Great question. You're asking whether the half-life of heparin can be back-calculated from a known bolus + infusion regimen. The answer is: yes, with some assumptions, using first-order pharmacokinetic principles.
Setup
Given:
- Bolus: 1000 IU IV at time 0
- Maintenance infusion: 500 IU/hour for 3 hours
- Total infusion dose: 500 × 3 = 1500 IU over 3 hours
What You'd Need to Calculate Half-Life
To actually calculate the half-life, you need at least one plasma heparin level (anti-Xa or aPTT-based concentration) measured at a known time. Without a blood level, you can only predict expected behavior using an assumed half-life.
However, if you measure levels, here's the math:
PK Model: One-Compartment, First-Order Elimination
Step 1 - Concentration after bolus alone (no infusion)
$$C(t) = \frac{D}{V_d} \cdot e^{-k_e t}$$
Where:
- D = dose (IU)
- V_d = volume of distribution (~60-70 mL/kg for UFH, ~4-5 L in a 70 kg person)
- k_e = elimination rate constant = 0.693 / t½
Step 2 - With simultaneous infusion (bolus + constant rate infusion)
The combined concentration equation is:
$$C(t) = \frac{D_{bolus}}{V_d} \cdot e^{-k_e t} + \frac{R_0}{V_d \cdot k_e}\left(1 - e^{-k_e t}\right)$$
Where:
- R₀ = infusion rate = 500 IU/hr
- t = time in hours
Step 3 - Back-calculating half-life from two measured levels
If you draw two blood samples (e.g., at t = 1 hr and t = 3 hr), you get C₁ and C₂. Then:
$$k_e = \frac{\ln(C_1) - \ln(C_2)}{t_2 - t_1}$$
$$t_{1/2} = \frac{0.693}{k_e}$$
Numerical Example (Assuming t½ = 60 min = 1 hr)
Using k_e = 0.693/hr, V_d = 5000 mL (5L), R₀ = 500 IU/hr:
| Time | Bolus Component | Infusion Component | Total C (IU/mL) |
|---|
| 0 hr | 1000/5000 = 0.200 | 0 | 0.200 |
| 1 hr | 0.200 × e⁻⁰·⁶⁹³ = 0.100 | (500/5000×0.693)×(1−0.5) = 0.072 | 0.172 |
| 2 hr | 0.200 × e⁻¹·³⁸⁶ = 0.050 | 0.144×(1−0.25) = 0.108 | 0.158 |
| 3 hr | 0.200 × e⁻²·⁰⁷⁹ = 0.025 | 0.144×(1−0.125) = 0.126 | 0.151 |
At 3 hours, if infusion is then stopped, the level at t=3 hr is ~0.151 IU/mL, and it will halve to ~0.075 IU/mL by t=4 hr (one more half-life).
Practical Answer
With your regimen (1000 IU bolus + 500 IU/hr × 3 hr):
- You cannot calculate the half-life from the dose alone
- You can calculate it if you measure heparin level at end of infusion (t=3 hr) and again at t=4 or 5 hr after stopping
- Use: t½ = 0.693 / k_e, where k_e is derived from the slope of the log-concentration vs. time graph after stopping the infusion
Clinically, the expected t½ in a dialysis patient on this regimen would be approximately 40-60 minutes, slightly longer than a normal patient (~30-45 min) due to modestly reduced clearance.