4.4: Clinical Pharmacokinetics (Dosing Adjustments & Non-linear Kinetics)

4.4 Clinical Pharmacokinetics (Dosing Adjustments & Non-linear Kinetics)

Clinical pharmacokinetics applies mathematical relationships to safe, individualised drug dosing. By understanding drug absorption, distribution, metabolism, and excretion, clinicians can design dosing regimens that maintain therapeutic serum concentrations while avoiding systemic toxicity. This is especially crucial for drugs with narrow therapeutic windows and in patient populations with altered organ function.

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Designing Loading Doses and Maintenance Doses

When initiating drug therapy, the time required to reach steady-state concentration (Css) is determined solely by the drug’s elimination half-life (t1/2). Approximately 4 to 5 half-lives are needed to reach steady state. In acute clinical scenarios (e.g., treating severe sepsis with gentamicin or controlling rapid ventricular rate in atrial fibrillation with digoxin), waiting for steady state is clinically unacceptable. In these situations, a loading dose (LD) is administered to rapidly achieve the target therapeutic concentration.

The Loading Dose Equation

The loading dose is designed to fill the volume of distribution (Vd) to the target steady-state concentration (Css). It is independent of drug clearance:

LD = (Css * Vd) / F

Where:

• Css is the target plasma concentration (mg/L).
• Vd is the volume of distribution (L).
• F is the bioavailability fraction (expressed as a decimal from 0 to 1; for intravenous administration, F = 1).

Clinical Example: Loading Dose Calculation

A patient requires an intravenous loading dose of a drug to immediately achieve a target plasma concentration of 10 mg/L. The drug's volume of distribution is 0.5 L/kg, and the patient weighs 80 kg.

1. Calculate total Vd: 0.5 L/kg * 80 kg = 40 L.
2. Calculate loading dose (IV, so F = 1): LD = (10 mg/L * 40 L) / 1 = 400 mg.

The Maintenance Dose Equation

Once the target concentration is achieved, a maintenance dose (MD) must be administered to replace the amount of drug eliminated from the body over time. The maintenance dose is directly dependent on drug clearance (Cl):

MD = (Css * Cl * tau) / F

Where:

• Cl is the clearance rate (L/h).
• tau is the dosing interval (h).
• For continuous intravenous infusions, the rate of infusion (R0) is: R0 = Css * Cl

Clinical Example: Maintenance Dose Calculation

For the same patient (80 kg), the target Css is 10 mg/L. The drug clearance is 2 L/h, and the oral bioavailability (F) is 0.8. The physician wants to dose the drug every 12 hours (tau = 12 h).

1. Calculate maintenance dose: MD = (10 mg/L * 2 L/h * 12 h) / 0.8 = 240 mg / 0.8 = 300 mg every 12 hours.

Exam Tip: Remember that a change in Vd alters the loading dose, whereas a change in clearance (Cl) alters the maintenance dose.

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Renal Impairment and the Cockcroft-Gault Equation

In patients with renal impairment, the clearance of hydrophilic, renally eliminated drugs decreases. To avoid accumulation and toxicity, maintenance doses must be adjusted based on the patient's estimated glomerular filtration rate. In Australian clinical practice (referenced in the Australian Medicines Handbook [AMH] and therapeutic guidelines), the Cockcroft-Gault (C-G) equation remains the gold standard for adjusting drug doses in renal impairment, rather than the eGFR reported by pathology labs (which is normalised to a standard body surface area of 1.73 m^2).

The Australian Cockcroft-Gault Formula

Unlike the North American formula which uses serum creatinine in mg/dL, the standard Australian formula uses micromol/L (µmol/L):

CrCl (mL/min) = [ (140 - Age) * Weight (kg) * Constant ] / Serum Creatinine (µmol/L)

Where the constant is:

• 1.23 for males
• 1.04 for females

Selecting the Appropriate Weight

Choosing the correct weight parameter is a common source of exam traps:

1. Actual Body Weight (ABW): Used if the patient's actual weight is less than their Ideal Body Weight (IBW).
2. Ideal Body Weight (IBW): Used for normal-weight or obese patients when calculating creatinine clearance for drugs that do not distribute into fat, as adipose tissue does not produce creatinine.
   • IBW (males) = 50 kg + 0.9 kg per cm over 152 cm
   • IBW (females) = 45.5 kg + 0.9 kg per cm over 152 cm
3. Adjusted Body Weight (AdjBW): Used in obese patients (e.g., actual weight > 120% of IBW or BMI >= 30) for specific drugs like aminoglycosides: AdjBW = IBW + 0.4 * (ABW - IBW)

Clinical Adjustment Strategies

Renal adjustments are made in two ways:

• Dose Reduction: Lowering the individual dose while keeping the interval constant (e.g., gabapentin). This minimises peak-to-trough fluctuations.
• Interval Extension: Increasing the time between doses (e.g., extending gentamicin or fluconazole intervals). This is ideal for concentration-dependent antibiotics where high peaks are needed but low troughs are required to prevent toxicity.

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Hepatic Impairment Dosing Adjustments

Unlike renal clearance, there is no single endogenous marker (like serum creatinine) to quantify hepatic clearance. Hepatic drug clearance depends on liver blood flow, intrinsic metabolic enzyme activity (primarily cytochrome P450 enzymes), and plasma protein binding.

The Child-Pugh Classification

The Child-Pugh score is a semi-quantitative tool used to grade the severity of liver cirrhosis. It scores five clinical and laboratory criteria:

1. Total bilirubin
2. Serum albumin
3. INR (prothrombin time)
4. Ascites (none, mild, moderate/severe)
5. Hepatic encephalopathy (none, grade I-II, grade III-IV)

The total score classifies patients into:

• Class A (Score 5-6): Mild hepatic impairment. Generally requires no dose adjustment.
• Class B (Score 7-9): Moderate impairment. Requires cautious dose reductions (typically 25-50%).
• Class C (Score 10-15): Severe impairment. High risk of toxicity; avoid hepatotoxic or highly metabolised drugs, or reduce doses by 50-75%.

Perfusion-Limited vs. Capacity-Limited Clearance

• High Extraction Ratio Drugs (EH > 0.7): Clearance depends primarily on hepatic blood flow (perfusion-limited). These drugs undergo extensive first-pass metabolism when given orally. In liver cirrhosis, shunting of blood around the liver bypasses metabolism, leading to a dramatic increase in systemic bioavailability.
  • Examples: Morphine, propranolol, verapamil, glyceryl trinitrate.
  • Adjustment: Oral doses must be significantly reduced (often by 50% or more) in hepatic impairment.
• Low Extraction Ratio Drugs (EH < 0.3): Clearance depends on intrinsic metabolic capacity and protein binding (capacity-limited). Bioavailability is unchanged, but systemic clearance is reduced.
  • Examples: Phenytoin, warfarin, valproate, diazepam.
  • Adjustment: Monitor clinical markers (INR for warfarin) or drug levels (phenytoin) closely.

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Therapeutic Drug Monitoring (TDM)

Therapeutic Drug Monitoring (TDM) involves measuring drug concentrations in body fluids (usually plasma or serum) to individualise dosing.

Indications for TDM

TDM is indicated when:

1. The drug has a narrow therapeutic index (the margin between the effective and toxic concentration is small).
2. There is a direct correlation between serum concentration and clinical efficacy or toxicity.
3. The clinical response cannot be easily measured by simple physiological markers (unlike blood pressure for antihypertensives).
4. The pharmacokinetics of the drug are highly variable or unpredictable.

Key TDM Drugs in Australian Practice

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Non-linear (Michaelis-Menten) Kinetics

Most drugs at therapeutic doses exhibit linear (first-order) kinetics, where clearance is constant and the rate of drug elimination is directly proportional to concentration. The drug's half-life remains constant, meaning doubling the dose will double the steady-state plasma concentration.

However, some drugs exhibit non-linear (zero-order or saturable) kinetics within the therapeutic range. This is described by the Michaelis-Menten equation:

Rate of Elimination = (Vmax * C) / (Km + C)

Where:

• Vmax is the maximum rate of metabolism.
• Km is the Michaelis constant (concentration at which the elimination rate is half of Vmax).
• C is the plasma concentration.

Transition from First-Order to Zero-Order

• At low concentrations (C << Km): The equation simplifies to Rate = (Vmax / Km) * C. Elimination is first-order, meaning clearance is constant and concentrations rise proportionally with dosage.
• At high concentrations (C >> Km): The metabolic enzymes become fully saturated, and the equation simplifies to Rate = Vmax. Elimination is zero-order. The body eliminates a constant amount of drug per unit time, regardless of the concentration. Clearance decreases and the half-life increases as concentration rises.

The Classic Example: Phenytoin

Phenytoin metabolic pathways (via CYP2C9 and CYP2C19) saturate at or near the therapeutic range (10-20 mg/L).

• Clinical Consequence: Once metabolic pathways are saturated, any small increment in the daily dose (e.g., from 300 mg to 350 mg daily) will exceed the capacity of the enzymes. This causes a disproportionate, non-linear jump in steady-state concentration, potentially precipitating acute toxicity (nystagmus, ataxia, slurred speech, confusion).
• Practice Guideline: Dosage adjustments for phenytoin must be small (e.g., 25-50 mg increments) and monitored with follow-up serum levels after steady state is reached. Because clearance is reduced at high concentrations, the time required to reach a new steady state is significantly prolonged (often taking 7 to 14 days or longer).