腰椎椎体边缘骨质增生的模拟
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摘要
骨质增生是一种关节多发疾病，它普遍地困扰着人类。因此，骨质增生引起了人们的广泛的关注和研究。目前，对于骨质增生的研究，很多医学界的工作者只是从生理、生物化学和生物力学的角度定性的研究了骨质增生的病因和发病机理。而运用骨功能适应性定量理论研究骨质增生，国内外未见报道，只有朱兴华等人进行了膝内翻时引起骨质增生的探讨研究。
腰椎关节是人体最重要的关节之一，由于负重大且活动幅度较大，因此腰椎关节是骨质增生的好发部位之一。在引起腰椎关节椎体平台上骨质增生的原因中，腰椎间盘退形性改变是一个主要的因素。腰椎间盘退形性改变时，椎体平台上所承受的载荷向椎体平台边缘偏移，使得椎体平台边缘产生应力集中，为了缓解这种应力集中，椎体平台边缘形成骨质增生，使关节重新稳定。在本文中，我们把骨自由化理论和有限元方法相结合，依据腰椎间盘退形性改变引起腰椎椎体平台边缘骨质增生的生理过程，从力学和生物学角度出发，在计算机上模拟出了腰椎间盘退形性改变引起的腰椎椎体平台边缘的骨质增生。我们根据骨刺形成的生理过程和形态，引用朱兴华、刘百奇对增生出的骨刺上承受的载荷及其分布形式做出的假设，即增生出的骨刺上承受的载荷的分布形式符合方程。其中，是和椎体平台峰值应变以及骨刺的生理形态有关的常数，是骨刺上任意一点到腰椎关节椎体平台边缘的水平距离，单位为mm。于是，我们确定了模拟过程中作用在模型上的载荷。
然后，我们从初始外形不确定的（采用74×74矩形方板模型，模型中每个单元的弹性模量、泊松比、和密度都是相同的）有限元模型出发，把骨再造理论和有限元方法结合，运用Fortran语言编写有限元程序，对第三腰椎椎体冠状面的外部形状和内部结构同时进行了模拟。我们采用线性骨再造速率方程作为模拟过程中的控制方程，采用朱兴华、王挺峰提出的新的收敛准则作为骨再造的迭代控制方法。最后得出的结果表明：从初始外形不确定（采用不规则矩形板的外形作为初始外形）的有限元模型出发，对第三腰椎椎体的外部形状和内部结构同时进行模拟，其模拟结果与真实情况比较接近。
接着，我们把先前得到的第三腰椎椎体的外部形状和内部结构的模拟结
果为初始模型，这个初始模型仍为一个74×74矩形方板模型。但是，模型中每个单元的弹性模量、密度都不再是均匀的，这些数值可以从我们模拟的正常情况下椎体结构的模拟结果得到。然后，在这个初始模型上作用椎间盘退形性改变时的载荷，骨刺上作用的载荷分布符合方程：。采用线性骨再造速率方程作为模拟过程中的控制方程，采用采用朱兴华、王挺峰提出的新的收敛准则作为骨再造的迭代控制方法。最后模拟出了椎间盘退形性改变情况下的椎体平台冠状面边缘的骨质增生。另外，我们还模拟了由于韧带-椎间盘、椎体间隙的形成引起的骨质增生。椎间隙韧带下分离后形成间隙，因多同时伴有局部微血管的撕裂与出血而形成韧带-椎间盘间隙血肿。随着韧带下间隙的血肿形成，纤维母细胞即开始活跃，并逐渐长入血肿内，渐而以肉牙组织取代血肿。随着血肿的机化老化和钙盐沉积，最后形成突向椎体周围的骨赘。
最后根据我们的模拟结果，我们得出了以下结论：
采用骨自优化理论与有限元相结合的方法能够模拟骨质增生。随着椎间盘退化程度的加剧，增生骨刺的高度，宽度和体积随之增大。这是因为，椎间盘退化引起椎体平台边缘应力集中，骨结构为了适应新的力学环境，形成骨质增生，随椎间盘退化程度加剧，应力集中加剧，增生也就更加严重。
椎间盘退形性改变引起的骨质增生，并不是无限制的。当增生达到一定程度后，缓解了应力集中，骨结构重新适应了新的力学环境，使腰椎关节重新达到一个新的稳定状态。
许多特殊行业的人工作时，如跳水运动员跳水时，腰椎关节很容易发生很大的异常载荷，本文只考虑了正常运动情况下的载荷。在下一步的研究中，我们准备在考虑这些异常载荷的情况下，模拟腰椎椎体平台的骨质增生。由于这些异常载荷的作用，增生出的骨刺的高度、宽度、体积和密度可能都会增大。
The incidence of osteoarthritis(OA) is so high that the disease attracts a great deal of researcher. At present, most of the researchs on the pathogeny and the pathogenesis of osteoarthritis are from the point of physiology, biochemistry and biomechanics. but it is not reported at home and overseas studying osteoarthritis through using bone functional adaptability theory.
Lumbar vertebrae is the foremost bearing force articulation, and it is the position which occurs osteoarthritis most easily. Many factors cause the osteoarthritis on the flat roof of the lumbar centrum, but the intervertebral discs degeneration is the dominative one. In the edge condition, the load on the flat roof of the lumbar centrum deviating from mid to medial results in stress concentration at the medial of the roof of the lumbar centrum. To release this condition, osteoarthritis occurs so as to make the articulation re-stable. In this paper, according to the physiological forming progress of osteoarthritis on the medial edge of the flat roof of the lumbar centrum which is caused by intervertebral discs degeneration, the simulation of osteoarthritis is made on computer from the point of view on biomechanics and physiology through using the bone functional adaptability theory combined with the finite element method.
we adopt the force analysis method of lumbar vertebrae put forward by Pawel Kurowski. when a person of a 60 kilograms of weights is standing on one foot, the load and it’s distribution on the flat roof of the lumbar centrum , under healthy and degenerated discs condition, are respectively get. Then, according the physiological forming progress and the shape of the spur, we adopt the hypothesis the that was proposed by Liu Baiqi that the pressure distribution on the spur matches the equation: ,in which, “a” is a constant which is related with the shape of the spur and the peak value of the stress on the flat roof of the lumbar centrum, and “b” is the level distance from a point on the spur to the medial edge of the flat roof, the unit is mm.
First, we simulated the interior structure and the exterior shape of the
lumbar centrum, using a finite two-dimensional element model which takes the shape of a rectangular plate as the initial model form. In the simulation, we take linear bone remodeling velocity equations as the manipulative equation. According to the simulative result of the part, we draw some conclusions as follows: We can simulate the structure of the lumbar vertebrae, through taking linear bone remodeling velocity equation as the manipulative equation, and the simulative structure of the lumbar vertebrae is very similar with the actual structure.
Then, we take the simulative structure as the initial model, applying the load when the intervertebral disc is slightly degenerated and moderately degenerated . The load distribution on the spur matches the equation: .So, we simulate the osteoarthritis on the edge of the flat roof of the lumbar vertebrae, by taking linear bone remodeling velocity equations as the manipulative equation.
Finally, according to the simulative result of the part, we draw some conclusions as follows:
The osteoarthritis can be simulated through using bone self-optimizing theory combined with the finite element method.With the severity of the discs degeneration, the height, width and area of the spur increase.
The increase of osteoarthritis is not unlimited, when the spur increase to some extent, the stress concentration is released. The bone structure adapt itself to the loading condition, which makes the Lumbar vertebrae joint reach a new stable condition.
Under the intervertebral discs degeneration condition, the abnormal load which is much bigger than the normal occurs more easily. We only consider the normal load in this paper. In the farther study, the abnormal load will be considered. The height, width and area of the spur perhaps increase more ,because of the action of the abnormal load.
腰椎关节是人体最重要的关节之一，由于负重大且活动幅度较大，因此腰椎关节是骨质增生的好发部位之一。在引起腰椎关节椎体平台上骨质增生的原因中，腰椎间盘退形性改变是一个主要的因素。腰椎间盘退形性改变时，椎体平台上所承受的载荷向椎体平台边缘偏移，使得椎体平台边缘产生应力集中，为了缓解这种应力集中，椎体平台边缘形成骨质增生，使关节重新稳定。在本文中，我们把骨自由化理论和有限元方法相结合，依据腰椎间盘退形性改变引起腰椎椎体平台边缘骨质增生的生理过程，从力学和生物学角度出发，在计算机上模拟出了腰椎间盘退形性改变引起的腰椎椎体平台边缘的骨质增生。我们根据骨刺形成的生理过程和形态，引用朱兴华、刘百奇对增生出的骨刺上承受的载荷及其分布形式做出的假设，即增生出的骨刺上承受的载荷的分布形式符合方程。其中，是和椎体平台峰值应变以及骨刺的生理形态有关的常数，是骨刺上任意一点到腰椎关节椎体平台边缘的水平距离，单位为mm。于是，我们确定了模拟过程中作用在模型上的载荷。
然后，我们从初始外形不确定的（采用74×74矩形方板模型，模型中每个单元的弹性模量、泊松比、和密度都是相同的）有限元模型出发，把骨再造理论和有限元方法结合，运用Fortran语言编写有限元程序，对第三腰椎椎体冠状面的外部形状和内部结构同时进行了模拟。我们采用线性骨再造速率方程作为模拟过程中的控制方程，采用朱兴华、王挺峰提出的新的收敛准则作为骨再造的迭代控制方法。最后得出的结果表明：从初始外形不确定（采用不规则矩形板的外形作为初始外形）的有限元模型出发，对第三腰椎椎体的外部形状和内部结构同时进行模拟，其模拟结果与真实情况比较接近。
接着，我们把先前得到的第三腰椎椎体的外部形状和内部结构的模拟结
果为初始模型，这个初始模型仍为一个74×74矩形方板模型。但是，模型中每个单元的弹性模量、密度都不再是均匀的，这些数值可以从我们模拟的正常情况下椎体结构的模拟结果得到。然后，在这个初始模型上作用椎间盘退形性改变时的载荷，骨刺上作用的载荷分布符合方程：。采用线性骨再造速率方程作为模拟过程中的控制方程，采用采用朱兴华、王挺峰提出的新的收敛准则作为骨再造的迭代控制方法。最后模拟出了椎间盘退形性改变情况下的椎体平台冠状面边缘的骨质增生。另外，我们还模拟了由于韧带-椎间盘、椎体间隙的形成引起的骨质增生。椎间隙韧带下分离后形成间隙，因多同时伴有局部微血管的撕裂与出血而形成韧带-椎间盘间隙血肿。随着韧带下间隙的血肿形成，纤维母细胞即开始活跃，并逐渐长入血肿内，渐而以肉牙组织取代血肿。随着血肿的机化老化和钙盐沉积，最后形成突向椎体周围的骨赘。
最后根据我们的模拟结果，我们得出了以下结论：
采用骨自优化理论与有限元相结合的方法能够模拟骨质增生。随着椎间盘退化程度的加剧，增生骨刺的高度，宽度和体积随之增大。这是因为，椎间盘退化引起椎体平台边缘应力集中，骨结构为了适应新的力学环境，形成骨质增生，随椎间盘退化程度加剧，应力集中加剧，增生也就更加严重。
椎间盘退形性改变引起的骨质增生，并不是无限制的。当增生达到一定程度后，缓解了应力集中，骨结构重新适应了新的力学环境，使腰椎关节重新达到一个新的稳定状态。
许多特殊行业的人工作时，如跳水运动员跳水时，腰椎关节很容易发生很大的异常载荷，本文只考虑了正常运动情况下的载荷。在下一步的研究中，我们准备在考虑这些异常载荷的情况下，模拟腰椎椎体平台的骨质增生。由于这些异常载荷的作用，增生出的骨刺的高度、宽度、体积和密度可能都会增大。
The incidence of osteoarthritis(OA) is so high that the disease attracts a great deal of researcher. At present, most of the researchs on the pathogeny and the pathogenesis of osteoarthritis are from the point of physiology, biochemistry and biomechanics. but it is not reported at home and overseas studying osteoarthritis through using bone functional adaptability theory.
Lumbar vertebrae is the foremost bearing force articulation, and it is the position which occurs osteoarthritis most easily. Many factors cause the osteoarthritis on the flat roof of the lumbar centrum, but the intervertebral discs degeneration is the dominative one. In the edge condition, the load on the flat roof of the lumbar centrum deviating from mid to medial results in stress concentration at the medial of the roof of the lumbar centrum. To release this condition, osteoarthritis occurs so as to make the articulation re-stable. In this paper, according to the physiological forming progress of osteoarthritis on the medial edge of the flat roof of the lumbar centrum which is caused by intervertebral discs degeneration, the simulation of osteoarthritis is made on computer from the point of view on biomechanics and physiology through using the bone functional adaptability theory combined with the finite element method.
we adopt the force analysis method of lumbar vertebrae put forward by Pawel Kurowski. when a person of a 60 kilograms of weights is standing on one foot, the load and it’s distribution on the flat roof of the lumbar centrum , under healthy and degenerated discs condition, are respectively get. Then, according the physiological forming progress and the shape of the spur, we adopt the hypothesis the that was proposed by Liu Baiqi that the pressure distribution on the spur matches the equation: ,in which, “a” is a constant which is related with the shape of the spur and the peak value of the stress on the flat roof of the lumbar centrum, and “b” is the level distance from a point on the spur to the medial edge of the flat roof, the unit is mm.
First, we simulated the interior structure and the exterior shape of the
lumbar centrum, using a finite two-dimensional element model which takes the shape of a rectangular plate as the initial model form. In the simulation, we take linear bone remodeling velocity equations as the manipulative equation. According to the simulative result of the part, we draw some conclusions as follows: We can simulate the structure of the lumbar vertebrae, through taking linear bone remodeling velocity equation as the manipulative equation, and the simulative structure of the lumbar vertebrae is very similar with the actual structure.
Then, we take the simulative structure as the initial model, applying the load when the intervertebral disc is slightly degenerated and moderately degenerated . The load distribution on the spur matches the equation: .So, we simulate the osteoarthritis on the edge of the flat roof of the lumbar vertebrae, by taking linear bone remodeling velocity equations as the manipulative equation.
Finally, according to the simulative result of the part, we draw some conclusions as follows:
The osteoarthritis can be simulated through using bone self-optimizing theory combined with the finite element method.With the severity of the discs degeneration, the height, width and area of the spur increase.
The increase of osteoarthritis is not unlimited, when the spur increase to some extent, the stress concentration is released. The bone structure adapt itself to the loading condition, which makes the Lumbar vertebrae joint reach a new stable condition.
Under the intervertebral discs degeneration condition, the abnormal load which is much bigger than the normal occurs more easily. We only consider the normal load in this paper. In the farther study, the abnormal load will be considered. The height, width and area of the spur perhaps increase more ,because of the action of the abnormal load.
引文
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