Over 50 years ago, Homer Smith (1952) introduced the concept that the urine flow could be thought of as two separate compartments: one component containing osmotically active particles (osmoles) at the same concentration as that present in the plasma, and the other component consisting of either free water excreted (when the kidney is forming dilute urine) or free water reabsorbed (when the kidney is forming concentrated urine).

Thus, V = Cosm + CH₂O

where V is urine flow, Cosm is osmolal clearance, and CH₂O is free water clearance.

The volume of plasma that is cleared of osmoles per unit time (Cosm) × plasma osmolality (Posm) is equal to the urinary excretion of osmoles [urine osmolality (Uosm) × urine flow]. In mathematical form, it is as follows:

Cosm × Posm = Uosm × V

Cosm = Uosm × V/Posm

Therefore,

CH₂O = V – Cosm = V – (Uosm × V/Posm) = V(1 – Uosm/Posm)

It can be readily seen that if urine is dilute, that is, Uosm < Posm, free water clearance will be positive, and if urine is concentrated, that is, Uosm > Posm, free water clearance will be negative (this means free water is being reabsorbed by the kidney). Observing the Uosm gives important qualitative information, but calculating free water clearance gives quantitative information.

Although free water clearance is a valid physiologic concept for the management of disorders of serum sodium concentration, it has been supplanted by the electrolyte-free water clearance (Goldberg, 1981).

Electrolyte-free water clearance (CeH₂O) means the clearance of water free of electrolytes (sodium, potassium, and accompanying anions) but not other solutes. Urine contains many other osmotically active particles, such as urea and ammonium, in addition to electrolytes. Excretion of these substances is not in general relevant in predicting the response to fluid management in dysnatremic states.

To derive the formula for CeH₂O, one substitutes electrolyte clearance (approximated by the clearance of the sum of sodium, potassium, and accompanying anions) for Cosm. Thus, the Cosm term is replaced by C(Na + K) × 2. Analogous to Cosm,

C(Na + K) × 2 = [U(Na + K) × 2] × V/P(Na + K) × 2 = U(Na + K) × V/P(Na + K)

Therefore,

CeH₂O = V – [U(Na + K) × V/P(Na + K)] = V{1 – [U(Na + K)/PNa]}

Note the K is dropped from the plasma term as it is numerically negligible.

Measurement of CeH₂O is very helpful in predicting the response to fluid therapy in dysnatremic states. This is particularly true in cases of hypernatremia (Leehey et al., 1989). This is best illustrated by some examples.

Take two patients with hypernatremia. They both have a plasma sodium concentration (PNa) of 160 mmol/L, a Posm of 350 mmol/kg, and a Uosm of 500 mmol/kg. Urine sodium concentration (UNa) and urine potassium concentration (UK) will vary depending on the situation. In Patient 1, the kidney is avidly reabsorbing sodium and water (UNa 10, UK 30; 24-hour urine volume 500 mL). This would be typical of a dehydrated hypotensive patient from a nursing home. In Patient 2, the kidney is excreting sodium and potassium and is polyuric (UNa 50, UK 30; 24-hour urine volume 4 L). This would be typical of an ICU patient who is recovering from shock who was previously resuscitated with many liters of saline and is now undergoing a solute diuresis (Bodonyi-Kovacs and Lecker, 2008; Sam et al., 2012).