Intracranial deformation caused by brain tumors: assessment of 3-D surface by magnetic resonance imaging

A shape analysis technique has been developed to quantify intracranial deformation as a means of objectively assessing treatment for brain tumor. Conventional measurements of tumor volume are prone to ambiguity and error, so instead the authors are investigating the secondary space occupying effects of tumor, namely the deformation of structures within the brain. In order to avoid surface segmentation problems in MR images and to facilitate computation, the B-splines method has been introduced to approximate digital 3-D image surfaces. Using the mean curvature and the Gaussian curvature the authors classify a surface into 4 basic types: planar, parabolic, elliptic, and hyperbolic. The deformation of a surface can be described by measuring the geometric changes in these basic types. The method is independent of size, domain (translation), and viewpoint (rotation). These invariance properties are important as they overcome problems caused by wide variations in brain size within the normal population as well as small differences in patient orientation during acquisition. Experimental results show the potential of the technique in objectively monitoring patient response to treatment