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A Numerical Model of Total Shoulder Arthroplasty for Implant Reaction Forces Estimation

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A Numerical Model of Total Shoulder Arthroplasty for Implant Reaction Forces Estimation
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  A Numerical Model of Total Shoulder Arthroplasty for Implant Reaction Forces Estimation (Lauranne) Sins 1,2,3 , (Pierre-Olivier) Lemieux 1,2 , (Patrice) TŽtreault 3 , (Natalia) Nu–o 1, 2 , (Fabien) Billuart 4 , (Nicola) Hagemeister 1, 2, 3   1 ƒcole de technologie supŽrieure (ETS), MontrŽal (QC), Canada 2 Laboratoire de recherche en imagerie et orthopŽdie (LIO), MontrŽal (QC), Canada 3 Centre de recherche du centre hospitalier de lÕUniversitŽ de MontrŽal (CRCHUM), H™pital Notre-Dame, MontrŽal (QC), Canada 4 Ceraver, Roissy, France Introduction During shoulder implant conception, the knowledge of prosthetic head translations and forces acting on the artificial joint during shoulder movement is an important aspect. In fact, prosthetic head translation is increased in shoulder arthroplasty, compared to the normal joint, due to the absence of passive structures [1]. In recent finite element models, this aspect has been the matter of research [2]. However, these analyses are very complex and time consuming. A more simple solution is the use of inverse dynamic musculoskeletal studies as with the Anybody Modeling System. But the current computational musculoskeletal models simulate neither humeral head translation nor joint contact between two implant surfaces. Currently the way to evaluate the total glenohumeral joint reaction force (GH-JRF) is to calculate it as the sum of all muscular, ligamentous, inertia and external forces at the center of rotation of the humeral head. This GH-JRF is enforced by 2 constraints; one that enforces the humeral head to stay inside the glenoid cavity and another that neglects humeral head translation [3]. The objective of this study was to develop an inverse dynamic computational model of a total shoulder arthroplasty allowing the estimation of 1) prosthetic head displacements, 2) reaction forces at the prosthetic head Ð glenoid implant interface, and 3) muscular forces, especially the deltoid. Methods The present model was developed using the AnyBody Modeling System (ver 5.0.1, AnyBody Technology A/S, Aalborg, Danemark), based on the arm and shoulder morphologies of the Delft shoulder group [4]. An elevation in the scapular plane from 15¡ to 120¡ was simulated using the International Society of Biomechanics (ISB) coordinates systems [5]. The combined movements of three bones (humerus, scapula and clavicle) were based on linear regression coefficients [7], while the hand was constrained to stay in the plane form by three scapular anatomical landmarks (angulus inferior, trigonum spinae, angulus acromialis). In order to compute the reaction force (GH-JRF), a surface force contact algorithm was implanted into our model, adapted from a previous study on the knee [8]. It implies implementation of two contacting STL surfaces of the total shoulder arthroplasty (Ulys prosthesis, Ceraver, Roissy, France) to calculate penetration. A pressure module between both surfaces was set at 8.5e8MPa, defining a linear law between penetration volume and force. The GH-JRF, resulting from the penetration between the 2 surfaces, is a 3D force vector located at the center of pressure. Unlike the current models, no constraints were applied on the humeral head translations. Rather, a force dependant kinematics algorithm available in the version 5.0.1 of Anybody was used. This algorithm allows reproducing the elastic deformations of a joint. To achieve the analysis, the constraint enforcing the head to stay inside the glenoid cavity was removed. Linear springs with stiffness !  acting in the opposite direction of the deformation were added to avoid divergence. In the present study, this deformation was defined in the anterior-posterior (x-axes) and inferior-superior (y-axes) directions of the glenoid plane ( !  ! !""" ! ! ! ) (Figure 1). Figure 1: Glenoid plane  Results The computed humeral head translations were 2.8mm in both the Anterior-Posterior and Inferior-Superior directions. The Figure 2 shows the pattern of displacement during the simulated motion, visualized in the x-y plane of the implant glenoid. The maximum deltoid resultant force is about 350N at 95¡ of abduction. Figure 2: Humeral head displacement during abduction Discussion The observed translations are comparable to what was measured in vivo which was about 2mm in both AP and IS directions [9]. The deltoid forces are of the same order of magnitude than previous experimental studies (300N for 75¡ of abduction) [10]. One limitation of the present study is the fact that the model allows to predict only small humeral head translation. The model needs to be improved to predict higher translations, which may occur while simulating pathological situations involving GH instability. These results show that the musculoskeletal model presented here is promising. However, the simulated kinematics may be not representative of the complex tasks performed on a daily basis. Thus, the present model should now be used to explore more complex movements, such as hair combing and reaching a top shelf. A recent study has shown that these movements require a complex interaction of humerus plane of elevation, elevation and axial rotations [13]. This complex interaction may lead to different patterns of contact force and humeral translations. Conclusion This study is a first proposal to include prosthetic head translations into a musculoskeletal model and to allow estimation of contact surface between two shoulder implant surfaces. These aspects are key points to evaluate glenoid loosening, which is the most important complication in shoulder arthroplasty [11]. The cause of this issue is related by the so-called Òrocking horse effectÓ, which is a series of several phenomena [12]. First, the prosthetic head translations are increased compared to an intact shoulder [9]. Since the translations are increased, the humeral head generates forces on the glenoid implant rim, producing a rotational movement especially with respect to an anterior-posterior plane. The present musculoskeletal model will allow exploring the effect of glenoid implant design on this phenomenon by implementing several designs of glenoid implant. Acknowledgements The authors would like to thank the Fonds de recherche Nature et technologies QuŽbec (FQRNT) which funded this research References Makhsous, et al. (2001). Engineering in [1]Medicine and Biology Society, Proceedings of the 23rd Annual International Conference of the IEEE. Istanbul. pp. 1500-1503. Terrier, A., et al. (2008). Medical [2]Engineering & Physics, 30(6), 710-716. Lemieux, P. O., Hagemeister, N., TŽtreault, [3]P., & Nu–o, N. (2012). Comput. Methods Biomech. Biomed. Engin Van der Helm, F. C. T. (1994). J Biomech. [4]27(5), 527-550 Wu, G., et al. (2005). J Biomech, 38(5), 981-[5]992. Ludewig, P., et al. (2009). J Bone Joint Surg [6]Am, 91(2), 378-389. De Groot, J. H., & Brand, R. (2001). Clin [7]Biomech, 16(9), 735-743 Bei, Y., & Fregly, B. J. (2004). Medical [8]engineering & physics, 26(9), 777-89. Graichen, H., (2005). Journal of [9] biomechanics, 38(4), 755-60. Wuelker, et al. (1995). J Biomech, 28(5), [10]489-499. Bohsali, K. I., Wirth, M. a, & Rockwood, C. [11]A. (2006). The Journal of bone and joint surgery. American volume, 88(10), 2279-2292 Franklin, J.L., et al. (1988). J Arthroplasty, [12]3(1), 39-46. Van Andel et al. (2008).. Gait & Posture, [13]27(1), 120-127.
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