Application of spherical harmonics derived space rotation invariant indices to the analysis of multiple sclerosis lesions' geometry by MRI

In the longitudinal study of multiple sclerosis (MS) lesions, varying position of the patient inside the MRI scanner is one of the major sources of assessment errors. We propose to use analytical indices that are invariant to spatial orientation to describe the lesions, rather than focus on patient repositioning or image realignment. Studies were made on simulated lesions systematically rotated, from in vitro MS lesions scanned on different days, and from in vivo MS lesions from a patient that was scanned five times the same day with short intervals of time between scans. Each of the lesions' 3D surfaces was approximated using spherical harmonics, from which indices that are invariant to space rotation were derived. From these indices, an accurate and highly reproducible volume estimate can be derived, which is superior to the common approach of 2D slice stacking. The results indicate that the suggested approach is useful in reducing part of the errors that affect the analysis of changes of MS lesions during follow-up studies. In conclusion, our proposed method circumvents the need for precise patient repositioning and can be advantageous in MRI longitudinal studies of MS patients.