Introduction

Microstructural changes due to cancer treatments are prevalent before macrostructural size changes¹. More complex modeling may be more sensitive to these changes but requires additional data or challenges hardware limitations. Here, we analyze the time-dependent diffusion signal using two different models: a two-pool model with exchange that assumes well-mixed pools, and a two-pool model that incorporates spin starting location into the boundary conditions using a “partially absorbing wall” assumption. Model parameters, including water exchange and intracellular fraction, are examined following induction of cell death.

Methods

An acute myeloid leukemia cell line (AML-5) was cultured in suspension with alpha-MEM, FBS and penicillin/streptomycin. Apoptosis was induced with 10 μg/mL of cisplatin for 36 hours. Control cells were untreated. Each group was centrifuged at 2400 g to pack the cells into a pellet. Approximately 1x10⁹ cells were used in each NMR tube. Five biological replicates were performed.

A 7T vertical small bore Bruker scanner was used with a 40/30 mm quadrature receive and transmit coil. Diffusion was quantified with DTI-STEAM-EPI (1 direction, 7 b-values=0-5000s/mm², TE/TR=35ms/1.5s, 7 mixing times TM=6.7-233ms).

Diffusion was fitted with two different models: a two-pool partially absorbing wall² and a Bloch equation-based model of water exchange between two pools³. For both models, one pool is a spherical intracellular pool with a single radius and an extracellular pool. We assume the spin density for both the intracellular and extracellular pools are equivalent so that the water fractions and volume fractions are the same. Fit uncertainty was calculated using the Akaike information criterion (AIC) to compensate for the different number of parameters.

After MRI, cells were fixed in 10% formalin for at least two weeks before histological processing and staining with haematoxylin and eosin (H&E).

Results

Fits using the partially absorbing wall model were noticeably poorer than the Bloch equation model (Figure 1). The fit parameters from the Bloch equation model also had smaller confidence intervals for more parameters (Figure 2).

The intracellular water fraction showed a significant decrease in both models, while the water exchange only increased for the Bloch equation model. The radius did not show a significant change for either model (Figure 3).

Histology demonstrates the morphological changes due to apoptosis, as well as the variation between experiments (Figure 4).

Discussion/Conclusion

The intracellular fraction for the control for the partially absorbing wall and Bloch equation model (0.6 ± 0.2 and 0.77 ± 0.08, respectively) is within the range of the theoretical value for close randomly packed spheres, which is around 0.64, but the partially absorbing wall model shows a larger range between biological replicates. Similarly, the radius in the control group (4.4 ± 0.7 µm and 5.1 ± 0.3, respectively) was in the expected range of 5 microns with the partially absorbing wall model having a larger variation. The intracellular water exchange rate (6 ± 7 s^-1 and 4.9 ± 0.9 s^-1, respectively) is higher than previous findings in AML cells measured with relaxation methods⁴ but in line with higher exchange values that have been measured in HeLa cells⁵.

In the apoptotic group, both models demonstrated a decrease in intracellular fraction (0.36 ± 0.09 and 0.5 ± 0.1, respectively), which is expected as the cells begin to shrink and thus lose intracellular volume. For the partially absorbing wall model the water exchange does not significantly change, while the Bloch equation model demonstrates a significant increase in the water exchange (4 ± 2 s^-1 and 10 ± 3 s^-1, respectively). We expect the water exchange to increase due to the increased surface area to volume from blebbing and increased membrane permeability and from previous experiment in AML cells demonstrating increased exchange 36 hours after cisplatin treatment⁴. The radius does not show a significant change in either model (5 ± 2 µm and 5.2 ± 0.7 µm, respectively), whereas we would expect the radius to decrease as cells shrink during apoptosis. This could be due to morphological variations seen in the histology or the inaccuracy of modelling the complex membrane blebbing and apoptotic process as spherical cells with identical radii.
The values for the intracellular fraction in both models and both groups are lower than previous findings⁴ due to limitation of only fitting a single sphere size. With different sizes and shapes, especially in the apoptotic group, the packing would be increased and thus have a greater intracellular fraction.

The partially absorbing wall model might be expected to better describe the data than the Bloch equation model as the partially absorbing wall model incorporates the initial location of the spins. Our fitting of the diffusion data shows the converse. Here, we used the Talbot inversion method as it provided more stable parameter values relative to the Gaver-Stehfest inversion method. Unfortunately, the change in inversion method did not improve the fits.

Both models were sensitive to intracellular fraction while the Bloch equation model was also sensitive towards water exchange. Therefore, the Bloch equation model is sufficiently sensitive to microscopic cell death for realistically attainable diffusion MRI scan parameters. Future work will extend this method in vivo and investigate the inconsistencies of the partially absorbing wall model.

Acknowledgements

We would like to acknowledge MRI protocols and assistance from Wilfred Lam and Ryan Oglesby; Anoja Giles for help with cell culture and Gregory Czarnota for access to their lab space and materials. Funding/support provided by Natural Sciences and Engineering Research Council of Canada.