. 2015 Aug 17;10(8):e0134477. doi: 10.1371/journal.pone.0134477

Table 4. Number of tubes at each depth x.

	OM OS	OM IS	IM
LDL and LAL	$2 N_{0}^{C D}$	$2 N_{0}^{C D}$	$N_{0}^{L D L} e^{- 1.213 (x - x_{O M / I M})}$
SDL and SAL	$4 N_{0}^{C D}$	$4 N_{0}^{C D}$	-
DVR	0.6 $(N_{0}^{L D L} + N_{0}^{S D L})$	0.6 $(N_{0}^{L D L} + N_{0}^{S D L}) -$ 0.6 $N_{0}^{S D L} \frac{(x - x_{O S / I S})}{(x_{O M / I M} - x_{O S / I S})}$	0.6N ^LDL(x)
CD	$N_{0}^{C D}$	$N_{0}^{C D}$	$N_{0}^{C D} e^{- 1.04 (x - x_{O M / I M})}$

The numbers of tubes at each depth x are defined relative to the number of collecting ducts, $N_{0}^{C D} = 4000$ (total number of tubes: 24000 nephrons and 48000 vasa recta) [58]. In the outer medulla, the ratio of nephrons to collecting ducts is assumed to be 6:1. The ratio of short to long nephrons is assumed to be 2:1. The total number of nephrons and collecting ducts are assumed to decrease exponentially in the inner medulla (decay λ ^loop = -1.213 and λ ^CD = -1.04). The ratio of the number of descending vasa recta to nephrons is taken to be 0.6:1 at x = 0 [59]. The position of the OS-IS junction is taken as 0.7 mm, the OM/IM junction as 2 mm, the upper/lower inner medulla junction at 3.3 mm, and the total length of the medulla as 6mm [58, 60].