**5.5 Implementing lumbar muscles**

Multifidus muscle: The multifidus muscle is divided into 19 fascicles on each side according to descriptions by the group of Bogduk (Bogduk et al., 1992a; Macintosh & Bogduk, 1986). The multifidus can be modeled as three layers with the deepest layer having the shortest fibres and spanning one vertebra. The second layer spans over two vertebrae, while the third layer goes all the way from L1 and L2 to posterior superior iliac spine (Zee et al., 2007). The rather short span of the multifidus fascicles makes it possible to model them as line elements without via-points (Figure 14(a)).

Erector spinae muscle: According to (Macintosh & Bogduk, 1987; 1991), there are four divisions of the erector spinae: longissimus thoracis pars lumborum, iliocostalis lumborum pars lumborum, longissimus thoracis pars thoracis and iliocostalis lumborum pars thoracis. The fascicles of the longissimus thoracis and iliocostalis lumborum pars lumborum originate from the transverse processes of the lumbar vertebrae and insert on the iliac crest close to the posterior superior iliac spine (Zee et al., 2007). The fascicles of the longissimus thoracis pars thoracis originate from the costae 1-12 close to the vertebrae and insert on the spinous process of L1 down to S4 and on the sacrum. The fascicles of the iliocostalis lumborum pars thoracis originate from the costae 5–12 and insert on the iliac crest. Since muscles of the two pars thoracis are automatically generated by LifeMOD, only muscles of the two pars lumborum need to be added to the model as shown in Figure 14(b).

Development of a Detailed Human Spine Model with Haptic Interface 179

Abdominal muscles: Two abdominal muscles are included in the model: obliquus externus and obliquus internus. Modelling of these muscles requires the definition of an artificial segment with a zero mass and inertia (Zee et al., 2007). This artificial segment mimics the function of the rectus sheath on which the abdominal muscles can attach (Figure 15(a)). The obliquus externus and internus are divided into 6 fascicles each (Stokes & Gardner-Morse, 1999). Two of the modeled fascicles of the obliquus externus run from the costae to the iliac crest on the pelvis, while the other four originate on the costae and insert into the artificial rectus sheath as can be seen in Figure 15(a). Three of the modelled fascicles of the obliquus internus run from the costae to the iliac crest, while the other three originate from the iliac

Fig. 15. (a) external oblique muscle (b) internal oblique muscle (c) detailed spine model in

Since LifeMOD and ADAMS provide tools that only generate concentrated or distributed forces, it is not possible to implement directly intra-abdominal pressure into the spine model. To overcome this difficulty, a new approach to intra-abdominal pressure modeling is proposed. Initially, an equivalent spring structure able to mimic all mechanical properties of intra-abdominal pressure such as tension/compression, anterior/posterior shear, lateral

skeleton mode (d) detailed spine model in ellipsoid mode

**5.6 Adding intra-abdominal pressure** 

crest and insert into the artificial rectus sheath (Figure 15(b)).

Psoas major muscle: The psoas major muscle is divided into 11 fascicles according to different literature sources (Andersson et al., 1995; Bogduk et al., 1992b; Penning, 2000). The fascicles originate in a systematic way from the lumbar vertebral bodies and T12 and insert into the lesser trochanter minor of the femur with a via-point on the pelvis (iliopubic eminence) (Figure 14(c)). Bogduk found that the psoas major had no substantial role as a flexor or extensor of the lumbar spine, but rather that the psoas major exerted large compression and shear loading on the lumbar joints (Bogduk et al., 1992b). This implies that the moment arm for the flexion/extension direction is small and hence the via-points for the path were chosen in such a way that the muscle path ran close to the centre of rotation in the sagittal plane.

Fig. 14. (a) multifidus muscle (b) erector spinae pars lumborum muscle (c) psoas major muscle (d) quadratus lumborum muscle

Quadratus lumborum muscle: For modelling the quadratus lumborum, the description given by Stokes and Gardner-Morse was followed (Stokes & Gardner-Morse, 1999). They proposed to represent this muscle by five fascicles. The muscle originates from costa 12 and the anterior side of the spinous processes of the lumbar vertebrae and has in the model a common insertion on the iliac crest (Figure 14(d)).

Psoas major muscle: The psoas major muscle is divided into 11 fascicles according to different literature sources (Andersson et al., 1995; Bogduk et al., 1992b; Penning, 2000). The fascicles originate in a systematic way from the lumbar vertebral bodies and T12 and insert into the lesser trochanter minor of the femur with a via-point on the pelvis (iliopubic eminence) (Figure 14(c)). Bogduk found that the psoas major had no substantial role as a flexor or extensor of the lumbar spine, but rather that the psoas major exerted large compression and shear loading on the lumbar joints (Bogduk et al., 1992b). This implies that the moment arm for the flexion/extension direction is small and hence the via-points for the path were chosen in such a way that the muscle path ran close to the centre of rotation in the

Fig. 14. (a) multifidus muscle (b) erector spinae pars lumborum muscle (c) psoas major

Quadratus lumborum muscle: For modelling the quadratus lumborum, the description given by Stokes and Gardner-Morse was followed (Stokes & Gardner-Morse, 1999). They proposed to represent this muscle by five fascicles. The muscle originates from costa 12 and the anterior side of the spinous processes of the lumbar vertebrae and has in the model a

muscle (d) quadratus lumborum muscle

common insertion on the iliac crest (Figure 14(d)).

sagittal plane.

Abdominal muscles: Two abdominal muscles are included in the model: obliquus externus and obliquus internus. Modelling of these muscles requires the definition of an artificial segment with a zero mass and inertia (Zee et al., 2007). This artificial segment mimics the function of the rectus sheath on which the abdominal muscles can attach (Figure 15(a)). The obliquus externus and internus are divided into 6 fascicles each (Stokes & Gardner-Morse, 1999). Two of the modeled fascicles of the obliquus externus run from the costae to the iliac crest on the pelvis, while the other four originate on the costae and insert into the artificial rectus sheath as can be seen in Figure 15(a). Three of the modelled fascicles of the obliquus internus run from the costae to the iliac crest, while the other three originate from the iliac crest and insert into the artificial rectus sheath (Figure 15(b)).

Fig. 15. (a) external oblique muscle (b) internal oblique muscle (c) detailed spine model in skeleton mode (d) detailed spine model in ellipsoid mode
