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Dr Atheer Zgair
Practice problems
Q1: A patient with tonic-clonic seizures is given phenobarbital 100 mg intravenously daily until steady-state occurs. Pharmacokinetic constants for phenobarbital in the patient are: k = 0.116 d-^1 , VD = 75 L. Calculate the steady-state concentration 23 hours after the last dose. Solution The steady-state concentration following multiple IV injections can be calculated by the following equation
C =
𝑫 𝑽𝑫
𝒆−𝒌𝒕 𝟏 − 𝒆−𝒌𝝉^
23 hours after the last dose = 23 24 = 0.96 d
C =
𝟏𝟎𝟎 𝟕𝟓
𝒆−𝟎.𝟏𝟏𝟔^ 𝒙^ 𝟎.𝟗𝟔 𝟏 − 𝒆−𝟎.𝟏𝟏𝟔^ 𝒙^ 𝟏^
) = 10.9 mg/L
Q2: A patient with gram-negative pneumonia is administered tobramycin 140 mg every 8 hours until steady state is achieved. Pharmacokinetic parameters for tobramycin in the patient are: V = 16 L, k = 0.30 h−^1. Calculate the steady-state concentration immediately after a 1- hour infusion. Note tobramycin is administered as an infusion over 1 hour. Solution
C =
𝑲𝟎 𝐾𝑽𝑫
1 −𝑒−𝑘𝑡′ 𝟏 − 𝒆−𝒌𝝉^
C =
𝟏𝟒𝟎
- 3 𝑥 16
1 −𝑒−^0.^3 𝑥^1 𝟏 − 𝒆−𝟎.𝟑^ 𝒙^ 𝟖^
) = 8.3 mg/L
Q3: A patient with an arrhythmia is administered 250 mg of quinidine orally (as 300 mg quinidine sulfate tablets) every six hours until steady state occurs. Pharmacokinetic constants for quinidine in the patient are: V = 180 L, k = 0.0693 h−^1 , F = 0.7. Calculate the postabsorption, postdistribution steady-state concentration just before the next dose Solution Just before the next dose means that the time of calculating the plasma concentration is 6 hours (t = 6). C = 𝑭𝑫
𝒆−𝒌𝒕 𝟏 − 𝒆−𝒌𝝉^
C =
𝟎.𝟕 𝟑𝟎𝟎
𝒆−𝟎.𝟎𝟔𝟗𝟑^ 𝒙^ 𝟔 𝟏 − 𝒆−𝟎.𝟎𝟔𝟗𝟑^ 𝒙^ 𝟔^
) = 1.9 mg/L
Dr Atheer Zgair Q4: A patient receiving theophylline 300 mg intravenously every 6 hours has a predose concentration equal to 2.5 mg/L and postdose concentrations of 9.2 mg/L one hour and 4. mg/L five hours after the second dose is given. Calculate k and VD. Solution
K = -
log 𝐶 2 −log 𝐶 1 𝑡 2 −𝑡 1
x 2.
K = -
log 4. 5 −log 9. 2 5 − 1
x 2.3 = 0.179-^1 h.
VD =
𝐷 (𝐶 0 − 𝐶𝑝𝑟𝑒𝑑𝑜𝑠𝑒)
C 0 can be calculated from following equation
C = 𝑪𝟎. 𝒆−𝒌𝒕
4.5 = 𝑪𝟎. 𝒆−𝟎.𝟏𝟕𝟗^ 𝒙^ 𝟓
𝑪𝟎 = 11 mg/L
VD =
300 11 − 2. 5
= 35.3 L
Q5: a patient is prescribed gentamicin 100 mg infused over 60 minutes every 12 hours. A predose steady-state concentration (Cpredose) is drawn and equals 2.5 mg/L. After the 1-hour infusion, a steady-state maximum concentration (Cmax) is obtained and equals 7.9 mg/L. Calculate k and VD Solution Since the patient is at steady state, it can be assumed that all predose steady-state concentrations are equal. Because of this the predose steady-state concentration 12 hours after the dose can also be considered equal to 2.5 mg/L and used to compute the elimination rate constant (k) of gentamicin for the patient:
K = -
log 𝐶 2 −log 𝐶 1 𝑡 2 −𝑡 1
x 2.
K = -
log 2. 5 −log 7. 9 12 − 1
x 2.3 = 0.105-^1 h.
VD =
𝑘 0 ( 1 −𝑒−𝑘𝑡′) 𝑘 [ 𝐶𝑚𝑎𝑥 −(𝐶𝑝𝑟𝑒𝑑𝑜𝑠𝑒. 𝑒−𝑘𝑡′) VD = 100 𝑚𝑔/1ℎ ( 1 −𝑒−^0.^105 𝑥^1 )
- 105 [ 7. 9 −( 2. 5. 𝑒−^0.^105 𝑥^1 ) = 16.8 L
Dr Atheer Zgair Q9: Calculate the dose and the dosage interval for a patient that needs to be treated for complex partial seizures with intravenous phenobarbital. The target Cssmax and Cssmin are 30 and 25 mg/L, respectively. The population PK parameters for phenobarbital are: k = 0.139 d−^1 and VD = 50 L. Solution 𝝉 = 𝑙𝑛 𝐶𝑠𝑠𝑚𝑎𝑥 − 𝑙𝑛 𝐶𝑠𝑠𝑚𝑖𝑛 𝑘
𝑙𝑛 30 − 𝑙𝑛 25
- 139 = 1.3 day (this value is rounded to 1 day for practical use) D = Cssmax VD (1 - 𝑒−𝑘𝝉) D = 30 x 50 (1 - 𝑒−^0.^139 𝑥^ 𝟏) = 202 mg (this dose is rounded to 200 mg for practical use). Therefore, the calculated dose of phenobarbital would be IV injection of 200 mg every day. Q10: A patient receiving tobramycin for the treatment of intraabdominal sepsis. Using pharmacokinetic parameters (VD = 20 L, k = 0.087 h−^1 ) calculate a tobramycin dose (infused over 1 hour) that would provide maximum (Cssmax) and minimum (Cssmin) steady-state concentrations of 6 mg/L and 1 mg/L, respectively. 𝝉 = 𝑙𝑛 𝐶𝑠𝑠𝑚𝑎𝑥 − 𝑙𝑛 𝐶𝑠𝑠𝑚𝑖𝑛 𝑘
- 087
- 1 = 22 h (round to practical dosage interval of 24 h) K 0 = Cssmax k VD ( 1 - 𝑒−𝑘𝝉 1 - 𝑒−𝑘𝒕′ ), K 0 = 6 x 0.087 x 20 ( 1 - 𝑒−^0.^087 𝑥^24 1 - 𝑒−^0.^087 𝑥^1 ) = 110 mg The patient would be prescribed tobramycin 110 mg infused over 1 hour every 24 hours Q11: a patient with simple partial seizures that needs to receive valproic acid capsules (population pharmacokinetic parameters are V = 12 L, k = 0.05 h−^1 , Tmax = 3 h, F = 1.0). Calculate the optimum dose and dosage interval to achieve maintain steady-state maximum (Cssmax) and minimum (Cssmin) concentrations of 80 mg/L and 50 mg/L, respectively. 𝝉 = 𝑙𝑛 𝐶𝑠𝑠𝑚𝑎𝑥 − 𝑙𝑛 𝐶𝑠𝑠𝑚𝑖𝑛 𝑘
- Tmax, 𝝉 = 𝑙𝑛 80 − 𝑙𝑛 50
- 05
- 3 = 12.4 h (round to a practical interval of 12 h) D = Cssmax VD 𝐹
1 - 𝑒−𝑘𝝉 𝑒−𝑘𝑻𝒎𝒂𝒙
), D =
80 x 12 1
1 - 𝑒−^0.^05 𝑥^12 𝑒−^0.^05 𝑥^ 𝟑^
) = 503 mg (round to practical dose of 500 mg)
The patient would be prescribed valproic acid capsules 500 mg orally every 12 hours.
Dr Atheer Zgair Q12: a patient with an atrial arrhythmia needing treatment with procainamide sustained- release tablets (clearance equals 24 L/h; F = 0.85, 𝝉 = 12 h for sustained-release tablet). The target average steady-state procainamide concentration is 5 mg/L. Calculate the dose of procainamide required to achieve this concentration.
D =
𝐶𝑠𝑠 𝐶𝑙𝝉 𝐹
5 𝑥 24 𝑥 𝟏𝟐
- 85
= 1694 𝑚𝑔 (round to a practical dose of 1500 mg)
The patient would be prescribed procainamide sustained-release tablets 1500 mg orally every 12 hours.
Practice Problems
1. PZ is a 35-year-old, 60-kg female with a Staphylococcus aureus wound
infection. While receiving vancomycin 1 g every 12 hours (infused over one
hour), the steadystate peak concentration (obtained one-half hour after the end
of infusion) was 35 mg/L, and the steady-state trough concentration (obtained
immediately predose) was 15 mg/L. (A) Using one compartment IV bolus
equations, compute the pharmacokinetic parameters for this patient. (B) Using
the patient-specific pharmacokinetic parameters calculated in part A, compute a
new vancomycin dose that would achieve Cssmax = 30 mg/L and Cssmin = 7.
mg/L.
2. KL is a 65-year-old, 60-kg female being treated for septic shock. Among other
antibiotics, she is being treated with tobramycin 60 mg every 8 hours (infused
over 1 hour). Steady-state serum concentrations are: Cssmax = 7.1 mg/L, Cssmin
= 3.1 mg/L.
Using one compartment intermittent intravenous infusion equations, compute
the pharmacokinetic parameters for this patient and use them to individualize
the tobramycin dose to achieve Cssmax = 8 mg/L and Cssmin = 1.0 mg/L.
3. MM is a 54-year-old, 68-kg male being treated with procainamide 750-mg
regular release capsules every 6 hours for an arrhythmia. The following steady-
state concentration is available: Cssmin = 1.5 mg/L (obtained immediately
predose). Calculate a dose that will achieve a Cssmin = 2.5 mg/L.
Dr Atheer Zgair The Cockcroft-Gault method should only be used in
1. Patients ≥18 years old.
2. When actual weight within 30% of their ideal body weight (IBW)
IBWmale (in Kg) = 50 + 2.3 (Ht – 60) IBWfemale (in Kg) = 45 + 2.3 (Ht – 60) Where Ht is the height in inches ( 1 inch = 2.45 cm)
- Stable serum creatinine concentrations. For example, a 55-year-old, 80-kg, 5-ft 11-in male has a serum creatinine equal to 1. mg/dL. The estimated creatinine clearance would be IBWmale (in Kg) = 50 + 2.3 (Ht – 60) Note that 1 foot = 12 inches IBWmale (in Kg) = 50 + 2.3 ( 71 – 60) = 75.3 kg Therefore, BW (80 kg) is within 30% of IBW (75.3 kg) so that Cockcroft-Gault method can be used to calculate CrClest CrClest = [( 140 −age)^ ⁄BW]
- SCr
[( 140 − 55 )^ ⁄ 80 ]
- 9 = 50 mL/min
Note: in obese patients where Cockcroft-Gault method can’t be used alternative equations
can be applied: CrClest = ( 137 −𝑎𝑔𝑒)[( 0. 285. 𝑊𝑡)+( 12. 1. 𝐻𝑡^2 )]
- SCr
…………… for males
CrClest = ( 146 −𝑎𝑔𝑒)[( 0. 287. 𝑊𝑡)+( 9. 74. 𝐻𝑡^2 )]
- SCr
………………. for females
Dr Atheer Zgair Estimation of Drug Dosing and Pharmacokinetic Parameters Using Creatinine Clearance It is widely accepted that dosage adjustment is required when patient is treated with a medication that eliminated by the kidney. One of three methods is commonly used for dose adjust. These are:
- Decrease the drug dose and retain the usual dosage interval.
- Retain the usual dose and increase the dosage interval.
- Simultaneously decrease the dosage and prolong the dosage interval. For drugs with narrow therapeutic indexes, measured or estimated creatinine clearance may be used to estimate pharmacokinetic parameters for a patient based on prior studies conducted in other patients with renal dysfunction. For example, for digoxin, an equation that describes the relationship between digoxin clearance (Cl) and creatinine clearance (CrCl in mL/min) is: Cl (in mL/min) = 1.303 ⋅ CrCl + ClNR where ClNR is nonrenal clearance and equals 20 mL/min in patients with moderate-severe heart failure and 40 mL/min in patients with no or mild heart failure. This equation is derived from the linear relationship between digoxin Cl and CrCl Digoxin volume of distribution decreases in patients with decreased renal function according to the following equation: VD (in L) = 226 + [(298 ⋅ CrCl)/(29.1 + CrCl)] where CrCl is in mL/min. The decline in volume of distribution presumably occurs because of displacement of tissue-bound digoxin. For the aminoglycoside antibiotics, an equation that represents the relationship between aminoglycoside antibiotic elimination rate constant (k) and creatinine clearance (CrCl in mL/min) is: k (in h−^1 ) = 0.00293 ⋅ CrCl + 0.
Dr Atheer Zgair Child-Pugh Scores for Patients with Liver Disease
- The Child-Pugh score for a patient with normal liver function is 5.
- A Child-Pugh score equal to 8–9 is grounds for a moderate decrease (~ 25%) in initial daily drug dose for agents that are primarily (≥60%) hepatically metabolized.
- A score of 10 or greater indicates that a significant decrease in initial daily dose (~ 50%) is required for drugs that are mostly liver metabolized. For example, the usual dose of a medication that is 95% liver metabolized is 500 mg every 6 hours, and the total daily dose is 2000 mg/d. For a hepatic cirrhosis patient with a Child-Pugh score of 12, an appropriate initial dose would be 50% of the usual dose or 1000 mg/d. The drug could be prescribed to the patient as 250 mg every 6 hours or 500 mg every 12 hours. The method used to reduce the dose for patients with liver dysfunction will depend on the route of administration and the available dosage forms. For example, if the medication is only available as an oral capsule, it is likely that the usual dose will be given to a patient with liver disease but the dosage interval will be prolonged. However, if the drug is given parenterally, it may be possible to simultaneously modify the dose and dosage interval to attain the same maximum and minimum steady-state concentrations in patients with hepatic dysfunction as those encountered in patients with normal liver function.
