Question

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.

Answer 1

Volume of distribution (V_d)= 7.4 l/kg and weight of the patient = 90.1 kg

V_d = 7.4 x 90.1 = 666.74 liter

V_d = 666.74 x 10³ or 6.6674 x 10⁵ ml

Plasma concentration of drug after 1 hour (C_t) = 170 ng/ml

C_t = 170 x 10^-9 gram/ml or 1.70 x 10^-4 mg/ml

Remaining dose of drug in body after 1 hour (D_t) = C_t x V_d

D_t = (1.70 x 10^-4) x (6.6674 x 10⁵)

D_t = 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 D_t = ‑ (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