Sensitivity of MR diffusion measurements to variations in intracellular structure: effects of nuclear size

Abstract

Magnetic resonance imaging measurements of the apparent rate of water diffusion in tumors are sensitive to variations in tissue cellularity, which have been shown useful for characterizing tumors and their responses to treatments. However, because of technical limitations on most MRI systems, conventional pulse gradient spin echo (PGSE) methods measure relatively long time scales, during which water molecules may encounter diffusion barriers at multiple spatial scales, including those much greater than typical cell dimensions. As such they cannot distinguish changes on subcellular scales from gross changes in cell density. Oscillating gradient spin echo (OGSE) methods have the potential to distinguish effects on restriction at much shorter time and length scales. Both PGSE and OGSE methods have been studied numerically by simulating diffusion in a three-dimensional, multicompartment tissue model. The results show that conventional measurements with the PGSE method cannot selectively probe variations over short length scales and, therefore, are relatively insensitive to intracellular structure, whereas results using OGSE methods at moderate gradient frequencies are affected by variations in cell nuclear sizes and can distinguish tissues that differ only over subcellular length scales. This additional sensitivity suggests that OGSE imaging may have significant advantages over conventional PGSE methods for characterizing tumors.

Fig. 1

Schematic diagram of a simplified 3D tissue model. Black regions represent cell nuclei, gray regions represent cytoplasm and the space outside the spherical cells are extracellular space. Each compartment has its own intrinsic parameters, such as diffusion coefficient. Interfaces between different compartments have permeabilities to mimic cell membranes and nuclear envelopes. Note that the whole tissue is periodic but only a unit cell (shown above) was needed in the simulation, which implemented a revised periodic boundary condition in an improved finite difference method.

Fig. 2

Simulated ADCs and ADC differences of two different tissues (N/C 6.2% and 22.0%, respectively). (a) Simulated ADCs with respect to diffusion times by the PGSE method. (b) Simulated ADCs with respect to frequencies of applied oscillating gradients in the OGSE method. (c) ADC differences of two tissues by the PGSE method. The shaded region shows the applicable diffusion time range in typical PGSE measurements. (d) ADC differences of two tissues by the OGSE method. The shaded region shows the applicable oscillating gradient frequency range in typical OGSE measurements.

Fig. 3

Simulated ADCs change with the variation of N/C (the ratio of nuclear volume to cell volume). The solid line represents the ADCs with the fast exchange approximation. The dotted lines and dashed lines represent ADCs obtained by the PGSE method and OGSE methods, respectively.

Fig. 4

Maximum contrast for the OGSE method between tissue_I and tissue_II as a function of gradient frequency in three typical cases. G_max is the gradient amplitude. The dashed line denotes the conditions for studies on small animal scanners with G_max = 100 G/cm and TE = 40 ms; the dotted line represents diffusion studies with G_max = 40 G/cm and TE = 40 ms; the dash-dot line depicts the conditions for in vivo diffusion studies on human scanners with G_max = 8 G/cm and TE = 80 ms. For comparison, signal contrast obtained by the PGSE method at Δ = 40 ms and b = 1 ms/μm² is also showed as the solid line.