A finite-element approach to the direct computation of relative cardiovascular pressure from time-resolved MR velocity data

Sebastian B S Krittian, Pablo Lamata, Christian Michler, David A. Nordsletten, Jelena Bock, Chris P. Bradley, Alex Pitcher, Philip J. Kilner, Michael Markl, Nic P. Smith*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow.

Original languageEnglish (US)
Pages (from-to)1029-1037
Number of pages9
JournalMedical Image Analysis
Issue number5
StatePublished - Jul 2012


  • 4D flow
  • Direct flow evaluation
  • MRI
  • Pressure Poisson equation
  • Relative pressure field

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Health Informatics
  • Radiology Nuclear Medicine and imaging
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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