The Cavalieri method has been applied in combination with gradient echo magnetic resonance imaging (MRI) to investigate the increase in the volume of the fetus and fetal brain in the third trimester of pregnancy. Eighteen women with singleton pregnancies were recruited. Birthweights for the fetuses all lay within the 10-90th centile based on Liverpool data. A regression analysis, weighted using values derived from the coefficient of error predicted for each volume estimate, revealed a linear relationship between total fetal volume and gestational age (R2 5 0.88) and between fetal brain volume and gestational age (R2 5 0.71) during the third trimester. Fetal volume increased by an average of 25.2 ml per day and fetal brain volume increased by an average of 2.3 mL per day. Fetal brain volume is on average a constant proportion (10%, SD 5 2%) of total fetal volume throughout the third trimester. Volume data were also obtained for eight fetuses diagnosed as abnormal. The volume of seven of the eight abnormal fetuses fell outside the 95% confidence interval established from the data obtained for the normal fetuses. However, for only three of the eight abnormal fetuses did brain volume fall outside the 95% confidence interval established for normals, possibly due to brain sparing occurring in asymmetrical growth retardation. The volume of the fetus and fetal brain may be readily estimated directly using the Cavalieri method and magnetic resonance imaging. These parameters represent potentially useful information for assessing fetal growth.

We investigated whether a relationship exists between frontal lobe volume and fluid intelligence as measured by both Cattell's Culture Fair test and the Wechsler Adult Intelligence Scale-Revised (WAISR) Performance scale, but not with crystallized intelligence as measured by the WAIS-R Verbal scale, in healthy adults, using two well-established image analysis techniques applied to high-resolution MR brain images. Firstly, using voxel-based morphometry (VBM), we investigated whether a significant relationship exists between gray matter concentration and fluid intelligence on a voxel-by-voxel basis. Secondly, we applied the Cavalieri method of modern design stereology in combination with point counting to investigate possible relationships between macroscopic volumes of relevant brain regions defined as dorsolateral, dorsomedial, orbitolateral, and orbitomedial prefrontal cortex on the basis of neuroanatomical landmarks, and fluid intelligence. We also examined the effect on these relationships of normalizing regional brain volumes to intracranial volume. VBM analysis revealed a positive correlation between gray matter concentration in the medial region of prefrontal cortex and Culture Fair scores (corrected for multiple comparisons), and also WAIS-R Performance Intelligence sum of scaled scores (SSS) (uncorrected for multiple comparisons before controlling for age, and this converges with the stereological finding of the positive correlation between volume of dorsomedial prefrontal cortex normalized to intracranial volume and Culture Fair scores after controlling for age. WAIS-R Verbal Intelligence SSS showed no correlations. We interpret our findings, from independent analyses of both VBM and stereology, as evidence of the importance of prefrontal cortex in supporting fliuid in telligence.

In 1979, the World Health Organization (WHO) established criteria based on tumour volume change for classifying response to therapy as (i) progressive disease (PD), (ii) partial recovery (PR), and (iii) no change (NC). Typically, the tumour volume is reported from diameter measurements, using the calliper method. Alternatively, the Cavalieri method provides unbiased volume estimates of any structure without assumptions about its shape. In this study, we applied the Cavalieri method in combination with point counting to investigate the changes in tumour volume in four patients with high grade glioma, using 3D MRI. In particular, the volume of tumour within the enhancement boundary, the enhancing abnormality (EA), was estimated from T1 weighted images, and the volume of the non-enhancing abnormality, (NEA) enhancing abnormality, was estimated from T2 relaxation time and magnetic transfer ratio tissue characterization maps. We compared changes in tumour volume estimated by the Cavalieri method with those obtained using the calliper method. Absolute tumour volume differed significantly between the two methods. Analysis of relative change in tumour volume, based on the WHO criteria, provided a different classification using the calliper and Cavalieri methods. The benefit of the Cavalieri method over the calliper method in the estimation of tumour volume is justified by the following factors. First, Cavalieri volume estimates are mathematically unbiased. Second, the Cavalieri method is highly efficient under an appropriate sampling density (i.e. EA volume estimates can be obtained with a coefficient of error no higher than 5% in 2-3 min). Third, the source of variation of the volume estimates due to disagreements between observers, and within observer, is much greater in the positioning of the calliper diameters than in the identification of the tumour boundaries when applying the Cavalieri method. Additionally, the error prediction formula, available to estimate the coefficient of error of Cavalieri volume estimates from the data, allows us to establish more precise classification criteria against which to identify potentially clinical significant changes in tumour volume.

We have applied the Cavalieri method of modern design stereology with magnetic resonance imaging for estimating the volume of whole-body muscle and fat compartments in four patients with muscular dystrophy, a patient with myopathy, five controls, an anorexic subject, and a body builder. Detailed systematic series (ie, 50) of axial MR images (T1-weighted, TR/TE 400/10msec) were obtained throughout the whole body of each subject. The results showed that 15, 20, and 35 axial sections through the body are sufficient to secure coefficients of error (CEs) on the estimates of total muscle and fat volume of around 10%, 5%, and 3% respectively in muscular dystrophy patients and controls. The mean normalized volumes of muscle in four muscular dystrophy patients were decreased by 27% (t-test: P<0.05), and those of total fat were increased by 12% (t-test: P>0.05) relative to controls. The Cavalieri method provides a direct, efficient, and mathematically unbiased approach for studying human body compartments and may have application in assessing treatment efficacy in patients with muscular dystrophy. J. Magn. Reson. Imaging 2000; 12: 467-475.

This prospective study investigated the relationship between changes in the MRI dynamic enhancement of cervical carcinoma early during radiotherapy, and tumour regression rate throughout radiotherapy. A total of 36 MRI examinations was performed in seven patients with cervical carcinoma, including a T2 weighted sequence weekly during radiotherapy and also a multislice dynamic Gd-DTPA enhanced sequence before and after the first 2 weeks of radiotherapy. Tumour enhancement was determined on dynamic images using a region of interest and signal-to-noise ratio method. Serial tumour volumes over time on T2 weighted images were estimated using the Cavalieri method of modern design-based stereology to obtain tumour regression rate. It was found that peak and mean enhancement prior to radiotherapy ranged from 3.0 to 13.3, and from 1.9 to 12.2, respectively. After 2 weeks of radiotherapy, peak and mean enhancement ranged from 7.5 to 13.0, and from 6.3 to 10.6, respectively. The change in peak and mean tumour enhancement between dynamic scans ranged, respectively, from 22.0 to 8.4 and from 24.5 to 8.5. Tumour volume decreased exponentially with time (p,0.01). Tumour regression rates ranged from 2.0% to 15.2% per day, and correlated positively with changes of both peak and mean tumour enhancement (p,0.01). It is concluded that MRI dynamic enhancement during the first 2 weeks of radiotherapy may provide early prediction of tumour regression rate, and therefore be of value in designing treatment schedules for cervical carcinoma.