PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

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Materials and Methods 3.2. Conclusions about the early analytical-kinetical models After the comprehensive review of these models, general conclusions have to be drawn in order to create a new model that is able to answer questions that until now have not been dealt with. In order to establish this new model, let us look at the main modelling questions and make decisions towards the model creation with a brief explanation. 1 st QUESTION: Which human locomotion should be modelled? ANSWER: Considering three simple facts, it is adequate to choose the locomotion of squatting: a) According to the studies of Reilly et al. [Reilly et al., 1972] and Dahlqvist et al. [Dahlqvist et al., 1982], the greatest magnitude of the patellofemoral forces (F pf, F pt , F q ) appears during squatting motion, b) Squatting is an frequently (everyday) practiced movement, which also has clinical importance as being a rehabilitation exercise, c) From the mathematical point of view, the squatting movement provides more possibility to create a simpler but accurate analytical model. For these reasons, the chosen locomotion is the squat. 2 nd QUESTION: Should numerical or analytical model be used? ANSWER: Although most of the earlier published mathematical models are considered as analytical models, only the work of Denham and Bishop [Denham and Bishop, 1978], Nisell et al. [Nisell et al., 1986] and Mason et al. [Mason et al., 2008] provide closed-form analytical solutions regarding the patellofemoral forces. The rest of the mathematical models describe the phenomenon by non-linear equation systems that make the calculation clumsy. In addition, if a numerical model is used, no closed form analytical correspondence can be created between the biomechanical factors such as patellar length-height, patellar tendon length or the anatomical angles. As a major aim of this thesis, an analytical-kinetical model will be created, thus the forces can be analytically derived from equilibrium equations. 3 rd QUESTION: Should we consider static of dynamic model? ANSWER: A significant question in the biomechanical research whether the human locomotion should be modelled with static or dynamic models. The static-dynamic choice actually depends more on the locomotion. Regarding the running, it is adequate that the model is dynamic since the motion is carried out rapidly, hence significant inertial forces may arise. In contrary, squatting is rapid only in special cases. The clinical relevance of the squatting on the one hand is a lower-extremity strengthening exercise, while on the other hand a postoperative ACL rehabilitation program. A mention must be made that for patients with total knee arthroplasty, rapid squatting is contraindicated. – 66 –
Materials and Methods For the sake of clarity, the following duration(s) can be credited to normal squat exercise: Innocenti et al. [Innocenti et al., 2011] reported 20 sec of descending time in their study from 0˚ to 120˚ of flexion angle, while Fukagawa et al. [Fukagawa et al., 2012] discovered age-related correlation about deep squat kinematics. Their findings showed that the average normal deep squat duration situates between 3 and 6 sec as a function of age. Due to the slow motion, how generally the squat is carried out, the inertial forces can be safely disregarded. This fact was more comprehensively confirmed by the study of Krabbe et al. [Krabbe et al., 1997], who dealt thoroughly with the importance of the inertial forces of the lower extremity joints (hip, knee and ankle) during running. They stated that the inertial forces could be neglected, if the horizontal velocity of the subject is not more than 5 m/s. During squatting, no horizontal velocity can be interpreted, but the average vertical speed is much lower than 5 m/s. Based on this fact, we can conclude that the inertial effect on the patellofemoral forces under squat movement can be neglected as well. Consequently, a static squat model will be used. 4 th QUESTION: Should two- or three dimensional model be used? ANSWER: Two-dimensional modelling is widely accepted and used in case of kinetic investigation, since the forces have their major effect in the sagittal plane and minor effect in the coronal plane [Singerman et al., 1994, Miller, 1991]. Furthermore, the change of the force-transmission can be explained as follows: the patellofemoral forces directly depend on the distance between the line of body weight (the centre of gravity line) and the instantaneous point of rotation of the patellofemoral joint [Schindler and Scott, 2011]. Figure 3.1. The patellofemoral forces and centre of gravity [Schindler and Scott, 2011] If the posture changes (e.g. leaning forward or backward), then this distance alters as well which leads to substantial changes in the force transmission. In the coronal plane this influence is negligible (Figure 3.1). Naturally, a three-dimensional model has the advantage that it is more similar to the real human knee joint. Nevertheless, according to the models in the literature [Wisman et al., 1980, Hirokawa, 1991, Hefzy and Yang, 1993], they are also more difficult to handle. As for the modelling point of view, regarding the patellofemoral and tibiofemoral forces, a twodimensional model can also provide accurate results with the advantage of easy handling. Thus, the new analytical-kinetical model is consequently two-dimensional. – 67 –
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SZENT ISTVÁN UNIVERSITY KINETICS A
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CONTENTS NOMENCLATURE AND ABBREVIAT
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NOMENCLATURE AND ABBREVIATIONS F pf
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ψ : Angle between the quadriceps t
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v CTt : Tangential velocity compone
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Introduction 1. INTRODUCTION AND OB
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1.3. Aims of the PhD thesis Introdu
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Literature review 2. LITERATURE REV
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Literature review Figure 2.3. The f
Page 19 and 20: Literature review Figure 2.6. Patel
Page 21 and 22: Literature review Figure 2.8. Compo
Page 23 and 24: Literature review The knee carries
Page 25 and 26: Literature review For this reason,
Page 27 and 28: Literature review Figure 2.12. Thre
Page 29 and 30: Literature review As a short overvi
Page 31 and 32: Literature review Moment arm 60 [mm
Page 33 and 34: Literature review I. They demonstra
Page 35 and 36: Literature review The presented mod
Page 37 and 38: Literature review ε angle [˚] 100
Page 39 and 40: Literature review Fpf/Fq [-] 1.2 1
Page 41 and 42: Literature review β angle [˚] Mal
Page 43 and 44: Literature review Figure 2.35. Mech
Page 45 and 46: Literature review Moment arm 60 [mm
Page 47 and 48: Literature review Let us follow the
Page 49 and 50: Literature review Finally, the pate
Page 51 and 52: Literature review Figure 2.43. Tota
Page 53 and 54: Literature review One great advanta
Page 55 and 56: Literature review Implant wear is t
Page 57 and 58: 2.3.2. General numerical models Lit
Page 59 and 60: a) The tibia plateau is a flat surf
Page 61 and 62: Literature review From their calcul
Page 63 and 64: Literature review Although a simila
Page 65 and 66: Literature review Slide/Roll [-] 1
Page 67 and 68: Literature review Figure 2.62. Mult
Page 69: Materials and Methods 3.1. Methodol
Page 73 and 74: Materials and Methods 9 th QUESTION
Page 75 and 76: Materials and Methods 3.3. New anal
Page 77 and 78: Materials and Methods 3.3.3. Free-b
Page 79 and 80: Materials and Methods Figure 3.6. F
Page 81 and 82: Materials and Methods By the introd
Page 83 and 84: Materials and Methods 3.4. Experime
Page 85 and 86: Materials and Methods Figure 3.7. C
Page 87 and 88: Materials and Methods All of the pa
Page 89 and 90: Materials and Methods 3.4.5. Measur
Page 91 and 92: x c Materials and Methods ∑ Fi
Page 93 and 94: Materials and Methods Probability D
Page 95 and 96: Materials and Methods Figure 3.18.
Page 97 and 98: Materials and Methods By doing so,
Page 99 and 100: 3.4.7.2. Steps of the approach Mate
Page 101 and 102: Materials and Methods All the funct
Page 103 and 104: Materials and Methods β [º] 40 20
Page 105 and 106: Materials and Methods If the center
Page 107 and 108: Materials and Methods By the use of
Page 109 and 110: Materials and Methods Thus, one pri
Page 111 and 112: Materials and Methods I. The patter
Page 113 and 114: 3.6.3. Geometrical models Materials
Page 115 and 116: Materials and Methods − − −
Page 117 and 118: 3.6.4.3. Contact [MSC.ADAMS] Materi
Page 119 and 120: Materials and Methods Besides the k
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Materials and Methods By multiplyin
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Results 4. RESULTS 4.1. Results reg
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Results This closely equal percenta
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Results Fpf/BW [-] 8 Fekete et al.
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Results In reality, human subjects
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Results 4.2. Results regarding the
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Results 0.8 Χ [-] 1 Sliding-rollin
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Results Χ [-] 1 Sliding-rolling ra
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Results Among the tested prostheses
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Results χ [-] 1 Averaged sliding-r
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Results Χ [-] 1 Sliding-rolling ra
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4.3. New scientific results Results
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Results 3 rd Thesis: Based on the m
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Conclusions and Suggestions 5. CONC
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Conclusions and Suggestions Suggest
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Summary 6. SUMMARY In this doctoral
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Appendix APPENDIX A1. Bibliography
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Appendix [31] Csizmadia B. M., Nán
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Appendix [61] Gill H. S., O’Conno
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Appendix [93] Klebanov B. M., Barla
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Appendix [123] Nägerl H., Frosch K
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Appendix [154] Reuben J. D., McDona
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Appendix [187] Wahrenberg H., Lindb
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Appendix 6. Fekete G., Kátai L.: M
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Appendix Figure 3. Setting Stitchin
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Appendix Fpf/Fq [-] 1.2 h = 6 mm h
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Appendix η1 angle [˚] 6 Hirokawa
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Appendix Figure 13. Mechanical mode
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Appendix Ψ angle [˚] 10 Van Eijde
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Appendix Figure 19. Mechanical mode
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Appendix - 177 -
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PhD Fekete - SZIE version - 2.2 - Szent István Egyetem

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