kineticModel: Pharmacokinetic Models

Description

Kinetic curves from single compartment models are computed from kinetic parameters.

Usage

kineticModel(time, par, model = "extended", aif = "fritz.hansen")

Arguments

time

is a vector of acquisition times (in minutes).

par

is a list of kinetic parameters; e.g., list("ktrans"=0.5,"kep"=1).

model

is a character string that identifies the type of compartmental model to be used. Acceptable models include: “weinmann” Tofts & Kermode AIF convolved with single compartment model “extended” (default) Weinmann model extended with additional vascular compartment, ...

aif

is a character string that identifies the type of arterial input function (AIF) to be used. Acceptable AIF models include: tofts.kermode, fritz.hansen

Value

Computed pharmacokinetic curve.

Details

Compartmental models are the solution to the modified general rate equation (Kety 1951). The specific parametric models considered here include the basic Kety model $C_{t} (t) = K^{t r a n s} [C_{p} (t) \otimes \exp (- k_{e p} t)],$ where $\otimes$ is the convolution operator, and the so-called extended Kety model $C_{t} (t) = v_{p} C_{p} (t) + K^{t r a n s} [C_{p} (t) \otimes \exp (- k_{e p} t)] .$ The arterial input function must be literature-based (with fixed parameters).

References

Fritz-Hansen, T., Rostrup, E., Larsson, H.B.W, Sondergaard, L., Ring, P. and Henriksen, O. (1993) Measurement of the arterial concentration of Gd-DTPA using MRI: A step toward quantitative perfusion imaging, Magnetic Resonance in Medicine, 36, 225-231.

Tofts, P.S., Brix, G, Buckley, D.L., Evelhoch, J.L., Henderson, E., Knopp, M.V., Larsson, H.B.W., Lee, T.-Y., Mayr, N.A., Parker, G.J.M., Port, R.E., Taylor, J. and Weiskoff, R. (1999) Estimating kinetic parameters from dynamic contrast-enhanced $T_{1}$ -weighted MRI of a diffusable tracer: Standardized quantities and symbols, Journal of Magnetic Resonance, 10, 223-232.

Tofts, P.S. and Kermode, A.G. (1984) Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts, Magnetic Resonance in Medicine, 17, 357-367.

Weinmann, H.J., Laniado, M. and Mutzel, W. (1984) Pharmacokinetics of Gd-DTPA/dimeglumine after intraveneous injection into healthy volunteers, Physiological Chemistry and Physics and Medical NMR, 16, 167-172.

Examples

Run this code

# NOT RUN {
data("buckley")
xi <- seq(5, 300, by=5)
img <- array(t(breast$data)[,xi], c(13,1,1,60))
mask <- array(TRUE, dim(img)[1:3])
time <- buckley$time.min[xi]

fit.lm <- dcemri.lm(img, time, mask, aif="fritz.hansen")
par.lm <- c("vp"=fit.lm$vp[3], "ktrans"=fit.lm$ktrans[3], "kep"=fit.lm$kep[3])
curve.lm <- kineticModel(time, par.lm)
plot(time, img[3,1,1,], xlab="time", ylab="contrast agent concentration")
lines(time, curve.lm, lwd=2, col=2)

fit.bayes <- dcemri.bayes(img, time, mask, aif="fritz.hansen")
par.bayes <- c("vp"=fit.bayes$vp[3], "ktrans"=fit.bayes$ktrans[3],
               "kep"=fit.bayes$kep[3])
curve.bayes <- kineticModel(time, par.bayes)
lines(time, curve.bayes, lwd=2, col=4)
legend("bottomright", c("Levenburg-Marquardt (extended/fritz.hansen)",
                        "Bayesian Estimation (extended/fritz-hansen)"),
       lwd=2, col=c(2,4))
cbind(time, img[3,,,], curve.lm, curve.bayes)[20:30,]
# }

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