In these analyses, spinal stability increased with increased abdominal pressurization. However, the degree of stability was not substantially influenced by forcing either transversus or obliques to be active, either at 10% or 20% of maximum activation. This casts doubt on the proposed mechanism of action of specific lumbar stabilization exercise regimens that have been proposed for low back pain rehabilitation. In fact, in some cases forced increased activation of abdominal muscles produced decreased lumbar stability. This key finding indicates that intra-abdominal pressure increases stability, but forcing component parts of the abdominal wall (transversus, obliques or rectus) to be preferentially active does not systematically increase stability. No patterns associating forced activations with either an increase or a decrease in stability were identified, and both increases and decreases were observed in approximately equal numbers.
The findings reported here are considered to be ‘robust’, because the sensitivity analyses showed that the calculated spinal stability was altered minimally compared to changes in the muscle stiffness (and model geometry parameters).
Since these findings were obtained from an analytical model, several limitations should be noted. While human activities involve infinite number of permutations of forces and moments, the current study employed three pure moments (about each principal axis) of magnitudes up to 60 Nm to provide a representative and objective sample of realistic activities. The greatest effort about each axis that was analyzed (60 Nm) is equal to average maximum efforts reported for women making maximum voluntary efforts in axial rotation (other effort directions and male subjects can generate higher moments) [Stokes and Gardner-Morse 1995
], so it is considered representative of the range of efforts in every-day life,
The analysis used anthropometric data as compiled by Stokes and Gardner-Morse 
. These values correspond to an averaged adult skeleton, and with muscle cross sectional areas taken from anatomical dissections and from the male and female ‘Visible Humans’. No attempt was made to vary these values to represent people of different body type, and the values used may be quite representative since values the size and position of the muscles of people having differing body mass index varies by only about 10% [Wood et al., 1996
]. The magnitudes of the intra-abdominal pressure expressed as a ratio of the moment (effort) was 0.6 kPa per Nm when the pressure was 10 kPa, which is a physiological ratio according to Stokes et al. 
The diaphragm must also be activated to support any pressure differential between abdomen and thorax. In these analyses the diaphragm and pelvic floor muscles were considered to be rigid (i.e. isometric), so the stress in them and the relative roles of their activation and possible elastic strains associated with tissue stretching were not considered, since under isometric circumstances they would not affect the spinal stability.
The analytically derived muscle activations and recruitment patterns were based on hypothetical muscle stress and strain optimization employing a ‘cost function’ approach. These only represent one of a potentially huge number of individual activation patterns that might be employed by humans,.and coactivation patterns among the entire muscle set may vary considerably from these assumptions. The realism of biomechanical models can be improved in the ‘EMG-assisted’ approach that employs data from EMG studies to provide initial estimates of muscle activations, subsequently adjusted to ensure static equilibrium of net moments and forces at articulations. We did not use EMG data as inputs for the model because the complexity of the model (number of individually activated muscles included) makes EMG ‘drive’ impractical.
The analyses were static in that they did not include dynamic inertial effects or time delays or variation in muscle activation ‘sequencing’. Spinal buckling events may be more likely to occur under dynamic conditions. The possible variations in muscle activation over time in real-life activities were therefore not included. However, the cost-function approach does predict varying activation patterns (relative activation of different muscles) as the effort magnitude increases.
A limitation of these analyses is uncertainty about muscle stiffness properties and these are poorly understood, especially the stiffness of the abdominal wall muscles perpendicular to the lines of action of the muscle fibers and the value of ‘short range’ stiffness that is thought to be appropriate in buckling analyses. However, the findings concerning spinal stability were found to be relatively insensitive to the values of these parameters in the analyses.
The increase in lumbar stability with abdominal muscle activation was expected, based on findings in previous studies [Arjmand and Shirazi-Adl, 2006
; Gardner-Morse and Stokes, 1998
; Kavcic et al., 2004
]. These previous analyses have demonstrated analytically that spinal stability is generally increased with antagonistic activation of abdominal muscles, but have not been able to explore the interactions with IAP that added physiological realism to the present study. The prior models have not employed the representation of the abdominal muscles that permitted investigation of variations in the relative activation of the abdominal muscles while maintaining compatibility with the IAP, made possible here by considering the abdominal wall as a pressure vessel with curved muscles containing the pressure. More importantly, other models have not investigated relative contributions of different muscle groups as they relate to rehabilitation exercises. The stiffness of muscle increases with its degree of activation and in these biomechanical analyses spinal stability depended on this activation-dependent muscle stiffness because the ligamentous spine is known to be unstable [Crisco et al., 1992
There are no experiments in which spinal instability is deliberately produced and documented in living humans with muscle activity. Buckling of axially loaded fingers may be the nearest analogous case of instability in a multi-joint system. Therefore validation of our analyses against empirical data is not possible, and these kinds of analyses ‘belong to a certain category of models in science for which there are no tools for model validation’ [Cholewicki and McGill 1996
Because the abdominal muscles were modeled as curved structures they could contain a pressure within the abdomen and equally any tension in these muscles was necessarily associated with a rise in abdominal pressure. Thus all activities involving abdominal muscle activation required a rise in IAP in the model, and this probably explains why IAP is raised in most physiological efforts. In some modeled cases with forced activation of abdominal muscles there was no plausible analytical solution because the required muscle forces would result in a pressure higher than that specified. These cases are shown as missing values in .
The model employed here has previously been compared with physiological behavior with regard to statics (magnitudes of internal forces in a stable equilibrium condition) [Stokes et al., 2010
]. It was reported that the calculated spinal compression forces were in the range 250 N (with 5 kPa IAP and zero effort) to 1202 N (60 Nm extension effort) while in vivo
spinal compression forces range from 500 N (passive standing) to 2000 N (lifting activity), based on intra-discal pressure measurements. The magnitudes of abdominal muscle activation predicted by the model were also comparable with those reported in electromyographic studies [Arjmand and Shirazi-Adl, 2006
; Thelen et al., 1995
; Cresswell et al., 1992
; de Looze et al., 1999
; McCook et al., 2009
The present study reports relative values of the smallest eigenvalue as a measure of spinal stability. Other analytical studies have used the ‘stability index’ [Howarth et al., 2004
] as a measure of stability which is actually a product of 18 eigenvalues, and the relevance of this derived number to the most likely (i.e.
smallest eigenvalue buckling mode) has been questioned [Gardner-Morse et al., 2006
]. The magnitude of the smallest eigenvalue provides a comparative measure of the stability of the system, and it is non-dimensional (has no physical units). Thus, the larger the eigenvalue the more stable a system is.
This study revisits the fundamental question: why raise IAP when this often requires antagonistic muscle activity? It is thought that IAP unloads and/or stabilizes the spine. Approximately, doubling the muscle activation doubles the pressure according to simplified statics. Thus, IAP and abdominal wall muscle activation are linked. Antagonistic muscle activity generally helps to stabilize a joint, but also increases the joint loading. In the case of the lumbar spine, the associated IAP also generates an extension moment that serves to unload the spine [Stokes et al., 2010
Given that the degree of lumbar stability was not substantially influenced by forcing either transversi or obliques to be active at 10% or 20% of maximum activation in the biomechanical model, doubt is cast upon the proposed mechanism of action of specific abdominal muscle exercise regimens [Richardson et al. 2004
] that have been advocated for low back pain rehabilitation. Since the present work is based on a static analysis of spinal loading, it did not address the possible effects of delays in muscle recruitment that have been reported [Radebold et al., 2000
; Radebold et al., 2001
; van Dieën et al., 2003
] and shown analytically to influence spinal stability by Franklin et al. 
. However, earlier observations of delayed anticipatory postural adjustments of the deep abdominal muscles in people with low back pain have not been consistently substantiated in subsequent studies [Gubler et al., 2010
While the mechanism of action is important to understand, the clinically important question is whether or not a specific stabilization exercise regime is effective at increasing function and decreasing pain levels and recurrences in people with low back pain. Early clinical studies provided promise of the specific stabilization approach [O'Sullivan et al., 1997
; Hides et al., 1996
; Hides et al., 2001
; Stuge et al., 2004a
; Stuge et al., 2004b
] but recent studies have not substantiated these findings. For example, improvements in both activity and patient's impression of recovery were small in both the short and long term following a motor control exercise regime in patients with chronic low back pain [Costa et al., 2009
]. Koumantakis et al. 
added specific stabilization exercises to general exercise for people with nonspecific low back pain and reported a greater reduction in disability immediately post-treatment in the general exercise group only. Recently, a trial comparing specific stabilization exercises (called ‘motor control exercises’ in the study), high-load sling exercises, or general exercises did not show any overall group effects in pain levels, disability, and fear-avoidance beliefs in people with chronic low back pain [Unsgaard-Tøndel, et al., 2010
] and demonstrated no added benefit of specific exercises over general exercises in this population. Thus, there is no clear clinical evidence that specific stabilization exercise regimens that target specific retraining of TA and multifidus muscles are better than other forms of exercises in people with chronic low back pain [Macedo et al., 2009
; Rackwitz et al., 2006
; Standaert et al., 2008
]. Our biomechanical analyses would suggest that preferential activation of the deep abdominal muscles does not provide additional lumbar stability and may provide insight as to why this clinical approach has not proven to provide superior patient outcomes.
Analytical studies provide support for the idea that the human lumbar spine may be at risk for buckling events responsible for sudden onset of certain forms of back pain. It is possible that individual variations in anatomy or muscle recruitment patterns could place certain individuals at higher risk of such events. The present study provides an explanation for the mechanism of the stabilizing effect of abdominal wall muscular activation associated with intra-abdominal pressurization, and additionally demonstrates analytically that forced activation of selected abdominal muscle layers would not necessarily provide additional lumbar stability. However, this remains a theoretic construct that would be difficult to validate scientifically. The predictions of analytical models might be tested for validity indirectly by comparison with epidemiological studies of human populations and clinical studies of the effects of treatments such as exercise regimens and muscle re-education programs.
Based on predictions from a buckling model analysis pressurization of the abdomen increased lumbar spinal stability, but the degree of spinal stability was not substantially influenced by forcing either transversus abdominis or oblique muscles to be active. This supports the use of rehabilitation regimens that encourage abdominal activity pressurization by activation of abdominal wall muscles, but casts doubt on the supposed mechanism of action of specific abdominal muscle exercise regimens that have been proposed for low back pain rehabilitation.