What is the single intravenous bolus dose necessary to produce a plasma drug concentration of 170 nanograms per milliliter one hour after the injection? The answer needs to be in milligrams.
A = 1,251.2 nanograms per milliliter
B = 786 nanograms per milliliter
Alpha = 0.6573 hr-1
Beta = 0.1339 hr-1
The reported central compartment volume of distribution is 7.4 L/kg and the patient weighs 90.1 kilograms.
Volume of distribution (Vd)= 7.4 l/kg and weight of the patient = 90.1 kg
Vd = 7.4 x 90.1 = 666.74 liter
Vd = 666.74 x 103 or 6.6674 x 105 ml
Plasma concentration of drug after 1 hour (Ct) = 170 ng/ml
Ct = 170 x 10-9 gram/ml or 1.70 x 10-4 mg/ml
Remaining dose of drug in body after 1 hour (Dt) = Ct x Vd
Dt = (1.70 x 10-4) x (6.6674 x 105)
Dt = 11.335 x 10 = 113.35 mg
Also Alpha = 0.6573 hr-1, Beta = 0.1339 hr-1
Elimination constant (K) = α + β = 0.6573 + 0.1339
K = 0.7910 hr-1
From the formula
log Dt = ‑ (K x t)/2.3 + log D0
log 113.35 = - (0.791 x 1)/2.3 + log D0
log 113.35 – log D0 = - (1/2.90)
log (113.35/D0) = - (1/2.90)
log (113.35/D0) = - 0.345
D0/113.35 = Antilog 0.345
D0/113.35 = 2.213
D0 = 113.35 x 2.213
D0 = 250.85 mg
What is the single intravenous bolus dose necessary to produce a plasma drug concentration of 170...
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