To compare in simulation the sensitivity and specificity of double-diffusion-encoding (DDE) and double-oscillating-diffusion-encoding (DODE) sequences to microstructural features such as pore size and eccentricity.Double-diffusion-encoding (DDE) sequences [1,2] illustrated in Fig. 1a) concatenate two single pulsed field gradients separated by a mixing time. In the long mixing time regime, varying the relative angle between the two gradient pairs provides sensitivity to microscopic anisotropy [1,3], which allows accurate characterisation of heterogeneous tissues such as grey matter [4,5] and can provide insight in disease [6]. Previous studies on designing diffusion gradients have shown that the choice of sequence parameters is important for enhancing sensitivity to pore size [7,8] and using oscillating gradients can further increase the contrast [9-11]. Recent work replaced the pulsed gradients in a DDE sequence with oscillating gradients, and suggested that the new double-oscillating-diffusion-encoding (DODE, Fig. 1b) promises improved sensitivity to microstructural features [12]. However, the impact of a particular choice of sequence parameters has not been thoroughly investigated. This study analyses the effect of varying different sequence parameters on the sensitivity of DDE and DODE sequences to pore size and eccentricity.

We use a model of randomly oriented finite cylinders with diameter d and eccentricity L/d to represent diffusion substrates featuring microscopic anisotropy. We investigate the difference between parallel and perpendicular measurements for DODE and DDE sequences with different varying parameters for a wide range of substrates with pore diameters d between 0.5 and 10μm and elongations L/d between 1 and 10. For DODE sequences we vary independently gradient strength G, number of periods N and pulse duration δ, while for DDE we vary G, δ and diffusion time ∆. The maximum gradient strength used in this study is G=300mT/m and the maximum duration is 140ms, values that can be achieved in practical applications. We also analyse the effect of noise and label the regions where the difference is larger than the standard deviation of the noise for different levels of SNR={20,50,100,1000}. This highlights which substrates can be distinguished from isotropic pores, given the diffusion sequence and SNR level. The time interval between the first and second gradient waveforms is fixed to 20ms for all sequences. All simulations are performed using the MISST software [13].

Figure 2 presents the difference between parallel and perpendicular measurements of DODE and DDE sequences as a function of pore size and elongation, showing which substrates are distinguishable from isotropic pores for different sequence parameters and noise levels. Different rows in panels a) and b) have sequences with different varying parameters. Decreasing G shifts sensitivity towards larger and more elongated pores for both DODE and DDE. Thus, a high gradient strength of 300mT/m is necessary to provide contrast in substrates with elongated pores and diameters between 2 to 4μm, while a low gradient strength G=50mT/m is needed for larger pores with diameter between 4 and 10μm. For DDE sequences, increasing diffusion time does increase sensitivity to both pore size and eccentricity, which can be seen as a sharper colour gradient in panel b) bottom row. Decreasing the gradient duration δ in DDE sequences has a similar effect to decreasing the gradient strength and shifts the sensitivity towards larger and more eccentric pores. In the case of DODE sequences, varying the number of oscillation periods N increases sensitivity to pore diameter for elongated pores, i.e. there is a stronger colour gradient in vertical direction. The results show that DDE and DODE have slightly different contrasts and a combination of sequences can improve the estimation of microstructural features. DODE sequences provide higher sensitivity to pore size for elongated pores (sharper colour gradient in vertical direction), while DDE sequences are more sensitive to pore eccentricity (sharper colour gradient in horizontal direction). These findings are consistent with previous results showing that oscillating gradients increase the sensitivity to axon diameter in the presence of orientation dispersion [11].By changing the sequence parameters we can control which substrates are distinguishable from isotropic pores based on the signal difference. Moreover, as DDE and DODE sequences can provide different contrasts, a combination of these sequences enhances the sensitivity to different microstructural features. Previous studies have optimized the acquisition protocol for model-based approaches [7], however, here we show for the first time the importance of choosing the right sequence parameters for estimating model-free metrics based on the signal difference, given constraints for gradient strength and acquisition time. Future work aims to investigate the sensitivity of broader range of sequences.