Effects of resting modes on human lumbar spines with different levels of degenerated intervertebral discs: a finite element investigation
© Fan et al. 2015
Received: 19 August 2014
Accepted: 14 August 2015
Published: 24 August 2015
The negative effect of long-term working load on lumbar is widely known. However, insertion of different resting modes on long-term working load, and its effects on the lumbar spine is rarely studied. The purpose of this study was to investigate the biomechanical responses of lumbar spine with different levels of degenerated intervertebral discs under different working-resting modes.
Four poroelastic finite element models of lumbar spinal segments L2-L3 with different grades of disc degeneration were developed. Four different loading conditions represented four different resting frequencies, namely, no rest, one-time long rest, three-time moderate rests, and five-time short rests, on the condition that the total resting time was the same except in the no rest mode. Loading amplitudes of diurnal activities included 100 N, 300 N, and 500 N.
With increasing resting frequency, the axial effective stress and fluid loss decreased, whereas the pore pressure and radial displacement increased. Under different resting frequencies, the changing rate of each biomechanical parameter was different.
Under a situation of fixed total resting time, high resting frequency was advisable. If sufficient resting frequency was unavailable for healthy people as well as patients with mildly and moderately degenerated intervertebral discs, they could similarly benefit from relatively less resting frequencies. However, one-time rest will not be useful in cases where intervertebral discs were seriously degenerated. Reasonable working-resting modes for different degrees of disc degeneration, which could assist patients achieve a better restoration, were provided in this study.
Intervertebral discs are pads of hydrated fibrocartilage comprising gelatinous nucleus and fiber-reinforced annulus fibrosus. These discs lie between vertebral bodies, and ensure the flexibility of spine as well as the transmission of load by maintaining the balance between internal osmotic pressure and external pressures. In this process, fluid flow, which causes variations in disc height and proteoglycans content, is an important step [1–3]. However, intervertebral discs often suffer from degeneration because of aging and poor working environment, and it could be other plausible reasons for disc degeneration, such as genetic inheritance, inadequate metabolite transport, and loading history, which may directly change the normal hydrated environment and fluid flow and indirectly result in instability and reduction of the carrying capacity [1, 4–6]. Thus, investigating the changes of biomechanical parameters for different degrees of disc degeneration to explore relevant mechanism of disc degeneration and search for effective treatment strategies has significant value.
Disc degeneration is a progressive process that involves two changes: exterior geometry change that includes a decreased disc height, growth of osteophyte, and diffused border between annulus and nucleus [7–10] and interior material change that consists of increased nucleus stiffness, reduced water content, and changed permeability [11–13]. The biomechanical behavior of lumbar is greatly influenced by these changes. The results of compressive tests for normal and degenerated discs showed that the segmental motion increases with disc degeneration, but decreases when the degeneration advances to a severe degree [14–16]. An in vivo study for volunteers with normal and degenerated discs reported that intradiscal pressure (IDP) gradually reduces with disc degeneration . A compressive test on the nucleus demonstrated that the effective aggregate modulus decreases with increasing degeneration, whereas the permeability gradually increases .
Although numerous in vivo and in vitro experiments on disc degeneration have been conducted, the detailed distribution of the internal biomechanical parameters could not be measured by in vivo study and the different complex loading conditions for one sample could not be conducted through in vitro study because inevitable damage to the sample could not be prevented [12, 18]. With the rapid development of computer technology, researchers have adopted the finite element analysis (FEA) to simulate the biomechanical responses of lumbar spine. Compared with the elastic material model that does not have the capability to express fluid behavior, the poroelastic material model is more fit for describing the material property of spine components because fluid flow plays a key role in daily spinal physiological activities. Furthermore, accurate prediction of how the spine responds under complex loads has been proven using the lumbar spine modeled by poroelastic material [11, 18–21]. Changes in the geometrical and material parameters that occurred in different degenerated discs are investigated, and the results showed that the axial displacement, facet force, and total fluid loss are reduced with increasing degeneration [5, 22]. Results of the analysis of four intervertebral discs with different degenerated grades showed that the IDP is highest in flexion, and that IDP increases with the severity of degeneration . The investigation of the processes that result in mechanical damage for different degenerated discs demonstrated that the number of cycles to failure sharply decreases with increasing degeneration and that the damages in healthy and moderately degenerated discs initiate at the posterior inner annulus and propagate outwards toward its periphery, whereas in serious degenerated case, damage initiates at the posterior outer annulus and propagates circumferentially .
Most finite element (FE) studies in the current literature have simulated diurnal working or constant load. The distribution of internal stress, changes in displacement, and number of repeated lifting that can lead to disc damage under diurnal working or constant load have been investigated in detail [24–26]. However, knowledge of the responses of lumbar spine when the working load consists of different resting modes is minimal. Such investigation can help people identify how and when to have a rest and how long each rest takes will be favorable for restoring degenerated intervertebral disc.
Therefore, this study aimed to explore appropriate working-resting modes in diurnal activity for healthy people and for the patients with degenerated intervertebral discs by creating four poroelastic FE models of lumbar spinal segments L2-L3 and then investigating their biomechanical responses under different loading conditions. Furthermore, establishing a FE model that can precisely express mechanical properties is important. Accurate anatomic structural data are required in constructing such a FE model. To meet the requirement, four sets of CT images of typical lumbar spines with different grades of disc degeneration were selected. This study may provide ideal working-resting modes for different grades of disc degeneration and serve as the theoretical basis for prevention and treatment of disc degeneration.
Specimens of lumbar spines with different grades of degenerated intervertebral discs
The study was approved by the ethics committee of the First Hospital of Jilin University. CT data from different individuals may have differences in terms of size, or other differences due to physiological variabilities. Thus, four volunteers with typical grades of different degenerated intervertebral discs were selected based on the procedure of Wilke et al. , which classifies different degenerative conditions into four grades. Written informed consent for participation in the study was obtained from the participants. Based on the CT images, the degrees of disc degeneration of the above four lumbar spines were sorted into Grades 0 to 3, based on the height loss as well as the number and length of osteophytes.
Establishment of FE models
Mechanical properties of poroelastic materials in the FE models for all L2-L3 segments
a. Elastic properties of the lumbar except nucleus pulposus
Elastic modulus (MPa)
Poisson’s ratio (μ)
Annulus ground substance
Neo-Hookean C10 = 0.315, D = 0.688
Fitting from test data
The linear-elastic properties of cancellous bone, cortical bone, and cartilage endplates were based on Schmidt et al. . The linear-elastic properties of annular fiber were based on Xu et al. . The hyper-elastic properties of annulus ground substance were based on Schmidt et al. , Schmidt et al. , and Galbusera et al. . The hyper-elastic properties of ligaments/facet were based on Sharma et al. .
b. Porous properties of the lumbar spine except nucleus pulposus
M (Eq. (1))
k = 1e−13
k = 1e−20
k0 = 7e−15
Annulus ground substance
k0 = 3e−16
The porous properties of cancellous bone, cortical bone, cartilage endplates, and annulus ground substance were based on Argoubi and Shirazi-Adl .
c. Poroelastic material properties of all the nucleus pulposus
M (Eq. (1))
C10 = 0.12, D = 2.475
k0 = 3e−16
C10 = 0.185, D = 1.88
k0 = 5e−16
C10 = 0.25, D = 1.285
k0 = 7e−16
C10 = 0.315, D = 0.688
k0 = 9e−16
The hyper-elastic properties of nucleus pulposus for Grade 0 to 3 were based on Schmidt et al. , Schmidt et al. , and Schmidt et al. . The porous properties of nucleus pulposus for Grade 0 to 3 were based on Johannessen et al. , Massey et al. , and Argoubi and Shirazi-Adl .
Boundary and loading conditions
The six degrees of freedom of the nodes at the bottom of the inferior endplate of L3 were all constrained. The phenomenon of the healthy disc swelling because of osmotic potential was simulated by a 0.25 MPa boundary pore pressure at the outer surface of the spine [3, 5, 19]. Boundary pore pressure was linearly reduced to 0.1 MPa from the non-degenerated intervertebral disc to the seriously degenerated one because of consideration to the loss of proteoglycans caused by disc degeneration . The Interaction Property “TIE” in ABAQUS was used to define all the surface to surface contacts in the FE models .
Creep is an important characteristic in lumbar mechanical activity. Thus, comparing the changing creep parameters with the experiments can validate the accuracy of our FE model. To enhance the comprehensiveness and accuracy of the validation, two verifications of numerical analyses were conducted for two parts: one for validating the creep characteristic of intervertebral disc, in which the lumbar specimen was subjected to 1 MPa pressure for 20 min for comparison with the experiment , and the other for validating the strains of the vertebral bodies that changed with time under compressive force of 1000 N for 0.5 h for comparison with the in vitro study . Additional details on the model validation and mesh sensitivity analyses were described in the Discussion section.
Axial effective stress in the nucleus
Axial effective stress is the pressure sustained by the solid phase in the poroelastic model. The axial direction was the same as the loading direction.
The increased/decreased changing rates in this study were described by: increased/decreased changing rate = (Result of Case 2/3/4 - Result of Case 1)/Result of Case 1 × 100 %.
Axial effective stress in the posterior annulus
Pore pressure in the nucleus
Sensitivity analyses of material parameters in FEA
The sensitivity of the results to the values assigned to the parameters of the Grade 0 model was analyzed as well, such as changes in the permeability and boundary pore pressure. The results showed that when permeability was doubled, the pore pressure in the nucleus increased by 7.531 % in Case 2, 9.494 % in Case 3 and 11.332 % in Case 4. Furthermore, when the boundary pore pressure was reduced to 0.2 MPa, the pore pressure in the nucleus increased by 10.281 % in Case 2, 12.383 % in Case 3, and 14.521 % in Case 4. Therefore, the changing trends were similar and the conclusions obtained were the same as those of our study with normal material values. This indicated that moderately changing parameter values had slight effects on the conclusions.
The effects of different working-resting modes on different levels of degenerated intervertebral discs were investigated in this study. The cases designed in current study could represent the actual working-resting conditions in different professions. Case 1 was served as a control; Case 2 represented the normal working-resting condition that works in the morning and afternoon sessions and rests at noon; Case 3 represented the professions, such as teachers who enjoy a rest period after several classes; and Case 4 represented the professions whose working and resting times are not fixed, such as the group of students or waiters who have short rest periods after their respective short work periods. Meanwhile, 10 h working time, 6 h resting time, and 8 h sleeping time in one day conform to normal people’s living habit. Therefore, all these designed cases were in accordance with most of real-life cases. Thus, this study could provide a basis for clinical studies on different professions.
The predicted radial displacement results of the non-degenerated segments in Case 1 agreed well with the in vitro measured radial displacement. The average deformation of disc in the anterior region is 0.86 mm with the range of 0.46 mm-1.34 mm under 500 N . Our predicted radial displacement of 0.624 mm (Fig. 8a) was within this range and near the mean value. Another numerical analysis showed that the peak and ending pressure of the normal disc could reach 0.47 MPa and 0.26 MPa after 16 h of calculation under constant 500 N , which were similar to our results in Case 1 (Fig. 7a). The axial effective stresses in mildly, moderately and seriously degenerated discs were reported to be in the ranges of 0.10 ± 0.10 MPa, 0.14 ± 0.24 MPa, and 0.25 ± 0.29 MPa respectively after a 16 h diurnal activity . Our predicted results in Case 1 under the same condition were all within this ranges, which was 0.045 MPa in mildly degenerated model, 0.065 MPa in moderately degenerated model, and 0.161 MPa in seriously degenerated model, respectively (Fig. 5b-d). These comprehensive comparisons with previous experiments and FEA in terms of displacement, pore pressure, and axial effective stress validated the accuracy of our results.
The predicted elastic and creep strains in different regions of this FE model under compressive force of 1000 N for 0.5 h
a. The predicted elastic and creep strains in different regions of L2
b. The predicted elastic and creep strains in different regions of L3
Comparisons of element size, number, and IDP of our different levels of degenerated models with different mesh densities
The edge length of elements (mm)
Number of elements
The changing rate of pore pressure in the center of the nucleus was reduced with increasing frequency for the healthy, mildly degenerated discs (Fig. 12c). For the moderately degenerated disc, the highest changing rate occurred in Case 3 as the axial effective stress. On the contrary, the changing rate of pore pressure for the seriously degenerated disc increased when the resting frequency was on the rise, of which the increasing percentage of Case 2 was nearly 2 %, but in Case 4 it reached 28.001 %. Pore pressure resists mechanical stress in the solid matrix of the disc by hydration of molecules and the proteoglycans will be extruded during high pressure. This could explain the phenomenon where a suddenly compressive force leads to maximum pore pressure at 8 h and then dissipate gradually. Thus, proper increasing pore pressure can decrease the load sustained by the solid phase, which was beneficial to restoration of the degenerated disc . Therefore, the results of pore pressure advised patients to have more resting frequency under fixed resting time such as in Case 4. Subsequently, as shown in Fig. 12d, the radial displacement for all discs expressed an adverse trend that negatively affected the restoration of the degenerated disc when the resting frequency was on the rise. However, the maximum changing rate was less than 5 %. The disc fluid loss also indicated very slight differences among the different resting frequencies for healthy and mildly degenerated discs and a slight distinction in the seriously degenerated disc with less than 10 % as shown in Fig. 12e. The changing rates of radial displacement and fluid loss in different cases were minimal; thus, the restoration of the degenerated disc may not be influenced too much by different resting modes.
Results from the abovementioned phenomena demonstrated that for the normal and mildly degenerated discs, all the changing rates of biomechanical parameters reduced gradually with the increase in the resting frequency. However, the highest changing rate for moderately degenerated disc occurred in Case 3. Unlike the less degenerated discs, all the changing rates in the seriously degenerated disc started to increase from Cases 2 to 4; thus, almost no help was available in Case 2 to restore the degenerated disc. Healthy people and patients with degenerated discs were advised to divide fixed resting time into short and separated periods as much as possible, as illustrated by Case 4. In this way, axial effective stress could be reduced and pore pressure could be increased to a maximum, which were beneficial to restoration of the damaged disc. Additionally, relatively less resting frequency, such as in Case 3, also enhanced the efficiency of the restoration of healthy, mildly degenerated, and especially for moderately degenerated discs under the circumstance that too many resting frequencies were unavailable. For the serious patient, a slight effect of one-time rest was noted even though the resting time was sufficiently long enough.
Previous in vitro studies suggested that the intervertebral disc is a tissue with small cell proliferation and regeneration capacity both in annulus fibrosus and nucleus pulposus [44–46]. Cell proliferation and regeneration capacity can be increased by external stimulation to promote the restoration of intervertebral discs. Thus, more biological repair mechanisms can be taken into account to relieve the pain caused by disc degeneration. Running exercise can serve as a better external stimulation to increase extracellular matrix production and cell number in the annulus fibrosus [47, 48]. Different working-resting modes that were beneficial to different levels of degenerated intervertebral discs have been predicted in current study. Thus, combining with the phenomenon where moderate exercise has positive effects on cell proliferation in intervertebral disc, exercise-resting modes that are beneficial to different levels of degenerated intervertebral discs could also be determined by the similar numerical simulations.
However, excessive running does not always enhance proliferation, and that the decrease in progenitor proliferation seen in long-term running is possibly mediated by mechanisms involving a stress response in the animal . Cell proliferation could be promoted only under moderate exercise; excessive exercise may lead to negative effects . Thus, determining different exercise-resting modes that are beneficial to different degenerated intervertebral discs is crucial. Although different working-resting modes that were fit for different degenerated models have been predicted in the current study, the external load sustained by the lumbar spine in working and exercising conditions differed. Hence, in our future work, a number of new running-resting cases will be designed to investigate their positive effects on the different levels of degenerated intervertebral discs.
Numerous assumptions in the creation of our FE models persisted. Focal clefts and cavities were neglected in modeling degenerated discs. Meanwhile, the interaction condition “TIE” was used to link the facet joint and vertebral body because of the convergence problem, which was slightly unrealistic. Finally, the muscular constitution was not simulated in the current models. The muscular tissue may not only bear parts of external loads, but may also influence the restoration of intervertebral disc. Thus, a lack of muscular constitution in the FE models can exert certain effects on the predicted results. However, the conclusions were obtained by comparing the mechanical responses of different degenerated models, and this study emphasized observation of the effects of different working-resting modes on different levels of degenerated models. The effects of muscular constitution were not considered for all different degenerated models, and exterior geometry and interior material changes caused by degeneration were the main concern for all the different degenerated models. Therefore, the conclusions may not significantly influenced by the exclusion of the muscular constitution. Although our FE models were based on the abovementioned assumptions, the model validation ensured the accuracy of our models. Thus, the accuracy of our results can be vouched. Moreover, meaningful clinical advice can be obtained because of the precise modeling and analytical method implemented.
In summary, the biomechanical responses of different degenerated intervertebral discs under different working-resting modes were analyzed using three-dimensional poroelastic FE models. The predicted responses revealed that to keep the intervertebral disc healthy, the fixed resting time should be divided into separated periods as much as possible for all intervertebral discs with different grades of degeneration, especially for the seriously degenerated intervertebral disc because one long resting period showed minimal effect on the aim of decreasing the harmful biomechanical responses to the lumbar.
Finite element analysis
This work was supported by the Natural Science Foundation of China (No. 11322223, 11432016, 81471753), and the Graduate Innovation Fund of Jilin University (No. 2014088).
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