In the Python microstructure modelling language it is possible to generate complex ... using basic math operators and/or decorated with a "Model Decorator.
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We show that diffusion microstructure modeling including crossing fibers, complex microstructure compartment models and compartment-specific T2’s is possible on an extensive 384 volume multi-shell dMRI data set. The usage of 100mT/m gradients and multi-band (simultaneous multislice) imaging was crucial in obtaining this ActiveAx optimized dataset. In future work it will be explored to which degree this data can support axonal density, dispersion and diameter distributions in the entire human white matter. With increasing availability of stronger gradients (>=80mT/m) and simultaneous multislice imaging in clinical machines, GPU accelerated microstructure modeling tools will become critical to this endeavor.
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((((T2().fix('T2') .ren('T2', 'T2short'), ((((Weight().ren('w', 'w_cyl'), CylinderGPD() .fix('d', 1.7e9) .fix('theta') .fix('phi')), '*'), ((Weight().ren('w', 'w_zep'), Zeppelin().fix('phi') .fix('d', 1.7e-9) .fix('theta')), '*')), '+')), '*'), ((T2().fix('T2', 0.5) .ren('T2', 'T2long'), Weight().ren('w', 'w_ball'), Ball().fix('d', 3.0e-9)), '*')), '+')), '*')
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The MMWMD model (also known as ActiveAx) was estimated using a 3 compartment model (CylinderGPD, Zeppelin and Ball). The T2s for CylinderGPD and Zeppelin (short T2) and Ball (long T2) were initialized from a previous (T2(), T2())fit. ((SignalScalar(),
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References: 1. Alexander D. (2010), Neuroimage, no. 52(4), pp. 1374-1389 2. Assaf Y. (2005), Neuroimage , no. 27(1), pp. 48-58 3. Behrens A. (2007), Neuroimage, no. 34(1), pp. 144-155 4. De Santis (2014), Magn. Reson. Med., no. 71, pp. 661–671 5. Panagiotaki E. (2011), NeuroImage, no. 59(3), pp. 2241-2254 6. Sotiropoulos S. (2013), Proc. Intl. Soc. Mag. Reson. Med. no. 21, pp. 0052 7. Zhang H. (2012), Neuroimaging, no. 61(4), pp.1000-1016
((SignalScalar(), ((((T2().fix('T2').ren('T2', 'T2short'), ((((Weight().ren('w', 'NDI'), Noddi_IC().fix('d', 1.7e-9) .fix('theta') .fix('phi')), '*'), ((Weight().ren('w', 'w_ec'), Noddi_EC().fix('d', 1.7e-9) .fix('theta') .fix('phi') .ren('kappa', 'k_ec')), '*')), '+')), '*'), ((T2().fix('T2', 0.5) .ren('T2', 'T2long'), Weight().ren('w', 'w_csf'), Ball().fix('d', 3.0e-9)), '*')), '+')), '*')
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ActiveAx (LM: 310 seconds, normally ~1 hour)
In the Python microstructure modelling language it is possible to generate complex hierarchical multi-compartment models for dMRI using a tree structure written as an hierarchical list. Compartment models are combined using basic math operators and/or decorated with a "Model Decorator Function" (for example, a noise model). For instance: (Ball(), Stick(), '+') A more complete Ball&Stick example, with volume fractions ((SignalScalar(), ((((Weight().ren('w', ‘f_ball'), (weights) and Ball- and StickT2().fix('T2', 0.5).ren('T2', 'T2_ball'), Ball().fix('d', 1.7e-9)), specific T2's is on the right. '*'), ((Weight().ren('w', ‘f_stick'), Unique parameter maps are T2().fix('T2_short').ren('T2', 'T2_stick'), ensured with the rename (ren) Stick().fix('d', 1.7e-9)), '*')), command. To fix parameters to '+')), specific values one can use the '*') fix command with either a constant or previously calculated results (constants or per voxel).
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NODDI was estimated with a 3 compartment model (EC, IC and Ball) with a 500ms T2 for the Ball compartment and a short T2 for the EC and IC compartments. Various parameters were initialized from previous (T2(), T2()) and (Ball(), Stick()) fits.
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Microstructure model specification language
For reprints or registering to the (release) mailing list: robbert.harms@ maastrichtuniversity.nl
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The OO design abstracts microstructure compartment models, noise models and optimization and sampling routines, such that more can be added in a modular way. Using the toolbox one can build complex models by combining "Estimatable Functions" (e.g. compartment models). Together with a prior, parameter codec and proposal function these models can be handed to any CLRoutine (e.g. LM optimizer) to be able to estimate the parameters using different optimization and sampling techniques.
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Object Oriented Design
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((SignalScalar(), ((((Weight().ren('w', 'w_ball'), T2().fix('T2', 0.5) .ren('T2', 'T2long'), Ball().fix('d', 3.0e-9)), '*'), ((T2().fix('T2') .ren('T2', 'T2short'), ((((Weight().ren('w', 'w_stick1'), Stick().fix('d', 1.7e-9)), '*'), ((Weight().ren('w', 'w_stick2'), Stick().fix('d', 1.7e-9) .ren('theta', 'theta1') .ren('phi', 'phi1')), '*')), '+')), '*')), '+')), '*')
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Charmed Noddi Ball and Stick Tensor AxCaliber ActiveAx (MMWMD) …
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Ball and two Sticks was estimated with a fixed 500ms T2 for the Ball compartment and a short T2 for the Stick models. The directions of the first Stick and the short T2 were initialized were initialized from previous (T2(), T2()) and (Ball(), Stick()) fits (i.e.: a cascade)5.
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Ball and 2 Sticks (LM: 31 seconds, normally ~20 minutes)
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Multi-shell HARDI data was acquired from a single subject on a Siemens 3T CONNECTOM Skyra system with maximum gradient strength of 100 mT/m and 32-channel RF-coil at the Center for Magnetic Resonance Research (CMRR), University of Minnesota, USA. Acquisition and preprocessing were performed according to the Human Connectome Project 3T diffusion MRI protocols (Sotiropoulous, 2013), modified to a 4-shell ActiveAx protocol (Alexander, 2010) at 1,8mm isotropic. Acquired shells were (b-value, TE, directions): 1) 595 s/mm2, 55 ms, 128; 2) 1025 s/mm2, 74 ms, 64; 3) 1950 s/mm2, 79 ms, 64; 4) 3350 s/mm2, 74 ms, 64, for a total of 384 volumes and 24 b0’s. All shells were acquired twice with multi-band factor 4, once with phase encode directions LR, once with RL. Matched T2-relaxometry data was acquired with spin-echo EPI at TEs between 35ms and 140ms, to allow multi-compartment T2 modeling.
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University, Maastricht, Netherlands, 2Icahn School of Medicine, New York, NY, USA 3University of Minnesota, Minneapolis, MN, USA
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Multi-shell high angular resolution diffusion MRI (dMRI) is increasingly used to estimate models of brain white matter that include either multiple fiber directions in each voxel (e.g. Behrens, 2007) or microstructural information such as axonal density, diameters and/or dispersion (Assaf, 2005; Alexander, 2010; Zhang, 2012). Combining the modeling of multiple direction and microstructural information has proved challenging but possible on clinical time multi-shell HARDI data with a constant TE which is suboptimal for most shells (De Santis, 2014). This study has two main objectives: 1.Investigating complex diffusion microstructure modeling on multi-shell multiTE diffusion MRI acquired with a high-end 100mT/m MRI system 2.Creating a GPU accelerated flexible Python toolbox needed to make microstructure analysis of large multi-shell dMRI datasets tractable
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Robbert Harms1, Matteo Bastiani1, Junqian Xu2, Essa Yacoub3, Rainer Goebel1, Alard Roebroeck1
Introduction
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White matter microstructure modelling using a modular and extensible gpu accelerated toolkit
