Calculating the dose of isotopes needed for DLW studies.
The maximum enrichment above background for 18Oxygen should be about 3000 ppm. The accuracy of measurements may be compromised with values that are much greater than this due to the limits of the isotope analysis technique. Deuterium washes out of the body slower than 18oxygen, so we can use less of this isotope. We normally enrich with deuterium to half the extent of the 18oxygen.
The minimum duration of an experimental measurement is dependant on the time taken for sufficient divergence of the labels to have occurred, and also for sufficient isotope to have been washed out of the body (about 10% of the initial enrichment). This translates into a couple of hours for small animals but at least one day for larger animals. In most cases we use multiples of 24 hours (taken from the time of the initial sample), so the minimum duration for small animals would be 24 hours.
The maximum duration of an experimental measurement is set by the ability of the isotope analysis technique to separate the final isotope enrichment from the background enrichment (a minimum of 20 ppm excess) and the initial enrichment of the animal.
To calculate the actual dosage, multiply the desirable initial enrichment by the body water pool size of the animal and then divide this by the enrichment of the injectate:
dosage required (mls) = [0.65(Body Mass g) x DIE]/IE
where the constant 0.65 is the approximate proportion of the body comprised of water. This is only an approximate figure, and, if specific information is available, it should be substituted at this point. DIE is the desirable initial enrichment (in ppm), and IE is the injectate enrichment (also in ppm).
For every 10 fold increase in body mass the desirable initial enrichment (DIE) halves:
DIE for an animal of 10g = 2500 ppm,
DIE for an animal of 100g = 1250 ppm,
DIE for an animal of 1kg = 625 ppm,
DIE for an animal of 10kg = 300 ppm,
DIE for an animal of 100kg = 150 ppm.
Beyond 100kg the desirable enrichment should remain fixed at about 100 ppm excess.
Example: for a 25g mouse injected with a 20% solution (ie 20% 18oxygen) the DIE would be 2500ppm. The doseage would be [0.65 x 25 x 2500]/200000 = 40625/200000 = 0.2mls
Recapture window: The recapture window for small animals is shorter than that for larger animals as the half life (or turnover) of the isotopes is affected by the body mass of the animal. The half life for a 50g mammal is about 13 hrs, for a 1kg animal it is about 24 hrs, and for a 50kg mammal it is about 5 days. The turnover rate is also affected by the energy demands of the animal, so the half life may be shorter than expected for lactating animals, and longer than expected for sedentary/hibernating animals.
For a 10g animal with an initial enrichment of 2500ppm above background, the level of isotope will reduce to ~30ppm in 6 half lives (2500; 1250; 650; 325; 150; 75; 35), giving a maximum recapture window of around 3 days. For a 50kg animal injected to 150ppm above background, the isotope will be down to ~30ppm in 2 half lives, but as each half life is 5 days, the recapture window is ten days.