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Realistic simulations of diffusion MR spectroscopy: The effect of glial cell swelling on non-Gaussian and anomalous diffusion
André Döring1, Maryam Afzali1, Elena Kleban1, Roland Kreis2, and Derek K Jones1
1Cardiff University Brain Research Imaging Centre (CUBRIC), Cardiff University, Cardiff, United Kingdom, 2Departments of Radiology and Biomedical Research, University of Bern, Bern, Switzerland

Synopsis

An existing Monte-Carlo simulation was refined to allow realistic modeling of 150x150x150μm³ tissue samples. The approach was validated on a reference sample, where ground truth is known. The non-Gaussian and anomalous diffusion behavior in diffusion MR spectroscopy experiments was modeled in realistic tissue samples composed of 30 glial cells addressing a hypothesized cell swelling evoked by glial activation. The simulated results agree well with in vivo literature values and may help to improve the linkage between diffusion and histology.

Introduction

Diffusion MR spectroscopy (dMRS) can provide information on metabolite diffusion, which is partially cell-type specific and restricted to intracellular space. Thus, metabolite diffusion encodes the cellular microstructure with more specificity than water diffusion and can serve as a biomarker. However, to derive quantitative histological information from dMRS signal, novel modelling techniques are required.

The aim of this work is to extend existing GPU-based Monte-Carlo (MC) simulation techniques1 to allow efficient modelling of intracellular diffusion in realistic tissue samples for arbitrarily-shaped diffusion gradient-waveforms. We simulated non-Gaussian and anomalous diffusion in realistic glial cells for three types of diffusion-encoding gradient-waveforms: pulsed gradient spin echo (PGSE)2, oscillating gradient spin echo (OGSE)3 and spherical tensor encoding (STE)4,5. The modeled tissue sample of 150x150x150μm³ (40x40x40nm³ resolution) contained 30 isotopically distributed glial cells. Hypothesized cell-swelling evoked by glial activation6 was simulated by inflating the intracellular volume by 10%, 50% and 100%. Diffusion was modeled at a temporal resolution of 1μs for up to 500k random-walkers.

Methods

Tissue models: Simulations were validated with fully-dispersed capped cylinders (cf. Fig.1). As the simulation target, an isotropic reference tissue sample (RTS) was created from monkey glial cells taken from NeuroMorpho7,8 and meshed in NeuroMorphoVis9,10(cf. Fig.2).

Monte-Carlo simulation: Diffusion was modeled on a consumer GPU (Nvidia GTX 1070, 8GByte). The MC implementation of Nguyen et al.1 was extended:

  • Tissue mask: binary mask replaced by a Morton-encoded mask11,12 (8x less memory requirement; realistic VOIs of 150x150x150μm³ at 40x40x40nm³ resolution requires 5.3GByte memory)
  • Diffusion encoding: Reimplemented to support arbitrary diffusion gradient-waveforms
  • Voxelization: Implemented on GPU to efficiently convert tissue meshes to tissue masks11,12
  • Seeding: Reimplementation on GPU (approx. 20x faster)
  • GUI: GPU-simulator implemented as mex MatLab-plugin, including a MatLab GUI and the NOW-toolbox5,13 to create free gradient waveforms
Modeling: All simulations were performed at 40x40x40nm³ spatial and 1μs temporal resolution. The free diffusivity was set to 1.5×10-3mm²/s to reproduce restricted metabolite ADCs from 1.0-1.5×10-4mm²/s at b-values <4000s/mm² and diffusion times (TDs) between 30-200ms (cf. Fig.5). Cell-swelling (cf. Fig.3) was modeled using the solidify modifier in Blender to increase the intracellular volume by 10%(RTS+10%Vol), 50%(RTS+50%Vol) or 100%(RTS+100%Vol). While STE diffusion gradients were created with the NOW-toolbox5,13, OGSE encoding was realized by stretched-cosine diffusion gradient waveforms14.

  • Simulation validation: PGSE Δ/δ:50/10ms; b=0…30k s/mm² (n=31 values); 500k rnd. walkers
  • Non-Gaussian Diffusion: PGSE Δ/δ:70/10ms; STE dur:2x40ms; b=0…30k s/mm² (n=31); 500k rnd. walkers
  • Anomalous Diffusion: OGSE N/α:1/1, dur:2x30,2x50,2x70,2x80ms; PGSE Δ/δ:30,50,70,100,140,160,250,370,500/10ms; b=0…4k s/mm² (n=11); 100k rnd. walkers; mono-exponential ADC model

Results and Discussion

Depending on the number of random-walkers and gradient sampling points (gradient duration/temporal resolution) computation of a single direction takes 2-10min. This is considerably faster than for CPU-implementations (Camino15) or FEM approaches (SpinDoctor16), which can easily exceed 8hrs1 computation time.

Fig.1 proves a good agreement between the analytic solution17 and the MC simulation for capped cylinders, with maximal deviation <5%, which is probably related to sample anisotropy and can be resolved by adding more cylinders.

Fig.4 juxtaposes non-Gaussian diffusion behavior simulated for STE and PGSE encoding. In the mono-exponential range (<4000s/mm²) a 100% intracellular volume inflation yielded mean diffusivity (MD) increases by 20% for STE and 40% for PGSE. In this range, the simulation confirms rotation-invariance of STE, while PGSE reveals tissue anisotropy along the z-axis. At higher b-values, tissue anisotropy even appears for STE, which might indicate a discernible effect of TD anisotropy along different axes4. The attenuation behavior for PGSE encoding agrees well with human in vivo data for tCho18. The sensitivity towards cell-swelling increases at higher diffusion-weighting as reported for neuronal activation in functional dMRI19.

The effect of cell-swelling on anomalous diffusion is summarized in Fig.5, where TDs <20ms were modeled with OGSE and >20ms with PGSE encoding. The obtained MDs between 1.0×10-4mm²/s (TD=500ms) and 3.3×10-4mm²/s (TD=3.8ms) align well with values reported for glial markers (cholines/inositols)20. Though optimal sensitivity towards cell-swelling is observed at TDs of 5-100ms, it reduces only slightly even at longer TDs. In the ultra-short TD range (<5ms) a drastic reduction in sensitivity is observed, where diffusion is less affected by tissue confinement, but more by the cytoplasmic composition (e.g. organelles, macromolecules, proteins). Note, these results rely on a free diffusivity of 1.5×10-3mm²/s, which is close to the expected value in pure water. This would be in-line with reported water-like cytoplasmic viscosities21, but opposed to higher values22.

Reported ADC increases of tCho from 1.24 to 1.77×10-4mm²/s in neuroinflammation23 and from 1.28 to 1.42×10-4mm²/s in systemic lupus erythematosus24 (TD≈60ms) would reflect mean intracellular volume increases by 100% and 50%, respectively. However, we expect that real tissue cellular swelling is anisotropic, where single cells may experience more drastic morphological changes, while others remain unaffected.

Conclusion

Highly parallelized GPU computing with efficient memory-management allows simulation of metabolite diffusion in realistic tissue structures (>50×109 voxels).

Our results agree well with non-Gaussian and anomalous diffusion in glial markers. Determination of true intracellular viscosity is planned with detailed spectral analyses of OGSE at ultra-short TD supported by experimental data.

Glial swelling with volume-inflations of 50%-100% was shown to be resolvable with dMRS ideally at b-values >4000s/mm² and diffusion times of 10-100ms.

Acknowledgements

This work is supported by the Swiss National Science Foundation (SNSF #188142).

References

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19. Abe Y, Van Nguyen K, Tsurugizawa T, Ciobanu L and Le Bihan D. Modulation of water diffusion by activation-induced neural cell swelling in Aplysia Californica. Sci Rep 2017, 7:6178.

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Figures

Fig. 1: Comparison of the analytical solution with MC simulation for a PGSE diffusion experiment in a VOI of 130x130x130μm³ containing 200 fully dispersed capped cylinders (r=3μm, l=40μm) (cf. inset).

Fig. 2: Left: The reference tissue structure (RTS) consists of 30 monkey glial cells in a VOI of 150x150x150μm³. To create an isotropic tissue environment 15 different cells were placed twice, each randomly rotated, in the VOI. The Blender physics engine was used to avoid cell collision and overlap. Right: Overview of the 15 different glial cells [NeuroMorpho.org IDs are provided].

Fig. 3: Left: swelling of a glial cell (ID: 73137) with a volume increase by 10%, 50% or 100% (zoomed insets to highlight differences). Right: property changes of the RTS in volume (V), surface area (A) and surface area to volume ratio (A/V) upon cell-swelling for the entire VOI presented in Fig. 2.

Fig. 4: Simulation of non-Gaussian diffusion for spherical tensor (STE, left) and pulse gradient spin echo (PGSE, right) encoding comparing the reference tissue (RTS) and 100% swollen tissue (RTS+100%) structures.

Fig. 5: Top: Simulated anomalous diffusion behavior affected by cell-swelling for OGSE encoding at TD<20ms and PGSE encoding at TD>20ms. Bottom: ADC difference between diffusion in swollen tissue (RTS+10%Vol, RTS+50%Vol, RTS+100%Vol) and the reference tissue (RTS) structures.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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