Estimation of kidney volume and parenchymal volume

The total kidney volume (including the renal sinus) was estimated from ultrasound images using the following ellipsoid-KV3 formula proposed by Higashihara et al. (2015), which had better performance than the ellipsoid formula:

where LD (longitudinal diameter) is the maximum axis of the kidney in longitudinal plane, ML is the medio-lateral axis and AP the antero-posterior axis, both perpendicular to LD and passing through its midpoint (see Fig. S1).

The volume of the renal sinus was also estimated using the same approach. The parenchimal volume was established as the difference between the total kidney volume and the volume of the renal sinus. The volume of the kidney cortex was then estimated using a constant cortex/parenchyma ratio of 0.7 (Denic et al., 2017a, 2017b, Wang et al., 2014).

To verify the bias of this approach, a pilot study using CT images with contrast medium from 35 patients identified the cortical volume using the Cavalieri principle; the coefficient of correlation between the true parenchymal volume and the estimate using the ellipsoid was 0.8 (p < 0.01). Similarly, the coefficient of correlation between the true parenchymal volume and the estimate using the ellipsoid-KV3 was 0.8 (p < 0.01).

Furthermore, we also estimated the cortical volume using the formula by Nakazato, Ikehira & Imasawa (2017) as previously described.

The Pearson coefficient of correlation between the cortical volume and that estimated using the Nakazato formula was 0.62 (p < 0.01).