References & Methods

1. Population PK Model — Colin 2019

The prior pharmacokinetic parameters (population clearance, central volume V₁, peripheral volume V₂, and intercompartmental clearance Q) are derived from the pooled population analysis by Colin et al. This model was selected for its large adult dataset and its derivation of weight- and renal-function-scaled 2-compartment parameters appropriate for standard adult dosing contexts.

2. AUC-Guided Dosing Target — ASHP/IDSA/PIDS 2020

The therapeutic target of AUC₂₄/MIC 400–600 mg·h/L (assuming MIC = 1 mg/L) is consistent with the 2020 revised consensus guidelines from ASHP, IDSA, PIDS, and SIDP. These guidelines recommend AUC-based monitoring over trough-only monitoring for serious MRSA infections, citing improved nephrotoxicity outcomes and equivalent efficacy.

3. Obesity Model — FFM-Based PK (BMI ≥ 40)

For patients with BMI ≥ 40 kg/m², Vancomyzer™ activates an obesity-specific PK model. Vancomycin is hydrophilic and distributes poorly into adipose tissue, so volumes of distribution (V₁ and V₂) are scaled to Fat-Free Mass (FFM) rather than total body weight. Clearance remains TBW-based via Cockcroft-Gault CrCl, as renal elimination scales with total body weight. The model is derived from two population PK studies in obese adults, with FFM calculated using the Janmahasatian 2005 equations.

FFM (male)   = (9270 × TBW) / (6680 + 216 × BMI)
FFM (female) = (9270 × TBW) / (8780 + 244 × BMI)

V1 = 0.287 × FFM   (central volume — adipose excluded)
V2 = 0.89  × FFM   (peripheral volume — adipose excluded)
Q  = 1.23 L/h       (fixed intercompartmental clearance)
CL = 0.0571 × CrCl + 0.0158 × TBW

IIV (omega): ωCL = 0.29, ωV1 = 0.32, ωV2 = 0.28

4. Two-Compartment PK Mathematics

The concentration-time equations and multi-dose superposition principle are derived from classical pharmacokinetic theory. The two-compartment model with IV infusion input is described in the following foundational texts:

5. Key Equations Used

CL (L/h) = 4.10 × (WT/70)^0.75 × (0.83/SCr)^0.80 × age_factor

age_factor = exp(-0.026 × max(0, age - 35))

Reference patient: 35 yr, 70 kg, SCr 0.83 mg/dL → CL 4.10 L/h
SCr is the direct renal covariate — Cockcroft-Gault CrCl is NOT used.

k10 = CL / V1
k12 = Q / V1
k21 = Q / V2

α = [(k10 + k12 + k21) + √((k10 + k12 + k21)² - 4·k10·k21)] / 2
β = [(k10 + k12 + k21) - √((k10 + k12 + k21)² - 4·k10·k21)] / 2

A = (α - k21) / [V1·(α - β)]
B = (k21 - β) / [V1·(α - β)]

R0 = dose_mg / T_inf

During infusion (0 ≤ t ≤ T_inf):
  C(t) = R0 × [ A/α × (1 - e^(-α·t)) + B/β × (1 - e^(-β·t)) ]

After infusion (t > T_inf):
  C(t) = R0 × [ A/α × (1 - e^(-α·T_inf)) × e^(-α·(t - T_inf))
              + B/β × (1 - e^(-β·T_inf))  × e^(-β·(t - T_inf)) ]

C_total(t) = Σ C_single(t - k·τ)   for k = 0, 1, 2, ..., N-1
             where t ≥ k·τ

Number of doses simulated:
  t½β  = 0.693 / β
  N    = max(6, ceil(4 × t½β / τ) + 2)

This ensures the graph spans enough time for concentrations
to approach steady state (4-5 terminal half-lives).

AUC24 = (dose_mg / CL) × (24 / τ)

This is the exact steady-state AUC by linear pharmacokinetics.
Peak and trough use the steady-state superposition formula
(not the multi-dose simulation) for maximum numerical accuracy.