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A Genetic Algorithm for Optimal Design of Spectrally Selective k-Space

A Genetic Algorithm for Optimal Design of Spectrally Selective k-Space. Douglas C. Noll, Ph.D. Depts. of Biomedical Engineering and Radiology University of Michigan, Ann Arbor Supported by NIH Grant NS32756 Acknowledge the assistance of Sangwoo Lee. Outline.

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A Genetic Algorithm for Optimal Design of Spectrally Selective k-Space

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  1. A Genetic Algorithm for Optimal Design of Spectrally Selective k-Space Douglas C. Noll, Ph.D. Depts. of Biomedical Engineering and Radiology University of Michigan, Ann ArborSupported by NIH Grant NS32756 Acknowledge the assistance of Sangwoo Lee

  2. Outline • Background on Spectral-Spatial Imaging • Optimization using Genetic Algorithms • Optimization Results • Experimental Findings • Summary

  3. Stochastic Acquisitions • Sheffler and Hennig (MRM, 35:569-576, 1996) • Recognition that particular acquisitions could be spectrally and spatially selective • Spectral bandwidth ~ 1/Tread Stochastic K-Space Water Oil (From Sheffler & Hennig, MRM, 35:569-576, 1996)

  4. Rosette Acquisitions • Spectral properties similar to stochastic imaging, but: • Extra suppression of low spatial frequencies • Simple parameterization • No sharp corners in k-space (reduced slew req.) Water Fat

  5. SMART Imaging • Simultaneous Multislice Acquisition using Rosette Trajectories (SMART) • Excitation of several (e.g. 3) slices • Use of slice gradient to modulate slices to different frequencies • Use of spectral properties of acquisition to differentiate slices • Demodulation of raw data shifts from one slice to another

  6. SMART Imaging 3 Runs - Single-slice Rosette Imaging 1 Run - Triple-slice SMART Imaging Slice 1 Slice 2 Slice 3

  7. The Rosette k-space Trajectory • K-space can be described by:k(t) = A sin(w1 t)exp(i w2 t)w1 = oscillation frequencyw2 = rotation frequency • Peak gradient and slew rate constraints:gmax = (2p/g) A w1smax = (2p/g) A (w12 + w22) w2 w1

  8. Stochastic Rosettes • Rosette acquisitions can be randomized by treating each petal as a separate unit • Each petal can be characterized by two random numbers • Method: • Randomly select A from [0.9, 1.1]xA0 • Determine w1 from gmax equation • Determine w2,max from smax equation • Randomly select w2 from [0.5, 1.0]x w2,max

  9. Stochastic Rosettes • Petals are spliced together so that there are no discontinuities in the gradient waveforms Petal 3 Petal 1 Petal 2

  10. Challenge: Optimization • Stochastic rosette acquisitions: • Easy to design • Large number of parameters • No obvious relationship between parameters and acquisition performance • There are an infinite choice of parameters for stochastic rosette acquisitions

  11. Parameterization of Each Trajectory • Each petal is characterized by two random numbers, which we will call “genes” • For a trajectory with K=56 petals, there are K genes that make up a “chromosome” • Each candidate trajectory is characterized by a chromosome

  12. Genetic Algorithm Create InitialPopulation (e.g. N=64) Evaluate Cost Function Select “Mates” Mate by Swapping Random Segments of Chromosomes Done? Random Mutations (e.g. 2%)

  13. Cost Function • Each trajectory was evaluated by creating k-space data and reconstructing a simulation object: • The cost function that had two components: • Fidelity of on-resonant reconstruction (squared error vs. an artifact-free image) • Suppression of off-resonant data (average image energy for a range of off-resonant reconstruction frequencies)

  14. Genetic Algorithm Results • Average and best cost functions over 200 generations: Rapid early reduction from elimination of “unfit” members from the breeding pool

  15. Off-Resonance Behavior Stochastic Rosettes 0 Hz 50 100 150 200 Hz Standard Rosettes

  16. Off-Resonance Behavior • Periodic structure in regular rosettes gives uneven spectral behavior • Stochastic rosettes have a more uniform response, though at times larger

  17. Experimental Results - • Water/Oil Images in Phantom – each pair of images is reconstructed for a single data set 28 ms Readout Res: 3.3 x 3.3 mm gmax = 22 mT/m smax = 175 T/m/s Stochastic Rosettes Standard Rosettes Residual water Water Oil

  18. Summary • Stochastic rosette acquisitions are both spatially and spectrally selective • Optimization of acquisition parameters is a daunting task: • Approximately 100 parameters • No obvious relationship between parameters and performance • Gradient-based optimization methods do not work because the cost function space is too rough • Genetic algorithms are appropriate for this kind of problem

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