Arterial Input Functions

Parametric models for arterial input functions (AIFs) that are compatible with single compartment models for dynamic contrast-enhanced MRI (DCE-MRI).

aif.orton.exp(tt, AB, muB, AG, muG)

orton.exp.lm(
  tt,
  aif,
  guess = c(log(100), log(10), log(1), log(0.1)),
  nprint = 0
)

model.orton.exp(tt, aparams, kparams)

Arguments

tt	is a vector of acquisition times (in minutes) relative to injection of the contrast agent. Negative values should be used prior to the injection.
AB, muB, AG, muG	are parameters of the double exponential function that describe the AIF.
aif	is the vector of observed contrast agent concentrations (data) used to estimate the parametric model.
guess	Initial parameter values for the nonlinear optimization.
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.
aparams	is the vector of parameters (\(A_B\), \(\mu_B\), \(A_G\), \(\mu_G\)) associated with the AIF.
kparams	is the vector of parameters (\(v_p\), \(K^{trans}\), \(k_{ep}\)) associated with the “extended Kety model” for contrast agent concentration.

Value

aif.orton.exp and model.orton.exp return the AIF associated with the pre-specified parameter values.

orton.exp.lm returns a list structure with

The amplitude of the first exponential function.

muB

The decay rate of the first exponential function.

The amplitude of the second exponential function.

muG

The decay rate of the second exponential function.

info

The success (or failure) code from the Levenburg-Marquardt algorithm nls.lm.

message

The text message associated with the info paramters.

Details

aif.orton.exp displays the exponential AIF from Orton et al. (2008) for a known set of AIF parameter values. model.orton.exp displays the exponential AIF from Orton et al. (2008) for a known set of AIF and compartmental model parameter values. orton.exp.lm estimates the AIF parameters, using nonlinear optimization, using a vector of observed contrast agent concentrations.

References

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.

Author

Brandon Whitcher bwhitcher@gmail.com

Examples


data("buckley")
## Generate AIF params using the orton.exp function from Buckley's AIF
xi <- seq(5, 300, by=5)
time <- buckley$time.min[xi]
aif <- buckley$input[xi]
aifparams <- orton.exp.lm(time, aif)
aifparams$D <- 1 
unlist(aifparams[1:4])
#>          AB         muB          AG         muG 
#> 37.14845965  3.89506197  1.51615822 -0.01066004 

aoe <- aif.orton.exp(time, aifparams$AB, aifparams$muB, aifparams$AG,
                     aifparams$muG)
with(buckley, plot(time.min, input, type="l", lwd=2))
lines(time, aoe, lwd=2, col=2)
legend("right", c("Buckley's AIF", "Our approximation"), lty=1,
       lwd=2, col=1:2)

cbind(time, aif, aoe)[1:10,]
#>             time       aif      aoe
#>  [1,] 0.06666667 0.9126331 2.258002
#>  [2,] 0.15000000 2.8075149 3.779942
#>  [3,] 0.23333333 4.9157838 4.402032
#>  [4,] 0.31666667 5.9422838 4.506284
#>  [5,] 0.40000000 4.9813873 4.332074
#>  [6,] 0.48333333 4.0168210 4.025862
#>  [7,] 0.56666667 3.3262760 3.674312
#>  [8,] 0.65000000 2.8732966 3.326186
#>  [9,] 0.73333333 2.5805205 3.006701
#> [10,] 0.81666667 2.3837840 2.726828