رفتار ساختاری و توزیع تنش در استخوان های بلند از اندام انسان
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|28707||2010||10 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Biomechanics, Volume 43, Issue 5, 22 March 2010, Pages 826–835
Although stiffness and strength of lower limb bones have been investigated in the past, information is not complete. While the femur has been extensively investigated, little information is available about the strain distribution in the tibia, and the fibula has not been tested in vitro. This study aimed at improving the understanding of the biomechanics of lower limb bones by: (i) measuring the stiffness and strain distributions of the different low limb bones; (ii) assessing the effect of viscoelasticity in whole bones within a physiological range of strain-rates; (iii) assessing the difference in the behaviour in relation to opposite directions of bending and torsion. The structural stiffness and strain distribution of paired femurs, tibias and fibulas from two donors were measured. Each region investigated of each bone was instrumented with 8–16 triaxial strain gauges (over 600 grids in total). Each bone was subjected to 6–12 different loading configurations. Tests were replicated at two different loading speeds covering the physiological range of strain-rates. Viscoelasticity did not have any pronounced effect on the structural stiffness and strain distribution, in the physiological range of loading rates explored in this study. The stiffness and strain distribution varied greatly between bone segments, but also between directions of loading. Different stiffness and strain distributions were observed when opposite directions of torque or opposite directions of bending (in the same plane) were applied. To our knowledge, this study represents the most extensive collection of whole-bone biomechanical properties of lower limb bones.
Measuring the stiffness, strength and strain distribution of bones is extremely important to understand bone biomechanics (Fung, 1980), bone formation and adaptation (Lanyon, 1980; Fung, 1990), osteoporosis (NIH, 2000), and fractures (Rockwood et al.,1991). In some cases a theoretical approach was taken to explain the structural stiffness of the femur, exploiting straight (Toridis, 1969; Cristofolini et al., 1996a) or curved beam theory (Raftopoulos and Qassem, 1987; Fabeck et al., 2002). However, such simplified approach cannot be used to investigate subtle effects. (Martens et al., 1980) measured in vitro the torsional stiffness and strength of 46 femurs and 37 tibias (however, specimens were not tested in pairs, and only some of the femurs and tibias came from the same donor). Later, ( Martens et al., 1986) tested to failure 15 pairs of femurs in bending. Failure of the proximal femoral metaphysis has often been investigated in vitro (e.g. Yang et al., 1996; Lochmüller et al., 2002; Cristofolini et al., 2007). In all such studies, only structural properties were investigated, while the strain distribution was not measured. When the strain distribution was investigated in the femur, in most cases a single loading configuration was used (e.g. Field and Rushton, 1989). A very detailed study on femur strains, although limited to a single specimen, is ( Huiskes et al., 1981): they applied different loading configurations to a human femur instrumented with 100 strain gauges. Later, ( Cristofolini et al., 2009) measured strains in 12 pairs of human femurs (11 strain gauges in the proximal metaphysis), with 6 different loading configurations. Also, the strain distribution in the tibia has sometimes been measured ( Gray et al., 2008). Viscoelasticity of bone tissue has been demonstrated at the tissue-level (Lakes and Katz, 1979). The Young modulus increases by 10% when the strain-rate is increased by 3 orders of magnitude (Raftopoulos et al., 1993). Most creep takes place in the first seconds, and accounts for typically 5–10% of the strain immediately after load application (Sasaki et al., 1993). However, due to the limited viscoelasticity of bone, elastic models are often used to describe cortical (Carter and Spengler, 1978; Fung, 1980) and cancellous bone (Martens et al., 1983; Keaveny et al., 1994). In fact, when cancellous bone was tested at different rates, viscoelasticity became obvious only at very low strain-rates (Guedes et al., 2006). When whole bones are investigated, the practical effects of viscoelasticity are questionable (Cherraf-Schweyer et al., 2007). For instance, Cristofolini et al. (2009) showed that creep over 30 seconds. (most physiological motor tasks take place in a shorter timespan) accounts for only 0.1–3.0% of the initial strain value. In fact, in most Finite Element (FE) models, bone is modelled as a linear material (Helgason et al., 2008). Only recently strain-rate-dependent material properties were implemented in FE models (Helgason et al., 2008). This review shows some limitations of the current knowledge. Firstly, while the structural behaviour and strain distribution in the femur has been extensively studied (e.g. (Huiskes et al., 1981; Field and Rushton, 1989; Yang et al., 1996; Lochmüller et al., 2002; Cristofolini et al., 2007; Cristofolini et al., 2009)), limited information is available for the tibia: the stiffness was measured in several specimens (Martens et al., 1980; Cristofolini and Viceconti, 2000; Heiner and Brown, 2001), but the strain distribution was measured only proximally (Gray et al., 2008). To our knowledge, no biomechanical properties have been measured for the fibula. Moreover, most of the published studies on lower limb bones focus on single bones, not on entire sets of bones from the same donors. In addition, the practical effect of viscoelasticity on the structural behaviour and strain distribution of whole bones is unclear. It is not ascertained whether different loading rates within the physiological range cause a different response, and if a linear and symmetric mechanical behaviour should be expected in long bones. The aims of the present study were to: • Measure the stiffness and strain distributions of the different low limb bones from the same donors; • assess if there is any significant effect of viscoelasticity on the structural behaviour and strain distribution in whole bones for physiological strain-rates; • assess if the structure and material properties cause any difference in relation to the direction of the applied load, especially considering opposite directions of bending and torsion.
نتیجه گیری انگلیسی
Biomechanical factors such as the stiffness, strength and strain distribution of bones are key factors in determining bone formation and adaptation (Lanyon, 1980; Fung, 1990), osteoporosis (NIH, 2000) and fractures (Rockwood et al., 1991). Although stiffness and strength of lower limb bones have been investigated in the past, information is not complete. While the femur has been extensively investigated, little information is available about the strain distribution in the tibia, and the fibula has not been tested in vitro. In addition, past studies on lower limb bones focused on single bones, not on entire sets of bones from the same donors. This study was designed to measure the stiffness and strain distribution of the different low limb bones from the same donors; to assess if there is any significant effect of viscoelasticity in whole bones within a physiological range of strain-rates; to assess if there is any difference in the behaviour in relation to opposite directions of bending and torsion. Lower limb long bones (femurs, tibias and fibulas) from the same subjects were extensively tested and compared in vitro. The effect of viscoelasticity was visible in our tests, although quite moderate: minimal creep was measured while load was held, and a small difference was found in terms of structural stiffness and strain values, between high- and low-strain rate. When a significant effect was observed, the bones were stiffer at the high-strain-rate. This shows that in the range of physiological strain-rates ( Bergmann et al., 2001 and Bergmann et al., 2004), the effect of the loading speed does not affect the results dramatically. Significant differences existed between the stiffness and between the strain distributions measured when opposite direction of bending or torsion were applied. It is possible that such differences in terms of stiffness correspond to a similar difference in terms of strength. This suggests that bone structures not only are optimized for a given loading component (e.g. bending in a given plane), but also for a specific direction of bending within such plane. The values found for the torsional stiffness of the femur and tibia (Fig. 5 and Fig. 6) are compatible with Martens et al. (1980): they found a stiffness of 9.81±2.88 Nm/° for the femur, and 5.69±1.76 Nm/° for the tibia (more in-depth comparisons are not possible as in that study specimens were unpaired, femurs and tibias were unmatched and the strain distribution was not measured). Although controlateral bones are often used in comparative studies on surgical treatments, biomechanical differences between controlateral bones have been seldom quantitatively investigated. In a study on 54 pairs of femurs (Eckstein et al., 2004), a difference of 0.3–57% was found for the failure strength between right and left. A study on dogs (Markel et al., 1994) showed a difference of 8–35% for the stiffness of controlateral long bones. In a previous study on 12 pairs of proximal femurs (Cristofolini et al., 2009), we found a strain difference of 16–62% (depending on the strain measurement location) between controlateral specimens. The differences in the present study for the stiffness (1–37% for the diaphysis of the femur, 7–18% for the tibia, 22–61% for the fibula) and strain (4–28% for the diaphysis of the femur, 3–63% for the tibia, 1–67% for the fibula) are compatible with those studies. The small creep observed here (few percent) and the small difference found between high- and low-strain rates are compatible with previous findings: Sasaki et al. (1993) reported that most creep takes place in few seconds, and accounts for 5–10% of the strain immediately after load application. Raftopoulos et al. (1993) observed that the Young modulus varied by only 10% when the strain-rate varied by 3 orders of magnitude. Also in cancellous bone viscoelasticity becomes obvious only at very low strain-rates (Guedes et al., 2006). In fact, in many cases viscoelasticity is neglected altogether (Carter and Spengler, 1978; Fung, 1980; Martens et al., 1983; Keaveny et al., 1994; Helgason et al., 2008), and (Cherraf-Schweyer et al., 2007) questioned the practical effects of viscoelasticity on a whole bone. To our knowledge, the effect of opposite loading direction on whole bones has never been investigated. Thanks to the large number of strain gauges and repetitions available in the present study, and to the high repeatability of the test, small but in some case statistically significant differences were detected for opposite directions of loading, both in terms of stiffness and strain distribution (Table 5 and Fig. 9). As the theory of elasticity cannot explain such asymmetric behavior (Timoshenko and Goodier, 1982), such differences can only be explained by a non-symmetric behaviour of the bone tissue. In fact, bone exhibits a non-symmetric behaviour, with a difference of several % for the Young modulus in tension and compression (Reilly and Burstein, 1975; Fung, 1980). This study was limited by the fact that only two donors were investigated. Such donors were selected as part of a larger EU-funded project addressing a multi-scale approach to the human skeleton. At all stages of the project, it was confirmed that such donors adequately represented typical elderly subjects (https://www.biomedtown.org/biomed_town/LHDL/users/repository/;Viceconti et al., 2008). Including a larger number of donors in such an in-depth study would be extremely difficult. In fact, each region of each bone was instrumented with 8–32 triaxial strain gauges (over 600 grids were used in total); each bone was subjected to 6–12 different loading configurations. To our knowledge, no such a detailed study was ever performed on an entire series of bones from the lower limb. The loading speed (and the consequent strain-rates) explored in this study were limited. Larger strain-rate ranges were explored in the past (Raftopoulos et al., 1993; Guedes et al., 2006). However, the scope of this study was not to assess if bones are viscoelastic in general, but to verify whether viscoelasticity does significantly affect the structural stiffness and the strain pattern within a physiological range. Some differences were observed between controlateral specimens. It is unclear whether they are due to differences in terms of material properties, anatomical differences (or both). Further investigation is needed at different dimensional scales to elucidate donors’ laterality (body-level), possibly different material properties (tissue-level) and composition (sub-tissue-level). Another limitation relates to the fact that for some bones (e.g. tibia) the strong non-axisymmetry of the cross-section makes practical testing more difficult: a small alignment error (Conti et al., 2008) strongly affects the bending stiffness. This can explain why results for the tibia were somewhat less consistent. In summary, an extensive biomechanical characterization of the long bones of the human lower limb was carried out. A number of different loading configurations were applied to the femur, tibia and fibula. Viscoelasticity did not have any pronounced effect in the physiological range of loading rates explored in this study. The stiffness and strain distribution varied greatly between bone segments, but also between directions of loading. Surprisingly, different stiffness and strain distributions were observed when opposite directions of torque or opposite directions of bending (in the same plane) were applied.