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Contents lists available at ScienceDirect

Journal of Electromyography and Kinesiology
journal homepage: www.elsevier.com/locate/jelekin

A new method of estimating scapular orientation during various shoulder
movements: A comparison of three non-invasive methods

7

Aoi Matsumuraa,b, , Atsushi Uedaa, Yasuo Nakamuraa⁎ab

Graduate School of Health and Sports Science, Doshisha University, Kyoto, Japan
TAKE PHYSICAL CONDITIONING Inc., Kyoto, JapanA R T IC L E INFOA B S T R A C T

Keywords:
ShoulderScapulaAcromion marker cluster
Motion analysis

The conventional acromion marker cluster (AMC) method used to estimate scapular orientation cannot adequately represent complex shoulder movements due to soft tissue artifacts. The regression method may havenonlinear error changes depending on humeral elevation angle and elevation plane. Therefore, we aimed todevelop a new method of estimating scapular orientation using curved surface interpolation during various
shoulder movements, and to compare its accuracy with conventional and regression methods. Thirteen healthy
men were recruited. AMC and refractive markers for bony landmarks were placed on the skin. During the
preprocess, several shoulder postures, including diﬀerent arm elevations and elevation planes, were measured
using the motion capture system. Premeasured data were used to calibrate the positional relationship between
AMC and scapula using curved surface interpolation. Subsequently, scapular orientations were estimated bymeasuring AMC and body markers of any shoulder posture. To evaluate the accuracy of our methods, 25 elevation postures and six tasks involving postures common to activities of daily living were applied. For tasks
requiring greater arm elevation angles, the root mean square error was less in our method than in the conventional and regression methods. Therefore, our method could improve the accuracy of estimating scapularorientation in various elevation postures.

1. Introduction
The shoulder has a wide range of motion because of its anatomical
structure. This enables dynamic movements involved in activities ofdaily living (ADL) and sports-related movements. To decrease mechanical stress to the glenohumeral joint or soft tissue, and to achievesmooth movements of the shoulder, the scapula requires cooperative
three-dimensional movements with humeral movements (Burkhart
et al., 2003). Understanding scapular kinematics during shoulder
movements provides important information for diagnosing and treating
shoulder disorders and for improving the performance of ADL andsports (Fayad, 2008; Meyer et al., 2008). A recent systematic review
reported that scapular movements changed in patients with shoulder
disorders (Struyf et al., 2011). However, it has also been reported that
there was no diﬀerence in the scapular movements of patients withshoulder disorders compared with asymptomatic controls (Ratcliﬀe
et al., 2014). Therefore, additional evidence is needed to better understand the relationship between shoulder and scapular movements.
Tracking scapular movement using markers attached to the bodysurface is diﬃcult because the scapula moves under the skin and soft⁎

tissue. Skin markers cannot adequately trace the trajectory of thescapular landmarks during arm movements (Matsui et al., 2006).
Therefore, the acromial method was developed to estimate scapularorientation (McQuade, 1998). Additionally, the acromion marker
cluster (AMC) method was developed to estimate scapular orientation
when applying the acromial method using the optical motion capturesystem (van Andel, 2009); this method has been widely used for measuring various shoulder and clavicle movements (Lempereur et al.,2014; Bet-Or et al., 2017). The marker cluster consists of multiple lightweight, small-based markers aﬃxed to the skin during the acromion
process. The positional relationship between the AMC and scapular
landmarks is calibrated using premeasured motion data, and the scapular orientation is then estimated by calibrating measured AMC data. In
most studies, this calibration process was performed with the arm at theresting position (0° of shoulder elevation) (van Andel, 2009; Janeset al., 2012; Warner et al., 2012). The error of the estimated scapula
orientation significantly increased beyond 120° of thoraco-humeral(TH) elevation (Karduna, 2001). Furthermore, the positional relationship between the AMC and scapula is not constant, due to soft tissue
deformity at high arm elevation angles that results in decreased

Corresponding author at: Graduate School of Health and Sports Science, Doshisha University, Kyoto, Japan.
E-mail address: a-matsumura@take-pc.co.jp (A. Matsumura).

https://doi.org/10.1016/j.jelekin.2018.11.007
Received 17 April 2018; Received in revised form 23 October 2018; Accepted 8 November 2018(OVHYLHU/WG$OOULJKWVUHVHUYHG

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A. Matsumura et al.

scapular estimation accuracy. To improve the accuracy of the AMC
method at high degrees of humeral elevation, the double calibration
approach was developed (Brochard et al., 2011). However, this approach can be used only for single-plane humeral movements, and not
for ADL or sports-related movements that involve multiplane movements. Thus, Nicholson et al. developed the regression method using
three multiple linear regression equations to estimate scapular orientation (Nicholson et al., 2017). They reported that the error of theregression method was less than approximately 8°. Moreover, Rappet al. compared the estimation errors of the regression method withthose of the AMC method with double calibration in several functional
positions (Rapp et al., 2017). The estimation errors for the regression
method were approximately 4–8°, and the error for the regression
method was smaller than that of the AMC for the whole measured
position. These reports suggest that estimation errors of scapular orientation can be reduced by using these several premeasured TH orientations. However, these previous studies developed regression
equations from certain postures, and verified estimation error at specific ADL postures. Therefore, the estimation error distribution in various shoulder elevation planes and elevation angles remains unclear. If
the estimation error distributions were represented nonlinearly by awider variation range of shoulder orientations, it is possible that estimation error of the shoulder orientation could be reduced by a nonlinear interpolation, depending on TH elevation plane and elevation
angle.
To reduce the estimation error of scapular orientation using AMC,
we aimed to develop a new estimation method for scapular orientation
using non-linear interpolation, and to compare the estimation accuracyof our method with that of the conventional AMC method, calibrated atonly the arm at rest position, and the recently reported regression
method. We hypothesized that our method would improve estimation
accuracy compared with the other methods in various shoulder elevation postures.

2.2. Instrumentation
Kinematic data were collected using an optical motion capturesystem (MAC3D system; Motion Analysis Corporation, USA) with asampling rate of 240 Hz. A cluster of small, light-weight markers wereapplied to the skin over the flat part of the acromion (Fig. 1A). This
cluster consisted of three 4-mm refractive markers placed in a triangular formation. The 12-mm reflective markers were applied to the C7
and Th8 spinous process, sternal notch, xiphoid process, medial epicondyle, and lateral epicondyle (Wu et al., 2005). A scapular locator(SL) was used to palpate the scapular bony landmarks (Fig. 1B). SL has
three adjustable pins to fit the acromial angle, trigonum spinae, andinferior angle of the scapula (Brochard et al., 2011). A 4-mm refractive
marker was fixed on the head of each locator pin. The investigator kept
the SL in close contact with the bony landmarks of the scapula during
measurement.
2.3. Measurement tasks
To evaluate estimation error distribution, we measured 25 postureswith the combination of several elevation planes and elevation angles.
These postures were assumed in a resting position, with 30–180° elevation in 0° (coronal plane) to 90° (sagittal plane) and the elbows fully
extended. Elevation and elevation angles were set in steps of 30°. We
referred to these tasks as the “elevating postures” (Fig. 2A). During theexperiment, subjects were seated on a chair with a semicircular adjustable guide to standardize the postures (Fig. 2B). We instructed themto point their middle finger at the marks on the guide without shoulder
pain and discomfort or compensatory trunk motion.
To evaluate functional postures, the following six postures were
measured: hand to head, forward reach, lateral reach, hand to mouth,
45° of arm elevation in 45° of the elevation plane (45° elevation), and135° of arm elevation in 45° of the elevation plane (135° elevation)(Fig. 3). We referred to these tasks as the “functional postures”. Additionally, we measured kinematic data in hand to spine, external
shoulder rotation, and extension for the regression method, which is
described later.
Subjects held both arms in each instructed posture for 3 s. The AMC,
SL, and other landmarks were measured simultaneously. Whole measurements were performed by one observer who had extensive experience with human anatomy and anatomical landmark palpation.

2. Materials and methods
2.1. Subjects
The right arms of 13 healthy men (age, 21.1 ± 2.4 years; height,
174.4 ± 7.0 cm; weight, 72.1 ± 10.9 kg) were measured. None had ahistory of musculoskeletal injury or neuromuscular disease involving
the upper arms. At the time of measurement, the participants did nothave any pain in their right shoulder at rest or in motion and reported
no pain during the previous one week. Participants were randomly
recruited from our institution and regularly performed various sports(baseball, gymnastics, and archery) from a recreational to a university
athlete level.
Oral and written informed consent was obtained from all participants. This study was approved by our institutional ethical committee(No. 16028).

2.4. Estimation of scapular orientation
To calculate the positional relationships between the AMC, scapular
landmarks, humerus, and trunk, the local coordinate system (LCS) of
the scapula (ΣS), humerus (ΣH), and thorax (ΣT) was determined (Wuet al., 2005). The LCS of the AMC (ΣA) was determined using the AMC
markers (Fig. 4A). RAi and RS-Ai (αi, βi, γi) were the coordinate transformation from the ΣAi to ΣTi and from the ΣAi to ΣSi at arbitrary postureFig. 1. (A) The acromion marker cluster that was placed on the flat part of the acromion process. (B) The positions of the scapular locator.
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A. Matsumura et al.

Fig. 2. (A) Elevating postures. (B) Experimental set-up.

Fig. 3. Functional postures: (A) hand to head; (B) forward reach; (C) lateral reach; (D) hand to mouth; (E) 45° elevation; (F) 135° elevation.

Fig. 4. (A) The coordinate system of the acromion marker cluster (AMC). (B) The coordinate transformations of the AMC method.
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A. Matsumura et al.

Fig. 5. An example of thin-plate spline interpolation for RS-A.

i, respectively. The αi, βi, and γi were the Euler angles of RS-Ai, whichwere related to the x-, y-, and z-axis of the scapular LCS, respectively.
Hence, scapular orientation RSi was determined using the following
equation:

R Si = RAiR S Ai ( i,coordinate transformation RSLi from ΣSi to ΣTi. ΣSi was determined bymeasuring the body marker using the SL (Fig. 7).
2.4.4. Regression method
According to Rapp’s study, multiple linear regression equations
were calculated to estimate the scapular orientation (Rapp et al., 2017).
The equations were generated using the pre-measured postures: arms at
rest, abduction, external rotation, extension, flexion, 30° elevation at
30° of elevation plane, hand to mouth, hand to head, forward reach,and hand to spine. After generating the regression equations, thescapular orientations were estimated.
All calculations were performed using the MATLAB platform(MATLAB R2018a; MathWorks, Natick, MA, USA.)i , i)The scapular orientation with respect to the thorax (ΣTi) was calculated using the Euler angle rotation order: external/internal rotation(y-axis), upward/downward rotation (x-axis), and anterior/posterior
tilt (z-axis) (Fig. 4B).

2.4.1. Our new estimation method
To improve estimation accuracy, it was necessary to modify RS-Ai
with successive changes in the arm posture. Therefore, RS-Ai (αi, βi, γi)
was modified by humeral movements involving TH elevation planeangle θi and elevation angle φi. The αi, βi, and γi were interpolated by
the following calibration functions: αi = α (θi, φi), βi = β (θi, φi), and γi= γ (θi, φi). The α () was calculated using αj, θj, and φj for the 10
premeasured postures j using thin-plate spline interpolation (Bookstein,1997) (Fig. 5). These postures were as follows: arm at rest position, 90°
and 150° of arm elevation in steps of 30° from 0° to 90° of the elevation
planes, and 180° of arm elevation in 30° of the elevation plane (Fig. 6).
The β () and γ () were calculated similarly. We selected these postures
to improve the accuracy of high arm elevation positions. However, toavoid time-consuming premeasurements, we set a limit of 10 postures
for each subject.

2.5. Evaluation of accuracy
To compare the accuracy of each estimation method, the Friedman
test was performed within estimation methods. The Wilcoxon-signed
rank test with Bonferroni correction was performed to compare thenew, conventional, and regression methods with the palpation method.
All statistical analyses were performed using SPSS version 24 (IBMCorp, Armonk, NY, USA), and the significance level was set at α = 0.05.
The error was calculated as the angular diﬀerence between the newand palpation methods. Angular diﬀerences for conventional and regression methods were also calculated. The estimation error of thescapular orientation was evaluated using the root mean square error(RMSE) of these angular diﬀerences.

2.4.2. Conventional method
Using the conventional method for comparison, RS-A0 (α0, β0, γ0)was a constant value that was calculated using the resting position(i = 0) (van Andel, 2009). Therefore, scapular orientation RS-CONi wasrepresented RAi RS-A0 (α0, β0, γ0).

3. Results
3.1. Elevating postures
Mean values for the new, conventional, regression, and palpation
methods across the 25 elevating postures are displayed in Table 1;

2.4.3. Palpation method
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A. Matsumura et al.

method and the palpation method had significant diﬀerences in hand tohead and forward reach. The conventional and palpation methods
significantly diﬀered in lateral reach and hand to mouth. The regression
and palpation methods significantly diﬀered in hand to head, forward
reach, and hand to mouth. The range of RMSE of our method was
3.0–8.6°. However, RMSE of the conventional method was 3.0–11.6°.
Additionally, RMSE of the regression method was 1.3–10.4°. The RMSE
of our new method and the regression method decreased comparedwith that of the conventional method for most tasks and axes of thescapular LCS. The error of our new method was less than that of theconventional method for high arm elevation angles, such as hand tohead, lateral reach, and 135° elevation. However, the error of our new
method was greater than that of the regression method for forward
reach. Moreover, there was no obvious diﬀerence in RMSE among thenew, conventional, and regression methods for hand to mouth and 45°
elevation. The RMSE of the regression method was smaller than our
method for hand to head and forward reach. The RMSE for lateral reachand 135° elevation was notably smaller in our method than in the regression method.
4. Discussion
To estimate scapular orientation in various shoulder postures, wedeveloped a new estimation method based on the AMC using curved
fitted interpolation. Using this new method, we first calibrated thepositional relationships between the AMC and the scapula that were
influenced by STA for variations in the TH elevation plane and elevation angle. We then compared estimation errors of the new method withthe palpation method, the conventional AMC method, and the recentlydeveloped regression method. The scapular orientation estimation error
in 25 elevating postures and 6 functional postures was investigated. The
elevating postures were set in steps of 30° at 0–180° of elevation angle
along 0–90° of the elevation plane. Our new method was able to estimate scapular orientation more accurately in various humeral postures,
especially in higher elevation angles, compared with the conventionaland regression methods. Moreover, the RMSE of the new method was
3–8° even in the functional postures, which was comparable to that of
the regression method. Therefore, based on these results, the new
method was able to improve the estimation accuracy of scapular orientation in various shoulder positions.
Previous studies commonly used the SL method for reference data tovalidate other estimation methods (van Andel, 2009; Brochard et al.,2011; Warner et al., 2012). Therefore, we adopted SL as a reference forcomparisons. In our palpation method using SL, the scapular orientations in 0° and 90° of elevation plane had similar angles to those inprevious studies; thus, our palpation method is considered to be a
suﬃcient reference for comparison with other estimation methods (vanAndel, 2009, Brochard et al., 2011).

Fig. 6. Calibration postures for thin-plate spline interpolation.

Fig. 7. The coordinate transformation of the palpation method.

RMSE is displayed in Table 2.
For the elevating postures, post-hoc tests revealed that there weresome significant diﬀerences between the new and palpation methods.
These significant diﬀerences are represented by the bold values inTable 1. Likewise, significant diﬀerences of the conventional and regression methods are represented in Table 1.
The maximum RMSE of our method was 8.1°; the RMSE of almost
every posture was less than 5° in our method. The maximum RMSE ofthe conventional method was 14.2°. The RMSE was mostly 5–8° between 30° and 90° of elevation angle; however, this increased beyond
the 120° of elevation angle. The maximum RMSE of the regression
method was 8.0°. The RMSE was approximately 4–8° in almost every
posture.

4.1. Scapular orientation estimations for elevating postures
Several previous studies reported that the estimation error of theconventional method increased when TH elevation angles were morethan 90° (Karduna, 2001; van Andel, 2009; Brochard et al., 2011). This
increased error was caused by soft tissue artifacts (STAs), such as
contraction of the deltoid and skin movement at TH elevation angles
more than 90°. To solve this problem, Nicholson et al. estimatedscapular orientation using regression equations (Nicholson et al., 2017),
which were generated using the TH orientations and the acromion
position (without acromion orientation) for calibration. They reported
that the error of the regression method was less than 8° compared withthe fluoroscopy. Additionally, Rapp et al. examined the estimation accuracy of the regression method at several functional postures (Rappet al., 2017); they reported that the regression method decreased theestimation error. In this study, the calibration procedure was performed
using several premeasured postures in multiple arm elevation planes

3.2. Functional postures
The scapular orientations for all methods in the functional postures
are displayed in Fig. 8. RMSE of functional postures is displayed inFig. 9. For the functional postures, post-hoc analysis revealed that our-RXUQDORI(OHFWURP\RJUDSK\DQG.LQHVLRORJ\  ²

A. Matsumura et al.

Table 1The scapular orientations in the elevating postures.
Upward (+)/Downward (−) rotation

Elevation angle

Elevation plane

Estimation method0°0°Palpation
Our method
Conventional method
Regression method

0.0
−0.1
0.0
−2.4

30°

30°
(3.5)
(3.5)
(3.6)
(2.4)

60°

90°

120°

150°

180°

1.2
0.9
1.9
6.1

(4.8)
(4.5)
(4.8)
(4.9)

10.0
9.8
9.8
14.5

(6.3)
(5.4)
(3.5)
(5.4)

24.4
24.3
22.8
26.4

(7.1)
(7.0)
(4.6)
(6.2)

40.0
40.2
33.3
39.5

(4.8)
(5.0)
(5.5)
(5.3)

49.6
49.6
39.9
47.3

(4.9)
(5.0)
(7.1)
(5.0)

56.1
54.8
45.1
54.3

(3.7)
(6.2)
(8.3)
(6.6)

Palpation
Our method
Conventional method
Regression method

2.5
−0.1
2.9
3.1

(5.7)
(4.9)
(4.3)
(5.7)

10.2
9.9
12.2
13.1

(7.3)
(5.7)
(3.6)
(6.3)

21.9
22.0
22.0
25.7

(4.7)
(4.7)
(3.8)
(5.9)

36.9
37.4
33.1
37.4

(5.1)
(4.3)
(5.4)
(6.4)

44.9
44.9
38.9
44.1

(4.3)
(4.2)
(6.8)
(6.2)

54.5
54.4
45.0
53.5

(4.3)
(4.4)
(8.3)
(6.3)

60°

Palpation
Our method
Conventional method
Regression method

1.9
−3.0
1.6
2.0

(4.6)
(7.6)
(6.8)
(5.7)

7.6
7.1
10.2
12.1

(5.6)
(5.5)
(4.2)
(6.3)

18.7
18.7
20.4
24.6

(4.7)
(4.7)
(3.6)
(6.1)

33.4
33.8
31.1
34.9

(4.0)
(6.3)
(5.2)
(6.9)

43.3
43.4
37.9
42.6

(4.2)
(4.2)
(6.9)
(7.4)

53.4
54.2
44.3
52.7

(3.3)
(5.1)
(7.8)
(5.6)

90°

Palpation
Our method
Conventional method
Regression method

2.4
−2.7
2.5
2.0

(4.2)
(5.7)
(4.8)
(6.7)

6.8
4.2
8.1
11.2

(5.6)
(4.7)
(4.1)
(5.1)

19.4
19.4
20.9
25.2

(5.9)
(6.0)
(5.2)
(6.3)

34.1
34.6
32.1
36.0

(4.7)
(5.0)
(3.8)
(6.1)

44.0
43.9
39.0
43.9

(3.9)
(3.8)
(6.6)
(4.4)

53.5
54.4
44.2
53.4

(4.3)
(5.7)
(6.9)
(4.6)

Internal (+)/External (−) rotation

Elevation angle

Elevation plane

Estimation method0°0°Palpation
Our method
Conventional method
Regression method

31.5
31.6
31.6
29.1

30°

30°
(4.3)
(4.1)
(4.3)
(7.0)

60°

90°

120°

150°

180°

27.1
25.5
25.2
25.0

(4.9)
(5.2)
(6.1)
(6.9)

24.9
23.3
23.7
23.8

(4.5)
(4.2)
(5.5)
(6.1)

20.0
19.8
21.2
21.4

(5.7)
(5.9)
(6.6)
(7.3)

19.0
19.8
22.0
20.3

(5.5)
(6.9)
(6.8)
(5.8)

22.4
22.5
26.6
21.9

(6.8)
(6.9)
(9.0)
(6.7)

24.4
24.7
34.5
28.9

(6.9)
(8.1)
(10.0)(7.6)

Palpation
Our method
Conventional method
Regression method

33.5
30.3
32.3
31.6

(4.7)
(4.8)
(4.7)
(4.9)

33.5
32.9
34.4
30.6

(5.3)
(6.2)
(6.2)
(4.0)

31.7
31.7
32.8
29.9

(5.1)
(5.0)
(6.6)
(5.1)

29.5
30.8
33.0
27.6

(5.4)
(5.1)
(6.8)
(6.1)

28.4
28.6
32.3
27.7

(5.8)
(5.8)
(6.8)
(6.1)

27.3
27.3
36.3
30.1

(8.1)
(8.4)
(10.2)(6.4)

60°

Palpation
Our method
Conventional method
Regression method

37.1
35.1
38.4
36.8

(3.7)
(6.5)
(3.8)
(4.2)

39.1
37.6
40.5
38.0

(4.0)
(5.5)
(4.0)
(4.4)

38.2
38.1
40.9
35.4

(5.0)
(4.9)
(4.4)
(5.4)

35.9
37.8
40.8
33.8

(5.3)
(4.0)
(5.8)
(6.7)

34.9
35.0
39.7
32.2

(4.4)
(4.2)
(6.5)
(6.4)

28.0
28.8
37.3
30.8

(6.3)
(8.8)
(8.5)
(6.3)

90°

Palpation
Our method
Conventional method
Regression method

39.1
34.7
38.4
40.1

(3.9)
(8.6)
(5.3)
(6.4)

42.3
41.8
46.4
42.3

(4.3)
(8.8)
(4.9)
(6.3)

42.4
42.4
47.6
39.8

(5.3)
(5.4)
(5.1)
(7.0)

41.7
41.3
48.2
38.5

(3.9)
(5.1)
(6.5)
(6.2)

37.5
37.4
45.0
36.0

(3.5)
(3.4)
(7.1)
(4.6)

29.3
29.4
39.0
30.7

(5.4)
(7.2)
(9.1)
(6.9)

Anterior (−)/Posterior (+) tilt

Elevation angle

Elevation plane

Estimation method0°0°Palpation
Our method
Conventional method
Regression method

−6.2
−6.2
−6.2
−8.8

30°

30°
(4.3)
(4.2)
(4.2)
(4.0)

60°

90°

120°

150°

180°

−5.5
−5.8
−5.1
−4.0

(3.0)
(3.2)
(3.7)
(3.5)

−4.1
−3.9
−1.3
−1.9

(3.9)
(3.9)
(4.1)
(3.8)

−0.8
−1.1
3.3
1.1

(3.5)
(3.3)
(6.8)
(4.7)

4.8
5.8
9.5
5.2

(5.1)
(6.1)
(8.3)
(5.0)

8.9
9.0
10.5
7.9

(6.3)
(6.3)
(10.1)
(6.3)

13.6
12.7
11.3
10.1

(7.8)
(9.5)
(12.0)(6.9)

Palpation
Our method
Conventional method
Regression method

−5.5
−3.8
−4.1
−4.3

(4.0)
(3.9)
(3.5)
(4.0)

−3.1
−3.4
−1.3
−2.0

(4.3)
(3.8)
(5.2)
(4.3)

−0.1
−0.1
2.2
0.9

(4.5)
(4.5)
(7.5)
(4.6)

3.9
3.9
6.2
3.7

(5.7)
(6.3)
(8.8)
(5.5)

7.1
7.0
7.9
5.5

(5.9)
(5.8)
(8.4)
(5.8)

10.7
10.7
9.4
9.1

(9.4)
(9.4)
(10.6)(7.0)

60°

Palpation
Our method
Conventional method
Regression method

−4.9
−4.5
−3.9
−5.1

(4.4)
(4.5)
(4.7)
(4.7)

−3.1
−3.6
−2.5
−2.8

(3.5)
(5.7)
(4.7)
(4.7)

−1.3
−1.4
1.2
0.4

(4.5)
(4.4)
(7.3)
(5.3)

1.9
3.0
3.5
2.3

(5.0)
(5.7)
(9.3)
(5.6)

5.8
5.9
5.0
4.4

(5.1)
(5.0)
(8.4)
(5.4)

12.2
10.5
9.4
8.6

(6.8)
(9.6)
(9.2)
(6.5)

90°

Palpation
Our method
Conventional method
Regression method

−4.8
−3.8
−5.0
−4.9

(3.6)
(7.0)
(5.1)
(4.9)

−3.2
−3.6
−3.2
−2.4

(3.8)
(5.4)
(5.5)
(4.6)

−0.2
−0.3
0.2
1.1

(4.5)
(4.4)
(8.4)
(5.7)

1.2
2.2
2.6
2.1

(5.1)
(5.9)
(9.7)
(5.9)

4.2
4.2
4.3
4.6

(5.3)
(5.1)
(9.9)
(5.0)

11.2
9.8
7.8
8.8

(6.8)
(9.2)
(10.8)(6.3)

Mean angles and standard deviation in degrees. Significant diﬀerences (p < 0.05) are indicated in bold.

before the estimation of the scapula orientation. To save time and toadjust the number of postures with the regression method, the numberof premeasured postures was limited to 10 postures. The base posture
was the arm at rest position, and other positions were more than 90° ofarm elevation in various elevation planes, where STA significantly affected the estimation accuracy. Moreover, we used thin-plate spline(TPS) for curve fitting interpolation to approximate the gap of the positional relationship between the AMC and scapula with changing elevation plane and elevation angle. The maximum RMSE of the new
method was 8° at the elevating postures. In contrast, the maximum
RMSE of the conventional method was 14.2°. The RMSE of the conventional method from 0° to 120° of elevation angle in this study was-RXUQDORI(OHFWURP\RJUDSK\DQG.LQHVLRORJ\  ²

A. Matsumura et al.

Table 2
The root mean square errors (degree) for each estimation method in the elevating postures.
Upward/Downward ration

Elevation angle

Elevation plane

Estimation method

0°

30°

60°

90°

120°

150°

180°

0°

Our method
Conventional method
Regression method

0.3
0.1
4.1

3.2
4.5
6.0

4.4
6.7
6.1

0.4
7.0
6.7

3.7
9.8
3.3

0.3
11.8
3.2

4.8
12.7
4.7

30°

Our method
Conventional method
Regression method

4.6
3.4
3.2

3.9
5.9
4.7

0.2
5.2
5.6

2.6
6.9
4.2

0.3
8.3
3.6

0.3
12.0
4.8

60°

Our method
Conventional method
Regression method

7.8
4.7
4.1

3.3
5.2
6.4

0.2
5.9
7.5

3.9
5.9
6.2

0.5
8.8
6.9

5.2
11.8
5.8

90°

Our method
Conventional method
Regression method

7.5
3.3
5.0

4.6
4.6
6.9

0.3
6.4
8.0

3.2
7.3
5.9

0.2
8.1
2.8

4.0
11.1
2.7

Internal/External rotation

Elevation angle

Elevation plane

Estimation method

0°

30°

60°

90°

120°

150°

180°

0°

Our method
Conventional method
Regression method

0.3
0.1
4.7

3.6
4.8
5.3

4.1
4.7
5.7

1.7
4.9
6.2

2.7
6.2
2.9

0.7
8.3
3.1

4.7
13.6
7.6

30°

Our method
Conventional method
Regression method

4.5
4.3
3.3

3.9
3.8
4.3

0.2
5.8
5.3

2.8
7.5
4.3

0.5
8.1
5.4

0.6
14.1
6.9

60°

Our method
Conventional method
Regression method

6.0
4.7
4.2

4.5
5.1
4.5

0.4
6.4
6.2

3.8
9.8
6.6

0.5
9.0
5.2

5.7
11.7
7.1

90°

Our method
Conventional method
Regression method

8.1
3.8
5.1

6.2
4.8
4.3

0.2
9.0
6.4

3.5
10.5
7.2

0.5
10.8
4.2

4.2
14.2
6.9

Anterior/Posterior tilt

Elevation angle

Elevation plane

Estimation method

0°

30°

60°

90°

120°

150°

180°

0°

Our method
Conventional method
Regression method

0.2
0.1
3.2

3.1
2.7
3.1

3.9
4.7
3.6

0.6
7.2
3.4

4.0
8.1
1.6

0.6
8.9
2.0

3.8
9.4
6.2

30°

Our method
Conventional method
Regression method

5.1
3.4
2.0

3.0
3.2
2.2

0.4
5.2
2.2

4.5
7.7
1.8

0.4
6.0
3.1

0.6
10.4
7.4

60°

Our method
Conventional method
Regression method

4.1
3.2
2.7

5.4
3.9
2.4

0.3
5.6
3.7

3.4
7.0
2.3

0.4
6.1
3.2

5.8
7.0
5.1

90°

Our method
Conventional method
Regression method

6.5
3.2
3.1

5.2
4.0
3.5

0.2
6.0
5.1

3.2
6.9
4.7

0.6
6.5
2.4

3.1
9.1
6.2

comparable to that in previous studies included in a previous systematic
review (Lempereur et al., 2014). The RMSE of the conventional method
increased at more than 120° of the elevation angle, which was in contrast to the finding of a previous study reporting that the estimation
accuracy decreased (Karduna, 2001), and RMSE of 7 of the 25 elevating
postures increased by more than 10°. Furthermore, the maximum RMSEof the regression method was 8.0°, which was lower than the conventional method. However, the RMSE of 17 of 25 elevating postures increased more than 5° in the regression method, whereas only 6 of the 25
elevating postures in our method had over 5° RMSE. In the new andregression methods, 6 and 10 of the 15 elevating postures without the
10 calibration postures were used for TPS interpolation, respectively.
Both the new and regression methods improved the estimation accuracyof the postures with over 90° elevation. Other TH orientation andparameters (AMC posture or orientation) are necessary as well. However, the RMSE of the new method decreased in a wide range ofshoulder postures compared with the regression method, with a good

estimation accuracy of 5° or less. According to the results of the conventional method, it was considered that the change of the error wascomplicated by STA due to elevation plane and elevation angle
changes. Therefore, it seemed that our new method, performed withcurved fitted interpolation using TH elevation plane and elevation
angle as input variables, improved estimation accuracy in a wide rangeof elevating postures compared with the regression method.
4.2. Scapular orientation estimations for the functional postures
For the functional postures, which included greater arm elevation
angles in postures such as hand to head, lateral reach, and 135° elevation, both the new and regression methods resulted in improved estimation accuracy compared to the conventional method. The estimation accuracy of hand to head was slightly better in the regression
method than in our new method, which was due to the diﬀerence of the
pre-measured postures. Regression equations, including the hand to-RXUQDORI(OHFWURP\RJUDSK\DQG.LQHVLRORJ\  ²

A. Matsumura et al.

values of regression methods were similar with the findings of Rappet al. (2017). The regression method used the supero-inferior andantero-posterior positions of the acromion with TH orientation to
generate regression equations. The scapula appeared to move toward
the lateral direction primarily during the lateral reach. However, theregression method did not consider the lateral transition of the acromion or suﬃciently improve estimation accuracy. In contrast, ourmethod corrected the relationship between the AMC and the scapula
using TPS and simultaneously measured the AMC orientation that responded to the orientation of the acromion with STA. Hence, it seemedthat our method could include actual postural change of the scapula byusing TPS. The regression method used acromion positions; however,
the acromion orientations were not used for generating regression
equations. Therefore, the estimation error of our method was considered small, suggesting that the estimation accuracy could be suﬃciently improved using our method. Accurate estimations of scapularorientation for ADL movements, in which the arm moves in high elevation angles and wide elevation planes, are possible using our method.
For forward reach, there was no significant diﬀerence in improvements of estimation accuracy between the new and conventional
methods. In contrast, the regression method improved the estimation
accuracy for upward rotation and posterior tilt, because forward reachposture was included in generating the regression equations, as with thehand to head posture. The RMSE of scapular orientation using the AMC
was reportedly 4.2–6.0° compared with the use of bone pins during
forward reaching (Bourne et al., 2007). In our study, the estimation
error of the new methods was slightly larger than Bourne’s results. It is
possible that the acromion slides further under the skin during forward
reach compared to during flexion, and thus the gap between the AMC
and the scapula could be larger during forward reach than during otherpostures. Therefore, caution is required when interpreting the results ofmovements such as forward reach. To improve the estimation accuracyof this posture, it may be eﬀective to include the forward reach posturein calibration postures when generating TPS equations.
For hand to mouth and 45° elevation, there was no obvious diﬀerence in the RMSE between the new, conventional, and regression
methods. We selected the premeasured postures to improve the accuracy during high elevation angles for calibration. Therefore, there were
few diﬀerences in the RMSE between the new and conventional
methods for the lower elevation postures.
4.3. Characteristics of the new method
The AMC was originally considered as the best method to directly
evaluate scapular orientation; however, performing the AMC in higher
TH elevation is diﬃcult as estimation error occurs by STA. In contrast,
the regression method attempts to reduce the eﬀect of STA by reducing
the numbers of the scapular land markers, as compared with the AMC
method. In the regression method, humeral orientations and the position of the acromion are employed to predict scapular orientation using
the regression equations. The regression method does not have suﬃcient scapula land marker to generate the scapular LCS. Therefore, theregression method lacks the data of scapular orientation calculated
from the scapular LCS at the arbitrary shoulder posture when scapularorientation is estimated using the regression equations. If the influenceof the STA can be suﬃciently corrected, it is possible to estimate
scapular orientation more accurately with the AMC in various humeral
postures. In this study, the new method appeared to significantly decrease the estimation error caused by STA. We selected the pre-measured postures wherein STAs are more like to occur and used the curved
fitted interpolation to correct the eﬀects of STA. Therefore, our method
estimated the change of the scapular orientation more directly from thebody surface by reducing STA as much as possible. However, ourmethod did not improve the estimation accuracy for forward reach. The
reason for this might be that the regression method using the positional
data of an acromion marker was more eﬀective in this posture, wherein

Fig. 8. Mean scapular orientation angles for each method in functional postures. The gray bars represent the average ± 1 SD during palpation. The centerdark gray lines represent the mean for palpation. The circles, squares, andtriangles represent the mean angles of new, conventional and regression
methods, respectively. *, † and ‡ represent significant diﬀerence for new,conventional, and regression methods (p < 0.05).

head position, were generated for the pre-measured postures. However,the RMSE of our method was also approximately less than 5°; thus, ourmethod had good estimation accuracy in the hand to head posture, withsimilar results to the regression method (MacLean et al., 2014). The
estimation accuracy of the new and regression methods also improvedin 135° elevation, and the RMSE was slightly better in the new methodthan in the regression method. It was considered that our method
generated the curved fitted interpolation using various elevating positions, thereby eﬀectively correcting STA in this posture. For lateralreach, the RMSE of our method was smaller than that of the regression
method. Rapp et al. reported that the RMSE of the regression method
was approximately 6–9° (Rapp et al., 2017). In this study, the RMSE-RXUQDORI(OHFWURP\RJUDSK\DQG.LQHVLRORJ\  ²

A. Matsumura et al.

Fig. 9. Root mean squared errors (RMSE) for the new, conventional, and regression methods in the functional postures. The white bars, black bars, and light gray bars
represent the RMSE of the new, conventional, and regression methods, respectively.

the scapular transition was larger. However, it may be necessary to
improve estimation accuracy for specific arm postures by modifying
pre-measured postures; further studies are needed for this purpose.

wider area were thus selected for specific tasks so that calibration could
be performed. Second, our method required a preprocess that included
premeasuring several postures for calibration, similar to the regression
method. For this preprocess, it took us approximately 3–5 min tomeasure all 10 postures with the AMC and SL. This procedure would
have been completed faster if the number of postures had been reduced.
However, estimation accuracy and measurement time were considered
trade-oﬀs. Spending more time than necessary for premeasurements
should be avoided because it is burdensome for study subjects. Our
results indicated that the number of premeasuring postures used in thisstudy was adequate. Finally, subjects in this study were healthy young

4.4. Limitations
There were some limitations in this study. First, estimating thescapular orientation outside the elevation planes and elevation angles
in the premeasured postures was diﬃcult. Therefore, error could be
increased for hand behind back and shoulder maximal horizontal adduction/abduction. Arm elevation planes and elevation angles with

-RXUQDORI(OHFWURP\RJUDSK\DQG.LQHVLRORJ\  ²

A. Matsumura et al.

men. The scapular muscle volume and skin mobility of elderly people
and patients with shoulder disorders may diﬀer from those of healthy
subjects. Therefore, it is possible that changes in the positional relationship between the AMC and scapula could diﬀer in other populations compared to those of the subjects in this study. However, thephysical characteristics of each subject were considered for calibration.
Therefore, the new estimation method could possibly be used for elderly adults or patients with shoulder disorders. However, further studies evaluating these and other specific populations are warranted toconfirm the accuracy of our estimation method.

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Nicholson, K.F., Richardson, R.T., Rapp, E.A., Quinton, R.G., Anzilotti, K.F., Richards,
J.G., 2017. Validation of a mathematical approach to estimate dynamic scapularorientation. J. Biomech. 54, 101–105.
Rapp, E.A., Richardson, R.T., Russo, S.A., Rose, W.C., Richards, J.G., 2017. A comparisonof two non-invasive methods for measuring scapular orientation in functional positions. J. Biomech. 61, 269–274.
Ratcliﬀe, E., Pickering, S., McLean, S., Lewis, J., 2014. Is there a relationship between
subacromial impingement syndrome and scapular orientation? A systematic review.
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and movement in unimpaired shoulders, shoulder impingement syndrome, and glenohumeral instability. Scand. J. Med. Sci. Sports 21, 352–358.
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Biomech. 38, 981–992.

5. Conclusions
We developed a new estimation method using curve fitting interpolation and investigated the estimation accuracy of scapular orientations in 25 elevating postures and six functional postures. Our method
was able to improve the estimation accuracy in various elevating postures, particularly for higher arm elevating positions, and resulted inestimations similar to those of the regression methods for lower elevating positions with the exception of the forward reaching posture. In
the future, our method might be able to improve the estimation accuracy of the forward reaching posture if this posture is added into thecalibration process. However, the estimation accuracy of our method
for arm postures other than those included in the calibrated postures isstill unclear, as they were not examined. This study was performed with
only healthy male subjects, and thus future studies should clarify
whether our method is applicable for patients with shoulder disorders.

Aoi Matsumura (PT, CSCS) received his MSc degree from
Kyoto University in 2013. His field of research includes
biomechanics of human movement and clinical investigation in patients and athletes. He is working at TAKE
PHYSICAL CONDITIONING as a physical therapist and engages conditioning and training for athletes.

Conflicts of interest
The authors declare that there is no conflict of interest.
Financial disclosure
The authors state that there is no financial disclosure and personal
relationships with other people or organizations that could inappropriately influence the present work.

Atsushi Ueda (PT) received his MSc degree from Doshisha
University in 2018. His research interest is biomechanics ofhuman movement, especially baseball. He is working at
Hankai Hospital as a physical therapist and engages rehabilitation for patients with musculoskeletal disorders.

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Yasuo Nakamura receives Ph.D. degree from Niigata
University in 1998. Currently, he is Professor in the Facultyof Health and Sports Science at Doshisha University. His
research interests are sports biomechanics of the overhand
throwing motion including the scapula movements, especially baseball pitching.

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