dcemriS4 (version 0.20.1)

dcemri.lm: 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

## S3 method for class 'array':
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: [object Object],[object Object],[object Object],[object Object]

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

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

user

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

verbose

is a logical variable (default = FALSE) that allows text-based feedback during execution of the function.

...

Additional parameters to the function.

Value

• Parameter estimates and their standard errors are provided for the masked region of the multidimensional array. All multi-dimensional arrays are provided in nifti format.

  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).

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 $$C_t(t)=K^{trans}\left[C_p(t)\otimes\exp(-k_{ep}t)\right],$$ where $\otimes$ is the convoluation operator, and the so-called extended Kety model $$C_t(t)=v_pC_p(t)+K^{trans}\left[C_p(t)\otimes\exp(-k_{ep}t)\right].$$ 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.

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

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])