Study of Stress Distribution in the Tibia During Stance Phase Running Using the Finite Element Method

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1 Ksetsrt J. (Nt. Sci.) 48 : (2014) Study of Stress Distriution in the Tii During Stnce Phse Running Using the Finite Element Method Thepwchr Ruchirh 1, Tumrong Puttpitukporn 1, * nd Siriporn Ssimontonkul 2 ABSTRACT Tii frctures re common in the elderly who hve osteoporosis. Stress distriutions in the tii of two osteoporosis ptients were studied to investigte the cuse of this frcture nd the effects of contct res on the distl end of the tii, ody weight nd knee flexion ngles on the tiil stresses were determined using finite element nlysis. Three-dimensionl tiil models were constructed from computed tomogrphy imges of legs using the Mimics V progrm nd the Geomgic V.10 progrm. These models were imported to the Cti V.5 progrm to perform the finite element nlysis for determining stress distriutions in the tii. The finite element models showed tht the mximum von Mises stress found on the tii of the femle ptient ws higher thn in the mle ptient since the contct re on the distl end of the femle ws smller thn in the mle. Furthermore, the mximum von Mises stress occurred ner the middle of the posterior tii t 30º knee flexion nd ws slightly shifted towrd the medil tii during 30 90º knee flexion. As ody weight incresed, the mximum von Mises stress lso incresed. Moreover, the mximum von Mises stresses otined from the smller contct re were % (for femle ptient) nd % (for mle ptient) higher thn those determined from lrger contct re. Keywords: tii, computed tomogrphy imges, finite element nlysis, osteoporosis INTRODUCTION Brittle ones re common prolem mong the elderly with osteoporosis nd cn esily led to one frcture (Ntionl Institute of Helth, 2014). Computed tomogrphy (CT) imges nd the finite element method hve een used to oserve stress distriution in the one. Khmpgdee (2010) nlyzed the stress in the hed of n osteonecrotic hip joint using the finite element method in the Cosmos progrm. Ssimontonkul et l. (2007) reported tht running led to the occurrence of mximl compressive nd posterior sher forces pplied to the distl end of the tii t mid stnce, which relted to stress frcture of the tii. The ojectives of this reserch were to oserve stress distriutions in the tii during the stnce phse of running nd to determine the effects of contct re on the distl end of the tii, ody weight nd knee flexion ngles on tii stresses using finite element nlysis. Three-dimensionl finite element models (FEMs) 1 Deprtment of Mechnicl Engineering, Fculty of Engineering, Ksetsrt University, Bngkok 10900, Thilnd. 2 Progrm in Sports Biomechnics, Fculty of Sports Science, Ksetsrt University, Bngkok 10900, Thilnd. * Corresponding uthor, e-mil: Received dte : 25/03/14 Accepted dte : 24/07/14

2 730 Ksetsrt J. (Nt. Sci.) 48(5) of the tii consisting of corticl nd cncellous ones sed on the CT imges of two osteoporosis ptients were constructed using the Mimics V (Mterilise; Leuven, Belgium), the Geomgic V.10 (3D Systems; Rock Hill, SC, USA), nd the Cti V.5 (Dssult Systèmes; Wlthm, MA, USA) progrms. Two contct res on the distl end of the tii were modeled ccording to the studies of Kur et l. (1998) nd Wn et l. (2006). Kur et l.(1998) reported on the contct re of the nkle joint with xil loding nd in positions of mximl dorsiflexion, plntr flexion, supintion nd prontion, while Wn et l. (2006) estimted n in vivo rticulr crtilge contct re of the humn tlocrurl joint during the simulted stnce phse of wlking. The pplied lods t the distl end of the tii determined y Ssimontonkul et l. (2007) were used. The fixed res on medil nd lterl condyles were modeled ccording to the study of Eisenhrt-Rothe et l. (2003) who found tht contct res of the ptellofemorl nd tiio-femorl joints depended on knee flexion ngles. Mteril nd Methods Vlidted model To vlidte the ccurcy of the FEM method in the Cti progrm, cntilever em ws modeled consisting of solid cylinder (50 mm dimeter nd 300 mm length) s shown in Figure 1. The FEM ws formed using 1,9751 tetrhedrl elements. The lods pplied to the free end were compressive force of 400 N nd sher force of 200 N. The mteril properties were Young s modulus of 70 GP nd Possion s rtio of Three-dimensionl tiil models The CT imges of the legs of two osteoporosis ptients ( 38 yer-old mle nd 64 yer-old femle) were used to crete the three-dimensionl tiil models. The CT imges were imported into the Mimics V progrm to erse irrelevnt ones nd to correct the right tiil surfces consisting of corticl nd cncellous ones s shown in Figures 2 nd 3. Then, those tiil surfces were repired using the Geomgic V.10 progrm. Figures 4 nd 5 show the repired surfces of the tiil ones of the femle ptient nd mle ptient, respectively. Finlly, the Cti V.5 progrm ws used to crete the ssemly modeling of corticl nd cncellous ones s shown in Figure 6. Finite element modeling The FEM of the right tii consisted of corticl nd cncellous ones. Twenty-four cse studies were investigted to determine the effects of contct res on the distl end of the tii, odyweight nd knee flexion ngles on tiil stresses s shown in Tle 1. These FEMs were formed y tetrhedrl elements in which the numers of elements were tested to otin the ccurte results shown in Tle 2. Contct surfces without friction were constructed etween the inner surfce of the corticl one nd the outer surfce of the cncellous one. Figure 1 Vlidted model.

3 Ksetsrt J. (Nt. Sci.) 48(5) mm mm Figure 2 Computed tomogrphy scn imges of the tiil one of femle ptient: () Corticl one; () Cncellous one mm mm Figure 3 Computed tomogrphy scn imges of the tiil one of mle ptient: () corticl one nd () cncellous one.

4 732 Ksetsrt J. (Nt. Sci.) 48(5) Figure 4 Repired surfces of the tiil one of femle ptient: () Corticl one; () Cncellous one. Figure 5 Repired surfces of the tiil one of mle ptient: () Corticl one; () Cncellous one. Figure 6 Three-dimensionl tiil models consisting of corticl nd cncellous ones: () Femle ptient; () Mle ptient.

5 Ksetsrt J. (Nt. Sci.) 48(5) 733 Tle 1 Cse studies clssified y contct res on the distl end of the tii, knee flexion ngles nd ody weight. Cse study numer Femle Ptient Mle Kur et l. (1998) Contct re (distl end) Wn et l. (2006) Knee flexion ngle ( ) Body weight (kg) 30º 30 90º Tle 2 Numer of nodes nd elements used in the finite element models. Cse study Numer of nodes Numer of elements 1 3 3,493 14, ,500 14, ,483 14, ,493 14, ,441 12, ,449 12, ,452 12, ,443 12,888

6 734 Ksetsrt J. (Nt. Sci.) 48(5) Mteril properties The mteril properties of the corticl nd cncellous ones otined from Reilly nd Burstein (1975) nd Pcific Reserch Lortories (2002) re provided in Tle 3. Boundry conditions The contct res on the distl end of the tii were modeled ccording to the studies of Kur et l. (1998) nd Wn et l. (2006). Figure 7 shows these contct res on the distl end of the FEMs specified y Kur et l. (1998) which were mm 2 for femle nd mm 2 for mle. Figure 8 shows the contct res on the distl end of the FEMs specified y Wn et l. (2006) which were mm 2 (39.93% of the rticulr surfce) for femle nd mm 2 (41.41% of the rticulr surfce) for mle. Therefter, compressive nd posterior sher forces estimted from three ody weights consisting of 40, 60 nd 80 kg from Ssimontonkul et l.(2007) were pplied to the FEM to oserve the effect of weight ering (Tle 4). The fixed contct res on the proximl end of tiis were modeled ccording to the study of Eisenhrt-Rothe et l. (2003). Figure 9 shows these fixed contct res which totled mm 2 for oth femle nd mle ptients. At 30 o knee flexion, the centroids of the fixed contct Tle 3 Mteril properties of tiil ones (Reilly nd Burstein, 1975; Pcific Reserch Ls Inc. (2002). Bone type Young s modulus (GP) Poisson rtio Density (kg.m -3 ) Corticl one ,700 Cncellous one Contct re Contct re Figure 7 Contct res on the distl end of tii specified y Kur et l. (1998): () Femle ptient; () Mle ptient. Contct re Contct re Figure 8 Contct res on the distl end of tiis specified y Wn et l. (2006): () Femle ptient; () Mle ptient.

7 Ksetsrt J. (Nt. Sci.) 48(5) 735 res were 3.2 mm elow the centroid of the medil condyle nd 2.2 mm ove the centroid of the lterl condyle. During o knee flexion, the centroids of the fixed contct res were 0.9 mm elow the centroid of the medil condyle nd 3.5 mm ove the centroid of the lterl condyle. RESULTS Figure 10 shows the contour plot of von Mises stress of the vlidted model. The mximum von Mises stress found t the fixed end ws 9.06 MP which yielded n error of less thn 1.3%. Figure 11 shows the plot of mximum von Mises stress versus the numer of elements for femle ptient (cse study 5) nd mle ptient (cse study 17) to vlidte the FE models. It ws found tht the numers of elements in the FEMs were greter thn 14,000 elements for the tiil one of the femle ptient while there were 12,800 elements for the tiil one of the mle ptient. The mximum von Mises stresses for cse studies 1 24 re shown in Tles 5 nd 6. Figures 12 nd 13 show the von Mises stress distriutions on the tiil surfces for cse studies DISCUSSION The FEMs show tht the cse studies with the contct re specified y Wn et l. (2006) yielded higher mximum von Mises stresses thn ones with the contct re specified y Kur et l. (1998). This might hve resulted from the fct tht the contct res of Wn et l. (2006) were smller thn those of Kur et l. (1998). Moreover, Tle 4 Applied forces on the contct re on the distl end of the tii. Body weight (kg) Compression force (N) Posterior sher force (N) 40 3, , , Fixed c Fixed d Fixed Fixed Figure 9 Fixed contct res on the proximl end of tii: () Femle ptient with 30º knee flexion; () Femle ptient with 30 90º knee flexion; (c) Mle ptient with 30º knee flexion; (d) Mle ptient with 30 90º knee flexion.

8 736 Ksetsrt J. (Nt. Sci.) 48(5) Mximum von Mises stress (MP) Mle Femle Figure 10 Contour plot of the von Mises stress distriution (MP) in the vlidted model ,000 20,000 30,000 40,000 50,000 60,000 70,000 Numer of elements Figure 11 Numer of elements versus mximum von Mises stress for femle ptient (cse study 5) nd mle ptient (cse study 17) with the contct re specified y Kur et l. (1998), o knee flexion, nd kg ody weight. Tle 5 Mximum von Mises stresses t 30 o knee flexion for different mle nd femle ody weights. Body weight (kg) Mximum von Mises stress (MP) Kur et l. (1998) Wn et l. (2006) Femle Mle Femle Mle Tle 6 Mximum von Mises stresses during 30 o -90 o knee flexion different mle nd femle ody weights. Body weight (kg) Mximum von Mises stress (MP) Kur et l. (1998) Wn et l. (2006) Femle Mle Femle Mle

9 Ksetsrt J. (Nt. Sci.) 48(5) 737 the mximum von Mises stress found on the tii of the femle ptient ws higher thn on the mle ptient since the contct re on the distl end of the femle ws smller thn on the mle. For the cse studies with 30 o knee flexion, the mximum von Mises stresses were found t the middle of the posterior tii. However, for the cse studies with o knee flexion, the loction of the mximum von Mises stresses shifted little more towrd the medil tii. As the ody weight incresed, the mximum von Mises stress incresed. For mle ptient, the knee flexion ngle hd little impct on the mximum von Mises stress. However, for femle ptient, the mximum von Mises stress incresed s the knee ngle incresed. Figure 12 Von Mises stress distriution (MP) on tiil surfce of femle ptient for cse studies l.

10 738 Ksetsrt J. (Nt. Sci.) 48(5) CONCLUSION The tii models consisting of corticl nd cncellous ones were successfully constructed using CT imges. The stress distriutions in the tii of two osteoporosis ptients were studied using FEM nlyses. It ws found tht the mximum von Mises stress occurred ner the middle of the posterior tii. The mximum von Mises stress found on the tii of the femle ptient ws higher thn for the mle ptient. As the ody weight incresed, the mximum von Mises stress incresed. Moreover, the FEM using the contct re specified y Wn et l. (2006) resulted in % (femle ptient) nd % (mle ptient) greter mximum von Mises stress compred with using contct res specified y Kur et l. (1998). Figure 13 Von Mises stress distriution (MP) on tiil surfce of mle ptient for cse studies m x.

11 Ksetsrt J. (Nt. Sci.) 48(5) 739 ACKNOWLEDGEMENTS The uthors cknowledged Phrmongkutklo Hospitl for the kind provision of CT imges nd Ntionl nd Mteril Technology Center (MTEC) for the use of the softwre progrms. LITERATURE CITED Eisenhrt-Rothe R.V., M. Sieert, C. Bringmnn, T. Vogl, K.H. Englmeier nd H. Grichen A new in vivo technique for determintion of 3D kinemtics nd contct res of the ptello-femorl nd tiio-femorl joint. J. Biomech. Eng. 37: Khmpkdee. M Anlysis of the Stress on Femorl Hed Ischemi Using Finite Element Method. MSc thesis, Srinkhrinwirot University, Bngkok, Thilnd. Kur, H., H.B. Kitok, Z.P. Luo. And K. A. An Mesurement of surfce contct re of the nkle joint. Clin. Biomech. 13: Ntionl Institute of Helth Osteoporosis. [Aville from: medlineplus/osteoporosis.html]. [Sourced: 6 August 2014] Pcific Reserch Ls Inc Biomechnicl Testing Mteril. [Aville from: secure.swones.com/product/io/composite. sp]. [Sourced: 3 April 2002]. Reilly, D.T. nd A.H. Burstein, The elstic nd ultimte properties of compct one tissue. J. Biomech. Eng. 8: Ssimontonkul, S. B.K. By nd M.J. Pvol Bone contct forces on the distl tii during the stnce phse of running. J. Biomech. Eng. 40(15): Wn. L, R.J. de Asl, H.E. Rush nd G.Li Determintion of in-vivo rticulr crtilge contct res of humn tlocrurl joint under weight-ering conditions. Osteorthritis nd Crtilge 14:

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