Magnetisation transfer (MT) has been found to contribute to parameter estimation bias in sequences used in the two-pool relaxometry technique, mcDESPOT. Recent work shows that using controlled saturation magnetisation transfer (CSMT) RF-pulses, a two-pool system (free- and bound-pools) can behave as a single pool with modified equilibrium magnetisation and longitudinal relaxation rate. Here, we investigate the use of CSMT to model MT-effects in a three-pool system (exchange + MT) and show that under these conditions, signal behaves as a two-pool system and matches a mcDESPOT model but characterised by different parameters than those originally assumed.
Multicomponent DESPOT (mcDESPOT) models tissue response using a system of two or more exchanging ‘free’ (i.e. MR-visible) magnetisation components.1 In its two-pool form, mcDESPOT has been used for characterisation of white matter (WM), with the two components usually identified as intra/extracellular water (slow-relaxing) and myelin-water (fast-relaxing). The myelin water fraction (MWF) calculated from these estimates has been shown to consistently overestimate the value derived from multiecho CPMG methods.2,3 WM is known to yield a strong magnetisation transfer (MT) effect that is not ordinarily modelled in mcDESPOT; other work has suggested this to be a source for MWF overestimation.4,5
The MT-effect may be modelled by the addition of a ‘bound’ (i.e. macromolecular) pool of magnetisation.5,6 RF-pulses rotate ‘free’ magnetisation, but saturate ‘bound’ magnetisation according to applied RF-power W (Equation 1), where B1,rms is RMS pulse amplitude over the whole sequence and G is bound-pool absorption factor.
W=πG(Δ)γ2B21,rms
The recently proposed controlled saturation magnetisation transfer (CSMT) approach has been shown to allow a simple two-pool MT-system (i.e. one free-pool, one bound-pool) to behave as a single free-pool during DESPOT-style relaxometry by keeping W constant over all acquisitions, irrespective of the applied flip angle (FA).7
In this work, we aim to extend this approach to consider a system with two free components, of the type typically modelled in mcDESPOT. We consider how a ‘ground-truth’ scenario with three pools (i.e. two free-pools and one bound-pool) will produce parameter estimation bias when fitted using a two-pool model that does not include any bound component (hereafter referred to as the ‘mcDESPOT’ model).
Figure 1 illustrates our three-pool configuration, including a bound-pool to account for MT-effects.5 We use the Bloch-McConnell equations to model the evolution of magnetisation for such a system and calculate steady-state solutions independently for SPGR and bSSFP. We then fit a mcDESPOT model to three-pool (ground-truth) signals, simulated using either controlled (i.e. same W regardless of FA) or uncontrolled saturation methods. Least-square criteria, using fmincon in Matlab2016b, were applied.
Comparison of the differential equations governing mcDESPOT and three-pool models suggests that the latter can be fitted using a mcDESPOT model, with 'apparent' parameters shown in Figure 2. Note that the assumption made in this derivation is that the bound-pool is in a steady-state.
When saturation is uncontrolled, a mcDESPOT model fits poorly (NRMSE = 6.4%) to simulated three-pool data, particularly for SPGR (Figure 3a). This results in inaccurate parameter estimation due to the dependence of each apparent parameter on RF-power. In contrast, the same model fits very well (NRMSE = 0.03%) for simulated controlled saturation data (Figure 3b). The signal predicted using the mcDESPOT model with the apparent parameter values in Figure 2 also fits very well (NRMSE = 0.25%), although not perfectly because the bound-pool steady-state assumption is an approximation. Using CSMT, a three-pool system behaves as a two-pool model, characterised by the parameters in Figure 2; model dimensionality is reduced without explicit modelling of a bound-pool, as has been performed previously.5
Figure 2 indicates that given no direct exchange between MR-visible pools, an apparent exchange (ΔkFS) remains that is solely mediated by the bound-pool; these additional exchange pathways are highlighted in Figure 1. This implies that the exchange rates observed using mcDESPOT could reflect exchange mediated purely by MT. ΔkFS increases almost linearly with kB but decreases for larger B1,rms, as magnetisation entering the bound-pool is lost through saturation.
Figures 4 and 5 use the derived parameter expressions to investigate how mcDESPOT fitting would be influenced by the presence of a bound-pool, assuming kFS = 0 and kB = kBF = kBS. Figure 4 suggests that the apparent MWF (in Figure 2) is not the same as the true MWF, defined as M0FM0F+M0S, but the relationship is monotonic and relatively insensitive to changes in bound-pool fraction. It also consistently overestimates MWF, as others have observed. However, Figure 4c shows that MWFapp is strongly influenced by RF-power level, with lower W leading to a closer relationship to the ground-truth.
Figure 5 demonstrates that higher B1,rms leads to reduced apparent longitudinal relaxation times, as has been reported before.7 This has clear implications for the use of T1 as a quantitative tissue parameter.
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