Drug Elimination Kinetics

Kinetics of Drug Elimination

• Drug elimination is the combined process of metabolic inactivation and excretion.
• Knowledge of a drug's elimination kinetics is used to create dosage regimens and adjust them to individual needs.
• Drug administration methods vary based on ADME (absorption, distribution, metabolism, excretion) principles.
• Example drugs and their administration:
  • Paracetamol is administered 3-4 times daily.
  • Morphine is effective through intramuscular injection (IM)
  • Insulin is effective through subcutaneous injection (SC).

Drug Elimination Kinetics: Zero Order (Linear)

• The rate of elimination remains constant regardless of drug concentration.
• Rate of elimination is expressed as Rate = k
• The plasma drug concentration at any time (t) can be calculated using the formula C = -Kt + Co, where:
  • C is the concentration at time t.
  • Co is the initial concentration.
  • K is the zero-order elimination constant.
• Carrier-mediated excretion in the proximal renal tubules typically eliminates drugs following zero-order kinetics.
• Carriers become saturated, resulting in a constant transport rate.
• Examples of drugs include aspirin, ethanol, and phenytoin
• Elimination is concentration-independent.
• Concentration vs. time graphs are linear.
• Increased doses will increase t1/2 and the chance of toxicity.

Drug Elimination Kinetics: First Order (Exponential)

• First-order kinetics describes the elimination of most drugs at typical doses.

• The amount of drug decreases at a rate proportional to the concentration.

• Represented as Rate = -KC.

• The concentration of a drug in plasma at any time (t) can be determined by:

• C = Co e-kt or lnCt = -Kt + lnCo

• Co is the initial concentration at t = 0.

• Ct is the concentration at time t.

• ln is the natural logarithm, approximately equal to 2.303 log.

• Drug concentration vs time plots are non-linear and decay exponentially.

• Log of drug concentration vs time plots are linear.

• The t1/2 half-life remains constant, irrespective of drug concentration.

Pharmacokinetic Parameters

• Volume of Distribution (VD)
• Plasma Half-Life (t1/2)
• Plasma Clearance (CL)
• Bioavailability

Volume of Distribution (VD)

• Drugs can distribute into:
  • Plasma (4 liters)
  • Interstitial Fluid (10 liters)
  • Intracellular Fluid (28 liters)
• Plasma Compartments:
  • If a drug has a very large molecular weight or binds significantly to plasma proteins, it remains trapped in the vascular compartment, thus the plasma volume is 4L
  • Heparin shows limited distribution (4L), due to large molecular weight or extensive protein binding.
• Extracellular Fluid:
  • Hydrophilic drugs with low molecular weight move through capillaries to the interstitial fluid
  • These drugs cannot cross cell lipid membranes to enter the intracellular water phase
  • They distribute into a volume of plasma water and interstitial fluid, which is about 14L
  • Aminoglycoside antibiotics follow this distribution pattern.
• Total Body Water:
  • Hydrophobic drugs with low molecular weight can enter the interstitial and intracellular fluids
  • They distribute throughout the total body water, about 42L

Apparent Volume of Distribution

• The fluid volume needed to encompass the entire drug in the body provided that the drug concentration through out is the same as measured in plasma.
• This gives information on how its distributed in the body.
• Units are Volume.
• VD assumes uniform drug distribution in a single compartment.
• Most drugs distribute unevenly across multiple compartments.
• VD doesn't correspond to a real physical volume.
• VD reflects the ratio of drug in extraplasmic spaces vs plasma.
• Determinants of VD include:
  • Tissue binding capacity (increases VD)
  • Drug binding to plasma proteins (decreases VD)
• Volume of distribution can be very small if the drug primarily stays in the blood (warfarin with V = 5-7 L).
• Volume of distribution can be very large if the drug disperses in the body and mainly binds to tissues (digoxin with V = 500 L)
• Large Vd means longer half-life and action duration because the drug is unavailable to excretory organs.
• Used to calculate amount of drug concentration to achieve desired plasma concentration.

Clearance (CL)

• Clearance refers to the theoretical plasma volume from which a drug is completely eliminated per unit of time.
• It links the rate of elimination to plasma concentration.
• Organ clearance is additive.
• Systemic elimination processes occur in the kidney, liver, and other organs.
  • CL renal = Rate of Elimination kidney(mg/hr)/concentration (mg/L)
  • CL hepatic = Rate of Elimination liver (mg/hr)/concentration (mg/L)
  • CL total body = CL renal + CL hepatic+ CL pulmonary+ CL other
• The most important of these is renal.
• It is not possible to measure and sum all individual clearances, so total clearance is derived from the steady-state equation.
  • CL total = k*VD
• For example:
  • Clearance = 10 L/hr
  • Volume of Distribution = 100 L
  • Elimination Rate Constant (k) ?
  • CL = KVD k = 10 Lhr-1 / 100 L = 0.1 hr-1

Bioavailability (F)

• Bioavailability (F) represents the fraction of drug that enters systemic circulation in an unchanged state from the administration site.
• Bioavailability is impacted by rate and extend of absorption, and first-pass metabolism in the liver and gut wall.
• F= Amount of drugs entering the systemic circulation / Dose administered OR AUC after oral dose AUC - Area under the curve AUC after I.V. dose
• Absolute bioavailability measures the systemic availability of a drug after extravascular administration, comparing the area under the concentration-time curve to that after IV administration.
• Relative bioavailability compares systemic availability from one drug product to another.
• For the same dose of IV vs oral, it is given by:
• F = AUCoral (A) / AUCoral (B)*

Half-Life (t1/2)

• Plasma drug concentration reduces to half of its original value.

• Half life for first-order kinetics: T1/2 = 0.693 x Vd / CL Where ln 2 = 0.693 OR t1/2 = ln 2 / K = 0.693 / K

• Half life for zero-order kinetics: t1/2 = 0.5Co/ Ko t1/2is proportional to Co when the dose is increased t1/2 is proportional to 1/Ko when the dose is reduced

• Significance of half-life:

  • Indicates the time required to reach steady state concentration after a dosage regimen is initiated (usually after 4 half- lives)
  • The time required to remove a drug from the body
  • Estimation of dosing interval

• Clinical situations resulting in changes in drug half-life is increased by: - Diminished renal plasma flow or hepatic blood flow in cardiogenic shock, heart failure, or hemorrhage - Decreased metabolism, when another drug inhibits its biotransformation or in hepatic insufficiency

• The half-life of a drug is decreased by: - Increased hepatic blood flow - Increased metabolism - Decreased protein binding

• Drug elimination and half-life notes:

• After one half life (t1/2), 50% of the drug will have been eliminated from the body

• After four half live, > 90% of the drug will be eliminated from the body and negligible amount of drug will remain in the body.

• The half-life time of theophylline is 9hrs, so it takes 36hours (4xT1/2) for a bolus of IV dose of theophylline to be eliminated the body of a patient with asthma

Drug Accumulation With Repeated Doses

• Doses accumulate in body until dosing stops
• It takes an infinite time (in theory) to eliminate all of a given dose
• If the dosing interval is shorter than four half-lives, accumulation will be detectable.
• Aminoglycoside renal toxicity (Gentamicin) increases when delivered as constant infusion rather than intermittently.
• Renal cortex accumulation of aminoglycoside leads to renal damage.

Steady-State Plasma Concentration

• Steady state occurs with repeated doses over a period of tome.
• At this point, the amount of drug is in equilibrium (elimination = input).
• For drugs utilizing first order kinetics, steady state is achieved after 4-5 half lives.
• Necessary for maintaining drug concentration within therapeutic window, balancing efficacy and toxicity.
• Steady state is important for maintaining drug effects.
• Rapid biotransformation and excretion will affect this.
• The maximum drug effect can be expected at this stage.
• At steady state:
• Cpss = dose rate/CL
  • Dose Rate = target Cpss x CL
• Loading dose are given for achieving target concentration, and the therapeutic effect of the drug is needed immediately
• Loading dose are useful for for drugs that are eliminated from the body relatively slowly,
• Disadvantage include patient ay be exposed abruptly to a toxic concentration for a long time
• With I.V. Adminsitration:
• LD(mg)= VD(L)x target conc.(mg/L)
• With Oral Route of Administration: Loading dose = -VD x Desired plasma concentration/ Bioavailability
• Maintenance dose is smaller than the loading dose, maintains the concentration and achieves and maintains a target
• When at steady state, dose rate in = rate of elimination.
• MD(mg/hr) =CL x target concentration(mg/L)