Quantification of Spinal Cord Atrophy From Magnetic Resonance Images Via a B-Spline Active Surface Model O. Coulon, 1,4 * S.J. Hickman, 2 G.J. Parker, 3 G.J. Barker, 2 D.H. Miller, 2 and S.R. Arridge 1 A method is presented that aims at segmenting and measuring the surface of the spinal cord from MR images in order to detect and quantify atrophy. A semiautomatic segmentation with very little intervention from an operator is proposed. It is based on the optimization of a B-spline active surface. The method al- lows for the computation of orthogonal cross-sections at any level along the cord, from which measurements are derived, such as cross-sectional area or curvature. An evaluation of the accuracy and reproducibility of the method is presented. Magn Reson Med 47:1176 –1185, 2002. © 2002 Wiley-Liss, Inc. Key words: active surface; atrophy; spinal cord; multiple scle- rosis Quantitative assessment of disease progression in multiple sclerosis (MS) using MRI is an important issue for thera- peutic monitoring and understanding the development of disability. In particular, the relationship between spinal cord atrophy and development of disability has been the subject of recent interest (5,7,13,16,17) and a correlation between atrophy and disability has been demonstrated. Although imaging techniques have improved signifi- cantly and provide convenient images to study the spinal cord, reliable and reproducible postprocessing and image analysis techniques to measure spinal cord atrophy are still limited. Atrophy is mostly assessed by measuring cross-sectional area at specific levels, typically C2 and C5 (5,17), along the cervical cord. This creates several prob- lems, including the choice of the level at which the mea- surements are performed, the cord orientation, and the cord segmentation process. To provide nonbiased area measurements, the image, or part of the image, needs to be reformatted (17), or acquired (5), with slices perpendicular to the cord. The concept of “perpendicular to the cord” is somewhat imprecise and operator-dependent for a struc- ture which is not a strict cylinder or a surface of revolu- tion. It has not been formally defined in the above-men- tioned publications. Moreover, spinal cord cross-sectional area has often been measured either manually or using intensity-based 2D processing techniques. The limitations of such methods are various: because the orientation of the cord changes along its axis, measurements are restricted to a predefined level at which cord and slices are orthogonal; intensity-based segmentation is hindered by the signifi- cant intensity variations caused by surface coils typically used during acquisition; 2D measurements are more prone to being biased by partial volume effect than 3D measure- ments; manual analysis are more time-consuming and more sensitive to intra- and interoperator variability. We present here a method that aims to solve those prob- lems. The method is based on a 3D extraction of the cer- vical cord surface and the computation of a medial axis, used to define orthogonal cross-sections anywhere along the cord. The segmentation method is semiautomated with very few interventions by the operator, based on the opti- mization of a parameterized active surface. Cross-sectional area measurements can be provided globally as well as locally at any point along the cord. We show that the method provides accurate and reproducible measure- ments. MATERIALS AND METHODS MR Images were acquired on a Signa 1.5T system (GE Medical Systems, Milwaukee, WI), with a phased array spinal coil for data reception. Volume-acquired inversion- prepared fast spoiled gradient echo (IR-FSPGR) acquisi- tion was performed (60  1 mm slices, TI 450 ms, TE 4.2 ms, TR 17.8 ms, flip angle 20°, matrix 256  256, field of view 25  25 cm, 7-min acquisition time). A group of nine control subjects were scanned with scan-rescan (two sessions on the same day). Segmentation In IR-FSPGR images, the cervical cord appears as a bright structure against a dark background (the cerebrospinal fluid space), with cylindrical topology (Fig. 3a). Segmen- tation difficulties can arise due to artifacts (e.g., move- ment-induced, see Ref. 11), noise, and proximity of other structures such as vertebrae (particularly at the C5/C6 level). Because of its cylindrical topology and the ultimate goal of making measurements, we chose to represent the cord surface with a B-spline parametric surface. B-spline functions have been used successfully to represent general (15) or anatomical shapes (1,2,14) and have several advan- tages. They provide a compact representation, because the whole surface is defined by a mesh of control points (Fig. 1a), and the resulting surface is smooth and differentiable (in our case the surface is defined with bicubic splines and therefore C 2 ). Curvatures and other differential character- istics can be computed analytically from the representa- tion. An interesting property of B-spline surfaces is local- 1 Department of Computer Science, University College London, London, UK. 2 NMR Research Unit, Institute of Neurology, University College London, London, UK. 3 Imaging Science and Biomedical Engineering, University of Manchester, Manchester, UK. 4 Laboratoire des Sciences de l’Information et des Syste ` mes, Centre National de la Recherche Scientifique, Marseille, France. Grant sponsors: Wellcome Trust (to O.C. and S.J.H.); AstraZeneca Pharma- ceuticals PLC (to G.J.P.); Multiple Sclerosis Society of Great Britain and Northern Ireland (to G.J.P.). *Correspondence to: Olivier Coulon, Laboratoire des Sciences de l’Information et des Syste ` mes, e ´ quipe LXAO, Ecole Supe ´ rieure d’Inge ´ nieurs de Luminy, Campus de Luminy, case 925, 13288 Marseille cedex 9, France. E-mail: Olivier.Coulon@esil.univ-mrs.fr Received 12 July 2001; revised 13 January 2002; accepted 13 January 2002. DOI 10.1002/mrm.10162 Published online in Wiley InterScience (www.interscience.wiley.com). Magnetic Resonance in Medicine 47:1176 –1185 (2002) © 2002 Wiley-Liss, Inc. 1176