Response to Letter to the Editor by Triano

Abstract

We would like to thank Dr Triano for showing interest in our publication.1Tsung BY Evans J Tong P Lee RYW Measurement of lumbar spine loads and motions during rotational mobilization.J Manipulative Physiol Ther. 2005; 28: 238-244Abstract Full Text Full Text PDF PubMed Scopus (14) Google Scholar His analysis was correct, and our method would be subject to serious error if we did not take into account the changes in the orientation of the L5/S1 segment. However, the reader had missed the description in the main text (p 239, column 2, paragraphs 2-3). We had indeed performed the appropriate coordinate transformation with reference to the instantaneous orientation of the L5/S1 segment. There were no such errors as described by the reader. Data transformation was carried out in two stages. Stage 1 involved transforming the force plate data to loads acting at L5/S1 using the equation provided in Fig 1 (p 239, column 2, paragraph 2). In this stage, the L5/S1 load data were computed according to a coordinate system, which was parallel to that of the force plate, as pointed out by the reader. The reader had missed out stage 2, which was clearly explained in the text (p 239, column 2, paragraph 3): “The 3-dimensional coordinates of the two anterior superior iliac spines and the midpoint of a line joining the two posterior superior iliac spines were recorded. This allows determination of the origin and orientation of the local coordinate system of the spine in relation to the sacral motion sensor. The forces and moments acting at the spine were then transformed from the global coordinate system of the force plate to the local coordinate system of the spine. The transformation was updated for every instant of data collection according to the current position and orientation of the spine as defined by the sacral sensor.” Stage 2 involved transforming the data according to the instantaneous orientation of the L5/S1 segment. In this stage, the F (force) and M (moment) vectors were transformed by the direction cosine matrix, which was derived from the Euler orientations of the segment.2Goldstein H Classical mechanics.2nd ed. Addison-Wesley, Reading (Mass)1980Google Scholar Mathematically, we may describe the two stages by one equation, but this will not explain our rationale. We prefer to describe the transformation in two stages so that it can be easily understood by an average reader who may not have the mathematical knowledge. Unfortunately, the reader missed out the main text description and misinterpreted how the analysis was carried out. We are delighted to see that the reader appreciated the importance of performing the appropriate coordinate transformation, which could have been ignored in many other studies. We had not overlooked this issue and had designed the experiment using sound engineering principles. Measurement of Lumbar Spine Loads and Motions During Rotational MobilizationJournal of Manipulative & Physiological TherapeuticsVol. 28Issue 9PreviewThe authors Tsung et al are to be congratulated for their recent 3-dimensional evaluation of lumbar spine mobilization procedures (JMPT 2005;28:238-44). Quantitative biomechanical estimates are important to their relative risks and means by which performance can be enhanced. Full-Text PDF