The Effect of Size and Location of Tears in the Supraspinatus Tendon on Potential Tear Propagation.

James Thunes Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260

R. Matthew Miller Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260; Orthopaedic Robotics Laboratory, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260

Siladitya Pal Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247667, India

Sameer Damle Department of Chemical Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260

Richard E. Debski Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260; Orthopaedic Robotics Laboratory, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260; Department of Orthopedic Surgery, University of Pittsburgh, Pittsburgh, PA 15260

Spandan Maiti1 Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260; Department of Chemical Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15260 e-mail: [email protected]

1

The Effect of Size and Location of Tears in the Supraspinatus Tendon on Potential Tear Propagation Rotator cuff tears are a common problem in patients over the age of 50 yr. Tear propagation is a potential contributing factor to the failure of physical therapy for treating rotator cuff tears, thus requiring surgical intervention. However, the evolution of tears within the rotator cuff is not well understood yet. The objective of this study is to establish a computational model to quantify initiation of tear propagation in the supraspinatus tendon and examine the effect of tear size and location. A 3D finite element (FE) model of the supraspinatus tendon was constructed from images of a healthy cadaveric tendon. A tear of varying length was placed at six different locations within the tendon. A fiberreinforced Mooney–Rivlin material model with spatial variation in material properties along the anterior–posterior (AP) axis was utilized to obtain the stress state of the computational model under uniaxial stretch. Material parameters were calibrated by comparing computational and experimental stress–strain response and used to validate the computational model. The stress state of the computational model was contrasted against the spatially varying material strength to predict the critical applied stretch at which a tear starts propagating further. It was found that maximum principal stress (as well as the strain) was localized at the tips of the tear. The computed critical stretch was significantly lower for the posterior tip of the tear than for the anterior tip suggesting a propensity to propagate posteriorly. Onset of tear propagation was strongly correlated with local material strength and stiffness in the vicinity of the tear tip. Further, presence of a stress-shielded zone along the edges of the tear was observed. This study illustrates the complex interplay between geometry and material properties of tendon up to the initiation of tear propagation. Future work will examine the evolution of tears during the propagation process as well as under more complex loading scenarios. [DOI: 10.1115/1.4030745]

Introduction

Rotator cuff tears are a significant clinical problem and are commonly found in the population over 55 yr of age [1,2]. While physical therapy is a common initial treatment option [3], it fails in up to 50% of patients [4]. Sonography and magnetic resonance imaging (MRI) studies following treatment with nonoperative management in rotator cuff patients show that tears in a significant percentage of patients will increase in size over time [5,6], potentially requiring surgical repair. Earlier surgical intervention 1 Corresponding author. Manuscript received December 24, 2014; final manuscript received May 26, 2015; published online June 23, 2015. Assoc. Editor: Kristen Billiar.

Journal of Biomechanical Engineering

usually results in better clinical outcomes [7–9]. Thus, there is a need for early identification of these patients for whom physical therapy alone is insufficient. Early identification of these cases will improve treatment decisions leading to decreased recovery time and increased mobility. Unfortunately, there are currently no clear guidelines for the treatment of rotator cuff tears based on its initial characteristics. This fact is evidenced by the American Academy of Orthopaedic Surgeons guidelines on optimizing the management of rotator cuff problems, with many recommendations being “weak” or “inconclusive” [10]. Tear size and location have been indicated as potentially important factors related to the clinical outcomes [11]. Therefore, an improved understanding of how initial characteristics of rotator cuff tears influence its eventual propagation is necessary to improve clinical outcomes.

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The rotator cuff is a complex assembly of tendons and muscles providing stability to the glenohumeral joint. However, it has been observed clinically and shown in cadavers that the majority of tears in the rotator cuff are located in the supraspinatus (SSP) tendon [12]. In vitro testing has revealed that tears commonly occur in the mechanically stiffer anterior or middle thirds of the tendon [13]. Additionally, full-thickness rotator cuff tears propagate toward the region of highest strain [14,15]. Taken together, these facts signify that the biomechanical behavior of the rotator cuff is important for tear initiation and propagation. While in vitro biomechanical experimentation yields high fidelity results, the limited availability of human specimens, cost of testing, and pathologies associated with cadavers constrain the number and complexity of experiments that can be done. Using FE-based biomechanical analyses, a large number of simulations may be conducted, allowing for a systematic examination of the effects of various biophysical parameters on tear evolution in the tendon. These computational models, however, should include accurate geometric and structural representation of the tendon for better simulation outcomes. Moreover, these models should be experimentally validated to yield high fidelity results. Recent computational modeling work using FE analysis has investigated stress distributions in the supraspinatus and other rotator cuff tendons [16–18]. Analyses have shown that the stress state in the intact tendon is highest in the anterior region of the articular side; corresponding to clinically observed regions of tear initiation [19,20]. A recent study of tear size in the rotator cuff showed that increasing tear size resulted in higher stresses around the tear tips [21]. These studies have assumed the tendon material properties to be isotropic and homogeneous. However, the presence of load-bearing collagen fibers directed primarily in the mediolateral direction renders the tendon material transversely isotropic. Moreover, experiments have demonstrated a variation of mechanical stiffness and strength across the tendon in the AP direction [22]. These structural features of the tendon material are expected to significantly influence ensuing stress distribution and thus should be incorporated in the computational model. Accordingly, the objective of the study is: (1) to develop a FE model for the supraspinatus tendon considering these biomechanical features; and (2) to quantify the effect of a tear size and location on the mechanical response of the tissue.

2

Methods

2.1 Solid Model of the Supraspinatus Tendon. A solid model of the supraspinatus tendon was constructed from 2D images of a representative cadaveric tendon. Dimensions of the cadaveric tendon were extracted from the images using ImageJ (NIH, Bethesda, MD). To create the 3D model from these data, the thickness was approximated from reported values in the literature [23]. Thickness ranged from 5 mm at the anterior edge to 2.5 mm at the posterior edge (see Fig. 1(a)). Maximum dimensions of the tendon were 31.8 mm along the medial–lateral (ML) axis and 35.1 mm along the AP axis. The solid model of the tendon (Fig. 1(a)) was created using Autodesk Inventor 2013 (Autodesk, Mill Valley, CA). A sharp full-thickness tear oriented in the AP direction was placed at six different locations on the model tendon. The tear was modeled as a plane orthogonal to the plane of symmetry of the tendon and passing through the entire thickness of the tendon (Fig. 1(a)). Three tear locations were chosen 5 mm from the representative “tendon insertion” at the lateral edge and the other three were located 10 mm from the lateral edge. At each level, tears were placed in the posterior, middle, or anterior region of the tendon. Finally, at each location, tears of three different sizes, namely, 4, 8, or 16 mm, respectively, were placed. An additional set of 20 mm tears was placed at the posterior, middle, and anterior locations 5 mm from the lateral edge. For anterior tears, the points marked with filled circles in Fig. 1(a) correspond to the anterior tear tip while for the posterior tears, these points correspond to the posterior tip. For the middle tears, the points shown in the figure indicate the midpoint of each tear. FE meshes were constructed from the solid models using Trelis Pro 15 (csimsoft, American Fork, UT). A representative mesh composed of four-noded tetrahedral elements (8062 nodes and 36,670 elements) with an 8 mm tear in the anterior location 5 mm from the lateral edge is shown in Fig. 1(b). The vicinity of the tear was meshed with small elements (with respect to the rest of the mesh) to better capture the anticipated sharp gradients of the stress field in that region. To ensure mesh convergence, the element size in the vicinity of the stress concentrations was varied from 0.5 to 0.125 mm. Maximum stress was recorded using a nonlocal stress averaging method based on Mergheim et al. [24] and Maiti et al. [25].

Fig. 1 Geometry and boundary conditions. (a) Two lines of tears at 5 and 10 mm from the lateral surface (representing the tendon insertion) are defined. A tear will be placed at either the posterior (P), middle (M), or anterior (A) location. For the different sizes, the out tip of the tear will be constant for the posterior and anterior tears. For the middle tears, the midpoint will be constant across sizes. (b) The boundary conditions and representative mesh (8062 nodes and 36,670 four-noded tetrahedral elements). The lateral surface is fixed. A displacement is applied to the medial surface. Movement in the AP and bursal directions is also fixed at the medial surface. The mesh shows an initially zero thickness tear (8 mm long) in the middle location 5 mm from the lateral surface.

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Transactions of the ASME


The method averages the stress at the tear tip by applying a constant weight to stresses enumerated at all mesh nodes within a 1-mm diameter sphere centered on the tear tip. The refinement at the tips of the tear was increased until the change in stress was less than 1%. This change was met with an element size of 0.375 mm, which was subsequently used for all the simulations reported in this article. 2.2 Constitutive Law for Tendon Material. The supraspinatus tendon is a highly aligned tissue with the primary fiber direction along the ML axis [26,27]. The degree of organization varies with position in the tendon, with highest alignment in the medial portion of the tendon. Within the lateral region, alignment was higher in the anterior portion. Thus, a transversely isotropic material model based on Weiss et al. [28] and Gasser et al. [29] was adopted to simulate the supraspinatus tendon subjected to finite strain. It was assumed that the strain energy function, W, can be decomposed into two parts as, W ¼ WM þ Wf , where WM denotes the contribution of the nonfibrous matrix while Wf is the contribution of collagen fibers. The matrix was modeled as a nearly incompressible Mooney–Rivlin material described by 1 WM ðI1 ; I2 ; JÞ ¼ jðJ 1Þ2 þ c1 ðI1 3Þ þ c2 ðI2 3Þ 2

(1)

where c1 and c2 are the Mooney–Rivlin material parameters, and j is a large penalty parameter enforcing the constraint of incompressibility. Further, the Jacobian J is defined as J ¼ detðFÞ > 0 with F as the deformation gradient. Denoting C ¼ FT F as the right Cauchy–Green tensor, itsh first and second invariants are i defined as I1 ¼ trC and I2 ¼ ðtrCÞ2 tr C2 =2, respectively, while their deviatoric counterparts are I1 ¼ J 2=3 I1 , and I2 ¼ J 4=3 I2 . A single family of collagen fibers, oriented along a ML direction, was assumed to represent the collagenous part of the material. Accordingly, the following form for Wf was chosen: 8 h i < k1 2 exp k2 ðI4 1Þ 1 I4 > 1 Wf ¼ 2k2 (2) : 0 I4 1 with k1 and k2 as two material parameters. I4 is the fourth pseudoinvariant of the right Cauchy–Green tensor and is defined as I4 ¼ a0 CaT0 with C ¼ J 2=3 C and a0 as the direction of the collagen fibers in the reference configuration. Collagen fibers are unable to support any compressive load, and accordingly the strain energy is zero whenever the fibers are in compression (I4 1). Cauchy stress tensor can be obtained from the strain energy function as follows: r ¼ 2J 1 F

@W T F @C

(3)

The constitutive model requires five material parameters: c1 and c2 for the noncollagenous matrix, and k1 , k2 , and a0 for the collagen fibers. Among these, a0 was chosen to be oriented along the ML direction, and thus did not need any calibration as the SSP tendon, as with many other tendons, has highly aligned fibers [30]. Similar arguments have been made in the literature to model this tendon [31]. 2.3 Calibration of Material Parameters. Itoi et al. [22] and Matsuhashi et al. [23] reported a variation in the supraspinatus tendon material properties along the AP axis of the supraspinatus tendon. Their experiments demonstrated that the elastic modulus of the anterior region of the tendon is approximately twice that of the posterior region of the tendon. To reflect this fact in our computational model for the tendon, the domain was split into three Journal of Biomechanical Engineering

regions, each spanning 1/3rd of the width of the tendon in the AP direction measured along the top edge. The posterior region was denoted as zone 1, the anterior region as zone 3 while the middle region was designated as zone 2 (see Fig. 1(a)). Zone 2 was defined as a transition region, where the stiffness varied linearly between the stiffness for zones 1 and 3. To follow the experimental data [22,23], the stiffness of the tendon in zone 3 was taken as twice that of zone 1. For the material model chosen, zones 1 and 3 each require the calibration of four independent parameters (c1 , c2 , k1 , and k2 ). To simplify this task, it was assumed that the change in material stiffness in the AP direction is solely due to the change in properties of collagen fibers while matrix properties remain constant. This assumption is justified as fibers are the primary load-bearing component of the tendon and thus matrix material stiffness should not have any significant effect on overall mechanical behavior. Moreover, an examination of Eq. (2) revealed a greater sensitivity of the parameter k2 on the stress–strain curve for the fibers. Accordingly, only this parameter was varied between zones 1 and 3, and calibration of a total of four parameters (c1 , c2 , and k1 for the entire domain, and k2 for zones 1 and 3) for the model was required. Simulated constitutive response for the FE model was fit with the experimental data [15] using the lsqcurvefit least square fitting procedure available in MATLAB 2010b (Mathworks, Natick, MA). This particular MATLAB function may provide only a local minimum; accordingly the curve fitting procedure was performed 50 times using randomly generated initial guesses for the parameters for each simulation run. It was found that the solutions from all these runs coincided with each other ensuring the attainment of the global minimum. Reported values in the literature suggest that the strength is approximately 20 MPa in the anterior region and 10 MPa in the posterior region [22,23]. Thus, the strength of tendon material was given a variation similar to that of stiffness along the AP direction. To wit, zone 1 was given a strength value of 10 MPa, the strength in zone 3 was 20 MPa, while zone 2 was a linear transition between those two values. Simulations on the model supraspinatus tendon without any tear yielded a maximum stress of 20 MPa in the vicinity of the lateral edge at the junction of zones 1 and 2, a typical location for experimentally observed tear initiation. In addition, applied stretch corresponding to this magnitude of stress was found to be 1.12, in the physiological range for tear initiation in the supraspinatus tendon. 2.4 Simulation Methodology. A custom, nonlinear quasistatic FE analysis program, developed in our lab, was used to conduct the FE analyses. This code has successfully been used to simulate biomechanical behavior of various tissues and biomaterials [32,33]. Due to symmetry in the thickness direction, only half of the tendon was analyzed with a symmetry plane orthogonal to the thickness direction of the tendon. To computationally represent the experimental setup for tensile testing of the supraspinatus tendon, the lateral edge of the FE model was fixed in all directions. The medial edge was subjected to an applied stretch in the ML direction while all other surfaces were treated as stress-free surfaces. A maximum stretch of 1.2 (sufficient to reach a stress greater than the material strength in all cases) increasing linearly over 1000 increments was applied on the medial edge to capture nonlinear constitutive response accurately. A total of 21 simulations were performed: three tear locations along the AP direction, four tear sizes for each location along the bottom row, and three tear sizes for each location along the top row. Selected tear cases (three tear sizes in the anterior location 5 mm from the lateral edge) were also simulated with a homogeneous material (i.e., no variation of the material parameters across the width of the tendon) to contrast with the material described in Sec. 3.3. The material used for these cases was the same, but without any variation in strength along the AP direction. Material parameters were found in the same manner as the other AUGUST 2015, Vol. 137 / 081012-3


cases; the simulated stress–strain response was fit to the experimental data. 2.5 Simulation Data Analysis. Resultant force at each FE node at the lateral surface was recorded for each increment of the applied stretch. These forces were summed over all nodes on that surface and divided by the current surface area to obtain the resultant Cauchy stress. Together with the applied stretch at each increment, and tracked over the course of the analysis, the stress–stretch response was obtained. Physical experiments in the literature report strain contours on the tendon [15]. For this reason, Green–Lagrange strain contours, in addition to Cauchy stress contours were exported for all load steps. Maximum principal stress (rmax ) distributions for the entire computational domain were enumerated for each increment of the applied stretch. The magnitude of principal stress at a given point was computed by the nonlocal stress averaging scheme mentioned in Sec. 3.1. This nonlocal stress averaging was performed to minimize the effect of noise in the simulated stress field on its pointwise evaluation. Critical stretch, kc , is defined as the applied stretch at which rmax at any location in the domain attained the local material strength. According to maximum principal stress failure criterion, the material will fail whenever rmax at any point exceeds material strength at that point [34]. Consequently, critical stretch denotes incipient failure at a given point in the domain, and thus can be used as a biomechanical indicator for further propagation of a pre-existing tear. To quantify the effect of tear size on the size of the stressshielded region, a linear regression was performed at each location with the independent and dependent variables the tear size and the volume of the region, respectively. The regression was performed using the MATLAB fitlm function.

3

Results

3.1 Material Parameters. The computational model was validated against experimental uniaxial stress–stretch response of the supraspinatus tendon. The computational data were fit against the case that most closely represented the experimental geometry (an 8 mm tear placed 5 mm from the lateral edge at the anterior location). Two separate cases were considered: one with varying material parameters, and another with constant material parameters for the entire domain (Table 1). The fit between the experimental and simulated stress–stretch response over the range in Fig. 2 was R2 ¼ 0:997 for varying material parameters as well as for the constant material parameter case. To ensure that calibrated material parameters were a good approximation of the physical system, stress–strain response for all the computational cases was also plotted (Fig. 2). Observe that due to the variation in tear location and size, the stress–stretch response varies by case. It was shown above that the stress–strain responses for the tear case approximating the physical experiment

Fig. 2 Experimental versus simulated stress–strain curves. The dashed line shows the experimental response of a representative tendon in uniaxial tension. An 8 mm tear located in the anterior region 5 mm from the lateral edge was used to determine the material parameters (solid line). The extents of the shaded region show the range of the stress–strain response for all cases tested. The response for the one material case is shown with open triangles.

are good fits to the experimental data. However, there is a large variation in both size and location for the other cases. From the figure, the experimental response is bounded by the simulated response; in general, the smaller tears are stiffer while the stiffness is reduced for larger tears.

3.2 Effect of the Tear on the Stress and Strain Distribution in the Tendon. The introduction of a tear into the tendon causes stress (and strain) concentrations at the tips of the tear (Fig. 3). A tendon with an 8 mm long tear located in the anterior region of the tendon 5 mm from the lateral edge and subjected to a maximum applied stretch of 1.15 was chosen for demonstration purposes. The maximum principal stresses and strains are found at the posterior and anterior tips of the tear. However, the magnitudes of the maximum principal stress and strain are different for these tips; a greater magnitude for both quantities can be seen at the posterior tip for this particular case. The stresses at the posterior tip were 210% higher (37.5 MPa versus 12 MPa) while the strains were 180% higher (0.28 versus 0.10). A variation in maximum principal stress and strain occurs in the AP direction away from the tear resulting from the variation in geometry as well as material properties in this direction. However, away from the tear, there is little change in the ML stress

Table 1 Material properties for the material models. The varying material model has three regions, the posterior and anterior regions are specified below (zones 1 and 3 in Fig. 1(a)), the material properties in the middle region vary between the posterior and anterior properties. There is only one set of material parameters for the constant material case. Matrix

Material model Varying Constant

Posterior region Anterior region

Fiber

c1 (MPa)

c2 (MPa)

k1 (MPa)

k2

rc (MPa)

1.0 1.0 1.0

1.0 1.0 1.0

5.23 5.23 5.23

20 30 25

10 20 15

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Fig. 3 Tendon with an 8 mm anterior tear 5 mm from the lateral edge. A stretch of 1.15 is applied to the medial edge. The contours show the ML strain component (a) and the ML stress component (b).



component along the ML axis. Simulations with the other tear cases reveal qualitatively similar trends, although the magnitude of the stresses and strains varied with tear size and location. 3.3 Effect of Size and Location of the Tears on the Maximum Principal Stress State in the Tendon. The stress state in the vicinity of the tear was significantly impacted by size and location of the tear (Fig. 4). All tears shown in this figure were located 5 mm from the lateral edge of the tendon in the anterior, middle, and posterior regions, respectively (see Fig. 1(a) for location markers). Three tear sizes, 4 mm, 8 mm, and 16 mm, were considered at each location. The maximum principal stress contours depicted in Fig. 4 were extracted for an applied stretch of 1.12— approximately the maximum critical stretch. For all tear size and locations, stress concentrations can be observed at both tear tips. However, the magnitudes of the maximum principal stresses are different for the posterior and anterior tips of the same tear. For all tears located in the anterior region, maximum principal stress was highest in the vicinity of the posterior (left) tip. For example, the maximum principal stresses were 30.1 MPa and 9.4 MPa for the posterior and anterior tips, respectively, for the 4 mm tear case. As the size of the initial tear increased, the extent and magnitude of the maximum principal stress at posterior tip were reduced (as shown by reducing area and intensity of the red contour). The maximum principal stress at the posterior tip was 30.1 MPa for the 4 mm tear, reducing to 22 MPa for the 16 mm tear. However, stress magnitude at the posterior tip was still higher than for the corresponding anterior tip. For instance, maximum principal stress at the anterior tip for 16 mm tear case was 15.1 MPa, considerably

less than that for the posterior tip. For the tears at the middle region, the magnitude of maximum principal stress was comparable at both the tips (the difference in the stresses at the tear tips was 4, 0.1, and 3.5 MPa for the 4, 8, and 16 mm tear cases, respectively). Finally for tears at the posterior location, an elevated maximum principal stress can be clearly seen at the anterior (right) tip. As an example, the stress magnitude was 15.1 MPa for the posterior tip versus 24.1 MPa for the anterior tip with the 16 mm tear case. The magnitude and extent of the maximum principal stress at anterior tip increased with the increasing initial tear size; for instance increasing from 18.1 MPa to 24.1 MPa for the 4 mm and 16 mm tear cases, respectively. The results for the tears 10 mm away from the lateral edge are qualitatively similar to the tears 5 mm away from the lateral edge and are not shown in this article. There is a large variation in the critical stretch for the different tear cases (Tables 2 and 3). The critical stretch for the posterior tip was lower for the majority of the cases studied (17 out of 21 simulations), signifying a propensity of the tears to propagate in the posterior direction. Also note that the critical stretch for the posterior tip decreased as the initial tear size was increased. Between the shortest and longest tears at the same location, there is a decrease in the critical stretch for the posterior tip between 9% and 30% depending on tear location. However, critical stretch corresponding to the anterior tip for the tears studied did not show such correlation. To contrast the aforementioned simulations with a heterogeneous tendon material with constant mechanical stiffness cases, further analyses were performed (see Table 1 for corresponding material parameters). Three tears of size 4, 8, and 20 mm, respectively, were located in the anterior region 5 mm away from the

Fig. 4 Stress in the ML direction for tears 5 mm from the lateral edge with an applied stretch of 1.12. The areas directly around the tear are shown. Significant stress concentrations are seen at the tips of the tear. The magnitude of the stress concentrations is not the same between anterior and posterior tips or between different tears. Table 2

Critical stretch for the tears 5 mm from the lateral edge when posterior and anterior tips reach their respective strength

Location

5 mm from insertion

Size

Posterior

Middle

Anterior

Journal of Biomechanical Engineering

Strength (MPa)

Critical stretch

(mm)

Posterior tip

Anterior tip

Posterior tip

Anterior tip

4 8 16 20 4 8 16 20 4 8 16 20

10 10 10 10 18.2 16.4 12.7 10.9 20 20 13.6 10

13.6 17.3 20 20 20 20 20 20 20 20 20 20

1.101 1.088 1.094 1.079 1.113 1.098 1.085 1.076 1.098 1.104 1.088 1.076

1.101 1.107 1.107 1.157 1.107 1.107 1.129 1.154 1.179 1.151 1.142 1.132

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Table 3 Critical stretch for the tears 10 mm from the lateral edge when posterior and anterior tips reach their respective strength Location

10 mm from insertion

Size

Posterior Middle Anterior

Strength (MPa)

(mm)

Posterior tip

Anterior tip

Posterior tip

Anterior tip

4 8 16 4 8 16 4 8 16

10 10 10 18.2 16.4 12.7 20 18.6 11.4

13.6 17.3 20 20 20 20 20 20 20

1.082 1.069 1.076 1.116 1.101 1.088 1.113 1.107 1.082

1.101 1.098 1.116 1.113 1.101 1.116 1.126 1.116 1.113

Table 4 Comparison of critical stretch for constant or varying material properties Critical stretch Tear size (mm) 4 8 20

Critical stretch

Constant material case

Varying material case

1.085 1.094 1.094

1.098 1.104 1.076

lateral edge. Assuming that the strength of the constant material case is proportional to the strength in the varying material parameter cases, there is a difference in the critical stretches between the two sets of material models (Table 4). For the 4 and 8 mm tears, the critical stretches are 13% and 9% lower for the constant material cases, respectively. With a 20 mm tear, the critical stretch for the constant material case is 23% higher than for the varying material case. 3.4 Stress-Shielded Region in the Vicinity of the Tear. Besides a region of elevated stress in the vicinity of the tear tip, another interesting observation was the presence of a low stress region between the tear tips (Fig. 5). To further examine this phenomenon, the contours shown in Fig. 4 were replotted in Fig. 5. The contours for maximum principal stresses were scaled in this figure such that magnitudes under 1 kPa are black while those above 1 kPa are white. Black regions in this figure thus show regions of very low stress that can be considered as stressshielded regions. The extent of these regions did not vary significantly with the location of the tear. However, a positive correlation between the size of the initial tear and the extent of the stress-

shielded region was found. R2 was 0.95, 0.96, and 0.99 for the posterior, middle, and anterior locations, respectively. Similar results were observed for the tears 10 mm away from the lateral edge.

4

Discussion

4.1 Computational Model. One major improvement for the current computational model over existing models is the inclusion of varying stiffness of the tendon along the AP axis. However, addition of this variation significantly complicates fitting of the material model to the experimental data. Interestingly, the experimental data could be fitted well even with constant material properties. However, the ensuing stress state in the tendon for these two material cases is different. Thus, fitting of the experimental stress–strain data alone does not govern the stress field in the tendon; structural features of the tendon material also play a significant role in the stress distribution. Additionally, the material properties alone do not control overall stress–strain response of the material. Tear size and location also produce a marked variation in the resultant stress (as shown by the shaded region in Fig. 2). 4.2 Effect of the Tear on the Stress and Strain Distribution in the Tendon. The presence of a tear had a strong effect on the stress and strain distributions in the tendon. However, this effect was local; modification of the biomechanical state was always observed in the vicinity of the tear. Maximum principal stress and strain at both the tear tips were sharply elevated over a very small volume of material in the immediate vicinity of the tear tip. The magnitude of strains found by simulations is comparable to those reported in Miller et al. [15] in the vicinity of the tear tip. Reported experimental data in the literature typically focus on the

Fig. 5 Stress in the ML direction for tears 5 mm from the lateral edge. The stress contours have been scaled such that low stress regions are shown in black. There are large regions of low stress at the flanks of the tears. This region grows as the tear size increases. Further, the region lateral to the tear has significantly higher area than the region medial to the tear.

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strain fields in the tendon as opposed to stresses as the surface strain distribution is an experimentally measurable quantity (see, e.g., Refs. [14,15,35]). Our simulation results demonstrate that maximum principal surface strain and principal volumetric stress are always colocalized at the tear tips and thus either can be used to study the biomechanical response of the tendon. Consequently, stress was chosen as the parameter of interest for subsequent simulations. 4.3 Effect of Size and Location of the Tears on the Maximum Principal Stress State in the Tendon. Differences in the magnitude of concentrated stress were observed by comparing the stress contours surrounding the different tears. For all the tears studied, the magnitude of elevated stresses at the two tips of the tear was different. It was found that the majority of the simulated tears have a propensity to propagate in the posterior direction, the region of high strain. This is in accordance with our experimental observations [15] and can be explained, in part, by the variation of biomechanical properties and thickness along the AP direction of the tendon. As the tip is located more posteriorly, the strength of the tissue also reduces at the tip location. Thus, although there is a stress concentration (of different magnitudes) at both the tips, the posterior tip may reach the local strength value before the anterior tip by virtue of being located at a low strength region of the tendon. Therefore, the stress alone is a poor indicator of tear propagation; one must look at the stress in relation to the local strength. The simulations using constant mechanical stiffness throughout the domain further accentuated role of local material properties. Tears for this case also had a tendency to propagate posteriorly, possibly due to geometric features accounted for by the tendon model. However, the magnitude for critical stretch for each tear was different than their counterpart with varying material property cases. For 4 mm and 8 mm tears, the posterior tip was located in a low strength and stiffness zone compared to the varying property case. Consequently, critical stretch for both these tear sizes was lower for the constant material property case. However, for 20 mm case, the posterior tear tip was located in a higher stiffness and strength region compared to the varying property situation, and accordingly the critical stretch for constant stiffness case was higher. Thus, it can be concluded that biomechanical properties in the vicinity of the tear tip have a dominant role in determining the onset of tear propagation.

properties around the tear should be different than the rest, a fact not accounted for in the current computational study. Finally, it was assumed that tear propagation and subsequent failure of the supraspinatus tendon occur whenever maximum principal stress at a point reaches local material strength. While this criterion may be suitable to study initiation of tear propagation, it does not characterize the course of propagation. For example, once started in AP direction, the tear may later change direction and move in the ML direction, or even arrest completely depending on the local biomechanical state and physiological conditions. Failure criteria solely based on principal stress or strain may not capture these peculiarities of tear propagation.

5

Conclusions

This work has developed a new FE model of the supraspinatus tendon with a sharp tear using a transversely isotropic material model with a variation of material properties along the AP direction. The material parameters were calibrated from experimental load–displacement data obtained from a human supraspinatus tendon specimen with a surgically introduced tear. Simulations results reveal that there is a highly stressed region at the tips of the tear, and a stress-shielded region in the region between the tips. Further, variation of material properties along AP direction in conjunction with the size and location of the tear influences the stress state in the tendon. As compared with a homogeneous material model, differences in stress state at the tear tips show that local variation in material properties are important factors in tear propagation. For most of the simulation cases studied, a propensity for the tear to propagate posteriorly was noticed. This propensity is due to geometric and material variation in the tendon. Future work will focus on patient-specific tendon geometries and the effect of tissue remodeling to further quantify individual biomechanical response of the rotator cuff tendon to the presence of a tear.

Acknowledgment Support provided by the Department of Orthopaedic Surgery, the Department of Bioengineering, the Pittsburgh Chapter of the ARCS Foundation, and Sandia National Laboratories and NPSC Graduate Fellowship is gratefully acknowledged.

References 4.4 Stress-Shielded Region in the Vicinity of the Tear. An interesting feature of a tear in the supraspinatus tendon is the presence of a lightly stressed region not only in proximal region along the length of tear, but also in the surrounding tissue. These zones, adjacent to the tear edges, are the only regions of the tendon, which remain unloaded even under extreme loading. The presence of these stress-shielded regions can have profound effects on the material integrity of the tendon over relatively long time scales. As the tear tips may be strengthened due to remodeling in patients with chronic tears, the stress-shielded regions may be weakened due to the same process. 4.5 Limitations of the Current Work. The developed model is highly idealized with the absence of finer details such as: presence of the rotator cable, insertion of the tendon to the humeral head, or localized disorganization of collagen fibers and its effect on material properties [26,27]. Additionally, initial tear shapes studied are representative of acute tears surgically created in the tendon and may not be applicable to chronic tendon tears. Moreover, the model tendon was not influenced by loading of the infraspinatus tendon. However, the computational model incorporates sufficient biomechanical details to allow for the examination of general trends of stress variation in the tendon and its possible implication on the propagation of the tear. The tendon is expected to remodel when a tear is initiated and accordingly biomechanical Journal of Biomechanical Engineering

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Effect of tear location on propagation of isolated supraspinatus tendon tears during increasing levels of cyclic loading.

Are anterior supraspinatus tendon tears more prone to propagation? Commentary on an article by Daisuke Araki, MD, PhD, et al., "Effect of tear location on propagation of isolated supraspinatus tendon tears during increasing levels of cyclic loading".

Strain distribution due to propagation of tears in the anterior supraspinatus tendon.

The influence of partial subscapularis tendon tears combined with supraspinatus tendon tears.

Up-regulation of Glutamate in Painful Human Supraspinatus Tendon Tears.

Effect of tear size, corticosteroids and subacromial decompression surgery on the hierarchical structural properties of torn supraspinatus tendons.

Supraspinatus Intramuscular Calcified Hematoma or Necrosis Associated with Tendon Tear.

Effect of supraspinatus tendon injury on supraspinatus and infraspinatus muscle passive tension and associated biochemistry.

Age, trauma and the critical shoulder angle accurately predict supraspinatus tendon tears.

A study on the vascular supply of the supraspinatus tendon.

Lower muscle regenerative potential in full-thickness supraspinatus tears compared to partial-thickness tears.

The diagnostic accuracy of five tests for diagnosing partial-thickness tears of the supraspinatus tendon: A cohort study.

Supraspinatus tendon load during abduction is dependent on the size of the critical shoulder angle: A biomechanical analysis.

Does partial tear repair of adjacent tendons improve the outcome of supraspinatus tendonfull-thickness tear reinsertion?

Changes in the Chemical Barrier Composition of Tears in Alzheimer's Disease Reveal Potential Tear Diagnostic Biomarkers.

Sonoelastography findings of supraspinatus tendon in rotator cuff tendinopathy without tear: comparison with magnetic resonance images and conventional ultrasonography.

The potential effect of anatomic relationship between the femur and the tibia on medial meniscus tears.

Influence of Hyperlipidemia on the Treatment of Supraspinatus Tendinopathy With or Without Tear.

ARTHROSCOPIC REPAIR OF SMALL AND MEDIUM TEARS OF THE SUPRASPINATUS MUSCLE TENDON: EVALUATION OF THE CLINICAL AND FUNCTIONAL OUTCOMES AFTER TWO YEARS OF FOLLOW-UP.

Arthroscopic repair of anterosuperior rotator cuff tears: in-continuity technique vs. disruption of subscapularis-supraspinatus tear margin: comparison of clinical outcomes and structural integrity between the two techniques.

Bilateral triceps tendon tear.

Clinics in diagnostic imaging (151). Acromioclavicular joint geyser sign with chronic full-thickness supraspinatus tendon (SST) tear.

The effect of caffeine on tear secretion.

US in peroneal tendon tear.