How to Calculate Elimination Rate Constant Pharmacokinetics

by

Elimination Rate Constant (ke) Calculator

Pharmacokinetics Analysis Tool

Results:

Elimination Rate Constant (ke): h-1

Estimated Half-life (t1/2): hours

Elimination Percentage: % per hour

Please ensure all values are positive and that the initial concentration is greater than the final concentration.

How to Calculate Elimination Rate Constant Pharmacokinetics

In pharmacokinetics, the elimination rate constant (ke) is a value that describes the rate at which a drug is removed from the body. It represents the fraction of the drug that is eliminated per unit of time (e.g., 0.1 per hour means 10% of the drug is removed every hour).

The ke Formula

The calculation is based on first-order kinetics, which applies to most drugs at therapeutic doses. The primary formula used when two plasma concentration points are known is:

ke = (ln(C1) – ln(C2)) / Δt
  • C1: Initial drug concentration
  • C2: Final drug concentration
  • Δt: The time elapsed between the two measurements
  • ln: The natural logarithm

Why is the Elimination Rate Constant Important?

Understanding ke is crucial for several clinical reasons:

  1. Determining Half-Life: Once you have ke, you can calculate the half-life using the formula t1/2 = 0.693 / ke.
  2. Dosing Intervals: It helps pharmacists and doctors decide how often a drug should be administered to maintain steady-state levels.
  3. Clearance Relationship: It connects the volume of distribution (Vd) to clearance (CL) via CL = ke × Vd.

Step-by-Step Calculation Example

Suppose a patient is given a dose of an antibiotic. The blood concentration 2 hours after administration is 12 mg/L (C1). Six hours later (total 8 hours after dose), the concentration is 4 mg/L (C2).

  • Step 1: Identify the time interval (Δt) = 8h – 2h = 6 hours.
  • Step 2: Calculate the natural log of concentrations: ln(12) ≈ 2.485 and ln(4) ≈ 1.386.
  • Step 3: Apply the formula: ke = (2.485 – 1.386) / 6 = 1.099 / 6.
  • Step 4: Result: ke = 0.183 h-1.
  • Step 5: Half-life: 0.693 / 0.183 ≈ 3.78 hours.
function calculateKe() { var c1 = parseFloat(document.getElementById('initialConc').value); var c2 = parseFloat(document.getElementById('finalConc').value); var t = parseFloat(document.getElementById('timeInterval').value); var resultsArea = document.getElementById('resultsArea'); var errorArea = document.getElementById('errorArea'); // Reset display resultsArea.style.display = 'none'; errorArea.style.display = 'none'; // Validation if (isNaN(c1) || isNaN(c2) || isNaN(t) || c1 <= 0 || c2 <= 0 || t = c1) { errorArea.innerText = "Final concentration (C2) must be less than initial concentration (C1) to calculate elimination."; errorArea.style.display = 'block'; return; } try { // k_e calculation: (ln(C1) – ln(C2)) / t var ke = (Math.log(c1) – Math.log(c2)) / t; // Half-life calculation: 0.693 / k_e var thalf = 0.693147 / ke; // Percentage elimination: (1 – e^-ke) * 100 (approximately ke * 100 for small ke) var percent = (1 – Math.exp(-ke)) * 100; // Display results document.getElementById('keResult').innerText = ke.toFixed(4); document.getElementById('thalfResult').innerText = thalf.toFixed(2); document.getElementById('percentResult').innerText = percent.toFixed(2); resultsArea.style.display = 'block'; } catch (e) { errorArea.innerText = "An error occurred during calculation. Please check your inputs."; errorArea.style.display = 'block'; } }

Leave a Comment