Unbiased and efficient estimation of bladder volume with MR imaging

Almost all methods of measuring residual volume of urine in the bladder of patients undergoing urologic assessment are biased to an unknown extent. The authors describe the application of an unbiased stereologic technique for estimating the volume of bladder urine known as the Cavalieri method. The method requires imaging of a series of systematic (ie, equally spaced) parallel sections through the bladder. Such data can be conveniently obtained with magnetic resonance (MR) imaging. If sampling begins at a position randomly chosen within the distance corresponding to the section interval. bladder volume is estimated without bias as the sum of the areas of the bladder sections on the images multiplied by the section interval. Computer‐aided point‐counting techniques represent an efficient means of obtaining the required section area estimates. Optimum sectioning and point counting densities for estimating bladder volume were established by analyzing detailed data sets obtained in five volunteers. It was shown that if an average of only 20 points were counted in each of only five systematic sections through the bladder, the volume of bladder urine was estimated with a coefficient of error of about 5%. By studying these five volunteers and an additional 13 with MR imaging and the Cavalieri method, the authors showed that the difference between the volume of urine in the bladder before and after micturition is unbiased (ie, shows no systematic difference) with respect to the volume of urine voided by the subjects.