Pharmacokinetic Models

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Description

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

Usage

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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

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^{trans}≤ft[C_p(t)\otimes\exp(-k_{ep}t)\right],

where o is the convolution operator, and the so-called extended Kety model

C_t(t)=v_pC_p(t)+K^{trans}≤ft[C_p(t)\otimes\exp(-k_{ep}t)\right].

The arterial input function must be literature-based (with fixed parameters).

Value

Computed pharmacokinetic curve.

Author(s)

Brandon Whitcher, Volker Schmid

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.

See Also

dcemri.lm, dcemri.bayes, dcemri.spline

Examples

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data(buckley)
img <- array(t(breast$data)[,(1:60)*5], c(13,1,1,60))
time <- buckley$time.min[(1:60)*5]
mask <- array(rep(TRUE, 13), c(13,1,1))
fit.lm <- dcemri.lm(img, time, mask, aif="fritz.hansen")
curve.lm <- kineticModel(time, list("ktrans"=fit.lm$ktrans[3],
                         "kep"=fit.lm$kep[3], "vp"=fit.lm$vp[3]))
## Not run: curve.lm

plot(time, img[3,1,1,], xlab="time", ylab="conc")
lines(time, curve.lm)

fit.bayes <- dcemri.bayes(img, time, mask, aif="fritz.hansen")
curve.bayes <- kineticModel(time, list("ktrans"=fit.bayes$ktrans[3],
                            "kep"=fit.bayes$kep[3], "vp"=fit.bayes$vp[3]))
lines(time, curve.bayes, col="blue")
cbind(time, img[3,1,1,], curve.lm, curve.bayes)[20:30,]