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.
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