Diffusion Numerical Phantoms
Hong-Hsi Lee1
1Massachusetts General Hospital, Charlestown, MA, United States

Synopsis

Keywords: Contrast mechanisms: Microstructure, Contrast mechanisms: Diffusion

Performing diffusion simulations in numerical phantom mimicking realistic tissue microstructure helps to test the sensitivity of diffusion MRI to tissue features and validate the biophysical models. Realistic cell geometries for simulations have been directly reconstructed from the microscopy data of biological tissues in 3-dimension. In addition to the diffusion within intra-cellular space, it is possible to perform simulations of diffusion in the extra-cellular space, as well as of the exchange between intra- and extra-cellular spaces. The tissue preparation preserving extra-cellular space in histology is non-trivial, prompting the development of pipelines to generate semi-realistic tissue microstructure by packing multiple artificial “cells”.

Introduction

To balance between accuracy and precision in estimation of tissue parameters through biophysical modeling of diffusion MR signal, assumptions are inevitably made to simplify tissue microgeometry [1]. It is necessary to validate the assumptions of models before use, either through experiments in physical phantoms [2], or testing the model functional forms in animals and human subjects [3], or numerical simulations [2]. So far, numerical simulation is the most flexible and economic choice among all kinds of validation. To create a numerical phantom for diffusion simulations, we can (i) arrange, pack, and combine multiple simple shapes, (ii) reconstruct cell geometries in microscopy data, and (iii) generate cell/tissue-mimicking geometries using a generative model.

Packing of simple shapes

To mimic a realistic microstructure geometry, we can arrange, pack and combine multiple simple shapes, in either 2d [4-7] or 3d [8-16], with a length scale similar to the biological tissue of interest.

For simulations within a porous medium, e.g., restricted diffusion in intra-axonal space of the WM, the packing of isolated pores has no influence on simulation results [17]. However, for simulations including a non-porous medium, e.g., hindered diffusion in the extra-axonal space of the WM, simulation results depend dramatically on the packing geometry [18-20].

Parallel cylinders packed in a square or a hexagonal lattice [21-25] are common models for highly aligned WM axons. However, histological studies [26-28] indicate a random packing geometry for WM axons,which is non-trivial while building a numerical phantom [4,29,30]. It is time-consuming to create a random packing geometry by brute-force methods [5,8], which can be accelerated by placing objects sequentially in descending order of size [31], thereby altering the structural disorder making it less randomly packed.

Instead, by applying a collision-driven packing generation algorithm [32-34], numerical phantoms can be generated composed of more than thousands of randomly densely packed circles or spheres in any kinds of radius distribution within minutes. Also, an open-source software (AxonPacking) [35] based on molecular dynamic approaches is available for generating randomly packed circles in Gamma distributed radii and corresponding g-ratio in accordance with histological observations.

Realistic cell geometry in microscopy data

Benefiting from the recent advances in microscopy, realistic cell geometries for simulations have been directly reconstructed from the microscopy data of neuronal tissues in 2 dimension (2d) [36,37] and 3d [38-41].

To generate the 3d substrates based on microscopy data for diffusion simulations, we can translate the voxelized cell segmentation into either smoothed meshes or binary masks [38]. Each approach has its own pros and cons [42].

For the smoothed-mesh approach, the generated cell model has smooth surface, potentially having surface-to-volume ratio similar to the real cells. However, it is non-trivial to decide on the degree of smoothing while generating the cell model. In addition, in simulations, the problem of floating-point precision may arise, especially for determining whether a random walker encounters a membrane.

For the binary mask approach, it is fast and simple to translate the discrete microscopy data into the 2d pixelated or 3d voxelized cell geometries. Further, the corresponding simulation kernel is easy to implement and maintain, and has low computational complexity with minimal problem of floating-point precision. On the other hand, the generated cell model has unrealistic surface-to-volume ratio due to its “boxy” cell surface.

Generative model of cell geometries

Performing MC simulations in realistic cell geometries helps to test the sensitivity of diffusion MRI to tissue features and validate the biophysical models. In addition to the examples of diffusion within intra-cellular space, it is also possible to perform simulations of diffusion in the extra-cellular space, as well as of the exchange between intra- and extra-cellular spaces. The tissue preparation preserving extra-cellular space in histology is non-trivial, prompting the development of pipelines to generate semi-realistic tissue microstructure by packing multiple artificial “cells”, such as MEDUSA [43] and ConFiG [44], whose generated microgeometry potentially could be transformed to 3d voxelized data or meshes. Furthermore, it is possible to augement the database of tissue micro-geometries by training a neural network, such as generavie adversarial network [45].

Outlook

Here we provide an outlook for the next generation simulation tools. So far, most of the implementations of diffusion simulations focus on the MR sequence with radiofrequency pulses of 90˚ and 180˚, such as the spin-echo and stimulated-echo sequences. To simulate other MR sequences, such as the steady-state free precession sequence [46], it is required to combine the diffusion simulation with the Bloch simulator in MR system. Furthermore, the generation of accurate cell segmentation for simulations in microscopy-based geometry is time-consuming and labor-intensive; performing diffusion simulations directly in a mesoscopic diffusivity map, obtained via a transformation of the microscopy intensity, could largely simplify the validation pipeline — however, such segmentation-less simulation must itself be thoroughly validated.

Acknowledgements

HHL is supported by the Office Of The Director (OD) and National Institute Of Dental & Craniofacial Research (NIDCR) of NIH with the award number DP5OD031854.

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