Synopsis

To better understand how the underlying microstructure and pathology affect the DT-CMR signal in vivo, more realistic numerical models that account for irregular myocyte configurations such as sheetlets are necessary. We manually segmented cardiomyocytes from pig histology and confirmed that the resulting substrate is representative of the local microstructure through automatic segmentation of the surrounding tissue with a convolutional neural network. Monte Carlo random walk simulations, covering short and long mixing times and varying compartment diffusivities, show a mismatch between the results for the histology-based substrate and a simple cuboid model with comparable ECV and mean cell size.

Introduction

Diffusion tensor cardiovascular magnetic resonance (DT-CMR) is unique in that it enables non-invasive inference of the underlying cardiac microstructure. Recent work^1,2,3 has demonstrated abnormalities in DT-CMR parameters related to sheetlet orientation for hypertrophic and dilated cardiomyopathy patients. However, the exact relationship between measured DT-CMR signal and underlying pathology is not yet fully understood.

Numerical simulations are a promising approach to synthesise the DT-CMR data of a known microstructure, thus allowing for the in silico investigation of physiological changes such as myocyte hypertrophy or disarray. Current methods^4,5 model cardiomyocytes as well-defined shapes in regular arrangements, which lack the sheetlet structure found in the myocardium. We have developed simulations using a histology-based virtual microstructure and show here that this simulation substrate is representative of the local microstructure by using deep learning supported automatic segmentation, and contrast the simulated DT-CMR parameters to a simple cuboid model. This simulation substrate is used to investigate the effect of intra- and extra-cellular diffusivities on the DT-CMR parameters.

Methods

Pig heart histology was obtained through wide-field microscopy of 10μm thick radial—longitudinal slices from a transmural block². The heart was arrested in a contracted (systolic-like) state and stained with Masson trichrome. A stack of 10 slices with spacing 100μm was registered rigidly and 3x3mm² regions in the mid-myocardium were extracted for processing.

Numerical simulations were performed using an in-house Monte Carlo random walk algorithm capable of efficiently handling arbitrary cell geometries. The simulated tissue substrate is based on a subset of this histology. A 400x500μm² region was selected and cardiomyocytes manually segmented to obtain a ground truth image (Figure 1A). Individual cells were simplified as polygons and extruded in the image-normal direction to create polyhedrons with normally distributed lengths (120μm ± 5%). This 3D tissue block was replicated to fill the imaging voxel, applying a 10deg/mm rotation along the transmural direction. A second block was created consisting of equally-sized cuboids 2μm apart, with cross-sectional area matching the mean area of the segmented cardiomyocytes (Figure 1B). Transmural rotation was applied in the same way.

We considered two values for the extra-cellular diffusivity D_e, 2μm²/ms and 3μm²/ms, and in each case varied the intra-cellular diffusivity D_i from 0.5μm²/ms to D_e in steps of 0.5μm²/ms. The cell membranes were impermeable. Three pulse sequences were simulated: Stejskal–Tanner pulse gradient spin-echo (PGSE)⁶, second-order motion-compensated spin echo (M012-SE)⁷, and monopolar stimulated echo acquisition mode (STEAM)⁸, each with a b-value of 450s/mm² in 6 encoding directions and a 2.8x2.8x8.0mm³ voxel.

The histology data was classified with the aid of a fully-convolutional neural network. To do so, we implemented the U-net architecture⁹ in the TensorFlow framework¹⁰ with 4 layers, 16 features, and 3 colour channels. The network was trained for 10 hours on the manually segmented ground truth image before evaluating the image stack. The resulting segmentation was processed to extract cells and compute their size and shape distributions.

Results

Figure 2 shows histograms comparing the cell geometry in the segmented ground truth image with the automatically-segmented surrounding tissue. The extra-cellular volume fraction was high at 34.5% and 32.0% respectively, which is attributed to fixation-induced tissue shrinkage.

Figures 3 and 4 show the observed DT-CMR parameters as a function of D_i (and D_e) for the two substrates. The results are separated into the three different pulse sequences.

Discussion

The size and shape distributions of the manually segmented ground truth tissue region used to create the simulation substrate show it is a good approximation to the surrounding tissue. When comparing the cuboid model to this realistic substrate, it becomes clear that the lack of sheetlets/shear layers results in a higher FA.

The automatic segmentation produces larger cells, as seen in the tail of the area distribution (Figure 2). This may be explained by the size of the segmented microscopy image (3x3mm²), which could cause a large number of cells to be cut diagonally as they rotate in the transmural direction, increasing their apparent cross-sectional area.

There is a clear dependence on the intra-cellular diffusivity but choosing a different extra-cellular diffusivity has less effect for the same D_i. Both SE sequences report similar parameters, but at long mixing times (STEAM) the sequence better senses the restriction perpendicular to the myocytes’ long axis.

Conclusion

Acknowledgements

References

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