Characterizing white matter pathology with quantitative magnetization transfer imaging: insight from a four-pool model

Introduction: Quantitative magnetization transfer imaging (QMTI) [1] allows in vivo mapping of the parameters of a two-pool model of MT in tissue [2] by the analysis of off-resonance saturation data, and is useful in the study of human white matter (WM). The two-pool model parameters are the restricted-to-free proton pool size ratio (F), the forward magnetization transfer rate (kf), and the relaxation parameters of the model compartments (R1f, T2f, R1r, T2r) [1]. However, as it has been clearly established that WM has at least two separate water compartments [3], a more comprehensive model should include four proton pools (myelin solids, myelin water, non-myelin water, and non-myelin solids) [4]. This four-pool model has been used to characterize in vitro samples of bovine optic nerve [5] and fresh bovine WM [6]. By simulating pulsed off-resonance saturation gradient echo (GRE) measurements, we investigated the ability of the two-pool model, more tractable for in vivo imaging, to reflect the more complete four-pool model, and potential changes due to pathology. Specifically, we examined the effect of increases in the inter-compartmental exchange of water, of reductions in the solid pool sizes (myelin and non-myelin), and of a simple model of pure demyelination (decreased myelin liquids and solids), on two-pool MT observations. Methods: A modified version of the four-pool model of bovine WM at 37°C (Figure 1) was constructed from an existing model [6], with changes to the treatment of the solid pools [7]. The coupling between compartments was modeled by first-order exchange rates Rij for diffusion and MT. Simulations of MT-weighted GRE experiments [1] were conducted. Gaussian noise was added to the resulting MT data to produce an SNR of 100, and analyzed using the rectangular pulse model of [1] to yield the two-pool parameters. For each simulation, results from 500 noise iterations were averaged. First, as diffusivity changes of up to 50% have been reported in literature [8,9], the water exchange rate RD was increased by 25 to 100% to simulate plausible pathological changes. Second, the solid pool sizes were reduced, in 25% steps (myelin and non-myelin separately). Finally, pure demyelination was simulated by 25 to 100% reductions in myelin content (solid and liquid). Results: The two-pool MT model fits the simulated signal of the baseline four-pool model well (mean residual per point = 1%), and the parameters are reasonable (F = 0.21±0.01, kf = 5.8±0.9 s , R1f = 1.2 s , T2f = 71±6 ms, T2f = 10.1±0.3 μs). The MT signal was mildly affected by variations in the water exchange rate: the estimate of F was not affected (change < 1%), while kf increased by up to 17% and T2f decreased by a maximum of 9%, for a 100% increase in the water exchange rate. Simulated MT curves from models with reduced solid pool sizes are plotted in Figure 2, and the resulting changes in F are plotted in Figure 3. In addition, reductions in non-myelin solids resulted in a large linear decrease in kf (as much as 80%) and a negligible change in T2f, while reduced myelin solids resulted in a small, monotonic decrease of T2f (< 20%) with little impact on kf. Lastly, simulated MT curves from our model of demyelination behaved similarly to Figure 2 (right). Normalized estimates of F, kf, and T2f versus demyelination are plotted in Figure 3. In all simulations, T2r and R1f did not vary and were consistently recovered (10 μs & 1.2 s, respectively). Discussion: Based on our simulation results, a two-pool model is sufficient to describe off-resonance MT behavior in WM. Our observations relative to water exchange agree qualitatively with observations in bovine optic nerve [5]; however, water exchange has a less dramatic impact on parameters of the two-pool MT model than on the MT of the individual water components. This suggests that pathology affecting water exchange between the myelin and intra-/extra-cellular compartments, perhaps via membrane permeability variations, have very limited influence on twopool parameter estimates from MT measurements in WM. These observations are in contrast to results from simulations of myelin water imaging [10], which showed significant sensitivity to water exchange variations. While the overall MT is more greatly affected by theoretical reductions in the non-myelin solid pool size, the estimate of F is robust and sensitive to changes in either the myelin or non-myelin solid pools. Most of the signal change is absorbed by the exchange rate kf. Two-pool MT estimates are also sensitive to our model of pure demyelination: we observed a robust linear decrease in F which reflected the input value, accompanied by a relatively large increase in T2f, and a comparatively smaller increase in kf for large myelin decreases (loss > 50%). A more realistic model of demyelination should include a decrease of the exchange rates, to reflect common observations in lesions. In closing, two-pool QMT fits are sensitive to certain changes in the four-pool model: F is robust despite the existence of multiple solid pools, while parameters such as kf and T2f might provide insight into changes in the more complete fourpool model from limited two-pool observations. References: [1] Sled & Pike, MRM 46:923 (2001). [2] Morrison & Henkelman, MRM 33:475 (1995). [3] Menon & Allen, MRM 20:214 (1991). [4] Harrison & Henkelman MRM 33:490 (1995). [5] Stanisz et al. MRM 42:1128–36 (1999). [6] Bjarnason et al. MRM 54:1070–81 (2005). [7] Portnoy & Stanisz, MRM 58:144 (2007). [8] Bammer et al., MRM 44:583 (2000). [9] Filippi et al., Neurology 56:304 (2001). [10] Levesque & Pike, ISMRM 2007, p.2142. MT MT diffusion