NolteWeisser_AluminiumKinetics

The compartmental model for aluminium kinetics in human body of Nolte et al [1,2], as reparameterized by Weisser et al [3], implemented under mrgsolve and R.

Remarks

The model file contains the mean parameter set — as presented in the supplementary appendix of [3] — so this is used in calculations by default. However, it can be changed in R (without changing the model file) as this is only a specification for defaults, and can be overridden, see Examples.

I tried to double-check everything, but no guarantee of course. I welcome every suggestion or correction!

Examples

Necessary libraries:

library( mrgsolve )
library( lattice )

We first load the model:

mod <- mread( "NolteWeisser" )

## Compiling NolteWeisser ... done.

Reproducing retentions using the mean parameter set

Let's first simulate what happens for oral dosing, using the mean parameter set (replicating Figure 4b of the supplementary appendix of [3]):

e <- ev( time = 0, evid = 1, amt = 1, cmt = "STO" )
out <- mrgsim( ev( mod, e ), end = 10000, delta = 0.1 )

xyplot( PLASMA*100 + U*100 + LIV*100 + MUS*100 + BON*100 ~ time, data = out@data[ -1, ], type = "l",
        scale = list( log = TRUE ),
        auto.key = list( text = c( "Plasma", "Urine", "Liver", "Muscle", "Bone" ),
                         lines = TRUE, points = FALSE, columns = 2 ),
        xlab = "Time [h]", ylab = "Aluminium [% ID]" )

Iv dosing, using the mean parameter set (replicating Figure 4a of the supplementary appendix of [3]):

e <- ev( time = 0, evid = 1, amt = 1, cmt = "PC" )
out <- mrgsim( ev( mod, e ), end = 10000, delta = 0.1 )

xyplot( PLASMA*100 + U*100 + LIV*100 + MUS*100 + BON*100 + FAE*100 ~ time, data = out@data[ -1, ],
        type = "l", scale = list( log = TRUE ),
        auto.key = list( text = c( "Plasma", "Urine", "Liver", "Muscle", "Bone", "Faeces" ),
                         lines = TRUE, points = FALSE, columns = 2 ),
        xlab = "Time [h]", ylab = "Aluminium [% ID]" )

Reproducing the retention function of Priest (2004) and updating the parameters

In his influential publication [4], Priest gave the following long-term (overall) retention function: R_t = 0.293e^−0.595t + 0.114e^−0.172t + 0.065e^−0.000401t, where t ≥ 1 is measured in days. (Of note, two out of the three half-lives presented in the original paper after this retention function are erroneous due to minor numerical mistakes, as confirmed by Priest in personal communication (14-Mar-2013): the first should be 1.16 days instead of 1.4 and the second should be 4.03 days instead of 40.)

Let's confront it with the predictions from our model:

out <- mrgsim( ev( mod, e ), end = 20*24, delta = 0.1 )
out@data$RETPRIEST <- 0.293*exp( -0.595*out@data$time/24 ) + 0.114*exp( -0.172*out@data$time/24 ) +
  0.065*exp( -0.000401*out@data$time/24 )
xyplot( RETENTION + RETPRIEST ~ time, data = out@data[ -1, ], type = "l", xlab = "Time [h]",
        ylab = "Aluminium [% ID]", xlim = c( 24, 20*24 ),
        auto.key = list( text = c( "Nolte (mean parameters)", "Priest (2004)" ),
                         columns = 2, lines = TRUE, points = FALSE ) )

The difference is substantial, a major reason of which is the fact the Priest used a single subject. Luckily, the parameters estimated from this subject are available (column labelled 'Nolte' in Table 1 of the Appendix of [3]), so we can assess the model using these, instead of the mean values.

This will also demonstrate how to update the parameters within the analysis (i.e. with the model file left untouched):

modNolte <- param( mod, KPTPC = 0.9091, KPCPT = 14.29, KPCIC = 20.00, KICPC = 5.000, KICIT = 17.40,
                   KITIC = 3.636, KLIVIN = 0.6300, KLIVOUT = 0.0550, KMUSIN = 0.0417,
                   KMUSOUT = 1.117e-03, KBONIN = 0.3750, KBONOUT = 7.000e-05, KU = 7.143,
                   KTD = 0.01667, KSD = 4.000, KDR = 0.2500, KRS = 0.02778 )
outNolte <- mrgsim( ev( modNolte, e ), end = 20*24, delta = 0.1 )
out@data$RETNOLTE <- outNolte@data$RETENTION
xyplot( RETENTION + RETPRIEST + RETNOLTE ~ time, data = out@data[ -1, ], type = "l", xlab = "Time [h]",
        ylab = "Aluminium [% ID]", xlim = c( 24, 20*24 ),
        auto.key = list( text = c( "Nolte (mean parameters)", "Priest (2004)",
                                   "Nolte (Priest's parameters)" ),
                         columns = 2, lines = TRUE, points = FALSE ) )

Acknowledgement

I really appreciate the help of Karin Weisser for answering my questions that came up during this reimplementation of the model.

References

1. Nolte E, Beck E, Winklhofer C, Steinhausen C. Compartmental model for aluminium biokinetics. Hum Exp Toxicol. 2001 Feb;20(2):111-7.
2. Steinhausen C, Kislinger G, Winklhofer C, Beck E, Hohl C, Nolte E, Ittel TH, Alvarez-Brückmann MJ. Investigation of the aluminium biokinetics in humans: a 26Al tracer study. Food Chem Toxicol. 2004 Mar;42(3):363-71.
3. Weisser K, Stübler S, Matheis W, Huisinga W. Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products. Regul Toxicol Pharmacol. 2017 Aug;88:310-321.
4. Priest ND. The biological behaviour and bioavailability of aluminium in man, with special reference to studies employing aluminium-26 as a tracer: review and study update. J Environ Monit. 2004 May;6(5):375-403.