The FE model includes: vertebral body, intervertebral discs, main ligaments, and muscles (as shown in Figure 1A). Most anatomical geometry of the model comes from the CT scanning of 75-year-old women without clinical symptoms of lumbar degeneration. Lamellar thickness is 0.5 mm and resolution is 512 × 512. Then MIMICS software (Version 12.0, Materialize Inc., Leuven, Belgium) was used for the three-dimensional reconstruction. The intervertebral disc, endplate cartilage, and ligament were reconstructed according to anatomical position and reference from the radiologist. In order to make the FE model more consistent with the morphological characteristics of the target population, we adjusted the intervertebral space according to Shao's study (22). Elastic modulus of cancellous bone was adjusted according to the BMD of Chinese women population in Wu's report (23). The BMD was calculated based on equation (1)

Herein age was 60, and young's modulus was calculated by equation (2)

Young's modulus of vertebrae spongy bone for Chinese elderly women was obtained, as shown in Appendix Data 1.

Since there is not available cadaver experimental data of the muscle for validation, in order to ensure the biofidelity of our model, we removed the muscle, then the lumbar FE model was validated by comparing its predictions with range of motion (ROM) observed in vitro under the flexion (8 Nm), extension (6 Nm) loading condition without preloading (24). The same as the description of the experiment in vitro, the boundary condition of the lumbar FE model without muscle was set identically with experiments in vitro, as shown in Figure 1B.

In order to simulate the movement of an elderly woman in the process of lifting a child, the main muscles that maintain the stability of the trunk and waist when load-bearing were added into the model: Erector spinae, rectus abdominis, internal oblique muscle, external oblique muscle, lumbar major muscle, quadratus lumborum and multifidus. The psoas, multifidus, and quadratus lumborum muscle groups are reported to act as stabilizers of the lumbar spine. The erector spinae and the abdominal muscles are the primary locomotors of the spine. The parameters of the material properties are in the attachment (I–II), referring to the findings of Christophy (25). We referred to spine surgeons in Xiangya 3rd hospital when deciding the muscle starting and stopping points. The material parameters were converted according to PCSA (physiological cross-sectional area) and maximal force with equation (3), herein σ was the maximum engineering stress, F_max was the maximum force, the PCSA was the physiological cross-sectional area.

These variables were utilized as parameters of the fiber element parameter in LS-DYNA (LS-DYNA3D 971, LSTC, Livermore, CA, USA), as shown in Appendix II, and calculated in finite element model simulations. Similar settings were used to simulate the neck muscle response in the front impact study by Matthew's group (26).

In order to simulate the motion trajectory of an elderly woman lifting a child, a high-speed camera imaging system (Redlake MotionXtra HG-LE, DEL Imaging Systems, LLC. Chesshire. CT, US) was used to obtain the lumbar spine track in the process of volunteers lifting a dummy representative of a 3-year-old, as shown in Figures 2A,C. A standard 3-year-old child model (weight 16 kg, height 115 cm, P3 child dummy, Hunan SAF Automobile technology Co. Ltd, China) was used in this experiment. After labeling on the lumbar spine of the volunteers (Labeling spot was located on Spinous), video with a speed of 200 frames per second was recorded. (The characteristics of the volunteers: Age 76, 159.3 cm, 60.4kg, which is near the approximate the median of Chinese elderly women). The posture of the FE model was adjusted, as shown in Figures 2B,D, the range of motion of lumbar FE model was set identically to the volunteer's experiments. Three postures were simulated, the stress of the lumbar spine was calculated and predicted under bending without lifting posture, bending with lifting 3-year-old child posture, and upright with lifting 3-year-old child posture, respectively.

Repetitive loading lower than ultimate loads may cause failure (21), which presents a certain functional relationship between the action frequency and maximum stress. In this study, an equation was deduced from low cycle and high cycle fatigue studies with a genetic algorithm, as shown in equation (4). Herein σ_eff was effective stress, the unit was kPa, N was the number of cycles to failure.

Based on the effective stress of vertebral spongy bone calculated from the 2.4 section, the combined genetic algorithm and the equation (4), our study quantitatively predicted the limited frequency of the lumbar vertebral spongy bone during the movement of elderly women lifting children.

As shown in Figure 3, the ROM predicted by the lumbar FEM were in good agreement with the in vitro results at all segmental levels (24), except the L5-S1 ROM predicted was 13.7°, which was slightly above the in vitro result 9.43 ± .5°.

The experimental result showed that the maximum erector spinae tension was 4.32 kN, 4.9 kN, and 3.7 kN, in the bending without lifting weight, the bending with lifting 3-year-old child, and upright with 3-year-old child posture respectively, as shown in Figure 4. The calculated maximum intradiscal pressure was located in L5-S, which were 3.56 Mpa, 5.38 Mpa, and 1.47 Mpa, in the bending without lifting weight, the bending with lifting 3-year-old child, and upright with 3-year-old child posture respectively, as shown in Figure 5. The maximum effective stress contribution of endplate cartilage was located in posterior edge of L5 up and down endplate cartilage, which were 16.55 Mpa, 23.58 Mpa, and 26.55 Mpa in the bending without lifting weight, the bending with lifting 3-year-old child, and upright with 3-year-old child posture respectively, as shown in Figure 6.

The detailed sagittal views of the effective stress in lumbar vertebrae spongy bone were shown in Figure 7, as the vertebrae spongy bone was the primary compression-bearing structure. In the bending without lifting posture, the maximum effective stress of vertebrae spongy bone was located in the lateral posterior part and the vertebral pedicle of L5, which was 26.3 Mpa. When the 3-year-old child was lifted, the maximum effective stress contribution of the vertebrae spongy bone was moved into the middle posterior part and vertebral pedicle of L5, which was 38.5 Mpa, an increase of 46.3% compared to the bending without lifting weight posture. More increments occurred in the upright with 3-year-old child posture, the maximum effective stress contribution of the vertebrae spongy bone was moved into the bottom part and vertebral pedicle of L5, which was 53.8 Mpa, an increase of 39.7% compared to the bending with lifting posture. In spongy bone, the cycle to failure was intimately correlated to the effective stress, according to the cycle of failure vs. and the stress curve, the cycle to failure of lumbar vertebrae spongy bone in three different postures were shown in Table 1.

Before and after lifting, the maximum muscle force in bending posture has no significant change, the primary tense muscles were erector spinae, psoas major, quadratus lumborum, obliquus internus abdominis, obliqus externus abdominis, and rectus abdominis. After upright with lifting of 3-year-old baby, the muscular tension of erector spinae was relaxed, the maximum muscle force was decreased 24.5%. Ekholm measured that the erector spinae tension was 3.9 kN in lifting 12.8 kg with straight knees, and decreased 20.4% compared to lifting 12.8 kg with bending posture (28). Our muscle analysis result was in good agreement with the previous lumbar loading kinematic study, which will improve the biofidelity of this FE modeling and provide a more accurate prediction to muscle kinematic response analysis.

After lifting a 3-year-old child, the calculated intradiscal pressure was 1.51 times that of the bending without lifting posture, compared to after upright with 3-year-old child posture, the calculated intradiscal pressure in bending posture with the same loading was 2.38 times that of upright posture. As Sato measured the in vivo volunteer introdiscal pressure in different body postures, the different postures had a significant influence on intradiscal pressure, the intradiscal pressure in bending posture was reported to be 2.45 times that of the upright posture in the same loading (29). As the increased intradiscal pressure was considered as the primary impact factor of intervertebral disc degeneration in old age population (30). Collectively, the bending posture will cause the intradiscal pressure to increase, the increased intradiscal pressure will increase the risk of lumbar degeneration, typically the elderly women who frequently lift babies in a bending posture, this bending loading-bear posture might expedite the intravertebrae disc degeneration of the elder women.

In three different postures, the maximum effective stress of endplate cartilage is both located on the upper and lower endplates of L5. After lifting a 3-year-old child in a bending posture, the maximum effective stress of endplate cartilage is increased to 1.42 times that of the bending without lifting posture. More incrementally, upright with lifting 3-year-old child posture, was 1.6 times that of in the bending without lifting posture. As Adams reported, the repeated increase of endplate cartilage compression will cause the change of stress contribution in adjacent intravertebrae disc, and the annulus fibrosus cell appeared metabolically abnormal (31). Taken all together, these results suggested that the cyclic lifting motion of a 3-year-old child in daily life will aggravate the degeneration of intravertebrae disc.

Equivalent stress distribution of lumbar spongy bone: When the old woman is not lifting children, posterior vertebral pedicle of L4–L5 bears the largest force, which is 26.3 Mpa. When the old woman was bending and lifting a child, the effective stress on this part significantly increased by 44.3%. A larger increment occurred when the subject is standing upright after lifting a child and the effective stress reaches 53.8 Mpa. This is consistent with Pollintine's finding (32, 33). This change in stress suggests that when elderly women lift a child and finally reach the state of being upright, the pressure on posterior vertebral pedicle reaches its peak. After conferring to fatigue data (21), we found that in the case of bending without lifting, the fatigue limit is rather high, which is 515 times, so no obvious fatigue risk exists in this situation. The fatigue limitation frequency of the bending with lifting 3-year-old child posture is 275 times. Basically, a few risks of fatigue exist in this situation as well. In the case of upright with lifting a child, the corresponding fatigue limitation frequency of maximum load-bearing in the posterior vertebral body is low to 18 times. The result suggests that if the movements of upright and lifting a three-year-old child is done over 18 times continuously, the posterior vertebral body and pedicle spongy bone of L4–L5 will face the risk of fatigue failure.

However, it should be noted that the fatigue curves we referred to are based on in vitro experiments of cadaverous spongy bone. Nevertheless, the material properties of in vivo and in vitro spongy bone are different. Taylor's study found that spongy bone in vivo can self-repair the injury caused by stress fatigue (21). Thus it can be speculated that in vivo spongy bone has a higher fatigue tolerance than in vitro spongy bone. However, since there is no reference data about the relationship between the load-bearing of in vivo spongy bone and its fatigue, our calculation is based on the in vitro data. Therefore, the risk frequency (18 times) in this study can only be considered as a conservative reference value for the limiting frequency of the lifting child movement in elder women.

Actually, the lifting movement which our study focused on is called Knee Straight Lifting (KSL), the fracture risk of which is the highest among all common kinds of lifting movements (7). For Chinese women over 55 years old, lumbar loading is a high-risk factor for lumbar degeneration (11). Mechanical and biological factors, which were interconnected and amplified each other (34, 35), were considered the primary roles of lumbar degeneration. In this study, the lifting baby motion will accelerate the lumbar degeneration and increase the risk of fracture in the following ways: increasing intervertebral disc pressure, increasing endplate cartilage pressure, and fatigue failure of vertebral spongy bone due to the repeated loading-bear. Increasing bone strength and avoiding high-risk action are two approaches to prevent such risk. This study provides a reference for elderly women in China and East Asia, which is trying to avoid continuous straight-standing action in the daily movement of lifting children. In a word, the frequency of KSL movement especially with burden should not be too much. The experimental model and stress analysis fully considered several closely related factors: BMD degeneration (23), muscle movement (25), ligament material parameters, and patient-specific skeletal geometry of asymptomatic elderly women. The article aims to simulate the biomechanical characteristics of Chinese elderly women as accurately as possible and quantitatively analyzes the movement of lifting children, which happens frequently in Chinese elderly women. The study possesses following characteristics. First, we added the main muscles and ligaments of the waist into the model, which helps to simulate the dynamic process of lifting a child with higher biofidelity. Second, in the motion simulation, the model simulated the process of lifting a child according to the result of high-speed photography in volunteers' experiments. Thirdly, the fatigue property of vertebral spongy bone was taken into consideration. We combined the research result with fatigue curve and get the fatigue limit frequency of vertebral part bearing the most pressure and quantified the effect of such pressure on the vertebral body's fatigue failure.