...related low-back disorders (Andersson, 1981; Marras al., 1995). Industry has responded to this risk by modifying the workplace in order to decrease lifting and carrying tasks, often replacing them with pushing and pulling exertions. However, there is epidemiologic risk associated with pushing and pulling tasks as well. Of all industrial back injuries in the United States, Canada, and the U.K., 20% have been attributed to push or pull activities (Damkot, Pope, Lord, Frymoyer, 1984; Hoozemans, van der Beek, Frings-Dresen, van Dijk, & van der Woude, 1998). It is expected that this injury rate will increase in response to the trend toward a growing number of push-related tasks in the workplace. Despite the fact that 50% of industrial manual materials handling includes pushing and pulling tasks (Baril-Gingras & Lortie, 1995), the biomechanics of pushing exertions remains poorly understood (Schibye, Sogaard, Martinsen, & Klausen, 2001; van der Beek, Hoozemans, Frings-Dresen, & Burdorf, 1999). Specifically, we are aware of no previously published analyses attempting to quantify spinal stability during pushing exertions.

Biomechanical risk factors for low-back disorders include trunk moment and external force, given their relationship with spinal load and stability (Chaffin & Page, 1994; Granata & Marras, 1996; National Institute for Occupational Safety and Health, 1981). Few studies have quantified trunk moment during pushing exertions (deLooze, van Greuningen, Rebel, Kingma, & Kuijer, 2000; Kumar, 1994). Research conducted in industrial settings has reported that workers lean against the objects to be pushed, resulting in vertical as well as horizontal forces (deLooze et al., 1995; van der Beek, Kluver, Frings-Dresen, & Hoozemans, 2000). The vector direction of the external force tends to pass close to the lumbosacral junction of the spine during these pushing tasks, thereby minimizing trunk moments (deLooze et al., 2000). Because moment is thought to be less during pushing than during lifting, preliminary estimates suggest spinal load is also less during pushing than during lifting (deLooze et al., 1995; Schibye et al., 2001). However, those analyses neglected the influence of trunk muscle cocontraction (Lee, Chaffin, Waikar, & Chung, 1989). Trunk muscle cocontraction is known to dramatically increase spinal load and may contribute to risk of low-back injury during pushing tasks. Estimates of stability suggest high levels of cocontraction must be recruited during pushing exertions. Therefore spinal stability during pushing exertions should be investigated.

To maintain spinal stability, the bending stiffness of the spinal column must increase in proportion to the applied compressive load (Meakin, Hukins, & Aspden, 1996). In the absence of muscular support, the bending stiffness of the osteoligamentous spine is small (Stokes, Gardner-Morse, Churchill, & Laible, 2002), and the spinal column is unstable under combined external and anatomic loads that exceed 88 N (Crisco & Panjabi M.M., 1992; Crisco, Panjabi, Yamamoto, & Oxland, 1992). Fortunately, stiffness of active skeletal muscles increases with force (Kearney & Hunter, 1990; Morgan, 1977) such that recruitment of the paraspinal muscles can augment the bending stiffness of the trunk and spine (Cholewicki, Jurulu, Radebold, Panjabi, & McGill, 1999; Gardner-Morse & Stokes, 2001; Kettler, Hartwig, Schultheis, Claes, & Wilke, 2002). Paraspinal muscle activation increases with lifting effort (Chaffin, 1969; Schultz & Anderson, 1981). Hence, during lifting exertions, the muscle activity recruited to achieve equilibrium also contributes to spinal stability.

Conversely, during pushing exertions very little paraspinal muscle activation is necessary to achieve equilibrium (deLooze et al., 2000; Kumar, 1994). This may suggest that equilibrium conditions of pushing may be less stable than equilibrium conditions of lifting. Additional stability can be achieved through neuromotor recruitment of muscle stiffness by means of cocontraction (Bergmark, 1989; Cholewicki, Panjabi, & Khachatryan, 1997; Gardner-Morse, Stokes, & Laible, 1995; Granata & Wilson, 2001). When equilibrium conditions become increasingly unstable, then greater demand is placed on the neuromuscular controller to recruit antagonistic cocontraction. The purpose of the current study was to quantify external load vectors and trunk moment during pushing to estimate the equilibrium level of stability at a variety of effort levels and handle heights. Results illustrate the need to consider muscle cocontraction when considering pushing exertion.

METHODS

Model

Stability associated with equilibrium levels of exertion were estimated from a two-dimensional biomechanical model (see Appendix). A simple sagittal-plane inverted-pendulum representation of the spine (Figure 1) shows that potential energy with respect to the base of the spine is related to the external force, [F.sub.Ext], the weight of the trunk, Mg, and muscle controlled trunk stiffness, k,

(1) V = Mg [d.sub.cm] cos[[theta].sub.cm] + [F.sub.Ext] {[d.sub.cm] xos([[theta].sub.cm] - [theta]) + [d.sub.F] cos([[theta].sub.F] - [phi])} + 1/2k[([[theta].sub.cm] - [[theta].sub.0]).sup.2],

in which [d.sub.cm] represents length of the vector from L5-S1 junction to the trunk center of mass (CM) and [d.sub.F] is the vector length from CM to the applied force at the push handle. Angles [[theta].sub.cm], [[theta].sub.F], and [phi] are the angles of the vector [d.sub.cm], [d.sub.F], and the angle of the force vector with respect to vertical. The neutral angle [[theta].sub.0] represents the equilibrium of the vector [d.sub.cm] (Cholewicki & McGill, 1996). Trigonometric terms result from the scalar product between the forces, [F.sub.Ext], Mg, and position vectors, [d.sub.F] and [d.sub.cm]. Equilibrium is determined from the negative first derivative with respect to trunk angle, [[theta].sub.cm] (Appendix),

(2) [M.sub.LS] = Mg [d.sub.cm] sin[[theta].sub.cm] + [F.sub.Ext] [d.sub.cm]sin([[theta].sub.cm] - [phi]),

in which [M.sub.LS] represents the internal trunk moment attributed to muscle activation about the lumbosacral junction. Because the system is at an equilibrium posture, [[theta].sub.cm] = [[theta].sub.0], the term associated with trunk stiffness is zero and therefore is not included in Equation 2. Spinal load can be estimated from the vector sum of muscle-generated forces and external forces, [F.sub.Ext]. Muscle-generated forces can be estimated from the equilibrium trunk moment, [M.sub.LS]. This underestimates spinal load because muscle cocontraction and antagonistic recruitment patterns are ignored (Granata & Marras, 1995b; Hughes, Bean, & Chaffin, 1995). Future efforts must include muscle recruitment patterns in calculations of spinal load during pushing (Marras & Granata, 1997). To maintain static stability, the second derivative of potential energy must be greater than zero (Crisco & Panjabi, 1992; Granata & Orishimo, 2001). Hence trunk rotational stiffness must be greater than critical stiffness, [k.sub.Cr], which satisfies the stability equality

(3) k > [k.sub.Cr] = Mg [d.sub.cm] cos[[theta].sub.cm] + [F.sub.Ext] [d.sub.cm] cos([[theta].sub.cm] - [phi]).

[FIGURE 1 OMITTED]

Bergmark represented musculoskeletal stiffness as a linear relationship with muscle force (Bergmark, 1989). It has been demonstrated that joint rotational stiffness is proportional to joint moment (Granata, Wilson, & Padua, 2002; Weiss, Hunter, & Kearney, 1988), with similar trends observed in the trunk (Gardner-Morse & Stokes, 2001; Cholewicki, Simons, & Radebold, 2000). Therefore, for small angle disturbances with respect to the equilibrium posture, [[theta].sub.cm], trunk stiffness can be represented as

(4) k = q [M.sub.LS],

in which q is the stiffness gradient. Some authors have reported the relation in Equation 4 scaled by muscle length (Cholewicki & McGill, 1996; Gardner-Morse et al., 1995), but this does not change the static behavior of our model. By combining Equations 2 through 4, the minimum stiffness gradient necessary for stability can be determined (i.e., a critical gradient [q.sub.Cr]). Small values of [q.sub.Cr] represent improved stability potential. Consequently, stability of equilibrium conditions will be defined as...

NOTE: All illustrations and photos have been removed from this article.



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