The application of total vertical projections for the unbiased estimation of the length of blood vessels and other structures by magnetic resonance imaging

Abstract

A new stereological method has recently been developed to estimate the total length of a bounded curve in 3D from a sample of projections about a vertical axis. Unlike other methods based on serial section reconstructions, the new method is unbiased (i.e., it has zero systematic error). A basic requirement, not difficult to fulfill in many cases, is that the masking of one structure by another is not appreciable. The application of the new method to real curvilinear structures using a clinical magnetic resonance (MR) imager is illustrated. The first structure measured was a twisted water-filled glass tube of known length. The accuracy of the method was assessed: With six vertical projections, the tube length was measured to within 2% of the true value. The second example was a living bonsai tree, and the third was a clinical application of MR angiography. The possibility of applying the method to other scientific disciplines, for example, the monitoring of plant root growth, is discussed.