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Noll 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

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Noll Outline Background on Spectral-Spatial ImagingBackground on Spectral-Spatial Imaging Optimization using Genetic AlgorithmsOptimization using Genetic Algorithms Optimization ResultsOptimization Results Experimental FindingsExperimental Findings SummarySummary

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Noll Stochastic Acquisitions Sheffler and Hennig (MRM, 35:569-576, 1996)Sheffler and Hennig (MRM, 35:569-576, 1996) Recognition that particular acquisitions could be spectrally and spatially selectiveRecognition that particular acquisitions could be spectrally and spatially selective Spectral bandwidth ~ 1/T readSpectral bandwidth ~ 1/T read StochasticK-Space Water Oil (From Sheffler & Hennig, MRM, 35:569-576, 1996)

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Noll Rosette Acquisitions Spectral properties similar to stochastic imaging, but: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

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

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

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Noll The Rosette k-space Trajectory K-space can be described by: k(t) = A sin( 1 t)exp(i 2 t) 1 = oscillation frequency 2 = rotation frequencyK-space can be described by: k(t) = A sin( 1 t)exp(i 2 t) 1 = oscillation frequency 2 = rotation frequency Peak gradient and slew rate constraints: g max = (2 / ) A 1 s max = (2 / ) A ( 1 2 + 2 2 )Peak gradient and slew rate constraints: g max = (2 / ) A 1 s max = (2 / ) A ( 1 2 + 2 2 ) 1111 2222

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Noll Stochastic Rosettes Rosette acquisitions can be randomized by treating each petal as a separate unitRosette acquisitions can be randomized by treating each petal as a separate unit Each petal can be characterized by two random numbersEach petal can be characterized by two random numbers Method:Method: 1.Randomly select A from [0.9, 1.1]xA 0 2.Determine 1 from g max equation 3.Determine 2,max from s max equation 4.Randomly select 2 from [0.5, 1.0]x 2,max

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Noll Stochastic Rosettes Petals are spliced together so that there are no discontinuities in the gradient waveformsPetals are spliced together so that there are no discontinuities in the gradient waveforms Petal 1 Petal 3 Petal 2

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Noll Challenge: Optimization Stochastic rosette acquisitions: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 acquisitionsThere are an infinite choice of parameters for stochastic rosette acquisitions

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Noll Parameterization of Each Trajectory Each petal is characterized by two random numbers, which we will call “genes”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”For a trajectory with K=56 petals, there are K genes that make up a “chromosome” Each candidate trajectory is characterized by a chromosomeEach candidate trajectory is characterized by a chromosome Petals1234…K Genes A1A1A1A1 A2A2A2A2 A3A3A3A3 A4A4A4A4 AKAKAKAK 2,1 2,2 2,3 2,4 2,K

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

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Noll Cost Function Each trajectory was evaluated by creating k- space data and reconstructing a simulation object:Each trajectory was evaluated by creating k- space data and reconstructing a simulation object: The cost function that had two components: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)

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

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Noll Off-Resonance Behavior 0 Hz50 100 150 200 Hz Stochastic Rosettes Standard Rosettes

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

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Noll Experimental Results - Water/Oil Images in Phantom – each pair of images is reconstructed for a single data setWater/Oil Images in Phantom – each pair of images is reconstructed for a single data set Residualwater Water Oil StochasticRosettesStandardRosettes 28 ms Readout Res: 3.3 x 3.3 mm g max = 22 mT/m s max = 175 T/m/s

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Noll Summary Stochastic rosette acquisitions are both spatially and spectrally selectiveStochastic rosette acquisitions are both spatially and spectrally selective Optimization of acquisition parameters is a daunting task: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 problemGenetic algorithms are appropriate for this kind of problem

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