MULTIOBJECTIVE SHAPE OPTIMIZATION STRATEGY TO INCREASE PERFORMANCE OF HOLLOW STEMS USED IN ARTIFICIALLY REPLACED HIP JOINTS

Transcription

1 Internatonal Journal of Mechancal Engneerng and Technology (IJMET) Volume 9, Issue 11, November 2018, pp , Artcle ID: IJMET_09_11_082 Avalable onlne at ISSN Prnt: and ISSN Onlne: IAEME Publcaton Scopus Indexed MULTIOBJECTIVE SHAPE OPTIMIZATION STRATEGY TO INCREASE PERFORMANCE OF HOLLOW STEMS USED IN ARTIFICIALLY REPLACED HIP JOINTS Ghas Kharmanda Department of Bomedcal Engneerng, Lund Unversty, Lund, Sweden Imad Antypas and Alexey Dyachenko Department of desgn prncples of machnes, Don State Techncal Unversty, Rostov-on-Don, Russan Federaton ABSTRACT The artfcal replaced hp jont represents the major success story n orthopedc surgery n the twenteth century; there s much nterest n extendng research on hp jont even further. The stress dstrbuton n the dfferent bone tssues of a femur s sgnfcantly altered after an artfcal replacement. Thus, there s a strong need to ncrease the prosthess performance consderng several crtera. A new multobjectve shape optmzaton strategy s presented to ncrease the performance of the hollow stems used n the artfcally replaced hp jonts. Two stem models are consdered n ths study: sold and hollow stems. The shape optmzaton presents the detaled desgn stage when studyng the hp prostheses n order to mprove ther performance. Several objectves are consdered, that leads to develop a new multplcatve formulaton as a performance scale to defne the best compromse between several requrements. Numercal applcatons consderng several daly loadng cases, s presented out to show the advantages of the hollow stem model relatve to the sold one. When consderng the hollow stem, the developed multobjectve functon s reduced almost 46% relatve to the sold stem. It s shown that from an optmzaton of the stress levels usng a new goal functon and consderng several daly loadng cases, t s concluded that t s possble to obtan a more unform stress dstrbuton. In addton, t s found that a sgnfcant ncrease of the stress levels around the metal/bone nterface s obtaned, leadng to favorable remodelng process Keywords: Hp prosthess, Hollow stem, Sold stem, Shape optmzaton. Cte ths Artcle Ghas Kharmanda and Imad Antypas and Alexey Dyachenko, Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts, Internatonal Journal of Mechancal Engneerng and Technology, 9(11), 2018, pp edtor@aeme.com

2 Ghas Kharmanda and Imad Antypas and Alexey Dyachenko 1. INTRODUCTION The number of total hp replacements s growng, wth over 800,000 beng carred out annually. The ncrease s partcularly notceable for younger people, who n general are more actve and therefore mpose larger and more frequent loads on the jont than the more tradtonal elderly people. Prostheses for young persons are therefore prone to falure; leadng to an ncreased ncdence of early revson operatons [1]. The technology of artfcal jont replacements has evolved rapdly over the last forty years and has become an overwhelmng success [2]. Artfcal hp replacement can lead to a dramatc relef of pan and restoraton of the jont functons for patents sufferng from osteoarthrts, rheumatod arthrts, congental deformtes or post traumatc dsorders [3]. The most frequently afflcted jont s the hp, whch s replaced wth a metallc jont. Ths replacement represents a major success and there s an nterest n extendng research on hp jont even further. The natural stress dstrbuton n the bone tssue of a femur s sgnfcantly modfed after a hp replacement [4]. The stress reducton n the bone due to the hgh elastc modulus of the mplants s referred as stress sheldng. It has been found that stress sheldng n the adjacent bone could result n consderable dsuse osteopoross, subsequently leadng to loosenng of the prosthess. Therefore, t s hghly desrable that the stress dstrbuton n the bone adjacent to the prosthess should be unform, because t provdes a physologc stmulus for bone. Furthermore, to avod resorpton of the bone tssue the mnmum stress level n the bone tssues should not be less than a threshold value [5]. Several conceptual stem desgns can be consdered [6]. One parameter n the stem desgn s the outer geometry of the stem. Here, the rectangular secton stems allowng a secure daphyseal press-ft n the frontal plane of the femoral canal wll be consdered. In contrast to a crcular stem, the rectangular desgn provdes superor rotatonal stablty and ncreases the mechancal fxaton as well as reduces wear [7; 8]. A second choce related to the geometry s to consder that a shouldered stem has been shown by Kharmanda et al. [9] to lead to a reducton of the maxmum stress n the dfferent bone tssues relatve to the non-shouldered stem. The thrd choce concerns the materal selecton. Kharmanda et al. [9] concluded that the ttanum alloy (T-6Al-4V) for both cup and stem, and ceramc alloy (Al2O3) for both lner and ball provdes mnmum stress transfer to adjacent bone regon. Ths result has been valdated by experments [10; 11]. In ths paper, shape optmzaton concept s ntegrated nto stem desgn n order to mprove overall mplant-bone performance. A multobjectve functon s proposed to mprove the structure performance by: maxmzng the mnmum stress of metal/bone nterface, mnmzng the stress ntervals and maxmzng the complance. Numercal examples llustrate the potental of the proposed strategy and also the mportance of the optmzed hollow stem. 2. LITERATURE REVIEW Several optmzaton strateges have been developed to study the relaton between cementless hp stems performance and desgn: Huskes and Boeklagen [12] frst ntroduced a method for shape optmzaton, whereby the fnte element method s used teratvely to determne optmal prosthetc desgns. An optmal load-transfer mechansm s used to avod stress concentratons. Katouzan and Davy [13] proposed a method to mnmze the stress n bone adjacent to stem. Next, Chang et al. [14] proposed to mnmze the dfference between the stran energy densty of the ntact femur and the mplanted bone edtor@aeme.com

3 Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts El-Shekh et al. [15] optmzed both desgn and materal selecton n load-bearng components n artfcal hp jonts. In these optmzaton procedures new stem desgns were obtaned consderng only one performance crteron. However, Fernandes et al. [16] developed a mult-crtera shape optmzaton procedure and appled t to two-dmensonal models. From pont of vew mult-objectve optmzaton, Ruben et al. [17] proposed a double objectve functon takes nto account the ntal stablty of the femoral stem and the effect of stress sheldng on bone adaptaton after the surgery. An addtve formulaton was proposed wth coeffcent calbraton technques. However, Kharmanda [6; 18] proposed a multplcatve form s proposed as an effcent technque for 2D and 3D problems where the desgn choce s the Austn Moore stem. Austn Moore (AM) prosthess, hstorcally, has served as a good mplant over the years n the management of femoral neck fracture n elderly. Ths prosthess s wdely used n hosptals and clnc due to ts low cost and smple surgcal procedure and satsfactory prognoss [19]. The Improved Austn-Moore (IAM) proposed by Kharmanda [6] leads to a good performance relatve to sold one. However, two man drawbacks can be observed n ths model. Frst, the 2D geometrc model of the set mplant/bone s not correct. There s a gap between trabecular bone and the stem that s not realstc. The marrow cavty seems to be too large. Wth ths confguraton the half bottom of the stem s structurally useless. Second, the ball should be consdered durng the optmzaton process to take nto account the appled force poston. Therefore, n the current paper, a multplcatve form s proposed as an effcent technque to provde the best compromse between several crtera. The gap between cancellous (or trabecular) bone and the stem s modfed and the ball effect s also consdered snce the locaton of the forces nduce bendng state durng the optmzaton process. 3. MATERIALS & METHODS 3.1. Hp and stem modelng An llustraton of the hp replacement s shown n Fg. 1 where both a sold stem and a hollow stem are consdered. For smplcty the hole n Fg. 1 s represented by a crcular hole. The stem n both cases s assumed to be made of ttanum-based alloy (T-6Al-4V) and the ball by a ceramc alloy (Al2O3). The ball part of the hp replacement s also shown n Fg. 1 as ths s an mportant part when consderng the loadng condtons,.e. the locaton of the forces s mportant snce t nduce bendng state that must carred by the bone part. For smplcty as the purpose of ths work s to ndcate the possbltes when usng shape optmzaton n the desgn of stems a 2D model s consdered. As already ndcated n ths study a hollow stem s consdered and ts nfluence on the stress dstrbuton s consdered. The shape optmzaton approach s employed to fnd the best shape of the hole such that an optmal desgn can be found wth respect to an optmzed objectve functon edtor@aeme.com

4 Ghas Kharmanda and Imad Antypas and Alexey Dyachenko a b c Fgure 1: Illustraton of a) 3-dmensonal stem, b) the 2-dmensonal sold stem and c) the 2- dmensonal hollow stem. The ball part of the hp replacement s also llustrated 3.2. Mechancal propertes It s well-known that bone tssues possess a complcated mcrostructure [20; 21]. The bone also adapts to the actual loadng and thus s n general heterogeneous and ansotropc. In the present analyss, the materal propertes of bone have for smplcty been assumed as lnearly elastc and sotropc [22]. The mechancal propertes of human bone vary wth sex, age, race, and many other factors. Senapat and Pal [19] smulated the uncemented hp jont usng the elastc propertes lsted n Table 1. In ths work, the marrow tssue s neglected because t s not consdered n a sold state [23; 24]. Table 1: Propertes of dfferent studed layers [MPa] [MPa] [MPa] Al 2O 3 Alloy T-6Al-4V Alloy Cortcal tssue Cancellous tssue Marrow tssue The performance of a hp replacement s drectly related to the ablty to transfer the load unformly from the components to the surroundng bone. A regon of the bone whch s whch s subject to low load levels wll undergo resorpton (Wolf s law [25]) whch wll lead to loosenng and eventually loss of functonalty of prostheses. For ths reason, the mnmum stress value n the surroundng bone has to be kept above a certan mnmum levels. The mnmum stress s related the natural Stran Energy Densty (SED). For lnear elastcty, the SED can be wrtten as: = 1 2 :: (1) where s the stran tensor and s the elastc tensor. Accordng to Huskes et al. [26], the natural SED s estmated at the perosteal bone surface as: = MPa. On the bass of Eq. (1), the mnmum stress value can be computed as follows: edtor@aeme.com

5 Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts = 2 (2) where s the unaxal Young s modulus. To ensure long-term fxaton, the mnmum stress value n the surroundng bone has to exceed the threshold value Boundary condtons Rudman et al. [27] demonstrated that when lgamentous and muscular forces are ncluded, the stresses n proxmal femur are predomnantly compressve. Ths would appear to make better use of the mechancal propertes of bone, whch s stronger n compresson than n tenson [28]. For example, the Ultmate Tensle Strength equals to 132 MPa whle the Compressve Strength s 192 MPa [28]. In the present work three representatve daly loadng condtons of one-legged stance (L1), extreme ranges of moton of abducton (L2), and adducton (L3) are assumed [29], as shown n Fg. 2. a b c Fgure 2: a) One-legged stance case (L1), b) Abducton case (L2), and c) Adducton case (L3) The objectve of fxaton s to elmnate the relatve moton between loaded mplant and supportng bone, to produce an acceptable lmt of contact stresses on bone, and mantan the stresses n bone close to the normal physologc pre-mplantaton level. For a sold stem, ngrown fxaton by tssue should happen by the bone growth nto porous portons of coated stem [30] Shape optmzaton process Let us frst start wth defnng our desgn varables denoted ( = 1,...,). In the present study these varables are related to the shape of the hole n the stem. These desgn varables are allowed to change durng the optmzaton process such that a best soluton for a certan objectve. Based on ths, we seek to realze four ams: The frst one s to maxmze the mnmum stress value n the surroundng bone. As dscussed n relaton to Eq. (1) and Eq. (2), the mnmum stress n the bone tssue has to exceed a crtcal threshold value. Ths crteron s of major mportance at the nterface between the bone and the mplant snce bone resorpton potentally can lead to loosng of the mplant. Therefore, our goal s to fnd a desgn that maxmzes the stress level at the nterface. The second and thrd objectves are to mnmze cortcal and cancellous stress ntervals (the dfference between the maxmum and mnmum stress values) such that a homogeneous stress dstrbuton n both cortcal and cancellous tssues s obtaned. Stress concentratons n the bone materal wll not be optmal snce non-standard load cases mght lead to fracture and also resorpton of the bone tssue. In addton, low stress level n the nteror of the bone tssue mght also lead to bone resorpton. Snce our objectve s to fnd a desgn such that the stress dstrbuton s homogeneous the dfference between the maxmum and the mnmum stress level wll be mnmzed. The mplant wll due to the hgher stffness of metal lead to a stffenng of the bone edtor@aeme.com

6 Ghas Kharmanda and Imad Antypas and Alexey Dyachenko mplant assembly. To show the generalty of the presented strategy, the stffness s ncluded n the objectve functon. Instead of makng use of the stffness, we maxmze the complance:!"#$%& = '( ).'* ) (3) where '( ) s force vector and '* ) s the dsplacement such that the natural stuaton s approached. The objectves can be summarzed as: 1 / '+ ( )) = 0 / 9:; /6 7 23!$?@A7?@A B7A <?CBDE7@AFG(H 7 ) 4/6 where all stresses are von Mses effectve stresses. Moreover, 7 23 s the mnmum stress at 9:; the metal/bone nterface, 7 9:; and 7 23 are the maxmum and mnmum stress n the cortcal 9=3 bone, fnally 7 9=3 and 7 23 are the maxmum and mnmum stress n the cancellous bone. In addton to these objectves addtonal constrants are also of conduced mportance such as: the maxmum stresses must be lower than the correspondng allowable stresses (metal and bone layers), the mnmum stress at the metal bone nterface must be hgher than the target stress values, the complance should be close to the target one, the dmenson boundares. The objectves summarzed n Eq. (4) are formulated n a sngle objectve usng a multplcatve format. In our prevous works [2], the multplcatve format has been shown to verfy the optmalty condtons and has been appled on several mult-objectve optmzaton problems. The mathematcal formulaton of ths problem can be wrtten as follows: mn : F( x ) = s. t. : x U : g ( x ) = σ 1 : g ( x ) = σ 2 K / J / I Cor Cor Can Can ( σ ( x ) σ ( x ))(. σ ( x ) σ ( x )) Cor max Can max : g ( x ) = σ ( x ) σ 3 T : g ( x ) = σ 4 : g ( x ) = σ 5 M max Ball max x x L Complance( x ( x ) σ ( x ) σ Cor w Can w M / B mn ( x ) σ ( x ) σ M w Ball w ( x ) 0 ( x ) 0 ( x ) T max M / B ). σ mn : g ( x ) = Complance( x ) C 0 6 max where +( ) s a composte objectve functon form and are the desgn varables whch n the present problem are bounded between lower L and upper M values. ( ) s the target 4 stress value dscussed n Eq =NN and 7 are respectvely the maxmum von Mses stress values n the metallc stem and n ceramc ball. 4 6 O and O are respectvely the allowable stress values of the stem and ball materals. mn ( x ) mn (4) (5) edtor@aeme.com

7 Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts 4. RESULTS 4.1. Bone complance smulaton Fnte element smulatons allow us to fnd the complance (nverse of rgdty) and the stress feld. When ntroducng the mplant, we seek to preserve the orgnal stffness. Fgs. 3a, b and c show the von Mses stress dstrbuton for dfferent studed cases of the orgnal bone. For the three studed case, the maxmum stresses are respectvely located on the ball, on the neck and on the lower femoral bone cut secton. a b c Fgure 3: von-mses dstrbuton for the three loadng cases a) L1, b) L2 and c) L3 The complance of the second case s bgger than the frst one although the von Mses stress lmts are smaller. Table 4 Results for the bone wthout stem usng the three studed cases Output Parameters L1 L2 L3 9:; (MPa) =3 (MPa) :; 23 (MPa) (MPa) (N.m) Shape optmzaton results Fgs 4a and c show smplfed 2D geometrcal models for the studed sold stem and the resultng optmzed one wth cortcal and cancellous bone tssues. Fg. 4c shows the 8 desgn varables (coordnates x and y) edtor@aeme.com

8 Ghas Kharmanda and Imad Antypas and Alexey Dyachenko a b c Fgure 4 Geometry models for a) sold stem, b) parameterzed hole, and c) hollow one We frst study the three dfferent loadng cases L1, L2 and L3 beng presented n Fg. 1 n order to fnd the most crtcal loadng case. Fg. 5a shows smplfed boundary condtons and mesh models for the frst and thrd loadng cases (L1 and L3). Fg. 5b shows smplfed boundary condtons and mesh models for the second loadng case L2. Accordng to Table 5, the thrd loadng case s most dangerous one because the maxmum stress n the cancellous bone s the closest to the yeld stress (Table 3). As a consequence, the shape optmzaton of the hollow stem s appled on the thrd case. Fg. 5c shows smplfed boundary condtons and mesh models of the optmzed hollow stem when consderng the thrd loadng case L3. a b c Fgure 5: a) Boundary condtons for L1 and L3, b) Boundary condtons L2, and c) Boundary condtons for hollow stem when consderng L3 Fgs. 6a, b and c show the von-mses stress dstrbuton for the three loadng cases of the mplant-bone study. Fgure 6d shows the von-mses stress dstrbuton of the optmzed hollow stem edtor@aeme.com

9 Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts a b c d Fgure 6: Stress dstrbuton for bone layers a), b), c) for three loadng case L1, L2 and L3 for sold stem, and d) for hollow stem Table 5 Smulaton of sold and hollow stems for dfferent loadng cases Output Sold Stem Hollow Parameters L1 L2 L3 Stem 9:; (MPa) =3 (MPa) (MPa) (MPa) :; (MPa) (MPa) /6 (MPa) !"#$%&( ) Objectve DISCUSSION AND CONCLUSIONS To ncrease the performance of hp replacement, t s the objectve to obtan a unform transfer of loads from the stem to all surroundng bone tssues. Shape optmzaton s used to fnd the optmal poston of the hole coordnates to facltate homogenous stress dstrbuton (smooth nner hole boundares). Based on the numercal smulaton, t s concluded that the hollow stem leads to a sgnfcant ncrease of the mnmum stress value at the metal/bone nterface to be: MPa. When ncreasng ths value, the bone resorpton s reduced accordng to Wolf s law [25]. Furthermore, the complance of the hollow stem s also ncreased relatve to the sold stem. In order to mprove the complance to be closer to the orgnal one, szng and materal optmzaton should be ntegrated n the desgn process. In addton, the bone stresses are reduced relatve to the bone smulaton wthout stem (Table 4). Fnally, t can be noted that the objectve functon s reduced by 46% takng nto the stress nterval reducton and the metal/bone stress nterface ncrease. Furthermore, the major mportance becomes very sgnfcant after the bone ngrowth nto the holes (healng perod). To model the phenomena of the ngrowth of bone, a 3D optmzaton process should be carred out. To start our optmzaton developments, several ponts are consdered from the prevous works [6]. After that, the advantage of the hollow stem s demonstrated relatve to the sold one usng shape optmzaton process. The optmum hole dstrbuton leads to more relable fxaton relatve to the sold stems wth porous coated surfaces. The numercal valdaton usng shape edtor@aeme.com

10 Ghas Kharmanda and Imad Antypas and Alexey Dyachenko optmzaton technology shows the mportance of optmum hole dstrbuton nto stem desgn. Ths promsng result allows us at least to parameterze and optmze the nner stem geometry that leads to control the stress dstrbutons and ncrease the mnmum stress value at the metal/bone nterface relatve to sold stem. The great mportance s to largely reduce the bone stresses after healng perod. As a perspectve, t wll be very mportant to develop a mathematcal model descrbng the ngrowth of bone nto holes durng the healng perod. The use of shape optmzaton technology shows the mportance of optmum hole n the stem desgn. Numercal applcatons on dfferent loadng cases show the advantages of the ntegraton of the shape optmzaton strategy nto the hollow stem desgn. In addton, t s very mportant to ntegrate the uncertanty concepts when consderng more complex loadng schemes that may appear n the real-lfe events. For example, the dynamc of movements (.e. gat cycle) can be consderng surgcal constrants to mprove both of performance, relablty and durablty. ACKNOWLEDGEMENTS The authors would lke to acknowledge Pr. Mathas Walln from Lund Unversty for hs valuable dscusson and comments n the optmzaton aspects. REFERENCES [1] Gross, S. and Abel, E. W. A fnte element analyss of hollow stemmed hp prostheses as a means of reducng stress sheldng of the femur. Journal of Bomechancs, 34, 2001, pp [2] Kharmanda, G. and El-Ham, A. Bomechancs: Optmzaton, Uncertantes and Relablty, ISTE & Wley, January 2017, pp. 254, ISBN: [3] Babanamansour, P., Ebrahman-Hossenabad, M. and Zargar-Kharaz, A. Desgnng an Optmzed Novel Femoral Stem. Journal of Medcal Sgnals and Sensors, 7(3), 2017 Jul-Sep., pp [4] Herrera, A., Rebollo, S., Ibarz, E., Mateo, J., Gabarre, S. and Graca, L. Md-Term Study of Bone Remodelng After Femoral Cemented Stem Implantaton: Comparson Between DXA and Fnte Element Smulaton. The Journal of Arthroplasty, 29, 2014, pp [5] Kharmanda, G. Relablty analyss for cementless hp prosthess usng a new optmzed formulaton of yeld stress aganst elastcty modulus relatonshp. Materals and Desgn, 65, January 2015, pp [6] Kharmanda, G. Integraton of mult-objectve structural optmzaton nto cementless hp prosthess desgn: Improved Austn-Moore model. Computer Methods n Bomechancs and Bomedcal Engneerng, 19(14), 2016, DOI: / [7] Gonzalez, C. D. Probablstc Fnte Element Analyss of Un-cemented Total Hp Replacement. PhD thess. School of Engneerng Scences, Boengneerng Scences Research Group, Unversty of Southampton, March [8] Bae, J. Y., Farooque, U., Lee, K. W., Km, G. H., Jeon, I. and Yoon, T. R. Development of hp jont prostheses wth modular stems. Computer-Aded Desgn, 43, 2011, pp [9] Kharmanda, G., Mulk, S. and Sabsab, Y. Compter-Aded Desgn of Internal Replacement Models In Orthopedcs Surgery. Research Journal of Aleppo Unversty, seres of Engneerng Scences, 105, 2012, pp [10] Garno, J.-P. Modern ceramc-on-ceramc total hp systems n Unted State. Clncal Orthopaedcs, 379, October 2000, pp. 41. [11] Knahr, K. and Pospschll, M. Revson Strateges n Total Hp Arthroplasty wth Regard to Ceramc Artculatons. European Musculoskeletal Revew, 2006, pp s_pdfs/knahr_0.pdf [12] Huskes, R. and Boeklagen, R. Mathematcal shape optmzaton of hp prosthess desgn. J. Bomechancs, 22(8/9), 1989, pp [13] Katouzan, H. and Davy, D. T. Three-dmensonal shape optmzaton of femoral components of total hp prostheses. Boengneerng Conference ASME, 24, 1993, pp edtor@aeme.com

11 Multobjectve Shape Optmzaton Strategy to Increase Performance of Hollow Stems Used n Artfcally Replaced Hp Jonts [14] Chang, P. B., Wllams, B. J., Bhalla, K. S. B., Belknap, T. W., Santner, T. J., Notz, W. I. and Bartel, D. L. Desgn and analyss of robust total jont replacements: fnte element model experments wth envronmental varables. Journal of Bomechancal Engneerng, 123, 2001, pp [15] El-Shekh, H. F., MacDonald, B. J. and Hashm, M. S. J. Fnte element smulaton of the hp jont durng stumblng: a comparson between statc and dynamc loadng. Journal of Materals Processng Technology, , 2003, pp [16] Fernandes, P. R., Folgado, J. and Ruben, R. B. Shape optmzaton of a cementless hp stem for a mnmum of nterface stress and dsplacement. Comput Methods Bomech Bomed Eng, 7(1), 2004, pp [17] Ruben, R. B., Folgado, J. and Fernandes, P. R. On the optmal shape of hp mplants. Journal of Bomechancs, 45, 2012, pp [18] Kharmanda, G. and El-Ham, A. Relablty n Bomechancs. USA: ISTE & Wley, November 2016, pp ISBN: [19] Senapat, S.-K. and Pal, S. UHMWPE-alumna Ceramc Composte: a Proposed Metal Substtute for Artfcally Replaced Hp Jont. IE (I) Journal.MC, 85, January [20] Shokry, A. On the determnaton of dffuson coeffcents n bone, PhD thess, Lund Unversty, May [21] Shokry, A., Lndberg, G., Kharmanda, G. and Ståhle, P. A superposton procedure for calculaton of effectve dffuson and elastc parameters of sparsely porous materals. Journal of Transport n Porous Meda, 118(3), 2017, pp [22] Kharmanda, G. and Shokry, A. Investgaton and valdaton of a new optmzed yeld stress/elastcty modulus formulaton for bone fracture dentfcaton. Internatonal Conference on Mechancs of Complex Solds and Fluds, ICMCSF, Llle, France, May 17-22, [23] Kharmanda, G., El-Ham, A. and Ibrahm, M. H. Integraton of relablty and optmzaton concepts nto orthopedc prosthess desgn: Applcaton on hp prosthess desgn. Journal of Uncertantes and Relablty of Multphyscal Systems, 17-1, Jan DOI: /ISTE.OP [24] Kharmanda, G. and Antypas, I. Relablty-based desgn algorthm for artfcally replaced hp prosthess consderng materal property uncertanty. Internatonal Conference "Actual ssues of mechancal engneerng" 2018 (AIME 2018), Novosbrsk, Russa, Aprl [25] Wolff, J. The Law of Bone Remodelng. Berln Hedelberg, New York: Sprnger- Verlag, 1986 (translaton of the German 1892 edton). [26] Huskes, R., Wenans, H., Grootenboer, H. J., Dalstra, M., Fudala, B. and Slooff, T. J. Adaptve Bone-Remodelng Theory Appled To Prosthetc-Desgn Analyss. Journal of Bomechancs, 20, 1987, pp [27] Rudman, K. E., Aspden, R. M. and Meakn, J. R. Compresson or tenson? The stress dstrbuton n the proxmal femur. Bomedcal engneerng onlne, 5(12), Feb [28] Keaveny, T. M. Strength of Trabecular Bone. In: Cown S. C., ed., Bone Mechancs Handbook. Vol. 16. Second edton. London: CRC Press, 2001, [29] Beaupré, G. S., Orr, T. E. and Carter, D. R. An approach for tme-dependent bone modelngand remodelng-applcaton: a prelmnary remodelng smulaton. Journal of Orthopaedc Research, 8(5), 1990, pp [30] Ruben, R. B., Folgado, J. and Fernandes, P. R. Three-dmensonal shape optmzaton of hp prostheses usng a multcrtera formulaton. Structural and Multdscplnary Optmzaton, 34, 2007, pp edtor@aeme.com