Ardenkjær-Larsen, Jan Henrik

Hansen, Rie Beck

Hanson, Lars G.

Laustsen, Christoffer

Mariager, Christian

Schulte, Rolf F.

In this study we demonstrate how reconstruction for IDEAL spiral CSI (spectroscopic imaging scheme developed for hyperpolarized dynamic metabolic MR imaging) can be improved by using regularization with a sparsity constraint. By exploiting sparsity of the spectral domain, IDEAL spiral CSI can achieve chemical shift encoding by acquisition of only few time-shifted echoes. The minimum number of echoes required to avoid noise amplification can be decreased by means of regularization enforcing spectral sparsity, hereby reducing scan time. Improvements achieved by using regularized reconstruction are demonstrated for in vivo data from a hyperpolarized cardiac study of a pig

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Downloaded from orbit.dtu.dk on: Dec 18, 2017Improved reconstruction for IDEAL spiral CSIHansen, Rie Beck; Mariager, Christian; Laustsen, Christoffer; Schulte, Rolf F.; Ardenkjær-Larsen, JanHenrik; Hanson, Lars G.Publication date:2017Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Hansen, R. B., Mariager, C., Laustsen, C., Schulte, R. F., Ardenkjær-Larsen, J. H., & Hanson, L. G. (2017).Improved reconstruction for IDEAL spiral CSI. Abstract from  ISMRM 25th Annual Meeting & Exhibition,Honolulu, United States.Improved reconstruction for IDEAL spiral CSIRie B Hansen , Christian Ø Mariager , Christoﬀer Laustsen , Rolf F Schulte , Jan H Ardenkjær-Larsen , and Lars GHansonDepartment of Electrical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark, MR Research Centre, Aarhus University, Aarhus,Denmark, GE Global Research, Munich, GermanySynopsisIn this study we demonstrate how reconstruction for IDEAL spiral CSI (spectroscopic imaging scheme developed for hyperpolarized dynamicmetabolic MR imaging) can be improved by using regularization with a sparsity constraint. By exploiting sparsity of the spectral domain, IDEALspiral CSI can achieve chemical shift encoding by acquisition of only few time-shifted echoes. The minimum number of echoes required to avoidnoise ampliﬁcation can be decreased by means of regularization enforcing spectral sparsity, hereby reducing scan time. Improvementsachieved by using regularized reconstruction are demonstrated for in vivo data from a hyperpolarized cardiac study of a pig.IntroductionIDEAL spiral CSI  is a spectroscopic imaging scheme developed for hyperpolarized dynamic metabolic MR imaging. The spectral-spatialencoding is based on a single-shot spiral, whereas the chemical shift encoding is based on echo-time shifting between excitations. Hereby, thesparsity of the spectral domain is exploited for faster imaging. To avoid noise ampliﬁcations in the reconstruction, a certain number of echoes isrequired. Here we propose, however, that noise ampliﬁcation from acquiring less echoes can be decreased by using regularization with asparsity constraint instead of using matrix inversion in the reconstruction. By acquiring less echoes, the individual image scan time isdecreased, which can be utilized for better dynamic resolution or more slices in hyperpolarization studies.MethodsFigure 1 shows the spectral encoding scheme of IDEAL spiral CSI. The chemical shift encoding for the IDEAL scheme is:with , where  is the measured data for the m  echo and the n  k-space sample and  is the q  metabolitedistribution in k-space. If  is well-conditioned,  can be reconstructed by matrix inversion: denotes the Moore-Penrose pseudo-inverse. Saving scan time by acquiring less echoes, increases the condition number of , which leads tonoise ampliﬁcation when it is inverted. To limit this, the reconstruction can be regularized by enforcing a sparsity constraint using the L1-normand by solving the minimization problem given by the following objective function:where , and  is a regularization parameter weighting the constraint enforced by the L1-norm. This reconstruction approachwas implemented in the pre-existing IDEAL spiral CSI reconstruction pipeline iteratively for each k-space sample using fminsearch in Matlab.The regularization parameter was empirically selected to  = 100.000.The method was demonstrated using in vivo data from a hyperpolarized [1- C]pyruvate cardiac study of a healthy female Danish domestic pigweighing 30 kg. For the hyperpolarization experiment, the pig was ﬁrst sedated with an intramuscular injection of Stressnil (2.0 mg/kgbodyweight) and Midazolam (0.1 mg/kg) and subsequently anaesthetized via continuous intravenous infusion of both Propofol (12 mg initialbolus dose, 0.4 mg/kg/h thereafter for maintenance) and Fentanyl for analgesia (8 µg/kg/h). The pig was intubated and mechanically ventilated(60 % O -air mix) using a respirator system (GE Healthcare, Broendby, Denmark). A whole-body clinical 3T GE HDx MR scanner (GE Healthcare,Milwaukee, WI, USA) was used for imaging together with a bore-insertable C volume resonator (clamp shell design) integrated into the patienttable for excitation (GE Healthcare, Milwaukee, WI, USA). Two arrays with 8 receive channels each  were placed to cover the heart (RapidBiomedical, Rimpar, Germany). The IDEAL spiral CSI was cardiac triggered with 4 excitations per trigger, 11 echoes, echo-time shifting of 0.9 ms,12 excitations per image, and 8 image repetitions [TE/TR 1.1/100 ms, ﬂip angle 15°, matrix 60x60, FOV 240x240 mm , in-plane nominalresolution 4 mm, slice thickness 50 mm]. Data were averaged over the 8 repetitions before reconstruction.ResultsFigure 2 shows the reconstruction results from using all 11 echoes, using only 7 echoes with matrix inversion reconstruction, and from using 7echoes with regularized reconstruction. The condition number of  was equal to 1.4 with 11 echoes and 2.8 with 7 echoes. The highercondition number is evident from the greater noise level in some of the metabolite images in Figure 2(b), especially for alanine and lactate. Therelative error for using 7 echoes compared to 11 for matrix inversion reconstruction was 24 %. Figure 2(c) shows how the reconstruction usingregularization is qualitatively improved in terms of less noise. This is supported quantitatively by means of a relative error of 19 %.Discussion1 2 2 3 111 231= ( )ym,n ∑qEm,qeiωq tnξq kn=Em,q ei Tωq Em ym,n th th ( )ξq kn thE ( )ξq kn( ) = (ξq kn e−iωq tn E†yn)q† E||E − | + λ|| |minxxn yn |22 xn |1= ( )xn ξq kn eiωq tn λλ1321322EUsing regularization in the IDEAL spiral CSI reconstruction can reduce noise ampliﬁcation as demonstrated in the lactate images of Figure 2.Signal distribution in the pyruvate-hydrate images in Figure 2(a) was, however, not retrievable using regularization. In this study theregularization parameter  was empirically selected, but a more thorough investigation of parameter choice could potentially improve thereconstruction. Compared to matrix inversion in IDEAL spiral CSI a longer reconstruction time is expected.ConclusionRegularization of the IDEAL spiral CSI reconstruction can improve results, by reducing noise ampliﬁcation from matrix inversion. This wasdemonstrated in vivo through qualitatively and quantitatively overall improved metabolite images. Shorter scan times can hereby be pursuedwith low penalty.AcknowledgementsThis work has been partly funded by the Danish Council for Independent Research (DFF – 4005-00531) and the Danish National ResearchFoundation (DNRF124).References1. Wiesinger F, Weidl E, Menzel MI, et al. IDEAL spiral CSI for dynamic metabolic MR imaging of hyperpolarized [1- 13C]pyruvate. Magn ResonMed. 2012;68(1):8-16.2. Ringgaard S, Schulte RF, Tropp J, et al. 13C RF coil combination for cardiac and abdominal human and pig studies. In: Proc. Intl. Soc. Mag.Reson. Med. ; 2016:2152.λFiguresFigure 1: Acquisition scheme for IDEAL spiral CSI from .Figure 2: Reconstruction results for IDEAL spiral CSI of the short-axis of the heart for the ﬁve metabolites (from top down): lactate, pyruvate-hydrate, alanine, pyruvate, and bicarbonate. (a) Matrix inversion reconstruction using 11 echoes, (b) matrix inversion reconstruction using 7echoes, and (c) regularized reconstruction using 7 echoes.1

Improved reconstruction for IDEAL spiral CSI

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Improved reconstruction for IDEAL spiral CSI

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