Propofol TCI Models
Key Data & Bibliography

1. Origins & Historical Context

The Gepts Foundation (1987)

All three models trace their lineage to the original propofol pharmacokinetic work of Gepts et al. (1987), who studied propofol disposition as a constant-rate infusion at 3, 6, and 9 mg·kg⁻¹·hr⁻¹ in three groups of six patients undergoing surgery under regional anaesthesia. Their data were best described by a three-compartment open mammillary model with central elimination in 17 of 18 patients.

Marsh Model (1991)

Marsh et al. published their model as part of a study of pharmacokinetic model-driven infusion in 20 children. The model is a pragmatic adaptation of the Gepts model, with all compartmental volumes scaled linearly to total body weight. The single modification from Gepts was an increase in the central compartment volume to 0.228 L/kg — importantly, no published explanation for this adjustment exists.

Schnider Model (1998–1999)

Developed from two combined pharmacokinetic–pharmacodynamic studies in 24 healthy volunteers (11 female, 13 male; weight 44–123 kg; age 25–81 yr; height 155–191 cm). The studies used constant infusions of propofol at 25, 50, 100, or 200 µg·kg⁻¹·min⁻¹ over 60 minutes, with arterial blood sampling. The model uniquely fixes V₁ at 4.27 L for all patients, with only V₂ varying with age and clearance varying with weight, height, and lean body mass.

Eleveld Model (2018)

Developed from a pooled analysis of 30 previously published pharmacokinetic studies from the WorldSIVA Open TCI initiative, incorporating 1,033 patients aged 0.5–88 years and weighing 0.68–160 kg. Five of these studies also contained BIS observations enabling combined PK-PD modelling. This remains the broadest validation dataset of any propofol PK model to date.

2. Volume Equations — Confirmed from Literature

Marsh Model Volumes

Source: Marsh et al. Br J Anaesth. 1991, as tabulated in Absalom et al. Br J Anaesth. 2009 (Table 1).

V₁  =  0.228  × weight (kg)       [L]
V₂  =  0.463  × weight (kg)       [L]
V₃  =  2.893  × weight (kg)       [L]

Rate constants (FIXED — do not vary with any covariate):
k₁₀ = 0.119  min⁻¹
k₁₂ = 0.112  min⁻¹   (Note: Diprifusor uses 0.114 — typographical error in Marsh 1991)
k₂₁ = 0.055  min⁻¹
k₁₃ = 0.042  min⁻¹
k₃₁ = 0.0033 min⁻¹
ke₀ = 0.26   min⁻¹   (unpublished; associated TTPE ≈ 4.5 min)

For a 70 kg patient: V₁ = 15.96 L · V₂ = 32.41 L · V₃ = 202.5 L

Schnider Model Volumes

Source: Schnider et al. Anesthesiology. 1998 and 1999, as tabulated in Absalom et al. Br J Anaesth. 2009 (Table 1).

V₁  =  4.27  L  (FIXED — independent of all covariates)
V₂  =  18.9 − 0.391 × (age − 53)  [L]   (decreases with advancing age)
V₃  =  238   L  (FIXED — independent of all covariates)

LBM (James equation):
  Male:   LBM = 1.1  × wt − 128 × (wt/ht)²   [kg]
  Female: LBM = 1.07 × wt − 148 × (wt/ht)²   [kg]   (ht in cm)

Clearance (k₁₀) — varies with weight, LBM, height:
  k₁₀ = [0.443 + 0.0107×(wt−77) − 0.0159×(LBM−59) + 0.0062×(ht−177)] / V₁

k₁₂ = [0.302 − 0.0056×(age−53)] / V₁
k₂₁ = k₁₂ × V₁ / V₂
k₁₃ = 0.196 / V₁
k₃₁ = 0.0035
ke₀ = 0.456  min⁻¹  (TTPE ≈ 1.69 min)

For a 40-year-old, 70 kg, 170 cm male: V₁ = 4.27 L (fixed) · V₂ ≈ 23.1 L · V₃ = 238 L (fixed)

Eleveld Model Volumes

Source: Eleveld et al. Br J Anaesth. 2018;120(5):942–959. Reference individual: 35-year-old, 70 kg, 170 cm male, no concomitant opioids.

V₁  =  6.28   L      (allometric weight scaling + age decay)
V₂  =  25.5   L      (allometric weight scaling + age decay)
V₃  =  273    L      (fat-free mass adjusted)
CL  =  1.79   L/min  (clearance — ¾ power allometric)
Q₂  =  1.75   L/min  (inter-compartmental)
Q₃  =  1.11   L/min  (inter-compartmental)
ke₀ =  0.146  min⁻¹  (age-dependent)

Scaling approach:
V₁ scales with weight (Emax/sigmoid function) and age (exponential decay)
V₂ scales with weight and age (exponential decay)
V₃ scales with fat-free mass (FFM) using Al-Sallami equation
CL scales with weight (¾ power allometric) × age × sex × opioid status
ke₀ = 0.146 + 0.0035 × (35 − min(age, 75))  [approximate]

Fat-Free Mass (Al-Sallami equation — used instead of James LBM):
  Calculated from weight, height, BMI, and sex
  More reliable than James equation in obesity

3. Full Parameter Tables

Table 1 — Compartment Volumes at Standard Patient (70 kg, 40 yr, 170 cm Male)

Table 2 — Marsh Parameter Table (from Absalom et al. 2009, Table 1)

These are the exact values published in the key review paper confirming the Diprifusor/Marsh parameters.

4. Model Comparison Summary

5. Clinical Implications of Volume Differences

Why V₁ matters most clinically

The central compartment volume V₁ directly determines the initial bolus dose required to achieve a target plasma concentration. A smaller V₁ means a higher peak concentration for any given dose. The four-fold difference in V₁ between Marsh (15.96 L) and Schnider (4.27 L) at 70 kg is the most clinically significant parameter difference between these models, explaining the very different induction behaviour of TCI pumps using each model.

Age effects on V₂

Schnider's V₂ decreases linearly with age above 53 years (18.9 − 0.391 × (age − 53)). This reflects reduced muscle mass in elderly patients and means the fast peripheral compartment holds less drug, leading to higher and more prolonged plasma concentrations for the same infusion rate. Marsh ignores age entirely, which can result in relative overdosing of elderly patients.

Obesity and V₃

For lipophilic drugs like propofol, the large slow peripheral compartment V₃ (fat, bone, skin) is the key driver of the context-sensitive half-time — the time for plasma concentration to fall by 50% after stopping an infusion depends on how much drug has accumulated in V₃. Eleveld's fat-mass-adjusted V₃ means obese patients have a proportionally larger V₃, which correctly predicts prolonged recovery after long TIVA in this population. Marsh overestimates V₃ by scaling with total body weight, while Schnider's fixed V₃ of 238 L may underestimate it in obese patients.

6. Correction Note for Educational Simulations

7. Complete Bibliography