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Convex gradient optimization for increased spatiotemporal resolution and improved accuracy in phase contrast MRI


Decades of research have helped mitigate numerous sources of error in phase contrast MRI (PC-MRI), nevertheless chemical shift induced phase errors (CS errors) and spatiotemporal undersampling errors (STU errors) remain critical sources of error for which a cogent error mitigation strategy is needed. CS errors, which arise in PC-MRI because the complex signal for perivascular fat chemically shifts across the vessel wall and corrupts the complex blood signal, can be mitigated with an in-phase TE (TEIN) and a high receiver bandwidth [1]. STU errors arise from suboptimal spatiotemporal resolution. The objective was to design a PC-MRI sequence with improved sequence efficiency and evaluate the impact on mitigating both CS and STU errors.


Hargreaves et al. [2] have shown that convex optimization (CVX) can be used to minimize gradient waveform durations subject to both hardware constraints (maximum available gradient amplitude and slew rate) and pulse sequence constraints (e.g. VENC, RF pulse, slice thickness, FOV, bandwidth, matrix size). We developed CVX PC-MRI to achieve improved spatiotemporal resolution to reduce STU errors while using the minimum TEIN (TEIN,MIN) to reduce CS errors for a fixed breath hold duration. Flow measurements were obtained at 3T (Siemens Trio) using a conventional flow compensated and flow encoded (FCFE) PC-MRI sequence and CVX PC-MRI optimized for high spatial resolution (CVX-SR) or high temporal resolution (CVX-TR). All sequences mitigated CS errors with a high receiver bandwidth and TEIN. CVX permits using TEIN,MIN = 2.46 ms while the FCFE sequence can only achieve TEIN = 4.92 ms. Total flow and peak velocity measurements were acquired in the ascending aorta (aAo), main pulmonary artery (PA), and right/left pulmonary arteries (RPA/LPA) of ten (N = 10) normal volunteers (Table 1).

Table 1 PC-MRI parameters.


The sequence efficiencies (readout duration/TR) were 17.7% for FCFE, 30.5% for CVX-SR, and 31.4% for CVX-TR. Measurements of total flow and peak velocity were significantly higher (P < 0.05) for CVX-SR and CVX-TR compared to FCFE (Table 2). On average, CVX-SR measured 8.1% higher total flow and 3.8% higher peak velocity and CVX-TR measured 5.1% higher total flow and 10.5% higher peak velocity.

Table 2 In vivo (N = 10) PC-MRI measures of total flow and peak velocity.


CVX PC-MRI nearly doubles sequence efficiency, reduces CS and STU errors, and produces more accurate measurements of blood flow and peak velocity. CVX-SR reports the highest total flow and CVX-TR reports the highest peak velocities, but further improvements in spatiotemporal resolution may still be needed for accurate quantification.


This work was enabled by research support from Siemens Medical Solutions and the Department of Radiological Sciences to DBE.


  1. 1.

    Middione MJ, Ennis DB: The effects of chemically shifted perivascular fat in quantitative phase contrast MRI. Magn Reson Med. 2013, 69: 391-401. 10.1002/mrm.24262.

    PubMed Central  Article  PubMed  Google Scholar 

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    Hargreaves BA, Nishimura DG, Conolly SM: Time-optimal multidimensional gradient waveform design for rapid imaging. Magn Reson Med. 2004, 51 (1): 81-92. 10.1002/mrm.10666.

    Article  PubMed  Google Scholar 

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Correspondence to Daniel B Ennis.

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Middione, M.J., Wu, H.H. & Ennis, D.B. Convex gradient optimization for increased spatiotemporal resolution and improved accuracy in phase contrast MRI. J Cardiovasc Magn Reson 16, W36 (2014).

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  • Pulmonary Artery
  • Peak Velocity
  • Spatiotemporal Resolution
  • Siemens Trio
  • Sequence Efficiency