Manisha Aggarwal^{1}

This lecture will cover the concepts and applications
of oscillating-gradient diffusion MRI acquisition methods to probe tissue
microstructure using short effective diffusion times. We will discuss how
oscillating diffusion-encoding gradients can be used to characterize restricted
diffusion in neuronal tissues, using selective sampling of the temporal
diffusion spectrum D(*ω*) over discrete
narrow frequency bands. We will then explore the applications as well as some current
limitations of OGSE diffusion MRI acquisitions for probing tissue
microstructure over varying length scales.

- To understand the concept of time-dependent diffusion in biological tissues

- To understand the concept of oscillating-gradient acquisitions with short diffusion time

- To explore applications of OGSE sequences for probing tissue microstructure

**Time-dependent diffusion in neuronal tissue**

In systems of restricted diffusion, the apparent diffusion coefficient (ADC) depends on the effective diffusion time, i.e., the finite time interval over which random spin displacements are sampled in diffusion MRI [1]. For free diffusion, ADC is independent of diffusion time. However, in the case of restricted or hindered diffusion, as in biological tissues, the diffusing spins interact increasingly with restricting boundaries as diffusion time increases and the estimated ADC is consequently lower than the intrinsic diffusion coefficient. Measuring this time-dependence can provide useful insights into the microstructural properties of tissue, e.g., surface-to-volume ratio [2]. In order to probe short spatial scales that are relevant for neuronal tissue, e.g. at the sub-cellular level, very short diffusion times are necessary which are not usually practical to achieve using conventional pulsed gradient spin echo (PGSE) sequences under gradient constraints.

**Oscillating
vs. pulsed diffusion-encoding gradients**

Oscillating gradient waveforms for diffusion encoding
can be used to attain very short effective diffusion times, and are capable of probing
length scales much shorter than PGSE methods [3]. OGSE acquisitions
at higher frequencies are sensitive to the effects of restrictions at
sub-cellular length scales, and have been used to experimentally observe the
time-dependence of ADC in the brain. It is convenient to interpret diffusion
measurements made with oscillating gradients using the framework proposed by
Stepišnik [4]. The temporal
diffusion spectrum D(*ω*) is the
Fourier transform of the spin velocity autocorrelation function, and the shape
of the spectrum can provide unique information about underlying tissue
microstructure and the varying scales of spatial restrictions [3-5]. While PGSE sequences with long
diffusion times typically sample the diffusion spectrum in a limited frequency range
centered at *ω* = 0,
appropriately-designed oscillating-gradient waveforms can theoretically be used
to sample D(*ω*) at well-defined higher
frequencies, and by changing this frequency, the shape of the spectrum can be
probed. In practice, optimized oscillating-gradient waveforms such as apodized
cosine and cosine-trapezoid have narrow non-zero gradient power spectra peaks
at selected frequencies, and can allow sampling of discrete narrow frequency
bands of D(*ω*) [6-8].

**Applications
for probing tissue microstructure**

OGSE methods have been used to demonstrate
clear frequency/time-dependence of ADC in the rodent brain [9-11] as well as in the human brain [12,13]. Studies using simulations and *in vitro* experiments, e.g., in systems
of packed beads or cells, have demonstrated the sensitivity of OGSE
measurements to microstructural properties such as cell size, intracellular
volume fraction, and surface-to-volume ratio [14,15]. Recent studies have also examined
the efficacy of OGSE sequences to estimate small axon diameters in white matter
[16,17]. The sensitivity of OGSE-based
measurements to variations in sub-cellular scale structures in the brain, in
particular, has been used to detect and characterize pathological changes in
animal models of tumor [18,19], stroke [20,21], and epilepsy [22]. Further, the use
of non-uniform OGSE gradient waveforms has also been proposed to probe restriction
length scales and pore size distributions in the brain [23].

While the time-dependence of
diffusion coefficient has been well-observed in the brain, recent studies using
OGSE and PGSE acquisitions have also demonstrated distinct time-dependence of
diffusion kurtosis in both gray matter [24-26] and white matter [26]. Examining the
non-Gaussian behavior of the diffusion signal at short diffusion times and high
*b*-values could potentially provide further
insights to characterize microstructural tissue compartments.

Currently, gradient strength is a
potential practical limiting factor for OGSE acquisitions particularly on
clinical scanners. Since the *b*-value
decreases as the gradient frequency increases, this potentially limits the
highest frequencies that can be sampled for a given maximum gradient strength. Precise
localization of *ω* is also dependent on the total oscillating-gradient waveform duration, which in practice is constrained by TE and SNR
requirements. However, OGSE measurements even at moderately low frequencies are
capable of detecting restrictions to water diffusion at spatial scales much
smaller than the diameter of a single cell, thereby resulting in unique sensitivity
of the measured ADC to contributions from subcellular structures [3]. In conclusion, exploring the time-dependent
behavior of the diffusion MR signal in the short diffusion time regime can
provide rich information to probe restricted neuronal tissue microenvironments,
which is typically not accessible with standard PGSE acquisitions.

1. Stepišnik, J., Time-dependent self-diffusion by NMR spin-echo. Physica B: Condensed Matter, 1993. 183(4): p. 343-350.

2. Latour, L.L., K. Svoboda, P.P. Mitra, and C.H. Sotak, Time-dependent diffusion of water in a biological model system. Proc Natl Acad Sci U S A, 1994. 91(4): p. 1229-33.

3. Gore, J.C., J. Xu, D.C. Colvin, T.E. Yankeelov, E.C. Parsons, and M.D. Does, Characterization of tissue structure at varying length scales using temporal diffusion spectroscopy. NMR Biomed, 2010. 23(7): p. 745-56.

4. Stepišnik, J., Analysis of NMR self-diffusion measurements by a density matrix calculation. Physica B+C, 1981. 104(3): p. 350-364.

5. Callaghan, P.T. and J. StepiŠNik, Frequency-Domain Analysis of Spin Motion Using Modulated-Gradient NMR. Journal of Magnetic Resonance, Series A, 1995. 117(1): p. 118-122.

6. Parsons, E.C., Jr., M.D. Does, and J.C. Gore, Temporal diffusion spectroscopy: theory and implementation in restricted systems using oscillating gradients. Magn Reson Med, 2006. 55(1): p. 75-84.

7. Drobnjak, I., B. Siow, and D.C. Alexander, Optimizing gradient waveforms for microstructure sensitivity in diffusion-weighted MR. Journal of Magnetic Resonance, 2010. 206(1): p. 41-51.

8. Ianuş, A., B. Siow, I. Drobnjak, H. Zhang, and D.C. Alexander, Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI. Journal of Magnetic Resonance, 2013. 227: p. 25-34.

9. Does, M.D., E.C. Parsons, and J.C. Gore, Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain. Magn Reson Med, 2003. 49(2): p. 206-15.

10. Aggarwal, M., M.V. Jones, P.A. Calabresi, S. Mori, and J. Zhang, Probing mouse brain microstructure using oscillating gradient diffusion MRI. Magn Reson Med, 2012. 67(1): p. 98-109.

11. Kershaw, J., C. Leuze, I. Aoki, T. Obata, I. Kanno, H. Ito, et al., Systematic changes to the apparent diffusion tensor of in vivo rat brain measured with an oscillating-gradient spin-echo sequence. Neuroimage, 2013. 70: p. 10-20.

12. Van, A.T., S.J. Holdsworth, and R. Bammer, In vivo investigation of restricted diffusion in the human brain with optimized oscillating diffusion gradient encoding. Magn Reson Med, 2014. 71(1): p. 83-94.

13. Baron, C.A. and C. Beaulieu, Oscillating gradient spin-echo (OGSE) diffusion tensor imaging of the human brain. Magn Reson Med, 2014. 72(3): p. 726-36.

14. Xu, J., M.D. Does, and J.C. Gore, Sensitivity of MR diffusion measurements to variations in intracellular structure: effects of nuclear size. Magn Reson Med, 2009. 61(4): p. 828-33.

15. Jiang, X., H. Li, J. Xie, P. Zhao, J.C. Gore, and J. Xu, Quantification of cell size using temporal diffusion spectroscopy. Magn Reson Med, 2016. 75(3): p. 1076-85.

16. Drobnjak, I., H. Zhang, A. Ianus, E. Kaden, and D.C. Alexander, PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study. Magn Reson Med, 2016. 75(2): p. 688-700.

17. Xu, J., H. Li, K.D. Harkins, X. Jiang, J. Xie, H. Kang, et al., Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy. NeuroImage, 2014. 103: p. 10-19.

18. Reynaud, O., K.V. Winters, D.M. Hoang, Y.Z. Wadghiri, D.S. Novikov, and S.G. Kim, Surface-to-volume ratio mapping of tumor microstructure using oscillating gradient diffusion weighted imaging. Magn Reson Med, 2016. 76(1): p. 237-47.

19. Colvin, D.C., T.E. Yankeelov, M.D. Does, Z. Yue, C. Quarles, and J.C. Gore, New insights into tumor microstructure using temporal diffusion spectroscopy. Cancer Res, 2008. 68(14): p. 5941-7.

20 Aggarwal, M., J. Burnsed, L.J. Martin, F.J. Northington, and J. Zhang, Imaging neurodegeneration in the mouse hippocampus after neonatal hypoxia-ischemia using oscillating gradient diffusion MRI. Magn Reson Med, 2014. 72(3): p. 829-40.

21. Wu, D., Martin, L.J, F.J. Northington, and J. Zhang, Oscillating gradient diffusion MRI reveals unique microstructural information in normal and hypoxia-ischemia injured mouse brains. Magn Reson Med, 2014. 72(5): p. 1366-74.

22. Aggarwal, M., O. Gröhn, and A. Sierra, Altered hippocampal microstructure in the epileptogenic rat brain revealed with diffusion MRI using oscillating field gradients. Proc. International Society for Magnetic Resonance in Medicine, 2016: p. 1083.

23. Shemesh, N., G.A. Alvarez, and L. Frydman, Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo (NOGSE) NMR. J Magn Reson, 2013. 237: p. 49-62.

24. Portnoy, S., J.J. Flint, S.J. Blackband, and G.J. Stanisz, Oscillating and pulsed gradient diffusion magnetic resonance microscopy over an extended b-value range: implications for the characterization of tissue microstructure. Magn Reson Med, 2013. 69(4): p. 1131-45.

25. Pyatigorskaya, N., D. Le Bihan, O. Reynaud, and L. Ciobanu, Relationship between the diffusion time and the diffusion MRI signal observed at 17.2 Tesla in the healthy rat brain cortex. Magn Reson Med, 2014. 72(2): p. 492-500.

26. Aggarwal, M., K. Martin, M. Smith, and P.A. Calabresi, Diffusion-time dependence of diffusional kurtosis in the mouse brain using pulsed and oscillating gradients. Proc. International Society for Magnetic Resonance in Medicine, 2018.