Biomechanical Properties of Paraspinal Muscles Influence Spinal Loading-A Musculoskeletal Simulation Study

Abstract

Paraspinal muscles are vital to the functioning of the spine. Changes in muscle physiological cross-sectional area significantly affect spinal loading, but the importance of other muscle biomechanical properties remains unclear. This study explored the changes in spinal loading due to variation in five muscle biomechanical properties: passive stiffness, slack sarcomere length (SSL), in situ sarcomere length, specific tension, and pennation angle. An enhanced version of a musculoskeletal simulation model of the thoracolumbar spine with 210 muscle fascicles was used for this study and its predictions were validated for several tasks and multiple postures. Ranges of physiologically realistic values were selected for all five muscle parameters and their influence on L4-L5 intradiscal pressure (IDP) was investigated in standing and 36° flexion. We observed large changes in IDP due to changes in passive stiffness, SSL, in situ sarcomere length, and specific tension, often with interesting interplays between the parameters. For example, for upright standing, a change in stiffness value from one tenth to 10 times the baseline value increased the IDP only by 91% for the baseline model but by 945% when SSL was 0.4 μm shorter. Shorter SSL values and higher stiffnesses led to the largest increases in IDP. More changes were evident in flexion, as sarcomere lengths were longer in that posture and thus the passive curve is more influential. Our results highlight the importance of the muscle force-length curve and the parameters associated with it and motivate further experimental studies on in vivo measurement of those properties.

Keywords: biomechanics; intradiscal pressure; lumbar spine; muscle; musculoskeletal model; passive stiffness; sarcomere.

FIGURE 1

Fundamental muscle force-length curve was adopted from Millard et al. (2013). Normalized muscle force ${\tilde{F}}^M$ is equal to 1 at optimum sarcomere length which is assumed to be 2.8 μm in humans. Multiplying ${\tilde{F}}^M$ by the specific tension gives the maximum force per unit area a muscle can produce when fully activated which depends on the sarcomere length [graph (A)]. The nonnormalized force-length curves may not be the same for all muscles or individuals, and the generated forces could vary with regard to certain parameters including [graph (B)] posture-specific in situ sarcomere length (SL) and the specific tension (SpT) or [graph (C)] slack sarcomere length (SSL) and stiffness scaling factor (K). Note that five different values were considered and tested for each parameter in this study but only two or three representative values for each parameter are shown in this figure. The gray color refers to the values used for the baseline model.

FIGURE 2

Tracking target frames instead of target points in the new solution method. In the previous model (Malakoutian et al., 2016b), the full trajectory of two symmetric target points located at the right and left of the thorax was assigned as input and tracked by the model (A); while in the new solution method, only rotation of the thorax was given as input (B and C) and followed by the model (D).

FIGURE 3

Comparison between the predicted L4-L5 IDP by the model and those measured in vivo for five different activities (Wilke et al., 2001).

FIGURE 4

Intervertebral rotations for two activities of 10° extension and 40° flexion were predicted by the model (blue) and observed in 50 male subjects (orange, Wong et al., 2004). The error bars represent the mean ± one standard deviation.

FIGURE 5

The effect of different slack sarcomere length (SSL) values on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles, and psoas (EXT + PS), and all 210 muscles in the model (ALL). Grey/black bars represent the baseline values.

FIGURE 6

The effect of different passive force-length curve scaling constants (K in $\frac{N}{c{m}^2}$ ) on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles, and psoas (EXT + PS), and all 210 muscles in the model (ALL). Grey/black bars represent the baseline values.

FIGURE 7

The effect of different passive force-length curve scaling constants (K in $\frac{N}{c{m}^2}$ ) combined with a slack sarcomere length (SSL) of 2.4 μm to the targeted muscles on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles and psoas (EXT + PS), and all 210 muscles in the model (ALL). The black horizontal lines represent the baseline values.

FIGURE 8

The effect of different supine/prone in situ sarcomere length on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles, and psoas (EXT + PS), and all 210 muscles in the model (ALL). The black horizontal lines represent the baseline values.

FIGURE 9

The effect of different supine/prone in situ sarcomere lengths combined with a slack sarcomere length (SSL) of 2.4 μm to the targeted muscles on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles and psoas (EXT + PS), and all 210 muscles in the model (ALL). The black horizontal lines represent the baseline values.

FIGURE 10

The effect of different specific tension (SpT) values on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles and psoas (EXT + PS), and all 210 muscles in the model (ALL). Grey bars represent the baseline values.

FIGURE 11

The effect of different pennation angles on L4-L5 IDP in upright standing and 36° flexion for four scenarios: changes applied to multifidus (MUL), extensor muscles (EXT), extensor muscles, and psoas (EXT + PS), and all 210 muscles in the model (ALL). The black horizontal lines represent the baseline values.