骨的多孔介质弹性力学行为及力—电效应研究
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摘要
骨作为一种多孔的材料结构系统,在生理环境中经常受到循环载荷的作用,例如日常生活中的行走、跑步、跳跃等活动。而这些活动(力)能够被骨“感受”并“适应’'(Wolff定理),那么这是通过怎样一个机制完成的呢?尽管现在还没有一个明确的定论,但是要弄清楚这种机制必须从骨的微观组成结构——骨单元水平着手。因为它可能与骨微观结构内部液体流动而产生的一系列效应有关,如骨内液体的压力分布、扩散、化学运输、流体剪应力、流动电位等等。这些效应还可能是骨生长和骨重建的诱导机制,因此本文以此背景为出发点建立了不同尺度的骨的多孔介质弹性力学模型,研究了外载荷的作用下其内部液体的压力分布及流动行为。
骨的力-电效应根据机理又分为压电效应和流动电位效应(动电效应)。压电效应多存在与干骨中,而在湿骨或活体骨中主要以流动电位为主,所以本文又建立了骨小管及哈弗管的流动电位模型来揭示活体骨的力传导和力-电耦合机制。
此外,本文还运用多孔介质弹性理论对骨材料结构(宏观尺度)进行了理论建模,研究了实验室条件下的多孔弹性响应。考虑到以前的实验都是在骨材料(小尺寸)水平进行的,而生命状态的骨大都是作为一个整体结构来承受外部载荷,如行走、跑步和跳跃等,因此致力于研究整体大段骨结构在动态载荷过程中产生的电位幅值及其分布特点,不仅是弄清楚电信号影响骨细胞生长机理的必要步骤,也是实现骨治疗和骨重建的生理基础。为此,结合建立的理论模型,我们利用INSTRON(8874)试验机对大段牛股骨进行了模拟人日常活动(行走、跑步)受力状态下的力-电效应的实验研究。
综上,具体的工作清单及主要结论如下：
(一)、应用多孔介质弹性力学原理分别建立了中空的和考虑哈弗液体的骨单元(～150μm)理论模型,研究了载荷变形下骨单元内部液体的压力分布及流动行为,从而架起了骨单元内液体压力场、流速场与外界载荷(轴向、周期)之间的桥梁。主要结论如下：
(ⅰ)与中空(不考虑哈弗液体)骨单元模型相比,考虑哈弗(管)液体存在的骨单元模型中的液体压力场和流速场会明显增大。
(ⅱ)一般来说,骨单元内液体的压力和流速幅值随着载荷幅值(应变幅值)和频率(考虑哈弗液体的骨单元除外)的增大而增大。
(ⅲ)骨单元内液体的压力和流速幅值与应变率成正比,并且真正决定骨单元多孔介质弹性力学行为的是应变率。
(ⅳ)在周期性的载荷作用下,骨单元内部液体的压力梯度呈现周期性的变化,这样导致液体的周期性往返流动。
(ⅴ)在中空的骨单元模型中,渗透率对液体压力幅值的影响要大于流速幅值。
(二)、在(一)的基础上建立了骨小管(～500nm)的流动电位模型,建立了外界载荷(轴向、周期)与骨小管内液体的流动及流动电位的关系,同时考察了载荷大小、频率等因素对这一流动电位的影响。主要结论如下：
(ⅰ)骨小管内液体产生的流动电位随着外部载荷大小(应变幅值)和频率的增加而增大。
(ⅱ)影响流动电位的决定因素是应变率,并且在应变率相同的情况下,含哈弗管液体的骨单元模型中,骨小管产生的流动电位要大于中空骨单元模型中产生的流动电位。
(ⅲ)在周期性的载荷作用下,流动电位呈现周期性的变化,这主要是由于骨小管内液体的周期性往返流动造成的。
(ⅳ)骨小管内的流动电位随小管半径的增大而增大,但是与骨小管的长度无关。
(三)、应用多孔介质弹性力学原理建立了实验条件下的四种骨材料(～mm)理论模型,并研究了它们各自的多孔介质弹性力学行为,并得到了以下一些结论：
(ⅰ)骨材料试件的多孔介质弹性力学行为与骨单元尺度下的相类似,骨内液体的压力和流速幅值均正比于外部载荷大小(应变幅值)、频率和应变率,但是决定骨材料内部液体的压力和流速特性的是载荷的应变率。
(ⅱ)在周期性的载荷作用下,骨材料内部液体的压力梯度和流动行为呈现周期性的变化。
(ⅲ)在骨材料尺度,渗透率对液体压强的影响要大于流速。
(ⅳ)一维流动模型中产生的流动电位幅值正比于载荷幅值和频率,并由应变率决定；另外流动电位随着渗透率的增大而减小。
(四)、对大段牛股骨结构(～cm)进行了人日常活动(行走、跑步)受力状态下的力-电效应实验研究,得到了在模拟人行走和跑步状态下的力-电电位,并与理论模型进行了对比。结论如下：
(ⅰ)当牛股骨给以人正常行走和跑步状态下的载荷和频率时,它都会产生力-电效应,跑步状态下产生的电压较行走的大。据此说明人在行走或跑步时也会产生电信号,并且跑步时的电压较行走时大；行走和跑步过程中产生的电压随载荷和频率的增大而增大。
(ⅱ)在行走和跑步的载荷状态下都将产生两个电位峰值,一个是脚后跟着地时(加载)所形成的负峰值,另一个是前脚掌离地时(卸载)所形成的正峰值,而且后一个峰值大于前一个峰值(绝对值)。
(ⅲ)骨在受拉伸和压缩时力-电特性不相同,在相同的应变率或应力梯度下受拉伸时产生的压电电位大于受压缩时的值。
(ⅳ)产生的电位幅值与载荷幅值、频率、应变率密切相关,实验曲线中近似地显示出正比例关系,与理论结果相符。
Cortical bone, as a poroelastic material and composite system, often bears cyclic loads that might come from walking, running or other daily activities. These activities can make bone "feel" and "adapt", but what is the mechanism? In order to explore it, researches should be conducted in the level of osteon, because the mechanism may be related with strain-derived fluid stimuli such as fluid shear stress, fluid pressure gradient, chemotransport and stress/strain-generalized potentials (SGP), etc. These effects may be the activated signals of bone growth and bone remodeling. Therefore, it is significant to propose a biomechanical osteon model to examine its intraosseous pressure characteristics and fluid flowing behavior.
Bone's Stress-Generated Potentials (SGP) mainly includes piezoelectric potential and streaming potential. The piezoelectric potential generally arouses in the loaded dry bone, while the streaming potential is in the wet or living bone. Therefore, we chose our task to model the streaming potential produced in bone canaliculi to explore the mechanisms of mechanotransduction and electromechanotransduction.
Besides, the macroscopical bone material specimens were modeled by using the poroelasticity theory and its poroelastic responses were studied under laboratory conditions. Most previous experimental studies were conducted on the level of bone material. However, physiological bones bear the external dynamic loading as a whole structure, such as walking, running and jumping. Therefore, it has a more realistic reference value to test the SGP produced in the large whole bone structure. Thus, under simulated physiological loading states (walking and running), we examined the cattle femur (large bone structure)'s SGP by INSTRON (8847) testing machine.
From the above, the more detailed task list and the main conclusion are as follows:
(1) We respectively proposed a hollow and Haversian fluid (pressure) contained osteon model (～150μm) to examine its intraosseous pressure characteristics and fluid flowing behavior under the external loading environments. The relationship among the external loads (axial and cyclic), intraosseous pressure, and fluid velocity was established. Some conclusions are obtained below:
(1) The fluid pressure amplitude in the Haversian fluid (pressure) considered osteon model is much higher than that in hollow osteon model.
(ii) Generally, the increase of axial strain amplitude and frequency can result in the increase of fluid pressure and velocity amplitudes.
(iii) Both the pore pressure and fluid velocity amplitudes are proportionate to the amplitude of strain rate.
(iv) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(v) At the hollow osteon scale, the pressure is strongly affected by permeability variations whereas fluid velocity is not.
(2) Base on (1), a streaming potential model produced in bone canaliculi (-500nm) was established and examined its influence of loading amplitude, frequency, and permeability, etc.
(i) The streaming potential amplitude (SPA) is proportional to the pressure amplitude difference, strain amplitude, frequency and strain rate amplitude. However, the key loading factor governing the SP is the strain rate and it can be seen as a representative loading parameter under the physiological state.
(ii) The SPA produced in the canaliculi of Haversian fluid contained osteon model is larger than that of hollow osteon (not considering Haversian fluid) model.
(iii) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(iv) The larger canaliculi radius, the larger SPA produced, but the SPA is independent of the canaliculi length.
(3) The macroscopical bone material specimens (-mm) were modeled by using the poroelasticity theory and its poroelastic responses were studied under laboratory conditions. Its poroelastic behaviors also have been compared with the osteon scale model.
(i) The poroelastic behaviors of bone material specimens are similar to that of osteon scale:Both the pore fluid's pressure and velocity amplitudes are proportionate to the strain amplitude, frequency and strain rate amplitude. However, the key loading factor governing its poroelastic behavior is the strain rate.
(ii) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(iii) At the bone material scale, the pressure is strongly affected by permeability variations whereas fluid velocity is not.
(iv) In the one dimensional flow model, the streaming potential amplitude (SPA) is proportional to the pressure amplitude difference, strain amplitude, frequency and strain rate amplitude. Besides, the increase of the permeability results in the decrease of SPA.
(4) Under simulated human physiological loading states (walking and running), we obtained the cattle femur's (large bone structure:-mm) SGP by INSTRON (8847) testing machine and made a comparison with theoretical analysis.
(ⅰ) The cattle femur, being given the human's normal walking and running state of load and frequency, will generate electric potential. Voltage amplitude generated by running is larger than that of walk. The electric potential amplitude will become larger with the load and frequency increases.
(ⅱ) There will have two electric potential peaks under the conditions of walking and running. One of them is a negative peak which is generated by heel landing (loading), the other is a positive peak generated when the front sole off the ground (unloading). The second potential peak is larger than that of the first one.
(ⅲ) Bones have different electric properties in the condition of tension and compression. Under the same strain rate or stress gradient, the electric potential value generated by tensile is greater than that of compression.
(ⅳ) The electric potential amplitude is approximately proportional to the loading amplitude, frequency, strain rate, which agrees with the conclusion of theoretical model.
骨的力-电效应根据机理又分为压电效应和流动电位效应(动电效应)。压电效应多存在与干骨中,而在湿骨或活体骨中主要以流动电位为主,所以本文又建立了骨小管及哈弗管的流动电位模型来揭示活体骨的力传导和力-电耦合机制。
此外,本文还运用多孔介质弹性理论对骨材料结构(宏观尺度)进行了理论建模,研究了实验室条件下的多孔弹性响应。考虑到以前的实验都是在骨材料(小尺寸)水平进行的,而生命状态的骨大都是作为一个整体结构来承受外部载荷,如行走、跑步和跳跃等,因此致力于研究整体大段骨结构在动态载荷过程中产生的电位幅值及其分布特点,不仅是弄清楚电信号影响骨细胞生长机理的必要步骤,也是实现骨治疗和骨重建的生理基础。为此,结合建立的理论模型,我们利用INSTRON(8874)试验机对大段牛股骨进行了模拟人日常活动(行走、跑步)受力状态下的力-电效应的实验研究。
综上,具体的工作清单及主要结论如下：
(一)、应用多孔介质弹性力学原理分别建立了中空的和考虑哈弗液体的骨单元(～150μm)理论模型,研究了载荷变形下骨单元内部液体的压力分布及流动行为,从而架起了骨单元内液体压力场、流速场与外界载荷(轴向、周期)之间的桥梁。主要结论如下：
(ⅰ)与中空(不考虑哈弗液体)骨单元模型相比,考虑哈弗(管)液体存在的骨单元模型中的液体压力场和流速场会明显增大。
(ⅱ)一般来说,骨单元内液体的压力和流速幅值随着载荷幅值(应变幅值)和频率(考虑哈弗液体的骨单元除外)的增大而增大。
(ⅲ)骨单元内液体的压力和流速幅值与应变率成正比,并且真正决定骨单元多孔介质弹性力学行为的是应变率。
(ⅳ)在周期性的载荷作用下,骨单元内部液体的压力梯度呈现周期性的变化,这样导致液体的周期性往返流动。
(ⅴ)在中空的骨单元模型中,渗透率对液体压力幅值的影响要大于流速幅值。
(二)、在(一)的基础上建立了骨小管(～500nm)的流动电位模型,建立了外界载荷(轴向、周期)与骨小管内液体的流动及流动电位的关系,同时考察了载荷大小、频率等因素对这一流动电位的影响。主要结论如下：
(ⅰ)骨小管内液体产生的流动电位随着外部载荷大小(应变幅值)和频率的增加而增大。
(ⅱ)影响流动电位的决定因素是应变率,并且在应变率相同的情况下,含哈弗管液体的骨单元模型中,骨小管产生的流动电位要大于中空骨单元模型中产生的流动电位。
(ⅲ)在周期性的载荷作用下,流动电位呈现周期性的变化,这主要是由于骨小管内液体的周期性往返流动造成的。
(ⅳ)骨小管内的流动电位随小管半径的增大而增大,但是与骨小管的长度无关。
(三)、应用多孔介质弹性力学原理建立了实验条件下的四种骨材料(～mm)理论模型,并研究了它们各自的多孔介质弹性力学行为,并得到了以下一些结论：
(ⅰ)骨材料试件的多孔介质弹性力学行为与骨单元尺度下的相类似,骨内液体的压力和流速幅值均正比于外部载荷大小(应变幅值)、频率和应变率,但是决定骨材料内部液体的压力和流速特性的是载荷的应变率。
(ⅱ)在周期性的载荷作用下,骨材料内部液体的压力梯度和流动行为呈现周期性的变化。
(ⅲ)在骨材料尺度,渗透率对液体压强的影响要大于流速。
(ⅳ)一维流动模型中产生的流动电位幅值正比于载荷幅值和频率,并由应变率决定；另外流动电位随着渗透率的增大而减小。
(四)、对大段牛股骨结构(～cm)进行了人日常活动(行走、跑步)受力状态下的力-电效应实验研究,得到了在模拟人行走和跑步状态下的力-电电位,并与理论模型进行了对比。结论如下：
(ⅰ)当牛股骨给以人正常行走和跑步状态下的载荷和频率时,它都会产生力-电效应,跑步状态下产生的电压较行走的大。据此说明人在行走或跑步时也会产生电信号,并且跑步时的电压较行走时大；行走和跑步过程中产生的电压随载荷和频率的增大而增大。
(ⅱ)在行走和跑步的载荷状态下都将产生两个电位峰值,一个是脚后跟着地时(加载)所形成的负峰值,另一个是前脚掌离地时(卸载)所形成的正峰值,而且后一个峰值大于前一个峰值(绝对值)。
(ⅲ)骨在受拉伸和压缩时力-电特性不相同,在相同的应变率或应力梯度下受拉伸时产生的压电电位大于受压缩时的值。
(ⅳ)产生的电位幅值与载荷幅值、频率、应变率密切相关,实验曲线中近似地显示出正比例关系,与理论结果相符。
Cortical bone, as a poroelastic material and composite system, often bears cyclic loads that might come from walking, running or other daily activities. These activities can make bone "feel" and "adapt", but what is the mechanism? In order to explore it, researches should be conducted in the level of osteon, because the mechanism may be related with strain-derived fluid stimuli such as fluid shear stress, fluid pressure gradient, chemotransport and stress/strain-generalized potentials (SGP), etc. These effects may be the activated signals of bone growth and bone remodeling. Therefore, it is significant to propose a biomechanical osteon model to examine its intraosseous pressure characteristics and fluid flowing behavior.
Bone's Stress-Generated Potentials (SGP) mainly includes piezoelectric potential and streaming potential. The piezoelectric potential generally arouses in the loaded dry bone, while the streaming potential is in the wet or living bone. Therefore, we chose our task to model the streaming potential produced in bone canaliculi to explore the mechanisms of mechanotransduction and electromechanotransduction.
Besides, the macroscopical bone material specimens were modeled by using the poroelasticity theory and its poroelastic responses were studied under laboratory conditions. Most previous experimental studies were conducted on the level of bone material. However, physiological bones bear the external dynamic loading as a whole structure, such as walking, running and jumping. Therefore, it has a more realistic reference value to test the SGP produced in the large whole bone structure. Thus, under simulated physiological loading states (walking and running), we examined the cattle femur (large bone structure)'s SGP by INSTRON (8847) testing machine.
From the above, the more detailed task list and the main conclusion are as follows:
(1) We respectively proposed a hollow and Haversian fluid (pressure) contained osteon model (～150μm) to examine its intraosseous pressure characteristics and fluid flowing behavior under the external loading environments. The relationship among the external loads (axial and cyclic), intraosseous pressure, and fluid velocity was established. Some conclusions are obtained below:
(1) The fluid pressure amplitude in the Haversian fluid (pressure) considered osteon model is much higher than that in hollow osteon model.
(ii) Generally, the increase of axial strain amplitude and frequency can result in the increase of fluid pressure and velocity amplitudes.
(iii) Both the pore pressure and fluid velocity amplitudes are proportionate to the amplitude of strain rate.
(iv) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(v) At the hollow osteon scale, the pressure is strongly affected by permeability variations whereas fluid velocity is not.
(2) Base on (1), a streaming potential model produced in bone canaliculi (-500nm) was established and examined its influence of loading amplitude, frequency, and permeability, etc.
(i) The streaming potential amplitude (SPA) is proportional to the pressure amplitude difference, strain amplitude, frequency and strain rate amplitude. However, the key loading factor governing the SP is the strain rate and it can be seen as a representative loading parameter under the physiological state.
(ii) The SPA produced in the canaliculi of Haversian fluid contained osteon model is larger than that of hollow osteon (not considering Haversian fluid) model.
(iii) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(iv) The larger canaliculi radius, the larger SPA produced, but the SPA is independent of the canaliculi length.
(3) The macroscopical bone material specimens (-mm) were modeled by using the poroelasticity theory and its poroelastic responses were studied under laboratory conditions. Its poroelastic behaviors also have been compared with the osteon scale model.
(i) The poroelastic behaviors of bone material specimens are similar to that of osteon scale:Both the pore fluid's pressure and velocity amplitudes are proportionate to the strain amplitude, frequency and strain rate amplitude. However, the key loading factor governing its poroelastic behavior is the strain rate.
(ii) With an external cyclic loading, the induced fluid pressure gradient and flow behavior are also cyclic.
(iii) At the bone material scale, the pressure is strongly affected by permeability variations whereas fluid velocity is not.
(iv) In the one dimensional flow model, the streaming potential amplitude (SPA) is proportional to the pressure amplitude difference, strain amplitude, frequency and strain rate amplitude. Besides, the increase of the permeability results in the decrease of SPA.
(4) Under simulated human physiological loading states (walking and running), we obtained the cattle femur's (large bone structure:-mm) SGP by INSTRON (8847) testing machine and made a comparison with theoretical analysis.
(ⅰ) The cattle femur, being given the human's normal walking and running state of load and frequency, will generate electric potential. Voltage amplitude generated by running is larger than that of walk. The electric potential amplitude will become larger with the load and frequency increases.
(ⅱ) There will have two electric potential peaks under the conditions of walking and running. One of them is a negative peak which is generated by heel landing (loading), the other is a positive peak generated when the front sole off the ground (unloading). The second potential peak is larger than that of the first one.
(ⅲ) Bones have different electric properties in the condition of tension and compression. Under the same strain rate or stress gradient, the electric potential value generated by tensile is greater than that of compression.
(ⅳ) The electric potential amplitude is approximately proportional to the loading amplitude, frequency, strain rate, which agrees with the conclusion of theoretical model.
引文
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