A New Method of Contact Stress Measurement for Analyzing Internal Impingement Syndrome of the Shoulder: Potentials and Preliminary Evaluation
A New Method of Contact Stress Measurement for Analyzing Internal Impingement Syndrome of the...
Jang, Seong-wook;Yoo, Yon-Sik;Kim, Yoon Sang
2020-06-17 00:00:00
applied sciences Article A New Method of Contact Stress Measurement for Analyzing Internal Impingement Syndrome of the Shoulder: Potentials and Preliminary Evaluation 1 2 1 , Seong-wook Jang , Yon-Sik Yoo and Yoon Sang Kim * BioComputing Laboratory, Department of Computer Science and Engineering, Institute for Bioengineering Application Technology, Korea University of Technology and Education (KOREATECH), Cheonan 31253, Korea; elderlord@koreatech.ac.kr Camp 9 Orthopedic Clinic, Hwaseong 18505, Korea; ybw1999@gmail.com * Correspondence: yoonsang@koreatech.ac.kr; Tel.: +82-41-560-1496 Received: 30 April 2020; Accepted: 15 June 2020; Published: 17 June 2020 Abstract: Shoulder impingement syndrome causes critical disorders such as rotator cu tear or superior labrum anterior to posterior (SLAP) lesion in both the general public and in athletes whose sports involve throwing. Nevertheless, the biomechanics of the syndrome still have not been clarified. Contact stress measurement in vivo during shoulder motion is essential to identifying the biomechanics of the syndrome. There have been no reports to date regarding internal impingement syndrome among the syndrome studied by using the finite element method (FEM). The proposed method simulates the internal impingement syndrome according to shoulder motion using the FEM. The method solves the critical process zone error at the supraspinatus tendon insertion according to impingement of the 3D biomechanical model by relaxing the boundary condition for representation of shoulder motion. The simulation results confirmed that the proposed method allowed for the analysis of internal impingement syndrome by measuring contact stress (23.13 MPa) during shoulder motion. The performance of the proposed method was examined through the dierential displacement (maximum 3.28 mm) in shoulder motion by boundary condition relaxation. The result of the simulation was consistent with the clinical findings. Keywords: internal impingement syndrome; soft tissue injury; supraspinatus tendon; finite element analysis 1. Introduction Shoulder impingement syndrome causes supraspinatus tendon injury to throwing athletes such as baseball players [1,2]. The syndrome is also present in the general public, including computer workers and the elderly, as well as elite athletes engaged in throwing activities [3–5]. Recently, studies are underway to identify the main causal factors in shoulder impingement syndrome and to develop appropriate prevention and treatment plans. The clinical cause of shoulder impingement syndrome has been known as supraspinatus tendon injury, caused by contact between musculoskeletal tissues inside the joint (subacromial space) [6]. However, the biomechanical mechanism still has not been clarified [2,7,8]. This study, which aims to identify the biomechanical mechanism of shoulder impingement syndrome, is essential in that supraspinatus tendon injury can lead to additional critical disorders such as rotator cu [9–12] or superior labrum anterior to posterior (SLAP) tears [13–15]. Typically, shoulder impingement syndrome consists of both external and internal impingement syndromes. External impingement syndrome involves a lesion or injury of the supraspinatus tendon caused by contact with the acromion Appl. Sci. 2020, 10, 4165; doi:10.3390/app10124165 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 4165 2 of 13 at subacromial space. External impingement syndrome cannot explain posterior shoulder pain during shoulder motion. Internal impingement syndrome analyses are required to explain posterior shoulder pain. Internal impingement syndrome involves a lesion or injury of the supraspinatus tendon caused by contact between the labrum and humeral head during shoulder motion. Internal impingement syndrome is thought to be fundamentally complex and multifactorial in its explanation of posterior shoulder pain [2]. Traditional studies for internal impingement syndrome estimate the mechanism of shoulder impingement syndrome through various methods based on arthroscopic findings, image diagnoses, and cadaveric experiments. The arthroscopic finding-based method [16] involves invasive observations of the interactions between musculoskeletal tissues in vivo. This method has the disadvantage that it cannot be used to experiment for injuries of soft tissues because of ethical issues. The image diagnosis-based method [3,6] noninvasively analyzes soft tissues in vivo by using medical imaging information scanned from magnetic resonance imaging (MRI) results. However, this method has a low accuracy problem because it measures the three-dimensional (3D) shape of internal impingement syndrome on a two-dimensional (2D) image. The cadaveric experiment-based method [14,17] measures the deformation of musculoskeletal tissues by using a mechanical device. This method has a low reliability problem because it is dicult to obtain sucient samples [18]. In other words, these methods are not suitable for the analysis of shoulder impingement syndrome because the arthroscopic finding-, image diagnosis-, and cadaveric experiment-based methods cannot measure the contact stress that occurred in vivo in the shoulder joint. Conventional studies are underway to analyze the biomechanical mechanism of shoulder impingement syndrome through computer simulations by using the finite element method (i.e., FE simulations). The FE simulations allow us to analyze the injury of musculoskeletal tissue in vivo by using a 3D biometric model. This method measures the contact stress between musculoskeletal tissues in vivo. As above, most of the previous studies have focused on external impingement syndrome among the shoulder impingement syndromes. Specifically, there were no reports found of internal impingement syndrome among the shoulder impingement syndromes studied by using the finite element method. In this paper, we propose a new contact stress measurement method for analyzing internal impingement syndrome of the shoulder. The proposed method simulates internal impingement syndrome of the supraspinatus tendon between the humeral head and labrum based on the finite element method. This allows for the analysis of internal impingement syndrome by measuring contact stress during shoulder motion. The performance of the proposed method is examined through a dierential displacement of the humerus according to shoulder motion. 2. Materials and Methods 2.1. Design and Setting The proposed method is designed in the following four steps, as shown in Figure 1: (1) shoulder geometric data acquisition; (2) shoulder material property representation; (3) boundary and loading condition definition for humeral motion and supraspinatus tendon loading; (4) boundary condition relaxation for humeral motion. Steps 1–3 of the proposed method have referred to the traditional shoulder modeling method and are applied to FE simulation [19]. In the first step, the geometry of the shoulder model, including bones (humerus and scapula) and soft tissues (supraspinatus tendon and labrum), is reconstructed based on medical imaging information. Material properties of cartilage are considered as those of bone according to the assumption that it does not aect the simulation results [20,21]. Herein, the medical imaging information includes computerized tomography (CT), computerized tomography arthrogram (CTA), and magnetic resonance (MR) images. Bone models of the humerus and scapula are derived from the CT images. The soft tissue models of the supraspinatus tendon and labrum are derived from the CTA and MR images. Appl. Sci. 2020, 10, 4165 3 of 13 The soft tissue models are constructed by stacking the contours extracted according to the consultation Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 12 of orthopedic surgeons [22]. The medical imaging information is acquired in three planes (axial, coronal, and sagittal planes). The accuracy of the shoulder model is enhanced by combining the models planes (axial, coronal, and sagittal planes). The accuracy of the shoulder model is enhanced by represented based on three planes. combining the models represented based on three planes. Figure 1. Block diagram of the proposed method. Figure 1. Block diagram of the proposed method. In the second step, the material properties are applied to the shoulder model to represent the In the second step, the material properties are applied to the shoulder model to represent the deformation of in vivo properties. The material properties are included in vertices of the elements deformation of in vivo properties. The material properties are included in vertices of the elements consisting of shoulder models. The humeral and scapular models are assumed to be rigid body consisting of shoulder models. The humeral and scapular models are assumed to be rigid body material material because bone has extremely high stiness compared to soft tissues. The material property of because bone has extremely high stiffness compared to soft tissues. The material property of the the labrum is modeled as linear elasticity with isotropy and homogeneity, and that of the supraspinatus labrum is modeled as linear elasticity with isotropy and homogeneity, and that of the supraspinatus tendon is modeled as hyperelasticity considering the large deformations. The material properties used tendon is modeled as hyperelasticity considering the large deformations. The material properties in the shoulder model were referenced from the conventional literature [23–26], and details are shown used in the shoulder model were referenced from the conventional literature [23–26], and details are in Table 1. shown in Table 1. Table 1. Parameters of material properties used in the proposed method. Table 1. Parameters of material properties used in the proposed method. Feature Type Mechanical Properties Number of Elements (Element Type) Reference Feature Type Mechanical Properties Number of Elements (Element Type) Reference Scapula 12,967 (S4R) [23] Scapula Rigid 12,967 (S4R) [23] E = 15,000 MPa, v = 0.3 Rigid body E = 15,000 MPa, v = 0.3 Humerus 3482 (S4R) [23] Humerus body 3482 (S4R) [23] Labrum Linear Linearelasticity E = 33 MPa, v = 0.497 5622 (C3D8R) [24] Labrum E = 33 MPa, v = 0.497 5622 (C3D8R) [24] elasticity Supraspinatus W = exp[ (I 3)] = 2(I 3) Hyper-elasticity 1775 (C3D8R) [25,26] tendon = 0.12 MPa, = 1.0 Supraspinatus Hyper- [ ( )] = exp − 3 = 2( − 3) 1775 (C3D8R) [25,26] tendon elasticity α = 0.12 MPa, β = 1.0 In the third step, the boundary and load conditions are defined to represent shoulder motion, In the third step, the boundary and load conditions are defined to represent shoulder motion, as as shown in Figure 2. The boundary condition is humeral abduction, generated based on screw motion. shown in Figure 2. The boundary condition is humeral abduction, generated based on screw motion. Generally, the screw motion is used to represent the shoulder motion based on Chasles’ theorem [27]. Generally, the screw motion is used to represent the shoulder motion based on Chasles’ theorem [27]. Because actual shoulder motion is not rotated based on spherical coordinates, it is hard to represent Because actual shoulder motion is not rotated based on spherical coordinates, it is hard to represent humeral abduction among musculoskeletal tissue. To solve this, the humeral abduction is represented humeral abduction among musculoskeletal tissue. To solve this, the humeral abduction is represented as a screw motion between two postures (neutral position and abducted position). The humeral model as a screw motion between two postures (neutral position and abducted position). The humeral superimposed on the scapula model among bone models was derived based on CT images scanned model superimposed on the scapula model among bone models was derived based on CT images from the two postures, and it was used in the screw motion of the humerus. The represented humeral scanned from the two postures, and it was used in the screw motion of the humerus. The represented abduction is achieved as rotation and translation on the basis of the screw axis. The load condition is humeral abduction is achieved as rotation and translation on the basis of the screw axis. The load pretension pulled from the distal to proximal side of the supraspinatus tendon, and this is performed condition is pretension pulled from the distal to proximal side of the supraspinatus tendon, and this simultaneously with humeral abduction. is performed simultaneously with humeral abduction. Appl. Sci. 2020, 10, 4165 4 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 12 Figure Figure 2. 2. H Humeral umeral m motion otion b between etween neutral neutral and and abducted abducted position. position. Figure 2. Humeral motion between neutral and abducted position. Fine modeling and motion generation are important because FE simulations are aected by Fine modeling and motion generation are important because FE simulations are affected by Fine modeling and motion generation are important because FE simulations are affected by geometry and motion trajectory [28]. However, an error occurred in the critical process zone of the geometry and motion trajectory [28]. However, an error occurred in the critical process zone of the geometry and motion trajectory [28]. However, an error occurred in the critical process zone of the insertion site of the supraspinatus tendon in FE simulations based on the conventional method (steps 1 insertion site of the supraspinatus tendon in FE simulations based on the conventional method (steps insertion site of the supraspinatus tendon in FE simulations based on the conventional method (steps to 3), as shown in Figure 3a. The error is indicated when excessive distortion of the supraspinatus 1 to 3), as shown in Figure 3a. The error is indicated when excessive distortion of the supraspinatus 1 to 3), as shown in Figure 3a. The error is indicated when excessive distortion of the supraspinatus tendon model occurs because of specific rotational movements of the humeral model, as shown in tendon model occurs because of specific rotational movements of the humeral model, as shown in tendon model occurs because of specific rotational movements of the humeral model, as shown in Figure 3b. Furthermore, excessive distortion in the numerical analysis often interrupts calculations. Figure 3b. Furthermore, excessive distortion in the numerical analysis often interrupts calculations. Figure 3b. Furthermore, excessive distortion in the numerical analysis often interrupts calculations. This can be attributed to a computational stability problem caused by compression of the soft tissue This can be attributed to a computational stability problem caused by compression of the soft tissue This can be attributed to a computational stability problem caused by compression of the soft tissue model between the humeral and scapular models, along with the displacement boundary condition. model between the humeral and scapular models, along with the displacement boundary condition. model between the humeral and scapular models, along with the displacement boundary condition. This problem makes the volume of soft tissues approach zero, and thus, the accuracy decreases This problem makes the volume of soft tissues approach zero, and thus, the accuracy decreases in FE This problem makes the volume of soft tissues approach zero, and thus, the accuracy decreases in FE in FE simulations. According to the conventional study [10] that quantifies the injury caused by simulations. According to the conventional study [10] that quantifies the injury caused by partial- simulations. According to the conventional study [10] that quantifies the injury caused by partial- partial-thickness tears of the supraspinatus tendon, the injury begins at the insertion site. This supports thickness tears of the supraspinatus tendon, the injury begins at the insertion site. This supports that thickness tears of the supraspinatus tendon, the injury begins at the insertion site. This supports that that the error occurs on critical process zones. the error occurs on critical process zones. the error occurs on critical process zones. (a) (b) (a) (b) Figure 3. Excessive distortion on the critical process zone: (a) the critical process zone of supraspinatus Figure 3. Excessive distortion on the critical process zone: (a) the critical process zone of supraspinatus Figure 3. Excessive distortion on the critical process zone: (a) the critical process zone of supraspinatus tendon; tendon; ( (b b)) the the excessive excessive distortion distortion on on the the supraspinatus supraspinatus tendon. tendon. tendon; (b) the excessive distortion on the supraspinatus tendon. In the fourth step, this problem can be solved by relaxing the displacement boundary condition of In the fourth step, this problem can be solved by relaxing the displacement boundary condition of In the fourth step, this problem can be solved by relaxing the displacement boundary condition of the humeral model to prevent excessive deformation. By using the Abaqus VUEL commercial computer the humeral model to prevent excessive deformation. By using the Abaqus VUEL commercial computer the humeral model to prevent excessive deformation. By using the Abaqus VUEL commercial computer program, we developed a method that enables relaxation of the boundary condition in accordance with program, we developed a method that enables relaxation of the boundary condition in accordance with program, we developed a method that enables relaxation of the boundary condition in accordance with the interactions of adjacent materials while adhering to the desired boundary condition. The method the interactions of adjacent materials while adhering to the desired boundary condition. The method of the interactions of adjacent materials while adhering to the desired boundary condition. The method of of the displacement boundary condition relaxation can be explained as a hybrid concept that combines the displacement boundary condition relaxation can be explained as a hybrid concept that combines the displacement boundary condition relaxation can be explained as a hybrid concept that combines the tie conditions for two nodes of the Abaqus *MPC (multi-point constraints) commands and elastic the tie conditions for two nodes of the Abaqus *MPC (multi-point constraints) commands and elastic Appl. Sci. 2020, 10, 4165 5 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 12 the tie conditions for two nodes of the Abaqus *MPC (multi-point constraints) commands and elastic flexibility, as shown in Figure 4. The first step involved constructing a dummy identical to the object flexibility, as shown in Figure 4. The first step involved constructing a dummy identical to the object whose displacement boundary condition was to be monitored. The same boundary condition was then whose displacement boundary condition was to be monitored. The same boundary condition was applied to this dummy model in the corresponding location. A line connecting the same location in then applied to this dummy model in the corresponding location. A line connecting the same location the real humerus model (follower) and dummy model (guide) was established. This line was assumed in the real humerus model (follower) and dummy model (guide) was established. This line was to be a two-node truss element, whose property is defined as a “user element” (VUEL). The property assumed to be a two-node truss element, whose property is defined as a “user element” (VUEL). The of this user element is defined as follows. If the two endpoints show dierent displacement values, property of this user element is defined as follows. If the two endpoints show different displacement resistance is generated in proportion to the amount of dierence by applying a penalty function. If the values, resistance is generated in proportion to the amount of difference by applying a penalty penalty function is suciently large, interactions between the adjacent materials do not interfere with function. If the penalty function is sufficiently large, interactions between the adjacent materials do the entered displacement boundary. However, if the penalty function is too weak, slight dierences in not interfere with the entered displacement boundary. However, if the penalty function is too weak, displacement may occur between the two endpoints in cases of interaction. slight differences in displacement may occur between the two endpoints in cases of interaction. Figure 4. Abaqus user element (VUEL) connecting the dummy and humerus model. Figure 4. Abaqus user element (VUEL) connecting the dummy and humerus model. The penalty function is assumed to have types of potential energy, including kinetic energy, The penalty function is assumed to have types of potential energy, including kinetic energy, with with the following Hamilton principle. the following Hamilton principle. t . . . . 1 1 1 1 F = T V = m u u + m u u 1 1 1 2 2 2 2 2 Φ = T − V = t ̇ ∙ ̇ + ̇ ∙ ̇ (1) 2 2 u(t) ( ) ( ) ( P u P u + f u u d u u dt 1 1 2 2 2 1 2 1 (1) ( ) − (− ∙ − ∙ + ( − ) ∙ ( − ) Kinetic energy is denoted by T, and potential energy exerted by the external force and the strain energy are represented by V. The truss element has two nodes and the subscript denotes the node index. (u u ) denotes the dierence in the displacement vector of nodes 1 and 2 of the truss. 2 1 Kinetic energy is denoted by T, and potential energy exerted by the external force and the strain Along the equation of motion, the variation of the penalty function will vanish. energy are represented by V. The truss element has two nodes and the subscript denotes the node index. ( − ) denotes the diffe rence in the displacement vector of nodes 1 and 2 of the truss. . . . . 1 1 F = m u u + m u u 1 1 1 2 2 2 Along the equation of m t otion 2, the variati2 on of the penalty function will vanish. R (2) u(t) P u P u + f(u u )d(u u ) dt 1 1 2 2 2 1 2 1 1 1 δΦ = δ ̇ ∙ ̇ + ̇ ∙ ̇ 2 2 After taking the variati on on each term and using the integral by part, the following conditions (2) can be established for each node: ( ) − − ∙ − ∙ + ( − ) ∙ ( − ) .. P f(u u ) + m u = 0 (3) 1 2 1 1 1 .. After taking the variation on each term and using the integral by part, the following conditions P + f(u u ) + m u = 0 (4) 2 2 2 2 can be established for each node: ( ) (3) − − − + ̈ = 0 − + ( − ) + ̈ = 0 (4) Appl. Sci. 2020, 10, 4165 6 of 13 These equations imply that external, internal, and inertial forces are physically balanced in equilibrium. If acceleration can be ignored and the current position deviates from the position in equilibrium, Taylor expansion can be applied in the vicinity of the current position, which yields the following equation. 2 3 2 3 " # 0 0 0 0 0 6 7 6 7 f (u u ) f (u u ) u P + f(u u ) 6 2 1 2 1 7 1 6 1 2 1 7 6 7 6 7 6 7 = 6 7 (5) 0 0 0 4 5 4 5 0 0 f (u u ) f (u u ) u P + f(u u ) 2 1 2 1 2 2 1 2 3 6 7 P + f(u u ) 6 7 1 2 1 0 6 7 6 7 is the force in the initial position, and f (u u ) is the dierential of the 2 1 4 5 P f(u u ) 2 2 1 function in the initial position. If the function of internal force f(u u ) is assumed to have a linear 2 1 functional form, the strain energy relative to the x, y, z direction components of the displacement can 2 2 2 1 1 1 be expressed by K (x x ) + K (y y ) + K (z z ) . x 2 1 y 2 1 z 2 1 2 2 2 In this case, 2 3 2 32 3 6 P + f (u u ) 7 K 0 0 K 0 0 u x 2 6 76 7 6 1x 1 7 x x 1x 6 76 7 6 7 6 76 7 6 7 6 76 7 6 7 6 76 7 6 7 P + f (u u ) 0 K 0 0 K 0 u y 6 y y 76 1y 7 6 1y 2 1 7 6 76 7 6 7 6 76 7 6 7 6 76 7 6 7 6 76 7 6 7 0 0 K 0 0 K u P + f (u u ) 6 z z 76 1z 7 6 1z z 2 1 7 6 76 7 6 7 6 76 7 =6 7 (6) 6 76 7 6 7 6 76 7 6 7 K 0 0 K 0 0 u P + f (u u ) 6 x x 76 2x 7 6 7 2x x 2 1 6 76 7 6 7 6 76 7 6 7 6 76 7 6 0 7 6 76 7 6 7 0 K 0 0 K 0 u ( ) 6 y y 76 2y 7 6 P + f u u 7 2y y 2 1 6 76 7 6 7 4 54 5 6 7 4 5 0 0 K 0 0 K u z z 2z P + f (u u ) 2z z 2 or [K][u] = [F] can be used as the matrix form. If a positive-definite system is used, changes in the penalty function relative to changes in u are negative or zero, as per Equation (2). In other words, " # h i F = P f(u u ) P + f(u u ) 2 2 2 1 1 1 " # (7) h i P + f(u u ) 1 1 2 1 = P f(u u ) P + f(u u ) [K] 0 1 2 1 2 2 1 ( ) P f u u 2 2 1 If acceleration cannot be ignored in Equations (3) and (4), Equation (8) is solved by applying an explicit method. " #" # " # .. m 0 u P + f(u u ) 1 1 1 1 .. = (8) 0 m u P f(u u ) 2 2 2 2 1 After obtaining the acceleration of nodes 1 and 2, the resulting value is integrated to obtain the displacement in the next time step [29,30]. In Abaqus/Explicit user element (VUEL) subroutines, a mass matrix and force matrix can be computed with the values entered. These values can include the initial positions of the nodes pertaining to an element, displacement relative to the initial position, and incremental displacement at the current time increment Dt. In this study, to ignore the inertial force generated by mass, the mass of the truss element was set to a low value. However, this value should have been suciently high to ensure a sucient time increment because it was related to the frequency of the motion, according to the following Equation (9). 0 r 1 B C B C e B C Dt = minBL C = min (9) @ A E K The force matrix is calculated from the right term of Equation (8). 2.2. Finite Element Simulation The FE simulations applied with the proposed method were performed in an environment, including humeral motion, pretension of the supraspinatus tendon, and miscellaneous conditions, as shown in Appl. Sci. 2020, 10, 4165 7 of 13 Figure 5. The humeral motion is generated by screw motion with relaxation control of the boundary condition. The dummy model for the relaxation control of the displacement boundary condition in the FE modeling is defined as the guidance for humeral motion. The humeral model, the actual object of analy As pips l, . S is ci.d 2e 02 f0 in , 1e 0d , x a Fs Ot Rh P e EE fo Rl R lo Ew VIe EW r. Additionally, the proximal end of the supraspinatus tendo7 n oifs 12 p ulled constantly by a force of 10 N to maintain pretension [31]. The miscellaneous conditions include scapular conditions include scapular fixation, a tie condition, and a contact condition. The scapular, which is fixation, a tie condition, and a contact condition. The scapular, which is the basis of humeral motion, is the basis of humeral motion, is fixed at the initial position. The humerus and supraspinatus tendon fixed at the initial position. The humerus and supraspinatus tendon are tied based on the footprint. In the are tied based on the footprint. In the contact condition between soft tissues, the applied coefficient contact condition between soft tissues, the applied coefficient of friction is 0 to represent slip caused by of friction is 0 to represent slip caused by actual moisture. The bone models, defined as a rigid body, actual moisture. The bone models, defined as a rigid body, are modeled by linear quadrilateral elements, are modeled by linear quadrilateral elements, which are shell elements (S4), in order to reduce the which are shell elements (S4), in order to reduce the computations. The soft tissue models, which are computations. The soft tissue models, which are likely to come into contact with one another, are likely mto odc eo le m d e by in ltio ne ca o rn te ta tr ca t h w ed itr h on o n ee lea m neo ntts he (r C , 3 aD re 4) m . odeled by linear tetrahedron elements (C3D4). Figure 5. Finite element simulation environment. Figure 5. Finite element simulation environment. Table 2 is pseudo-code of FE simulation applied with the proposed method. The spring constant Table 2 is pseudo-code of FE simulation applied with the proposed method. The spring constant (K) of (K tr ) uss of tris usassumed s is assum to edbe to K be = K = = K = , whi , wh ch ich is ian s an isotr isotr opic opicfeatur feature e,, and and be be analyzed analyzed sstep tep b by y step. x y z step. If spring constants are increased, the synchronization between the guidance model and follower If spring constants are increased, the synchronization between the guidance model and follower model model increases, and this can come close to the case where the displacement boundary condition is increases, and this can come close to the case where the displacement boundary condition is given given directly to the analyzed model. directly to the analyzed model. Table 2. Pseudo-code for FE simulations applied with the proposed method. Table 2. Pseudo-code for FE simulations applied with the proposed method. Data Finite element model by the acquired shoulder geometry Data Finite element model by the acquired shoulder geometry Result Shoulder motion without excessive distortion and its contact stress measurement result Result Shoulder motion without excessive distortion and its contact stress measurement result For =1 to n do For K = 1 to n do Boundary condition generation for humeral motion based on screw axis Boundary condition generation for humeral motion based on screw axis Loading condition generation for initial pretension of supraspinatus tendon Loading condition generation for initial pretension of supraspinatus tendon if not at excessive distortion of finite element then if not at excessive distortion of finite element then Displacement boundary condition relaxation by penalty function occurrence Displacement boundary condition relaxation by penalty function occurrence Contact stress measurement between supraspinatus tendon and labrum Contact stress measurement between supraspinatus tendon and labrum else else close; close; end end end end Appl. Sci. 2020, 10, 4165 8 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 12 3. Results 3. Results We constr We co ucted nstructhe ted pr the oposed propose method d method and and successfully successfully s simulated imulated it, it, asas shshown own in F in igFigur ure 6. e If6 th . e If the displacement boundary condition is relaxed by a truss element, the excessive element destruction at displacement boundary condition is relaxed by a truss element, the excessive element destruction at the soft tissue can be prevented at the point where the binding force of truss and the reaction from the soft tissue can be prevented at the point where the binding force of truss and the reaction from the the supraspinatus tendon and scapula reach a balance between one another. supraspinatus tendon and scapula reach a balance between one another. (a) (c) (b) Figure 6. The finite element simulation result by the proposed method: (a) Screenshot of the finite Figure 6. The finite element simulation result by the proposed method: (a) Screenshot of the finite element simulation result; (b) The point for peak contact stress measurement on the labrum; (c) Stress element simulation result; (b) The point for peak contact stress measurement on the labrum; (c) Stress change curve between supraspinatus and labrum according to humeral angle. change curve between supraspinatus and labrum according to humeral angle. Figure 6a shows the result of simulation, where the relaxation control of the displacement Figure 6a shows the result of simulation, where the relaxation control of the displacement boundary condition is applied to the glenohumeral joint. The peak contact stresses were measured at boundary condition is applied to the glenohumeral joint. The peak contact stresses were measured at the final position and at a peak point where the contact stress on the labrum was highest, as shown the final position and at a peak point where the contact stress on the labrum was highest, as shown in in Figure 6b. Figure 6c presents a peak stress change curve between the supraspinatus tendon and Figure 6b. Figure 6c presents a peak stress change curve between the supraspinatus tendon and the the labrum according to humeral motion. The peak contact stresses measured at final motion, with labrum according to humeral motion. The peak contact stresses measured at final motion, with spring spring constants of 100, 200, and 300 N/mm, were 9.49, 13.47, and 23.13 MPa, respectively. As a result, constants of 100, 200, and 300 N/mm, were 9.49, 13.47, and 23.13 MPa, respectively. As a result, the stress distribution is concentrated at the point where the posterosuperior labrum impinges on the supraspinatus tendon, and the measurements of peak stress showed that contact stress increases with the stress distribution is concentrated at the point where the posterosuperior labrum impinges on the the increase in the spring constant. supraspinatus tendon, and the measurements of peak stress showed that contact stress increases with Figure 7 shows the comparison of the boundary condition (the guidance) and the humeral the increase in the spring constant. motion (the follower) by the proposed method: The boundary condition is the humeral motion of the Figure 7 shows the comparison of the boundary condition (the guidance) and the humeral motion 6-DOF (degree of freedom), including the translation (posterior, superior, lateral one) and rotation (the follower) by the proposed method: The boundary condition is the humeral motion of the 6-DOF (elevation, horizontal extension, external rotation). The humeral motion of the 6-DOF was (degree of freedom), including the translation (posterior, superior, lateral one) and rotation (elevation, represented with reference to the joint coordinate system of ISB recommendation [32]. horizontal extension, external rotation). The humeral motion of the 6-DOF was represented with reference to the joint coordinate system of ISB recommendation [32]. Appl. Sci. 2020, 10, 4165 9 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 12 (a) (b) (c) (d) (e) (f) Figure 7. The motion comparison of guidance and follower by the proposed method: (a) Posterior Figure 7. The motion comparison of guidance and follower by the proposed method: (a) Posterior translation; (b) Superior translation; (c) Lateral translation; (d) Elevation; (e) Horizontal extension; (f) translation; (b) Superior translation; (c) Lateral translation; (d) Elevation; (e) Horizontal extension; External rotation. (f) External rotation. The performance of the proposed method was examined from the differential displacement. The The performance of the proposed method was examined from the dierential displacement. differential displacement means that distance between the displacement of humeral head centers (the The dierential displacement means that distance between the displacement of humeral head centers guidance and follower). We defined the humeral head center as the center of a sphere that fits the (the guidance and follower). We defined the humeral head center as the center of a sphere that fits the humeral head, as shown in Figure 8a. Figure 8b shows the change in the distance between the humeral humeral head, as shown in Figure 8a. Figure 8b shows the change in the distance between the humeral head centers of the guidance and follower according to humeral angles. When the humeral angle is small, head centers of the guidance and follower according to humeral angles. When the humeral angle is the distance between the humeral head centers is close to zero. However, after a certain degree of rotation small, the distance between the humeral head centers is close to zero. However, after a certain degree is generated, the distance between the guidance and follower becomes clear because of the surrounding of rotation reaction is . T generated, he distances the betw distance een the cebetween nters measthe ured guidance at final mo and tion,follower with sprinbecomes g constants clear of 10because 0, 200, of and 300 N/mm, were 4.68, 3.67, and 3.28 mm, respectively. This means that the proposed method the surrounding reaction. The distances between the centers measured at final motion, with spring allows for FE simulations of shoulder motion with a differential displacement of 3.28 mm. constants of 100, 200, and 300 N/mm, were 4.68, 3.67, and 3.28 mm, respectively. This means that the proposed method allows for FE simulations of shoulder motion with a dierential displacement of 3.28 mm. Appl. Sci. 2020, 10, 4165 10 of 13 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 12 (b) (a) Figure 8. The analysis of dierential displacement among humeral head center of guidance and Figure 8. The analysis of differential displacement among humeral head center of guidance and follower: (a) Definition of humeral head center; (b) Change of the dierential displacement among follower: (a) Definition of humeral head center; (b) Change of the differential displacement among humeral head center of guidance and follower according to humeral angles. humeral head center of guidance and follower according to humeral angles. 4. Discussion 4. Discussion 4.1. Principal Results 4.1. Principal Results In this study, we proposed a new method of contact stress measurement for the analysis of In this study, we proposed a new method of contact stress measurement for the analysis of shoulder shoulder internal impingement syndrome. The traditional FE simulations for shoulder motion consist of internal impingement syndrome. The traditional FE simulations for shoulder motion consist of geometric geometric data acquisition, material property representation, boundary and loading condition definition, data acquisition, material property representation, boundary and loading condition definition, and and experimental validation [19]. The FE simulations (three steps), except for the experimental experimental validation [19]. The FE simulations (three steps), except for the experimental validation validation step, were problematic in that they could not simulate excessive distortion of the models step, were problematic in that they could not simulate excessive distortion of the models such as that such as that due to shoulder motion. Therefore, the proposed method focused on the control of due to shoulder motion. Therefore, the proposed method focused on the control of shoulder motion shoulder motion to enable simulations with excessive distortion of the model. to enable simulations with excessive distortion of the model. The proposed method solved the critical process zone error of supraspinatus tendon insertion due The proposed method solved the critical process zone error of supraspinatus tendon insertion due to excessive distortion of the 3D biomechanical model by relaxing the boundary condition for shoulder to excessive distortion of the 3D biomechanical model by relaxing the boundary condition for motion representation. Boundary condition relaxation is useful for calculations when representing shoulder motion representation. Boundary condition relaxation is useful for calculations when complex musculoskeletal structures, such as the human shoulder complex. Hereby, this allowed for representing complex musculoskeletal structures, such as the human shoulder complex. Hereby, this contact stress measurements in vivo, which was impossible to do in conventional studies based on allowed for contact stress measurements in vivo, which was impossible to do in conventional studies motion analysis and cadaveric experiments. The peak contact stress measured from the simulation based on motion analysis and cadaveric experiments. The peak contact stress measured from the results was 23.13 MPa, with spring constants of 300 N/mm. The measurement result was similar simulation results was 23.13 MPa, with spring constants of 300 N/mm. The measurement result was to ultimate stress (26.60 Mpa) of the supraspinatus tendon, which was measured in the cadaveric similar to ultimate stress (26.60 Mpa) of the supraspinatus tendon, which was measured in the cadaveric environment of Itoi et al. [33]. The performance of the proposed method was examined through the environment of Itoi et al. [33]. The performance of the proposed method was examined through the dierential displacement (maximum 3.28 mm) in shoulder motion by boundary condition relaxation. differential displacement (maximum 3.28 mm) in shoulder motion by boundary condition relaxation. The dierential displacement was similar to the translation (3.73 mm) of the humeral head center, The differential displacement was similar to the translation (3.73 mm) of the humeral head center, which which Massimini et al. [33] measured using biaxial fluoroscopy. This means that it is possible to Massimini et al. [33] measured using biaxial fluoroscopy. This means that it is possible to analyze analyze internal impingement syndrome in the shoulder motion process. From the analysis results internal impingement syndrome in the shoulder motion process. From the analysis results of internal of internal impingement syndrome, strong contact was observed between posterosuperior labrum impingement syndrome, strong contact was observed between posterosuperior labrum and undersurface and undersurface of the posterior supraspinatus tendon. The analysis results are consistent with of the posterior supraspinatus tendon. The analysis results are consistent with the findings of Jobe [6], the findings of Jobe [6], who described the junction of the posterior supraspinatus and anterior who described the junction of the posterior supraspinatus and anterior infraspinatus tendons as a infraspinatus tendons as a highly vulnerable area [22]. highly vulnerable area [22]. 4.2. Limitations 4.2. Limitations The limitation of this study is that the proposed method has not been experimentally validated. The limitation of this study is that the proposed method has not been experimentally validated. Experimental verification for typical FE simulations would require the use a cadaver rather than a Experimental verification for typical FE simulations would require the use a cadaver rather than a living living body. However, cadaveric experiments have low reliability because a living body and cadavers body. However, cadaveric experiments have low reliability because a living body and cadavers have have dierent material properties. Therefore, this study is more meaningful than the conventional different material properties. Therefore, this study is more meaningful than the conventional method in that it simulates based on the motion of a living body from a new perspective. Moreover, the material properties are not accurate because a nonlinear hyperelastic model is used, which does not Appl. Sci. 2020, 10, 4165 11 of 13 method in that it simulates based on the motion of a living body from a new perspective. Moreover, the material properties are not accurate because a nonlinear hyperelastic model is used, which does not consider viscosity and shear force, and the precision of the FE simulation result is low because a shoulder model (case) of only one subject was used. Although the proposed method has a large error, it can be expected to provide basic data with high precision and accuracy if the number of cases is increased and the material model is improved. 5. Conclusions In this study, we proposed a new contact stress measurement method for analyzing internal impingement syndrome of the shoulder. The proposed method simulates impingement syndrome of the supraspinatus tendon between the humeral head and labrum based on the finite element method. Inaccurate trajectory of shoulder motion causes impingement of the humerus and scapula, and this can influence the structure of soft tissues within the shoulder. To solve this problem, in this study, the humeral motion is given a degree of freedom through the connection of truss elements between the guidance and follower, which are based on user-defined elements. This allows for the analysis of internal impingement syndrome by measuring contact stress during shoulder motion. To date, there is no such study to our knowledge that utilizes FE simulations to analyze internal impingement syndrome. The proposed method is significant in that it opens the door for future researchers to explore the phenomenon of posterior shoulder pain more completely. Author Contributions: Conceptualization, Y.-S.Y.; Formal analysis, Y.-S.Y.; Methodology, S.-w.J.; Supervision, Y.S.K.; Visualization, S.-w.J.; Writing—original draft, S.-w.J.; Writing—review and editing, Y.S.K. All authors have read and agree to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. 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