Multi-compartment Models and Non-linear pharmacokinetics for RRB, KGMU, KSSSCI, MPESB Pharmacist Exams / GPAT / DPEE / Drugs Inspector Exams / D.Pharm, B.Pharm, and Pharm.D.
• Multicompartment Models are also known as Delayed Distribution Models.
• Loading (Priming) Dose (XL): It is defined as the amount of an initial dose of a certain drug needed to reach a target plasma concentration.
• The loading dose (LD) where the target concentration is Css is calculated by the formula
LD = V X Css
Where, V = Apparent volume of distribution and
Css = Steady state plasma concentration of the drug
• Maintenance Dose (XM) is defined as the dose needed to maintain the concentration within the therapeutic window (Css) when given repeatedly at a constant interval.
• Problems:
1. What is a loading dose of drug A (V = 20L, oral bioavailability = 40%, target plasma concentration = 5 mg/l)?
Sol. Loading dose (XL) = Css.av X (V/F)
XL = 5 mg/L X (20L / 0.40) = 250 mg
2. What is the maintenance dose (XM) of drug A for plasma level of 5 mg/L, TID, p.o. Cl is 7.5 L/h, F is 75%?
Sol. Maintenance dose (XM) = Css,av X Cl (total) X dosing interval, (T) / F
TID i.e. three times a day i.e. dosing interval (T) = 8hrs
XM = 5 mg/L X 7.5 L/h X 8 hrs / 0.75 = 400 mg.
3. What is the I.V. loading dose to give a serum theophylline concentration of 12 mg/L in a 60 kg man? (V for theophylline is 0.7 L/kg)
Sol. Loading dose (XL) = Css.av X V
XL = (12 mg/L) (0.7 L/kg) (60 kg)
= 504 mg
• The elimination rate constant is the rate at which drug is removed from the body assuming first-order elimination. It is often represented by K or KE. Its unit is time^-1 i.e. 1/time. (Note: Here ^ indicates raised to the power of).
• Steady State / Plateau Principle: Steady-state (plateau) conditions are attained when the rate of drug entering the system (dose per unit time) equals the rate of drug exiting the system and no further drug accumulation occurs.
• In practice, during a repeat-dose regimen, steady state is assumed to be reached in 5 half-lives unless dose interval is very much longer than t½. The time taken to reach steady-state does not depend on dose size, dosing interval and number of doses.
• Linear pharmacokinetics always exhibits linear relation between dose (single or multiple doses) and plasma concentration of a drug i.e. in a given interval always the same drug fraction is eliminated.
• For a drug exhibiting linear kinetics all semilog plots of C (concentration) versus t(time) for different doses when corrected for dose administered, are superimposable. This is called principle of superposition.
• Non-linear pharmacokinetics shows a mixture of first-order and zero-order rate processes and the pharmacokinetic parameters change with the size of the dose administered.
• The non-linear pharmacokinetic behaviour is also called as dose-dependent, mixed-order, and capacity-limited kinetics.
• Non-linear or dose-dependent pharmacokinetics can be described by Michaelis-Menten equation as:
− dC / dt = Vmax C / Km + C
where, − dC / dt = Rate of decrease of drug concentration with time,
Vmax = Maximum rate of the process,
Km = Michaelis-Menten constant (drug concentration at which the rate of process is 50% of Vmax) and
C = Drug concentration in the body
• Example: The elimination rate of a drug with a concentration 0.8 µg/mL, Km of 0.1 mg/mL and a Vmax of 0.5 mg/mL per hour
As per above Equation
Solution: Elimination rate = Vmax C / Km + C
= (0.5 X 0.8) / (0.1 + 0.8)
= 0.4/0.9
= 0.444 µg/mL/h.
• Dosage regimen is the decision of drug administration regarding formulation, route of administration, drug dose, dosing interval and treatment duration.
MCQs
1. Regarding two compartment pharmacokinetics all are true EXCEPT:
(a) a drug is always removed from the peripheral compartment.
(b) a drug with a high volume of distribution is likely to be lipophilic.
(c) a drug can have a short duration of action while being eliminated very slowly.
(d) most anaesthetic drugs are modelled well with a two-compartment model.
2. Time required to reach the steady state after a dosage regimen depends on ______.
(a) Route of administration (b) Half life of a drug
(c) Dosage interval (d) Dose of drug
3. The loading dose of a drug is usually based on ______.
(a) Total body clearance of the drug
(b) Percentage of drug bound to plasma protein
(c) Fraction of drug excreted unchanged in urine
(d) Apparent volume of distribution and desired drug concentration in plasma
4. Non-linear pharmacokinetics is also known as _______.
(a) dose dependent (b) enzyme capacity limited
(c) saturation pharmacokinetics (d) All of the above
5. The characteristic of non-linear pharmacokinetics include _______.
(a) Area under the curve is proportional to the dose
(b) Elimination half-life remains constant
(c) Area under the curve is not proportional to the dose
(d) Amount of drug excreted through remains constant
6. Which of following drug shows non-linearity in hepatic excretion?
(a) Carbamazepine (b) Propranolol
(c) Penicillin (d) Thiopental
7. Drugs that show nonlinear pharmacokinetics have which of the following property?
(a) A constant ratio of drug metabolites is formed as the administered dose increases.
(b) The elimination half- life increases as the administered dose increases.
(c) The area under the plasma drug concentration versus time curve increases in direct proportion to an increase in the administered dose.
(d) Both low and high doses follow first -order elimination kinetics.
8. Which of the following statements about Km, the Michaelis constant in Michaelis-Menten kinetics is correct?
(a) is defined as the concentration of substrate required for the reaction to reach maximum velocity.
(b) is defined as the dissociation constant of the enzyme-substrate complex.
(c) is expressed in terms of the reaction velocity.
(d) is a measure of the affinity the enzyme has for its substrate
Check your answers below:
Recommended book for the preparation of GPAT and Drugs Inspector Exams, "ESSENTIAL PHARMACY REVIEW FOR DRUGS INSPECTOR EXAMS", NIRALI PRAKASHAN, PUNE
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Recommended book for the preparation of RRB Pharmacist Exam, "PHARMACIST RECRUITMENT EXAM", NIRALI PRAKASHAN, PUNE
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Check your Answers:
1. (a)
2. (b)
3. (d)
4. (d)
5. (c)
6. (a)
7. (b)
8. (d)
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