In-vitro Identification of Shoulder Joint and Muscle DynamicsBased on Motion Capture and Musculoskeletal Computation

Akihiko Murai1, Yusuke Kawano2, Ko Ayusawa3, Mitsunori Tada1, Noboru Matsumura2, and Takeo Nagura2

Abstract— Dynamics properties of shoulder joint and muscleare experimentally identified under different musculoskeletalconditions for a digital human model with accurate dynamics.Passive swing motions of scapula and upper limb bones incadaveric specimen with and without muscles are measuredby an optical motion capture system. External forces that areapplied to the scapula bone are simultaneously measured bya force plate. The dynamics identification process consists of3 steps: 1) identify the inertial parameters of the cadavericspecimen with and without muscles respectively, 2) identifythe viscosity of the glenohumeral joint from the specimenwithout muscles, and 3) identify the viscosity of the shouldermuscles from the specimen with muscles and the identifiedjoint viscosity. These parameters are identified in six cadavericspecimens. Their joint viscosities are 5.33E-02 ± 1.33E-02Nms/rad (without muscles) and 1.07E-01 ± 2.28E-02 Nms/rad(with muscle), and their muscle viscosities are 6.69E+02 ±8.11E+02 Ns/m (mean ± SD). The identified joint viscositycorresponds with the literature value. This measurement andidentification algorithm would improve the dynamics of thedigital human model and realize the accurate muscle activityestimation and the motion simulation.

I. INTRODUCTION

Human shoulder joint consists of a skeleton system withclavicle, scapula, and humerus bones, and a muscle-tendonnetwork with multiple muscles. Coupled with such complexkinematics structure, this joint has a dynamics characteristicstypified by a resistance caused by joint and muscle viscoelas-ticity. Therefore, the dynamics behaviors of this joint becomesignificantly complex. Part of muscle activities do not appearto observable motions because such activities are consumedby balancing with this resistance. Such kinematics complex-ity as well as the dynamics complexity make accurate humanmodeling, motion analysis, and simulation difficult.

Kamata et al. clarified the function of the lumbrical musclein the free finger motion by examining the three dimensionalfinger tip trajectory under the different force levels of thelumbrical muscle [1]. Such data and knowledge are requiredfor building an accurate digital human model in biome-chanics and thumb finger reconstruction in orthopedics, andcorresponding data and knowledge are desired for the shoul-der joint. The significant difference between the finger jointand the shoulder one is their dynamics characteristics. The

1A. Murai and M. Tada are with Digital Human Research Group, TheNational Institute of Advanced Industrial Science and Technology (AIST),Tokyo, Japan. a.murai@aist.go.jp

2Y. Kawano, N. Matsumura, and T. Nagura are with Department ofOrthopedic Surgery, Keio University School of Medicine, Tokyo, Japan.

3K. Ayusawa is with Interactive Robotics Research Group, The NationalInstitute of Advanced Industrial Science and Technology (AIST), Tokyo,Japan.

dynamics, including the inertial parameters and the joint andmuscle viscosities, which are negligible in the finger joints,heavily influence on the shoulder joint motion. Therefore,the joint and muscle dynamics becomes important as well astheir kinematics for developing the digital human shouldermodel.

In this research, we experimentally identify the dynamicsof shoulder joint and muscle under the different muscu-loskeletal conditions. Human joint dynamics and musculo-tendon parameters have been estimated from the in-vivomeasurements [2], [3], [4], [5]. In-vivo estimation has severallimitations: 1) measured data are the combination of thejoint and muscle dynamics and the effects by the humansomatosensory reflex motion, 2) cannot identify the jointdynamics effects from the muscle ones separately. Thisresearch overcomes these limitations by conducting the in-vitro measurements. The passive shoulder swing motionsof the cadaveric specimen with and without muscles aremeasured by the optical motion capture system. The externalforces that are applied to the scapula bone are simultaneouslymeasured by the force plate. The dynamics identificationprocess consists of 3 steps: 1) identify the inertial param-eters of the cadaveric specimen with and without musclesrespectively, 2) identify the viscosity of the glenohumeraljoint from the specimen without muscles, and 3) identify theviscosity of the shoulder muscles from the specimen withmuscles and the identified joint viscosity.

The rest of this paper is organized as follows. Section IIdescribes the algorithm for the identification of the inertialproperties and the joint and muscle dynamics. The exper-imental results are presented in Section III, followed bydiscussion and concluding remarks in Section IV.

II. INERTIAL AND DYNAMICS PROPERTIESIDENTIFICATION ALGORITHM

The inertial parameters (the mass and the center of mass(COM)) and the dynamics (the joint and muscle viscosities)of the shoulder joint are identified through the followingsteps. These parameters are identified step by step for thecomputational stability. The joint and muscle viscositieschange when the related muscles are contracted [6]. Here, weidentify the viscosities that purely come from their physicalproperties. We use the passive swing motion data of thecadaveric specimen with and without muscles. θM+J ∈RNJ−6, F ext

M+J ∈ R6, θJ ∈ RNJ−6, and F extJ ∈ R6

(NJ : the number of generalized coordinates) represent themotion and the external force data from the specimen withand without muscles, respectively.

A. Inertial Parameter Identification

First, the inertial parameters of the specimen with muscles(ϕM+J ∈ R10NL (NL: the number of links)) are identifiedfrom θM+J , θ̇M+J , θ̈M+J , and F ext

M+J by the dynamicscomputation of the multibody system [7]. Then, the jointtorque τM+J ∈ RNJ−6 is computed from ϕM+J , θM+J ,their time derivatives, and F ext

M+J by the inverse dynamicscomputation of the multibody system [8]. Same algorithm isapplied to the specimen without muscles to compute ϕJ ∈R10NL and τJ ∈ RNJ−6 from θJ and F ext

J .

B. Joint Viscosity Identification

The joint torque τJ is caused by the joint dynamicsbecause we measure the fully passive swing motions onthe cadaveric specimen without muscles. We model the jointdynamics as follows:

τJ = dJ θ̇J . (1)

dJ ∈ RNJ−6×NJ−6 is the diagonal matrix whose (k, k)-thvalue is the viscosity of the k-th joint and θ̇J ∈ RNJ−6 isthe joint angle velocity. We optimize dJ so that the error∥τJ − dJ θ̇J∥ would be minimized.

C. Muscle Viscosity Identification

The joint torque τM+J is caused by the joint and muscledynamics. We model the joint and muscle dynamics asfollows:

τM+J = τJ + τM (2)τM = JT

M (θM+J )dM l̇M

= JTM (θM+J )dMJM (θM+J )θ̇M+J . (3)

τM is the joint torque that comes from the muscle viscosity,dM ∈ RNM×NM (NM : the number of muscles) is thediagonal matrix whose (k, k)-th value is the viscosity ofthe k-th muscle, l̇M ∈ RNM is the muscle length velocity,and JM (θM+J ) = δlM/δθM+J ∈ RNM×NJ−6 is theJacobian matrix of the muscle length w.r.t. the joint angle.Fig. 1 shows the shoulder musculoskeletal model [9] that isused to compute the musculoskeletal kinematics. This modelonly considers the major muscles relevant to the motionsof the glenohumeral joint. This simplification leaves us11 muscles: Biceps Brachii Caput Longum, Biceps BrachiiCaput Breve, Coracobrachialis, Deltoideus Pars Acromi-alis, Deltoideus Pars Spinalis, Infraspinatus, Subscapularis,Supraspinatus, Teres Major, Teres Minor, and Triceps BrachiiCaput Longum. The Jacobian matrix JM (θM+J ) is com-puted based on the muscles alignments of this model. Here,we optimize dM for τM+J and subtract the effects of dJ

for the computational stability. The total viscosity dM+J ∈RNJ−6×NJ−6 is also identified by minimizing ∥τM+J −dM+J θ̇M+J∥ for the comparison with the literature.

III. EXPERIMENTAL RESULTS

Six fresh-frozen cadaveric upper limbs amputated at theclavicle are used. After institutional review board review andexemption, the relevant records are accessed. The specimens

[front][back]

DeltoideusAcromialis

DeltoideusSpinalis

Infraspinatus

TeresMinor

TeresMajor

TricepsBrachiiLongum

Supraspinatus

Coracobrachialis

BicepsBrachiiLongum

Subscapularis

BicepsBrachiiBreve

Fig. 1. Shoulder musculoskeletal model [9].

are free from apparent musculoskeletal disorders. There are4 male and 2 female specimens, with a mean age of 78.7years (range 40 - 101). The cadaveric upper limb is thawed atroom temperature immediately before testing. The specimenis prepared by removing the skin and subcutaneous fat. Theshoulder muscles that connect between the proximal anddistal of clavicle are removed or physically severed. Theskin and subcutaneous fat peripheral to the radiocarpal jointare left. 1.6 mm threaded stainless steel wires are drilledto fix the humeroulnar, radioulnar, and radiocarpal jointrespectively to avoid the self collisions.

The specimen is fixed by interleaving its scapula with themetallic plate and bars as shown in the right side of Fig. 2.Then, the plate is fixed to the force plate (BP400600-2000;AMTI, MA, USA) with the custom-build fixation apparatusas shown in the left side of Fig. 2. Three optical markerswith a diameter of 9 mm are fixed to the scapula, humerus,ulna, radius, and third metacarpal bone with the threadedstainless steel pins and the custom-build triangular fixationapparatus, respectively. The motions of these markers duringthe fully passive swings of the upper limb are recorded bythe commercial optical motion capture system (ProReflexMCU120; Qualisys, Gothenburg, Sweden) in 200 Hz. Theexternal forces that are applied to the scapula during theswings are simultaneously measured with the force platein 2000 Hz. The position and the orientation of the forceplate are precisely calibrated using the weight with opticalmarkers, and the external force data (F ext

M+J and F extJ ) are

represented in the same coordinate system as the motion data(θM+J and θJ ).

First, the fully passive swing motions of the upper limbwith the muscle are measured (θM+J and F ext

M+J ). Then, weremove or physically sever the muscles that connect betweenthe scapula, humerus, radius, and ulna bones. The skin,subcutaneous fat, and muscles peripheral to the radiocarpaljoint are left. The fully passive swing motions of this upperlimb without the muscles are measured (θJ and F ext

J ).The cadaveric specimen is scanned using computed to-

mography (CT) to measure the positional relationships be-tween the optical markers and the bones. The surface ge-

optical motion capture system (Qualysis)

force plate (AMTI)

fixation apparatus

cadaveric specimen

metallic plate

2-metallic bar

4-φ5mm bolt-nut

[back view of cadaveric specimen]

Fig. 2. Measurement environment with motion capture system and force plate, and fixation apparatus for cadaveric specimen.

CT data for Scapula

CT data for Humerus

marker models for Humerus

marker models for Scapula

musculoskeletal model

Fig. 3. Surface geometry data from CT images and the musculoskeletalmodel.

ometries of markers and bones created from the CT imagesare fit into each bone model respectively, and the markermodels are aligned based on the fitted surface geometries asshown in Fig. 3. The marker models are fit into the markertrajectories from the motion capture data to reconstruct thebones motions at the inverse kinematics computation.

Tables I-II show the experimental results that are identifiedin the six cadaveric specimens. Table I represents the inertialparameters and the joint dynamics that are identified from thespecimens without muscles. Table II represents the inertialparameters and the joint and muscle dynamics that areidentified from the specimens with muscles. Here, COMrepresents the distance between the glenohumeral joint centerand COM, the joint viscosity is dJ , the total viscosity

is dM+J , and the muscle viscosity is dM . The estimatedmuscles represent the mass difference between ϕM+J andϕJ , and the measured muscles represent the mass of theremoved muscles. All results are expressed in mean ± SD.

TABLE IJOINT PARAMETERS OF SPECIMENS WITHOUT MUSCLES

specimen # mass COM joint viscosity[kg] [m] [Nms/rad]

01 2.02E+00 4.25E-01 7.61E-0202 2.04E+00 4.60E-01 5.51E-0203 1.90E+00 3.87E-01 5.80E-0204 2.05E+00 4.34E-01 5.25E-0205 2.09E+00 4.79E-01 4.62E-0206 2.03E+00 4.16E-01 3.18E-02

mean ± 2.02E+00 ± 4.33E-01 ± 5.33E-02 ±SD 5.99E-02 2.98E-02 1.33E-02

IV. DISCUSSION

We can observe the following points in the experimentalresults:

1) The motion and external force measurement with thecadaveric specimen and the kinematics and dynamicscomputation realize the identification of the inertialparameters and the joint and muscle dynamics.

2) Table I shows the inertial parameters and the jointviscosities of the specimens without muscles. Theidentified joint viscosities become 5.33E-02 ± 1.33E-02 Nms/rad.

3) Table II shows the inertial parameters and the totalviscosities of the specimens with muscles. The iden-tified total viscosities become 1.07E-01 ± 2.28E-02Nms/rad, which correspond with the literature value(0.2 Nms/rad) that is shown in [3]. The viscosity maybecome larger in the human body than the cadaveric

TABLE IIJOINT PARAMETERS OF SPECIMENS WITH MUSCLES

specimen # mass estimated muscles measured muscles COM total viscosity muscle viscosity[kg] [kg] [kg] [m] [Nms/rad] [Ns/m]

01 2.64E+00 6.14E-01 7.65E-01 3.47E-01 1.05E-01 2.41E+0202 2.43E+00 3.89E-01 5.43E-01 3.87E-01 1.06E-01 3.23E+0203 2.26E+00 3.61E-01 4.44E-01 3.35E-01 1.06E-01 3.62E+0204 2.65E+00 6.03E-01 7.88E-01 3.88E-01 9.54E-02 2.56E+0205 2.66E+00 5.62E-01 9.36E-01 4.35E-01 1.52E-01 2.48E+0306 2.60E+00 5.77E-01 9.67E-01 3.47E-01 7.60E-02 3.52E+02

mean ± 2.54E+00 ± 5.18E-01 ± 7.40E-01 ± 3.73E-01 ± 1.07E-01 ± 6.69E+02 ±SD 1.48E-01 1.03E-01 1.91E-01 3.42E-02 2.28E-02 8.11E+02

specimen because the nerve system, especially the so-matosensory reflex, works against the external forces.

4) Table II also shows that the identified muscle viscosi-ties become 6.69E+02 ± 8.11E+02 Ns/m. Their stan-dard deviation becomes significantly large because thisparameter is sensitive to the muscle moment arm thatis computed based on the conventional musculoskeletalmodel [9]. The authors are developing the volumetricmusculoskeletal model that realize the accurate musclemoment arm estimation [10], and this model wouldimprove this joint dynamics identification.

5) In Table II, the estimated muscle mass becomes smallerthan the measured one, because this method estimatesthe mass that physically moves in synchronizationwith the glenohumeral joint motion. Some part ofthe muscles around the scapula do not move at theglenohumeral joint motion. This algorithm can identifysuch functional dynamics properties.

These results have the following implications:1) In biomechanics, it implies that the motion and external

force measurement can estimate the inertial parametersas well as the joint dynamics at the medical and reha-bilitation fields. This algorithm leads to the quantitativerehabilitation and medical diagnosis.

2) In robotics, the identified joint and muscle dynamicscan be implemented to the musculoskeletal model [9],[10], [11], and would improve the somatosensory infor-mation estimation. Such models lead to a more correctunderstanding of human motion control / generationmechanisms.

3) We have also been interested in experimental validationof our musculoskeletal model. The present results ofestimating the reasonable inertial parameters and thejoint dynamics provide validation for the appropriatekinematics and dynamics computation.

Several directions remain for future work. We validate theidentification results by comparing them with the existingliterature values in this paper. Applying the same procedureto a mechanical joint with known parameters would evaluatethe accuracy of our identification. Our musculoskeletal modelcurrently does not include the passive joint dynamics. Weexpect that adding the joint dynamics that is identified inthis research would significantly improve the somatosensory

information estimation by computing the muscle activitiesthat balance with this passive resistance. The digital humanmodel with accurate joint dynamics would realize a morecorrect understanding of human motion control / generationmechanism that is useful for the medical, rehabilitation, andsports science fields.

ACKNOWLEDGEMENT

The authors would like to sincerely thank the ClinicalAnatomy Laboratory, Department of Anatomy, Keio Univer-sity School of Medicine, Tokyo, Japan, for allowing accessto the fresh cadaver upper extremity specimens.

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