## 4 Discussion
We reported that extending the minor axis length past the hilar depression and substituting that measurement for renal width and entering it into the ellipse-based formula provides a more accurate estimation of renal parenchymal area. In the present study, we sought to confirm this observation by applying this formula to both left and right kidneys, healthy and diseased, from male and female mice and rats. We evaluated kidneys from healthy male CD-1 mice and CD-1 mice with chronic aristolochic acid nephropathy and healthy 129/Sv mice (male and female) and 129/Sv (male and female) submitted to diabetic nephropathy. In the disease models, animals were placed on 1% NaCl to accelerate kidney disease. Tubulointerstitial matrix accumulation, a hallmark sign of renal scarring, was evident in these disease models. Kidneys were also sourced from healthy male rats, male rats with chemically-induced glomerulosclerosis and male and female obese ZSF\(1\) rats representing a model of metabolic syndrome and renal extracellular matrix accumulation [22]. For each kidney, renal parenchymal area measurements were made in H&E-stained coronal sections. In our hands, use of the existing method consistently underestimated renal dimensions by \(\sim\)15%. Regardless of the source and nature of the kidney, use of our modified formula afforded greater fidelity to the measured renal parenchymal area than use of the existing formula. Given these stringent evaluation conditions, these data suggest that the modified formula is applicable across a range of kidneys and its use is reproducible across operators (KC, KL, MK). Furthermore, we tested the hypothesis that this modified formula for renal parenchymal area can be used as a better estimation of TKV. Indeed, use of the extended minor axis provided an estimate of TKV in excellent agreement with measured kidney volume. Moreover, in this study, kidney volumes spanned an 11-fold range, a range consistent with the TKV of PKD patients in early vs. end-stage disease [19]. Consistent with published reports [11; 12; 13; 15], use of the existing formula in our hands underestimated TKV. Considering that both calculations used the same major axis and renal thickness measurement, it is logical to assume that underestimation of TKV relates to use of the minor axis measurement. Together these data provide a foundation for use of this modified technique to estimate renal dimensions. However, this study exhibits some limitations. For one, it has yet to be concluded if the findings of this study hold true only in rodents; the accuracy of the formula in calculating renal parenchymal area and TKV in kidneys from higher species including humans remains to be determined. The modified formula does not consider the effects of reverse renal remodeling and potential hysteresis in response to interstitial tissue catabolism on renal parenchymal area. It is entirely possible that the modified formula may not find application with irregular renal contours as a result of a disease like nephrosclerosis. That being said, even the existing ellipse-based formula would fail in such an instance. All findings in this study were concluded from microscopic observations of H&E-stained coronal renal sections. These findings may not fully translate to findings retrieved from the targeted modality: ultrasound.