Pharmacokinetic Modeling of Dynamic Contrast-Enhanced MRI Data

Maximum-a-posteriori (MAP) estimation for single compartment models is performed using literature-based or user-specified arterial input functions.

dcemri.map(conc, ...)

# S4 method for array
dcemri.map(
  conc,
  time,
  img.mask,
  model = "extended",
  aif = NULL,
  user = NULL,
  ab.ktrans = c(0, 1),
  ab.kep = ab.ktrans,
  ab.vp = c(1, 19),
  ab.tauepsilon = c(1, 1/1000),
  maxit = 5000,
  samples = FALSE,
  multicore = FALSE,
  verbose = 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 “orton.cos” Extended model using Orton's raised cosine AIF “kety.orton.cos” Kety 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) or `user` for the `orton.exp` model and `orton.exp` model; `user` for the `orton.cos` model and `orton.cos` model.
user	Vector of AIF parameters. For Tofts and Kermode: \(a_1\), \(m_1\), \(a_2\), \(m_2\); for Orton et al.: \(A_b\), \(\mu_b\), \(A_g\), \(\mu_g\).
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.
maxit	The maximum number of iterations for the optimization procedure.
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.

Value

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

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

Fractional occupancy by plasma.

sigma2

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

time

Acquisition times (for plotting purposes).

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

Details

Implements maximum a posteriori (MAP) estimation for the Bayesian model in Schmid et al. (2006).

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]

## MAP estimation with extended Kety model and Fritz-Hansen default AIF
fit.map.vp <- dcemri.map(img, time, mask, aif="fritz.hansen")
## Nonlinear regression with extended Kety model and Fritz-Hansen default AIF
fit.lm.vp <- dcemri.lm(img, time, mask, aif="fritz.hansen")

plot(breast$ktrans, fit.map.vp$ktrans, xlim=c(0,1), ylim=c(0,1),
     xlab=expression(paste("True ", K^{trans})),
     ylab=expression(paste("Estimated ", K^{trans})))
points(breast$ktrans, fit.lm.vp$ktrans, pch=3)
abline(0, 1, lwd=2, col=2)
legend("bottomright", c("MAP Estimation (fritz.hansen)",
                        "Levenburg-Marquardt (fritz.hansen)"), pch=c(1,3))


## MAP estimation with Kety model and Fritz-Hansen default AIF
fit.map <- dcemri.map(img, time, mask, model="weinmann", aif="fritz.hansen")
## Nonlinear regression with Kety model and Fritz-Hansen default AIF
fit.lm <- dcemri.lm(img, time, mask, model="weinmann", aif="fritz.hansen")

cbind(breast$kep, fit.lm$kep[,,1], fit.lm.vp$kep[,,1], fit.map$kep[,,1],
      fit.map.vp$kep[,,1])
#>             [,1]      [,2]      [,3]      [,4]      [,5]
#>  [1,] 0.32355345 0.2348731 0.2348731 0.2356731 0.2356962
#>  [2,] 0.48521013 0.4167250 0.4167250 0.4170607 0.4170742
#>  [3,] 0.55671514 0.4979371 0.4979372 0.4981651 0.4981680
#>  [4,] 0.59642650 0.5438920 0.5438921 0.5440587 0.5440795
#>  [5,] 0.62161139 0.5734775 0.5734776 0.5736243 0.5736333
#>  [6,] 0.02202843 2.2508666 2.2509156 2.2398360 2.2396892
#>  [7,] 0.32664921 0.3567631 0.3567634 0.3572666 0.3572627
#>  [8,] 0.73047326 0.6098186 0.6098180 0.6101053 0.6101285
#>  [9,] 0.86170469 0.6946350 0.6946319 0.6948689 0.6949021
#> [10,] 0.55671514 0.4294708 0.4294700 0.4301810 0.4302156
#> [11,] 0.55671514 0.4650526 0.4650528 0.4653740 0.4653682
#> [12,] 0.55671514 0.5278610 0.5278610 0.5281173 0.5281034
#> [13,] 0.55671514 0.5540183 0.5540182 0.5543170 0.5543132
cbind(breast$ktrans, fit.lm$ktrans[,,1], fit.lm.vp$ktrans[,,1],
      fit.map$ktrans[,,1], fit.map.vp$ktrans[,,1])
#>              [,1]      [,2]      [,3]      [,4]      [,5]
#>  [1,] 0.145599052 0.3817053 0.3817053 0.3822287 0.3822429
#>  [2,] 0.218344559 0.5947945 0.5947945 0.5950718 0.5950952
#>  [3,] 0.250521815 0.6951413 0.6951414 0.6953527 0.6953499
#>  [4,] 0.268391926 0.7530097 0.7530098 0.7531700 0.7531903
#>  [5,] 0.279725126 0.7906144 0.7906145 0.7907517 0.7907595
#>  [6,] 0.009912791 0.5241719 0.5241820 0.5221588 0.5221473
#>  [7,] 0.146992146 0.4680227 0.4680229 0.4683815 0.4683723
#>  [8,] 0.328712966 0.8593235 0.8593229 0.8596005 0.8596348
#>  [9,] 0.387767110 0.9811911 0.9811879 0.9814133 0.9814754
#> [10,] 0.250521815 0.5521834 0.5521828 0.5527387 0.5527606
#> [11,] 0.250521815 0.6226405 0.6226407 0.6229096 0.6229033
#> [12,] 0.250521815 0.7692656 0.7692656 0.7695114 0.7694966
#> [13,] 0.250521815 0.8430926 0.8430926 0.8434068 0.8433965