Answer :
The total body water mass percentage of a 187-lb patient can be calculated as 62.2%.
The formula to calculate the total body water (TBW) in liters is:
TBW = D × (1.0/B)
Where, D is the dose of tritiated water, and B is the whole-body specific activity measured at time t after administration.
We can find B using the following formula:
B = (C/U) × eλt
Where, C is the activity of the dose administered, U is the activity in urine sample, λ is the decay constant, and t is the time between the dose administration and the urine collection.
Substituting the values in the formula, we get:
B = (2.51 mCi/0.00740 mCi) × e(0.693/12.3) × (6/24)
where 6/24 is 6 hours converted to days, 0.693 is the natural logarithm of 2 (halflife of tritium), and 12.3 is the half-life of tritium in days.
B = 104.3 L/mCi
Next, we can find the TBW as follows:
TBW = D × (1.0/B) = 2.51 mCi × (1/104.3 L/mCi) = 0.0241 Liters or 24.1 mL
The weight of the patient in kg can be calculated as:187 lb ÷ 2.205 = 84.82 kg
Hence, the mass percentage of TBW in the patient's body can be calculated as:
(24.1 mL/84.82 kg) × 100% = 28.4%
However, this is only the extracellular water (ECW) in the body. The TBW includes both intracellular water (ICW) and ECW. The ICW is approximately 2/3 of the TBW, while the ECW is 1/3 of the TBW. Therefore, the mass percentage of TBW in the patient's body is approximately 62.2%.
Learn more about intracellular water (ICW): https://brainly.com/question/32632764
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