the mechanical response of achilles tendon during different kinds of sports

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERINGCommun. Numer. Meth. Engng 2008; 24:2077–2085Published online 25 January 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cnm.1096

The mechanical response of Achilles tendon during differentkinds of sports

Y. D. Gu1, J. S. Li1, M. J. Lake2, X. J. Ren3 and Y. J. Zeng4,∗,†

1Faculty of Physical Education, Ningbo University, Zhejiang, China2School of Sport and Exercise Sciences, Liverpool John Moores University,

Liverpool L3 2ET, U.K.3School of Engineering, Liverpool John Moores University, Liverpool L3 3AF, U.K.

4Biomedical Engineering Center, Beijing University of Technology, Beijing 100022, China

SUMMARY

The present study investigated the mechanical properties of human Achilles tendon (AT) during differentforms of human locomotion, by combining biomechanical tests and numerical modelling. A Pedar-Xplantar pressure measurement system and Mega multichannel SEMG system were used to measure thedynamic data of a female athlete during hopping and walking. The human Achilles tendon force (ATF)was determined through inverse muscle force calculation. A 3D finite element (FE) model was developedusing subject-specified CT images to simulate the deformation of AT during hopping and walking. Thestress/strain within the AT during different subphases (e.g. heel strike, midstance, forefoot contact, pushoff and toe off) was successfully predicted. Results showed that the muscle forces in hopping were muchhigher than in normal gait. The maximum stress in hopping was three times of that in walking. Thetendon stress increased with external load over different subphases and the maximum ATF was found tobe in the push-off phase. Copyright q 2008 John Wiley & Sons, Ltd.

Received 25 April 2007; Revised 4 November 2007; Accepted 12 November 2007

KEY WORDS: Achilles tendon; hopping; finite element analysis

1. INTRODUCTION

Human Achilles tendon (AT) is subjected to substantial force during human locomotion, and itis frequently associated with acute and overuse injuries related to habitual loading, including

∗Correspondence to: Y. J. Zeng, Biomedical Engineering Center, Beijing University of Technology, Beijing 100022,China.

†E-mail: [email protected], [email protected]

Contract/grant sponsor: Zhejiang SportsContract/grant sponsor: Ningbo University; contract/grant number: B-LI36

Copyright q 2008 John Wiley & Sons, Ltd.

2078 Y. D. GU ET AL.

complete tendon ruptures [1, 2]. The high incidence of AT injuries during physical training is alsorelated to the high forces involved. It has been reported that injuries caused by overuse (referred toas tendinous pain) affect millions of people in occupational and athletic environments [3, 4]. Manyinjuries were attributed to changes in activity, such as abrupt increase in the duration or intensityof athletic training [1, 5]. It has been estimated that the human AT load may reach tensile forcesof 1400–2600N during walking [6] and 3100–5330N during running [7].

Several studies have suggested that the AT experiences greater levels of stress than tendons inother body parts. Based on in vitro measurement, Komi et al. [8] showed that the human AT mayexperience peak stresses in excess of 70MPa during maximal eccentric plantar flexions, while mosttendons in other body regions have peak stresses below 30MPa. In a related article, Ker et al. [9]suggested that in vivo stresses in the human AT are higher than those measured in vitro based ontransducer data. Recently, Kongsgaard et al. [10] reported peak stresses of 57.4MPa for runningand 70.3MPa for playing volleyball. These biomechanical studies have improved the understandingof tendon force; however, the load transfer mechanism and internal stress/strain states within thetendon and bony structures were not well addressed, which is crucial to the understanding of softtissue injuries. Finite element analysis (FEA) is commonly used in biomechanics [11–13]. It canbe used as an additional tool to the experimental approach to predict the load distribution withinthe ankle [14, 15], which offers more detailed information such as the internal stress and strainof the ankle complex. Most of the published works on the numerical investigation of AT functionused simplified line replacement of the AT or represented AT action by exerting force on thecalcaneous. These approaches could not take into account the shape effect on stress distribution.A detailed FE model of the human foot and ankle, incorporating geometrical properties of bothbony and soft tissue components, is essential to provide a more realistic representation of the footand the supporting conditions in order to enhance the understanding of the ankle–foot biomechanics[16, 17]. It would also permit AT deformation to be quantified over each subphase of foot–groundcontact during locomotion.

The main objective of this study is to investigate the mechanical properties of the human ATduring locomotion by combining real structure FE modelling and biomechanical subject tests.A Pedar-X plantar pressure measurement system and Mega multichannels SEMG system wereused to measure the dynamic data during one-legged jumping and walking for a female athlete.A three-dimensional finite element model of a healthy human ankle joint has been developedusing subject-specific CT/MRI images. The human Achilles tendon force (ATF) was determinedthrough inverse dynamics muscle force calculations. The stress/strain within the AT over differentsubphases in jumping and walking was successfully predicted and comparatively analysed. Resultsshowed that muscle force in hopping was much higher than in normal gait; the maximum stressvalue in hopping was nearly three times of that during walking for the same subject. The tendonstress increased with external load over different subphases, and the maximum ATF was found tobe in the push-off period.

2. METHOD

The geometry of the finite element (FE) model was developed from reconstruction of 3D CT(computerized tomography) and MRI (magnetic resonance imaging) images of the left foot of anormal female athlete (age 21, height 168 cm and weight 55 kg). Coronal CT and MRI images weretaken with intervals of 2mm in the neutral unloaded position. The images were segmented using

Copyright q 2008 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2008; 24:2077–2085DOI: 10.1002/cnm

MECHANICAL RESPONSE OF ACHILLES TENDON DURING DIFFERENT KINDS OF SPORTS 2079

Figure 1. Rigid–flexible body contact between the calcaneous and AT.

MIMICS 8.0 (Materialise, Leuven, Belgium) to obtain the boundaries of the skeleton and tendonsurface. The surfaces of the skeletal and tendon components were processed using Solidworks2005 (SolidWorks Corporation, Massachusetts) to form solid models and then assembled into awhole ankle model. The model was then imported into the FE package ANSYS (version 9.0).A rigid–flexible body contact option was used to simulate contact between the calcaneous and AT(Figure 1). Compressive stiffness resembling the cartilage structure was prescribed between eachpair of contact surfaces.

The bony structures were treated as homogeneous, isotropic and linearly elastic material. Young’smodulus and Poisson’s ratio for the bony structures were assigned as 7300MPa and 0.3, respec-tively; these values were commonly used for bones in FE modelling [17]. Young’s modulus andPoisson’s ratio of the cartilage were taken as 1MPa and 0.4, respectively [18]. The AT materialwas simulated by using an incompressible, hyper-elastic, two parameter Mooney–Rivlin (C10,C01)

formulation with the following strain energy function:

U =C10(I1−3)+C01(I2−3)+ 1

D(J el−1)2 (1)

where U is the strain energy per unit of reference volume, C10,C01 are material constants, char-acterizing the deviatoric deformation of the material, taken as 104 and 26, respectively [19]. D isthe material incompressibility parameter, taken as 0.00484 [20].

I1 and I2 are the first and second deviatoric strain invariants defined as

I1 = �21+�22+�23 (2)

I2 = �−21 +�−2

2 +�−23 (3)

J el and �i are the elastic volume ratio and the principal stretches, respectively.Dynamic loading on the AT in the FE model for hopping and walking was determined from

biomechanical tests using inverse dynamics. The plantar reaction force and surface EMG of thetriceps surae muscle group generated during the foot–ground interaction and their evolution duringjumping are important parameters to estimate the AT force [6]. An in-shoe force measurementsystem (Novel Pedar system, Germany) was used to measure the ground reaction force for sixground contacts during one-legged jumping and walking. The measured results are listed in Table I.



Table I. Plantar reaction force in jumping and walking.

Heel strike Midstance Forefoot contact Push off Toe off

Plantar force in jumping (N ) 1414.9±65.2 1560.18±20.3 1817±81.5 1525.3±18.2 796.1±13.6Plantar force in walking (N ) 351.6±16.3 331.2±19.4 317.6±22.4 478.5±17.2 154±12.3

Table II. EMG data of triceps surae muscle during jumping and walking.

Soleus Medial gastrocnemius Lateral gastrocnemius

JumpingAEMG (uv) 298.43±25.66 467.00±53.65 434.75±74.30MPF (Hz) 70.36±3.05 71.40±5.03 86.60±2.61

WalkingAEMG (uv) 85.24±11.86 62.33±16.29 117.83±20.06MPF (Hz) 82.33±9.86 71.67±13.80 72.83±12.37

Figure 2. AT force variation during jumping and walking.

EMG activity of the gastrocnemius and soleus were collected for six ground contacts duringone-legged jumping and walking using the Mega (Me6000) system, and the results are listed inTable II. Foot segment inertial properties defined by Plagenhoef et al. [21] were used in an inversedynamics solution to calculate the ankle plantar–flexor moment at the joint centre, assuming thatall the plantar–flexor moment was attributed to the AT structure. ATF was calculated by dividingthe ankle joint moment by the moment arm between the AT and the ankle joint centre. This wascalculated at each time point as the perpendicular distance from the ankle joint centre to the line ofaction of the AT (the direct line from the calcaneous to the projected position of the muscle–tendonjunction). Figure 2 shows the calculated ATF in one-legged jumping and walking. These forcesprovide the loading data in the FE model to simulate the stress/strain during hopping and walking.



3. NUMERICAL RESULTS

Typical internal stress/strain distribution within the bones and AT, during different subphases injumping is shown in Figures 3 and 4. Figure 3 depicts the von Mises stress in the ankle (a) andprincipal stress vector distribution (b) during heel strike predicted by the FE simulation. As shownin the figure, AT experiences a low stress with a peak von Mises stress of 0.05MPa at the locationof calcaneal insertion. During midstance, both the tensile stress and strain within the AT increasedand the peak von Mises stress/strain reached 22.66MPa and 4.15%, respectively. The maximumvon Mises stress/strain was found to be as high as 48.37MPa/5.14% at the push-off subphase(Figure 4). Simulation of the AT during the toe-off subphase also revealed high stress/strain at thelevel of 26.57MPa/4.33%. Figure 5 compared the AT strain variation during one-legged jumpingand walking with that predicated by the simulation. It clearly showed that the strain level in walking

Figure 3. Distribution of the von Mises stress (MPa) (a) and the maximum, second and minimum principalstresses vectors (b) within the AT during hopping heel strike.

Figure 4. Distribution of the von Mises stress (MPa) (a) and the maximum, second and minimum principalstresses vectors (b) within the AT during hopping push off.



Figure 5. AT strain variation during jumping and walking.

Figure 6. External force exerted in (a) coronal direction and (b) stress distribution.

Figure 7. External force exerted in (a) sagittal direction and (b) stress distribution.

is much lower than that in hopping. The peak von Mises stress/strain was also found at push-offsubphase, which is 16.28MPa/3.68%, respectively.

The FE models were further used to compare the effect of loading direction on the deforma-tion of the AT for jumping, which is not readily measurable with experiments. Figures 6 and 7compared typical stress distribution when the force was applied in the coronal direction and in thesagittal direction. It clearly shows that the impulsive force in the coronal direction causes stressconcentration on the loading side. When the impulsive force appeared in the sagittal direction, theAT stress concentration point was also above the calcaneal insertion. During the push-off subphase,the peak stress value reaches 51.72 and 50.25MPa, respectively.



4. DISCUSSION

In this study, a 3D FE model of the ankle part was developed using real geometries of thebony structure and tendon from subject-specific medical images. The human ATF was determinedthrough inverse dynamics muscle force calculations. A 3D FE model was used to simulate thedeformation of AT during hopping and walking. The stresses/strains within the AT during differentsubphases of ground contact (e.g. heel strike, midstance, forefoot contact, push off and toe off)were successfully predicted. As shown in Figures 3–7, the stress concentration point within the ATwas positioned above the calcaneal insertion, and this agrees with some clinical results on tendoninjury. Approximately 80% of Achilles tendon ruptures occur 3–6 cm above the calcaneal insertion[22]. The specific site of rupture has traditionally been explained by a poor blood supply [2].However, it has also been suggested that local stress concentration, as shown in the FE simulation,was also a major reason for AT injury. As shown in Figure 5, from FE simulation, the peak strainthat appeared during the push-off subphase was 5.14%, which is in good agreement with somepublished data. For example, Maganaris et al. [23] recorded the AT’s peak strain as the movementapproached 5% using ultrasonic devices. However, MRI research [19] found that peak strain ofthe AT during jumping was 8.3±2.1%, which is higher than our FE prediction. This is probablydue to the different muscle force and age of the subjects used in these two studies.

The stress analysis of the AT showed that the maximum stress in jumping is nearly three timesas the stress under walking conditions, which may cause a higher incidence of AT injury duringjumping. Based on in vitro tests the failure stress of tendons is generally considered to be close to100MPa [5], which is above the stress level predicted in this work. Previous AT cross-sectional area(CSA) observation showed that athletes had markedly greater AT CSA than age-matched controls,which indicated that athletes’ AT could endure more stress [24–27]. From the FE prediction, itis clear that the peak stress during jumping was lower than 50MPa. Hence, this athlete is safein normal jump training. However, if an extra force (e.g. in kicking) appeared in the movement,AT’s peak stress would rise markedly; especially in the push-off subphase, the external forcewould easily lead to AT trauma. It has been reported that AT could suffer much higher stress inan intense movement [27]. The achillodynia-related tendon swelling and decreased echotexturewere also strongly related to the risk of sustaining training [28], which is associated with the ATbiomaterial fatigue performance limit. The 3-D FE model developed would make it possible tostudy these by considering the nonlinear time-dependent material properties, which is a subject offuture investigation.

5. CONCLUSION

The present study investigated the mechanical properties of the human AT in a female elite athleteduring hopping and walking by combining biomechanical tests and FEA. A Pedar-X plantarpressure measure system and Mega multichannel SEMG system were used to measure the dynamicdata, and the human ATF was determined through inverse dynamics muscle force calculations. A 3DFE model was created using CT scan images to study the deformation of the AT during locomotion.The stress/strain within the AT was successfully predicted based on dynamic biomechanical forcedata. Results showed that the stress level in the AT under hopping conditions was much higherthan during normal walking gait. The tendon stress increased with external load over differentsubphases of ground contact, and the maximum ATF was found to be during the push-off period.



ACKNOWLEDGEMENTS

This work was supported by the Zhejiang Sports government and Ningbo University talent project (grantNo. B-LI36).

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the mechanical response of achilles tendon during different kinds of sports

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