Vascular-coupled nephron tree

In order to examine the synchronization phenomena that can arise in larger ensembles of nephrons, we recently developed a model of a vascular-coupled nephron tree [35], focusing on the effect of the hemodynamic coupling. As explained above, the idea is here that, as one nephron reduces its arterioler diameter to lower the incoming blood flow, more blood is distributed to the other nephrons in accordance with the flow resistances in the network. An interesting aspect of this particular coupling is that the nephrons interact both via the blood flow that controls their tendency to oscillate and via the oscillations in this blood flow that control their tendency to synchronize. We refer to such a structure as a resource distribution chain, and we have shown that phenomena similar to those that we describe here... 

Fig. 12.19 Left sketch of a vascular-coupled nephron tree including the interlobular artery, the afferent arterioles and the glomeruli. Right oscillation amplitudes as function of the arterial pressure and the position of the branching point along the vascular tree.

The mathematical model of our vascular-coupled nephron tree thus consists of (i) 12 sets of coupled ODEs describing individual nephrons, (ii) a set of linear algebraic equations that determines the blood pressure drop from one branching point to another, and (iii) algebraic relations for the vascular interaction. 

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