- Email: [email protected]
Concept and development of an orthotropic FE model of the proximal femur
Journal of Biomechanics 36 (2003) 289–293
Short communication
Concept and development of an orthotropic FE model of the proximal femur Dieter Christian Wirtza,*, Thomas Pandorfb, Frank Portheinec, Klaus Radermacherc, Norbert Schiffersa, Andreas Prescherd, Dieter Weichertb, Fritz Uwe Nietharda a
Department of Orthopaedic Surgery, Technical University of Aachen, Paulwelsstr 30, Aachen 52074, Germany b Institute of Mechanics, Technical University of Aachen, Aachen, Germany c Helmholtz-Institute of Biomedical Engineering, Technical University of Aachen, Aachen, Germany d Institute of Anatomy, Technical University of Aachen, Aachen, Germany Accepted 22 August 2002
Abstract Purpose: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE ‘‘model femur’’ to realistically simulate three-dimensional bone remodelling. Methods: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2 mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known ‘‘densitydetermined’’ bony material properties (Young’s modulus; Poisson’s ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same ‘‘CT-density-characterized’’ volumetric group. In order to fix the principal directions of stiffness in FE areas with the same ‘‘density characterization’’, the cadaveric femurs were cut in 2 mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the ‘‘CT-density characterized’’ three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter’s criterion. Results: In the constructed ‘‘model femur’’, each FE is characterized by the principal directions of the stiffness and the ‘‘CTdensity-determined’’ material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. Conclusions: With the orthotropic ‘‘model femur’’, the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc). r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Finite-element model; Orthotropy; Bone remodelling; Femur>
1. Introduction In literature, many isotropic simulation models of the proximal femur have been described to calculate the functional adaptation of cortical and cancellous structures, (Couteau et al., 1998; Jacobs et al., 1997; Lengsfeld et al., 1996; Weinans et al., 1992). Since bony materials are not isotropic but rather anisotropic and
orthotropic, respectively (Carter et al., 1989; Savvidis and Stabrey, 1996; Wirtz et al., 2000; Yang et al., 1999), it was the object of our study to develop an orthotropic finite-element (FE) ‘‘femur reference model’’ to simulate bone remodelling more reasonably adapted to the physiological situations in vivo.
2. Materials and methods *Corresponding author. Tel.: +49-241-8089410; fax: +49-2418888453. E-mail address: [email protected] (D.C. Wirtz).
For orthotropic modelling of bony structures, four main developing steps had to be performed: (step 1) the
0021-9290/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 2 ) 0 0 3 0 9 - 3
290
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
three-dimensional reconstruction of femoral geometry and the generation of an FE mesh for the bone model, (step 2) the allocation of the material properties of the bone according to their density for each FE, (step 3) the exact definition of the principal stiffness directions for each FE, (step 4) the implementation of a numerical algorithm for time- and load-dependent remodelling of bone. Step 1: To reconstruct the three-dimensional geometry of the proximal femur, a pair of human femurs taken freshly from corpses were scanned by CT (Somatom Plus, Siemens, Erlangen) in 2 mm thick layers. These two-dimensional CT data served to reconstruct threedimensional CT models of each femur. Then, these three-dimensional CT models were loaded via a CAD
Fig. 1. CT reconstruction of the proximal femur with subsequent FE mesh generation (FE-CT-model) and CT densitometry: HU (CT)=mg/cm3 (calcium hydroxyl apatite).
interface into the image processing system DISOS (Helmholtz-Institute Aachen, Germany) and meshed with FEs (16.000 cuboid elements and 87.500 nodes in average per femur). Within these so-called ‘‘FE-CTmodels’’ of both proximal femurs each FE was characterized by its volumetrically determined ‘‘CT density’’ (Fig. 1). Step 2: Via CT densitometry, i.e. by converting the Hounsfield units (HU) in the CT into mg/cm3 of calcium hydroxyl apatite (Fig. 1), the material properties of the cancellous and cortical bony structures were assigned to each of the FEs using a data base from well-known ‘‘density-determined’’ bony material properties (Young’s modulus; Poisson’s ratio; tensile, compression and torsional strength; shear modulus) (Wirtz et al., 2000). Within this database all material parameters had been differentiated between cortical and cancellous bone as well as between axial and transverse direction of strain. Thus, each FE could be characterized by its density-defined as well as stiffness direction-determined (see step 3) material-specific properties. Step 3: To determine the spatial angle of the axes of orthotropy, the same pair of femurs which had been scanned by CT was cut into 2 mm thick slices in the frontal (left femur) and sagittal plane (right femur) using a hard microtome (Type MAKRO, Exakt, 0.2 mm diamond saw blade) (Fig. 2b). To guarantee registration of the exact three-dimensional geometry of the femurs the proximal parts were embedded into a 10 10 cm2 synthetic resin block each (Technovits) before cutting (Fig. 2a). The resulting femur slices (Fig. 2c) were scanned with 600 dpi resolution and the bitmaps were geometrically calibrated and transferred to the imaging processing system DISOS (Fig. 2d).
Fig. 2. (a) One pair of cadaveric femurs, proximal femur cast in Technovit 7143 to maintain the geometric proportions. (b) Water-cooled cutting procedure of the cadaveric femurs by means of hard microtome. (c) Femur slices with 2 mm thick layers, cut frontally. (d) Scanning procedure.
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
Based on these two-dimensional images of the frontal and sagittal plains, the stiffness directions of cancellous bone were determined by the orientation of the trabecular structures, and the stiffness directions of cortical bone by the orientation of the haversian system. So, the directions were identified manually within each cuboid of the FE mesh generated from the CT-based model and backprojected on the two-dimensional scans of the anatomic slices (Fig. 3). After finishing marking in the stiffness directions of each FE in each cutting plane, these geometric data of the left and right femur were matched yielding a three-dimensional model of the femur (so-called ‘‘FE-bone-model’’) with defined spatial
291
orientation of the privileged stiffness directions of the cortical and cancellous bone structures within each single FE. Step 4: By ‘‘matching’’ the density and material values in the FE-CT-model with the privileged stiffness directions in the FE-bone-model (Fig. 4), an orthotropic cubic FE model of the proximal femur was obtained. Hence, the material properties of each FE within this orthotropic model had been characterized by bone density and privileged stiffness directions. In the next step, the generated orthotropic cubic FE model was changed to an orthotropic FE model consisting of tetraeders (Fig. 5). For this process, the used interpolation
Fig. 3. Determining the preferred directions for each FE per femur slice, cortically according to osteon direction, cancellously according to the course of the trabecula.
Fig. 4. Matching of the FE-CT-model with the FE-bone-model.
292
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
Fig. 5. Three-dimensional orthotropic FE model, each FE determinated by its density (not shown) and priviliged stiffness direction presented in vectorial form.
program transferred the whole data configuration of the FE cubes to the centre of each FE tetraeder. To calculate the time- and load-related transformation behaviour of the bone, a corresponding iterative algorithm, in accordance with the Carter criteria (Beaupre! et al., 1990; Carter et al., 1987; Carter et al., 1989), was finally implemented which determines the changes in density and privileged stiffness directions for each single element (Pandorf et al., 1999). As kinematical boundary conditions, the femur was assumed to be clamped in the distal part close to the knee joint. Although this assumption is too rigid compared to physiological conditions, the influence on bone adaptation in the upper part of the bone seems to be negligible. As external forces, mean daily acting single loads on the centre of the hip joint and on the top of the trochanter major were to be applied according to Beaupre! et al. (1990). Non-mechanical stimuli of bone remodelling were not included into the model up to now.
3. Discussion Although since several years, some studies have been performed to generate anisotropic FE modelling of the
proximal femur (Bagge, 2000; Doblare! and Garcia, 2001; Jacobs et al., 1997), no real solution exists to the problem of finding the orthotropic material orientation to an optimal structure within a three-dimensional bone remodelling tool. The presented new simulation tool is a more comprehensive approach to this ‘‘three-dimensional problem’’ of orthotropy. Each FE has been determined by its bone density (derived from QCT), its densitydependent material properties (derived from a metaanalysis of literature), and the privileged stiffness directions of its orthotropic axes (derived from the spatial orientation of trabeculae and the haversian osteons). Thus, the non-homogeneous and orthotropic behaviour of bone has been considered three-dimensionally assuming transverse isotropy of cortical and especially cancellous bone, which is in accordance to the experimental data performed by several authors (Van Rietbergen et al., 1996; Zysset et al., 1998). Since the initial structure of the model is based on anatomic data, there is in fact—and in contrast to other anisotropic models reported in literature (Bagge, 2000; Doblare! et al., 2001; Jacobs et al., 1997)—the advantage of having a remodelling scheme with realistic parameters. Although the developed FE reference model has to be
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
validated in further studies, it seems to have the potential to become a valuable assistant in the discussion of clinical questions, e.g. concerning optimized planning of proximal femur osteotomies or the evaluation of different types of total joint replacement systems. As a restriction of this possible clinical value, the model cannot reproduce exactly the in vivo conditions. The kinematical boundary conditions are strongly simplified assuming loading conditions of only two acting forces at the hip centre and the trochanter major. Hence, the incorporation of the mechanical influence of other muscles and ligaments acting on the hip joint and the proximal femur, e.g. m.iliopsoas, m.quadriceps femoris, iliotibial tract, are necessary to obtain a numerical simulation tool which could be in fact more close to the in vivo conditions. But in this sense, other physiological factors influencing bone remodelling have also to be taken into account. Although biological factors such as immunological, hormonal and haemodynamical stimuli on bone adaptation are physiologically combined with the mechanical stimuli, a number of clinically observed bone resorption phenomena, e.g. osteoporosis, can numerically only be explained, if these non-mechanical factors are considered in numeric bone adaptation models. In consequence, further work has to be done to optimize the developed orthotropic FE model focusing on non-mechanical influences on bone adaptation as well as on the influence of soft tissues acting around the femur.
References Bagge, M., 2000. A model of bone adaptation as an optimization process. Journal of Biomechanics 33, 1349–1357. Beaupr!e, G.S., Orr, T.E., Carter, D.R., 1990. An approach for timedependent bone modeling and remodeling—application : a preliminary remodeling simulation. Journal of Orthopaedic Research 8, 662–670. Carter, D.R., Fyhrie, D.P., Whalen, R.T., 1987. Trabecular bone density and loading history: regulation of connectice tissue
293
morphology by mechanical energy. Journal of Biomechanics 20, 785–794. Carter, D.R., Orr, T.E., Fyhrie, D.P., 1989. Relationship between loading history and femoral cancellous bone architecture. Journal of Biomechanics 22, 231–244. Couteau, B., Hobatho, M.C., Darmana, R., Brignola, J.C., Arlaud, J.Y., 1998. Finite element modelling of the vibrational behaviour of the human femur using CT-based individualized geometrical and material properties. Journal of Biomechanics 31, 383–386. Doblar!e, M., Garcia, J.M., 2001. Application of an anisotropic boneremodelling model based on a damage–repair theory to the analysis of the proximal femur before and after total hip replacement. Journal of Biomechanics 34, 1157–1170. Garcia, J.M., Martinez, M.A., Doblare, M., 2001. An anisotropic internal–external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Computer Methods in Biomechanical and Biomedical Engineering 4, 355– 377. Jacobs, C.R., Simo, J.C., Beaupr!e, G.S., Carter, D.R., 1997. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. Journal of Biomechanics 30, 603–613. Lengsfeld, M., Kaminsky, J., Merz, B., Franke, R.P., 1996. Sensitivity of femoral strain pattern analyses to resultant and muscle forces at the hip joint. Medical Engineering Physics 18, 70–78. Pandorf, T., Haddi, A., Wirtz, D.C., Lammerding, J., Forst, R., Weichert, D., 1999. Numerical simulation of adaptive bone remodeling. Journal of Applied Mechanics-T 37, 639–658. Savvidis, E., Stabrey, H., 1996. Experimentally ascertained material data from human femora and an analysis of the directiondependent stress tolerance. Zeitschrift fuer Orthopaedie 134, 445– 451. Van Rietbergen, B., Odgaard, A., Kabel, J., Huiskes, R., 1996. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. Journal of Biomechanics 29, 1653– 1657. Weinans, H., Huiskes, R., Grootenboer, H.J., 1992. The behaviour of adaptive bone-remodeling simulation models. Journal of Biomechanics 25, 1425–1441. Wirtz, D.C., Schiffers, N., Pandorf, T., Radermacher, K., Weichert, D., Forst, R., 2000. Critical evaluation of known bony material properties to realize anisotropic FE-simulation of the proximal femur. Journal of Biomechanics 33, 1325–1330. Yang, G., Kabel, J., van Rietbergen, B., Odgaard, A., Huiskes, R., Cowin, S.C., 1999. The anisotropic Hooke’s law for cancellous bone and wood. Journal of Elasticity 53, 125–146. Zysset, P.K., Goulet, R.W., Hollister, S.J., 1998. A global relationship between trabecular bone morphology and homogenized elastic properties. Journal of Biomedical Engineering 120, 640–646.
Short communication
Concept and development of an orthotropic FE model of the proximal femur Dieter Christian Wirtza,*, Thomas Pandorfb, Frank Portheinec, Klaus Radermacherc, Norbert Schiffersa, Andreas Prescherd, Dieter Weichertb, Fritz Uwe Nietharda a
Department of Orthopaedic Surgery, Technical University of Aachen, Paulwelsstr 30, Aachen 52074, Germany b Institute of Mechanics, Technical University of Aachen, Aachen, Germany c Helmholtz-Institute of Biomedical Engineering, Technical University of Aachen, Aachen, Germany d Institute of Anatomy, Technical University of Aachen, Aachen, Germany Accepted 22 August 2002
Abstract Purpose: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE ‘‘model femur’’ to realistically simulate three-dimensional bone remodelling. Methods: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2 mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known ‘‘densitydetermined’’ bony material properties (Young’s modulus; Poisson’s ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same ‘‘CT-density-characterized’’ volumetric group. In order to fix the principal directions of stiffness in FE areas with the same ‘‘density characterization’’, the cadaveric femurs were cut in 2 mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the ‘‘CT-density characterized’’ three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter’s criterion. Results: In the constructed ‘‘model femur’’, each FE is characterized by the principal directions of the stiffness and the ‘‘CTdensity-determined’’ material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. Conclusions: With the orthotropic ‘‘model femur’’, the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc). r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Finite-element model; Orthotropy; Bone remodelling; Femur>
1. Introduction In literature, many isotropic simulation models of the proximal femur have been described to calculate the functional adaptation of cortical and cancellous structures, (Couteau et al., 1998; Jacobs et al., 1997; Lengsfeld et al., 1996; Weinans et al., 1992). Since bony materials are not isotropic but rather anisotropic and
orthotropic, respectively (Carter et al., 1989; Savvidis and Stabrey, 1996; Wirtz et al., 2000; Yang et al., 1999), it was the object of our study to develop an orthotropic finite-element (FE) ‘‘femur reference model’’ to simulate bone remodelling more reasonably adapted to the physiological situations in vivo.
2. Materials and methods *Corresponding author. Tel.: +49-241-8089410; fax: +49-2418888453. E-mail address: [email protected] (D.C. Wirtz).
For orthotropic modelling of bony structures, four main developing steps had to be performed: (step 1) the
0021-9290/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 2 ) 0 0 3 0 9 - 3
290
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
three-dimensional reconstruction of femoral geometry and the generation of an FE mesh for the bone model, (step 2) the allocation of the material properties of the bone according to their density for each FE, (step 3) the exact definition of the principal stiffness directions for each FE, (step 4) the implementation of a numerical algorithm for time- and load-dependent remodelling of bone. Step 1: To reconstruct the three-dimensional geometry of the proximal femur, a pair of human femurs taken freshly from corpses were scanned by CT (Somatom Plus, Siemens, Erlangen) in 2 mm thick layers. These two-dimensional CT data served to reconstruct threedimensional CT models of each femur. Then, these three-dimensional CT models were loaded via a CAD
Fig. 1. CT reconstruction of the proximal femur with subsequent FE mesh generation (FE-CT-model) and CT densitometry: HU (CT)=mg/cm3 (calcium hydroxyl apatite).
interface into the image processing system DISOS (Helmholtz-Institute Aachen, Germany) and meshed with FEs (16.000 cuboid elements and 87.500 nodes in average per femur). Within these so-called ‘‘FE-CTmodels’’ of both proximal femurs each FE was characterized by its volumetrically determined ‘‘CT density’’ (Fig. 1). Step 2: Via CT densitometry, i.e. by converting the Hounsfield units (HU) in the CT into mg/cm3 of calcium hydroxyl apatite (Fig. 1), the material properties of the cancellous and cortical bony structures were assigned to each of the FEs using a data base from well-known ‘‘density-determined’’ bony material properties (Young’s modulus; Poisson’s ratio; tensile, compression and torsional strength; shear modulus) (Wirtz et al., 2000). Within this database all material parameters had been differentiated between cortical and cancellous bone as well as between axial and transverse direction of strain. Thus, each FE could be characterized by its density-defined as well as stiffness direction-determined (see step 3) material-specific properties. Step 3: To determine the spatial angle of the axes of orthotropy, the same pair of femurs which had been scanned by CT was cut into 2 mm thick slices in the frontal (left femur) and sagittal plane (right femur) using a hard microtome (Type MAKRO, Exakt, 0.2 mm diamond saw blade) (Fig. 2b). To guarantee registration of the exact three-dimensional geometry of the femurs the proximal parts were embedded into a 10 10 cm2 synthetic resin block each (Technovits) before cutting (Fig. 2a). The resulting femur slices (Fig. 2c) were scanned with 600 dpi resolution and the bitmaps were geometrically calibrated and transferred to the imaging processing system DISOS (Fig. 2d).
Fig. 2. (a) One pair of cadaveric femurs, proximal femur cast in Technovit 7143 to maintain the geometric proportions. (b) Water-cooled cutting procedure of the cadaveric femurs by means of hard microtome. (c) Femur slices with 2 mm thick layers, cut frontally. (d) Scanning procedure.
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
Based on these two-dimensional images of the frontal and sagittal plains, the stiffness directions of cancellous bone were determined by the orientation of the trabecular structures, and the stiffness directions of cortical bone by the orientation of the haversian system. So, the directions were identified manually within each cuboid of the FE mesh generated from the CT-based model and backprojected on the two-dimensional scans of the anatomic slices (Fig. 3). After finishing marking in the stiffness directions of each FE in each cutting plane, these geometric data of the left and right femur were matched yielding a three-dimensional model of the femur (so-called ‘‘FE-bone-model’’) with defined spatial
291
orientation of the privileged stiffness directions of the cortical and cancellous bone structures within each single FE. Step 4: By ‘‘matching’’ the density and material values in the FE-CT-model with the privileged stiffness directions in the FE-bone-model (Fig. 4), an orthotropic cubic FE model of the proximal femur was obtained. Hence, the material properties of each FE within this orthotropic model had been characterized by bone density and privileged stiffness directions. In the next step, the generated orthotropic cubic FE model was changed to an orthotropic FE model consisting of tetraeders (Fig. 5). For this process, the used interpolation
Fig. 3. Determining the preferred directions for each FE per femur slice, cortically according to osteon direction, cancellously according to the course of the trabecula.
Fig. 4. Matching of the FE-CT-model with the FE-bone-model.
292
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
Fig. 5. Three-dimensional orthotropic FE model, each FE determinated by its density (not shown) and priviliged stiffness direction presented in vectorial form.
program transferred the whole data configuration of the FE cubes to the centre of each FE tetraeder. To calculate the time- and load-related transformation behaviour of the bone, a corresponding iterative algorithm, in accordance with the Carter criteria (Beaupre! et al., 1990; Carter et al., 1987; Carter et al., 1989), was finally implemented which determines the changes in density and privileged stiffness directions for each single element (Pandorf et al., 1999). As kinematical boundary conditions, the femur was assumed to be clamped in the distal part close to the knee joint. Although this assumption is too rigid compared to physiological conditions, the influence on bone adaptation in the upper part of the bone seems to be negligible. As external forces, mean daily acting single loads on the centre of the hip joint and on the top of the trochanter major were to be applied according to Beaupre! et al. (1990). Non-mechanical stimuli of bone remodelling were not included into the model up to now.
3. Discussion Although since several years, some studies have been performed to generate anisotropic FE modelling of the
proximal femur (Bagge, 2000; Doblare! and Garcia, 2001; Jacobs et al., 1997), no real solution exists to the problem of finding the orthotropic material orientation to an optimal structure within a three-dimensional bone remodelling tool. The presented new simulation tool is a more comprehensive approach to this ‘‘three-dimensional problem’’ of orthotropy. Each FE has been determined by its bone density (derived from QCT), its densitydependent material properties (derived from a metaanalysis of literature), and the privileged stiffness directions of its orthotropic axes (derived from the spatial orientation of trabeculae and the haversian osteons). Thus, the non-homogeneous and orthotropic behaviour of bone has been considered three-dimensionally assuming transverse isotropy of cortical and especially cancellous bone, which is in accordance to the experimental data performed by several authors (Van Rietbergen et al., 1996; Zysset et al., 1998). Since the initial structure of the model is based on anatomic data, there is in fact—and in contrast to other anisotropic models reported in literature (Bagge, 2000; Doblare! et al., 2001; Jacobs et al., 1997)—the advantage of having a remodelling scheme with realistic parameters. Although the developed FE reference model has to be
D.C. Wirtz et al. / Journal of Biomechanics 36 (2003) 289–293
validated in further studies, it seems to have the potential to become a valuable assistant in the discussion of clinical questions, e.g. concerning optimized planning of proximal femur osteotomies or the evaluation of different types of total joint replacement systems. As a restriction of this possible clinical value, the model cannot reproduce exactly the in vivo conditions. The kinematical boundary conditions are strongly simplified assuming loading conditions of only two acting forces at the hip centre and the trochanter major. Hence, the incorporation of the mechanical influence of other muscles and ligaments acting on the hip joint and the proximal femur, e.g. m.iliopsoas, m.quadriceps femoris, iliotibial tract, are necessary to obtain a numerical simulation tool which could be in fact more close to the in vivo conditions. But in this sense, other physiological factors influencing bone remodelling have also to be taken into account. Although biological factors such as immunological, hormonal and haemodynamical stimuli on bone adaptation are physiologically combined with the mechanical stimuli, a number of clinically observed bone resorption phenomena, e.g. osteoporosis, can numerically only be explained, if these non-mechanical factors are considered in numeric bone adaptation models. In consequence, further work has to be done to optimize the developed orthotropic FE model focusing on non-mechanical influences on bone adaptation as well as on the influence of soft tissues acting around the femur.
References Bagge, M., 2000. A model of bone adaptation as an optimization process. Journal of Biomechanics 33, 1349–1357. Beaupr!e, G.S., Orr, T.E., Carter, D.R., 1990. An approach for timedependent bone modeling and remodeling—application : a preliminary remodeling simulation. Journal of Orthopaedic Research 8, 662–670. Carter, D.R., Fyhrie, D.P., Whalen, R.T., 1987. Trabecular bone density and loading history: regulation of connectice tissue
293
morphology by mechanical energy. Journal of Biomechanics 20, 785–794. Carter, D.R., Orr, T.E., Fyhrie, D.P., 1989. Relationship between loading history and femoral cancellous bone architecture. Journal of Biomechanics 22, 231–244. Couteau, B., Hobatho, M.C., Darmana, R., Brignola, J.C., Arlaud, J.Y., 1998. Finite element modelling of the vibrational behaviour of the human femur using CT-based individualized geometrical and material properties. Journal of Biomechanics 31, 383–386. Doblar!e, M., Garcia, J.M., 2001. Application of an anisotropic boneremodelling model based on a damage–repair theory to the analysis of the proximal femur before and after total hip replacement. Journal of Biomechanics 34, 1157–1170. Garcia, J.M., Martinez, M.A., Doblare, M., 2001. An anisotropic internal–external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Computer Methods in Biomechanical and Biomedical Engineering 4, 355– 377. Jacobs, C.R., Simo, J.C., Beaupr!e, G.S., Carter, D.R., 1997. Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. Journal of Biomechanics 30, 603–613. Lengsfeld, M., Kaminsky, J., Merz, B., Franke, R.P., 1996. Sensitivity of femoral strain pattern analyses to resultant and muscle forces at the hip joint. Medical Engineering Physics 18, 70–78. Pandorf, T., Haddi, A., Wirtz, D.C., Lammerding, J., Forst, R., Weichert, D., 1999. Numerical simulation of adaptive bone remodeling. Journal of Applied Mechanics-T 37, 639–658. Savvidis, E., Stabrey, H., 1996. Experimentally ascertained material data from human femora and an analysis of the directiondependent stress tolerance. Zeitschrift fuer Orthopaedie 134, 445– 451. Van Rietbergen, B., Odgaard, A., Kabel, J., Huiskes, R., 1996. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. Journal of Biomechanics 29, 1653– 1657. Weinans, H., Huiskes, R., Grootenboer, H.J., 1992. The behaviour of adaptive bone-remodeling simulation models. Journal of Biomechanics 25, 1425–1441. Wirtz, D.C., Schiffers, N., Pandorf, T., Radermacher, K., Weichert, D., Forst, R., 2000. Critical evaluation of known bony material properties to realize anisotropic FE-simulation of the proximal femur. Journal of Biomechanics 33, 1325–1330. Yang, G., Kabel, J., van Rietbergen, B., Odgaard, A., Huiskes, R., Cowin, S.C., 1999. The anisotropic Hooke’s law for cancellous bone and wood. Journal of Elasticity 53, 125–146. Zysset, P.K., Goulet, R.W., Hollister, S.J., 1998. A global relationship between trabecular bone morphology and homogenized elastic properties. Journal of Biomedical Engineering 120, 640–646.