dcemriS4 (version 0.55)

dcemri.bayes: Bayesian Methods for Pharmacokinetic Modeling of Dynamic Contrast-Enhanced MRI Data

Description

Bayesian analysis of contrast agent concentration time curves from DCE-MRI.

Usage

dcemri.bayes(conc, ...)
# S4 method for array
dcemri.bayes(conc, time, img.mask, model = "extended",
  aif = NULL, user = NULL, nriters = 3000, thin = 3, burnin = 1000,
  tune = 267, ab.ktrans = c(0, 1), ab.kep = ab.ktrans, ab.vp = c(1, 19),
  ab.tauepsilon = c(1, 1/1000), samples = FALSE, multicore = FALSE,
  verbose = FALSE, dic = FALSE, ...)

Arguments

conc

Matrix or array of concentration time series (last dimension must be time).

...

Additional parameters to the function.

time

Time in minutes.

img.mask

Mask matrix or array. Voxels with mask=0 will be excluded.

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

"kety.orton.exp"

Kety model using Orton's exponential 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) or user for the orton.exp and kety.orton.exp model.

user

Vector of AIF parameters. For Tofts and Kermode: \(a_1\), \(m_1\), \(a_2\), \(m_2\); for Orton et al.: \(A_b\), \(\mu_b\), \(A_g\), \(\mu_g\).

nriters

Total number of iterations.

thin

Thining factor.

burnin

Number of iterations for burn-in.

tune

Number for iterations for tuning. The algorithm will be tuned to an acceptance rate between 0.3 and 0.6.

ab.ktrans

Mean and variance parameter for Gaussian prior on \(\log(K^{trans})\).

ab.kep

Mean and variance parameter for Gaussian prior on \(\log(k_{ep})\).

ab.vp

Hyper-prior parameters for the Beta prior on \(v_p\).

ab.tauepsilon

Hyper-prior parameters for observation error Gamma prior.

samples

If TRUE output includes samples drawn from the posterior distribution for all parameters.

multicore

If TRUE algorithm is parallelized using multicore.

verbose

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

dic

If TRUE, the deviance information criterion (DIC) and effective number of parameters (pD) will be computed. If "samples = TRUE", then samples of the DIC and pD will be given.

vp

Fractional occupancy in the plasma space.

Value

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

ktrans

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

ktranserror

Error on \(K^{trans}\).

kep

Rate parameter for transport from the EES to plasma.

keperror

Error on \(k_{ep}\).

ve

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

vperror

Error on \(v_e\).

vp

Fractional occupancy by plasma.

sigma2

The residual sum-of-squares from the model fit.

time

Acquisition times (for plotting purposes).

DIC

Deviance information criterion.

DIC.map

Contribution to DIC per voxel.

pD

Effective number of parameters.

pD.map

Constribution to pD per voxel.

Note, not all parameters are available under all models choices.

Details

See Schmid et al. (2006) for details.

References

Schmid, V., Whitcher, B., Padhani, A.R., Taylor, N.J. and Yang, G.-Z. (2006) Bayesian methods for pharmacokinetic models in dynamic contrast-enhanced magnetic resonance imaging, IEEE Transactions on Medical Imaging, 25 (12), 1627-1636.

See Also

dcemri.lm, dcemri.map, dcemri.spline

Examples

# 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]

## Bayesian estimation with Fritz-Hansen default AIF
fit.bayes <- dcemri.bayes(img, time, mask, aif="fritz.hansen",
                         nriters=1000, thin=2, burnin=200)

## Bayesian estimation with "orton.exp" function fit to Buckley's AIF
aif <- buckley$input[xi]
aifparams <- orton.exp.lm(time, aif)
aifparams$D <- 1
fit.bayes.aif <- dcemri.bayes(img, time, mask, model="orton.exp",
                              aif="user", user=aifparams,
                              nriters=1000, thin=2, burnin=200)

plot(breast$ktrans, fit.bayes$ktrans, xlim=c(0,1), ylim=c(0,1),
     xlab=expression(paste("True ", K^{trans})),
     ylab=expression(paste("Estimated ", K^{trans}, " (Bayesian)")))
points(breast$ktrans, fit.bayes.aif$ktrans, pch=2)
abline(0, 1, lwd=2, col=2)
legend("right", c("extended/fritz.hansen","orton.exp/user"), pch=1:2)

fit.lm <- dcemri.lm(img, time, mask, aif="fritz.hansen")
fit.lm.aif <- dcemri.lm(img, time, mask, model="orton.exp", aif="user",
                        user=aifparams)

plot(breast$ktrans, fit.bayes$ktrans, xlim=c(0,1), ylim=c(0,1),
     xlab=expression(paste("True ", K^{trans})),
     ylab=expression(paste("Estimated ", K^{trans})))
points(breast$ktrans, fit.bayes.aif$ktrans, pch=2)
points(breast$ktrans, fit.lm$ktrans, pch=3)
points(breast$ktrans, fit.lm.aif$ktrans, pch=4)
abline(0, 1, lwd=2, col=2)
legend("bottomright", c("Bayesian Estimation (fritz-hansen)",
                        "Bayesian Estimation (orton.exp)",
                        "Levenburg-Marquardt (weinmann/fritz.hansen)",
                        "Levenburg-Marquardt (orton.exp/user)"), pch=1:4)
# }