Convert linear elimination to quadratic elimination
See also
Other PD:
addBaseline1exp(),
addBaselineConst(),
addBaselineExp(),
addBaselineLin(),
addDirectLin(),
convertEmax(),
convertLogLin()
Examples
readModelDb("PK_2cmt_no_depot") |>
addIndirectLin(stim="out") |>
convertQuad()
#>
#>
#> ── rxode2-based free-form 3-cmt ODE model ──────────────────────────────────────
#> ── Initalization: ──
#> Fixed Effects ($theta):
#> lcl lvc lvp lq propSd lkin lkout lEk
#> 1.0 3.0 5.0 0.1 0.5 0.1 0.1 0.1
#> effectSd uEk2
#> 0.1 0.1
#>
#> States ($state or $stateDf):
#> Compartment Number Compartment Name
#> 1 1 central
#> 2 2 peripheral1
#> 3 3 R
#> ── Multiple Endpoint Model ($multipleEndpoint): ──
#> variable cmt dvid*
#> 1 Cc ~ … cmt='Cc' or cmt=4 dvid='Cc' or dvid=1
#> 2 effect ~ … cmt='effect' or cmt=5 dvid='effect' or dvid=2
#> * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#>
#> ── Model (Normalized Syntax): ──
#> function() {
#> ini({
#> lcl <- 1
#> label("Clearance (CL)")
#> lvc <- 3
#> label("Central volume of distribution (V)")
#> lvp <- 5
#> label("Peripheral volume of distribution (Vp)")
#> lq <- 0.1
#> label("Intercompartmental clearance (Q)")
#> propSd <- c(0, 0.5)
#> label("Proportional residual error (fraction)")
#> lkin <- 0.1
#> label("zero order response production(kin)")
#> lkout <- 0.1
#> label("first order rate response loss (kout)")
#> lEk <- 0.1
#> label("linear effect constant (Ek)")
#> effectSd <- c(0, 0.1)
#> label("additive error for effect")
#> uEk2 <- 0.1
#> label("untransformed quadratic slope (Ek2)")
#> })
#> model({
#> Ek2 <- uEk2
#> kin <- exp(lkin)
#> kout <- exp(lkout)
#> Ek <- exp(lEk)
#> cl <- exp(lcl)
#> vc <- exp(lvc)
#> vp <- exp(lvp)
#> q <- exp(lq)
#> kel <- cl/vc
#> k12 <- q/vc
#> k21 <- q/vp
#> d/dt(central) <- kel * central - k12 * central + k21 *
#> peripheral1
#> d/dt(peripheral1) <- k12 * central - k21 * peripheral1
#> Cc <- central/vc
#> Cc ~ prop(propSd)
#> R(0) <- kin/kout
#> d/dt(R) <- kin - kout * R * (1 + (Ek * Cc + Ek2 * Cc^2))
#> effect <- R
#> effect ~ add(effectSd)
#> })
#> }
readModelDb("PK_2cmt_no_depot") |>
addDirectLin() |>
convertQuad()
#>
#>
#> ── rxode2-based free-form 2-cmt ODE model ──────────────────────────────────────
#> ── Initalization: ──
#> Fixed Effects ($theta):
#> lcl lvc lvp lq propSd uEk effectSd uEk2
#> 1.0 3.0 5.0 0.1 0.5 0.1 0.1 0.1
#>
#> States ($state or $stateDf):
#> Compartment Number Compartment Name
#> 1 1 central
#> 2 2 peripheral1
#> ── Multiple Endpoint Model ($multipleEndpoint): ──
#> variable cmt dvid*
#> 1 Cc ~ … cmt='Cc' or cmt=3 dvid='Cc' or dvid=1
#> 2 effect ~ … cmt='effect' or cmt=4 dvid='effect' or dvid=2
#> * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#>
#> ── Model (Normalized Syntax): ──
#> function() {
#> ini({
#> lcl <- 1
#> label("Clearance (CL)")
#> lvc <- 3
#> label("Central volume of distribution (V)")
#> lvp <- 5
#> label("Peripheral volume of distribution (Vp)")
#> lq <- 0.1
#> label("Intercompartmental clearance (Q)")
#> propSd <- c(0, 0.5)
#> label("Proportional residual error (fraction)")
#> uEk <- 0.1
#> label("untransformed slope (Ek)")
#> effectSd <- c(0, 0.1)
#> label("additive error for effect")
#> uEk2 <- 0.1
#> label("untransformed quadratic slope (Ek2)")
#> })
#> model({
#> Ek2 <- uEk2
#> Ek <- uEk
#> cl <- exp(lcl)
#> vc <- exp(lvc)
#> vp <- exp(lvp)
#> q <- exp(lq)
#> kel <- cl/vc
#> k12 <- q/vc
#> k21 <- q/vp
#> d/dt(central) <- kel * central - k12 * central + k21 *
#> peripheral1
#> d/dt(peripheral1) <- k12 * central - k21 * peripheral1
#> Cc <- central/vc
#> Cc ~ prop(propSd)
#> effect <- Ek * Cc + Ek2 * Cc^2
#> effect ~ add(effectSd)
#> })
#> }
readModelDb("PK_2cmt_no_depot") |>
addEffectCmtLin() |>
convertQuad()
#>
#>
#> ── rxode2-based free-form 3-cmt ODE model ──────────────────────────────────────
#> ── Initalization: ──
#> Fixed Effects ($theta):
#> lcl lvc lvp lq propSd lke0 uEk effectSd
#> 1.0 3.0 5.0 0.1 0.5 0.1 0.1 0.1
#> uEk2
#> 0.1
#>
#> States ($state or $stateDf):
#> Compartment Number Compartment Name
#> 1 1 central
#> 2 2 peripheral1
#> 3 3 Ce
#> ── Multiple Endpoint Model ($multipleEndpoint): ──
#> variable cmt dvid*
#> 1 Cc ~ … cmt='Cc' or cmt=4 dvid='Cc' or dvid=1
#> 2 effect ~ … cmt='effect' or cmt=5 dvid='effect' or dvid=2
#> * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#>
#> ── Model (Normalized Syntax): ──
#> function() {
#> ini({
#> lcl <- 1
#> label("Clearance (CL)")
#> lvc <- 3
#> label("Central volume of distribution (V)")
#> lvp <- 5
#> label("Peripheral volume of distribution (Vp)")
#> lq <- 0.1
#> label("Intercompartmental clearance (Q)")
#> propSd <- c(0, 0.5)
#> label("Proportional residual error (fraction)")
#> lke0 <- 0.1
#> label("effect compartment rate (ke0)")
#> uEk <- 0.1
#> label("untransformed linear slope (Ek)")
#> effectSd <- c(0, 0.1)
#> label("additive error for effect")
#> uEk2 <- 0.1
#> label("untransformed quadratic slope (Ek2)")
#> })
#> model({
#> Ek2 <- uEk2
#> ke0 <- exp(lke0)
#> Ek <- uEk
#> cl <- exp(lcl)
#> vc <- exp(lvc)
#> vp <- exp(lvp)
#> q <- exp(lq)
#> kel <- cl/vc
#> k12 <- q/vc
#> k21 <- q/vp
#> d/dt(central) <- kel * central - k12 * central + k21 *
#> peripheral1
#> d/dt(peripheral1) <- k12 * central - k21 * peripheral1
#> Cc <- central/vc
#> Cc ~ prop(propSd)
#> d/dt(Ce) <- ke0 * (Cc - Ce)
#> effect <- Ek * Ce + Ek2 * Ce^2
#> effect ~ add(effectSd)
#> })
#> }