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Model: tmdd

Reference

Note: this is the general, fully-parameterized TMDD model.

Peletier LA, Gabrielsson J. Dynamics of target-mediated drug
disposition: characteristic profiles and parameter identification. 
J Pharmacokinet Pharmacodyn. 2012 Oct;39(5):429-51. 
doi: 10.1007/s10928-012-9260-6. Epub 2012 Aug 1. PMID: 22851162; 
PMCID: PMC3446204.

Example

This simulation replicates Figure 3 in the paper.

library(depot)
library(dplyr)
library(mrgsim.sa)
mod <- depot("tmdd", end = 600, delta = 0.1)

Doses

  • 1.5 mg/kg
  • 5.0 mg/kg
  • 15 mg/kg
  • 45 mg/kg
e <- expand.ev(amt = c(1.5, 5, 15, 45))

Note that these are mg/kg doses. Model parameters are also weight-normalized.

mod %>% mrgsim_e(e) %>% plot(L ~time, logy = TRUE)

Sensitivity analysis

  • Run on just the 5 mg/kg dose
  • Each parameter is varied between $\pm 2\sigma$ of log-normal distribution with 100% coefficient of variation
out <- mod %>%  
  parseq_cv(keRL, koff, kon, kout, kin, CL, .cv = 100) %>%
  ev(amt = 5) %>% 
  update(outvars = "L") %>%
  sens_each(recsort = 3) 
sens_plot(
  out, 
  "L", 
  logy = TRUE, 
  plot_ref = FALSE,
  xlab = "Time (h)", 
  ylab = "Concentration (mg/L)"
)

Check the actual values

p_name lo mid hi
CL 0.0001353 0.001 0.0073891
keRL 0.0004060 0.003 0.0221672
kin 0.0148869 0.110 0.8127962
koff 0.0001353 0.001 0.0073891
kon 0.0123155 0.091 0.6724041
kout 0.0012180 0.009 0.0665015

Code

[ param ]

Vt = 0.1
CLd = 0.003
CL = 0.001
kon = 0.091
koff = 0.001
kin = 0.11
kout = 0.009
keRL = 0.003
R0 = 12
Vc = 0.05;

[ cmt ] L R RL T

[ pk ]

R_0 = R0;

double keL = CL/Vc;

F_L = 1/Vc;

[ des ]

dxdt_L = - kon * L * R + koff * RL - keL * L - (CLd/Vc) * L + (CLd/Vt) * T;

dxdt_R = kin - kout * R - kon * L * R + koff * RL;

dxdt_RL = kon * L * R - (koff + keRL) * RL;

dxdt_T = (CLd/Vc) * L - (CLd/Vt) * T;

[ capture ] CP = L