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Figure 2. (a) 3D T1 weighted images of patient 1 showing examples of the volume measurement corresponding to (i) the Cavalieri method (left and middle columns) and (ii) the calliper method (right column), where the first and second rows correspond to the third time point, and the third and fourth rows to the fourth time point. (i) A stereological test system for point counting, available in ANALYZETM software, is overlain in four Cavalieri sections with uniform random position to obtain the enhancing abnormality (EA) volume estimation. (ii) Calliper measurements were made using the calliper device in ANALYZETM software. The measurement of the EA included the greatest diameter found on the axial images (red line), the diameter perpendicular to it on the same image (blue line), and the greatest diameter on a coronal image (green line). Details of the calculation of tumour volume and the precision of the Cavalieri method are given in the text. (b) Graph illustrating the mathematical analysis of tumour volume change between two time points according to the Cavalieri and calliper methods (spherical and ellipsoidal models), see worked example. Error bars indicate an approximate confidence interval for the true volume obtained as the Cavalieri volume estimate±twice the predicted standard error (we have assumed that the Cavalieri estimator is normally distributed, however its distribution is still an open problem).
