Optimized prediction of contact force application during side-lying lumbar manipulation

Abstract

Objectives: The purposes of this study included the following: (1) to predict L3 contact force during side-lying lumbar manipulation by combining direct and indirect measurements into a single mathematical framework and (2) to assess the accuracy and confidence of predicting L3 contact force using common least squares (CLS) and weighted least squares (WLS) methods.

Methods: Five participants with no history of lumbar pain underwent 10 high-velocity, low-amplitude lumbar spinal manipulations at L3 in a side-lying position. Data from 5 low-force criterion standard trials where the L3 contact force was directly measured were used to generate participant-specific force prediction algorithms. These algorithms were used to predict L3 contact force in 5 experimental trials performed at therapeutic levels. The accuracy and effectiveness of CLS and WLS methods were compared.

Results: Differences between the CLS-predicted forces and the criterion standard-measured forces were 621.0 ± 193.5 N. Differences between the WLS-predicted forces and the criterion standard-measured forces were -3.6 ± 9.1 N. The 95% limits of agreement ranged from 234.0 to 1008.0 N for the CLS and -21.9 to 14.7 N for the WLS. During both the criterion standard and experimental trials, the CLS overestimated contact forces with larger variance than the WLS.

Conclusion: This novel method to predict spinal contact force combines direct and indirect measurements into a single framework and preserves clinically relevant practitioner-participant contacts. As advanced instrumentation becomes available, this framework will enable advancements in training and high-quality research on mechanisms of spinal manipulative therapy.

Copyright © 2012 National University of Health Sciences. Published by Mosby, Inc. All rights reserved.

Figures

Fig 1

A, Practitioner and participant positions during the side-lying manipulation showing contact at the thigh, left shoulder, and L3 spinal level. B, Enlarged view of the thigh contact. C, Enlarged view of the shoulder contact.

Fig 2

Modified treatment table with embedded force platform in the body section. Note that the head, body, and foot sections are not connected.

Fig 3

Schematic of the data flow taken to predict spinal contact force.

Fig 4

Measured L3 force (◆) and predicted L3 force (○) from 1 participant showing 1 iteration of the k-fold cross-validation procedure. The weighting matrix, W, was optimized to minimize predictive error of L3 force in 4 criterion standard manipulations. L3 force from a fifth criterion standard manipulation was used to validate the optimized W by comparing the predicted force with the measured force. This was repeated 5 times for each participant, and the W with the smallest error was used to predict L3 force in the experimental trials.

Fig 5

Bland-Altman plot of the CLS (▲) force prediction and the WLS (○) force prediction (top panel) and enlarged Bland-Altman plot for the WLS force prediction only (bottom panel). This plot illustrates the average value of the measured force and the predicted force on the horizontal axis and the difference of the predicted force and the measured force on the vertical axis (prediction error). The dashed line shows the average prediction error of the CLS, and the solid line shows the average error of the WLS. Shaded regions represent the 95% limits of agreement for the 2 methods.

Fig 6

Average peak force magnitudes and SD measured at the 3 contact points during the experimental trials. The L3 contact force was compared between the experimental and criterion standard trials. *Significant difference.