A goal programming model for assessing sagittal spinal curvature under backpack carriage

Hung Kay Daniel CHOW, Siu Wai Simon LI

Research output: Contribution to conferencePapers


Introduction and Objectives: Previous research established that load carriage would induce immediate changes in spinal curvature which was associated with spine disorders. Neutral upright standing has been proposed as the healthy posture for minimizing spine loading. It was hypothesized that the maximum load should be one that induced minimum changes to the spine curvature in neutral upright stance. In this study, a multi-objective optimization goal programming (GP) model was developed and applied to determine the optimal limit of backpack load for upright standing. Methods: This was a single factor randomized repeated measure design. Spinal curvatures [in terms of the angles of cervical lordosis (CVL), upper thoracic kyphosis (UTK), lower thoracic kyphosis (LTK) and lumbar lordosis (LBL)] were measured non-invasively using five sensors affixed to the middle of the back of head, C7, T7, T12 and pelvis. All subjects were instructed to maintain a standardized and relaxed barefoot erect stance without load and with a backpack loaded at 5, 10, 15 and 20% of their body weights. The four curvature angles among the five sensors were measured by a motion analysis system. The sequence of experimental trials was randomized. Three trials for each unloaded and loaded conditions were recorded. Regression equations predicting the four loaded curvatures were obtained. The deviations of loaded from unloaded curvatures and the target levels of the predicted mean loaded curvatures were formulated as the cost and constraint functions of the GP model respectively. The sequence of optimization process of the GP was prioritized with respect to the magnitude of the mean loaded curvature deviations. The optimal mean loading condition was determined by solving the sequential optimization problems. Results: Ten young male adults (age between 20 and 29) were evaluated. The baselines of mean curvatures of CVL, UTK, LTK and LBL were 32.1°, 32.9°, 10.3°, and 17.2° respectively. The respective mean deviations under loaded conditions were -0.6°, -5.0°, 1.6°, and -2.1°. The r² of the 2nd order regressions were 0.97, 0.99, 0.91, and 0.91 respectively. The sequence of optimization process was UTKàLBLàLTKàCVL. On average, significant flattening of the CVL, UTK and LBL as well as significant increased curvature in LTK were observed (p<0.05). The mean allowable load limit was found to be 7.4% of body weight. The predicted mean curvatures of CVL, UTK, LTK and LBL were 29.6°, 26.8°, 13.1°, and 14.8° respectively. Conclusion: A symmetric backpack load at 7.4% of body weight was recommended, in order to achieve an optimal standing posture with minimal spinal curvature deviations from the unloaded condition.
Original languageEnglish
Publication statusPublished - Jul 2015


Chow, D. H., & Li, S. (2015, July). A goal programming model for assessing sagittal spinal curvature under backpack carriage. Paper presented at The XXV Congress of the International Society of Biomechanics (ISB 2015), Scottish Exhibition and Conference Centre, Glasgow, UK.


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