Trajectory implementations & literature

[Daval-G]

The goal of this issue is to list and discuss trajectories from the literature to implement. I gathered a bunch of articles, and I would be curious to know

• Which ones should be prioritized ? (would be nice for your future works)
• Which ones should not be reproduced ? (out-of-scope, too demanding computationally or in term of work, etc)

Feel also free to raise new questions, suggest new papers for discussion etc. and I will edit this post.

Here is a list of tasks related to trajectories from the literature that are not already implemented in MRI-NUFFT, along with a checklist for stuff that needs further exploration:

Trajectories

• 2D TWIRL from
  • "Twisting radial lines with application to robust magnetic resonance imaging of irregular flow", John I. Jackson et al. (1992)
• 3D radial trajectories (PR 3D radial trajectory bundle (clean) #115) from
  • "A Strategy for Sampling on a Sphere Applied to 3D Selective RF Pulse Design", Sam T. S. Wong and Mark S. Roos (1994)
  • "Fast isotropic volumetric coronary MR angiography using free‐breathing 3D radial balanced FFE acquisition", Stehning, C. et al. (2004)
  • "A radial sampling strategy for uniform k-space coverage with retrospective respiratory gating in 3D ultrashort-echo-time lung imaging", Jinil Park et al. (2016)
• 3D TPI from
  • "Fast Three Dimensional Sodium Imaging", Fernando E. Boada (1997)
• 3D spherical stack-of-spirals from
  • "Volumetric Spectroscopic Imaging with Spiral-Based k-Space Trajectories", Elfar Adalsteinsson et al. (1998)
• 2D Fibonacci spiral (PR Spiral patch #105) from
  • "Uniform K-Space Sampling with an Interleaved Fibonacci Spiral Acquisition", Harvey E Cline and Thomas R Anthony (1999)
• 2D WHIRL from
  • "An Optimized Center-Out k-Space Trajectory for Multishot MRI: Comparison With Spiral and Projection Reconstruction", James G. Pipe (1999)
• 2D Teardrop from
  • 'Teardrop, a novel non-raster readout for True FISP", Christopher Kumar Anand et al. (2001)
  • "Optimizing Teardrop, an MRI Sampling Trajectory", Christopher Kumar Anand et al. (2008)
• 2D variable density spiral (Vds spiral #129) from
  • "Fast 3D Imaging Using Variable-Density SpiralTrajectories With Applications to Limb Perfusion", Jin Hyung Lee et al. (2003)
• 3D genetic trajectory from
  • "Three dimensional k-space trajectory design using genetic algorithms", Sebastian Sabat et al. (2003)
• 3D guided missile trajectory from
  • "Fast Three Dimensional k-space Trajectory Design Using Missile Guidance", Ideas R. Mir et al. (2004)
  • "Undersampling k-Space Using Fast Progressive 3D Trajectories", Juan Spiniak et al. (2005)
• Improve 2D waves based on Bunched Phase Encoding from
  • "Bunched Phase Encoding (BPE): A New Fast Data Acquisition Method in MRI", Hisamoto Moriguchi and Jeffrey L. Duerk (2006)
• 3D revolving spheres from
  • "A 3D trajectory for undersampling k-space in MRSI applications", Sergio Uribe et al. (2007)
• 3D genetic trajectory from
  • "Random Volumetric MRI Trajectories via Genetic Algorithms", Andrew Thomas Curtis and Christopher Kumar Anand (2008)
• 3D DURGA from
  • "DURGA: A heuristically-optimized data collection strategy for volumetric Magnetic Resonance Imaging", Christopher Kumar Anand et al. (2008)
• 3D cylindrical radial from
  • "3D Undersampled Golden-Radial Phase Encoding Using Iterative Reconstructions and Inherent Regularization", C. Prieto et al. (2009)
• 3D Golden Means (PR 3D radial trajectory bundle (clean) #115) from
  • "Temporal Stability of Adaptive 3D Radial MRI Using Multidimensional Golden Means", Rachel W. Chan (2009)
  • "Generalization of three‑dimensional golden‑angle radial acquisition to reduce eddy current artifacts in bSSFP CMR imaging", Alexander Fyrdahl et al. (2021)
  • Golden Means from "Golden-Angle Radial MRI: Basics, Advances, and Applications", Li Feng (2022)
• 3D stack-of-rings from
  • "3D Magnetization-Prepared Imaging Using a Stack-of-Rings Trajectory", Holden H. Wu et al. (2010)
• 3D TURBINE (Add TURBINE trajectory #50 and Add TURBINE/REPI with EPI-based tools #137) from
  • "3D steady‐state diffusion‐weighted imaging with trajectory using radially batched internal navigator echoes (TURBINE)." McNab, Jennifer A., Daniel Gallichan, and Karla L. Miller. (2010).
  • "Ultrahigh resolution fMRI at 7T using radial‐cartesian TURBINE sampling." Graedel, Nadine N., Karla L. Miller, and Mark Chiew. (2022)
• 3D "Spiral" Phyllotaxis (PR 3D radial trajectory bundle (clean) #115) from
  • "Spiral Phyllotaxis: The Natural Way to Construct a 3D Radial Trajectory in MRI" Davide Piccini et al. (2011)
  • "Golden-Angle Radial MRI: Basics, Advances, and Applications", Li Feng (2022)
• 3D RAZER from
  • "RAZER: A Pulse Sequence for Whole-Brain Bolus Tracking at High Frame Rates", Sumeeth V. Jonathan et al. (2014)
• Improve 2D and 3D concentric rings based on
  • "Density-Weighted Concentric Circle Trajectories for High Resolution Brain Magnetic Resonance Spectroscopic Imaging at 7T", Lukas Hingerl et al. (2018)
  • "Three-dimensional, 2.5-minute, 7T phosphorus magnetic resonance spectroscopic imaging of the human heart using concentric rings", William T. Clarke (2022)
• 3D spiral staircase from
  • "Controlled aliasing for improved parallel imaging with a 3D spiral staircase trajectory", Ashley G. Anderson III et al. (2019)
  • "Fast 3D MR elastography of the whole brain using spiral staircase: Data acquisition, image reconstruction, and joint deblurring", Xi Peng et al. (2021)
• 3D T-Hex spirals from
  • "T-Hex: Tilted hexagonal grids for rapid 3D imaging", Maria Engel et al. (2020)
  • "Mono-planar T-Hex: Speed and flexibility for high-resolution 3D imaging", Maria Engel et al. (2021)
• Reproduce Looping Stars from
  • "Looping Star fMRI in Cognitive Tasks and Resting State", Beatriz Dionisio-Parra et al. (2020)
• AZTEK tools and 3D trajectories from
  • "AZTEK: Adaptive zero TE k-space trajectories", Tanguy Boucneau et al. (2020)
• Distinguish 3D Yarnball from currently implemented 3D Seiffert spirals based on
  • "Quantifying Lung Water Density with Ultrashort Echo Time Yarn-Ball MRI", William Quinn Meadus (2020)
• 3D REPI from (Add 3D-REPI #49 and Add TURBINE/REPI with EPI-based tools #137)
  • "Three Dimensional Radial Echo Planar Imaging for Functional MRI", Christoph A. Rettenmeier et al. (2022)
• 2D PILOT from
  • "PILOT: Physics-Informed Learned Optimized Trajectories for Accelerated MRI", Tomer Weiss et al. (2021)
• 2D trajectory from
  • "Learning Optimal K-space Acquisition and Reconstruction using Physics-Informed Neural Networks", Wei Peng et al. (2022)
• 2D trajectory from
  • "Bayesian Optimization of Sampling Densities in MRI", Alban Gossard (2023)
• 2D BJORK from
  • "B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI", Guanhua Wang et al. (2023)
• 3D SNOPY from
  • "Stochastic optimization of three-dimensional non-Cartesian sampling trajectory", Guanhua Wang et al. (2023)
• 2D and 3D ECCENTRIC from
  • "ECCENTRIC: a fast and unrestrained approach for high-resolution in vivo metabolic imaging at ultra-high field MR", Antoine Klauser et al. (2023)
• 3D PETALUTE from
  • "An Accelerated PETALUTE MRI Sequence for In Vivo Quantification of Sodium Content in Human Articular Cartilage at 3T", Cameron X. Villarreal et al. (2024)
  • "Accerated Preclinical UHF Abdominal T1 Mapping using Novel Rosette Accelerated Preclinical UHF Abdominal T1 Mapping using Novel Rosette Ultrashort Echo Time (PETALUTE) Ultrashort Echo Time (PETALUTE)", Alexandra Lipka et al. (2024)
• 3D Arc-ZTE from
  • "Arc-ZTE: Incoherent k-space sampling in time using continuously-slewed gradients for exible, dynamic, quiet Zero TE MRI", Shreya Ramachandran et al. (2024)

Check-list

• "Fast Three Dimensional Magnetic Resonance Imaging", Pablo Irarrazabal, Dwight G. Nishimura (1995)
• "Simple Analytic Spiral K-Space Algorithm", Gary H. Glover (1999)
• "Design of a logarithmic k-space spiral trajectory", Harvey E. Cline (2001)
• "Advances in sensitivity encoding with arbitrary k-space trajectories", Klaas P. Pruessmann et al. (2001)
• "Optimal Design of k-Space Trajectories Using a Multi-Objective Genetic Algorithm", Brian M. Dale et al. (2004)
• "Single TrAjectory Radial (STAR) Imaging", Gordon E. Sarty et al. (2004)
• "Design and Analysis of a Practical 3D Cones Trajectory", Paul T. Gurney et al. (2006)
• "A Fast Method for Designing Time-Optimal Gradient Waveforms for Arbitrary k-Space Trajectories", Michael Lustig et al. (2008)
• "Acquisition-weighted stack of spirals for fast high-resolution three-dimensional ultra-short echo time MR imaging",
  Yongxian Qian et al. (2008)
• "Comparison between Readout-Segmented ( RS )-EPI and an improved distortion correction method for Short-Axis Propeller ( SAP )-EPI", S. Skare et al. (2010)
• "A Looping Trajectory for Single-Shot 3D Imaging", R. W. Stobbe , and C. Beaulieu (2011)
• "Distributed spirals: A new class of three-dimensional k-space trajectories", Dallas C. Turley and James G. Pipe (2012)
• "Spiral Trajectory Design: A Flexible Numerical Algorithm and Base Analytical Equations" James G. Pipe et al. (2014)
• "Optimized three-dimensional sodium imaging of the human heart on a clinical 3T scanner", Neville D Gai (2014)
• "Fast and Robust Design of Time-Optimal k-Space Trajectories in MRI", Mathias Davids et al. (2015)
• "Hybrid radial-cones trajectory for accelerated MRI", Kevin M. Johnson (2016)
• "Variable Density Randomized Stack of Spirals(VDR-SoS) for Compressive Sensing MRI", Giuseppe Valvano et al. (2016)
• "Concentric rings K‐space trajectory for hyperpolarized 13C MR spectroscopic imaging." Jiang, Wenwen, Michael Lustig, and Peder EZ Larson. (2016)
• "Golden-ratio rotated stack-of-stars acquisition for improved volumetric MRI", Ziwu Zhou et al. (2017)
• "Squeezed Trajectory Design for Peak RF and Integrated RF Power Reduction in Parallel Transmission MRI", Qing Li et al. (2018)
• "Partial fourier shells trajectory for non-cartesian MRI", Tao et al. (2019)
• "Rotated spiral RARE for high spatial and temporal resolution volumetric arterial spin labeling acquisition", Fanny Munsch et al. (2020)
• "Three dimensional radial echo planar imaging for functional MRI", Christoph A. Rettenmeier et al. (2021)
• "Optimized three-dimensional ultrashort echo time: Magneticresonance fingerprinting for myelin tissue fraction mapping", Zihan Zhou et al. (2022)
• "High resolution free-breathing respiratory-resolved volumetric lung imaging at 0.55T using stack-of-spiral out-in bSSFP", Ziwei Zhao et al. (2024)
• "Silent Looping Star fMRI with enhanced Encoding and Reconstruction Performance", Ana Beatriz Solana et al. (2024)
• "Fast and Motion-Robust Non-Contrast MR Angiography using Centric kx–ky Trajectory.", Vadim Malis et al. (2024)
• "3D UTE With Twisted Trajectories", Michael Carl et al. (2024)
• "Efficient 3D cone trajectory design for improved combined angiographic and perfusion imaging using arterial spin labeling", Qijia Shen et al. (2024)

[Daval-G]

For context, I already have advanced implementations of the following trajectories:

• 3D genetic trajectory from
  • "Three dimensional k-space trajectory design using genetic algorithms", Sebastian Sabat et al. (2003)
• 3D guided missile trajectory from
  • "Fast Three Dimensional k-space Trajectory Design Using Missile Guidance", Ideas R. Mir et al. (2004)

I also have works in progress for:

• 2D TWIRL from
  • "Twisting radial lines with application to robust magnetic resonance imaging of irregular flow", John I. Jackson et al. (1992)
• 2D WHIRL from
  • "An Optimized Center-Out k-Space Trajectory for Multishot MRI: Comparison With Spiral and Projection Reconstruction", James G. Pipe (1999)

Finally, I believe the following three 3D radial trajectories are low-hanging fruits, if our focus is to reproduce literature:

• 3D radial trajectory from
  • "A Strategy for Sampling on a Sphere Applied to 3D Selective RF Pulse Design", Sam T. S. Wong and Mark S. Roos (1994)
  • "Fast isotropic volumetric coronary MR angiography using free‐breathing 3D radial balanced FFE acquisition", Stehning, C. et al. (2004)
  • "A radial sampling strategy for uniform k-space coverage with retrospective respiratory gating in 3D ultrashort-echo-time lung imaging", Jinil Park et al. (2016)
• 3D Golden Means from
  • "Temporal Stability of Adaptive 3D Radial MRI Using Multidimensional Golden Means", Rachel W. Chan (2009)
    Golden Means from "Golden-Angle Radial MRI: Basics, Advances, and Applications", Li Feng (2022)
• 3D "Spiral" Phyllotaxis from
  • "Spiral Phyllotaxis: The Natural Way to Construct a 3D Radial Trajectory in MRI" Davide Piccini et al. (2011)
    "Golden-Angle Radial MRI: Basics, Advances, and Applications", Li Feng (2022)

[paquiteau]

Thanks for the detail review ! I edited you answer for linking to relevant issue and add check boxes.

[chaithyagr]

This is just amazing list!
I think its best practice to have examples with respective papers within a folder called "examples/trajectories", to ensure we can have it visualized etc right within docs. WDYT?

[chaithyagr]

@paquiteau possibly some way to have nomenclature and trajectory repository? get_trajectory('name')(params)?

[paquiteau]

I don't see any difficulties for that. We can go two ways:

• A decorator on top of each trajectory function using the MethodRegister helper (as for density compensation for instance)

• Use some import-time logic to register all trajectories methods. We have a consistent initialize_<trajectory_name> naming scheme, so this should be fairly easy.

And we can even propose both! The advantage of the decorator is that it can be used in external packages to register extra trajectories.