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The Maastricht Diffusion Toolbox (MDT): Modular, GPU accelerated, dMRI microstructure modeling

Robbert Leonard Harms^1,2 and Alard Roebroeck¹

¹Maastricht University, Maastricht, Netherlands, ²Brain Innovation, Maastricht, Netherlands

Synopsis

MDT's object oriented modular design allows arbitrary user specification and combinations of dMRI compartment models, diffusion microstructure models, likelihood functions and optimization algorithms. Many diffusion microstructure models are included, and new models can be added simply by adding Python script files. GPU based computations allow for ~60x faster model fitting; e.g. the 81 volume example NODDI dataset can be fitted whole brain in about 40 seconds, which makes MDT ideal for population studies. MDT can be extended to other modalities and models such as quantitative MRI. The software is open source and freely available at https://github.com/cbclab.

Introduction

Recent advances in diffusion MRI (dMRI) modeling propose multi-compartment microstructure models that promise greater specificity over DTI^1,2⁠ and offer additional microstructure measures such as axonal density, dispersion and diameter distributions. Models of this type include (but not limited to) CHARMED³⁠, NODDI⁴⁠, AxCaliber⁵⁠, ActiveAx⁶⁠ and variations^7–10⁠. These multi-compartment models commonly require non-linear model fitting, which has considerable challenges in quality of fit (local minima, convergence) and runtime, where runtime in particular is often prohibitive for larger studies (>20 subjects) and population studies (>100 subjects). In this work we present a new unified dMRI microstructure analysis toolbox, the Maastricht Diffusion Toolbox (MDT), which can implement any microstructure model, comes pre-supplied with a library of models, has a unified implementation of cascading (chained optimization) and uses graphic card accelerated computations that allow for ~60x faster model fitting over traditional CPU based implementations. The software is open source and freely available at https://github.com/cbclab under an L-GPL license.

Methods

Figure 1 shows a (high level) overview of MDT and the Maastricht Optimization Toolbox (MOT). In MDT, compartments are combined using a high level Python-based scripting-language (see upper right in Figure 1) to form, together with a likelihood model, a multi-compartment model. MDT compiles these models to OpenCL C and uses MOT to optimize or sample them on the CPU and/or GPU (Graphics Processing Unit; graphics card) using the OpenCL framework, a free and open standard for heterogeneous parallelized computations. MDT features cascade models which offer an unified approach to chained optimization strategies in which parameters of a complex model are initialized with, or fixed to, values of a simpler model. Figure 2 shows three cascading strategies used as an example in this work. In the first, Cascade S0 (CS), the final desired model is initialized only with an S0 (b0 signal) estimate. Cascade Initialize (CI) extends this by initializing parameters of complex models from those of simpler models. Cascade Fixed (CF) is an adaption of CI in which some parameters are fixed instead of initialized, reducing dimensionality of later optimization steps. Out of the box, MDT comes with many popular diffusion models such as Tensor, Ball&Stick, NODDI, CHARMED and ActiveAx. New models can be added simply by adding Python script files (see Figure 1 top right). All models can be modularly combined with any likelihood model and any optimization and sampling routine. Additional MDT features are: support for provenance trace, batch fitting routines, detailed logging, data consistency checks and extensibility for optimization and sampling routines. MDT has a Python interface, a command line interface and a graphical interface (Figure 3) and is compatible with Linux, Mac and Windows and with most graphics card and CPU hardware. Processing reported here was done on a single AMD Fury X graphics card.

Results and discussion

To illustrate the performance of MDT and MOT, we fitted two common models, CHARMED_in3 (with 3 intra-axonal compartments) and NODDI to two diffusion MRI datasets of the HCP MGH Consortium1. Both datasets (1003 and 1004 from the HCP MGH Consortium) were acquired at a resolution of 1.5mm isotropic with 4 shells of b=1000, 3000, 5000, 10,000, s/mm^2, with respectively 64, 64, 128, 393 directions and with 40 b0 volumes. Figure 4 shows the fitting results of CHARMED_in3, highlighting some differences between the three cascading strategies CS, CI and CF with the Powell optimization algorithm and the Ball&Stick model as the cascading basis. Whole brain computation time was ~2 hours for CS, ~2 hours for CI and ~1 hour for CF for this complex model on this 552 volume dataset. Figure 5 shows the results of MCMC sampling (NODDI model fit using CF and Powell to initializing a random-walk metropolis MCMC sampler, 500 samples of the FR parameter posterior). Fitting and sampling this single slice took ~12 minutes on the 552 volume dataset. For smaller and better known datasets, such as the 81 volume example NODDI dataset, whole brain NODDI can be computed in ~40 seconds.

Conclusion

We here put forward MDT, a modular, GPU accelerated, dMRI microstructure modeling and analysis toolbox. The low costs of suitable graphics card (<400 euro) and the ensuing much reduced runtimes as well as the ease of modelling make MDT suitable for rapid model prototyping and whole brain analysis at a single workstation. On a moderate sized server or workstation it is feasible to analyse population studies of hunderds of subjects (see Harms et al. this conference). Finally, by splitting the software stack into MDT and MOT we envision software extensions to other modalities such as light microscopy or quantitative MRI.

Acknowledgements

No acknowledgement found.

References

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Figures

Left, UML diagram of MDT (top) and MOT (bottom) and their interaction. In MDT, multi-compartment models are constructed using multiple single compartments and a single likelihood model. Cascade models (see Figure 2) are built as a chain of multiple multi-compartment models. The multi-compartment models implement the MOT model interface, allowing them to be optimized and sampled using the OpenCL parallelized routines in MOT. The modeling flow on the right shows the use of Python scripting to construct arbitrary multi-compartment models, from which MDT builds the corresponding model equation and MOT optimizes that model on the CPU and GPU.

Illustration of the three different cascading strategies (for the example of the NODDI model): CS, CI and CF. The blue arrows indicate initialization of a parameter, the orange arrows indicate a fixation of a parameter.

Screenshot of the three interfaces to MDT. On the left, the graphical user interface, on the top right the command line interface and on the bottom right an example of Python scripting.

Parameter maps (CHARMED_in3, FR map; top row) and local restricted compartment 3D color-coded orientations (bottom row) for different cascading strategies (in columns) for a single HCP MGH subject (1003). The top row shows a thresholded FR map superimposed on a hindered fraction map in gray-scale.

MCMC sampling results of NODDI parameter posteriors on a single HCP MGH subject. The top two maps show the mean (left) and standard deviation (right) of the restricted volume fraction posterior. The middle row depicts the sampling chain after burn-in, the bottom row depicts the unnormalized posterior histogram of the NODDI FR parameter with the fitted Gaussian for the indicated voxel (arrows in maps).

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

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