Flow and Diffusion Images from Bayesian Spectral Analysis of Motion-Encoded NMR Data

  • E. J. Fordham
  • D. Xing
  • J. A. Derbyshire
  • S. J. Gibbs
  • T. A. Carpenter
  • L. D. Hall
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 70)


Quantitative imaging of steady laminar flow fields in up to three dimensions is achieved by NMR imaging with the addition of motion-encoding field gradient pulses; coherent flow is encoded as a phase shift, diffusive or dispersive processes as an attenuation. A sequence of images with incremented gradient pulse areas displays at each pixel a damped sinusoidal oscillation with frequency proportional to a convective flow velocity, and a Gaussian envelope dependent on local effective diffusivity. Velocity and diffusivity are obtained from a spectral analysis of such oscillations. Traditional Fourier analysis has been used with many images in such a sequence. Such approaches are not economical with data acquisition time; nor are error estimates available. The Bayesian spectral analysis of Bretthorst (1988, 1991), although currently applied mainly to spectroscopic data, permits also the routine analysis of noisy, heavily truncated, non-uniformly and sparsely sampled data. Bayesian error intervals are also available. We demonstrate a non-uniform sampling strategy that requires only four images to obtain velocity and diffusion images for various laminar liquid flows: water and a non-Newtonian polymer solution in a cylindrical pipe, and 3-dimensional flow of water in a duct of complex geometry. The latter experiment is in part made practicable by thus minimising the number of images acquired.


Diffusion Image Circular Pipe Gradient Pulse Vector Velocity Image Joint Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • E. J. Fordham
    • 1
  • D. Xing
    • 1
  • J. A. Derbyshire
    • 1
  • S. J. Gibbs
    • 1
  • T. A. Carpenter
    • 1
  • L. D. Hall
    • 1
  1. 1.Herchel Smith Laboratory for Medicinal ChemistryCambridge University School of Clinical MedicineCambridgeUK

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