Dynamic MRI Analysis

Dynamic MRI Analysis - Algorithm

The algorithms used for analysis of dynamic MRI data are detailed here. The following algorithms are covered:

Automatic identification of the Arterial Input Function (AIF) for brain perfusion.
Calculation of Brain Perfusion parameters (CBF, CBV, MTT, TTP).
Calculation of DCE-MRI parameters (K^trans, v_e, v_p).

Automatic AIF Finder

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.

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:

peak intensity * initial slope / tPeak

Thus, the scoring system favours pixels where there is a large change in signal intensity, with a rapid change immediately after the bolus injection, and with an early peak in intensity. The top-scoring pixels are retained as those pixels that are used for the arterial input function. The number of pixels retained after this second stage is user-configurable via the setting of the "No. of pixels" in the dialog.

After identification, as above, the [Gd]/time course of each of these AIF pixels is averaged to form the final AIF.

Deconvolution of the arterial input function from the tissue response function follows the method in Ostergaard L. et al. "High Resolution Measurement of Cerebral Blood Flow Using Intravascular Tracer Bolus Passages, I: Mathematical Approach and Statistical Analysis". Magn. Reson. Med. 36:715-728 (1996). The method is summarised below, and is repeated for every spatial pixel location in the image. First, the AIF matrix, A, is formed following Eq. [14] of Ostergaard 1996. Singular value decomposition is then used to construct A^-1 as V.W.U^T. The diagonal elements of W below a user-set threshold percentage (the SVD threshold) of the maximum value are set to zero.

The pre-contrast signal intensity for a pixel is averaged, and this average is used, in combination with the pulse sequence parameters and relaxivity, to calculate the post-contrast [Gd] time course for the tissue in that pixel.
The residue function, R(t), for the pixel is found from Eq. [18] of Ostergaard 1996.
The areas under the AIF curve and the tissue response curves are found using the trapezium rule, and the cerebral blood volume (CBV) is calculated as:
CBV=∫[Gd]_tissue dt / ∫[Gd]_artery dt
The tissue mean transit time (MTT) is found from the residue function for that tissue:
MTT=Σ (R_i-1 - R_i). (i-0.5).Δt / max(R))
where Δt is the time between images; and max(R) is the maximum value of the residue function. (R_i-1 - R_i) represents the fraction of blood that has a transit time of (i-0.5).Δt
Finally, the cerebral blood flow (CBV) is calculated as:
CBF = CBV / MTT
The time-to-peak (TTP) is simply computed as the time at which the maximum change in concentration occurs, minus the time of arrival in the contrast in the feeding artery (set by the user).

DCE-MRI

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]

where ρ is the user-specified relaxivity that may be different in the blood and the tissue; and R₁pre is the average pre-contrast R₁.

In the standard Tofts model, the tissue [Gd], C_t(t) is related to the plasma [Gd], C_p(t) by:

C_t(t) = K^trans∫₀^t C_p(τ) exp(-K^trans(t-τ) / v_e) dτ

where v_e is the extra-vascular extra-cellular space volume fraction. This model neglects any contribution to the signal intensity of the blood vessels inside the tissue of interest.

An alternative model ("Tofts with vp term") takes account of the contribution that the plasma volume makes to the signal intensity in the tissue. C_p(t) by:

C_t(t) = K^trans∫₀^t C_p(τ) exp(-K^trans(t-τ) / v_e) dτ + C_p(t)v_p

where v_p is the plasma volume fraction.

The iterative Levenburg-Marquardt method is used to perform the deconvolution, solving these expressions for K^trans, v_e and (optionally) v_p. 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 F_p (flow), PS (permeability-surface area product), v_e and v_p can be calculated.

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