Measurement and Description of Three-Dimensional Shoulder Range of Motion With Degrees of Freedom Interactions Diane Haering1 Laboratory of Simulation and Movement Modeling, Department o f Kinesiology, Universite de Montreal, 1700 rue Jacques Tetreault, Laval, QC H7N 0B6, Canada e-mail: [email protected]
Keywords: biomechanics, shoulder, modeling, range of motion, three-dimensional, angle-angle-angle diagram
1 Introduction
Maxime Raison EcolePolytechnique de Montreal and Centre de Readaptation Marie Enfant - Sainte-Justine UHC, Research & Engineering ChauApplied in Pediatrics (RECAP), 5200 rue Belanger, office GR-123, Montreal, QC HIT 1C9, Canada e-mail: [email protected]
Mickael Begon Laboratory of Simulation and Movement Modeling, Department of Kinesiology, Universite de Montreal, 1700 rue Jacques Tetreault, Laval, QC H7N 0B6, Canada e-mail: [email protected]
The shoulder is the most mobile joint o f the human body due to bony constraint scarcity and soft tissue function unlocking several degrees of freedom (DOF). Clinical evaluation o f the shoulder range of motion (RoM) is often limited to a few monoplanar meas urements where each DOF varies independently. The main objec tive o f this study was to provide a method and its experimental approach to assess shoulder 3D RoM with DOF interactions. Six teen participants performed four series o f active arm movements with maximal amplitude consisting in (1) elevations with fixed arm axial rotations (elevation series), (2) axial rotations at differ ent elevations (rotation series), both in five planes o f elevation, (3) free arm movements with the instruction to fill the largest vol ume in space while varying hand orientation (random series), and (4) a combination o f elevation and rotation series (overall series). A motion analysis system combined with an upper limb kinematic model was used to estimate the 3D joint kinematics. Thoracohumeral Euler angles with correction were chosen to represent rota tions. The angle-time-histories were treated altogether to analyze their 3D interaction. Then, all 3D angular poses were included into a nonconvex hull representing the RoM space accounting for DOF interactions. The effect o f series o f movements (n = 4) on RoM volumes was tested with a one-way repeated-measures ANOVA followed by Bonferroni posthoc analysis. A normalized 3D RoM space was defined by including 3D poses common to a maximal number o f participants into a hull o f average volume. A significant effect o f the series of movements (p < 0.001) on the vol umes o f thoracohumeral RoM was found. The overall series 'Corresponding author. Manuscript received October 29, 2013; final manuscript received May 2, 2014; accepted manuscript posted May 14, 2014; published online June 3, 2014. Assoc. Editor: Zong-Ming Li.
Journal of Biomechanical Engineering
measured the largest RoM with an average volume of 3.46 ± 0.89 million cubic degrees. The main difference between the series of movements was due to axial rotation. A normalized RoM hull with average volume was found by encompassing arm poses common to more than 50% of the participants. In general, the results con firmed and characterized the complex 3D interaction of shoulder RoM between the DOF. The combination o f elevation and rotation series (overall series) is recommended to fully evaluate shoulder RoM. The normalized 3D RoM hull is expected to provide a reli able reference to evaluate shoulder function in clinical research and for defining physiologic continuous limits in 3D shoulder computer simulation models. [DOI: 10.1115/1.4027665]
Shoulder RoM is a common indicator of shoulder function characterized by large mobility due to multiple joints, low bony congruency, and soft tissue function. In the shoulder, this mobility is mainly assured and limited by surrounding muscles [1], They consequently share it between all joints they cross and corre sponding degrees of freedom (DOF) configuration. For example, a shift of the range of arm axial rotation toward external rotation is observed as the arm is moved into a more anterior plane of eleva tion [2], Current methods to measure shoulder RoM lack consider ing consequent DOFs interactions. Beyond functional evaluation, shoulder RoM can help simula tion or animation of upper limb movements to resolve DOF redun dancies problems leading sometimes to nonphysiological solutions [3-5]. DOF interaction displays an obvious 3D nature that Euler or Cardan angle sequences do not account for. Yet, attempts to define 3D shoulder RoM are rare and still rely on pla nar measurements during which one DOF varies at a time [6]. These independent joint limits implemented in current models on each DOF joint miss reproducing physiological interaction. There fore, forward and inverse kinematics algorithms would benefit from physiologically interacting joint limits to ensure realistic ki nematics [7]. Goniometers, the most common tools in clinical or sports envi ronments, can neither be used for 3D nor for dynamic analyses [8]. According to the American Academy of Orthopaedic Sur geons, electromagnetic tracking system gave the “best available data for anatomic shoulder RoM” of normal shoulder motion [9], However, electromagnetic systems are limited for elevation angles higher than 120 deg [10] and arm axial rotation [11], Opti cal measurement is expected to increase the angular accuracy. Specifically, a redundant marker set coupled with least square optimization algorithm and kinematic chain model has shown to reduce skin movement artifacts [12]. Motion capture has already been used to track dynamic shoulder RoM but no extensive data are available. While measurement techniques exist, complemen tary model and protocol must be developed to account for DOF interactions. First, such a protocol requires a series of movements able to describe all feasible shoulder joint 3D poses, not identified yet. Then, individual factors, such as gender and age [13], or physical activities [14], can influence shoulder RoM in terms of ampli tude and DOFs interaction. Since a 3D continuous RoM cannot be averaged, a normative method should also be developed. Finally, the usual way to represent interactions between two joint angle-time-histories is the angle-angle diagram [15,16]. Extrapolation of this approach to a 3D angle-angle-angle dia gram seems promising to describe DOF interaction throughout shoulder RoM. The main objective of this study was to provide an experimen tal method for measuring and analyzing shoulder 3D RoM includ ing DOF interactions. The series of movements should describe the largest number of possible shoulder postures and be suited for
Copyright © 2014 by ASME
AUGUST 2014, Vol. 136 / 084502-1
b. R o ta tio n
s erie s
max. external
7 p la n e s o f e le v a t io n
F ig . 1
plateau
D e s c r ip tio n o f a r m m o v e m e n t s e r ie s r e la t iv e ly t o t h e t h o r a x w it h t h e a r m r e f e r e n c e
f r a m e a n d t h e c o r r e s p o n d in g a x e s o f r o t a t io n , (a ) “ E le v a t io n ” s e r ie s ,
(b)
“ R o t a t io n ” s e r ie s .
T h e s e v e n v e r tic a l p la n e s o f e le v a tio n a r e s e e n f r o m a b o v e . T h e m a x im a l e x t e r n a l, n e u t r a l, a n d m a x im a l in te r n a l r o ta tio n s o f t h e a r m a r e r e p r e s e n t e d d u r in g e le v a t io n . “ P la t e a u ” in d ic a t e s t h a t e le v a tio n is s to p p e d a t 3 0 d e g , 6 0 d e g , 9 0 d e g , 1 2 0 d e g , 1 5 0 d e g , a n d m a x im a l e le v a t io n , w h ile a m a x im a l e x t e r n a l- in t e r n a l r o ta tio n is p e r f o r m e d . N o te s : F o r c la r ity , t h e a r m is r e p r e s e n te d w ith e x te n d e d e lb o w d u r in g i n t e r n a l- e x t e r n a l r o t a t io n s ; h o w e v e r , in t h e r e a lity , t h e e lb o w w a s b e n t a t a b o u t 9 0 d e g . T h e a d d it io n s ig n in d ic a t e s t h a t e a c h c o m b in a t io n o f t h e r ig h t h a n d s id e is p e r fo r m e d in a ll s e v e n v e r tic a l p la n e s o f e le v a t io n .
any population. Subsequently, a ready-to-use set of data based on healthy population will be provided. 2
M ethods
2.1 Experiments. Eight male and eight female adults (24 ± 4 yr, 69 ± 11 kg, 171 ± 10 cm) were tested on their right dominant shoulder after giving informed consent approved by the local University Ethics Committee. None had history of shoulder dysfunction. Forty-five reflective skin markers were placed according to the kinematic models of Jackson et al. [17]
F ig . 2
and Fohanno et al. [18] for the shoulder and elbow, respectively. Markers trajectories were captured by motion capture 18 cam eras at 150 Hz (VICON T20S & T40S, Oxford, UK). Each participant performed six setup trials engaging each joint DOF [18,19], and three series of maximal amplitude active arm movements. During first series (termed as elevations, Fig. 1(a)), subjects were asked to reach maximal elevation in seven planes of elevation, with the arm successively held in maximal internal, maximal external, and neutral rotation. The second series (termed as rotations, Fig. 1(b)) consisted in maximal arm elevations in the same seven planes of elevation with maximum internal and
E x a m p le o f h u ll c o n s t r u c t io n f o r t h e f ir s t s e r ie s o f m o v e m e n t s ( e le v a t io n s ) , ( a ) P o s e s d u r in g e v o lu t io n o f t h e m o v e
m e n t d e fin e d b y 3 D a n g le s ,
(b) a n d
(c ) T e tr a h e d r a a n d n o n c o n v e x h u ll t h a t e n c o m p a s s e s a ll t h e p o s e s , r e s p e c tiv e ly .
084502-2 / Vol. 136, AUGUST 2014
Transactions of the ASME
x 106cubic degrees
1. Overall
2. Elevations
3. Rotations
kinematics based on generalized coordinates preventing joint dis location. Lower arm was added to correct soft tissue artifacts affecting arm axial rotation [11], Then, the model was calibrated to the participants using six setup trials for functionally locating shoulder centers and elbow axes of rotation [21,22]. Joints angletime-histories were estimated using inverse kinematics [23] from the recorded marker trajectories. Our method focused on a unique thoracohumeral shoulder joint to encompass multiple joint interactions. Following ISB recom mendation, humerus orientation (Fig. 1) relative to the thorax was described by the Euler angles extracted from rotation sequence: Ry(il/)Rx(9)Ry(—\l/ + (p)—i.e., successively plane of elevation, elevation, and axial rotation [20]. Final axial rotation breakdown between subtraction of initial plane of elevation anglc-i// and sub sequently corrected angle accounting for total axial rotation cp is expected to avoid superficial DOF interaction. To treat the three DOF time-histories together, a representation based on 3D angle(i^)-angle(0)-angle((p) diagram was proposed. Each arm pose was represented by a point in the 3D angular space (Fig. 2(a)). Then, a nonconvex hull encompassing thoracohumeral poses was created to delimit 3D RoM space [24]. After linking all points by tetrahedrons (Fig. 2(b)), a nonconvex hull was generated using outward faces (Fig. 2(c)). RoM volume the hull delimited was calculated by adding tetrahedron volumes and expressed in cubic degrees defined by the angle-angle-angle space. RoM non convex hulls and volumes were computed for each series of move ments and each subject. To test the influence of movement series (n = 4), a one-way repeated measures ANOVA with Bonferroni posthoc analysis was applied to the mean of the subject RoM volumes. The coefficient of variation of the RoM volumes (i.e., ratio between the standard devia tion and the mean value) was also computed to investigate interindi vidual variability. Since numerous intersubjects variability factors affect shoulder mobility [13,14], and 3D hulls cannot be directly averaged, a normalization method was proposed. For this purpose, all poses data obtained were tested for being inside the RoM of each
4. Random
Fig. 3 Boxplots representing the effects of movement series on maximal shoulder RoM volume with paired f-test. The series showing significant differences with each other are mentioned after one (p
Keywords: biomechanics, shoulder, modeling, range of motion, three-dimensional, angle-angle-angle diagram
1 Introduction
Maxime Raison EcolePolytechnique de Montreal and Centre de Readaptation Marie Enfant - Sainte-Justine UHC, Research & Engineering ChauApplied in Pediatrics (RECAP), 5200 rue Belanger, office GR-123, Montreal, QC HIT 1C9, Canada e-mail: [email protected]
Mickael Begon Laboratory of Simulation and Movement Modeling, Department of Kinesiology, Universite de Montreal, 1700 rue Jacques Tetreault, Laval, QC H7N 0B6, Canada e-mail: [email protected]
The shoulder is the most mobile joint o f the human body due to bony constraint scarcity and soft tissue function unlocking several degrees of freedom (DOF). Clinical evaluation o f the shoulder range of motion (RoM) is often limited to a few monoplanar meas urements where each DOF varies independently. The main objec tive o f this study was to provide a method and its experimental approach to assess shoulder 3D RoM with DOF interactions. Six teen participants performed four series o f active arm movements with maximal amplitude consisting in (1) elevations with fixed arm axial rotations (elevation series), (2) axial rotations at differ ent elevations (rotation series), both in five planes o f elevation, (3) free arm movements with the instruction to fill the largest vol ume in space while varying hand orientation (random series), and (4) a combination o f elevation and rotation series (overall series). A motion analysis system combined with an upper limb kinematic model was used to estimate the 3D joint kinematics. Thoracohumeral Euler angles with correction were chosen to represent rota tions. The angle-time-histories were treated altogether to analyze their 3D interaction. Then, all 3D angular poses were included into a nonconvex hull representing the RoM space accounting for DOF interactions. The effect o f series o f movements (n = 4) on RoM volumes was tested with a one-way repeated-measures ANOVA followed by Bonferroni posthoc analysis. A normalized 3D RoM space was defined by including 3D poses common to a maximal number o f participants into a hull o f average volume. A significant effect o f the series of movements (p < 0.001) on the vol umes o f thoracohumeral RoM was found. The overall series 'Corresponding author. Manuscript received October 29, 2013; final manuscript received May 2, 2014; accepted manuscript posted May 14, 2014; published online June 3, 2014. Assoc. Editor: Zong-Ming Li.
Journal of Biomechanical Engineering
measured the largest RoM with an average volume of 3.46 ± 0.89 million cubic degrees. The main difference between the series of movements was due to axial rotation. A normalized RoM hull with average volume was found by encompassing arm poses common to more than 50% of the participants. In general, the results con firmed and characterized the complex 3D interaction of shoulder RoM between the DOF. The combination o f elevation and rotation series (overall series) is recommended to fully evaluate shoulder RoM. The normalized 3D RoM hull is expected to provide a reli able reference to evaluate shoulder function in clinical research and for defining physiologic continuous limits in 3D shoulder computer simulation models. [DOI: 10.1115/1.4027665]
Shoulder RoM is a common indicator of shoulder function characterized by large mobility due to multiple joints, low bony congruency, and soft tissue function. In the shoulder, this mobility is mainly assured and limited by surrounding muscles [1], They consequently share it between all joints they cross and corre sponding degrees of freedom (DOF) configuration. For example, a shift of the range of arm axial rotation toward external rotation is observed as the arm is moved into a more anterior plane of eleva tion [2], Current methods to measure shoulder RoM lack consider ing consequent DOFs interactions. Beyond functional evaluation, shoulder RoM can help simula tion or animation of upper limb movements to resolve DOF redun dancies problems leading sometimes to nonphysiological solutions [3-5]. DOF interaction displays an obvious 3D nature that Euler or Cardan angle sequences do not account for. Yet, attempts to define 3D shoulder RoM are rare and still rely on pla nar measurements during which one DOF varies at a time [6]. These independent joint limits implemented in current models on each DOF joint miss reproducing physiological interaction. There fore, forward and inverse kinematics algorithms would benefit from physiologically interacting joint limits to ensure realistic ki nematics [7]. Goniometers, the most common tools in clinical or sports envi ronments, can neither be used for 3D nor for dynamic analyses [8]. According to the American Academy of Orthopaedic Sur geons, electromagnetic tracking system gave the “best available data for anatomic shoulder RoM” of normal shoulder motion [9], However, electromagnetic systems are limited for elevation angles higher than 120 deg [10] and arm axial rotation [11], Opti cal measurement is expected to increase the angular accuracy. Specifically, a redundant marker set coupled with least square optimization algorithm and kinematic chain model has shown to reduce skin movement artifacts [12]. Motion capture has already been used to track dynamic shoulder RoM but no extensive data are available. While measurement techniques exist, complemen tary model and protocol must be developed to account for DOF interactions. First, such a protocol requires a series of movements able to describe all feasible shoulder joint 3D poses, not identified yet. Then, individual factors, such as gender and age [13], or physical activities [14], can influence shoulder RoM in terms of ampli tude and DOFs interaction. Since a 3D continuous RoM cannot be averaged, a normative method should also be developed. Finally, the usual way to represent interactions between two joint angle-time-histories is the angle-angle diagram [15,16]. Extrapolation of this approach to a 3D angle-angle-angle dia gram seems promising to describe DOF interaction throughout shoulder RoM. The main objective of this study was to provide an experimen tal method for measuring and analyzing shoulder 3D RoM includ ing DOF interactions. The series of movements should describe the largest number of possible shoulder postures and be suited for
Copyright © 2014 by ASME
AUGUST 2014, Vol. 136 / 084502-1
b. R o ta tio n
s erie s
max. external
7 p la n e s o f e le v a t io n
F ig . 1
plateau
D e s c r ip tio n o f a r m m o v e m e n t s e r ie s r e la t iv e ly t o t h e t h o r a x w it h t h e a r m r e f e r e n c e
f r a m e a n d t h e c o r r e s p o n d in g a x e s o f r o t a t io n , (a ) “ E le v a t io n ” s e r ie s ,
(b)
“ R o t a t io n ” s e r ie s .
T h e s e v e n v e r tic a l p la n e s o f e le v a tio n a r e s e e n f r o m a b o v e . T h e m a x im a l e x t e r n a l, n e u t r a l, a n d m a x im a l in te r n a l r o ta tio n s o f t h e a r m a r e r e p r e s e n t e d d u r in g e le v a t io n . “ P la t e a u ” in d ic a t e s t h a t e le v a tio n is s to p p e d a t 3 0 d e g , 6 0 d e g , 9 0 d e g , 1 2 0 d e g , 1 5 0 d e g , a n d m a x im a l e le v a t io n , w h ile a m a x im a l e x t e r n a l- in t e r n a l r o ta tio n is p e r f o r m e d . N o te s : F o r c la r ity , t h e a r m is r e p r e s e n te d w ith e x te n d e d e lb o w d u r in g i n t e r n a l- e x t e r n a l r o t a t io n s ; h o w e v e r , in t h e r e a lity , t h e e lb o w w a s b e n t a t a b o u t 9 0 d e g . T h e a d d it io n s ig n in d ic a t e s t h a t e a c h c o m b in a t io n o f t h e r ig h t h a n d s id e is p e r fo r m e d in a ll s e v e n v e r tic a l p la n e s o f e le v a t io n .
any population. Subsequently, a ready-to-use set of data based on healthy population will be provided. 2
M ethods
2.1 Experiments. Eight male and eight female adults (24 ± 4 yr, 69 ± 11 kg, 171 ± 10 cm) were tested on their right dominant shoulder after giving informed consent approved by the local University Ethics Committee. None had history of shoulder dysfunction. Forty-five reflective skin markers were placed according to the kinematic models of Jackson et al. [17]
F ig . 2
and Fohanno et al. [18] for the shoulder and elbow, respectively. Markers trajectories were captured by motion capture 18 cam eras at 150 Hz (VICON T20S & T40S, Oxford, UK). Each participant performed six setup trials engaging each joint DOF [18,19], and three series of maximal amplitude active arm movements. During first series (termed as elevations, Fig. 1(a)), subjects were asked to reach maximal elevation in seven planes of elevation, with the arm successively held in maximal internal, maximal external, and neutral rotation. The second series (termed as rotations, Fig. 1(b)) consisted in maximal arm elevations in the same seven planes of elevation with maximum internal and
E x a m p le o f h u ll c o n s t r u c t io n f o r t h e f ir s t s e r ie s o f m o v e m e n t s ( e le v a t io n s ) , ( a ) P o s e s d u r in g e v o lu t io n o f t h e m o v e
m e n t d e fin e d b y 3 D a n g le s ,
(b) a n d
(c ) T e tr a h e d r a a n d n o n c o n v e x h u ll t h a t e n c o m p a s s e s a ll t h e p o s e s , r e s p e c tiv e ly .
084502-2 / Vol. 136, AUGUST 2014
Transactions of the ASME
x 106cubic degrees
1. Overall
2. Elevations
3. Rotations
kinematics based on generalized coordinates preventing joint dis location. Lower arm was added to correct soft tissue artifacts affecting arm axial rotation [11], Then, the model was calibrated to the participants using six setup trials for functionally locating shoulder centers and elbow axes of rotation [21,22]. Joints angletime-histories were estimated using inverse kinematics [23] from the recorded marker trajectories. Our method focused on a unique thoracohumeral shoulder joint to encompass multiple joint interactions. Following ISB recom mendation, humerus orientation (Fig. 1) relative to the thorax was described by the Euler angles extracted from rotation sequence: Ry(il/)Rx(9)Ry(—\l/ + (p)—i.e., successively plane of elevation, elevation, and axial rotation [20]. Final axial rotation breakdown between subtraction of initial plane of elevation anglc-i// and sub sequently corrected angle accounting for total axial rotation cp is expected to avoid superficial DOF interaction. To treat the three DOF time-histories together, a representation based on 3D angle(i^)-angle(0)-angle((p) diagram was proposed. Each arm pose was represented by a point in the 3D angular space (Fig. 2(a)). Then, a nonconvex hull encompassing thoracohumeral poses was created to delimit 3D RoM space [24]. After linking all points by tetrahedrons (Fig. 2(b)), a nonconvex hull was generated using outward faces (Fig. 2(c)). RoM volume the hull delimited was calculated by adding tetrahedron volumes and expressed in cubic degrees defined by the angle-angle-angle space. RoM non convex hulls and volumes were computed for each series of move ments and each subject. To test the influence of movement series (n = 4), a one-way repeated measures ANOVA with Bonferroni posthoc analysis was applied to the mean of the subject RoM volumes. The coefficient of variation of the RoM volumes (i.e., ratio between the standard devia tion and the mean value) was also computed to investigate interindi vidual variability. Since numerous intersubjects variability factors affect shoulder mobility [13,14], and 3D hulls cannot be directly averaged, a normalization method was proposed. For this purpose, all poses data obtained were tested for being inside the RoM of each
4. Random
Fig. 3 Boxplots representing the effects of movement series on maximal shoulder RoM volume with paired f-test. The series showing significant differences with each other are mentioned after one (p
