Transactions on Biomedicine and Health vol 3, 1996 WIT Press, ISSN

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1 Finite element analysis of hip prostheses and design of fixation devices for fractures in human femurs Z. Maldonado,* J. Bendayan,* R. Callarotti,* M. Cerrolaza* "Bioengineering Center, Faculty of Engineering, Central University of Venezuela, P.O. Box , Caracas A, Venezuela *Service oftraumatology and Orthopaedics, Universitary Hospital, Caracas, Venezuela Abstract This work reports some numerical analysis of hip prostheses and the design of an screw-based system prototype for fixation of head-femur fractures. The biomechanical performance of the hip is discussed. Some new designs of biomedical devices, obtained by using numerical analysis based upon the Finite Element Method (FEM) are presented and discusssed. The results are also discussed, showing the advantages and drawbacks of the obtained designs. 1. Introduction The analysis and design of internal prostheses for human hip replacement is a completely current topic of research over the world. Many researchers have proposed and developed prostheses for human hips by using numerical methods such as finite elements. The works of Chang & Perez*, Weinstein et ap, Crowninshield et al^, Beaudoin et al*, Huiskes*, Johansson et af, Meunier et af and Svesnsson et al* are a good sample of the interest of the scientific community in this field. However, these devices are somewhat difficult to get in developing countries, due to their high costs in the international market. In this sense, this work is devoted to the analysis and design of hip prostheses and fixation systems for non-trivial fractures in human bones, like the femur. The goal is the design and manufacturing of low cost devices, which can be used in real-life situations in our patients. The use of metallic stem prosthesis with spherical heads is sucessfull in many cases. However, some complications can arise, even causing the fracture of the prosthesis. Also, absorption or resorption of the bone can also be observed in some clinical cases, as reported in Jacob & Huggler^. Also, many

2 100 Simulation Modelling in Bioengineering researchers have suggested that the main reason for bone absorption is the high elasticity modulus of the prosthesis (200 Gpa) compared with the relatively low modulus of the bone (20 Gpa), which causes the develop of a stress concentration zone surrounding the cortical bone (Meunier et af, Svesnsson et al*). One way to overcome this drawback is the use of prostheses made up with composite materials, in order to reduce the sudden change in the stress pattern in the contact zone (Rotem ). Some numerical analysis leading to a new designs of such devices, carried out by the Venezuelan Bioengineering Center, are presented and discussed in this work. First, the numerical analysis of hip prostheses is performed and analyzed. Following, the design of an screw-based system prototype for the fixation of head-femur fractures is also discussed. 2. Biomechanical characteristics of human hip and femur Hip replacement is nowadays the most used medical approach to cure degenerative joint diseases or fractures of the proximal end of the femur. Figure 1 displays the femur-hip joint, showing the acetabulum position. Figure 1. Femur-hip joint A good description of the biomechanical behavior of the human hip can be found in Crowninshield et al^. With its complex mechanical properties and unique ability for self repair, bone is a fascinating structural material from both a clinical and engineering perspective. Bone fails when overloaded, initiating a complex series of biologic and biomechanical events directed toward repair and restoration of function. The biomechanical factors that determine whether a bone will fracture include the loads applied and the mechanical properties of bone and bone tissue. Humans engage in a wide variety of activities resulting in abroad range of loads. In addition, the mechanical properties of bone vary over a wide range, and several pathologic processes can alter these properties. The ultimate clinical objective of fracture treatment is to promote a fracture healing process that restores the structural capacity of the fractured bone. A range of fracture treatment approaches are available that provide wide

3 Simulation Modelling in Bioengineering 101 variation in mechanical stability. Forces that produces fractures cause injury to both the bone and surrounding soft tissue. This results in a inflammatory reaction in the zone of the injury. The release of vasoactive substances mediates the beneficial increase in the flow of blood to the injured part as well as the detrimental effects of edema and pain. Inflammatory substances and neural reflexes cause involuntary contraction of skeletal muscle groups around the fracture to provide to splitting, reduce painful motion at the fracture site and neighboring joints, and facilitate fracture healing. Fractures usually healed with non-operative methods, inability to directly control the position of fracture fragments within the soft tissue envelope led to problems with malunion and nonunion. The treatment of femoral head and neck fractures are aimed at restoring hip function. Rapid mobilization of the patient is thought to reduce the risks of medical complication and improve the functional outcome. Additionally, it decreases the costly length of stay in a acute care hospital. Failure of fracture fixation, nonunion, and avascular necrosis with symptomatic late segmental collapse have long been recognized as serious complication that compromise the results of treatment for femoral head and neck fractures. Striving to provide mobilization while avoiding these and other complication, the treatment scheme has evolved from close reduction and casting, to internal fixation, to prosthetic replacement and presently to a selective use of both prosthetic replacement and internal fixation. The majority of thefracturesof head and neck of femur employs internal fixation, after closed or open reduction, for example, plates and nails can be applied, they will funtion in this manner if applied to ther tension or distraction side of the fracture or nonunion. In addition to the anatomic situation noted previously, definite tension and compression sides can be identified at location where anatomic or pathologic curvature or angulation of the bone or fracture results in loading that is eccentric to the central axis of the bone with weight bearing and muscle activity. Because of its normal curvature, the femur is under tension anterolaterally and compression posteromedially. A telescoping hip screw is an example of the dynamic compression principle and is used optimally for pertrocantheric fractures of femur. The implant consists of two major parts. A large screw isfirmlyfixedto the head-neck fragment, and a barrel is rigidly affixed to the distal shaft fragment. Weight bearing and abductor muscle activity cause the screw shaft to slide through the barrel, resulting in impactation of the fracture surfaces and, ultimately, a stable load -sharing construct. The recently developed gamma locking nail for proximal femur fractures consists of a short, proximal intramedullary nail for femoral shaft, about the length of a conventional sliding hip screw side plate, with holes for two distal locking screws and a larger proximal hole through which is inserted a stout sliding femoral head lag screw is placed over a guide wire, the position of which is determined by a guide attached to the intramedullary nail. Obtaining an appropriate nail depth and rotational alignment are thus key surgical steps. After insertion of the lag screw,

4 102 Simulation Modelling in Bioengineering the same guide assembly is used for placing the distal locking screws. The implants is biomechanically sounds but it can be improve, if we can use an a lag screw for the hip combined with the a intramedullary screw in the proximal femur augmenting the close contact between the implant and the intramedullary channel, decreasing the use of interlocking screws and making easier the surgical technique. Prosthetic replacement is reserved for those chronologically older patients in whom internal fixation is unlikely to succeed those with marked osteopenia, fracture conminutation, or both. In general, such patients are physiologically elderly, with low functional demands. Their ambulation is at best restricted to their domicile, they may be unable to assist with their own care, and their life expectancy is often limited. They are thus less at risk of developing late complications that might require revision of an arthroplasty. Although different types of prosthetic replacement for the proximal femur have relative advantages and disadvantages, none can provide as durable and functional a hip as that regained by satisfactory bone healing. Furthermore, failure after internal fixation of a femoral neck fracture can be satisfactorily salvaged by total hip arthroplasty, which has a low rate of complications. Failed heniarthroplasties require a similar procedure, though a more difficult one with the possibly poorer results. Prosthetic replacement is selected for management of femoral neck fracture when the patient has preexisting hip joint pathology, a medical condition that precludes fracture healing, low functional demands, poor bone stock, and is physiologically older. This consideration is based on a estimate of the patient physiologic, not the chronologic, age. Although prosthesis eliminates concerns about fixation failure, nonunion, and avascular necrosis, they also introduce problems related to the prosthetic loosening, acetabular erosion, dislocation, infection, and the potential perioperative consequences of a more extensive surgical procedure. These difficulties were recognized soon after introduction of the first generation of well-accepted endoprostheses by Moore, Thompson, and others. The most frequent problems were loosening and protrusion with late pain, primarily in younger and more active patients who provide significant challenges to the durability of hip prostheses. Continuing efforts have led to improvements in prosthetic designs and techniques. 3. Numerical analysis of hip prostheses The numerical analysis of a metallic Charnely prosthesis (see Crenshaw** ) by using finite elements is performed herein. First, a bidimensional analysis of a simplified model of the prosthesis was carried out, by using a quadrilateral plane-strain finite-elements mesh. The goal is to determine the stress levels in the upper part of the prosthesis. It is considered that the prosthesis stem is in complete contact with the femur diaphisis. Three loading cases, corresponding to different human body movements, and produced by the body weight and the abductor muscles, were considered. Figure 2 displays thefiniteelement mesh,

5 Simulation Modelling in Bioengineering 103 the boundary conditions and a deformed shape corresponding to one loading case. Figure 2. a) FEM mesh and displacement boundary conditions b) Deformed shape for one loading case Figure 3 contains the stress distributions in the upper part of the prosthesis. Figure 3. Stress distributions in upper part of the prosthesis The analysis of the 2D model allows the biomedical engineer to get a rough information on the stresses acting in the prosthesis. It is clear that a 2D model

6 104 Simulation Modelling in Bioengineering of a prosthesis is only an approximation of the real problem, which is a three dimensional situation. It can be observed that the stress distributions change significantly related to the loading case considered. This fact is of the most importance when designing the prosthesis. Now, a three dimensional and more accurate model of the prosthesis is performed. The 3D geometric model of the prosthesis is carried out by using a '3D surface-modelling software' called ProEngineer^. This software produces the model geometry in an accurate manner, generating the nodal coordinates and element connectivitiesfiles,which are introduced in a 3D FEM software developed during this research. The main goal is to reduce the stress levels in the prosthesis and in the bone, by modifying the device geometry. The figure 4.a shows a three dimensional sketch required to generate the model of the prosthesis, while figure 4.b illustrates two 3D views of the model generated. Figure 4. a Three dimensional sketch to generate the model of the Charnely prosthesis

7 Simulation Modelling in Bioengineering 105 Figure 4.b Three dimensional model of the Charnely prosthesis The finite element analysis of this model was also carried out, by using a 3D hexaedric finite element mesh. The results are under discussion and, by this reason, they are not displayed herein. However, the preliminary analysis of these numerical results has shown that the 3D model is suitable for the analysis and that it represents adequately the main characteristics of the problem. Our Center is currently involved in the analysis and design of hip prosthesis with other geometries. Also, the materials to be used in the prosthesis construction are under evaluation. The paper of Rotem^ has discussed many interesting ideas related to the construction of prosthesis with composite materials. The author discusses the aspects related to the isoelastic prosthesis made with materials originally developed for the aerospace industry. The works of Chang & Perez* presented the tailoring of prosthesis made with advanced composite materials, while Weinstein et ap have carried out many tests on femoral components. All these works, among others, are being considered herein in order to design composite hip prostheses.

8 106 Simulation Modelling in Bioengineering 4. Adjustable screw-based system for femur head Another research line in our Center is the design of fixation systems for proximal femur fractures, involving the femur neck and the femur head. Our engineers and medical doctors have proposed a screw-based system prototype, which is schematically shown in figure 5. The vertical (main) screw is introduced into the femur diaphisis and it is inmobilized by using one or more small transversal screws. The upper fracture is then inmobilized by the introduction of two medium size screws, geometrically inclined regarding the main screw. The introduction of these screws is carried out by an external alignement system (not displayed in figure 5), which allows the medical surgeon to easily find the guides for the medium size screws. It should be remarked herein that this is only a preliminary design. Therefore, many modifications are expected in order to improve its performance. Moreover, experimental tests are currently being done to asses its biomechanical behavior. Also, the system must be tested into animals before it is used in human patients. 5. Discussion of results and conclusions The results of a research project for analysis and design of hip prostheses and a screw system to be used in the fixation of head-femur fractures were presented. Normally, this kind of research needs to be validated by using the devices with animals, before they are used in human patients. This validation is currently carried out by the researchers of the Bioengineering Center in animals provided by the Medicine Faculty of the Central University of Venezuela. It should be remarked herein that the proposed devices were carefully analyzed by using numerical techniques such finite element analysis. In their design, it were be considered many factors involved in the biomechanical characteristics of the human hip behaviour, such as real performance and nonconventional materials. The post evaluation should also be done if additional fixation is required (Mihalko^ ). The materials evaluation is another topic of the greatest importance, as their choice significantly affects the prosthesis performance (Muller^, Head et al" ). The stress levels obtained with the numerical analysis were optimized, in order to diminish their influence in the bone behaviour. It is well known that the stress distribution in the contact region of bone-prosthesis substantially affects the human bone behaviour. Even more, if this subject is not appropriately considered, some undesirable situations arise, such as bone reabsorption. In the case of the screws system for fixation of head-femur fractures, some practical aspects were taken into account. The installation of the device must be carefully analized, in order to ensure an optimum medical procedure during the surgery. Many biomechanical aspects were considered, such as for instance, the procedure to avoid head-femur rotation during the installation of the device.

9 Simulation Modelling in Bioengineering 107 Figure 5. Prototype of a screw-based fixation system We strongly believe that our desings really contribute to improve the fixation of fractures, as well as they simplify the medical practice, which are relevant factors of any biomedical device to be used in human patients.

10 108 Simulation Modelling in Bioengineering References 1. F.K. Chang and J.L. Perez, Stiffness and strength tailoring of a hip prosthesis made of advanced composite materials, J. ofbiomed. Mat. and Research, 24: (1990) 2. A.M. Weinstein, J.B. Koeneman, R.H. Johnson, R A Yapp, TM Hansen, J.A Szivek and P.P. Magee, Design and testing of a composite material K9 femoral component, Proc. of the 33rd Annual Meeting, Orthopaedic Research Society, January, San Francisco, California (1987) 3. RD Crowninshield, RC Johnston, J.G. Andrews and RA Brand, A biomechanical investigation of the human hip, J. of Biomechanics, 11:75-85 (1978) 4. A.J. Beaudoin, WM Mihalko, WR Krause and J.A. Cardea, Fern study of fracture fixation distal to femoral prosthesis, Trans. Orthop. Res. Soc., 14:406(1989) 5. R. Huiskes, Some fundamental aspects of human joint replacement, Ada Orthop. Scand.., 189:1-209 (1980) 6. JE Johansson, R McBroom, T.W. Barrington and G A Hunter, Fracture of the ipsilateral femur in patients with total hip replacement, J. Bone Jt. &/rg.,63a: (1981) 7. A. Meunier, P Christel, L. Sedel, J. Witvoet and D. Blanquaert, The influence of the Young's modulus of the material of an implanted femoral stem on the stress loading in the upper femur, International.Orthopaedics, 14:67-73 (1990) 8. N.L. Svesnsson, S. Valliapan and RD Wood, Stress analysis of human femur with implanted Charnely prosthesis, J. of Biomechanics, 10: (1977) 9. H.A Jacob and A.H. Huggler, An investigation into biomechanical causes of prosthesis stem lessening within the proximal end of the human femur, J. of Biomechanics, 13: (1980) 10. A. Rotem, Effect of implant material properties on the performance of a hip joint replacement, J. ofmedical Eng. & Tech, 18(6): (1994) 11. AH Crenshaw, Campbell's operative orthopaedics, C V Mosby Comp, St. Louis, Missouri (1987) 12. Proengineer User's Manual, Parametric Technology Corp., USA (1995) 13. WM Mihalko, AJ Beaudoin, J.A. Cardea and WR Krause, Finite element modelling of femoral shaft fracture fixation techniques post total hip arthroplasty, J. of Biomechanics, 25: (1992) 14. ME Muller, The benefits of metal-non-metal total hip replacements, Clin. Orthop. Rel Res., 311:54-59 (1995) 15. WC Head, D J Bauk and R.H. Emerson, Titanium as the material of choice for cementless femoral components in total hip arthroplasty, Clin. Orthop. Rel. Res., 311:85-90 (1995)

11 Membrane shear elasticity and depletion of membrane skeleton in red blood cell vesicles A. IgliZ,* H. Hagerstrand* "Faculty of Electrical Engineering and Medical Faculty, University ofljubljana, 1000Ljubljana, Slovenia ^Department ofbiology, Abo Akademi University, SF-20520, Abo/ Turku, Finland Abstract In this paper the shear energy of the membrane skeleton is calculated during the budding process of the red blood cell. It is shown, that the partial detachment of the skeleton in the budding region of the cell membrane and the consequent depletion of the membrane skeleton in red blood cell daughter vesicles is additionally favoured due to the accumulated shear deformations in the region of the neck between the daughter vesicle and the parent cell since they are relaxed in the detached state of the skeleton. 1 Introduction The membrane of red blood cell (RBC) can form during the budding process (see Gennis [1] ) small spherical daughter vesicles which are released from the RBC membrane in the vesiculation process, e.g. Hagerstrand & Isomaa [2]. The RBC membrane is essentially composed of two parts, the bilayer of lipid molecules and the continuous network of proteins, the membrane skeleton. The bilayer contains in addition to lipid molecules also some other