Yuxin Zhang^{1,2}, Óscar Peña-Nogales^{3}, James H. Holmes^{2}, and Diego Hernando^{1,2}

Advanced diffusion MRI acquisition strategies based on motion-compensated diffusion-encoding waveforms have been proposed to reduce the signal voids caused by tissue motion. However, quantitative diffusion measurements obtained from these motion-compensated waveforms may be biased relative to standard monopolar gradient waveforms. This study evaluated the effect of different diffusion encoding gradient waveforms on the signal decay and diffusion measurements, using Monte-Carlo simulations with different microstructures and several reconstruction signal models. The results show substantial bias in observed signal decay and quantitative diffusion measurements in the same microstructure across different gradient waveforms, in the presence of restricted diffusion.

Monte-Carlo simulations were performed based on the CAMINO package^{5}. Different tissue microstructures were simulated with different cell size (diameter=20$$${\mu{m}}$$$, separation=42$$${\mu{m}}$$$ for large cell and diameter=5$$${\mu{m}}$$$, separation=11$$${\mu{m}}$$$ for small cell size) and varying permeability of the cell boundaries. Permeability in this simulation was defined as the probability that a spin would pass through the cell membrane, ranging from p=0 (pure restricted intra-cellular diffusion) to p=1 (pure unrestricted Gaussian diffusion).

Five different diffusion gradient waveforms with the same set of b-values and the same diffusivity (2$$${\times}$$$10^{-3}$$${mm^{2}/s}$$$) and initial spins (10^{5}) were applied to each microstructure. The five waveforms (Fig.1) were designed with monopolar diffusion gradient (MONO), no motion-compensation CODE (CODE)^{3}, first moment nulling bipolar gradient (Bipolar)^{2}, first moment nulling CODE (CODE-M1) and both first and second moment nulling CODE (CODE-M1M2), respectively.

Signal with increasing b-values for each combination of microstructure and gradient waveform was simulated with CAMINO. To illustrate the different effects of diffusion waveforms on intra-cellular and extra-cellular spins with restricted diffusion, the signal ratio was calculated for both intra-cellular and extra-cellular spins with uniformly distributed large cell structure (p=0).$$R=\frac{Signal\,of\,intra-\,(or\,extra-)\,cellular\,spins\,with\,each\,waveform}{Signal\,of\,intra-\,(or\,extra-)\,cellular\,spins\,with\,monopolar\,diffusion\,sequence}.$$To compare the resulting quantitative diffusion measurements, diffusion parameters were estimated by least-squares fitting using three different diffusion MRI signal models: mono-exponential, kurtosis^{6}, and stretched exponential^{7}, respectively.

This study demonstrated bias in signal and quantitative diffusion measurements with different models in the same microstructure across different gradient waveforms, in the presence of restricted diffusion. As shown in previous studies, cell permeability is typically very small, ie: diffusion inside cells is highly restricted^{8}. Therefore, the bias observed in this work may have important consequences for the clinical accuracy and reproducibility of quantitative diffusion MRI performed with different diffusion waveforms. Previous studies^{9-11} have reported significantly lower diffusivity measurements using monopolar diffusion waveforms than bipolar waveforms. These results are in good qualitative agreement with our Monte-Carlo results. Importantly, the different sensitivity of various diffusion waveforms to microstructres might have application to the characterization of non-Gaussian diffusion in healthy and diseased tissue.

This study had several limitations. In addition to the shape of the waveforms themselves, moderate differences in diffusion times (within 15ms) across gradient waveforms may contribute to the observed variability in quantitative diffusion parameters. Although it is challenging to separate the effects of waveform shape and diffusion time, the variability observed in this work suggests that applying different waveforms results in different observed quantitative diffusion parameters in the presence of restricted diffusion. In addition, the Monte-Carlo simulation did not model micro-perfusion effects, eg: intra-voxel incoherent motion. Future Monte-Carlo studies including micro-perfusion effects are needed, as the quantification of these effects might be affected substantially by the choice of diffusion encoding waveform.

[1] Murphy, P., Wolfson, T., Gamst, A., Sirlin, C., & Bydder, M. (2013). Error model for reduction of cardiac and respiratory motion effects in quantitative liver DW-MRI. Magnetic resonance in medicine, 70(5), 1460-1469.

[2] Stoeck, C. T., Von Deuster, C., Genet, M., Atkinson, D., & Kozerke, S. (2015). Second-order motion-compensated spin echo diffusion tensor imaging of the human heart. Magnetic resonance in medicine.

[3] Aliotta, E., Wu, H. H., & Ennis, D. B. (2016). Convex optimized diffusion encoding (CODE) gradient waveforms for minimum echo time and bulk motion–compensated diffusion-weighted MRI. Magnetic resonance in medicine.

[4] Helpern, J.A., Ordidge, R.J and Knight RA. (1992). The effect of cell membrane water permeability on the apparent diffusioncoefficient of water. 11th ISMRM.

[5] Cook, P. A., Bai, Y. Nedjati-Gilani, et. al. (2006). Camino: open-source diffusion-MRI reconstruction and processing. In 14th scientific meeting of the international society for magnetic resonance in medicine (Vol. 2759). Seattle WA, USA.

[6] Jensen, J. H., Helpern, J. A., Ramani, A., Lu, H., & Kaczynski, K. (2005). Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magnetic Resonance in Medicine, 53(6), 1432-1440.

[7] Bennett, K. M., Schmainda, K. M., Rowe, D. B., Lu, H., & Hyde, J. S. (2003). Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magnetic resonance in medicine, 50(4), 727-734.

[8] Stanisz, G. J. (2003). Diffusion MR in biological systems: tissue compartments and exchange. Israel journal of chemistry, 43(1-2), 33-44.

[9] Rosenkrantz, A. B., Geppert, C., Kiritsy, M., Feiweier, T., Mossa, D. J., & Chandarana, H. (2015). Diffusion-weighted imaging of the liver: comparison of image quality between monopolar and bipolar acquisition schemes at 3T. Abdominal imaging, 40(2), 289-298.

[10] Dyvorne, H. A., Galea, N., Nevers, T., Fiel, M. I., Carpenter, D., Wong, E., ... & Babb, J. S. (2013). Diffusion-weighted imaging of the liver with multiple b values: effect of diffusion gradient polarity and breathing acquisition on image quality and intravoxel incoherent motion parameters—a pilot study. Radiology, 266(3), 920-929.

[11] Kyriazi, S., Blackledge, M., & Collins, D. J. (2010). Optimising diffusion-weighted imaging in the abdomen and pelvis: comparison of image quality between monopolar and bipolar single-shot spin-echo echo-planar sequences. European radiology, 20(10), 2422-2431.

Figure 1. The five diffusion waveforms used in this study are shown in this figure, including monopolar diffusion gradient (MONO), no motion compensation CODE (CODE), first moment nulling bipolar gradient (Bipolar), first moment nulling CODE (CODE-M1) and both first and second moment nulling CODE (CODE-M1M2). The dashed lines represent the 180$$$^\circ$$$ refocusing pulse.

Figure 2. Signal decay with increasing b-values is illustrated in this figure across different diffusion waveforms and different tissue microstructure. Under pure Gaussian diffusion (top left), signal decays are identical for different diffusion-encoding waveforms. However, large variability across waveforms is observed in the presence of restricted diffusion and smaller cell size.

Figure 3.
Ratios between the signal from spins with motion-compensated waveforms relative to the conventional monopolar diffusion waveform are plotted (intracellular: dashed lines, extracellular: solid lines). The variability of signal behavior across gradient waveforms is more prominent for intracellular spins (which are more affected by diffusion restrictions).

Figure 4. ADC values estimated from signal decays from different diffusion waveforms as a function of cell membrane permeability. The differences in ADC measurements across diffusion waveforms are larger with low cell boundary permeability, ie: more restricted diffusion structures.

Table 1. Diffusion parameters estimated with mono-exponential model (ADC), kurtosis model ($$${D_k}$$$, $$$k$$$) and stretched exponential model ($$$D_s$$$, $$${\alpha_{s}}$$$) across different sequences and different cell permeability (p). Bias across gradient waveforms is observed for all signal models in the presence of restricted diffusion.