof and Pandy, 2006; Murray et al., 1998). In the cervical spine, the most common methods are: straight lines from origin to insertion (Chancey et al., 2003; Vasavada et al., 1998), curved paths over wrapping surfaces (Suderman et al., in press; Vasavada et al., 2008) and curved paths using fixed via points (FVP) (Kruidhof and Pandy, 2006). Wrapping surfaces can account for superficial and deep soft tissue deformation, but the resulting paths are sensitive to the kinematics of the wrapping surface with respect to different bone segments (Suderman et al., in press). Fixed via points can be placed between the origin and insertion of a modeled muscle path to constrain muscle paths to wrap over bone, but they are not as effective for muscle paths that are constrained by overlying soft tissue. Although the methods for

n Corresponding author at: Department of Veterinary and Comparative Anatomy, Pharmacology and Physiology, Washington State University, Pullman, WA 99163, USA. Tel.: þ1 509 335 7435; fax: þ 1 509 335 4650. E-mail address: [email protected] (B.L. Suderman).

0021-9290/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2011.10.014

curved paths improve modeled path accuracy when compared to straight paths, they may not always work well over a large range of postures, or when taking into consideration deformation of soft tissue. A feature in musculoskeletal models that is not as commonly used as wrapping surfaces or FVPs is moving muscle points (MMP). Whereas, FVPs are defined in one posture and are statically linked to one bone or body segment in all postures, MMPs can move with respect to the body segment (usually a bone) to which the point is linked. This method allows for a muscle path to adjust to surrounding soft tissue, which can deform with changes in posture. We have developed an algorithm (using MRI) to model curved muscle paths using MMPs. We hypothesize that modeling curved muscle paths with MMPs during sagittal plane motion will provide more anatomically accurate neck muscle paths than paths with FVPs. 2. Materials and methods 2.1. Magnetic resonance image (MRI) acquisition The procedure to determine anatomic muscle paths was similar to that of Vasavada et al. (2008). Anatomic muscle paths of 15 neck muscle pairs (right/left)

B.L. Suderman, A.N. Vasavada / Journal of Biomechanics 45 (2012) 400–404 were obtained from magnetic resonance image (MRI) scans of two approximate 50th percentile male subjects (Gordon et al., 1989) (Table 1). Axial proton densityweighted images (TR¼ 2892 ms; TE¼ 9.0 ms; slice thickness 3.0 mm; gap 0.3 mm) were obtained from the base of the skull to the third thoracic vertebra to identify muscle boundaries. Sagittal plane T1-weighted images (TR ¼530 ms; TE ¼ 7.6 ms; slice thickness 3.0 mm; gap 0.3 mm) were obtained to determine vertebral position and orientation. Scans were obtained of each subject in five flexion/ extension postures: 301 flexion, 151 flexion, neutral, 151 extension and 301 extension. Subjects provided informed consent, and the protocol was approved by the local ethics board at The University of British Columbia.

2.2. Model description Two subject-specific models were created in OpenSim (Delp et al., 2007). All vertebral body and muscle positions were determined with respect to the sternal notch. The origin of vertebral body coordinate systems for C2–T3 was the average of the four corners of each vertebral body in the mid-sagittal scan. For C2–T3 the y-axis (pointing cephalad) connected the mid-points of the upper and lower endplates (Siegler et al., 2002), the x-axis (pointing anterior) was perpendicular to the y-axis passing through the origin and the z-axis (pointing right) was the crossproduct of the x and y axes (Fig. 1). For the skull and C1, the x-axis was the vector

Table 1 Anthropometric data for two male subjects and 50th percentile values for comparison (Gordon et al., 1989). Subject # Age Height (cm) Weight (kg) Neck circumference (cm) Head circumference (cm)

1 42 175.3 70.3 37.7 57.7

2 32 177.8 77.1 39.8 60.0

50th% NA 175.5 77.7 37.9 56.8

401

connecting: basion and opisthion, and anterior and posterior tubercle, respectively, with the origin at the mid-point. The position of the vertebral bodies with respect to the sternal notch was plotted versus angular head position through all five postures and smoothed using a cubic spline to define model kinematics. Fifteen muscle pairs (right/left) were analyzed: infrahyoids (Inf), sternocleidomastoid; clavicular (SCM-cm) and sternal (SCM-sm) heads, levator scapulae (LevSc), longissimus capitis (L-musCa) and cervicis (L-musCe), longus capitis (LCa) and colli (LCo), scalenus anterior (ScA), middle (ScM) and posterior (ScP), semispinalis capitis (SemCa) and cervicis (SemCe), and splenius capitis (SpCa) and cervicis (SpCe). Muscle paths were determined by the centroid of the individual muscle cross-sectional area (CSA) traced on consecutive axial slices (3.3 mm apart) (Jensen and Davy, 1975). The centroid path was smoothed using a b-spline with points at the same axial slice levels as the points on the unsmoothed centroid path.

2.3. Modeled muscle paths Three muscle paths were modeled for each muscle: straight, MMP and FVP. Straight muscle paths were modeled as a straight line from origin to insertion (first and last centroid points). Curved paths were modeled as piecewise linear lines-of-action using muscle points (fixed or moving). Modeled muscle points were determined for each muscle path as the intersection of the x–z plane of each body’s coordinate system (Skull–T3) with the smoothed centroid muscle path (Fig. 2A). Muscle points in the neutral posture, fixed to each vertebral coordinate system in all postures, were used to represent the FVP path (Fig. 2A and C). Muscle points from all 5 postures were used to determine the MMP path (Fig. 2A and B). The x and z coordinates represent anterior/posterior and medial/lateral position, respectively with respect to the vertebral origin. The y coordinate is always zero, as the muscle points are determined in the x–z plane of each vertebral body (y¼0). The coordinates were smoothed using a cubic fit over all 5 postures for the MMP path (Fig. 3). Fig. 3 depicts the location of the C4 MMP of the SemCa (with respect to the C4 vertebral body) at all postures; two of these points are also represented in Fig. 2: 01 neutral (Fig. 2A) and 301 extension (Fig. 2B). Fig. 4 displays all muscle path types: straight, FVP and MMP in all postures. Right and left muscle points were averaged to create symmetric muscle paths over the mid-sagittal plane.

200

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C5 C6

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C7 40

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Fig. 1. 2D projection of vertebral body position and orientation with respect to the sternal notch in the neutral posture for subject 1. A larger view of the C3 vertebral body is seen on the left to show the location of the upper and lower midpoints and the x and y axes, (z axis lateral to right). The x–z plane is used to define the muscle points.

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B.L. Suderman, A.N. Vasavada / Journal of Biomechanics 45 (2012) 400–404

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C5 FVP C6

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Straight Path

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Straight Path

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Fig. 2. Semispinalis capitis muscle showing the smoothed centroid path (*) and the three modeled paths; straight, moving muscle point and fixed via point. A: muscle points (o) are shown in the neutral posture as the intersection of the x–z plane of each vertebral body’s coordinate system with the smoothed centroid path. The straight path is shown as a line connecting the origin to the insertion. B: moving muscle points are shown in 301 extension. The position of the MMP remains within the smoothed centroid path, but changes with respect to the vertebral body origin. C: fixed via points are shown in 301 extension. The position of the FVPs does not change with respect to the vertebral body origins and thus does not remain within the smoothed centroid path.

-20 z left -30 x right/left -40 -30 Flexion

-15

0 Head Angle (degrees)

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30 Extension

Fig. 3. Example of moving muscle point trajectory for x and z coordinates with respect to the C4 vertebral body of the left semispinalis capitis muscle for subject 2 from 301 flexion to 301 extension. Actual position (hollow circle) is known at all 5 postures. Approximated position (solid line) is determined using a cubic fit. The y coordinate is not shown because the muscle point is always in the x–z plane of each vertebral body (y ¼0).

paths. For both subjects EM values over all muscles and postures were found to be significantly different (p o0.01, one-way repeated measures ANOVA) among all modeled paths; and MMP paths had significantly lower EM values than FVP paths (p o0.01, paired t-test) (Table 2). Moving muscle point paths also provided a larger mean percent improvement over straight paths compared to FVP paths [50.2% 717.3% (SD) vs. 38.3%724.8% averaged over all postures and subjects] (Fig. 5). In some muscles (SCM-cm, LCa, ScA, ScP and SpCe) the FVP paths produced larger error metrics than the straight path in certain postures (Table 2). The lowest percent improvement occurred most often in the 151 flexion and 301 extension postures for all muscles for both MMP and FVP paths.

2.4. Error metric An error metric (EM) was defined to determine the anatomical accuracy of the modeled paths (MMP, FVP or straight) compared to the smoothed centroid path (Vasavada et al., 2008). Error metric was defined as the average distance between the modeled muscle path (pmodeled ) and the smoothed centroid path (pcentroid ) at i i each axial slice level (i¼ 1 to n, at 3.3 mm increments; Eq. (1)). Pn centroid modeled 9p pi 9 EM ¼ 1 i ð1Þ n Error metric was compared among muscle path types: straight, MMP and FVP, using a repeated measures one-way ANOVA (a ¼0.05) including all 15 muscle pairs and 5 postures; each subject was analyzed separately. Each curved path (MMP and FVP) was compared to the straight path to calculate relative improvement. It was assumed that the EM of the straight path was the worst case scenario for modeling muscle paths, therefore percentage of improvement was calculated for each muscle in all 5 postures (Eq. (2)). % Improvement ¼

EMstraight EMcurved EMstraight

ð2Þ

3. Results Moving muscle points produced paths that were closer to the centroid path for all postures, compared to FVP or straight line

4. Discussion In this study we examined a new method to model curved muscle paths while maintaining the shape of the anatomic path that wraps around bone and other soft tissues. We hypothesized that MMPs would provide more anatomically accurate modeled muscle paths than FVPs. Our results support the hypothesis and indicate that MMPs are better suited than FVPs to describe the changes in muscle path due to changes in posture, because muscle paths are not fixed relative to bones. This method of implementing MMPs also appears to provide more accurate muscle paths than the alternative method of wrapping surfaces. In similar studies by Vasavada et al. (2008) and Suderman et al. (in press), curved muscle paths were also determined for the SCM-sm and SemCa using a single wrapping surface for each muscle. For both of these muscles, the MMP path provided a greater percent improvement in EM (compared to straight paths) in sagittal plane postures than the wrapped paths for both subjects; SCM-sm [64.2% vs. 24.3% (Vasavada et al., 2008)] and SemCa [81.7% vs. 73.6% (Vasavada et al., 2008) and 75.4% (Suderman et al., in press)].

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Fig. 4. Subject-specific model (subject 2) of the semispinalis capitis straight path (magenta), moving muscle point (red) and fixed via point path (cyan) from left to right; 301 extension, 151 extension, neutral, 151 flexion and 301 flexion. The dark points on the curved muscle path represent the muscle points. Segments between the muscle points are represented by straight lines. In the neutral position the MMP path is directly in line with the FVP path and is not visible. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 2 Error metric (mm) averaged over both subjects for straight (S), fixed via point (FVP) and moving muscle point (MMP) modeled paths, muscle abbreviations can be found in the methods section. 301 flexion

Inf SCM-sm SCM-cm LevSc L-musCa L-musCe LCa LCo ScA ScM ScP SemCa SemCe SpCa SpCe Ave

151 flexion

Neutral

151 extension

301 extension

S

FVP

MMP

S

FVP

MMP

S

FVP

MMP

S

FVP

MMP

S

FVP

MMP

5.94 5.29 11.74 5.30 9.79 4.62 4.92 4.91 4.87 6.93 7.26 18.35 6.13 10.01 4.73 7.39

6.04 5.70 6.10 5.46 3.86 4.55 4.54 3.86 3.80 3.81 5.73 4.67 3.24 7.32 6.15 4.99

4.61 2.97 3.67 3.54 2.74 3.03 4.03 2.87 3.11 2.66 3.25 3.29 2.40 2.70 2.86 3.18

6.44 5.62 11.13 7.33 11.31 5.80 7.73 6.31 6.05 8.60 8.48 20.47 7.53 7.99 6.65 8.50

3.46 4.67 5.17 5.77 5.20 5.58 7.20 5.71 4.55 4.70 4.32 5.72 4.51 5.85 5.40 5.19

3.02 3.54 4.34 5.36 4.83 5.15 5.69 4.45 4.08 4.40 3.86 5.56 4.35 5.10 5.00 4.58

4.63 5.55 10.60 7.58 15.19 7.92 3.96 8.77 4.17 6.05 6.39 25.50 10.96 11.17 8.18 9.11

2.94 2.73 3.20 3.41 3.20 3.42 2.57 2.82 2.62 2.81 2.90 3.64 2.87 3.89 2.69 3.05

3.32 3.05 3.47 4.58 4.02 4.22 3.72 3.60 3.20 3.45 3.45 4.03 3.60 4.79 3.68 3.75

5.49 6.21 12.48 10.79 14.62 8.00 3.99 10.43 3.97 5.53 6.72 27.79 9.83 10.42 8.22 9.63

4.52 5.57 7.07 8.02 4.48 5.03 4.20 4.20 4.39 4.48 5.83 4.32 3.51 4.80 4.75 5.01

3.45 4.12 5.08 4.81 3.27 3.70 3.32 3.39 3.39 3.60 4.91 3.40 2.66 3.79 3.66 3.31

5.57 9.35 16.26 18.56 22.16 14.95 7.19 15.72 7.14 7.59 4.54 35.71 15.44 19.33 17.42 14.46

3.42 5.49 9.02 11.43 7.00 6.06 3.92 4.16 3.62 4.42 5.36 7.05 4.94 8.15 8.54 6.17

2.76 4.46 5.31 5.45 4.18 3.95 3.14 3.30 3.08 3.35 3.57 4.87 3.54 5.17 4.11 4.02

Other approaches to modeling neck muscles include multibody (e.g., van der Horst et al., 1997) and finite element (FE) models (e.g., Hedenstierna, 2008). In a similar cervical spine model by van der Horst et al. (1997), muscle paths were modeled with straight line paths using fixed via points to allow muscles to curve around vertebrae (van der Horst et al., 1997). Muscle path changes due to deformation of soft tissue; however, were not considered. An advantage of FE models is that they can represent multiple muscle fibers within the muscle and thus have a range of moment arms for each muscle (Blemker and Delp, 2005). The MMP method only represents each muscle as one line-of-action, which assumes that all fibers shorten uniformly, resulting in one moment arm for each muscle (Blemker et al., 2007). In a FE model of the cervical spine by Hedenstierna (2008), one posture was acquired from MR images, and muscle volume deformation between postures was constrained using physical boundary conditions of adjacent surrounding tissues (Hedenstierna, 2008). Because the MMP method uses the centroid path data in multiple postures it may be used to improve curved muscle paths in multibody models or in FE models by providing an additional boundary condition for muscle volumes. One limitation of this study is that only two subjects were modeled and analyzed. However, 15 muscle pairs at 5 different postures were included for a total of 75 repeated measures in the one-way ANOVA, which provided confidence in the significant differences found between MMP and FVP paths for each subject individually. No comparison was made between subjects.

Resolution of the images was 0.46–0.58 mm/pixel, but resolution should not influence the findings that MMP paths were more accurate than FVP paths because both paths were defined using the same centroid path. Using the new method with MMPs provided a better anatomical fit than other methods, such as FVP or wrapping surfaces, because it utilized the centroid path over a range of postures, not just the neutral position. However, this requires acquisition of the actual path over multiple postures (i.e. multiple MRI scans). One limitation of the current model is that MMPs are determined in sagittal plane postures only. To accurately represent postures out of the sagittal plane, MRI scans would need to be acquired in other postures (axial rotation and lateral bending). The cost and computational time for each additional posture is quite large, thus this method would not be ideal to create subject-specific models for clinical diagnosis on a subject to subject basis. However, the MMP method can be implemented to create generic musculoskeletal models that can be used to estimate model properties such as muscle length, moment arm and joint moment, which have been shown to be more accurate with muscle paths modeled using the anatomic path (Arnold et al., 2000; Murray et al., 1998).

Conflict of interest statement The authors have no conflicts of interest interfering with this manuscript.

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100 90

MMP

FVP

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70 60 50 40 30 20 10 0 -10

S Se cP m Se Ca m Ce Sp C Sp a Ce A ve

SC Inf M SC -cm M -s Le m L- vS m c u L- sC m a us Ce LC a LC o Sc A Sc M

-20

Muscles Fig. 5. Percent improvement in error metric of moving muscle point paths and fixed via point paths compared to straight paths. Data shown are the mean and the standard deviation (error bars) over all postures and subjects, Inf-infrahyoids (sternothyroid, sternohyoid and thyrohyoid), SCM-cm – sternocleidomastoid (clavicular head), SCM-sm – sternocleidomastoid (sternal head), LevSc – levator scapula, L-musCa – longissimus capitis, L-musCe – longissimus cervicis, LCa – longus capitis, LCe – longus cervicis, ScA – scalenus anterior, ScM – scalenus medius, ScP – scalenus posterior, SemCa – semispinalis capitis, SemCe – semispinalis cervicis, SpCa – splenius capitis, SpCe – splenius cervicis.

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