A stereological study of MRI and the Cavalieri principle combined for diagnosis and monitoring of brain tumor volume.

In this study, we aimed to describe the application of the Cavalieri principle for the assessment of tumor volume using MRI without an over-projection/estimation effect. For this purpose, the volume of a patient's brain and the brain tumor volume, or the volume of the former tumor region, were estimated preoperatively and postoperatively using a combination of the Cavalieri principle and MRI. The previously described formula was modified for MRI measurements to eliminate the over-estimation effects of imaging. The total brain and tumor volumes estimated using the MRI of a representative patient with glioblastoma multiforme were: preoperative, 1562.46 cm³ and 81.59 cm³, respectively; and postoperative, 1571.72 cm³ and 86.92 cm³, respectively. The mean time to count points for an estimation of brain and tumor volume (or the volume of the former tumor region) were 14 minutes and 3 minutes, respectively. The coefficients of the errors of the estimates for brain and tumor volume (former tumor volume, postoperative) measurements were: preoperative 0.01 and 0.02; and postoperative 0.01 and 0.03, respectively. Our results show that the combination of MRI and the Cavalieri principle can provide an unbiased, direct and assumption-free estimate of the regions of interest. Therefore, the presented method could be applied efficiently without any need for special software, additional equipment or personnel other than that required for routine MRI in daily use.