Pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE) in mouse gliomas

Abstract

Solid tumor microstructure is related to the aggressiveness of the tumor, interstitial pressure and drug delivery pathways, which are closely associated with treatment response, metastatic spread and prognosis. In this study, we introduce a novel diffusion MRI data analysis framework, pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE), and demonstrate its feasibility in a mouse tumor model. In vivo and ex vivo POMACE experiments were performed on mice bearing the GL261 murine glioma model (n = 8). Since the complete diffusion time dependence is in general non-analytical, the tumor microstructure was modeled in an appropriate time/frequency regime by impermeable spheres (radius Rcell , intracellular diffusivity Dics ) surrounded by extracellular space (ECS) (approximated by constant apparent diffusivity Decs in volume fraction ECS). POMACE parametric maps (ECS, Rcell , Dics , Decs ) were compared with conventional diffusion-weighted imaging metrics, electron microscopy (EM), alternative ECS determination based on effective medium theory (EMT), and optical microscopy performed on the same samples. It was shown that Decs can be approximated by its long time tortuosity limit in the range [1/(88 Hz)-31 ms]. ECS estimations (44 ± 7% in vivo and 54 ± 11% ex vivo) were in agreement with EMT-based ECS and literature on brain gliomas. Ex vivo, ECS maps correlated well with optical microscopy. Cell sizes (Rcell = 4.8 ± 1.3 in vivo and 4.3 ± 1.4 µm ex vivo) were consistent with EM measurements (4.7 ± 1.8 µm). In conclusion, Rcell and ECS can be quantified and mapped in vivo and ex vivo in brain tumors using the proposed POMACE method. Our experimental results support the view that POMACE provides a way to interpret the frequency or time dependence of the diffusion coefficient in tumors in terms of objective biophysical parameters of neuronal tissue, which can be used for non-invasive monitoring of preclinical cancer studies and treatment efficacy. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: POMACE; diffusion time dependence; extracellular space; glioma; oscillating gradient spin echo; restrictions.

Figure 1

Frequency-dependent diffusion inside (A) the intracellular space for various cell radii (numerical calcul, R_cell = 1/4/10 μm, blue/green/black circles) and (B) extracellular space in the long / intermediate / short time regime. A. Oscillation frequencies f_OGSE in the range [0–225] Hz are best suited to detect time-dependent changes from the intracellular compartment in cancer cells (R_cell = 4 μm). B. The analytical expression for diffusion in the ECS in the intermediate time domain is in general unknown (second column). Outside the short-time regime (i.e. within the grey area), small time-dependent variations are expected from the extracellular compartment (double arrow), compared to intracellular diffusivity changes inside cancer cells (Fig. 1A, green).

Figure 2

Time-dependent diffusion over-fitting with four independent variables. A. Combination of PGSE and OGSE data (light and dark gray) in the range [31 ms ; 225 Hz] based on Eq. [3–6] and realistic estimates (ECS = 40%, R_cell = 4 μm, D_ics/D_ecs=1/2 μm²/ms, D_0,ecs = 2.7 μm²/ms). When fitting four independent variables, small variations due to noise (blue circles, SNR=50, 2 time-points per time / frequency) lead to bimodal distributions (blue lines) of the estimated ECS fraction (B), cell radius (C), intra-(D) and extracellular diffusivities (E). The red lines correspond to the parameter nominal values. Alternatively, when D_ics is fully constrained based on Eq. [8a] and OGSE data in the short time regime (f_OGSE > 88 Hz), the distributions of the parameter estimates (black lines) are centered around the nominal values.

Figure 3. PGSE and low frequency OGSE time dependence

A. In the tumor, PGSE (open circles) and OGSE data (closed circles) are fitted to Eq. [8b] and [8c]. The standard deviation over the ROI is indicated by the blue area. Parametric maps of ECS (B), R_cell (C), D_ics (D) and D_ecs (E) inside the tumor in vivo / ex vivo (top / bottom line). White areas in ECS maps indicate regions of very low cellular density (ECS>70 %).

Figure 4. Long time-dependence of the diffusion coefficient in the tumor

Both A. in vivo and B. ex vivo PGSE-based D(τ) decrease linearly with 1/τ. Standard deviations within the tumor ROI are represented by the blue / red areas. C. Comparison of the ECS diffusivities derived from the POMACE model (D_ecs, white) with values extrapolated from the PGSE data in the long time regime ( $D_{\mathit{ecs}}^{\infty }$, grey), and from the short-time regime at f_OGSE = 88 Hz (black) for in vivo (left column) and ex vivo (right column) PGSE measurements.

Figure 5. Comparison of ECS parametric maps

derived from A. the POMACE (Eqs. [8]) and B. EMT applied to the PGSE data (Eq. [9]) in three representative tumors. Areas of high ECS (>70%) are highlighted in white. C. At voxel level, ECS measurements appear strongly correlated in vivo (ρ =0.64) and ex vivo (ρ =0.84). The complete dataset (in vivo + ex vivo) is best fitted via the dotted line (slope=0.87). The unity line is plotted for visualization purposes.

Figure 6. Optical microscopy

performed on brain sections (100 μm thickness) used for ex vivo MRI (corresponding to Fig. 5A–B, ex vivo panel). Necrotic areas (black/white arrows) match the regions of high ECS (>70 %) estimated using MRI (Fig. 5). Similarly, regions of low ECS appear to match areas of tumor infiltration in Gray and White Matter.