Exam 2 Math Problems

If the plasma concentration of a drug just after an IV bolus dosing is 10 mg/L and the patient’s elimination rate constant is 0.1 1/h, predict what the plasma concentration (mg/L) will be 11 hours later.

3.33 mg/L

If the plasma concentration of a drug just after an IV bolus dosing is 10 mg/L and the patient’s elimination rate constant is 0.05 1/h, predict what the plasma concentration (mg/L) will be 11 hours later.

5.77 mg/L

When 20 IV bolus doses of a drug are given to a patient, where k = 0.048 1/h and (T) = 8 hours:

• a) calculate the accumulation factor

• b) if the peak plasma concentration after the first dose is 15 mg/L, predict the peak plasma concentration after the 20th dose?

• a) AF = 3.1

• b) C_max20 = 46.5 mg/L

A 200mg IV bolus dose of drug X is given to two different patients every 8 hours. Which patient (A or B) is likely to achieve higher maximum steady state plasma concentration?

Patient B

• Patient A = 8.34 mg/L

• Patient B = 14.50 mg/L

An ICU patient is dosed with a 150mg bolus of an analgesic drug with an apparent volume of distribution of 85L and an elimination rate constant of 0.043 1/h. For a three times daily regimen, what will be the minimum plasma concentration after the third dose?

C_min3 = 2.76 mg/L

If a drug with a half-life of 6 hours is given IV bolus every 8 hours and achieves a peak plasma concentration of 20 mg/L at steady state, what will be the peak plasma concentration after the third dose is administered?

C_max3 = 18.88 mg/L

After administration of a single 400mg oral dose of a drug, the plasma concentration time profile can be expressed as:

Cp = 400 (e^-0.05t -  e^-0.7t )

• Calculate the t_max and C_max

t_max = 4h

C_max = 304 mg/L

A patient receives an antimicrobial dose of 300mg IV every 6 hours. After steady state is reached, a peak level of 25mg/L is determined; the level of drug 5h after the steady state peak is 21.63 mg/L. What dose is required to attain an average steady state plasma level of 15 mg/L (Vd = 75L)?

195mg

For a drug with CL = 15 mL/min and Vd = 0.6 L/kg in a patient weighing 60kg, how much time will it take to reach 80% steady state?

64.4 h

A 60kg, 30-year-old man is receiving phenytoin for the treatment of seizures. When this patient was taking a daily dose of 300mg phenytoin, his steady state plasma concentration was 8 mg/L. Because phenytoin plasma concentration was well below therapeutic range, the patient’s daily dose was increased to 500mg phenytoin, which resulted in a steady-state plasma concentration of 30 mg/L. 

• a) Calculate the patient’s K_m (mg/L)

• b) Calculate the patient’s V_max (mg/day)

• c) Calculate the steady state concentration (mg/L) if the dose is 400mg daily

• d) Calculate the daily phenytoin dose (mg/day) if we need to achieve a steady state phenytoin plasma concentration of 20 mg/L in this patient

• a) K_m = 9.6 mg/L

• b) V_max = 660 mg/day

• c) C_ss = 14.77 mg/L

• d) Daily dose = 446 mg/day

After an IV bolus administration, how many half-lives are needed to reduce the concentration of a drug to 10% of the initial concentration?

3.3

Calculate the initial concentration of ampicillin (in mg/L) if the concentration of ampicillin remaining in the body after 6 hrs was 20.8mg, and the half-life of ampicillin is 1.3 hr. (round to the nearest whole number)

C₀ = 510 mg/L

The elimination half-life of a drug is 6 hours. If an IV bolus administration of a dose produces an initial concentration of 150 mcg/mL, how long will it take for the drug to be eliminated by 75% of its initial concentration?

12 hours

A 70kg patient is given an IV bolus dose of an antibiotic, and serum drug concentrations were determined at 2 hours and 5 hours after administration. The drug concentrations were 1.2 and 0.3 mcg/mL, respectively. What is the elimination half-life (hr) for this drug?

1.5 hr

For a drug with CL = 40 mL/min and Vd = 0.8 L/kg in a patient weighing 75kg, how much time (hr) will it take to reach 55% steady state after a continuous IV infusion?

20 hr

If C_max1, k, and tau are 50 mg/L, 0.4 1/h, and 6 hrs, respectively:

• a) what is the value of C_max2?

• b) what is the value of C_min2?

• a) C_max2 = 54.54 mg/L

• b) C_min2 = 4.95 mg/L

In a multiple IV dosing regimen, what is the minimum concentration after 10 doses if the dose is 200mg and the volume of distribution is 20L? Assume that tau = 6hrs and k = 0.5 1/h.

a. 1.05

b. 19.95

c. 0.53

d. 21.05

c. 0.53

A patient is receiving 400mg of an antibiotic as repeated IV bolus doses every 12 hours to treat her lung infection. The max and min steady state plasma concentrations of this antibiotic are 48 mg/L and 5 mg/L, respectively. Calculate the volume of distribution and the total body clearance of this antibiotic if the half-life of the drug is 6 hrs.

Vd = 11.08 L

CL = 1.3 L/h

A single dose of 500mg of an antibiotic was given as an oral tablet to a 70kg patient. The plasma concentration-time profile can be described by the following equation:

Cp = 10 (e^-0.1t -  e^-0.7t )

• a) Calculate the Vd

• b) Calculate C_max

• a) Vd = 58.3 L

• b) C_max = 6.19 mg/L

The elimination rate constant of quinidine sulfate is 0.087 1/h. The usual IV bolus dosing for this drug is 300mg every 12 hours in order to maintain effective and safe average blood levels in steady-state equal to 4 mcg/mL. If the dosing interval is changed to 8 hr, what will be the average drug concentration at steady-state?

6 mcg/mL (or 6 mg/L)