Effects of changes in dietary sodium (Na) intake on extracellular fluid (ECF) volume. The dietary intake of Na was increased from 2 to 5 g, and then returned to 2 g. The relationship between dietary Na intake (dashed line) and ECF volume (solid line) is derived from the model of Walser . In this model the rate of Na excretion is assumed to be proportional to the content of Na in the body (At) above a zero point (A0) at which Na excretion ceases. This relation can be expressed as dAt/dt = I - k(At - A0), where I is the dietary Na intake and t is time. The ECF volume is approximated as the total body Na content divided by the plasma Na concentration. (This assumption is strictly incorrect because approximately 25% of Na is tightly bound in bone; however, this amount is nearly invariant and can be ignored in the current analysis.) According to this construct, when dietary Na intake changes from level 1 to level 2, the ECF volume approaches a new steady state exponentially with a time constant of k according to the following equation:
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