The algorithms used for analysis of dynamic MRI data are detailed here. The following algorithms are covered:
The automatic AIF finder uses a two-stage process to find those pixels in
the input image(s) that have characteristics that are most like an
arterial input function.
peak intensity * initial slope / tPeak
Calculation of dynamic contrast-enhanced parameters follows the general approach
described in Tofts PS et al. "Estimating Kinetic Parameters from
Dynamic Contrast-Enhanced T1-weighted MRI of a Diffusible Tracer:
Standardized Quantities and Symbols" JMRI 10: 223-232
(1999). Refinements to the algorithms are taken from M.A. Horsfield and
B. Morgan "Algorithms for Calculation of Kinetic Parameters from
T1-Weighted Dynamic Contrast-Enhanced MRI". JMRI 20: 723-729 (2004).
All signal intensities are converted to [Gd] values by averaging
pre-contrast R1, and assuming that:
R1 = R1pre + ρ.[Gd]
In the standard Tofts model, the tissue [Gd], Ct(t) is related to the plasma [Gd],
Cp(t) by:
Ct(t) =
Ktrans∫0t Cp(τ)
exp(-Ktrans(t-τ) / ve) dτ
An alternative model ("Tofts with vp term") takes account of the contribution that the plasma
volume makes to the signal intensity in the tissue.
Cp(t) by:
Ct(t) =
Ktrans∫0t Cp(τ)
exp(-Ktrans(t-τ) / ve) dτ + Cp(t)vp
The iterative Levenburg-Marquardt method is used to perform the
deconvolution, solving these expressions for Ktrans,
ve and (optionally) vp. The solution that minimises the
summed squared difference between the measured tissue concentration/time
curve and the modelled tissue concentration/time according to the above
expressions, is obtained by iteratively making adjustments to the variable parameters.
The two-compartment exchange mode (2CXM) is that
described by Sourbron. A
bi-exponential residue function is deconvolved from the tissue response. From the parameters of
the bi-exponential form, the parameters Fp (flow), PS (permeability-surface area
product), ve and vp can be calculated.
Automatic AIF Finder
Stage 1
This makes a rapid sweep of all the pixels in the image
to identify those that have the largest signal intensity change. The
dynamic range in signal intensity over the whole time course is assessed.
The pixels are ranked in order of largest change,
and those pixels that show the largest change are retained after this
first sweep. The number of pixels retained is user-configurable via
the setting of the "No. of candidate pixels" in the dialog.
Stage 2
For each candidate pixel location, the signal intensity pre-contrast is averaged,
to find the baseline pre-contrast signal intensity. The pulse sequence
parameters and the relaxivity are then used to convert signal intensities
post-contrast to [Gd] values post-contrast.
A gamma-variate function is fitted to the post-contrast [Gd] time course
of each of the candidate pixels is examined. The characteristics of the
fitted gamma-variate function are evaluated to give a score to each of the
candidate pixels. The score is:
DCE-MRI