## N

Kt where C0 — Cb is the increment in isotopic concentration resulting from the administration of the dose, and N can be calculated as N = D/(C0 — Cb).

The foregoing equations have been written in terms of isotopic concentration (e.g., C = 2H/(2H + 1H)), but mass spectrometry measurements are in terms of ratio (e.g., R = 2H/1H) and in practice, for DLW calculations R or enrichment relative to a standard is invariably substituted for C with no effect on results at the low levels of enrichment applied in this methodology.

Principles of the Method

When Lifson first began his physiological experiments with newly available 18O in the mid-1950s, it was already well-known that oral dosing with

Figure 1 A simple one-compartment model of water turnover.

2H2O and its dilution in body water was a way of measuring body water mass and turnover. Lifson showed that the oxygen in carbon dioxide, the waste product of energy metabolism, was in equilibrium in the body with body water:

H2O + CO2 H2CO3

He realized, therefore, that the greater apparent turnover of body water measured with H218O in comparison to turnover measured with 2 H 2O (Figure 2) was a consequence of carbon dioxide production, as shown in Figure 3. Thus, there was potential for a method that would permit the measurement of total CO2 output and hence energy expenditure over long periods merely by isotopic analysis of samples of body fluids. Initially, the method was applied only to small animals because

6 8 Days

Figure 2 Exponential loss of 2H and 18O from body water. The insert shows the data on a log scale.

6 8 Days

Figure 2 Exponential loss of 2H and 18O from body water. The insert shows the data on a log scale.

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