# Validation of Lumbar Compressive Force Simulation in Forward Flexion Condition
## 4 Discussion
First, [PERSON]'s model is originally based on static condition where the contribution of dynamic motion is not taken into account, while [PERSON]'s model corrects the estimated static CF by using a dynamic coefficient k > 1. In the stoop case, which is the worst condition in forward flexion, k approaches 1.15. Second, the model of [PERSON] is based on the mechanical equilibrium at lumbar, while [PERSON] modified the constant term of the mechanical equation for compensating the error of the estimated result with respect to the actual human body condition. Third, in [PERSON]'s model, muscular force could be smaller than zero. This situation happens because the negative value of WB and HB can be obtained in [PERSON]'s model under the condition that LA approaches zero or when the load is horizontally close to the ankle. However, muscular force should always be positive. The muscular force with a negative sign implies that the CF estimated in [PERSON]'s model is smaller than the actual value; however, [PERSON]'s equation does not contain the negative moment arm; thus, the muscular force is positive. _IDPs_ are usually measured at the L4/L5 level rather than the L5/S1 level. However, the difference between the _IDPs_ measured at these positions is small. The in vitro experiment showed that the _IDP_ obtained at L4/L5 was in good agreement with that obtained at L5/S1. As shown in Table 5, the errors measured from the upright posture and flexion motion are as small as 0.02 and 0.03 MPa, respectively [39; 40; 41]. Therefore, the difference in the CF acting on L4/L5 and L5/S1 is considered negligible, and the invasive measurements measured at the L4/L5 level are used for comparison. The difference of 0.02 and 0.03 MPa is small and corresponds to only 3% of the total L5/S1 stress in both upright and flexion postures. Therefore, we used the invasive data at the L4/L5 level. Furthermore, based on a Munst-Whitney test, the [PERSON]'s measurement with six specimens shows no significant difference (\(p>0.05\)) between the stress at L4/L5 and L5/S1 at the significance level of 0.05 regardless of the posture. Thus, it is reasonable to use the \(IDP\) measured at the L4/L5 level instead of that at the L5/S1 level, which is difficult to measure in the invasive experiment. Muscle co-activation also affects the forward flexion. We focused on the extent of the contribution of the co-activation on the CF. [PERSON] performed an EMG-based co-contraction analysis using lumbar muscles' EMG [42]. He measured the preliminary, maximum isometric contractions of those muscles and estimated the muscular force of each muscle with the EMG-based model. Their result suggested a linear relationship between the peak net moment and peak force at L5/S1 during both 2D flexion and 3D flexion movements. This implies that the single back muscle model can also be used for both 2D and 3D models only considering CF [42]. Thus, we consider that the single muscle model is suitable for forward flexion motion. In the single-back muscle model, the representative muscular moment arm is important for muscular force estimation. The erector spinae is considered the major muscle in forward flexion [43]. The muscular moment arm is the distance between the vertebral body center and the erector spinae center in the sagittal plane. To obtain the muscular moment arm, the distance between the erector spinae geometrical center and the neutral line, which passes through the vertebral body center in the transverse plane, is calculated by magnetic resonance imaging (MRI) or computed tomography (CT) [44]. Table 6 shows the muscular moment arm estimated in previous studies. Most estimations are in the 5.3-7 cm range [18; 44; 45; 46; 47]. In this study, the lower limit (5.3 cm) was used to estimate the CF and evaluate extreme lumbar conditions. This value is also in the range of representative moment arm length estimated by [PERSON], which is suggested to be between 5-6 cm [42].