Phenomenological analysis of renal regulation of sodium and potassium balance

Abstract Extracellular fluid volume (ECF) is maintained within normal limits principally by the renal regulation of sodium excretion. Despite a wealth of studies on specific mechanisms, such as the renin-angiotensin-aldosterone system, there is little information as to exactly how ECF varies in response to variations in salt intake. For example, when intake and output of sodium are equal, what is the relationship between ECF and output (or intake)? When salt intake changes in a step fashion, what is the time course of the resulting changes in ECF and sodium excretion? Ludwig [1] was the first to recognize that ECF varied in response to salt intake. Strauss et al [2] suggested that "the amount of sodium excreted in the urine on any one day is a function of total body sodium on that day and particularly of that moiety which is in excess of the body's needs." Although their diagram indicates that this function should be a linear one, they did not offer any evidence for linearity. Hollenberg [3, 4] extended this concept by proposing that sodium balance in a normal subject is regulated about a set point defined as "the amount of sodium chloride in his body when he is in balance on no salt intake." He also proposed that ECF is a linear function of the logarithm of sodium intake (or output) as shown by the following statement: "… one would anticipate that the impact on the system of moving from a 10-mEq to a 30-mEq daily intake would be equivalent to that in moving from 30mEq to 100mEq and even more dramatically, on moving from 100 to 300mEq daily" [3]. Bonventre and Leaf [5, 6] disputed the idea of a fixed set point, suggesting that each sodium intake eventually leads to a new steady-state level of body sodium. However, they evidently accepted the view that the relationship between total body sodium and sodium intake or output at steady-state should be logarithmic, as indicated by their Figure 1. None of these authors has derived mathematical formulations of these relationships or presented data to support their hypotheses, except Strauss et al [2], who showed that sodium excretion decays exponentially in response to a very low salt intake, an observation that has been confirmed repeatedly [7–9]. This latter observation suggests that sodium excretion is a linear function, not a logarithmic function, of body sodium, as Strauss et al [2] apparently recognized. However, the slope of their linear diagram is 1.0, while the exponential decay constant they observed was 0.715 ± 0.028 day -1 . As shown below, both constants should be the same. Renal regulation of potassium excretion, from the phenomenological point of view, has received even less attention, despite many studies of the roles of aldosterone, distal sodium delivery, and other factors. It apparently has not been determined how much (if any) total body potassium varies with potassium intake or how fast adjustments occur. The purpose of this report is to examine what the consequences would be, in these terms, of a linear dependence of sodium and potassium excretion on total body sodium and potassium, respectively, and to compare these predictions with recalculations of reported studies in which normal subjects have been given varying intakes of sodium or potassium.