Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution

The development of a finite element model of the lumbar spine usually involves choosing among available alternatives to decide which values should be assigned to the material properties of the different spinal structures. Furthermore, the model has to be validated so that a reasonable approximation to the mechanical response of the lumbar spine is achieved. One approach for choosing such material properties involves calibrating the model by choosing the properties that produce the best fit with the in vitro mechanical response of the lumbar spine. This study proposes the use of an optimization method based on differential evolution to calibrate the finite element model of a functional spinal unit. Calibration was performed using reported in vitro data on the mechanical response of an intact lumbar functional unit and its successive reduced stages after the dissection of ligaments, facet joints, vertebral arch and nucleus pulposus. The loading conditions in the study were pure moments in flexion, extension, lateral bending and axial rotation. Considering all dissection stages and loading conditions, the maximum difference in vertebral rotation between the in vitro data and the model results was only 1.24°. Other model results such as facet loads and annulus fibrosus behavior also correlated well with reported data.     

Finite element analysis of the lumbar spine with a new cage using a topology optimization method

In recent years, degenerative spinal instability has been effectively treated with a cage. However, little attention is focused on the design concept of the cage. The purpose of this study was to develop a new cage and evaluate its biomechanical function using a finite element method (FEM). This study employed topology optimization to design a new cage and analyze stress distribution of the lumbar spine from L1 to L3 with a new cage by using the commercial software ANSYS 6.0. A total of three finite element models, namely the intact lumbar spine, the spine with double RF cages, and with double new cages, were established. The loading conditions were that 10Nm flexion, extension, lateral bending, and torsion, respectively, were imposed on the superior surface of the L1 vertebral body. The bottom of the L3 vertebral body was constrained completely. The FEM estimated that the new cage not only could be reduced to 36% of the volume of the present RF cage but was also similar in biomechanical performance such as range of motion, stress of adjacent disc, and lower subsidence to the RF cage. The advantage of the new cage was that the increased space allowed more bone graft to be placed and the cage saved material. The disadvantage was that stress of the new cage was greater than that of the RF cage.     

Comparative and functional anatomy of the mammalian lumbar spine

As an essential organ of both weight bearing and locomotion, the spine is subject to the conflict of providing maximal stability while maintaining crucial mobility, in addition to maintaining the integrity of the neural structures. Comparative morphological adaptation of the lumbar spine of mammals, especially in respect to locomotion, has however received only limited scientific attention. Specialised features of the human lumbar spine, have therefore not been adequately highlighted through comparative anatomy. Mathematical averages were determined of 14 measurements taken on each lumbar vertebrae of ten mammalian species (human, chimpanzee, orang-utan, kangaroo, dolphin, seal, Przewalski's horse, cheetah, lama, ibex). The revealed traits are analysed with respect to the differing spinal loading patterns. All examined mammalian lumbar spines suggest an exact accommodation to specific biomechanical demands. The lumbar spine has reacted to flexion in a predominant plane with narrowing of the vertebral bodies in quadrupeds. Torsion of the lumbar spine is withstood by an increase in the transverse distance between the inferior articular processes in the upper lumbar spine in primates, but lower lumbar spine in humans, quadrupeds and the seal. Sagittal zygapophyseal joint areas resist torsion in the seal and humans. Ventral shear is resisted by frontal zygapophyseal joint areas in humans and primates, and dorsal shear by encompassing joints in the ibex. The human fifth lumbar vertebra is remarkable in possessing the largest endplate surface area and the widest distance between the inferior articular processes, as an indicator of the high degree of axial load and torsion in bipedalism.     

Finite element analysis of the spondylolysis in lumbar spine

Spondylolysis is a fracture of the bone lamina in the pars interarticularis and has a high risk of developing spondylolisthesis, as well as traction on the spinal cord and nerve root, leading to spinal disorders or low back pain when the lumbar spine is subjected to high external forces. Previous studies mostly investigated the mechanical changes of the endplate in spondylolysis. However, little attention has been focused on the entire structural changes that occur in spondylolysis. Therefore, the purpose of this study was to evaluate the biomechanical changes in posterior ligaments, disc, endplate, and pars interarticularis between the intact lumbar spine and spondylolysis. A total of three finite element models, namely the intact L2-L4 lumbar spine, lumbar spine with unilateral pars defect and with bilateral pars defect were established using a software ANSYS 6.0. A loading of 10 N.m in flexion, extension, left torsion, right torsion, left lateral bending, and right lateral bending respectively were imposed on the superior surface of the L2 body. The bottom of the L4 vertebral body was completely constrained. The finite element models estimated that the lumbar spine with a unilateral pars defect was able to maintain spinal stability as the intact lumbar spine, but the contralateral pars experienced greater stress. For the lumbar spine with a bilateral pars defect, the rotation angle, the vertebral body displacement, the disc stress, and the endplate stress, was increased more when compared to the intact lumbar spine under extension or torsion.     

Calibration of the mechanical properties in a finite element model of a lumbar vertebra under dynamic compression up to failure

Finite element models (FEM) dedicated to vertebral fracture simulations rarely take into account the rate dependency of the bone material properties due to limited available data. This study aims to calibrate the mechanical properties of a vertebral body FEM using an inverse method based on experiments performed at slow and fast dynamic loading conditions. A detailed FEM of a human lumbar vertebral body (23,394 elements) was developed and tested under compression at 2,500 and 10 mm s⁻¹. A central composite design was used to adjust the mechanical properties (Young modulus, yield stress, and yield strain) while optimizing four criteria (ultimate strain and stress of cortical and trabecular bone) until the failure load and energy at failure reached experimental results from the literature. At 2,500 mm s⁻¹, results from the calibrated simulation were in good agreement with the average experimental data (1.5% difference for the failure load and 0.1% for the energy). At 10 mm s⁻¹, they were in good agreement with the average experimental failure load (0.6% difference), and within one standard deviation of the reported range of energy to failure. The proposed method provides a relevant mean to identify the mechanical properties of the vertebral body in dynamic loadings.     

随动载荷对腰椎小关节接触力的影响

目的研究不同大小随动载荷在腰椎不同姿态下对小关节接触力的影响。方法建立非线性三维有限元腰椎模型(L1~S1),并考虑小关节软骨的非均一厚度和非线性材料特征。对腰椎模型施加不同大小的随动力预载荷(0、0.5、0.8、1.2 k N)以及7.5 N·m不同方向上(前屈、后伸、侧弯、轴向旋转)的纯力矩,对比各运动节段两侧小关节上在不同加载工况下的接触力,并定量研究随动载荷对小关节不对称性的影响。结果随动载荷的应用会增大屈伸以及侧弯(同侧)状态下的小关节接触力,而减少侧弯(对侧)时的小关节接触力,而且这种增大(或减小)效应会随着随动载荷本身的增大而减弱。对于轴向扭转,预载荷对小关节力几乎没有影响。在腰椎不同的姿态下,随动载荷对于小关节接触力不对称性的影响按从大到小排列依次为:侧弯(同侧)、前屈、侧弯(对侧)、后伸、轴向扭转。结论随动载荷对腰椎小关节接触力的影响随腰椎运动姿态的不同而不同。在腰椎的生物力学研究中,小关节的不对称性需要被充分考虑,尤其是在生理载荷作用下腰椎后部结构的研究中。     

Effects of degenerated intervertebral discs on intersegmental rotations,intradiscal pressures,and facet joint forces of the whole lumbar spine

The effects of intervertebral disc (IVD) degeneration on biomechanics of the lumbar spine were analyzed. Finite element models of the lumbar spine with various degrees of IVD degeneration at the L4-L5 functional spinal unit (FSU) were developed and validated. With progression of degeneration, intersegmental rotation at the degenerated FSU decreased in flexion–extension and left–right lateral bending, intradiscal pressure at the adjacent FSUs increased in flexion and lateral bending, and facet joint forces at the degenerated FSU increased in lateral bending and axial rotation. These results could provide fundamental information for understanding the mechanism of injuries caused by IVD degeneration.     

双侧峡部裂对腰椎稳定性影响的实验研究

目的：研究双侧峡部裂对腰椎三维稳定性的影响。方法：实验材料为８具成人新鲜腰椎标本,切断Ｌ２双侧峡部,通过脊柱三维运动试验机,对标本施加前屈／后伸、侧弯和轴向旋转等６种力偶矩（１０Ｎ．ｍ）,由脊柱三维运动分析系统得到腰椎节段的运动范围。结果：双侧峡部断裂后,腰椎前屈／后伸及左／右旋转运动范围分别增加２６．６％、５５．９％、１００．９％、１１５．８％,较正常标本有显著性增大,而左／右侧弯变化不大。结论：峡部对腰椎三维稳定具有重要的力学作用,双侧峡部裂导致腰椎不稳。     

Metastatic Burst Fracture Risk Assessment Based on Complex Loading of the Thoracic Spine

The mechanical integrity of vertebral bone is compromised when metastatic cancer cells migrate to the spine, rendering it susceptible to burst fracture under physiologic loading. Risk of burst fracture has been shown to be dependent on the magnitude of the applied load, however limited work has been conducted to determine the effect of load type on the stability of the metastatic spine. The objective of this study was to use biphasic finite element modeling to evaluate the effect of multiple loading conditions on a metastatically-involved thoracic spinal motion segment. Fifteen loading scenarios were analyzed, including axial compression, flexion, extension, lateral bending, torsion, and combined loads. Additional analyses were conducted to assess the impact of the ribcage on the stability of the thoracic spine. Results demonstrate that axial loading is the predominant load type leading to increased risk of burst fracture initiation, while rotational loading led to only moderate increases in risk. Inclusion of the ribcage was found to reduce the potential for burst fracture by 27%. These findings are important in developing a more comprehensive understanding of burst fracture mechanics and in directing future modeling efforts. The results in this study may also be useful in advising less harmful activities for patients affected by lytic spinal metastases.     

Effect of strain rate on tensile properties of sheep disc anulus fibrosus.

We investigated the effect of loading rate on tensile properties of sheep bone-anulus-bone specimens in axial direction. Disc anulus Samples with adjacent bone attachments were prepared from lateral, posterior and anterior regions of sheep lumbar spinal segments. The specimens were then tested at different strain rates under non-destructive cyclic tensile loading followed by destructive tensile loading. Each specimen was prepared by embedding the bony parts in the polymethylmetacrylate (PMMA) exposing the anulus portion to support tension. The results of non-destructive cyclic tests indicated a decrease in the hysteresis energy loss as strain rate increased. In the destructive tests, no significant differences in ultimate stress, ultimate strain and strain energy density were observed at different strain rates or annulus locations. However, there was a significant increase in the modulus at linear region as strain rate increased. Two major modes of failure were observed; rupture in the anulus mid-substance and at the anulus-endplate junction. The former failure was more frequent with no clear pattern across strain rates and locations, while the latter failure at anulus-endplate junction occurred primarily at slow strain rates.     

Combining 3D tracking and surgical instrumentation to determine the stiffness of spinal motion segments: a validation study

The spine is a complex structure that provides motion in three directions: flexion and extension, lateral bending and axial rotation. So far, the investigation of the mechanical and kinematic behavior of the basic unit of the spine, a motion segment, is predominantly a domain of in vitro experiments on spinal loading simulators. Most existing approaches to measure spinal stiffness intraoperatively in an in vivo environment use a distractor. However, these concepts usually assume a planar loading and motion. The objective of our study was to develop and validate an apparatus, that allows to perform intraoperative in vivo measurements to determine both the applied force and the resulting motion in three dimensional space. The proposed setup combines force measurement with an instrumented distractor and motion tracking with an optoelectronic system. As the orientation of the applied force and the three dimensional motion is known, not only force-displacement, but also moment-angle relations could be determined. The validation was performed using three cadaveric lumbar ovine spines. The lateral bending stiffness of two motion segments per specimen was determined with the proposed concept and compared with the stiffness acquired on a spinal loading simulator which was considered to be gold standard. The mean values of the stiffness computed with the proposed concept were within a range of ±15% compared to data obtained with the spinal loading simulator under applied loads of less than 5 Nm.     

Validation efforts and flexibilities of an eight-year-old human juvenile lumbar spine using a three‐dimensional finite element model

The objective of this study was to develop a finite element model of the lumbar spinal column of an eight-year-old human spine and compare flexibilities under pure moments, adult, and pediatric loading with different material models. The geometry was extracted from computed tomography scans. The model included the cortical and cancellous bones, growth plates, ligaments, and discs. Adult, adolescent, and pediatric material models were used. Flexion (8 Nm), extension (6 Nm), lateral bending (6 Nm), and axial rotation (4 Nm) moments representing adult loads were applied to the three material models. Pediatric loading (0.5 Nm) was applied under these loadings to the eight-year-old spine using adult and pediatric material models. Flexibilities depended on spinal level, loading mode, and material model. Outputs incorporating the pediatric material model responded with increased flexibilities compared to the adult and adolescent material models, with one exception. This was true for the adult and pediatric loading conditions. While the sagittal and coronal bending responses were not considerably different between the adult and pediatric loadings, axial rotation responses were greater under the adult loading. This model may be used to determine intrinsic responses, such as stresses and strains, for improved characterizations of the juvenile spine behavior.     

颈椎人工椎间盘置换有限元分析

目的　建立C4~5节段PrestigeTM-LP颈椎人工椎间盘植入后的三维有限元模型,进行手术节段的运动分析。 方法 采用对成年男性的新鲜尸体的颈椎标本进行CT三维扫描方法建立C4~5节段和PrestigeTM-LP人工间盘有限元,模拟完成C4~5人工椎间盘置换手术。测量生理加载下手术节段前屈/后伸、侧弯及轴向旋转运动角度。结果 有限元模型对颈椎的结构,包括椎体间韧带、颈椎关节突关节、钩椎关节等均进行了精确的重建,并较好地模拟手术操作进行PrestigeTM-LP人工间盘植入。运动加载后运动角度,前屈5.7°,后伸3.5°,侧弯5.0°,旋转11.3°,与文献报道结果较为接近。 结论　有限元模型具有精确度高,手术模拟真实的特点,可作为颈椎人工椎间盘生物力学研究的一种较好途径。PrestigeTM-LP颈椎人工椎间盘置换可较好地保留手术节段的运动功能。     

Spinal muscles can create compressive follower loads in the lumbar spine in a neutral standing posture

The ligamentous spinal column buckles under compressive loads of even less than 100N. Experimental results showed that under the follower load constraint, the ligamentous lumbar spine can sustain large compressive loads without buckling, while at the same time maintaining its flexibility reasonably well. The purpose of this study was to investigate the feasibility of follower loads produced by spinal muscles in the lumbar spine in a quiet standing posture. A three-dimensional static model of the lumbar spine incorporating 232 back muscles was developed and utilized to perform the optimization analysis in order to find the muscle forces, and compressive follower loads (CFLs) along optimum follower load paths (FLPs). The effect of increasing external loads on CFLs was also investigated. An optimum solution was found which is feasible for muscle forces producing minimum CFLs along the FLP located 11 mm posterior to the curve connecting the geometrical centers of the vertebral bodies. Activation of 30 muscles was found to create CFLs with zero joint moments in all intervertebral joints. CFLs increased with increasing external loads including FLP deviations from the optimum location. Our results demonstrate that spinal muscles can create CFLs in the lumbar spine in a neutral standing posture in vivo to sustain stability. Therefore, its application in experimental and numerical studies concerning loading conditions seems to be suitable for the attainment of realistic results.     

动态固定位置对腰椎稳定性影响的实验研究

目的腰椎棘突间动态稳定装置Coflex是一种临床上腰椎退行性疾病手术治疗的器械,在置入时其U形底部与硬脊膜之间的距离是手术的关键,Coflex置入不同深度后对手术节段的影响是本文关注的问题。本文通过体外实验评估Coflex的U形底部与硬脊膜的距离对术后腰椎稳定性的影响。方法选取成年新鲜尸体腰椎(L1—L5)标本6具。每个标本按照实验过程分为6组模型:完整组(A组)、失稳组(B组)、10 mm安装组(C组)、5 mm安装组(D组)、0 mm安装组(E组)、融合组(F组)。对模型进行前屈/后伸、左右侧弯、左右旋转6个方向的运动测试,通过观察手术节段的运动角度和关节活动度(range of motion,ROM)来分析其稳定性。结果各实验组手术节段运动角度与完整组的相似性为E组D组C组B组F组;ROM的计算结果显示,E组的ROM值比其他组相对较小,刚度较大。结论前屈后伸、左右侧弯、左右旋转6种方向运动时,棘突间动态稳定装置Coflex置入位置距脊柱较近时,术后手术节段性能更加接近正常腰椎。     

脊椎破裂骨折之生物力学实验分析

胸腰椎的破裂骨折是一种党见的脊椎伤害,由于神经管常受到破裂骨块的压迫,常造成神经症状。牵引的力量加上后弯的矫正是目前被公认为手术或非手术方法治疗破裂骨折的重要原则。牵引的力量无论是在手术中应用内固定器或是在手术前应用脊椎牵引器就是希望藉着骨折复位进一步达到减压的可能性。过去的实验研究报告大多针对较少节数的腰椎施以轴向负载的生物刀学分析。很少实验对整条脊椎施以轴向负载并加以作生物刀学的量化分析。本实验的目的就是在以INSTRON材料试验机及脊椎牵引器探讨整条羊脊椎在外力牵引下的生物力学特性如应变分布、椎间盘变形量以及破坏负载。并试行制造破裂骨折以便进一步观察脊椎在牵引下的生物刀学特性实验结果我们由整条羊脊椎的应变分布图得知,在胸腰椎接合之区域有较大的应变值表示该区域局部所承受的力量较大,胸椎区域之应变值次之。而下腰椎区域之应变值则较小椎间盘总变形量在10kg时平均值为286mm,在20kg时为5．09mm,在30kg时为645mm。且羊脊椎在拉刀破坏试验时,平均最大负载为91．40kg。而在脊椎牵引器实验所得之应变分布与材料试验机实验所得之分布情形相近,但数值有较小之现象。由结果我们得到 在实验上脊柱承受牵引时,在胸腰椎接合之区域会承受较大的拉力     

Influence of lumbar spine rhythms and intra-abdominal pressure on spinal loads and trunk muscle forces during upper body inclination

Improved knowledge on spinal loads and trunk muscle forces may clarify the mechanical causes of various spinal diseases and has the potential to improve the current treatment options. Using an inverse dynamic musculoskeletal model, this sensitivity analysis was aimed to investigate the influence of lumbar spine rhythms and intra-abdominal pressure on the compressive and shear forces in L4-L5 disc and the trunk muscle forces during upper body inclination.Based on in vivo data, three different spine rhythms (SRs) were used along with alternative settings (with/without) of intra-abdominal pressure (IAP). Compressive and shear forces in L4-L5 disc as well as trunk muscle forces were predicted by inverse static simulations from standing upright to 55° of intermediate trunk inclination.Alternate model settings of intra-abdominal pressure and different spine rhythms resulted in significant variation of compression (763 N) and shear forces (195 N) in the L4-L5 disc and in global (454 N) and local (156 N) trunk muscle forces at maximum flexed position. During upper body inclination, the compression forces at L4-L5 disc were mostly released by IAP and increased for larger intervertebral rotation in a lumbar spine rhythm.This study demonstrated that with various possible assumptions of lumbar spine rhythm and intra-abdominal pressure, variation in predicted loads and muscles forces increase with larger flexion. It is therefore, essential to adapt these model parameters for accurate prediction of spinal loads and trunk muscle forces.     

不同运动状态下模拟人体腰椎结构特征变化的有限元分析

目的比较不同运动状态下正常与退变腰椎节段三维有限元模型的应力变化特点及量效关系,分析中医推拿手法对退变腰椎节段力学调衡作用机制。方法建立完整、真实人体脊柱退变腰椎节段(L4~5)三维有限元模型,模拟腰椎节段前屈与后伸的生理活动。在加载外力即中医推拿手法作用下,分析退变腰椎节段的应力变化特点以及外加载荷逐渐递增过程中退变腰椎节段的应力变化,并与正常腰椎节段在不同运动状态下的应力、应变改变趋势进行对比。结果在不同运动状态下,人体腰椎节段椎间盘内应力分布、髓核、纤维环等结构的弹性模量随着腰椎退变程度的增加呈逐渐增大的趋势。中医推拿手法作用后能改变椎间盘内的应力分布,一定程度地增大椎管内的空间,使神经根所受的应力减小,椎体、小关节应力、椎弓根应力后伸位大于前屈位;椎间盘内部应力前屈位大于后伸位;且均由上至下呈逐渐增大的趋势。结论中医推拿手法对人体退变腰椎节段力学环境的调衡起到改善和治疗腰椎间盘病变的目的。同时,与人体正常腰椎节段三维有限元模型对比,从生物力学环境与特性改变角度研究腰椎退变的过程,能够为中医推拿手法在临床中预防和治疗脊柱退行性疾病的推广应用提供科学依据,也为中医推拿手法有效地预防和治疗脊柱腰椎节段病损的生物力学机制的研究提供新研究思路。     

脊柱离体运动加载方法研究进展

离体脊柱生物力学测试研究对于理解和掌握脊柱的功能、损伤、退行性变以及脊柱植入物的影响均有重要的意义。脊柱生物力学的研究包括对脊柱的加载方法及脊柱运动状态的描述两个方面,脊柱的加载方法主要经历了从逐级加载到连续加载的过程。本文针对脊柱生物力学研究现状,分析国内外相关文献资料,总结了现有脊柱离体运动加载研究方法并对其进行了综述,为今后脊柱运动加载研究提供一定的参考和帮助。