Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Biao Wu; Xin Gao; Bing Qin; Michele Baldoni; Lu Zhou; Zhiyu Qian; Qiaoqiao Zhu

doi:10.1038/s41526-023-00253-8

Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Wu, Biao; Gao, Xin; Qin, Bing; Baldoni, Michele; Zhou, Lu; Qian, Zhiyu; Zhu, Qiaoqiao 2023-02-15 00:00:00 www.nature.com/npjmgrav ARTICLE OPEN Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study 1 1 1 2 1 1 1✉ Biao Wu , Xin Gao , Bing Qin , Michele Baldoni , Lu Zhou , Zhiyu Qian and Qiaoqiao Zhu The aim of this study was to quantitatively analyze the mechanical change of spinal segments (disc, muscle, and ligament) at various postures under microgravity using a full-body musculoskeletal modeling approach. Speciﬁcally, in the lumbar spine, the vertebra were modeled as rigid bodies, the intervertebral discs were modeled as 6-degree-of-freedom joints with linear force- deformation relationships, the disc swelling pressure was deformation dependent, the ligaments were modeled as piecewise linear elastic materials, the muscle strength was dependent on its functional cross-sectional area. The neutral posture and the “fetal tuck” posture in microgravity (short as “Neutral 0G” and “Fetal Tuck 0G”, in our simulation, the G constant was set to 0 for simulating microgravity), and for comparison, the relaxed standing posture in 1G and 0G gravity (short as “Neutral 1G” and “Standing 0G”) were simulated. Compared to values at Neutral 1G, the mechanical response in the lower spine changed signiﬁcantly at Neutral 0G. For example, the compressive forces on lumbar discs decreased 62–70%, the muscle forces decreased 55.7–92.9%, while disc water content increased 7.0–10.2%, disc height increased 2.1–3.0%, disc volume increased 6.4–9.3%, and ligament forces increased 59.5–271.3% at Neutral 0G. The fetal tuck 0G reversed these changes at Neutral 0G back toward values at Neutral 1G, with magnitudes much larger than those at Neutral 1G. Our results suggest that microgravity has signiﬁcant inﬂuences on spinal biomechanics, alteration of which may increase the risks of disc herniation and degeneration, muscle atrophy, and/or ligament failure. npj Microgravity (2023) 9:16 ; https://doi.org/10.1038/s41526-023-00253-8 INTRODUCTION semi-crouched, arms and legs ﬂexed, head and neck bent 8–10 forward (Fig. 1). How are the spinal segments loaded Microgravity exposure causes higher rates of back pain and disc 1,2 mechanically under this posture in microgravity are unknown, herniations in astronauts . Studies show that 52% of astronauts whether the mechanical loadings among the spinal segments report spinal pain during their space mission, with 86% of which were different in microgravity from those at neutral standing in 1G occurred in the lower back . The incidence of intervertebral disc gravity, and whether these difference (if any) possibly relate to herniation in astronauts returned back to the earth from lower back pain and/or disc herniation are also largely unknown. microgravity is much higher compared to that of matched control In addition, some astronauts claimed that low back pain is relieved on the earth, it is 4.3 times higher for lumbar discs, with the highest by periodic “fetal tuck posture” in microgravity, that is, curling risk appeared in the ﬁrst year after return to the earth ,and 21.4 knees to the chest posture (Fig. 1). How does this “fetal tuck” times higher for cervical discs . The reason for much higher risks of posture relieve lower back pain biomechanically and whether this low back pain and disc herniation in microgravity is not clear yet, posture is mechanically safe to spinal health are also largely some researchers proposed that intervertebral disc swelling due to unknown, yet of great interests to us. unloading in microgravity may be a possible mechanism . Thornton Thus, the aim of this study was to quantitatively analyze the et al. showed that the stature increased around 4–6cm (3% of mechanical change of various spinal segments in the lower back, stature) in microgravity . Recently Young and Rajulu reported that including disc load, disc swelling, disc morphology (height, cross- seated height increased by 4% on average in an in-ﬂight study .The sectional area, volume), muscle forces, and ligament forces at height increase in microgravity was thought mainly caused by spinal 6 5 neutral and “fetal tuck” postures under microgravity using a elongation through disc swelling and spinal curvature change . musculoskeletal modeling approach. This study is important for Intervertebral disc swelling in microgravity has not been measured understanding the biomechanical mechanisms of microgravity- directly, though. However, it is reported that body height changes related lower back pain and disc herniations, and this computa- diurnally following the circadian rhythm on the earth, that is, a tional model is helpful in guiding future design and development person is about 1.1% taller in the morning than at night ,due to that of spinal countermeasures under microgravity. intervertebral disc imbibes/extrudes water during the unloading at night/loading at day, causing the intervertebral disc height to ﬂuctuate diurnally. How much does human disc swell under RESULTS microgravity are largely unknown yet, and how these swelling The mechanical responses in the lumbar spine under Neutral 1G, changes in the discs affect adjacent spinal segments mechanically are also largely unknown yet. Standing 0G, Neutral 0G, and Fetal Tuck 0G conditions were reported (Figs. 2–5). Results between Standing 0G vs Neutral 0G In microgravity, the neutral body posture (relaxed ﬂoating) was found quite different from the neutral posture (relaxed were not signiﬁcantly different (Figs. 2–5), thus in the following standing) in a gravitational environment, in which the torso was results, we focused mainly on comparing differences between 1 2 Department of Biomedical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. Department of Biomedical Engineering, University of Miami, Miami, FL, USA. email: zqq@nuaa.edu.cn Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; B. Wu et al. Fig. 1 The postures simulated in 1G gravity and microgravity. a Relaxed standing posture in 1G gravity (Neutral 1G); this posture was also used in microgravity for comparison (Standing 0G), b relaxed ﬂoating posture in microgravity (Neutral 0G), and c fetal tuck posture in microgravity (Fetal Tuck 0G). Neutral 1G, Neutral 0G, and Fetal Tuck 0G since these three 0G (Fig. 3). The height increased by 3.0, 2.3, 2.1, 2.1, and 2.6%, the postures are commonly experienced by astronauts on the earth disc cross-sectional area increased by 6.1, 4.6, 4.2, 4.3, and 5.2%, and in a microgravity environment. and the disc volume increased 9.3, 7.0, 6.4, 7.0, and 7.9% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, respectively (Fig. 3). Compressive forces on lumbar discs Fetal tuck 0G vs Neutral 0G. Compared to results at Neutral 0G, Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the the disc height, cross-sectional area, and volume decreased at compressive forces on the lumbar discs decreased at Neutral 0G fetal tuck 0G (Fig. 3). The disc height decreased by 10.7, 9.9, 8.3, (Fig. 2a). It decreased by 70.2, 62.1, 63.5, 63.1, and 66.7% on L1L2, 7.5, and 7.0%, the disc cross-sectional area decreased 20.3, 18.9, L2L3, L3L4, L4L5, and L5S1 discs, respectively. 15.8, 14.4, and 13.5%, and the disc volume decreased 28.9, 26.9, 22.8, 20.9, and 19.6% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, Fetal tuck 0G vs Neutral 0G. Compared to values at Neutral 0G, respectively (Fig. 3). compressive forces increased at fetal tuck 0G. It increased by 932.2, 785.6, 742.9, 633.2, and 577.3% on L1L2, L2L3, L3L4, L4L5, Fetal tuck 0G vs Neutral 1G. Compared to results at Neutral 1G, the and L5S1 discs, respectively (Fig. 2a). disc height, cross-sectional area, and disc volume were smaller at fetal tuck 0G (Fig. 3). The height was 8.0, 7.9, 6.4, 5.5, and 4.6% Fetal tuck 0G vs Neutral 1G. Compared to values at Neutral 1G, smaller, cross-sectional area was 15.4,15.1, 12.3,10.7, and 9.0% the compressive force was larger at fetal tuck 0G. It was 207.6, smaller, and the disc volume was 22.2, 21.8,17.9, 15.7, and 15.4% 235.9, 207.3, 170.6, and 225.3% larger on L1L2, L2L3, L3L4, L4L5, smaller in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, respectively (Fig. 3). and L5S1 discs, respectively (Fig. 2a). Water content Shear forces on lumbar discs Neutral 0G vs Neutral 1G. Compared to results at Neutral 1G, the Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the water content increased at Neutral 0G. It increased by 5.2, 3.9, 3.6, shear force decreased. It decreased by 79.6, 92.1, 84.4, and 47.0% 3.7, and 4.4% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, on L2L3, L3L4, L4L5, and L5S1 discs, and it changed from 65 N to respectively (Fig. 4). −16 N on the L1L2 disc at Neutral 0G, “−” means the change of force direction (Fig. 2b). Fetal tuck 0G vs Neutral 0G. Compared to results at Neutral 0G, the water content decreased at fetal tuck 0G, it decreased by 18.8, Fetal tuck 0G vs Neutral 0G. The shear forces at fetal tuck 0G 17.3, 14.3, 12.9, and 12.0% in L1L2, L2L3, L3L4, L4L5, and L5S1 increased by 2062.9, 643.4, and 264.5% on L1L2, L4L5, and L5S1 discs, respectively (Fig. 4). discs, and it changed from 20 N to −101 N and 7 N to −17 N on the L2L3 and L3L4 discs, compared to those at Neutral 0G, “−” Fetal tuck 0G vs Neutral 1G. Compared to results at Neutral 1G, means the change of force direction (Fig. 2b). the water content was smaller at fetal tuck 0G. It was 14.5, 14.1, 11.3, 9.7, and 8.1% smaller in L1L2, L2L3, L3L4, L4L5, and L5S1 Fetal tuck 0G vs Neutral 1G. The shear force at fetal tuck 0G was discs, respectively (Fig. 4). 15.7 and 93.2% larger than those at Neutral 1G on L4L5 and L5S1 discs. It changed from 65 N to −354 N, 98 N to −101 N, 86 N to −17 N on the L1L2, L2L3, and L3L4 discs from Neutral 1G to fetal Muscle force tuck 0G, “−” means the change of force direction (Fig. 2b). Neutral 0G vs Neutral 1G. Compared to results at Neutral 1G, muscle forces decreased in most regions at Neutral 0G (Fig. 5a). Disc morphology The total force in MF, ES, PM, OE, OI, SR, TMF, and Tra groups in the Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the lumbar regions decreased 59.8, 55.7, 81.1, 75.7, 53.3, 82.5, 88.1, disc height, cross-sectional area, and volume increased at Neutral and 92.9%, while the total force in QL and RA muscle groups npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; B. Wu et al. Fig. 2 Comparison of mechanical forces on lumbar discs among various postures in 1G gravity and microgravity. a Compressive force and b shear force among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. Fig. 3 Comparison of disc morphology change among various postures in 1G gravity and microgravity. a Disc height, b cross-sectional area, and c disc volume change among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. Fig. 4 Comparison of water content in lumbar discs among various postures in 1G gravity and microgravity. Water content in a NP and b AF among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. NP nucleus pulposus, AF annulus ﬁbrosus. slightly increased, with an increase of 1 N (from inactivated state) the total force in Tra muscle group decreased from 12.3 N to 0 N and 25 N (from inactivated state), respectively. (deactivated) (Fig. 5a). Fetal tuck 0G vs Neutral 0G. Compared to values at Neutral 0G, Fetal tuck 0G vs Neutral 1G. The muscle forces at Fetal Tuck 0G muscle forces increased in most regions at fetal tuck 0G. It were larger compared to those at Neutral 1G (Fig. 5a). It was 7.7, increased by 1820.1%, 1828.8, 882.3, 7165.5, 1210.2, 1682.2, 154.1, 8.5, 1.9, 3.2, and 8.3 times those at Neutral 1G in MF, ES, PM, OE, 342.2, and 979.5% in MF, ES, PM, QL, OE, OI, SR, TMF, and RA, while and OI muscles. In QL, it was 40 N at Fetal Tuck 0G and 0 N in Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. Fig. 5 Comparison of muscle forces and ligament forces in lumbar spine among various postures in 1G gravity and microgravity. a Muscle forces and b ligament forces in lumbar spine among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. MF multiﬁdus, ES erector spinae, PM psoas major, QL quadratus lumborum, OE obliquus externus, OI obliquus internus, SR semispinalis, TMF thoracic multiﬁdus, RA rectus abdominis, Tra transversus abdominis, ALL anterior longitudinal ligament, PLL posterior longitudinal ligament, IS interspinous, SS supraspinous, FL ﬂavum, IT intertransverse. Neutral 1G. In RA, it was 268 N at fetal tuck 0G and 0 N at Neutral while the disc water content, disc height, cross-sectional area, 1G. It decreased in SR, TMF, and Tra muscles. volume, and ligament forces increased at Neutral 0G, compared to those at Neutral 1G. The fetal tuck position at 0G showed a reverse effect on these changes seen at Neutral 0G, with values much Ligament force larger than those at Neutral 1G. Neutral 1G vs Neutral 0G. Compared to values at Neutral 1G, the Both compressive and shear forces on lumbar discs decreased ligament forces increased at Neutral 0G, increased 142.6, 211.6, in microgravity at neutral postures, causing the water to ﬂow into 133.0, 127.0, 117.0%, and 121.1% in ALL, PLL, IS, SS, FL, and IT, discs due to unbalanced osmotic pressure in the disc and the respectively (Fig. 5b). lowered external forces on the disc, leading to the increase in water content in the discs. The increased water content caused Fetal tuck 0G vs Neutral 0G. The ligament forces increased at fetal the discs to swell, leading to larger disc size, as seen in increased tuck 0G, compared to those at Neutral 0G (except ALL ligament) disc height, area, and volume. (Fig. 5b). It increased 5.3, 744.9, 1258.7, 394.5, and 171.8% in PLL, Our simulated disc size change was reasonable with experi- IS, SS, FL, and IT, respectively. It decreased from 92 N to 0 N in ALL. mental data. Early studies reported that astronaut stature 4,12 increased up to 3% during ﬂight , recently Yong and Rajulu Fetal tuck 0G vs Neutral 1G. The ligament forces at fetal tuck 0G reported that the seated height of astronauts increased by was larger compared to those at Neutral 1G (except ALL 4±1% . According to Styf et al. that 35 to 60% of the spinal ligaments) (Fig. 5b). It was 228.2, 1868.9, 2984.4,1945.8, and elongation is due to increases in intervertebral disc height , thus 650.0% larger in PLL, IS, SS, FL, and IT. It was 38 N smaller in ALL the disc height increase in Yong and Rajulu’s study would be (i.e., 38 N in Neutral 1G, 0 N in fetal tuck 0G). 1.4 ± 0.35% to 2.4 ± 0.6%. Our simulated disc height change (i.e., 3.0, 2.3, 2.1, 2.11, and 2.6% for L1L2, L2L3, L3L4, L4L5, and L5S1 Variation analysis discs) are close to this range. Treffel et al. found that after 3-day Our results showed that when the disc height varied in the range exposure to simulated microgravity through dry immersion, disc of [−20%, 20%] of the original height, our simulated disc volume increased by 8 ± 9% (T12-L1) and 11 ± 9% (L5S1) . Our compressive force varied in the range of [−1.3%, 0.9%] (values simulated disc volume increase (e.g., 6.4–9.3%) were close to these were averaged over ﬁve lumbar discs, same for the following experimental data. data), muscle force in the range of [−4.6%, 3.3%], ligament force in It is proposed that expansion of the disc in microgravity may the range of [4.7%, −3.4%], and disc height change in the range of cause deformation of collagen in the annulus ﬁbrosis, surpassing [14.7%, −11.7%] of the original values, respectively. When the disc the physiological range of 3–4%, resulting in stimulation of the cross-sectional area varied in the range of [−20%, 20%] of the Type IV mechanoreceptors/free nerve endings, which might cause original area, our simulated disc compressive force varied in the the sinuvertebral nerves to continually transmit impulses, range of [1.4%, −1.5%], muscle force in the range of [5.6%, eventually resulting in a perception of low back pain . Our −5.8%], ligament force in the range of [−7.6%, 6.9%], and disc results on disc cross-sectional area and volume increases at height change in the range of [14.0%, −6.9%] of the original Neutral 0G were in the range of 4.2–6.1% and 6.4–9.3%, values, respectively. respectively, which may lead to deformation of the collagen in the annulus ﬁbrosus larger than the 3–4% range mentioned above, thus increasing the risk of nerve stimulation in the related DISCUSSION area and possibly causing pain. In this study, the mechanical change of various spinal segments in Our results showed that the “fetal tuck” posture in microgravity the lumbar regions, including disc load, disc swelling, disc may be beneﬁcial in counteracting those spinal changes seen in morphology, muscle force, and ligament force were quantitatively Neutral 0G. The disc compressive force, shear force, disc height analyzed and compared among Neutral 1G, Neutral 0G, and fetal and volume, and disc water content all reversed back toward the tuck 0G. Our results showed that discs compressive forces, shear values at Neutral 1G. This may help explain biomechanically why forces, and muscle forces decreased signiﬁcantly at Neutral 0G, astronauts ﬁnd that the “fetal tuck” posture helps relieve back pain npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA B. Wu et al. Table 1. Ligament forces predicted at fetal tuck 0G (fetal tuck), compared to failure forces from literature (Fail). Parameter Ligament L1L2 L2L3 L3L4 L4L5 L5S1 Fetal tuck Fail Fetal Tuck Fail Fetal tuck Fail Fetal tuck Fail Fetal tuck Fail Fetal tuck 0G force(N) ALL 0.0 415.27 0.0 496.39 0.0 401.23 0.0 489.29 0.0 258.27 PLL 25.3 366.8 90.0 909.8 57.8 389.1 18.7 659.0 0.0 628.7 IT 49.2 304.2 41.2 434.5 32.2 236.5 20.0 108.0 10.1 171.8 FL 122.8 59 147.9 59 100.2 59 38.2 59 11.2 59 IS 90.3 74.8 91.1 40.9 68.8 87.4 45.9 84.6 4.7 122.0 SS 142.3 169.0 128.7 55.4 97.9 52.8 71.3 85.9 9.4 168.9 ALL anterior longitudinal ligament, PLL posterior longitudinal ligament, IT intertransverse, FL ﬂavum, IS interspinous, SS supraspinous. a 39 From Pintar et al. (1992) . b 40 From Cornaz et al. (2021) . The bold values are higher than the fail values measured in literature (Column ‘Fail’), indicating the corresponding ligaments may be in higher risk of damage. in microgravity. However, the magnitudes of these changes at ligament forces continued to increase (except ALL), due to that Fetal Tuck 0G far surpassed the values at Neutral 1G. For example, at ‘fetal tuck’ posture, the spine ﬂexed forward, causing most of the compressive loads on the lumbar discs at Fetal Tuck 0G were, the ligaments to stretch even longer. While the ALL ligament on average, 2.9 times the value at Neutral 1G, reaching shortened due to the forward bending, thus resulting in a 936 N–1266 N. It was reported that cyclic compressive force decrease in its force. The large increase in the ligament forces at (1 Hz) at 867 N for 24 h causes disc herniations in a porcine cervical the “fetal tuck” posture may increase the risks of ligaments disc, which is proposed to be closest to human lumbar spines in damages. Our calculated forces in the FL ligament at L1-L4, the anatomy and biomechanical characteristics . The compressive IS ligament at L1-L3, and the SS ligament at L2-L4 were larger forces at fetal tuck posture in our simulation are much higher than than the failure forces measured by Pintar et al. and Cornaz this value, such a large load on the discs may increase the risk of et al. (Table 1). disc ﬁssure and/or disc herniation . Our variational analysis results indicate that variations in disc Disc load change in microgravity may also increase the risk of height and the cross-sectional area may not signiﬁcantly inﬂuence disc degeneration through deregulating the synthesis of the forces on lumbar discs, muscle forces, and ligament forces, it may glycosaminoglycan (GAG), one of the crucial biochemical compo- inﬂuence the disc height change at fetal tuck 0G. Our results nents of the disc matrix, the loss of which causes disc found a negative correlation between disc size and disc height degeneration . Studies have shown that GAG synthesis is change, at larger disc size (either through larger disc height or disc signiﬁcantly affected by mechanical loading, with the GAG cross-sectional area), the disc height change was smaller synthesis rate decreased signiﬁcantly with the load deviating compared to that at smaller disc size. 18–22 (either increasing or decreasing) from the optimum range . There are some limitations in this study. One limitation is that in Gao et al. showed that the GAG synthesis rate decreased by 74% modeling the disc’s mechanical behavior, linear relationships were at a load three times the optimal load, and decreased by 80% at a used for translational and rotational behaviors, and more complex load 0.1 times the optimal load at the end of an 8-h creep in the and realistic mechanical models, such as creep, were not NP . Since the disc load in Neutral 0G decreased to 0.3 times that considered in our model. This simpliﬁcation may affect the in the Neutral 1G, and in fetal tuck 0G increased to 2.9 times that deformation of the disc and forces on the muscle and ligaments. in the Neutral 1G, we speculate that the GAG synthesis rate would Another limitation is that in modeling muscle, the muscle strength decrease signiﬁcantly in both postures at microgravity. Actually, was assumed to be cross-sectional area dependent, this simpli- GAG content decrease has been observed by experimental ﬁcation may affect the muscle forces and other segmental force 24,25 studies . For example, Jin et al. found downregulated GAG calculations, in the future, more realistic muscle mechanical content in simulated microgravity on the earth in mice disc . models, will be considered. In addition, even though this model Fitzgerald et al. found loss of proteoglycan in the articular cartilage was well validated in the 1G environment, it was only partially (which is similar to intervertebral disc both in composition and validated due to limited experimental data available in micro- axial weight-bearing functions) of mice exposed to microgravity gravity conditions, we will keep validating our model when more for 30 days on the BION-M1 craft . These decreases in GAG experimental data are available in the future. Another limitation is synthesis rate in both postures at microgravity may lead to disc that the angles for fetal tuck posture used in this study was an degeneration . estimation from the gesture due to the lack of data. This Muscle forces decreased in the neutral posture in microgravity, estimation may be different from real situations and may affect this may cause muscle atrophy, a widely observed phenomenon the forces calculated. among astronauts returned from long-term microgravity expo- In conclusion, in this study, we quantitatively analyzed and 27–29 sure . At fetal tuck 0G, the muscle forces increased signiﬁ- compared the changes in intervertebral disc load, disc water cantly, much larger than those at the Neutral 1G, and the content, disc morphology (height, cross-sectional area, volume), maximum muscle activation level increased signiﬁcantly (in the muscle forces, and ligament forces in the lumbar spine among range of 10–43%), this posture may be helpful in maintaining high Neutral 1G, Neutral 0G, and fetal tuck 0G conditions using a muscle force thus preventing lumbar muscles from atrophy, musculoskeletal modeling approach. Our results showed that lumbar discs compressive forces, shear forces, and muscle forces however, it may be detrimental to other mechanical segments, such as discs. decreased signiﬁcantly at Neutral 0G, while the disc water content, The ligament forces increased in Neutral 0G, due to that disc disc morphology, and ligament forces increased at Neutral 0G, swelling in microgravity stretched the ligament, resulting in compared to those at Neutral 1G. The fetal tuck 0G showed increases in ligament length and force. At Fetal Tuck 0G, the reverse effects on these changes seen at Neutral 0G, with Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. magnitudes much larger than those at Neutral 1G, which may Table 2. Parameters for lumbar disc height (h ), cross-sectional area increase the risk of damage to discs, muscles, and/or ligaments. (A ), water content ϕ , and ﬁxed charge density c at Neutral 1G 0 0 Our results are important for understanding the biomechanical condition. mechanisms of microgravity-related disc health, and this study provides a tool for quantifying mechanical changes in various 2 w F 3 h [mm] A [mm ] ϕ c [mol/m ] 0 0 0 0NP spinal segments under various gravitational environments. NP AF L1L2 9 1425 0.85 0.775 261 METHODS L2L3 10.4 1658 242 Theoretical studies L3L4 11.5 1714 239 The effects of microgravity on the biomechanical changes of disc load, disc swelling (water content), disc morphology (height, volume, L4L5 11.8 1684 215 cross-sectional area), muscle force, and ligament forces in the lumbar L5S1 11.3 1709 217 regions were studied using a full-body musculoskeletal model developed with the AnyBody Modeling System (AnyBody Technol- ogy, Version 7.3, Denmark). The anatomical structure and sizes of the body segments were from a male with a height of 1.74 m and a Table 3. Ligament stiffness values in the model. weight of 72 kg .Speciﬁcally, in the lumbar spine, the model Ligament Stiffness (N/mm) Strain (%) includes ﬁve lumbar vertebrae, ﬁve intervertebral discs, ten major muscle groups [including lumbar multiﬁdus (MF), erector spinae (ES), Anterior longitudinal ligament (ALL) 36.2 <0,11> psoas major (PM), quadratus lumborum (QL), obliquus externus (OE), 115.9 <11, 41> obliquus internus (OI), semispinalis (SR), thoracic multiﬁdus (TMF), 43 <41, 51> rectus abdominis (RA), and transversus abdominis (Tra)], and six lumbar ligament groups [including anterior longitudinal ligament Posterior longitudinal ligament (PLL) 52.7 <0,11> (ALL), posterior longitudinal ligament (PLL), interspinous (IS), 127 <11,28> supraspinous (SS), ﬂavum (FL), and intertransverse (IT)]. 37.1 <28,37> For the mechanical behaviors, the vertebral bones were modeled Interspinous (IS), Supraspinous (SS) 13 <0,14> as rigid bodies. The intervertebral discs were modeled as 6 degrees 38.5 <14,36> of freedom joints with linear momentum-rotational deformation and linear force-translational deformation relationships : 10.3 <36,48> Flavum (FL) 23.4 <0,8> F ¼ k x ; (1) i i i 54.5 <8,20> M ¼ h θ ; (2) 12.5 <20,25> i i i Intertransverse (IT) 12.5 <0,9> where F is the reaction force on the disc, x is the translational i i th 61.4 <9,15> displacement along the i axis (i = anterior-posterior, proximal- distal, left-right lateral direction), M is the reaction moment on the j 25 <15,17> disc, θ is the rotational angle along the ith axis, k is the i i translational stiffness and h is the rotational stiffness of the disc, with values from the literature . The joint rotational centers for The compressive load on the disc (F ) due to body weight, ext ﬂexion were set with ﬁxed values taken from the literature . muscle forces, and ligament forces (in a direction perpendicular to To simulate the swelling effects of lumbar discs during the lower surface of the disc) was assumed to consist of two unloading in microgravity, the deformation-dependent swelling forces, namely, a swelling force (F ) generated by the swelling pressure of the intervertebral disc was introduced by the following pressure, and an elastic force (F ) generated by disc deformation. It equation : was calculated as: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 F ¼ F þ F ; (5) ext S E F ¼ RT c þ 4c 2c ; (3) −1 where R is the universal gas constant (8.3144 JK mol), T is the In this study, the average FCD in annulus ﬁbrosus (AF) was * + assumed to be 80% of that in the nucleus pulposus (NP) for temperature in Kelvin (310.15 K), c is the concentration of Na − 36 and Cl in the surrounding environment of the discs (150 mM). healthy discs based on experimental data , and the cross- sectional area of NP was assumed to be 40% of the whole disc c is the ﬁxed charge density (FCD) inside the disc, which is 35 37 dependent on disc deformation as follow : cross-sectional area, also based on experimental data . The w swelling pressure in the lumbar discs was estimated as: F F 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ c ¼ c ; (4) 0 w 2 2 2 2 ϕ þ J 1 F F F ¼ A RT 0:4 c þ 4c 2c þ 0:6 c þ 4c 2c ; S disc NP AF Where c is FCD inside the disc at the reference state (i.e., neutral (6) posture at 1G gravity, values were listed in Table 2), J is the volume ratio of the disc between the deformed and reference state. where A is the disc cross-sectional area, c is the mean FCD in disc NP Assuming that during swelling, the percentage changes in disc the NP, and c is the mean FCD in the AF. The average water AF w w w content in the disc was estimated by:ϕ ¼ 0:4ϕ þ 0:6ϕ , dimension were approximately similar in all three principle NP AF 3 w w where ϕ and ϕ are the water content in the NP and AF, directions, the volume ratio was estimated by: J = (h/h ) , where NP AF is disc height at reference respectively. h is disc height after deformation and h state (with values listed in Table 2). The ligaments were modeled as piecewise linear models, in which The water content in the disc is deformation dependent and is the stiffness is dependent on the strain, with values taken from ϕ þJ1 35 w w 38 calculated as follow :ϕ ¼ , where ϕ is disc water content experimental results by Chazal et al. . The values for the stiffness w 33 after deformation, and ϕ is disc water content at the reference canbe seeninBaldoni andGu andlistedbrieﬂyinTable 3.For the state (with values listed in Table 2). muscle, the maximum muscle strength was assumed to be its npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA B. Wu et al. functional cross-sectional area dependent, similar to that in the DATA AVAILABILITY literature . The values listed in Tables 2, 3 were the same in 1G and The data that support the ﬁndings of this study are available from the corresponding 0G conditions. author upon request. This model has been primarily validated against experimental 32 40 data under various daily postures . The compressive forces Received: 6 July 2022; Accepted: 10 January 2023; simulated with this model at 1G condition were compared well with the in vivo human data at 12 different everyday postures (including lying supine, sitting slouched, sitting straight, standing, standing with 36° ﬂexion, standing with 19° extension, standing with 24° rotation to the left, standing with 17° rotation REFERENCES to the right, standing with 18° bent to the right, standing with a 1. Kerstman,E.L., Scheuring, R. A.,Barnes, M. G., DeKorse,T. B.& Saile,L.G.Space weight lifted close to the chest, standing with a weight lifted adaptation back pain: a retrospective study. Aviat. Space Environ. Med. 83,2–7 (2012). while ﬂexed forward, and standing with a weight lifted with arm 2. Belavy, D. L. et al. Disc herniations in astronauts: what causes them, and what stretched), details could be seen in our previous publication . does it tell us about herniation on earth? Eur. Spine J. 25, 144–154 (2016). 3. Johnston, S. L., Campbell, M. R., Scheuring, R. & Feiveson, A. H. Risk of herniated Further validation in the 0G condition was included in the nucleus pulposus among U.S. astronauts. Aviat. Space Environ. Med. 81, 566–574 discussion below. (2010). 4. Thornton, W., Hofﬂer, G. & Rummel, J. Anthropometric changes and ﬂuid shifts. Numerical modeling Report No. NASA SP-377, 330-338 (NASA, 1977). 5. Young, K. S. & Rajulu, S. Changes in seated height in microgravity. Appl. Erg. 83, In this study, the neutral body posture (e.g., relaxed ﬂoating) in 102995 (2020). microgravity (denoted as “Neutral 0G”), the “fetal tuck” posture in 6. Styf, J. R. et al. Height increase, neuromuscular function, and back pain during 6 microgravity (denoted as “Fetal Tuck 0G”), and for comparison, the degrees head-down tilt with traction. Aviat. Space Environ. Med. 68,24–29 (1997). neutral body posture (e.g., relaxed standing) in 1G gravity 7. Tyrrell, A. R., Reilly, T. & Troup, J. D. Circadian variation in stature and the effects of (denoted as “Neutral 1G”) and the neutral body posture (e.g., spinal loading. Spine 10, 161–164 (1985). relaxed standing) in 0G gravity (denoted as “Standing 0G”) were 8. Grifﬁn, B. N. The inﬂuence of zero-g and acceleration on the human factors of simulated (Fig. 1). The images of the full-body musculoskeletal spacecraft design. (1978). model shown in Fig. 1 were from the Anybody database (AMMR 9. Andreoni, G. et al. Quantitative analysis of neutral body posture in prolonged 2.3.4) which were originally developed by de Zee et al. , Ignasiak microgravity. Gait Posture 12, 235–242 (2000). 41 42 43 44 10. Young, K. S., Kim, K. H. & Rajulu, S. Anthropometric changes in spaceﬂight. Hum. et al. , Maganaris , Dostal and Andrews , Herzog and Read , Factors 22, 187208211049008 (2021). and Hintermann, Nigg, and Sommer . 11. Sayson, J. V. et al. In 66th International Astronautical Congress (2015). The Neutral 1G and Standing 0G posture was simulated as 12. Brown, J. W. Crew Height Measurement. (NASA, 1977). follows: the sternoclavicular joint protraction was 23° and 13. Treffel, L. et al. Intervertebral disc swelling demonstrated by 3D and water con- sternoclavicular joint elevation was 11.5°. The glenohumeral tent magnetic resonance analyses after a 3-day dry immersion simulating ﬂexion was 8°, abduction was 10°, the elbows were ﬂexed microgravity. Front. Physiol. 7, 605 (2016). forward 8°, elbow pronation was −20°, the hip ﬂexion was −6°, 14. Sayson, J. V. & Hargens, A. R. Pathophysiology of low back pain during exposure the hip abduction was 5°, and the rest of the joint angles were to microgravity. Aviat. Space Environ. Med. 79, 365–373 (2008). set to 0° (Fig. 1a). 15. Yingling, V. R., Callaghan, J. P. & McGill, S. M. The porcine cervical spine as a model of the human lumbar spine: an anatomical, geometric, and functional The Neutral 0G was simulated according to data from NASA : comparison. J. Spinal Disord. 12, 415–423 (1999). the neck was bent forward 24° and the line of sight was lowered 16. Callaghan, J. P. & McGill, S. M. Intervertebral disc herniation: studies on a porcine 15° compared to that in Neutral 1G. The glenohumeral ﬂexion was model exposed to highly repetitive ﬂexion/extension motion with compressive 39°, the abduction was 35°, the elbows were ﬂexed forward 77°, force. Clin. Biomech. 16,28–37 (2001). the elbow pronation was 60°, the hip ﬂexion was 55°, the hip 17. Lyons, G., Eisenstein, S. M. & Sweet, M. B. Biochemical changes in intervertebral abduction was 16°, the hip external rotation was 17°, the knee disc degeneration. Biochim. Biophys. Acta 673, 443–453 (1981). ﬂexion was 55°, and the ankle plantar ﬂexion was 21°. The rest of 18. Chan, S. C., Ferguson, S. J. & Gantenbein-Ritter, B. The effects of dynamic loading the joint angles were set to 0° (Fig. 1b). on the intervertebral disc. Eur. Spine J. 20, 1796–1812 (2011). The fetal tuck 0G was simulated as follows: the pelvis was ﬂexed 19. Setton, L. A. & Chen, J. Cell mechanics and mechanobiology in the intervertebral disc. Spine 29, 2710–2723 (2004). forward 80° relative to the thorax, the neck was bent forward 24°, 20. Gao, X., Zhu, Q. & Gu, W. Analyzing the effects of mechanical and osmotic loading the sternoclavicular joint protraction was 23°, the sternoclavicular on glycosaminoglycan synthesis rate in cartilaginous tissues. J. Biomech. 48, joint elevation was 11.5°, the glenohumeral joint ﬂexion was 80°, 573–577 (2015). the glenohumeral joint external rotation was −90°, the elbow 21. Guilak, F., Ratcliffe, A. & Mow, V. C. Chondrocyte deformation and local tissue ﬂexion was 90°, the hip ﬂexion was 100°, the knee ﬂexion was strain in articular cartilage: a confocal microscopy study. J. Orthop. Res. 13, 150°, and the ankle plantar ﬂexion was 21°. The rest of the joint 410–421 (1995). angles were set to 0° (Fig. 1c). 22. O’Conor, C. J., Leddy, H. A., Beneﬁeld, H. C., Liedtke, W. B. & Guilak, F. TRPV4- In this study, the change of mechanical loadings on the lumbar mediated mechanotransduction regulates the metabolic response of chon- intervertebral discs, disc swelling (water content), disc morphol- drocytes to dynamic loading. Proc. Natl Acad. Sci. USA 111, 1316–1321 (2014). 23. Gao, X., Zhu, Q. & Gu, W. Prediction of glycosaminoglycan synthesis in inter- ogy, muscle forces, and ligament forces were quantitatively vertebral disc under mechanical loading. J. Biomech. 49, 2655–2661 (2016). analyzed and compared among Neutral 1G, Standing 0G, Neutral 24. Jin, L. et al. The effects of simulated microgravity on intervertebral disc degen- 0G, and fetal tuck 0G conditions. eration. Spine J. 13, 235–242 (2013). Most parameters were from experimental data that measured 25. Fitzgerald, J., Endicott, J., Hansen, U. & Janowitz, C. Articular cartilage and sternal from a certain demographic group. To show how this may affect ﬁbrocartilage respond differently to extended microgravity. NPJ Microgravity 5,3 the reliability of our results, as an example, we varied the disc (2019). height and cross-sectional area in the range of [−20%, 20%] of the 26. Antoniou, J. et al. The human lumbar intervertebral disc - Evidence for changes in original values, based on experimental data , and results under the biosynthesis and denaturation of the extracellular matrix with growth, such conditions were compared to the original ones. maturation, ageing, and degeneration. J. Clin. Invest 98, 996–1003 (1996). 27. LeBlanc, A. et al. Muscle volume, MRI relaxation times (T2), and body composition after spaceﬂight. J. Appl Physiol. 89, 2158–2164 (2000). Reporting Summary 28. Hides, J. A. et al. The effects of exposure to microgravity and reconditioning of Further information on research design is available in the Nature the lumbar multiﬁdus and anterolateral abdominal muscles: implications for Portfolio Reporting Summary linked to this article. people with LBP. Spine J. 21, 477–491 (2021). Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. 29. McNamara, K. P., Greene, K. A., Moore, A. M., Lenchik, L. & Weaver, A. A. Lum- ACKNOWLEDGEMENTS bopelvic muscle changes following long-duration spaceﬂight. Front. Physiol. 10, This study was supported by grants from the National Natural Science Foundation of 627 (2019). China (11902154), the Natural Science Foundation of Jiangsu (BK20190387). 30. Pintar, F. A., Yoganandan, N., Myers, T., Elhagediab, A. & Sances, A. Jr. Bio- mechanical properties of human lumbar spine ligaments. J. Biomech. 25, 1351–1356 (1992). AUTHOR CONTRIBUTIONS 31. Cornaz, F. et al. Intervertebral disc degeneration relates to biomechanical chan- B.W.: Model development and simulation, original draft preparation, X.G.: Data ges of spinal ligaments. Spine J. 21, 1399–1407 (2021). analysis and original draft preparation. M.B.: Model development. B.Q. and L.Z.: 32. Wilke, H., Neef, P., Hinz, B., Seidel, H. & Claes, L. Intradiscal pressure together with Literature review, project-related software preparation, and validation. Z.Q.: Manu- anthropometric data-a data set for the validation of models. Clin. Biomech. 16, script reviewing and editing. Q.Z.: Conceptualization and Methodology guidance. S111–S126 (2001). 33. Baldoni, M. & Gu, W. Effect of ﬁxed charge density on water content of IVD during bed rest: a numerical analysis. Med Eng. Phys. 70,72–77 (2019). COMPETING INTERESTS 34. Pearcy, M. J. & Bogduk, N. Instantaneous axes of rotation of the lumbar inter- The authors declare no competing interests. vertebral joints. Spine 13, 1033–1041 (1988). 35. Lai, W. M., Hou, J. S. & Mow, V. C. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113, 245–258 (1991). ADDITIONAL INFORMATION 36. Urban, J. P. G. & Maroudas, A. The measurement of ﬁxed charged density in the Supplementary information The online version contains supplementary material intervertebral disc. Biochim. Biophys. Acta 586, 166–178 (1979). available at https://doi.org/10.1038/s41526-023-00253-8. 37. Pooni, J. S., Hukins, D. W., Harris, P. F., Hilton, R. C. & Davies, K. E. Comparison of the structure of human intervertebral discs in the cervical, thoracic and lumbar Correspondence and requests for materials should be addressed to Qiaoqiao Zhu. regions of the spine. Surg. Radio. Anat. 8, 175–182 (1986). 38. Chazal, J. et al. Biomechanical properties of spinal ligaments and a histolo- Reprints and permission information is available at http://www.nature.com/ gical study of the supraspinal ligament in traction. J. Biomech. 18, 167–176 reprints (1985). 39. de Zee, M., Hansen, L., Wong, C., Rasmussen, J. & Simonsen, E. B. A generic Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims detailed rigid-body lumbar spine model. J. Biomech. 40, 1219–1227 (2007). in published maps and institutional afﬁliations. 40. Qin, B. et al. Effect of lumbar muscle atrophy on the mechanical loading change on lumbar intervertebral discs. J. Biomech. 139, 111120 (2022). 41. Ignasiak, D., Dendorfer, S. & Ferguson, S. J. Thoracolumbar spine model with articulated ribcage for the prediction of dynamic spinal loading. J. Biomech. 49, Open Access This article is licensed under a Creative Commons 959–966 (2016). Attribution 4.0 International License, which permits use, sharing, 42. Maganaris, C. N. In vivo measurement-based estimations of the moment arm adaptation, distribution and reproduction in any medium or format, as long as you give in the human tibialis anterior muscle-tendon unit. J. Biomech. 33, 375–379 appropriate credit to the original author(s) and the source, provide a link to the Creative (2000). Commons license, and indicate if changes were made. The images or other third party 43. Dostal, W. F. & Andrews, J. G. A three-dimensional biomechanical model of hip material in this article are included in the article’s Creative Commons license, unless musculature. J. Biomech. 14, 803–812 (1981). indicated otherwise in a credit line to the material. If material is not included in the 44. Herzog, W. & Read, L. J. Lines of action and moment arms of the major force- article’s Creative Commons license and your intended use is not permitted by statutory carrying structures crossing the human knee joint. J. Anat. 182, 213–230 (1993). regulation or exceeds the permitted use, you will need to obtain permission directly 45. Hintermann, B., Nigg, B. M. & Sommer, C. Foot movement and tendon excursion: from the copyright holder. To view a copy of this license, visit http:// an in vitro study. Foot Ankle Int. 15, 386–395 (1994). creativecommons.org/licenses/by/4.0/. 46. Peloquin, J. M. et al. Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration. J. Biomech. 47, 2452–2459 (2014). © The Author(s) 2023 npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj Microgravity Springer Journals http://www.deepdyve.com/lp/springer-journals/effect-of-microgravity-on-mechanical-loadings-in-lumbar-spine-at-XGafpfxsbT

Loading next page...

Publisher: Springer Journals
Copyright: Copyright © The Author(s) 2023
eISSN: 2373-8065
DOI: 10.1038/s41526-023-00253-8
Publisher site: See Article on Publisher Site

Abstract

www.nature.com/npjmgrav ARTICLE OPEN Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study 1 1 1 2 1 1 1✉ Biao Wu , Xin Gao , Bing Qin , Michele Baldoni , Lu Zhou , Zhiyu Qian and Qiaoqiao Zhu The aim of this study was to quantitatively analyze the mechanical change of spinal segments (disc, muscle, and ligament) at various postures under microgravity using a full-body musculoskeletal modeling approach. Speciﬁcally, in the lumbar spine, the vertebra were modeled as rigid bodies, the intervertebral discs were modeled as 6-degree-of-freedom joints with linear force- deformation relationships, the disc swelling pressure was deformation dependent, the ligaments were modeled as piecewise linear elastic materials, the muscle strength was dependent on its functional cross-sectional area. The neutral posture and the “fetal tuck” posture in microgravity (short as “Neutral 0G” and “Fetal Tuck 0G”, in our simulation, the G constant was set to 0 for simulating microgravity), and for comparison, the relaxed standing posture in 1G and 0G gravity (short as “Neutral 1G” and “Standing 0G”) were simulated. Compared to values at Neutral 1G, the mechanical response in the lower spine changed signiﬁcantly at Neutral 0G. For example, the compressive forces on lumbar discs decreased 62–70%, the muscle forces decreased 55.7–92.9%, while disc water content increased 7.0–10.2%, disc height increased 2.1–3.0%, disc volume increased 6.4–9.3%, and ligament forces increased 59.5–271.3% at Neutral 0G. The fetal tuck 0G reversed these changes at Neutral 0G back toward values at Neutral 1G, with magnitudes much larger than those at Neutral 1G. Our results suggest that microgravity has signiﬁcant inﬂuences on spinal biomechanics, alteration of which may increase the risks of disc herniation and degeneration, muscle atrophy, and/or ligament failure. npj Microgravity (2023) 9:16 ; https://doi.org/10.1038/s41526-023-00253-8 INTRODUCTION semi-crouched, arms and legs ﬂexed, head and neck bent 8–10 forward (Fig. 1). How are the spinal segments loaded Microgravity exposure causes higher rates of back pain and disc 1,2 mechanically under this posture in microgravity are unknown, herniations in astronauts . Studies show that 52% of astronauts whether the mechanical loadings among the spinal segments report spinal pain during their space mission, with 86% of which were different in microgravity from those at neutral standing in 1G occurred in the lower back . The incidence of intervertebral disc gravity, and whether these difference (if any) possibly relate to herniation in astronauts returned back to the earth from lower back pain and/or disc herniation are also largely unknown. microgravity is much higher compared to that of matched control In addition, some astronauts claimed that low back pain is relieved on the earth, it is 4.3 times higher for lumbar discs, with the highest by periodic “fetal tuck posture” in microgravity, that is, curling risk appeared in the ﬁrst year after return to the earth ,and 21.4 knees to the chest posture (Fig. 1). How does this “fetal tuck” times higher for cervical discs . The reason for much higher risks of posture relieve lower back pain biomechanically and whether this low back pain and disc herniation in microgravity is not clear yet, posture is mechanically safe to spinal health are also largely some researchers proposed that intervertebral disc swelling due to unknown, yet of great interests to us. unloading in microgravity may be a possible mechanism . Thornton Thus, the aim of this study was to quantitatively analyze the et al. showed that the stature increased around 4–6cm (3% of mechanical change of various spinal segments in the lower back, stature) in microgravity . Recently Young and Rajulu reported that including disc load, disc swelling, disc morphology (height, cross- seated height increased by 4% on average in an in-ﬂight study .The sectional area, volume), muscle forces, and ligament forces at height increase in microgravity was thought mainly caused by spinal 6 5 neutral and “fetal tuck” postures under microgravity using a elongation through disc swelling and spinal curvature change . musculoskeletal modeling approach. This study is important for Intervertebral disc swelling in microgravity has not been measured understanding the biomechanical mechanisms of microgravity- directly, though. However, it is reported that body height changes related lower back pain and disc herniations, and this computa- diurnally following the circadian rhythm on the earth, that is, a tional model is helpful in guiding future design and development person is about 1.1% taller in the morning than at night ,due to that of spinal countermeasures under microgravity. intervertebral disc imbibes/extrudes water during the unloading at night/loading at day, causing the intervertebral disc height to ﬂuctuate diurnally. How much does human disc swell under RESULTS microgravity are largely unknown yet, and how these swelling The mechanical responses in the lumbar spine under Neutral 1G, changes in the discs affect adjacent spinal segments mechanically are also largely unknown yet. Standing 0G, Neutral 0G, and Fetal Tuck 0G conditions were reported (Figs. 2–5). Results between Standing 0G vs Neutral 0G In microgravity, the neutral body posture (relaxed ﬂoating) was found quite different from the neutral posture (relaxed were not signiﬁcantly different (Figs. 2–5), thus in the following standing) in a gravitational environment, in which the torso was results, we focused mainly on comparing differences between 1 2 Department of Biomedical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. Department of Biomedical Engineering, University of Miami, Miami, FL, USA. email: zqq@nuaa.edu.cn Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; B. Wu et al. Fig. 1 The postures simulated in 1G gravity and microgravity. a Relaxed standing posture in 1G gravity (Neutral 1G); this posture was also used in microgravity for comparison (Standing 0G), b relaxed ﬂoating posture in microgravity (Neutral 0G), and c fetal tuck posture in microgravity (Fetal Tuck 0G). Neutral 1G, Neutral 0G, and Fetal Tuck 0G since these three 0G (Fig. 3). The height increased by 3.0, 2.3, 2.1, 2.1, and 2.6%, the postures are commonly experienced by astronauts on the earth disc cross-sectional area increased by 6.1, 4.6, 4.2, 4.3, and 5.2%, and in a microgravity environment. and the disc volume increased 9.3, 7.0, 6.4, 7.0, and 7.9% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, respectively (Fig. 3). Compressive forces on lumbar discs Fetal tuck 0G vs Neutral 0G. Compared to results at Neutral 0G, Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the the disc height, cross-sectional area, and volume decreased at compressive forces on the lumbar discs decreased at Neutral 0G fetal tuck 0G (Fig. 3). The disc height decreased by 10.7, 9.9, 8.3, (Fig. 2a). It decreased by 70.2, 62.1, 63.5, 63.1, and 66.7% on L1L2, 7.5, and 7.0%, the disc cross-sectional area decreased 20.3, 18.9, L2L3, L3L4, L4L5, and L5S1 discs, respectively. 15.8, 14.4, and 13.5%, and the disc volume decreased 28.9, 26.9, 22.8, 20.9, and 19.6% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, Fetal tuck 0G vs Neutral 0G. Compared to values at Neutral 0G, respectively (Fig. 3). compressive forces increased at fetal tuck 0G. It increased by 932.2, 785.6, 742.9, 633.2, and 577.3% on L1L2, L2L3, L3L4, L4L5, Fetal tuck 0G vs Neutral 1G. Compared to results at Neutral 1G, the and L5S1 discs, respectively (Fig. 2a). disc height, cross-sectional area, and disc volume were smaller at fetal tuck 0G (Fig. 3). The height was 8.0, 7.9, 6.4, 5.5, and 4.6% Fetal tuck 0G vs Neutral 1G. Compared to values at Neutral 1G, smaller, cross-sectional area was 15.4,15.1, 12.3,10.7, and 9.0% the compressive force was larger at fetal tuck 0G. It was 207.6, smaller, and the disc volume was 22.2, 21.8,17.9, 15.7, and 15.4% 235.9, 207.3, 170.6, and 225.3% larger on L1L2, L2L3, L3L4, L4L5, smaller in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, respectively (Fig. 3). and L5S1 discs, respectively (Fig. 2a). Water content Shear forces on lumbar discs Neutral 0G vs Neutral 1G. Compared to results at Neutral 1G, the Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the water content increased at Neutral 0G. It increased by 5.2, 3.9, 3.6, shear force decreased. It decreased by 79.6, 92.1, 84.4, and 47.0% 3.7, and 4.4% in L1L2, L2L3, L3L4, L4L5, and L5S1 discs, on L2L3, L3L4, L4L5, and L5S1 discs, and it changed from 65 N to respectively (Fig. 4). −16 N on the L1L2 disc at Neutral 0G, “−” means the change of force direction (Fig. 2b). Fetal tuck 0G vs Neutral 0G. Compared to results at Neutral 0G, the water content decreased at fetal tuck 0G, it decreased by 18.8, Fetal tuck 0G vs Neutral 0G. The shear forces at fetal tuck 0G 17.3, 14.3, 12.9, and 12.0% in L1L2, L2L3, L3L4, L4L5, and L5S1 increased by 2062.9, 643.4, and 264.5% on L1L2, L4L5, and L5S1 discs, respectively (Fig. 4). discs, and it changed from 20 N to −101 N and 7 N to −17 N on the L2L3 and L3L4 discs, compared to those at Neutral 0G, “−” Fetal tuck 0G vs Neutral 1G. Compared to results at Neutral 1G, means the change of force direction (Fig. 2b). the water content was smaller at fetal tuck 0G. It was 14.5, 14.1, 11.3, 9.7, and 8.1% smaller in L1L2, L2L3, L3L4, L4L5, and L5S1 Fetal tuck 0G vs Neutral 1G. The shear force at fetal tuck 0G was discs, respectively (Fig. 4). 15.7 and 93.2% larger than those at Neutral 1G on L4L5 and L5S1 discs. It changed from 65 N to −354 N, 98 N to −101 N, 86 N to −17 N on the L1L2, L2L3, and L3L4 discs from Neutral 1G to fetal Muscle force tuck 0G, “−” means the change of force direction (Fig. 2b). Neutral 0G vs Neutral 1G. Compared to results at Neutral 1G, muscle forces decreased in most regions at Neutral 0G (Fig. 5a). Disc morphology The total force in MF, ES, PM, OE, OI, SR, TMF, and Tra groups in the Neutral 0G vs Neutral 1G. Compared to values at Neutral 1G, the lumbar regions decreased 59.8, 55.7, 81.1, 75.7, 53.3, 82.5, 88.1, disc height, cross-sectional area, and volume increased at Neutral and 92.9%, while the total force in QL and RA muscle groups npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; B. Wu et al. Fig. 2 Comparison of mechanical forces on lumbar discs among various postures in 1G gravity and microgravity. a Compressive force and b shear force among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. Fig. 3 Comparison of disc morphology change among various postures in 1G gravity and microgravity. a Disc height, b cross-sectional area, and c disc volume change among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. Fig. 4 Comparison of water content in lumbar discs among various postures in 1G gravity and microgravity. Water content in a NP and b AF among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. NP nucleus pulposus, AF annulus ﬁbrosus. slightly increased, with an increase of 1 N (from inactivated state) the total force in Tra muscle group decreased from 12.3 N to 0 N and 25 N (from inactivated state), respectively. (deactivated) (Fig. 5a). Fetal tuck 0G vs Neutral 0G. Compared to values at Neutral 0G, Fetal tuck 0G vs Neutral 1G. The muscle forces at Fetal Tuck 0G muscle forces increased in most regions at fetal tuck 0G. It were larger compared to those at Neutral 1G (Fig. 5a). It was 7.7, increased by 1820.1%, 1828.8, 882.3, 7165.5, 1210.2, 1682.2, 154.1, 8.5, 1.9, 3.2, and 8.3 times those at Neutral 1G in MF, ES, PM, OE, 342.2, and 979.5% in MF, ES, PM, QL, OE, OI, SR, TMF, and RA, while and OI muscles. In QL, it was 40 N at Fetal Tuck 0G and 0 N in Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. Fig. 5 Comparison of muscle forces and ligament forces in lumbar spine among various postures in 1G gravity and microgravity. a Muscle forces and b ligament forces in lumbar spine among Neutral 1G, Standing 0G, Neutral 0G, and Fetal Tuck 0G. MF multiﬁdus, ES erector spinae, PM psoas major, QL quadratus lumborum, OE obliquus externus, OI obliquus internus, SR semispinalis, TMF thoracic multiﬁdus, RA rectus abdominis, Tra transversus abdominis, ALL anterior longitudinal ligament, PLL posterior longitudinal ligament, IS interspinous, SS supraspinous, FL ﬂavum, IT intertransverse. Neutral 1G. In RA, it was 268 N at fetal tuck 0G and 0 N at Neutral while the disc water content, disc height, cross-sectional area, 1G. It decreased in SR, TMF, and Tra muscles. volume, and ligament forces increased at Neutral 0G, compared to those at Neutral 1G. The fetal tuck position at 0G showed a reverse effect on these changes seen at Neutral 0G, with values much Ligament force larger than those at Neutral 1G. Neutral 1G vs Neutral 0G. Compared to values at Neutral 1G, the Both compressive and shear forces on lumbar discs decreased ligament forces increased at Neutral 0G, increased 142.6, 211.6, in microgravity at neutral postures, causing the water to ﬂow into 133.0, 127.0, 117.0%, and 121.1% in ALL, PLL, IS, SS, FL, and IT, discs due to unbalanced osmotic pressure in the disc and the respectively (Fig. 5b). lowered external forces on the disc, leading to the increase in water content in the discs. The increased water content caused Fetal tuck 0G vs Neutral 0G. The ligament forces increased at fetal the discs to swell, leading to larger disc size, as seen in increased tuck 0G, compared to those at Neutral 0G (except ALL ligament) disc height, area, and volume. (Fig. 5b). It increased 5.3, 744.9, 1258.7, 394.5, and 171.8% in PLL, Our simulated disc size change was reasonable with experi- IS, SS, FL, and IT, respectively. It decreased from 92 N to 0 N in ALL. mental data. Early studies reported that astronaut stature 4,12 increased up to 3% during ﬂight , recently Yong and Rajulu Fetal tuck 0G vs Neutral 1G. The ligament forces at fetal tuck 0G reported that the seated height of astronauts increased by was larger compared to those at Neutral 1G (except ALL 4±1% . According to Styf et al. that 35 to 60% of the spinal ligaments) (Fig. 5b). It was 228.2, 1868.9, 2984.4,1945.8, and elongation is due to increases in intervertebral disc height , thus 650.0% larger in PLL, IS, SS, FL, and IT. It was 38 N smaller in ALL the disc height increase in Yong and Rajulu’s study would be (i.e., 38 N in Neutral 1G, 0 N in fetal tuck 0G). 1.4 ± 0.35% to 2.4 ± 0.6%. Our simulated disc height change (i.e., 3.0, 2.3, 2.1, 2.11, and 2.6% for L1L2, L2L3, L3L4, L4L5, and L5S1 Variation analysis discs) are close to this range. Treffel et al. found that after 3-day Our results showed that when the disc height varied in the range exposure to simulated microgravity through dry immersion, disc of [−20%, 20%] of the original height, our simulated disc volume increased by 8 ± 9% (T12-L1) and 11 ± 9% (L5S1) . Our compressive force varied in the range of [−1.3%, 0.9%] (values simulated disc volume increase (e.g., 6.4–9.3%) were close to these were averaged over ﬁve lumbar discs, same for the following experimental data. data), muscle force in the range of [−4.6%, 3.3%], ligament force in It is proposed that expansion of the disc in microgravity may the range of [4.7%, −3.4%], and disc height change in the range of cause deformation of collagen in the annulus ﬁbrosis, surpassing [14.7%, −11.7%] of the original values, respectively. When the disc the physiological range of 3–4%, resulting in stimulation of the cross-sectional area varied in the range of [−20%, 20%] of the Type IV mechanoreceptors/free nerve endings, which might cause original area, our simulated disc compressive force varied in the the sinuvertebral nerves to continually transmit impulses, range of [1.4%, −1.5%], muscle force in the range of [5.6%, eventually resulting in a perception of low back pain . Our −5.8%], ligament force in the range of [−7.6%, 6.9%], and disc results on disc cross-sectional area and volume increases at height change in the range of [14.0%, −6.9%] of the original Neutral 0G were in the range of 4.2–6.1% and 6.4–9.3%, values, respectively. respectively, which may lead to deformation of the collagen in the annulus ﬁbrosus larger than the 3–4% range mentioned above, thus increasing the risk of nerve stimulation in the related DISCUSSION area and possibly causing pain. In this study, the mechanical change of various spinal segments in Our results showed that the “fetal tuck” posture in microgravity the lumbar regions, including disc load, disc swelling, disc may be beneﬁcial in counteracting those spinal changes seen in morphology, muscle force, and ligament force were quantitatively Neutral 0G. The disc compressive force, shear force, disc height analyzed and compared among Neutral 1G, Neutral 0G, and fetal and volume, and disc water content all reversed back toward the tuck 0G. Our results showed that discs compressive forces, shear values at Neutral 1G. This may help explain biomechanically why forces, and muscle forces decreased signiﬁcantly at Neutral 0G, astronauts ﬁnd that the “fetal tuck” posture helps relieve back pain npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA B. Wu et al. Table 1. Ligament forces predicted at fetal tuck 0G (fetal tuck), compared to failure forces from literature (Fail). Parameter Ligament L1L2 L2L3 L3L4 L4L5 L5S1 Fetal tuck Fail Fetal Tuck Fail Fetal tuck Fail Fetal tuck Fail Fetal tuck Fail Fetal tuck 0G force(N) ALL 0.0 415.27 0.0 496.39 0.0 401.23 0.0 489.29 0.0 258.27 PLL 25.3 366.8 90.0 909.8 57.8 389.1 18.7 659.0 0.0 628.7 IT 49.2 304.2 41.2 434.5 32.2 236.5 20.0 108.0 10.1 171.8 FL 122.8 59 147.9 59 100.2 59 38.2 59 11.2 59 IS 90.3 74.8 91.1 40.9 68.8 87.4 45.9 84.6 4.7 122.0 SS 142.3 169.0 128.7 55.4 97.9 52.8 71.3 85.9 9.4 168.9 ALL anterior longitudinal ligament, PLL posterior longitudinal ligament, IT intertransverse, FL ﬂavum, IS interspinous, SS supraspinous. a 39 From Pintar et al. (1992) . b 40 From Cornaz et al. (2021) . The bold values are higher than the fail values measured in literature (Column ‘Fail’), indicating the corresponding ligaments may be in higher risk of damage. in microgravity. However, the magnitudes of these changes at ligament forces continued to increase (except ALL), due to that Fetal Tuck 0G far surpassed the values at Neutral 1G. For example, at ‘fetal tuck’ posture, the spine ﬂexed forward, causing most of the compressive loads on the lumbar discs at Fetal Tuck 0G were, the ligaments to stretch even longer. While the ALL ligament on average, 2.9 times the value at Neutral 1G, reaching shortened due to the forward bending, thus resulting in a 936 N–1266 N. It was reported that cyclic compressive force decrease in its force. The large increase in the ligament forces at (1 Hz) at 867 N for 24 h causes disc herniations in a porcine cervical the “fetal tuck” posture may increase the risks of ligaments disc, which is proposed to be closest to human lumbar spines in damages. Our calculated forces in the FL ligament at L1-L4, the anatomy and biomechanical characteristics . The compressive IS ligament at L1-L3, and the SS ligament at L2-L4 were larger forces at fetal tuck posture in our simulation are much higher than than the failure forces measured by Pintar et al. and Cornaz this value, such a large load on the discs may increase the risk of et al. (Table 1). disc ﬁssure and/or disc herniation . Our variational analysis results indicate that variations in disc Disc load change in microgravity may also increase the risk of height and the cross-sectional area may not signiﬁcantly inﬂuence disc degeneration through deregulating the synthesis of the forces on lumbar discs, muscle forces, and ligament forces, it may glycosaminoglycan (GAG), one of the crucial biochemical compo- inﬂuence the disc height change at fetal tuck 0G. Our results nents of the disc matrix, the loss of which causes disc found a negative correlation between disc size and disc height degeneration . Studies have shown that GAG synthesis is change, at larger disc size (either through larger disc height or disc signiﬁcantly affected by mechanical loading, with the GAG cross-sectional area), the disc height change was smaller synthesis rate decreased signiﬁcantly with the load deviating compared to that at smaller disc size. 18–22 (either increasing or decreasing) from the optimum range . There are some limitations in this study. One limitation is that in Gao et al. showed that the GAG synthesis rate decreased by 74% modeling the disc’s mechanical behavior, linear relationships were at a load three times the optimal load, and decreased by 80% at a used for translational and rotational behaviors, and more complex load 0.1 times the optimal load at the end of an 8-h creep in the and realistic mechanical models, such as creep, were not NP . Since the disc load in Neutral 0G decreased to 0.3 times that considered in our model. This simpliﬁcation may affect the in the Neutral 1G, and in fetal tuck 0G increased to 2.9 times that deformation of the disc and forces on the muscle and ligaments. in the Neutral 1G, we speculate that the GAG synthesis rate would Another limitation is that in modeling muscle, the muscle strength decrease signiﬁcantly in both postures at microgravity. Actually, was assumed to be cross-sectional area dependent, this simpli- GAG content decrease has been observed by experimental ﬁcation may affect the muscle forces and other segmental force 24,25 studies . For example, Jin et al. found downregulated GAG calculations, in the future, more realistic muscle mechanical content in simulated microgravity on the earth in mice disc . models, will be considered. In addition, even though this model Fitzgerald et al. found loss of proteoglycan in the articular cartilage was well validated in the 1G environment, it was only partially (which is similar to intervertebral disc both in composition and validated due to limited experimental data available in micro- axial weight-bearing functions) of mice exposed to microgravity gravity conditions, we will keep validating our model when more for 30 days on the BION-M1 craft . These decreases in GAG experimental data are available in the future. Another limitation is synthesis rate in both postures at microgravity may lead to disc that the angles for fetal tuck posture used in this study was an degeneration . estimation from the gesture due to the lack of data. This Muscle forces decreased in the neutral posture in microgravity, estimation may be different from real situations and may affect this may cause muscle atrophy, a widely observed phenomenon the forces calculated. among astronauts returned from long-term microgravity expo- In conclusion, in this study, we quantitatively analyzed and 27–29 sure . At fetal tuck 0G, the muscle forces increased signiﬁ- compared the changes in intervertebral disc load, disc water cantly, much larger than those at the Neutral 1G, and the content, disc morphology (height, cross-sectional area, volume), maximum muscle activation level increased signiﬁcantly (in the muscle forces, and ligament forces in the lumbar spine among range of 10–43%), this posture may be helpful in maintaining high Neutral 1G, Neutral 0G, and fetal tuck 0G conditions using a muscle force thus preventing lumbar muscles from atrophy, musculoskeletal modeling approach. Our results showed that lumbar discs compressive forces, shear forces, and muscle forces however, it may be detrimental to other mechanical segments, such as discs. decreased signiﬁcantly at Neutral 0G, while the disc water content, The ligament forces increased in Neutral 0G, due to that disc disc morphology, and ligament forces increased at Neutral 0G, swelling in microgravity stretched the ligament, resulting in compared to those at Neutral 1G. The fetal tuck 0G showed increases in ligament length and force. At Fetal Tuck 0G, the reverse effects on these changes seen at Neutral 0G, with Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. magnitudes much larger than those at Neutral 1G, which may Table 2. Parameters for lumbar disc height (h ), cross-sectional area increase the risk of damage to discs, muscles, and/or ligaments. (A ), water content ϕ , and ﬁxed charge density c at Neutral 1G 0 0 Our results are important for understanding the biomechanical condition. mechanisms of microgravity-related disc health, and this study provides a tool for quantifying mechanical changes in various 2 w F 3 h [mm] A [mm ] ϕ c [mol/m ] 0 0 0 0NP spinal segments under various gravitational environments. NP AF L1L2 9 1425 0.85 0.775 261 METHODS L2L3 10.4 1658 242 Theoretical studies L3L4 11.5 1714 239 The effects of microgravity on the biomechanical changes of disc load, disc swelling (water content), disc morphology (height, volume, L4L5 11.8 1684 215 cross-sectional area), muscle force, and ligament forces in the lumbar L5S1 11.3 1709 217 regions were studied using a full-body musculoskeletal model developed with the AnyBody Modeling System (AnyBody Technol- ogy, Version 7.3, Denmark). The anatomical structure and sizes of the body segments were from a male with a height of 1.74 m and a Table 3. Ligament stiffness values in the model. weight of 72 kg .Speciﬁcally, in the lumbar spine, the model Ligament Stiffness (N/mm) Strain (%) includes ﬁve lumbar vertebrae, ﬁve intervertebral discs, ten major muscle groups [including lumbar multiﬁdus (MF), erector spinae (ES), Anterior longitudinal ligament (ALL) 36.2 <0,11> psoas major (PM), quadratus lumborum (QL), obliquus externus (OE), 115.9 <11, 41> obliquus internus (OI), semispinalis (SR), thoracic multiﬁdus (TMF), 43 <41, 51> rectus abdominis (RA), and transversus abdominis (Tra)], and six lumbar ligament groups [including anterior longitudinal ligament Posterior longitudinal ligament (PLL) 52.7 <0,11> (ALL), posterior longitudinal ligament (PLL), interspinous (IS), 127 <11,28> supraspinous (SS), ﬂavum (FL), and intertransverse (IT)]. 37.1 <28,37> For the mechanical behaviors, the vertebral bones were modeled Interspinous (IS), Supraspinous (SS) 13 <0,14> as rigid bodies. The intervertebral discs were modeled as 6 degrees 38.5 <14,36> of freedom joints with linear momentum-rotational deformation and linear force-translational deformation relationships : 10.3 <36,48> Flavum (FL) 23.4 <0,8> F ¼ k x ; (1) i i i 54.5 <8,20> M ¼ h θ ; (2) 12.5 <20,25> i i i Intertransverse (IT) 12.5 <0,9> where F is the reaction force on the disc, x is the translational i i th 61.4 <9,15> displacement along the i axis (i = anterior-posterior, proximal- distal, left-right lateral direction), M is the reaction moment on the j 25 <15,17> disc, θ is the rotational angle along the ith axis, k is the i i translational stiffness and h is the rotational stiffness of the disc, with values from the literature . The joint rotational centers for The compressive load on the disc (F ) due to body weight, ext ﬂexion were set with ﬁxed values taken from the literature . muscle forces, and ligament forces (in a direction perpendicular to To simulate the swelling effects of lumbar discs during the lower surface of the disc) was assumed to consist of two unloading in microgravity, the deformation-dependent swelling forces, namely, a swelling force (F ) generated by the swelling pressure of the intervertebral disc was introduced by the following pressure, and an elastic force (F ) generated by disc deformation. It equation : was calculated as: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 F ¼ F þ F ; (5) ext S E F ¼ RT c þ 4c 2c ; (3) −1 where R is the universal gas constant (8.3144 JK mol), T is the In this study, the average FCD in annulus ﬁbrosus (AF) was * + assumed to be 80% of that in the nucleus pulposus (NP) for temperature in Kelvin (310.15 K), c is the concentration of Na − 36 and Cl in the surrounding environment of the discs (150 mM). healthy discs based on experimental data , and the cross- sectional area of NP was assumed to be 40% of the whole disc c is the ﬁxed charge density (FCD) inside the disc, which is 35 37 dependent on disc deformation as follow : cross-sectional area, also based on experimental data . The w swelling pressure in the lumbar discs was estimated as: F F 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ c ¼ c ; (4) 0 w 2 2 2 2 ϕ þ J 1 F F F ¼ A RT 0:4 c þ 4c 2c þ 0:6 c þ 4c 2c ; S disc NP AF Where c is FCD inside the disc at the reference state (i.e., neutral (6) posture at 1G gravity, values were listed in Table 2), J is the volume ratio of the disc between the deformed and reference state. where A is the disc cross-sectional area, c is the mean FCD in disc NP Assuming that during swelling, the percentage changes in disc the NP, and c is the mean FCD in the AF. The average water AF w w w content in the disc was estimated by:ϕ ¼ 0:4ϕ þ 0:6ϕ , dimension were approximately similar in all three principle NP AF 3 w w where ϕ and ϕ are the water content in the NP and AF, directions, the volume ratio was estimated by: J = (h/h ) , where NP AF is disc height at reference respectively. h is disc height after deformation and h state (with values listed in Table 2). The ligaments were modeled as piecewise linear models, in which The water content in the disc is deformation dependent and is the stiffness is dependent on the strain, with values taken from ϕ þJ1 35 w w 38 calculated as follow :ϕ ¼ , where ϕ is disc water content experimental results by Chazal et al. . The values for the stiffness w 33 after deformation, and ϕ is disc water content at the reference canbe seeninBaldoni andGu andlistedbrieﬂyinTable 3.For the state (with values listed in Table 2). muscle, the maximum muscle strength was assumed to be its npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA B. Wu et al. functional cross-sectional area dependent, similar to that in the DATA AVAILABILITY literature . The values listed in Tables 2, 3 were the same in 1G and The data that support the ﬁndings of this study are available from the corresponding 0G conditions. author upon request. This model has been primarily validated against experimental 32 40 data under various daily postures . The compressive forces Received: 6 July 2022; Accepted: 10 January 2023; simulated with this model at 1G condition were compared well with the in vivo human data at 12 different everyday postures (including lying supine, sitting slouched, sitting straight, standing, standing with 36° ﬂexion, standing with 19° extension, standing with 24° rotation to the left, standing with 17° rotation REFERENCES to the right, standing with 18° bent to the right, standing with a 1. Kerstman,E.L., Scheuring, R. A.,Barnes, M. G., DeKorse,T. B.& Saile,L.G.Space weight lifted close to the chest, standing with a weight lifted adaptation back pain: a retrospective study. Aviat. Space Environ. Med. 83,2–7 (2012). while ﬂexed forward, and standing with a weight lifted with arm 2. Belavy, D. L. et al. Disc herniations in astronauts: what causes them, and what stretched), details could be seen in our previous publication . does it tell us about herniation on earth? Eur. Spine J. 25, 144–154 (2016). 3. Johnston, S. L., Campbell, M. R., Scheuring, R. & Feiveson, A. H. Risk of herniated Further validation in the 0G condition was included in the nucleus pulposus among U.S. astronauts. Aviat. Space Environ. Med. 81, 566–574 discussion below. (2010). 4. Thornton, W., Hofﬂer, G. & Rummel, J. Anthropometric changes and ﬂuid shifts. Numerical modeling Report No. NASA SP-377, 330-338 (NASA, 1977). 5. Young, K. S. & Rajulu, S. Changes in seated height in microgravity. Appl. Erg. 83, In this study, the neutral body posture (e.g., relaxed ﬂoating) in 102995 (2020). microgravity (denoted as “Neutral 0G”), the “fetal tuck” posture in 6. Styf, J. R. et al. Height increase, neuromuscular function, and back pain during 6 microgravity (denoted as “Fetal Tuck 0G”), and for comparison, the degrees head-down tilt with traction. Aviat. Space Environ. Med. 68,24–29 (1997). neutral body posture (e.g., relaxed standing) in 1G gravity 7. Tyrrell, A. R., Reilly, T. & Troup, J. D. Circadian variation in stature and the effects of (denoted as “Neutral 1G”) and the neutral body posture (e.g., spinal loading. Spine 10, 161–164 (1985). relaxed standing) in 0G gravity (denoted as “Standing 0G”) were 8. Grifﬁn, B. N. The inﬂuence of zero-g and acceleration on the human factors of simulated (Fig. 1). The images of the full-body musculoskeletal spacecraft design. (1978). model shown in Fig. 1 were from the Anybody database (AMMR 9. Andreoni, G. et al. Quantitative analysis of neutral body posture in prolonged 2.3.4) which were originally developed by de Zee et al. , Ignasiak microgravity. Gait Posture 12, 235–242 (2000). 41 42 43 44 10. Young, K. S., Kim, K. H. & Rajulu, S. Anthropometric changes in spaceﬂight. Hum. et al. , Maganaris , Dostal and Andrews , Herzog and Read , Factors 22, 187208211049008 (2021). and Hintermann, Nigg, and Sommer . 11. Sayson, J. V. et al. In 66th International Astronautical Congress (2015). The Neutral 1G and Standing 0G posture was simulated as 12. Brown, J. W. Crew Height Measurement. (NASA, 1977). follows: the sternoclavicular joint protraction was 23° and 13. Treffel, L. et al. Intervertebral disc swelling demonstrated by 3D and water con- sternoclavicular joint elevation was 11.5°. The glenohumeral tent magnetic resonance analyses after a 3-day dry immersion simulating ﬂexion was 8°, abduction was 10°, the elbows were ﬂexed microgravity. Front. Physiol. 7, 605 (2016). forward 8°, elbow pronation was −20°, the hip ﬂexion was −6°, 14. Sayson, J. V. & Hargens, A. R. Pathophysiology of low back pain during exposure the hip abduction was 5°, and the rest of the joint angles were to microgravity. Aviat. Space Environ. Med. 79, 365–373 (2008). set to 0° (Fig. 1a). 15. Yingling, V. R., Callaghan, J. P. & McGill, S. M. The porcine cervical spine as a model of the human lumbar spine: an anatomical, geometric, and functional The Neutral 0G was simulated according to data from NASA : comparison. J. Spinal Disord. 12, 415–423 (1999). the neck was bent forward 24° and the line of sight was lowered 16. Callaghan, J. P. & McGill, S. M. Intervertebral disc herniation: studies on a porcine 15° compared to that in Neutral 1G. The glenohumeral ﬂexion was model exposed to highly repetitive ﬂexion/extension motion with compressive 39°, the abduction was 35°, the elbows were ﬂexed forward 77°, force. Clin. Biomech. 16,28–37 (2001). the elbow pronation was 60°, the hip ﬂexion was 55°, the hip 17. Lyons, G., Eisenstein, S. M. & Sweet, M. B. Biochemical changes in intervertebral abduction was 16°, the hip external rotation was 17°, the knee disc degeneration. Biochim. Biophys. Acta 673, 443–453 (1981). ﬂexion was 55°, and the ankle plantar ﬂexion was 21°. The rest of 18. Chan, S. C., Ferguson, S. J. & Gantenbein-Ritter, B. The effects of dynamic loading the joint angles were set to 0° (Fig. 1b). on the intervertebral disc. Eur. Spine J. 20, 1796–1812 (2011). The fetal tuck 0G was simulated as follows: the pelvis was ﬂexed 19. Setton, L. A. & Chen, J. Cell mechanics and mechanobiology in the intervertebral disc. Spine 29, 2710–2723 (2004). forward 80° relative to the thorax, the neck was bent forward 24°, 20. Gao, X., Zhu, Q. & Gu, W. Analyzing the effects of mechanical and osmotic loading the sternoclavicular joint protraction was 23°, the sternoclavicular on glycosaminoglycan synthesis rate in cartilaginous tissues. J. Biomech. 48, joint elevation was 11.5°, the glenohumeral joint ﬂexion was 80°, 573–577 (2015). the glenohumeral joint external rotation was −90°, the elbow 21. Guilak, F., Ratcliffe, A. & Mow, V. C. Chondrocyte deformation and local tissue ﬂexion was 90°, the hip ﬂexion was 100°, the knee ﬂexion was strain in articular cartilage: a confocal microscopy study. J. Orthop. Res. 13, 150°, and the ankle plantar ﬂexion was 21°. The rest of the joint 410–421 (1995). angles were set to 0° (Fig. 1c). 22. O’Conor, C. J., Leddy, H. A., Beneﬁeld, H. C., Liedtke, W. B. & Guilak, F. TRPV4- In this study, the change of mechanical loadings on the lumbar mediated mechanotransduction regulates the metabolic response of chon- intervertebral discs, disc swelling (water content), disc morphol- drocytes to dynamic loading. Proc. Natl Acad. Sci. USA 111, 1316–1321 (2014). 23. Gao, X., Zhu, Q. & Gu, W. Prediction of glycosaminoglycan synthesis in inter- ogy, muscle forces, and ligament forces were quantitatively vertebral disc under mechanical loading. J. Biomech. 49, 2655–2661 (2016). analyzed and compared among Neutral 1G, Standing 0G, Neutral 24. Jin, L. et al. The effects of simulated microgravity on intervertebral disc degen- 0G, and fetal tuck 0G conditions. eration. Spine J. 13, 235–242 (2013). Most parameters were from experimental data that measured 25. Fitzgerald, J., Endicott, J., Hansen, U. & Janowitz, C. Articular cartilage and sternal from a certain demographic group. To show how this may affect ﬁbrocartilage respond differently to extended microgravity. NPJ Microgravity 5,3 the reliability of our results, as an example, we varied the disc (2019). height and cross-sectional area in the range of [−20%, 20%] of the 26. Antoniou, J. et al. The human lumbar intervertebral disc - Evidence for changes in original values, based on experimental data , and results under the biosynthesis and denaturation of the extracellular matrix with growth, such conditions were compared to the original ones. maturation, ageing, and degeneration. J. Clin. Invest 98, 996–1003 (1996). 27. LeBlanc, A. et al. Muscle volume, MRI relaxation times (T2), and body composition after spaceﬂight. J. Appl Physiol. 89, 2158–2164 (2000). Reporting Summary 28. Hides, J. A. et al. The effects of exposure to microgravity and reconditioning of Further information on research design is available in the Nature the lumbar multiﬁdus and anterolateral abdominal muscles: implications for Portfolio Reporting Summary linked to this article. people with LBP. Spine J. 21, 477–491 (2021). Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2023) 16 B. Wu et al. 29. McNamara, K. P., Greene, K. A., Moore, A. M., Lenchik, L. & Weaver, A. A. Lum- ACKNOWLEDGEMENTS bopelvic muscle changes following long-duration spaceﬂight. Front. Physiol. 10, This study was supported by grants from the National Natural Science Foundation of 627 (2019). China (11902154), the Natural Science Foundation of Jiangsu (BK20190387). 30. Pintar, F. A., Yoganandan, N., Myers, T., Elhagediab, A. & Sances, A. Jr. Bio- mechanical properties of human lumbar spine ligaments. J. Biomech. 25, 1351–1356 (1992). AUTHOR CONTRIBUTIONS 31. Cornaz, F. et al. Intervertebral disc degeneration relates to biomechanical chan- B.W.: Model development and simulation, original draft preparation, X.G.: Data ges of spinal ligaments. Spine J. 21, 1399–1407 (2021). analysis and original draft preparation. M.B.: Model development. B.Q. and L.Z.: 32. Wilke, H., Neef, P., Hinz, B., Seidel, H. & Claes, L. Intradiscal pressure together with Literature review, project-related software preparation, and validation. Z.Q.: Manu- anthropometric data-a data set for the validation of models. Clin. Biomech. 16, script reviewing and editing. Q.Z.: Conceptualization and Methodology guidance. S111–S126 (2001). 33. Baldoni, M. & Gu, W. Effect of ﬁxed charge density on water content of IVD during bed rest: a numerical analysis. Med Eng. Phys. 70,72–77 (2019). COMPETING INTERESTS 34. Pearcy, M. J. & Bogduk, N. Instantaneous axes of rotation of the lumbar inter- The authors declare no competing interests. vertebral joints. Spine 13, 1033–1041 (1988). 35. Lai, W. M., Hou, J. S. & Mow, V. C. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113, 245–258 (1991). ADDITIONAL INFORMATION 36. Urban, J. P. G. & Maroudas, A. The measurement of ﬁxed charged density in the Supplementary information The online version contains supplementary material intervertebral disc. Biochim. Biophys. Acta 586, 166–178 (1979). available at https://doi.org/10.1038/s41526-023-00253-8. 37. Pooni, J. S., Hukins, D. W., Harris, P. F., Hilton, R. C. & Davies, K. E. Comparison of the structure of human intervertebral discs in the cervical, thoracic and lumbar Correspondence and requests for materials should be addressed to Qiaoqiao Zhu. regions of the spine. Surg. Radio. Anat. 8, 175–182 (1986). 38. Chazal, J. et al. Biomechanical properties of spinal ligaments and a histolo- Reprints and permission information is available at http://www.nature.com/ gical study of the supraspinal ligament in traction. J. Biomech. 18, 167–176 reprints (1985). 39. de Zee, M., Hansen, L., Wong, C., Rasmussen, J. & Simonsen, E. B. A generic Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims detailed rigid-body lumbar spine model. J. Biomech. 40, 1219–1227 (2007). in published maps and institutional afﬁliations. 40. Qin, B. et al. Effect of lumbar muscle atrophy on the mechanical loading change on lumbar intervertebral discs. J. Biomech. 139, 111120 (2022). 41. Ignasiak, D., Dendorfer, S. & Ferguson, S. J. Thoracolumbar spine model with articulated ribcage for the prediction of dynamic spinal loading. J. Biomech. 49, Open Access This article is licensed under a Creative Commons 959–966 (2016). Attribution 4.0 International License, which permits use, sharing, 42. Maganaris, C. N. In vivo measurement-based estimations of the moment arm adaptation, distribution and reproduction in any medium or format, as long as you give in the human tibialis anterior muscle-tendon unit. J. Biomech. 33, 375–379 appropriate credit to the original author(s) and the source, provide a link to the Creative (2000). Commons license, and indicate if changes were made. The images or other third party 43. Dostal, W. F. & Andrews, J. G. A three-dimensional biomechanical model of hip material in this article are included in the article’s Creative Commons license, unless musculature. J. Biomech. 14, 803–812 (1981). indicated otherwise in a credit line to the material. If material is not included in the 44. Herzog, W. & Read, L. J. Lines of action and moment arms of the major force- article’s Creative Commons license and your intended use is not permitted by statutory carrying structures crossing the human knee joint. J. Anat. 182, 213–230 (1993). regulation or exceeds the permitted use, you will need to obtain permission directly 45. Hintermann, B., Nigg, B. M. & Sommer, C. Foot movement and tendon excursion: from the copyright holder. To view a copy of this license, visit http:// an in vitro study. Foot Ankle Int. 15, 386–395 (1994). creativecommons.org/licenses/by/4.0/. 46. Peloquin, J. M. et al. Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration. J. Biomech. 47, 2452–2459 (2014). © The Author(s) 2023 npj Microgravity (2023) 16 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA

Journal

npj Microgravity – Springer Journals

Published: Feb 15, 2023

References

Space adaptation back pain: a retrospective study

Kerstman, EL; Scheuring, RA; Barnes, MG; DeKorse, TB; Saile, LG
Disc herniations in astronauts: what causes them, and what does it tell us about herniation on earth?

Belavy, DL
Risk of herniated nucleus pulposus among U.S. astronauts

Johnston, SL; Campbell, MR; Scheuring, R; Feiveson, AH
Changes in seated height in microgravity

Young, KS; Rajulu, S
Height increase, neuromuscular function, and back pain during 6 degrees head-down tilt with traction

Styf, JR
Circadian variation in stature and the effects of spinal loading

Tyrrell, AR; Reilly, T; Troup, JD
Quantitative analysis of neutral body posture in prolonged microgravity

Andreoni, G
Anthropometric changes in spaceflight

Young, KS; Kim, KH; Rajulu, S
Intervertebral disc swelling demonstrated by 3D and water content magnetic resonance analyses after a 3-day dry immersion simulating microgravity

Treffel, L
Pathophysiology of low back pain during exposure to microgravity

Sayson, JV; Hargens, AR
The porcine cervical spine as a model of the human lumbar spine: an anatomical, geometric, and functional comparison

Yingling, VR; Callaghan, JP; McGill, SM
Intervertebral disc herniation: studies on a porcine model exposed to highly repetitive flexion/extension motion with compressive force

Callaghan, JP; McGill, SM
Biochemical changes in intervertebral disc degeneration

Lyons, G; Eisenstein, SM; Sweet, MB
The effects of dynamic loading on the intervertebral disc

Chan, SC; Ferguson, SJ; Gantenbein-Ritter, B
Cell mechanics and mechanobiology in the intervertebral disc

Setton, LA; Chen, J
Analyzing the effects of mechanical and osmotic loading on glycosaminoglycan synthesis rate in cartilaginous tissues

Gao, X; Zhu, Q; Gu, W
Chondrocyte deformation and local tissue strain in articular cartilage: a confocal microscopy study

Guilak, F; Ratcliffe, A; Mow, VC
TRPV4-mediated mechanotransduction regulates the metabolic response of chondrocytes to dynamic loading

O’Conor, CJ; Leddy, HA; Benefield, HC; Liedtke, WB; Guilak, F
Prediction of glycosaminoglycan synthesis in intervertebral disc under mechanical loading

Gao, X; Zhu, Q; Gu, W
The effects of simulated microgravity on intervertebral disc degeneration

Jin, L
Articular cartilage and sternal fibrocartilage respond differently to extended microgravity

Fitzgerald, J; Endicott, J; Hansen, U; Janowitz, C
The human lumbar intervertebral disc - Evidence for changes in the biosynthesis and denaturation of the extracellular matrix with growth, maturation, ageing, and degeneration

Antoniou, J
Muscle volume, MRI relaxation times (T2), and body composition after spaceflight

LeBlanc, A
The effects of exposure to microgravity and reconditioning of the lumbar multifidus and anterolateral abdominal muscles: implications for people with LBP

Hides, JA
Lumbopelvic muscle changes following long-duration spaceflight

McNamara, KP; Greene, KA; Moore, AM; Lenchik, L; Weaver, AA
Biomechanical properties of human lumbar spine ligaments

Pintar, FA; Yoganandan, N; Myers, T; Elhagediab, A; Sances, A
Intervertebral disc degeneration relates to biomechanical changes of spinal ligaments

Cornaz, F
Intradiscal pressure together with anthropometric data-a data set for the validation of models

Wilke, H; Neef, P; Hinz, B; Seidel, H; Claes, L
Effect of fixed charge density on water content of IVD during bed rest: a numerical analysis

Baldoni, M; Gu, W
Instantaneous axes of rotation of the lumbar intervertebral joints

Pearcy, MJ; Bogduk, N
A triphasic theory for the swelling and deformation behaviors of articular cartilage

Lai, WM; Hou, JS; Mow, VC
The measurement of fixed charged density in the intervertebral disc

Urban, JPG; Maroudas, A
Comparison of the structure of human intervertebral discs in the cervical, thoracic and lumbar regions of the spine

Pooni, JS; Hukins, DW; Harris, PF; Hilton, RC; Davies, KE
Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction

Chazal, J
A generic detailed rigid-body lumbar spine model

de Zee, M; Hansen, L; Wong, C; Rasmussen, J; Simonsen, EB
Effect of lumbar muscle atrophy on the mechanical loading change on lumbar intervertebral discs

Qin, B
Thoracolumbar spine model with articulated ribcage for the prediction of dynamic spinal loading

Ignasiak, D; Dendorfer, S; Ferguson, SJ
In vivo measurement-based estimations of the moment arm in the human tibialis anterior muscle-tendon unit

Maganaris, CN
A three-dimensional biomechanical model of hip musculature

Dostal, WF; Andrews, JG
Lines of action and moment arms of the major force-carrying structures crossing the human knee joint

Herzog, W; Read, LJ
Foot movement and tendon excursion: an in vitro study

Hintermann, B; Nigg, BM; Sommer, C
Human L3L4 intervertebral disc mean 3D shape, modes of variation, and their relationship to degeneration

Peloquin, JM

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Effect of microgravity on mechanical loadings in lumbar spine at various postures: a numerical study

Abstract

Journal

Recommended Articles

References

Our policy towards the use of cookies