骨功能适应性数值模拟的若干进展

骨能够响应外部力学载荷,在特定位置生成或吸收骨组织不但可以提高骨的力学功能效率,而且还能及时修复日常载荷下骨内产生的微裂纹,以防止骨折并延长骨骼寿命,这称为骨功能适应性。与传统实验研究方法相比,计算机数值模拟具有可控性、可行性和可预测性等优势。鉴于骨功能适应性机制研究有重要的力学生物学理论意义和骨科临床的实用价值,本文对近年来国内外骨功能适应性数值模拟的新进展作一综述。     

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

In this article, a phenomenological numerical model of bone remodeling is proposed. This model is based on the poroelasticity theory in order to take into account the effects of fluid movements in bone adaptation. Moreover, the proposed remodeling law is based on the classical 'Stanford' law, enriched in order to take into account the loading frequency, through fluid movements. This coupling is materialized by a quadratic function of Darcy velocity. The numerical model is carried out, using a finite element method, and calibrated using experimental results at macroscopic level, from the literature. First results concern cyclic loadings on a mouse ulna, at different frequencies between 1 Hz and 30 Hz, for a force amplitude of 1.5 N and 2 N. Experimental results exhibit a sensitivity to the loading frequency, with privileged frequency for bone remodeling between 5 Hz and 10 Hz, for the force amplitude of 2 N. For the force amplitude of 1.5 N, no privileged frequencies for bone remodeling are highlighted. This tendency is reproduced by the proposed numerical computations. The model is identified on a single case (one frequency and one force amplitude) and validated on the other ones. The second experimental validation deals with a different loading regime, an internal fluid pressure at 20 Hz on a turkey ulna. The same framework is applied, and the numerical and experimental data are still matching in terms of gain in bone mass density.     

骨重建数值仿真中的控制方程

人体骨组织有着复杂的结构和生理机制,骨重建理论经历了定性分析、定量计算和计算机定量数值模拟三个阶段。目前,存在力学模型和现象模型两类成熟的骨重建模型,力学模型的共性就是表观密度随一定的力学刺激而变化,现象模型由基本多细胞单元的损伤状态和孔隙度变化来决定。大多数股骨重建仿真模型仍然将骨量的分布看作是各向同性的,这就不能完全反映骨组织微构造的本构关系。本文是对骨重建仿真模型的控制方程进行综述。     

不同力学激励对骨重建数值模拟的影响

目的研究采用应变能密度、等效应力、等效应变3种不同力学激励对骨重建数值模拟结果的影响。方法建立股骨近端的二维有限元模型,基于力学稳态理论的重建控制方程并结合有限元法,分别用3种不同力学激励模拟股骨近端的内部结构及密度分布,并与CT数据计算得到的骨密度值进行定量分析比较。结果 3种力学激励模拟得到的重建结果均能反映出股骨近端的主要特征结构,但采用等效应力作为激励时得到的股骨密度曲线图的趋势和数值都与CT图像数据更为一致。结论在骨重建力学调控机制中,应力可能起主导作用。准确预测和模拟骨重建过程将对矫形外科、骨伤治疗、人工假体的优化和个体化设计等临床实践提供理论依据。     

Effects of iron overload on bone remodeling in pigs

For study of the effects of an iron overload on bone remodeling, 5 control pigs were compared with 5 pigs given a total dose of 10.8 g of parenteral iron in 36 days. Treated pigs developed an iron tissue overload demonstrated by a marked increase in bone and liver iron. Except for a modest increase in SGOT, there was no biochemical or histologic sign of liver damage. Serum levels of 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D were unchanged in the treated pigs. There was no accumulation of iron in the parathyroid glands and the serum immunoreactive parathyroid hormone level was unchanged in the treated animals. Bone histomorphometry after double tetracycline labeling showed that in the treated pigs osteoblast cell surfaces, double and total labeled surfaces, appositional rate, and formation at tissue level were significantly decreased, and reversal surfaces were increased. Mineralization was not impaired because the osteoid thickness was unchanged. From the morphometric measurements it was concluded that osteoblast recruitment and the collagen synthesis rate were decreased. Mean wall thickness, which indicates the amount of bone synthesized, was also lowered. In contrast, the osteoclastic resorption surfaces and the depth of lacunae resulting from osteoclast resorption were unchanged by treatment. Despite this imbalance between formation and resorption, trabecular bone mass estimated on trabecular bone volume and bone ash was unchanged after 36 days' treatment. Perls' stain revealed that iron deposits were present in osteoblast and osteoclast cells and also inside the bone matrix, because there was a linear deposit along the trabecular surfaces, cement line, and osteoid-mineralized bone interface. Therefore, because treatment induced no modification of the major humoral regulators of bone metabolism, it is suggested that iron, which was present in bone cells and matrix, could play a role in bone remodeling.     

Morphologic changes associated with functional adaptation of the navicular bone of horses

Failure of functional adaptation to protect the skeleton from damage is common and is often associated with targeted remodeling of bone microdamage. Horses provide a suitable model for studying loading-related skeletal disease because horses are physically active, their exercise is usually regulated, and adaptive failure of various skeletal sites is common. We performed a histologic study of the navicular bone of three groups of horses: (1) young racing Thoroughbreds (n = 10); (2) young unshod ponies (n = 10); and (3) older horses with navicular syndrome (n = 6). Navicular syndrome is a painful condition that is a common cause of lameness and is associated with extensive remodeling of the navicular bone; a sesamoid bone located within the hoof which articulates with the second and third phalanges dorsally. The following variables were quantified: volumetric bone mineral density; cortical thickness (Ct.Th); bone volume fraction, microcrack surface density; density of osteocytes and empty lacunae; and resorption space density. Birefringence of bone collagen was also determined using circularly polarized light microscopy and disruption of the lacunocanalicular network was examined using confocal microscopy. Remodeling of the navicular bone resulted in formation of transverse secondary osteons orientated in a lateral to medial direction; bone collagen was similarly orientated. In horses with navicular syndrome, remodeling often led to the formation of intracortical cysts and development of multiple tidemarks at the articular surface. These changes were associated with high microcrack surface density, low bone volume fraction, low density of osteocytes, and poor osteocyte connectivity. Empty lacunae were increased in Thoroughbreds. Resorption space density was not increased in horses with navicular syndrome. Taken together, these data suggest that the navicular bone may experience habitual bending across the sagittal plane. Consequences of cumulative cyclic loading in horses with navicular syndrome include arthritic degeneration of adjacent joints and adaptive failure of the navicular bone, with accumulation of microdamage and associated low bone mass, poor osteocyte connectivity, and low osteocyte density, but not formation of greater numbers of resorption spaces.     

Mechanobiological adaptation of subchondral bone as a function of joint incongruity and loading

Computed tomography (CT) has been employed to determine non-invasively the distribution of subchondral bone density in joints and to evaluate their dominant loading pattern. The objective of this study was to investigate the relationship between subchondral bone adaptation, joint incongruity and loading, in order to determine to what extent the loading conditions and/or geometric configuration can be inferred from the distribution of subchondral density. Finite element models of joints with various degrees of incongruity were designed and a current remodeling theory implemented using the node-based approach. Appropriate combinations of joint incongruity and loading yielded subchondral bone density patterns consistent with experimental findings, specifically a bicentric distribution in the humero-ulnar joint and a monocentric distribution in the humero-radial joint. However, other combinations of incongruity and loading produced similar subchondral density patterns. Both the geometric joint configuration and the loading conditions influence the distribution of subchondral density in such a way that one of these factors must be known a priori to estimate the other. Since subchondral density can be assessed by CT and joint geometry by magnetic resonance imaging, the dominant loading pattern of joints may be potentially derived in the living using these non-invasive imaging methods.     

Effects of the replacement of chloride by methylsulphate on the membrane currents in frog atrial trabeculae

The effect of the replacement of extracellular chloride by methylsulphate was investigated on isolated frog atrial trabeculae using the voltage clamp technique. In methylsulphate solution, the following results were obtained: 1. After a transient depolarization of the resting potential, the action potential was lengthened and the diastolic depolarization rate of the repetitive activity was reduced. 2. In voltage clamp conditions, the current-voltage relationships and the steady-state inactivation curves of both early and secondary inward currents were unaffected. 3. The study of the evolution of the instantaneous backgroundd current with membrane potential showed a decrease of the current values. 4. The first component of the time-dependent outward currents was unaffected but the second component was reduced without change of its time-constant value. Assuming the absolute value of the chloride equilibrium potential at about -30 mV, it was suggested that the lengthening of the action potential in methylsulphate solution might be explained by the decrease of an influx of chloride ions which should participate in the repolarization. The reduction of the diastolic depolarization rate might be due to the decrease of an outflux of chloride ions which should be involved in the inward background currents unmasked by the deactivation of the time-dependent outward currents.     

Effects of age and loading rate on equine cortical bone failure

Although clinical bone fractures occur predominantly under impact loading (as occurs during sporting accidents, falls, high-speed impacts or other catastrophic events), experimentally validated studies on the dynamic fracture behavior of bone, at the loading rates associated with such events, remain limited. In this study, a series of tests were performed on femoral specimens obtained post-mortem from equine donors ranging in age from 6 months to 28 years. Fracture toughness and compressive tests were performed under both quasi-static and dynamic loading conditions in order to determine the effects of loading rate and age on the mechanical behavior of the cortical bone. Fracture toughness experiments were performed using a four-point bending geometry on single and double-notch specimens in order to measure fracture toughness, as well as observe differences in crack initiation between dynamic and quasi-static experiments. Compressive properties were measured on bone loaded parallel and transverse to the osteonal growth direction. Fracture propagation was then analyzed using scanning electron and scanning confocal microscopy to observe the effects of microstructural toughening mechanisms at different strain rates. Specimens from each horse were also analyzed for dry, wet and mineral densities, as well as weight percent mineral, in order to investigate possible influences of composition on mechanical behavior. Results indicate that bone has a higher compressive strength, but lower fracture toughness when tested dynamically as compared to quasi-static experiments. Fracture toughness also tends to decrease with age when measured quasi-statically, but shows little change with age under dynamic loading conditions, where brittle "cleavage-like" fracture behavior dominates.     

Effects of structural and functional cerebellar lesions on sensorimotor adaptation of saccades

The cerebellum is critically involved in the adaptation mechanisms that maintain the accuracy of goal-directed acts such as saccadic eye movements. Two categories of saccades, each relying on different adaptation mechanisms, are defined: reactive (externally triggered) saccades and voluntary (internally triggered) saccades. The contribution of the medio-posterior part of the cerebellum to reactive saccades adaptation has been clearly demonstrated, but the evidence that other parts of the cerebellum are also involved is limited. Moreover, the cerebellar substrates of voluntary saccades adaptation have only been marginally investigated. Here, we addressed these two questions by investigating the adaptive capabilities of patients with cerebellar or pre-cerebellar stroke. We recruited three groups of patients presenting focal lesions located, respectively, in the supero-anterior cerebellum, the infero-posterior cerebellum and the lateral medulla (leading to a Wallenberg syndrome including motor dysfunctions similar to those resulting from lesion of the medio-posterior cerebellum). Adaptations of reactive saccades and of voluntary saccades were tested during separate sessions in all patients and in a group of healthy participants. The functional lesion of the medio-posterior cerebellum in Wallenberg syndrome strongly impaired the adaptation of both reactive and voluntary saccades. In contrast, patients with lesion in the supero-anterior part of the cerebellum presented a specific adaptation deficit of voluntary saccades. Finally, patients with an infero-posterior cerebellar lesion showed mild adaptation deficits. We conclude that the medio-posterior cerebellum is critical for the adaptation of both saccade categories, whereas the supero-anterior cerebellum is specifically involved in the adaptation of voluntary saccades.     

Mapping the imprint of bone remodeling by atomic force microscopy

Understanding bone remodeling is essential for understanding bone as a whole. Bone remodeling takes place through a stepwise cellular process, with osteoclasts carving small cavities, also known as resorption pits, into the surface of trabecular bone, followed by osteoblasts, which refill the pits with new soft bone collagen matrix tissue (osteoid). The detailed structure of the surface in the frontier of a resorption pit before, during, and after the osteoid is being laid down is not well known. We present detailed atomic force microscope (AFM) images from the edge, the front end, and the bottom of a resorption pit in a human trabecular bone sample that showed signs of incomplete remodeling. The images reveal a scalloped surface left behind by the osteoclasts and the surface morphology of preexisting bone tissue and new bone tissue. In addition, we display the bone formation front in the pit showing the anchor points between the new bone and the existing bone. We also found evidence of microcracking in the front end of the pit, suggesting that microcracking was the initiator of this particular resorption pit. We anticipate that AFM may initiate a more detailed understanding of the influence of the remodeling process on the structure of bone, as well as a better understanding of the surface on which new bone tissue can be anchored.     

Ultrasonic wave propagation in trabecular bone predicted by the stratified model

The objective of this study was to investigate ultrasound propagation in trabecular bone by considering the wave reflection and transmission in a multilayered medium. The use of ultrasound to identify those at risk of osteoporosis is a promising diagnostic method providing a measure of bone mineral density (BMD). A stratified model was proposed to study the effect of transmission and reflection of ultrasound wave within the trabecular architecture on the relationship between ultrasound and BMD. The results demonstrated that ultrasound velocity in trabecular bone was highly correlated with the bone apparent density (r=0.97). Moreover, a consistent pattern of the frequency dependence of ultrasound attenuation coefficient has been observed between simulation using this model and experimental measurement of trabecular bone. The normalized broadband ultrasound attenuation (nBUA) derived from the simulation results revealed that nBUA was nonlinear with respect to trabecular porosity and BMD. The curve of the relationship between nBUA and BMD was parabolic in shape, and the peak magnitude of nBUA was observed at 60% of bone porosity. These results agreed with the published experimental data and demonstrated that according to the stratified model, reflection and transmission were important factors in the ultrasonic propagation through the trabecular bone. © 2001 Biomedical Engineering Society. PAC01: 4380Vj, 4380Qf, 8763Df, 8710+e, 4325Ed, 8719-j     

Effects of vitamin E on bone remodeling in perimenopausal women: Mini review

Vitamin E is known to be the most important antioxidant in the body, protecting against the effects of toxic radicals. The main idea behind the studies on vitamin E and bone metabolism stems from the concept that oxidative stress may interfere with the bone formation activity of osteoblasts which in turn can lead to osteoporosis. This mini-review, summarizes the studies on the effects of vitamin E on bone mineral density, fracture risk, bone formation, and resorption markers in perimenopausal women. Current evidence does not the support daily use of vitamin E for protection against osteoporosis and hip fracture risk in perimenopausal women. However some benefit has been shown in some observational studies. Low vitamin E (>6.2 mg/day) intake seems to be associated with an OR of 3.0 of hip fracture in current smokers. Compared with the highest quintile of alpha-tocopherol intake, the lowest quintile of intake conferred a multivariable-adjusted HR of 1.86 for hip fracture and 1.20 for any fracture. Alpha-tocopherol supplementation may alter the alpha-tocopherol/gamma-tocopherol ratio; which in turn may be associated with decreased osteoblastic activity. Interventional studies, especially randomized controlled trials (RCT), evaluating a possible causal relationship between serum vitamin E levels and BMD and hip fracture risk in perimenopausal women are needed.     

Effects of neonatal sympathectomy and capsaicin treatment on bone remodeling in rats.

Bone metabolism may be influenced by the innervation of skeletal tissues. Neuropeptides such as vasoactive intestinal peptide, from sympathetic nerves, and calcitonin gene-related peptide, from sensory nerves, have been implicated as local modulators of bone metabolism. The effect of neonatal sympathectomy and of capsaicin-induced sensory denervation in rats was studied on the following: (i) the radial bone growth and apposition rate in tibiae (normal growth and modeling) and (ii) the percentage of periosteal surface of the mandible occupied by osteoclasts during induced remodeling. Neonate rats were treated with guanethidine, capsaicin, or appropriate vehicle. At seven weeks, maxillary molars were removed to induce remodeling on the buccal surface of the mandible. Animals were killed four days after surgery. Cross-sectional cortical area, medullary area, and periosteal apposition rate were measured by histomorphometry in ground sections of tibiae. The percentage of periosteal surface at the remodeling site occupied by osteoclasts (stained for acid phosphatase) was measured in frozen, undecalcified sections. There was no significant difference in cortical or medullary area or periosteal apposition rate in tibiae between each drug treatment and its control. However, the mandibular bone surface occupied by osteoclasts was increased 45.5% (P less than or equal to 0.005) in animals treated neonatally with guanethidine compared to controls. In contrast, the mandibular surface occupied by osteoclasts was decreased 21.2% (P less than or equal to 0.04) in animals treated neonatally with capsaicin compared to controls. The alteration of bone remodeling (osteoclast surface) by both treatments indicates that sensory and sympathetic nerves play a role in focal metabolism of bone.     

Effects of vitamin E on bone remodeling in perimenopausal women: Mini review

Vitamin E is known to be the most important antioxidant in the body, protecting against the effects of toxic radicals. The main idea behind the studies on vitamin E and bone metabolism stems from the concept that oxidative stress may interfere with the bone formation activity of osteoblasts which in turn can lead to osteoporosis. This mini-review, summarizes the studies on the effects of vitamin E on bone mineral density, fracture risk, bone formation, and resorption markers in perimenopausal women. Current evidence does not the support daily use of vitamin E for protection against osteoporosis and hip fracture risk in perimenopausal women. However some benefit has been shown in some observational studies. Low vitamin E (>6.2 mg/day) intake seems to be associated with an OR of 3.0 of hip fracture in current smokers. Compared with the highest quintile of alpha-tocopherol intake, the lowest quintile of intake conferred a multivariable-adjusted HR of 1.86 for hip fracture and 1.20 for any fracture. Alpha-tocopherol supplementation may alter the alpha-tocopherol/gamma-tocopherol ratio; which in turn may be associated with decreased osteoblastic activity. Interventional studies, especially randomized controlled trials (RCT), evaluating a possible causal relationship between serum vitamin E levels and BMD and hip fracture risk in perimenopausal women are needed.     

The structure of the trabeculae of cancellous bone. 1. The calcaneus

87 either cylindroid or laminar trabeculae, isolated from the perpendicular or inferior bundles of the human calcaneus, were embedded in methylmatecrylate and serially cut along longitudinal and transversal planes with a rotatory-blade saw. The microscopical study of the sections showed that in 83% of the samples secondary osteons run along the longitudinal axis of the trabeculae and their lumina either form a continuous channel network throughout each trabecula (37% of cases) or are restricted to discrete segments (46% of cases). The trabeculae entirely devoid of osteons (17%) are the thinnest, never exceeding 400 microns in thickness. This value is not even exceeded by the segments devoid of osteons in the trabeculae in which the Haversian canals occur only intermittently; conversely, the segments containing Haversian canals can reach and exceed 600 microns in thickness. The maximum distance of the osteocytic lacunae from filtering surfaces--i.e. outer surface of the trabeculae or inner surface of the Haversian canals--was found to be almost the same in the segments of the trabeculae that enclose or not osteons, even though the average trabecular thickness is greater in the former than in the latter regions. On the basis of these findings the formation of endotrabecular osteons may be viewed as a device that indirectly favours the metabolic exchange of deep-seated osteocytes while increasing the free surface area available for bone tissue reconstruction. It remains doubtful whether the Haversian systems may also contribute to improve the mechanical properties of the trabeculae. The arrangement of the collagen fibrils, which differs between cylindroid and laminar trabeculae, is apparently well suited to ensure the resistance of the trabeculae to mechanical loading through the use of the least amount of building material, in accordance with Wolff's law.     

糖皮质激素对膝关节周围成骨细胞一氧化氮合酶和骨重建的影响

目的研究糖皮质激素对膝关节成骨细胞一氧化氮合酶表达和软骨下骨质重建的影响。方法取健康SD大鼠24只，体重（0．45±0．02）kg，随机分为实验组（A组）和对照组（B组），每组12只。实验组每周一次左膝关节腔内注射复方倍他米松0．02ml／kg，对照组每周一次左膝关节腔内注射生理盐水0．02ml／kg。4周时对两组大鼠的左侧膝关节股骨成骨细胞的诱生型一氧化氮合酶（inducible nitric oxide synthase，iNOS）和内皮细胞型一氧化氮合酶（endothelial nitric oxide synthase，eNOS）免疫组织化学研究，测定其平均灰度值和平均积分光密度，同时进行左胫骨软骨下骨质显微结构观察。结果实验组和对照组iNOS免疫组化的结果均为阴性，实验组eNOS的表达显著低于对照组（P〈0．01），实验组左胫骨的软骨下骨质旱骨质疏松特征。结论糖皮质激素对膝关节成骨细胞内皮细胞型一氧化氮合酶的表达和软骨下骨质生成有明显的抑制作用。