An iterative procedure to estimate muscle lines of action in vivo

A method is described to estimate the line of action of muscles in the three-dimensional space from serial images of parallel muscle sections obtained in vivo by means of CT or MRI scanning. The external shape of a muscle, reconstructed from the series of parallel sections, is mathematically divided into a series of imaginary slices directed arbitrarily in the three-dimensional space. The line of action is estimated initially as a regression line through the centroids of these mathematical slices. A new series of mathematical slices is constructed perpendicular to the regression line and a new estimate of the line of action is obtained from their centroids. This procedure is repeated until the estimated line of action is perpendicular to the mathematical slices; it can then be considered as a reliable estimate of the line of action. The accuracy of the method has been tested for various reconstruction parameters and muscle shapes. The results of these tests show that the accuracy is relatively independent of the direction in which the sectional images have been made and that, except for relatively short and thick muscles, the estimated lines of action deviated less than about 2 degrees from the theoretical one. The presented method is a relatively simple mathematical technique which can be used easily for muscles reconstructed in vivo from routinely obtained sectional MRI or CT images.