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Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site
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Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site Sana Sadeghi, Hadi Taghizadeh∗ Tissue Mechanics Laboratory, Biomedical Engineering Department, Sahand University of Technology, PO. BOX 51335-1996, Tabriz, Iran
a r t i c l e
i n f o
Article history: Received 3 July 2019 Revised 21 January 2020 Accepted 26 January 2020 Available online xxx Keywords: Hard/soft connective tissue interface Microstructural modeling Fiber orientation Mineral deposition Soft tissue mechanics
a b s t r a c t The interface between the Achilles Tendon (AT) and calcaneus comprises soft and hard connective tissues. Such interfaces are vulnerable to mechanical damage. Tendon to Bone Insertion Region (TBIR) has unique microstructural characteristics for reinforcement. This region constitutes almost 10% of the AT’s distal end. The rest of the tendon (tendon proper) has longitudinal fiber orientation with no mineral content. Although, the TBIR lacks longitudinally organized fibers and at the same time, incorporates mineral molecules. In this study, a 3D computational model of the TBIR proposed to underline several reinforcement mechanisms. The obtained results showed that off-axis alignment of fibers, when coupled with the mineral deposition, shifts the stress concentration region to the tendon proper. In the case of altering each parameter individually, probable failure observed in the bone interface, which causes complications in surgical procedure or during healing. A gradual increase of mineral compensates for the stiffness mismatch between the AT and calcaneus. The proposed computational framework illustrated the complementary roles of fiber orientation and mineral molecules: nearly transverse orientation of fibers alleviated the stress concentration locally, while mineral deposition directly enhanced the TBIR stiffness. © 2020 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction The interface between the Achilles Tendon (AT) and calcaneus comprises soft and hard connective tissues. There are some other examples of such interfaces in the musculoskeletal system, including the direct attachment of gluteus maximus muscle to pelvis and cartilage-bone complex in synovial joints. In the case of muscles and synovial joints, the maximum attachment surface with bone relieves stress concentration in the interface. However, the attachment area for the tendon is minimal in order to increase the moment arm and to generate a precise motion at the respective joint. Therefore, these interfaces, especially Tendon to Bone Insertion Region (TBIR), are vulnerable to mechanical damage. The AT should possess a special microstructural arrangement in the attachment site in order to minimize the stress concentration. Consequently, the effective transfer of the muscular force (~2 kN, more than two times the body weight) over the small interface area to the bone is accomplished [1–4]. TBIR constitutes 10% of the AT’s distal end [5]. The rest of the tendon, which is named tendon proper, possesses longitudinally arranged fibers. Such fiber orientation plays the role of the main load-bearing element [6].
∗
Corresponding author. E-mail address: [email protected] (H. Taghizadeh).
However, experimental observations demonstrate off-axis oriented fibers in the TBIR [3], which implies different load-bearing mechanism(s) in this region. The gradual deposition of mineral molecules in TBIR is another feature that may contribute to the mechanical performance of AT. Mineral concentration increases from negligible amounts in tendon proper to more than 50% in the vicinity of the calcaneus [7]. In recent years, the microstructure of connective tissues within biomechanical models has attracted more attention from the biomechanics community because of its application in diagnostic and treatment methods [2,8]. AT injuries are among frequent incidences in athletes [9–11]. Even though TBIR experiences high-stress concentrations [3,7], the injury mostly occurs in the tendon proper [7]. Patient-specific simulations of the AT have shown that the injury is more sensitive to geometry rather than material properties [12,13]. However, in these studies, TBIR and its different microstructure have not been taken into account [11,12]. On the other hand, there are not consistent reports on the correlation of physical training and geometric adaptations such as increased AT cross-section [14,15]. There are some experimental studies on the quantification of TBIR microstructure in the literature [3,16,17]. However, the role of such microstructure on the biomechanical behavior of the AT is not established. Hence, this study explores the effect of microstructural features on the mechanical performance of the AT. For this purpose, the TBIR modeled as a functionally graded biomaterial,
https://doi.org/10.1016/j.medengphy.2020.01.010 1350-4533/© 2020 IPEM. Published by Elsevier Ltd. All rights reserved.
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finite element software was used to analyze the model and obtain the 3D contours.
2.2. Continuum framework
Fig. 1. Posterior view of a human leg illustrating a schematic of the AT, including the tendon proper and the TBIR. Blue threads denote the fibers, while the dark beads represent mineral molecules. Deviated fiber orientation and gradual deposition of mineral molecules in the TBIR are illustrated. It should be noted that the muscular force is exerted to the proximal section of the AT, and its distal end is fully fixed to the calcaneus.
with different mechanical properties along with it. The model postulated such that the contributions of each parameter, namely mineral deposition, fiber orientation, and dispersion, were studied separately. Such an approach can provide fresh insights toward the structure-function relationship of the TBIR. These types of relationships are of great interest to the biomedical engineering community [18,19]. This information can inspire the design of novel soft to hard tissue scaffolds for tissue engineering and even for industrial applications. 2. Materials and methods Based on obtained medical images, the geometry of an intact AT reconstructed. In this study, mechanical test data obtained from experimental studies of the AT. Furthermore, the range of microstructural parameters, i.e., fiber orientation and mineral concentration, were inspected from previous studies. The TBIR was regarded as a transition zone from tendon to bone and furnished with a microstructural hyperelastic strain energy density function (SEDF). The proposed model simulated in a finite element environment, and a parametric stress analysis carried out in order to evaluate the contributions of each parameter to the overall mechanical behavior of the TBIR. 2.1. Geometry Magnetic resonance images of AT in a healthy 34–year-old man provided according to ethical instructions of the Tabriz university of medical sciences (ethics approval ID: IR.TBZMED.REC.1398.1164). The MR images imported into Mimics software (Materialise, Belgium), and the tendon tissue marked by thresholding. The resulting cloud of points was then converted to a 3D body in Geomagic software (3D systems, US). As mentioned before, ten percent of the distal end of the tendon was partitioned and regarded as the TBIR. Fig. 1 shows a schematic illustration of AT representing its different regions. The geometry discretized with brick elements. To obtain mesh-independent results, we furnished the model with different numbers of elements, and the criterion for the suitable element number was chosen as stress difference less than 1% in a set of representative elements. This criterion satisfied with 26,100 elements. It should be noted that the mesh size was not constant through the model and finer mesh used for the TBIR. The ABAQUS
The first step to model the mechanical behavior of connective tissues is to choose a suitable form of the SEDF. Considering the microstructural features of the tissue constitute the primary steps for the allocation of appropriate SEDF. Histological examinations and imaging techniques provide such data. In this way, respective material parameters directly correlate with tissue’s structural components. AT undergoes large deformations during daily activities. It also represents incompressible behavior due to high water content. It is composed of aligned collagen fibers embedded in a noncollagenous ground substance, which leads to anisotropic behavior. In this study, the time-dependent behavior of the tendon and viscous effects were neglected. Hence, AT is attributed with a hyperelastic SEDF that is constituted of the isotropic and anisotropic energy terms [20]. These terms reflect the strain energy stored in the ground substance and fibers, respectively (Eq. (1)). The anisotropic term can capture the mechanical behavior of fiber families, while the Neo-Hookean strain energy assigned to the isotropic behavior of ground substance.
W = Wiso + Waniso Wiso = C10 (I1 − 3 ) k1 Waniso = (exp k2 (E f iber )2 − 1 ) k2 E f iber = κ (I1 − 3 ) + (1 − 3κ )(I4 − 1 )
(1)
where W, Wiso, and Waniso indicate total strain energy, isotropic and anisotropic ones, respectively. C10 , k1 , and k2 are material constants, and Efiber denotes the strain in the fiber direction. It should be noted that Efiber depends on fiber dispersion (κ ) and fiber orientation γ through I4 . I1 = λ21 + λ22 + λ23 denotes the first invariant of the right Cauchy-Green deformation tensor that depends on principal stretch ratios (λi ). Furthermore, I4 = λ21 cos2 γ + λ22 sin2 γ represents the stretch of a fiber family that lay in 1-2 plane, making the angle of γ with direction 1. Differentiation of the SEDF with respect to the deformation field gives the stress tensor (Eq. (2)). By imposing the incompressibility constraint, Cauchy stress for the proposed model is obtained as follows:
∂W ∂W − λ2 ∂ λ1 ∂ λ2 ∂ W ∂ I1 ∂ W ∂ I4 = λ1 + ∂ I1 ∂ λ1 ∂ I4 ∂ λ1 ∂ W ∂ I1 ∂ W ∂ I4 −λ2 + ∂ I1 ∂ λ2 ∂ I4 ∂ λ2
σ11 − σ22 = λ1
(2)
In the case of the tendon, physiological loading is a longitudinal extension (assumed in direction 1); therefore, the only non-zero component of stress isσ 11 . On the other hand, for uniaxial extension of a transversely isotropic (plane 2–3 is the plane of isotropy) and incompressible tissue, deformation field can be obtained as seen in Eq. (3),
1
λ1 = λ, λ2 = λ3 = √ λ
(3)
where λi denote principal stretch ratios. Substituting Eq. (1) into Eq. (2), for the deformation given in Eq. (3), the Cauchy stress for the proposed model is obtained (Eq. (4)).
Please cite this article as: S. Sadeghi and H. Taghizadeh, Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site, Medical Engineering and Physics, https://doi.org/10.1016/j.medengphy.2020.01.010
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S. Sadeghi and H. Taghizadeh / Medical Engineering and Physics xxx (xxxx) xxx Table 1 Material parameters for the microstructural model of the tendon-proper. C10 (MPa)
k1 (MPa)
k2 (dimensionless)
κ (dimensionless)
γ (°)
23.26
168.25
9.38
0
0
σ = σiso + σaniso σiso = 2C10 (λ2 − σaniso
1
) λ 2 λ2 κ + (1 − 3κ )cos2 γ = 2k1 ek2 (E f iber ) 2 − λ1 κ + (1 − 3κ )sin γ
(4)
The obtained Cauchy stress in the Eq. (4) enabled us to capture the mechanical response of the tissue to any given deformation field. However, the proposed material parameters should be initially allocated based on experimental test data. In this study, test data from Wren et al. [21] used to obtain material parameters. For this purpose, an objective function is proposed as the sum of differences between experimental stress and values obtained from SEDF stress in Eq. (4) for the range of deformations. Optimization algorithms are then recruited to determine material parameters (C10 , k1 , and k2 ) by minimization of the objective function. Detailed procedure to obtain the material parameters of a hyperelastic SEDF can be found in the previous paper of the authors (Taghizadeh et al. [22]) or other studies such as Rappel et al. [23]. Obtained material parameters provide the constitutive model for the tendon (Table 1).
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Table 2 Adopted material properties for the TBIR. Three microstructural parameters were studied, i.e., mineral concentration (C10 ), fiber orientation concerning the longitudinal axis of the tendon (γ ), and fiber dispersion (κ ). Based on proposed boundary values, a linear function is used to allocate the values of material parameters for intermediate TBIR zones. Simulation number
Evaluation parameter
1 2 3 4 5 6 7 8 9 10 11
C10 (kPa) C10 (kPa) C10 (kPa) γ (°) γ (°) γ (°) γ (°) κ (dimensionless) κ (dimensionless) κ (dimensionless) κ (dimensionless)
TBIR boundary values Tendon proper
Bone interface
25.44 25.44 25.44 2.48 2.48 2.48 2.48 0 0 0 0
623.34 301.57 120.13 22.13 33.28 43.25 71.26 0.198 0.27 0.297 0.333
Respective contours
Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.
2(A) 2(B) 2(C) 3(A) 3(B) 3(C) 3(D) 4(A) 4(B) 4(C) 4(D)
2.4. Loading and boundary conditions It is shown that the lateral and intermediate gastrocnemius muscles apply a tensile force of approximately 1620 Newton along the axial direction to the tendon [26]. In this study, the same load applied to the muscular end of AT. The calcaneus is considered as rigid body, and all freedom degrees of the boundary face of AT with the calcaneus were limited. To explore the probable failure region in AT, von Mises stress contours are extracted and compared. 3. Results and discussion
2.3. Modeling approach for TBIR 3.1. Mineral deposition Since the mechanical reinforcement of the mineral content is not direction-dependent, its contribution was integrated into the behavior of the ground substance (denoted by Wiso in Eq. (1)) and the respective material parameter, C10 . However, there is not any established relationship between the mineral concentration and respective tissue elasticity. To propose such a function, the hyperelastic behavior of the tissue interpolated as a linear function of mineral concentration. Bone with 100% mineral content and tendon proper without any minerals regarded as boundary values. For these boundary cases, the experimental data for bone (from Evans [24]) and tendon proper (from Wren et al. [21]) were assigned with Neo-Hookean SEDF and corresponding values of C10 obtained 1988.8 MPa for bone and 23.26 MPa for tendon proper (Table 1). Then for any intermediate concentrations, the respective value of C10 was allocated using the proposed function. There are inconsistent reports about the mineral concentration adjacent to the bone [7,25]; hence a parametric study on C10 is carried out to address various concentrations in the TBIR (Table 2). Collagen fibers contribute to the mechanical behavior of connective tissues in two ways: (1) orientation angle of collagen fibers with tissue axes and (2) fiber dispersion (κ ). Fiber orientation and dispersion were interpolated from γ = 0° and κ = 0 (corresponding to fully aligned fibers to the longitudinal axis of the tendon) in tendon proper to different values in the bone interface. It should be noted that k1 is a parameter with the dimension of stress and is used to calibrate the slope of the stress-strain response, and k2 is a dimensionless parameter to normalize the fiber extension. Then, the overall mechanical behavior of the tendon is captured through the mineral deposition parameter, C10 , and fiber response parameters, k1 and k2 . Such a model is capable of reflecting microstructural features directly into the macroscopic mechanical behavior of the AT. The TBIR was simulated with increasing values of dispersion parameter and changing fiber orientation (Table 2).
Fig. 2 represents stress contours due to the different functions adopted for increasing mineral content in TBIR. Additional information on adopted functions for each panel is provided in Table 2. It should be noted that all of the contours show the inner surface of the tendon, and the medial side of the tissue coincides with the upside of the contours. Panel A corresponds to increases of mineral concentration from zero in tendon proper to 30% in the bone interface. The stress is maximum in the middle and medial corners of the TBIR adjacent to the calcaneus. Section B indicates a similar simulation with a different mineral concentration in the bone interface (15%). The location and magnitude of the stress concentration in this model are similar to section A. In panel C with 5% mineral concentration in the bone interface, the maximum stress was in the same range; however, its location was mostly in the middle of boundary face with bone. These contours demonstrate that a large area of the bony interface is bearing the maximum stress, which is beneficial to reduce the failure and local detachment risk. Also, changing mineral concentration does not completely alter the stress profile and just mediates the concentration from the corner to the middle of the bony interface. Nevertheless, mineral deposition along the TBIR from the tendon to the bone, improves the tissue stiffness gradually and mostly compensates for the stiffness mismatch between tendon and bone. It should also be noted that, maximum stress values observed in these simulations, are in agreement with previous studies on tendon rupture [27]. 3.2. Fiber orientation Different patterns of fiber orientation along the TBIR simulated and related contours, are shown in Fig. 3. Panels A to D, correspond to increased fiber angle, starting from nearly axial fibers in tendon proper (γ = 0°) up to transverse configurations in the
Please cite this article as: S. Sadeghi and H. Taghizadeh, Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site, Medical Engineering and Physics, https://doi.org/10.1016/j.medengphy.2020.01.010
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Fig. 2. Von Mises stress contours due to increased mineral content with unchanged fiber orientation and dispersion along the TBIR. Boundary values of the C10 in the bone neighborhood are different (changes from 623 kPa in panel A to 120 kPa on panel C, which correspond to 30%, 15% and 5% mineral concentration, respectively). Stress concentration is shown in the middle and medial corner of the bone interface for panes A and B while for lower mineral concentration in pane C.
Fig. 3. Stress analysis of different orientations of collagen fibers and respective von Mises stress distribution in the TBIR. Contours from A to D demonstrate different ranges of orientation changes along the TBIR. All panels have similar fiber orientation in tendon proper (almost longitudinal), while in the bone interface fiber angles are approximately 20°, 30° 40° and 70°, respectively. (A) Stress concentration is observed in the middle of the bone interface. (B) The transition of the maximum stress region from the middle to corner. (C) Highly concentrated stress in medial corner due to diagonal arrangement of fibers adjacent to bone and (D) more transverse fibers distribute the stress on a more substantial zone of the medial corner.
neighborhood of bone (γ = 22.13° in pane A, γ = 33.28° in pane B, γ = 43.25° in pane C and γ = 71.26° in pane D). In panel A, with the smallest range of orientation change, the maximum stress observed in the middle of AT tissue adjoining with the bone. In other panels, the stress concentration is observed in the medial corner of the bone neighborhood. These results imply that small deviations (~20°) of the fiber angle throughout the TBIR have little impact on stress distribution in this region. In Fig. 3(B), a transi-
tion of maximum stress zone is observed from the middle to the medial corner. More deviations of the fiber angle through the TBIR (as illustrated in panel C), leads to very high and concentrated stresses in the medial corner of the bone interface. The diagonal orientation of fibers (angles close to 45°) leads to such abrupt stresses, which is close to the AT’s rupture limit. In Fig. 3(D), the maximum stress magnitude is in the same range as seen in panes A and B. However, the maximum stress region is tending toward
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Fig. 4. The effect of fiber dispersion on the stress profile in the TBIR. In panes A and B, maximum stress is observed in the middle of the attachment region to the bone. In panes C and D, maximum stress deviates from the middle toward the medial corner as a result of increased fiber dispersion. It should be noted that in pane D, the fibers dispersed in the vicinity of bone (κ = 0.33).
the middle from the medial corner. These findings are similar to axial orientation contours outlined in Fig. 2. It shows that nearly horizontal configurations of collagen fibers are not affecting the stress distribution regime adjacent to the bone. By comparing the presented results in Fig. 3 with the axial orientation of fibers in Fig. 2, it is evident that fibers should align in diagonal configuration (from 30° up to 60°) in order to impact the stress distribution pattern. Beyond this range, fibers are mostly perpendicular to the longitudinal axis of the tendon and practically have no role in its longitudinal strength. Such fibers lay mostly in the areas adjoining the bone and strengthen the tendon in the transverse plane tending to distribute the load over a larger area. It is shown that AT can withstand stresses up to 100 MPa [28], and our findings show a similar trend on stress values. Although, it seems that the diagonal orientation of the fibers in the vicinity of bone is not favorable considering the stress magnitude. Hence, the fibers near the bone interface should align in a direction perpendicular to the tendon axis (panel D), which is consistent with laboratory observations [3,16]. 3.3. Fiber dispersion Fig. 4 shows the results of altering the fiber dispersion while keeping the fiber angle and mineral concentration fixed along the TBIR. This figure represents the simulation results using no dispersion in the tendon proper (κ = 0), up to different dispersion values in the bone neighborhood (0.198 in pane A, 0.27 in pane B, 0.297 in pane C and 0.333 in pane D). In panes A and B, the outcome of changing κ is not significant compared to no dispersion states in Fig. 2. However, higher dispersion (and even the isotropic orienta-
tion case in panel D) is shown to distribute the maximum stress over a larger area. This finding is in agreement with the reports on the effect of dispersion in the mechanical response of other tissues such as arterial wall [29]. Observed patterns have some physiological implications, too. In the interface of soft and hard connective tissues, like the TBIR, fiber dispersion can diminish local stress concentrations in order to compensate for stiffness mismatch. Reduced stress concentration due to dispersed fibers constitutes the desired mechanical behavior in the TBIR [3]. 3.4. Realistic model of TBIR considering fiber orientation and mineral deposition The outcome of the simultaneous alteration of fiber orientation and mineral concentration along the TBIR is shown in Fig. 5. In panel A, mineral concentration is increased from zero in tendon proper to 30% in the bone interface, and at the same time, fiber orientation is altered gradually to γ = 22.13°. In the obtained stress contour, the maximum stress is observed in the tendon proper in the region with the lowest cross-sectional area. In pane B, another combination of the mineral deposition and changing fiber orientation is illustrated (15% mineral concentration and γ = 33.28° in the bone interface). Again, the maximum stress is observed in the region of the lowest cross-section in the tendon proper. Interestingly, most of the partial tearing and damage of the AT occur in the tendon proper, where it has the lowest cross-sectional area [11,30]. The magnitude of obtained stresses in both simulated cases is comparable to the previous reports [27,28]. Considering both of the parameters simultaneously (Fig. 5), leads to the shift of maximum stress from the bone interface to the
Please cite this article as: S. Sadeghi and H. Taghizadeh, Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site, Medical Engineering and Physics, https://doi.org/10.1016/j.medengphy.2020.01.010
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Fig. 5. Contours illustrate the simultaneous alteration of mineral deposition and fiber orientation along the TBIR. Resulting stress contours reveal that the location of maximum stress is shifted into the tendon proper where it has the lowest cross-sectional area. Two different combinations of fiber orientation and mineral depositions in A and B produced similar outcomes.
tendon proper. Comparing this finding with the contours of Figs. 2 and 3, the stress shift is due to the complementary functions of fibers and mineral molecules. If the tearing of the tendon occurs in the TBIR, surgical interventions and healing period will be significantly longer. As a result, the importance of the TBIR and its microstructural arrangement becomes multifold. It should be noted that in our simulations, mineral deposition plays a crucial role in matching the stiffness of the TBIR to that of bone, while the nearly transverse orientation of fibers leads to more uniform distribution of the stress across the bone interface. In previous studies [11,12], geometry was reported as the primary determinant of damage location in the AT and the effect of mechanical properties on stress patterns described as “lesssignificant.” However, contradictory reports on the influence of the training on the cross-sectional area of AT [27,31,32], implies that geometry does not play the central role in AT biomechanics. According to the results of the proposed study, the unique arrangement of microstructural features is the key factor determining the location of the maximum stress. Hence, the occurrence of the maximum stress in the tendon proper where it has the smallest cross-section. It is firstly due to complement roles of the TBIR microstructure (deposition of the mineral molecules and off-axis orientation of the collagenous network) and then due to the low cross-sectional area in the tendon proper region (geometrical parameters). It is shown that microstructural enhancements follow physical training in the AT, i.e., increased collagen synthesis [33]. This finding confirms the direct impact of AT microstructure on its biomechanics, as stated in this study.
4. Conclusion In this study, the Achilles Tendon biomechanics are attributed to the effect of increased mineral content, collagen fiber orientation, and dispersion. Such microstructure in the TBIR provides a stiffness gradient from tendon to bone, which is modeled using an innovative microstructural approach. The complement roles of increased mineral content and altered fiber orientation are illustrated. Collagen fibers distribute the stress locally, while increased mineral content improves the strength of the TBIR. Such close cooperation, protects the tendon-bone interface from mechanical damage and tearing by shifting the maximum stress region to the tendon proper. The impact of these findings will be manifold if we consider AT incidences among the most common sports injuries. The proposed computational framework can capture the biomechanical behavior of the AT and provides a more accurate mechanical model to study the failure of the tissue and to link the mechanics of the AT tissue to its microstructure. Declaration of Competing Interest None. Acknowledgment The authors would like to thank the Iran National Science Foundation (INSF) of I.R. Iran under Grant number 960 0 0521 for the financial support of this research.
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[15] Woo SL-Y, Gomez MA, Woo Y-K, Akeson WH. Mechanical properties of tendons and ligaments. Biorheology 1982;19(3):397–408. [16] Thomopoulos S, Williams GR, Gimbel JA, Favata M, Soslowsky LJ. Variation of biomechanical, structural, and compositional properties along the tendon to bone insertion site. J Orth Res 2003;21(3):413–19. [17] Thorpe CT, Screen HR. Tendon structure and composition. Adv Exp Med Biol 2016;920:3–10. [18] Courtecuisse H, Allard J, Kerfriden P, Bordas SP, Cotin S, Duriez C. Real-time simulation of contact and cutting of heterogeneous soft-tissues. Med Image Anal 2014;18(2):394–410. [19] Eleswarapu SV, Responte DJ, Athanasiou KA. Tensile properties, collagen content, and crosslinks in connective tissues of the immature knee joint. PLoS One 2011;6(10):e26178. [20] Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast Phys Sci Solids 20 0 0;61(1–3):1–48. [21] Wren TA, Lindsey DP, Beaupre GS, Carter DR. Effects of creep and cyclic loading on the mechanical properties and failure of human Achilles tendons. Ann Biomed Eng 2003;31(6):710–17. [22] Taghizadeh H, Tafazzoli-Shadpour M, Shadmehr MB, Fatouraee N. Evaluation of biaxial mechanical properties of aortic media based on the lamellar microstructure. Materials 2015;8(1):302–16. [23] Rappel H, Beex LA, Bordas SP. Bayesian inference to identify parameters in viscoelasticity. Mech Time-Depend Mater 2018;22(2):221–58. [24] Evans FG. Mechanical properties and histology of cortical bone from younger and older men. Anat Rec 1976;185(1):1–11. [25] Tang H, Buehler MJ, Moran B. A constitutive model of soft tissue: from nanoscale collagen to tissue continuum. Ann Biomed Eng 2009;37(6):1117–30. [26] Abrahams M. Mechanical behaviour of tendon in vitro. Med Biol Eng Comput 1967;5(5):433–43. [27] Kongsgaard M, Aagaard P, Kjaer M, Magnusson SP. Structural Achilles tendon properties in athletes subjected to different exercise modes and in Achilles tendon rupture patients. J Appl Physiol 2005;99(5):1965–71 (1985). [28] Hess GW. Achilles tendon rupture: a review of etiology, population, anatomy, risk factors, and injury prevention. Foot Ankle Spec 2010;3(1):29–32. [29] Niestrawska JA, Ch Haspinger D, Holzapfel GA. The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study. Comput Methods Biomech Biomed Eng 2018;21(2):99–112. [30] Smith JT, Bluman EM, Chiodo CP. Soft tissue disorders of the ankle. In: Katz JN, Blauwet CA, Schoenfeld AJ, editors. Principles of orthopedic practice for primary care providers. Springer; 2018. p. 339–60. [31] Reeves ND, Maganaris CN, Narici MV. Effect of strength training on human patella tendon mechanical properties of older individuals. J Physiol 2003;548(Pt 3):971–81. [32] Sommer HM. The biomechanical and metabolic effects of a running regime on the Achilles tendon in the rat. Int Orthop 1987;11(1):71–5. [33] Langberg H, Skovgaard D, Petersen LJ, Bulow J, Kjaer M. Type I collagen synthesis and degradation in peritendinous tissue after exercise determined by microdialysis in humans. J Physiol 1999;521(1):299–306 Pt 1.
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Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site Sana Sadeghi, Hadi Taghizadeh∗ Tissue Mechanics Laboratory, Biomedical Engineering Department, Sahand University of Technology, PO. BOX 51335-1996, Tabriz, Iran
a r t i c l e
i n f o
Article history: Received 3 July 2019 Revised 21 January 2020 Accepted 26 January 2020 Available online xxx Keywords: Hard/soft connective tissue interface Microstructural modeling Fiber orientation Mineral deposition Soft tissue mechanics
a b s t r a c t The interface between the Achilles Tendon (AT) and calcaneus comprises soft and hard connective tissues. Such interfaces are vulnerable to mechanical damage. Tendon to Bone Insertion Region (TBIR) has unique microstructural characteristics for reinforcement. This region constitutes almost 10% of the AT’s distal end. The rest of the tendon (tendon proper) has longitudinal fiber orientation with no mineral content. Although, the TBIR lacks longitudinally organized fibers and at the same time, incorporates mineral molecules. In this study, a 3D computational model of the TBIR proposed to underline several reinforcement mechanisms. The obtained results showed that off-axis alignment of fibers, when coupled with the mineral deposition, shifts the stress concentration region to the tendon proper. In the case of altering each parameter individually, probable failure observed in the bone interface, which causes complications in surgical procedure or during healing. A gradual increase of mineral compensates for the stiffness mismatch between the AT and calcaneus. The proposed computational framework illustrated the complementary roles of fiber orientation and mineral molecules: nearly transverse orientation of fibers alleviated the stress concentration locally, while mineral deposition directly enhanced the TBIR stiffness. © 2020 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction The interface between the Achilles Tendon (AT) and calcaneus comprises soft and hard connective tissues. There are some other examples of such interfaces in the musculoskeletal system, including the direct attachment of gluteus maximus muscle to pelvis and cartilage-bone complex in synovial joints. In the case of muscles and synovial joints, the maximum attachment surface with bone relieves stress concentration in the interface. However, the attachment area for the tendon is minimal in order to increase the moment arm and to generate a precise motion at the respective joint. Therefore, these interfaces, especially Tendon to Bone Insertion Region (TBIR), are vulnerable to mechanical damage. The AT should possess a special microstructural arrangement in the attachment site in order to minimize the stress concentration. Consequently, the effective transfer of the muscular force (~2 kN, more than two times the body weight) over the small interface area to the bone is accomplished [1–4]. TBIR constitutes 10% of the AT’s distal end [5]. The rest of the tendon, which is named tendon proper, possesses longitudinally arranged fibers. Such fiber orientation plays the role of the main load-bearing element [6].
∗
Corresponding author. E-mail address: [email protected] (H. Taghizadeh).
However, experimental observations demonstrate off-axis oriented fibers in the TBIR [3], which implies different load-bearing mechanism(s) in this region. The gradual deposition of mineral molecules in TBIR is another feature that may contribute to the mechanical performance of AT. Mineral concentration increases from negligible amounts in tendon proper to more than 50% in the vicinity of the calcaneus [7]. In recent years, the microstructure of connective tissues within biomechanical models has attracted more attention from the biomechanics community because of its application in diagnostic and treatment methods [2,8]. AT injuries are among frequent incidences in athletes [9–11]. Even though TBIR experiences high-stress concentrations [3,7], the injury mostly occurs in the tendon proper [7]. Patient-specific simulations of the AT have shown that the injury is more sensitive to geometry rather than material properties [12,13]. However, in these studies, TBIR and its different microstructure have not been taken into account [11,12]. On the other hand, there are not consistent reports on the correlation of physical training and geometric adaptations such as increased AT cross-section [14,15]. There are some experimental studies on the quantification of TBIR microstructure in the literature [3,16,17]. However, the role of such microstructure on the biomechanical behavior of the AT is not established. Hence, this study explores the effect of microstructural features on the mechanical performance of the AT. For this purpose, the TBIR modeled as a functionally graded biomaterial,
https://doi.org/10.1016/j.medengphy.2020.01.010 1350-4533/© 2020 IPEM. Published by Elsevier Ltd. All rights reserved.
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finite element software was used to analyze the model and obtain the 3D contours.
2.2. Continuum framework
Fig. 1. Posterior view of a human leg illustrating a schematic of the AT, including the tendon proper and the TBIR. Blue threads denote the fibers, while the dark beads represent mineral molecules. Deviated fiber orientation and gradual deposition of mineral molecules in the TBIR are illustrated. It should be noted that the muscular force is exerted to the proximal section of the AT, and its distal end is fully fixed to the calcaneus.
with different mechanical properties along with it. The model postulated such that the contributions of each parameter, namely mineral deposition, fiber orientation, and dispersion, were studied separately. Such an approach can provide fresh insights toward the structure-function relationship of the TBIR. These types of relationships are of great interest to the biomedical engineering community [18,19]. This information can inspire the design of novel soft to hard tissue scaffolds for tissue engineering and even for industrial applications. 2. Materials and methods Based on obtained medical images, the geometry of an intact AT reconstructed. In this study, mechanical test data obtained from experimental studies of the AT. Furthermore, the range of microstructural parameters, i.e., fiber orientation and mineral concentration, were inspected from previous studies. The TBIR was regarded as a transition zone from tendon to bone and furnished with a microstructural hyperelastic strain energy density function (SEDF). The proposed model simulated in a finite element environment, and a parametric stress analysis carried out in order to evaluate the contributions of each parameter to the overall mechanical behavior of the TBIR. 2.1. Geometry Magnetic resonance images of AT in a healthy 34–year-old man provided according to ethical instructions of the Tabriz university of medical sciences (ethics approval ID: IR.TBZMED.REC.1398.1164). The MR images imported into Mimics software (Materialise, Belgium), and the tendon tissue marked by thresholding. The resulting cloud of points was then converted to a 3D body in Geomagic software (3D systems, US). As mentioned before, ten percent of the distal end of the tendon was partitioned and regarded as the TBIR. Fig. 1 shows a schematic illustration of AT representing its different regions. The geometry discretized with brick elements. To obtain mesh-independent results, we furnished the model with different numbers of elements, and the criterion for the suitable element number was chosen as stress difference less than 1% in a set of representative elements. This criterion satisfied with 26,100 elements. It should be noted that the mesh size was not constant through the model and finer mesh used for the TBIR. The ABAQUS
The first step to model the mechanical behavior of connective tissues is to choose a suitable form of the SEDF. Considering the microstructural features of the tissue constitute the primary steps for the allocation of appropriate SEDF. Histological examinations and imaging techniques provide such data. In this way, respective material parameters directly correlate with tissue’s structural components. AT undergoes large deformations during daily activities. It also represents incompressible behavior due to high water content. It is composed of aligned collagen fibers embedded in a noncollagenous ground substance, which leads to anisotropic behavior. In this study, the time-dependent behavior of the tendon and viscous effects were neglected. Hence, AT is attributed with a hyperelastic SEDF that is constituted of the isotropic and anisotropic energy terms [20]. These terms reflect the strain energy stored in the ground substance and fibers, respectively (Eq. (1)). The anisotropic term can capture the mechanical behavior of fiber families, while the Neo-Hookean strain energy assigned to the isotropic behavior of ground substance.
W = Wiso + Waniso Wiso = C10 (I1 − 3 ) k1 Waniso = (exp k2 (E f iber )2 − 1 ) k2 E f iber = κ (I1 − 3 ) + (1 − 3κ )(I4 − 1 )
(1)
where W, Wiso, and Waniso indicate total strain energy, isotropic and anisotropic ones, respectively. C10 , k1 , and k2 are material constants, and Efiber denotes the strain in the fiber direction. It should be noted that Efiber depends on fiber dispersion (κ ) and fiber orientation γ through I4 . I1 = λ21 + λ22 + λ23 denotes the first invariant of the right Cauchy-Green deformation tensor that depends on principal stretch ratios (λi ). Furthermore, I4 = λ21 cos2 γ + λ22 sin2 γ represents the stretch of a fiber family that lay in 1-2 plane, making the angle of γ with direction 1. Differentiation of the SEDF with respect to the deformation field gives the stress tensor (Eq. (2)). By imposing the incompressibility constraint, Cauchy stress for the proposed model is obtained as follows:
∂W ∂W − λ2 ∂ λ1 ∂ λ2 ∂ W ∂ I1 ∂ W ∂ I4 = λ1 + ∂ I1 ∂ λ1 ∂ I4 ∂ λ1 ∂ W ∂ I1 ∂ W ∂ I4 −λ2 + ∂ I1 ∂ λ2 ∂ I4 ∂ λ2
σ11 − σ22 = λ1
(2)
In the case of the tendon, physiological loading is a longitudinal extension (assumed in direction 1); therefore, the only non-zero component of stress isσ 11 . On the other hand, for uniaxial extension of a transversely isotropic (plane 2–3 is the plane of isotropy) and incompressible tissue, deformation field can be obtained as seen in Eq. (3),
1
λ1 = λ, λ2 = λ3 = √ λ
(3)
where λi denote principal stretch ratios. Substituting Eq. (1) into Eq. (2), for the deformation given in Eq. (3), the Cauchy stress for the proposed model is obtained (Eq. (4)).
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S. Sadeghi and H. Taghizadeh / Medical Engineering and Physics xxx (xxxx) xxx Table 1 Material parameters for the microstructural model of the tendon-proper. C10 (MPa)
k1 (MPa)
k2 (dimensionless)
κ (dimensionless)
γ (°)
23.26
168.25
9.38
0
0
σ = σiso + σaniso σiso = 2C10 (λ2 − σaniso
1
) λ 2 λ2 κ + (1 − 3κ )cos2 γ = 2k1 ek2 (E f iber ) 2 − λ1 κ + (1 − 3κ )sin γ
(4)
The obtained Cauchy stress in the Eq. (4) enabled us to capture the mechanical response of the tissue to any given deformation field. However, the proposed material parameters should be initially allocated based on experimental test data. In this study, test data from Wren et al. [21] used to obtain material parameters. For this purpose, an objective function is proposed as the sum of differences between experimental stress and values obtained from SEDF stress in Eq. (4) for the range of deformations. Optimization algorithms are then recruited to determine material parameters (C10 , k1 , and k2 ) by minimization of the objective function. Detailed procedure to obtain the material parameters of a hyperelastic SEDF can be found in the previous paper of the authors (Taghizadeh et al. [22]) or other studies such as Rappel et al. [23]. Obtained material parameters provide the constitutive model for the tendon (Table 1).
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Table 2 Adopted material properties for the TBIR. Three microstructural parameters were studied, i.e., mineral concentration (C10 ), fiber orientation concerning the longitudinal axis of the tendon (γ ), and fiber dispersion (κ ). Based on proposed boundary values, a linear function is used to allocate the values of material parameters for intermediate TBIR zones. Simulation number
Evaluation parameter
1 2 3 4 5 6 7 8 9 10 11
C10 (kPa) C10 (kPa) C10 (kPa) γ (°) γ (°) γ (°) γ (°) κ (dimensionless) κ (dimensionless) κ (dimensionless) κ (dimensionless)
TBIR boundary values Tendon proper
Bone interface
25.44 25.44 25.44 2.48 2.48 2.48 2.48 0 0 0 0
623.34 301.57 120.13 22.13 33.28 43.25 71.26 0.198 0.27 0.297 0.333
Respective contours
Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.
2(A) 2(B) 2(C) 3(A) 3(B) 3(C) 3(D) 4(A) 4(B) 4(C) 4(D)
2.4. Loading and boundary conditions It is shown that the lateral and intermediate gastrocnemius muscles apply a tensile force of approximately 1620 Newton along the axial direction to the tendon [26]. In this study, the same load applied to the muscular end of AT. The calcaneus is considered as rigid body, and all freedom degrees of the boundary face of AT with the calcaneus were limited. To explore the probable failure region in AT, von Mises stress contours are extracted and compared. 3. Results and discussion
2.3. Modeling approach for TBIR 3.1. Mineral deposition Since the mechanical reinforcement of the mineral content is not direction-dependent, its contribution was integrated into the behavior of the ground substance (denoted by Wiso in Eq. (1)) and the respective material parameter, C10 . However, there is not any established relationship between the mineral concentration and respective tissue elasticity. To propose such a function, the hyperelastic behavior of the tissue interpolated as a linear function of mineral concentration. Bone with 100% mineral content and tendon proper without any minerals regarded as boundary values. For these boundary cases, the experimental data for bone (from Evans [24]) and tendon proper (from Wren et al. [21]) were assigned with Neo-Hookean SEDF and corresponding values of C10 obtained 1988.8 MPa for bone and 23.26 MPa for tendon proper (Table 1). Then for any intermediate concentrations, the respective value of C10 was allocated using the proposed function. There are inconsistent reports about the mineral concentration adjacent to the bone [7,25]; hence a parametric study on C10 is carried out to address various concentrations in the TBIR (Table 2). Collagen fibers contribute to the mechanical behavior of connective tissues in two ways: (1) orientation angle of collagen fibers with tissue axes and (2) fiber dispersion (κ ). Fiber orientation and dispersion were interpolated from γ = 0° and κ = 0 (corresponding to fully aligned fibers to the longitudinal axis of the tendon) in tendon proper to different values in the bone interface. It should be noted that k1 is a parameter with the dimension of stress and is used to calibrate the slope of the stress-strain response, and k2 is a dimensionless parameter to normalize the fiber extension. Then, the overall mechanical behavior of the tendon is captured through the mineral deposition parameter, C10 , and fiber response parameters, k1 and k2 . Such a model is capable of reflecting microstructural features directly into the macroscopic mechanical behavior of the AT. The TBIR was simulated with increasing values of dispersion parameter and changing fiber orientation (Table 2).
Fig. 2 represents stress contours due to the different functions adopted for increasing mineral content in TBIR. Additional information on adopted functions for each panel is provided in Table 2. It should be noted that all of the contours show the inner surface of the tendon, and the medial side of the tissue coincides with the upside of the contours. Panel A corresponds to increases of mineral concentration from zero in tendon proper to 30% in the bone interface. The stress is maximum in the middle and medial corners of the TBIR adjacent to the calcaneus. Section B indicates a similar simulation with a different mineral concentration in the bone interface (15%). The location and magnitude of the stress concentration in this model are similar to section A. In panel C with 5% mineral concentration in the bone interface, the maximum stress was in the same range; however, its location was mostly in the middle of boundary face with bone. These contours demonstrate that a large area of the bony interface is bearing the maximum stress, which is beneficial to reduce the failure and local detachment risk. Also, changing mineral concentration does not completely alter the stress profile and just mediates the concentration from the corner to the middle of the bony interface. Nevertheless, mineral deposition along the TBIR from the tendon to the bone, improves the tissue stiffness gradually and mostly compensates for the stiffness mismatch between tendon and bone. It should also be noted that, maximum stress values observed in these simulations, are in agreement with previous studies on tendon rupture [27]. 3.2. Fiber orientation Different patterns of fiber orientation along the TBIR simulated and related contours, are shown in Fig. 3. Panels A to D, correspond to increased fiber angle, starting from nearly axial fibers in tendon proper (γ = 0°) up to transverse configurations in the
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Fig. 2. Von Mises stress contours due to increased mineral content with unchanged fiber orientation and dispersion along the TBIR. Boundary values of the C10 in the bone neighborhood are different (changes from 623 kPa in panel A to 120 kPa on panel C, which correspond to 30%, 15% and 5% mineral concentration, respectively). Stress concentration is shown in the middle and medial corner of the bone interface for panes A and B while for lower mineral concentration in pane C.
Fig. 3. Stress analysis of different orientations of collagen fibers and respective von Mises stress distribution in the TBIR. Contours from A to D demonstrate different ranges of orientation changes along the TBIR. All panels have similar fiber orientation in tendon proper (almost longitudinal), while in the bone interface fiber angles are approximately 20°, 30° 40° and 70°, respectively. (A) Stress concentration is observed in the middle of the bone interface. (B) The transition of the maximum stress region from the middle to corner. (C) Highly concentrated stress in medial corner due to diagonal arrangement of fibers adjacent to bone and (D) more transverse fibers distribute the stress on a more substantial zone of the medial corner.
neighborhood of bone (γ = 22.13° in pane A, γ = 33.28° in pane B, γ = 43.25° in pane C and γ = 71.26° in pane D). In panel A, with the smallest range of orientation change, the maximum stress observed in the middle of AT tissue adjoining with the bone. In other panels, the stress concentration is observed in the medial corner of the bone neighborhood. These results imply that small deviations (~20°) of the fiber angle throughout the TBIR have little impact on stress distribution in this region. In Fig. 3(B), a transi-
tion of maximum stress zone is observed from the middle to the medial corner. More deviations of the fiber angle through the TBIR (as illustrated in panel C), leads to very high and concentrated stresses in the medial corner of the bone interface. The diagonal orientation of fibers (angles close to 45°) leads to such abrupt stresses, which is close to the AT’s rupture limit. In Fig. 3(D), the maximum stress magnitude is in the same range as seen in panes A and B. However, the maximum stress region is tending toward
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Fig. 4. The effect of fiber dispersion on the stress profile in the TBIR. In panes A and B, maximum stress is observed in the middle of the attachment region to the bone. In panes C and D, maximum stress deviates from the middle toward the medial corner as a result of increased fiber dispersion. It should be noted that in pane D, the fibers dispersed in the vicinity of bone (κ = 0.33).
the middle from the medial corner. These findings are similar to axial orientation contours outlined in Fig. 2. It shows that nearly horizontal configurations of collagen fibers are not affecting the stress distribution regime adjacent to the bone. By comparing the presented results in Fig. 3 with the axial orientation of fibers in Fig. 2, it is evident that fibers should align in diagonal configuration (from 30° up to 60°) in order to impact the stress distribution pattern. Beyond this range, fibers are mostly perpendicular to the longitudinal axis of the tendon and practically have no role in its longitudinal strength. Such fibers lay mostly in the areas adjoining the bone and strengthen the tendon in the transverse plane tending to distribute the load over a larger area. It is shown that AT can withstand stresses up to 100 MPa [28], and our findings show a similar trend on stress values. Although, it seems that the diagonal orientation of the fibers in the vicinity of bone is not favorable considering the stress magnitude. Hence, the fibers near the bone interface should align in a direction perpendicular to the tendon axis (panel D), which is consistent with laboratory observations [3,16]. 3.3. Fiber dispersion Fig. 4 shows the results of altering the fiber dispersion while keeping the fiber angle and mineral concentration fixed along the TBIR. This figure represents the simulation results using no dispersion in the tendon proper (κ = 0), up to different dispersion values in the bone neighborhood (0.198 in pane A, 0.27 in pane B, 0.297 in pane C and 0.333 in pane D). In panes A and B, the outcome of changing κ is not significant compared to no dispersion states in Fig. 2. However, higher dispersion (and even the isotropic orienta-
tion case in panel D) is shown to distribute the maximum stress over a larger area. This finding is in agreement with the reports on the effect of dispersion in the mechanical response of other tissues such as arterial wall [29]. Observed patterns have some physiological implications, too. In the interface of soft and hard connective tissues, like the TBIR, fiber dispersion can diminish local stress concentrations in order to compensate for stiffness mismatch. Reduced stress concentration due to dispersed fibers constitutes the desired mechanical behavior in the TBIR [3]. 3.4. Realistic model of TBIR considering fiber orientation and mineral deposition The outcome of the simultaneous alteration of fiber orientation and mineral concentration along the TBIR is shown in Fig. 5. In panel A, mineral concentration is increased from zero in tendon proper to 30% in the bone interface, and at the same time, fiber orientation is altered gradually to γ = 22.13°. In the obtained stress contour, the maximum stress is observed in the tendon proper in the region with the lowest cross-sectional area. In pane B, another combination of the mineral deposition and changing fiber orientation is illustrated (15% mineral concentration and γ = 33.28° in the bone interface). Again, the maximum stress is observed in the region of the lowest cross-section in the tendon proper. Interestingly, most of the partial tearing and damage of the AT occur in the tendon proper, where it has the lowest cross-sectional area [11,30]. The magnitude of obtained stresses in both simulated cases is comparable to the previous reports [27,28]. Considering both of the parameters simultaneously (Fig. 5), leads to the shift of maximum stress from the bone interface to the
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Fig. 5. Contours illustrate the simultaneous alteration of mineral deposition and fiber orientation along the TBIR. Resulting stress contours reveal that the location of maximum stress is shifted into the tendon proper where it has the lowest cross-sectional area. Two different combinations of fiber orientation and mineral depositions in A and B produced similar outcomes.
tendon proper. Comparing this finding with the contours of Figs. 2 and 3, the stress shift is due to the complementary functions of fibers and mineral molecules. If the tearing of the tendon occurs in the TBIR, surgical interventions and healing period will be significantly longer. As a result, the importance of the TBIR and its microstructural arrangement becomes multifold. It should be noted that in our simulations, mineral deposition plays a crucial role in matching the stiffness of the TBIR to that of bone, while the nearly transverse orientation of fibers leads to more uniform distribution of the stress across the bone interface. In previous studies [11,12], geometry was reported as the primary determinant of damage location in the AT and the effect of mechanical properties on stress patterns described as “lesssignificant.” However, contradictory reports on the influence of the training on the cross-sectional area of AT [27,31,32], implies that geometry does not play the central role in AT biomechanics. According to the results of the proposed study, the unique arrangement of microstructural features is the key factor determining the location of the maximum stress. Hence, the occurrence of the maximum stress in the tendon proper where it has the smallest cross-section. It is firstly due to complement roles of the TBIR microstructure (deposition of the mineral molecules and off-axis orientation of the collagenous network) and then due to the low cross-sectional area in the tendon proper region (geometrical parameters). It is shown that microstructural enhancements follow physical training in the AT, i.e., increased collagen synthesis [33]. This finding confirms the direct impact of AT microstructure on its biomechanics, as stated in this study.
4. Conclusion In this study, the Achilles Tendon biomechanics are attributed to the effect of increased mineral content, collagen fiber orientation, and dispersion. Such microstructure in the TBIR provides a stiffness gradient from tendon to bone, which is modeled using an innovative microstructural approach. The complement roles of increased mineral content and altered fiber orientation are illustrated. Collagen fibers distribute the stress locally, while increased mineral content improves the strength of the TBIR. Such close cooperation, protects the tendon-bone interface from mechanical damage and tearing by shifting the maximum stress region to the tendon proper. The impact of these findings will be manifold if we consider AT incidences among the most common sports injuries. The proposed computational framework can capture the biomechanical behavior of the AT and provides a more accurate mechanical model to study the failure of the tissue and to link the mechanics of the AT tissue to its microstructure. Declaration of Competing Interest None. Acknowledgment The authors would like to thank the Iran National Science Foundation (INSF) of I.R. Iran under Grant number 960 0 0521 for the financial support of this research.
Please cite this article as: S. Sadeghi and H. Taghizadeh, Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site, Medical Engineering and Physics, https://doi.org/10.1016/j.medengphy.2020.01.010
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Please cite this article as: S. Sadeghi and H. Taghizadeh, Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site, Medical Engineering and Physics, https://doi.org/10.1016/j.medengphy.2020.01.010