Effect of the intra-abdominal pressure and the center of segmental body mass on the lumbar spine mechanics - a computational parametric study

Abstract

Determination of physiological loads in human lumbar spine is critical for understanding the mechanisms of lumbar diseases and for designing surgical treatments. Computational models have been used widely to estimate the physiological loads of the spine during simulated functional activities. However, various assumptions on physiological factors such as the intra-abdominal pressure (IAP), centers of mass (COMs) of the upper body and lumbar segments, and vertebral centers of rotation (CORs) have been made in modeling techniques. Systematic knowledge of how these assumptions will affect the predicted spinal biomechanics is important for improving the simulation accuracy. In this paper, we developed a 3D subject-specific numerical model of the lumbosacral spine including T12 and 90 muscles. The effects of the IAP magnitude and COMs locations on the COR of each motion segment and on the joint/muscle forces were investigated using a global convergence optimization procedure when the subject was in a weight bearing standing position. The data indicated that the line connecting the CORs showed a smaller curvature than the lordosis of the lumbar spine in standing posture when the IAP was 0 kPa and the COMs were 10 mm anterior to the geometric center of the T12 vertebra. Increasing the IAP from 0 kPa to 10 kPa shifted the location of CORs toward the posterior direction (from 1.4 ± 8.9 mm anterior to intervertebral disc (IVD) centers to 40.5 ± 3.1 mm posterior to the IVD centers) and reduced the average joint force (from 0.78 ± 0.11 Body weight (BW) to 0.31 ± 0.07 BW) and overall muscle force (from 349.3 ± 57.7 N to 221.5 ± 84.2 N). Anterior movement of the COMs from -30 mm to 70 mm relative to the geometric center of T12 vertebra caused an anterior shift of the CORs (from 25.1 ± 8.3 mm posterior to IVD centers to 7.8 ± 6.2 mm anterior to IVD centers) and increases of average joint forces (from 0.78 ± 0.1 BW to 0.93 ± 0.1 BW) and muscle force (from 348.9 ± 47.7 N to 452.9 ± 58.6 N). Therefore, it is important to consider the IAP and correct COMs in order to accurately simulate human spine biomechanics. The method and results of this study could be useful for designing prevention strategies of spinal injuries and recurrences, and for enhancing rehabilitation efficiency.

Fig. 1

Subject specific musculoskeletal models of lumbosacral spine of subject #2 based on her coronal and sagittal X-ray images. Only right side muscles are shown in the sagittal view; (a) 58 pairs of superficial muscles (5 longissimus pars lumborum, 4 iliocostalis pars lumborum, 12 longissimus pars thoracis, 8 iliocostalis pars thoracis, 11 psoas, 5 quadratus lumborum, 6 external oblique, 6 internal oblique, and 1 rectus abdominis) and (b) 32 pairs of deep muscles (12 thoracic multifidus, 20 lumbar multifidus).

Fig. 2

Free body diagram (FBD) for force and moment equilibrium equations of L1-L2 motion segment; (a) coronal and sagittal x-ray images with external forces (segmental body weight and IAP force); (b) FBD for the L1-L2 motion segment and (c) the local coordinate system of the L1-L2 motion segment

Fig. 3

Normalized joint forces of all motion segments from T12-L1 to L5-S1 in standing posture with an IAP of 0 kPa and a COMs of 10 mm anterior to the geometric center of T12 vertebra

Fig. 4

Comparison of the joint force directions and CORs with (a) 0 kPa and (b) 10 kPa of IAP in sagittal and coronal views, and (c) the change of muscle forces with variation of IAPs in subject #1; only the activated muscles were shown

Fig. 5

Change of average (a) CORs and (b) joint forces of the three subjects when the IAP varies from 0 kPa to 10 kPa; When the IAP increased from 0 kPa to 10 kPa, CORs in all motion segments moved toward the posterior direction and joint forces decreased. The largest COR change was at the T12-L1 segment, and the smallest change was at the L5-S1. The positions of CORs were calculated in the local coordinate systems of the IVDs (origin: the geometric center point of each IVD), and the positive value represents the anterior position.

Fig. 6

Comparison of the joint force directions and the CORs with (a) −30 mm and (b) 70 mm of COMs in sagittal and coronal views, and (c) the change of muscle forces with different COMs positions of subject #1; Initially CORs shifted anteriorly with anterior shift of the COMs. When the COMs moved to 10 mm position, the COR of the T12-L1 reached the anterior boundary. Muscle forces and joint forces increased with further anterior shift of the COMs.

Fig. 7

Changes of the average (a) CORs and (b) joint forces of the three subjects when the COMs shifts from −30 mm to 70 mm; The CORs shifted anteriorly with anterior shift of the COMs. In the case when the COMs was 10 mm anterior from the geometric center of the T12, the COR of T12-L1 motion segment reached the anterior edge of the IVD in all three subjects. When the COMs moved further anteriorly, the COR in T12-L1 motion segment was constrained to the anterior disc edge and the CORs of the other segments moved slightly anteriorly while joint forces and muscle forces increased.