Pharmacokinetic Models for Dynamic Contrast-Enhanced MRI Data

Description

Parameter estimation for single compartment models is performed using literature-based or user-specified arterial input functions. The Levenburg-Marquardt algorithm does the heavy lifting.

Usage

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dcemri.lm(conc, time, img.mask, model="extended", aif=NULL,
          nprint=0, user=NULL, verbose=FALSE, ...)

Arguments

conc

is a multidimensional (1D-4D) array of contrast agent concentrations. The last dimension is assumed to be temporal, while the previous dimensions are assued to be spatial.

time

is a vector of acquisition times (in minutes) relative to injection of the contrast agent. Negative values should be used prior to the injection.

img.mask

is a (logical) multidimensional array that identifies the voxels to be analyzed. Has to have same dimension as conc minus temporal dimension.

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”Weinmann model extended with additional vascular compartment (default)

  • “orton.exp”Extended model using Orton's exponential AIF

  • “orton.cos”Extended model using Orton's raised cosine AIF

aif

is a character string that identifies the parameters of the type of arterial input function (AIF) used with the above model. Acceptable values are: tofts.kermode (default) or fritz.hansen for the weinmann and extended models; orton.exp (default) and user for the orton.exp model; orton.cos (default) and user for the orton.cos model. All AIF models set the parametric form and parameter values – except user where a set of user-defined parameter values are allowed.

nprint

is an integer, that enables controlled printing of iterates if it is positive. In this case, estimates of par are printed at the beginning of the first iteration and every nprint iterations thereafter and immediately prior to return. If nprint is not positive, no tracing information on the progress of the optimization is produced.

user

is a list with the following paramters required: D, AB, muB, AG, muG.

verbose

.

...

Additional parameters to the function.

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 \otimes is the convoluation 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 either literature-based (with fixed parameters) or the exponential AIF from Orton et al. (2008) with user-defined parameters.

Value

Parameter estimates and their standard errors are provided for the masked region of the multidimensional array. They include

ktrans

Transfer rate from plasma to the extracellular, extravascular space (EES).

kep

Rate parameter for transport from the EES to plasma.

ve

Fractional occupancy by EES (the ratio between ktrans and kep).

vp

Fractional occupancy by plasma.

ktranserror

Standard error for ktrans.

keperror

Standard error for kep.

vperror

Standard error for vp.

The residual sum-of-squares is also provided, along with the original acquisition times (for plotting purposes).

Author(s)

Brandon Whitcher, Volker Schmid

References

Ahearn, T.S., Staff, R.T., Redpath, T.W. and Semple, S.I.K. (2005) The use of the Levenburg-Marquardt curve-fitting algorithm in pharmacokinetic modelling of DCE-MRI data, Physics in Medicine and Biology, 50, N85-N92.

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.

Orton, M.R., Collins, D.J., Walker-Samuel, S., d'Arcy, J.A., Hawkes, D.J., Atkinson, D. and Leach, M.O. (2007) Bayesian estimation of pharmacokinetic parameters for DCE-MRI with a robust treatment of enhancement onset time, Physics in Medicine and Biology 52, 2393-2408.

Orton, M.R., d'Arcy, J.A., Walker-Samuel, S., Hawkes, D.J., Atkinson, D., Collins, D.J. and Leach, M.O. (2008) Computationally efficient vascular input function models for quantitative kinetic modelling using DCE-MRI, Physics in Medicine and Biology 53, 1225-1239.

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.bayes, dcemri.map, dcemri.spline, nls.lm

Examples

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data("buckley")

## Set up breast data for dcemri
xi <- seq(5, 300, by=5)
img <- array(t(breast$data)[,xi], c(13,1,1,60))
time <- buckley$time.min[xi]
aif <- buckley$input[xi]
mask <- array(TRUE, dim(img)[1:3])

## Generate AIF params using the orton.exp function from Buckley's AIF
aifparams <- orton.exp.lm(time, aif)
fit <- dcemri.lm(img, time, mask, model="orton.exp",
                 aif="user", user=aifparams)

## Scatterplot comparing true and estimated Ktrans values
plot(breast$ktrans, fit$ktrans, xlim=c(0,0.75), ylim=c(0,0.75),
     xlab=expression(paste("True ", K^{trans})),
     ylab=expression(paste("Estimated ", K^{trans})))
abline(0, 1, lwd=1.5, col="red")
cbind(breast$ktrans, fit$ktrans[,,1])