Bayesian Methods for Pharmacokinetic Modeling of Dynamic Contrast-Enhanced MRI Data

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

dcemri.bayes(conc, ...)

# S4 method for array
dcemri.bayes(
  conc,
  time,
  img.mask,
  model = "extended",
  spatial = 0,
  aif = NULL,
  user = NULL,
  nriters = 3000,
  thin = 3,
  burnin = 1000,
  tune = 267,
  ab.ktrans = if (spatial == 0) c(0, 1) else {     c(1e-04, 1e-04) },
  ab.kep = ab.ktrans,
  ab.vp = c(1, 19),
  ab.tauepsilon = c(1, 1/1000),
  samples = FALSE,
  parallel = 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
spatial	is an integer specifying spatial smoothing of kinetic parameters 0 no spatial smoothing, fit voxelwise 2 2D smoothing, fit slices separately 3 3D smoothing; Warning: this is computationally very expensive
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.
parallel	If `TRUE` algorithm is parallelized using parallel.
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 \(k_{ep}\).

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

vperror

Error on \(v_e\).

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.

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.

Author

Volker Schmid volkerschmid@users.sourceforge.net

Examples


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)