Michael Germuska^{1}, Thomas Okell^{2}, and Richard Wise^{1}

A blood transit transit heterogeneity (TTH) mapping method is presented based on the regularised fitting of multi-TI pCASL data. The method applies a gamma variate dispersion model to account for upstream flow dispersion and tissue transit heterogeneity. The approach is shown to have sufficient sensitivity to distinguish a range of TTH times in gray matter and results are comparable with previous ROI based approaches. The mapping of TTH has the potential to be a sensitive marker for cerebrovascular dysfunction.

Introduction

The standard ASL model does not consider the effects of dispersion of the arterial input function (AIF) or flow heterogeneity in the tissue residue function in the analysis. It assumes an ideal boxcar function is produced during tagging, which is maintained until the tagged blood exchanges with the tissue. However, the AIF may be dispersed due to non-plug like flow patterns in the feeding arteries, and the multiple arteriole/capillary pathways the blood traverses before exchanging with the tissue will influence the tissue residue function. An increase in microvascular transit time heterogeneity is theorised to restrict delivery of diffusion-limited substances (such as oxygen) to the tissue
The
kinetics of the ASL signal can be modelled by the convolution of an input
function, c(t), with the tissue residue function, r(t), multiplied by the
magnetization relaxation function, m(t). ^{4} Dispersion of the input
function and flow heterogeneity in the residue function is included via convolution with a gamma variate function. Thus, the ASL kinetic model including
dispersion can be described via equation 1.

$$\triangle M(t)=2M_{0b}f\left\{\left(\frac1{\beta^\alpha\Gamma(\alpha)}t^{\alpha-1}e^\frac{-t}\beta\right)\ast c(t)\ast r(t)m(t)\right\}$$

Where M_{0b} is the equilibrium
magnetization of arterial blood, f is perfusion, TTH = β/√α,
the mean transit time (MTT) = αβ,
and c(t), r(t) and m(t) take their normal definitions. Data fitting was
performed in MATLAB (Mathworks, MA) via non-linear least squares fitting with
regularisation parameters applied to MTT and TTH^{2}/MTT^{2}, and Gaussian smoothing applied to the perfusion data (FWHM=4.5mm). Additionally, FHWM 3.5mm smoothing was applied to the TTH maps for display. The magnitude of the regularisation parameters were chosen via a digital phantom simulation with the tSNR matched to in-vivo data (gray matter tSNR was found to be approximately 3.5 after Gaussian smoothing). ASL data was acquired from 5 volunteers (4 male, age = 35.6 ± 8.5 years). Imaging parameters: 3T Prisma scanner (Siemens, Erlangen), pCASL acquisition scheme with 2D EPI readout, pre-saturation, background suppression ^{5} and variable TR (minimised for each PLD). GRAPPA acceleration factor 2, 7/8 partial Fourier, 64x64 matrix, 220mm FOV, 6mm slice thickness, 35% slice gap, 16 slices, 4.8cm/s venc through-slice vascular crushing, TE = 17 ms. Eight post-labelling delays were acquired (PLDs = 150,400,650,900,1150,1400,1900,2400)
with 10
repeats for a total acquisition time of 9:05 minutes.

Results and Discussion

Using the
chosen PLD times and regularisation parameters, digital phantom simulations
predict that minimally biased estimates of TTH can be acquired with a mean
error of 0.14 seconds (for MTT times from 1 to 1.8 seconds and TTH from 0.1 to 0.7 seconds), see figure 1A for a summary of simulation results. Fits to in-vivo
voxels (figures 1B and 1C) demonstrate how the proposed kinetic model is
identical to the standard model for minimal TTH, but is able to better capture
the signal dynamics for increased dispersion. Mean gray matter values from the
5 healthy volunteers were; CBF 41.4 ± 4.2 ml/100g/min, MTT 1.41 ± 0.08 seconds,
and TTH 0.25 ± 0.03 seconds.
Figures 2-4
show example parameter maps from an individual subject. TTH is generally
small with little variation.
The small amount of transit heterogeneity detected is consistent with previous
studies of ASL dispersion in healthy volunteers ^{6-8} and
the
minimal microvascular
heterogeneity found in normal tissue ^{1}.

Conclusion

Voxel-wise measurement of transit time heterogeneity has the potential to be a sensitive marker for cerebrovascular dysfunction. We have presented a regularised fitting approach that allows TTH maps to be made from standard multi-TI pCASL imaging. Simulations suggest the method is robust and sensitive to vascular changes over a reasonable range of transit times. Optimisation of the acquisition scheme for the purpose of mapping TTH could provide improvement in the sensitivity of the method, while the inclusion of locally measured AIFs could help separate upstream dispersion effects from microvascular transit heterogeneity.We would like to thank Fabrizio Fasano (Siemens Healthineers) for assistance with pulse sequence programming and the Wellcome Trust for supporting this work: Wellcome Trust Strategic Award, ‘Multi-scale and multi-modal assessment of coupling in the healthy and diseased brain’, grant reference 104943/Z/14/Z.

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A: Digital phantom simulation for a range of MTT and TTH values. Axes show modelled values, colourscale represents TTH estimates. B and C: In-vivo fits in individual voxels with minimal TTH (B) and moderate TTH (C).

Example transit time
heterogeneity maps acquired from an individual subject.

Example mean transit time maps from an individual subject (corresponding subject to TTH maps in figure 2).

Example cerebral blood flow (CBF ml/100g/min) maps from an individual subject (corresponding subject to TTH maps in figure 2).