Integrable Pressure Gradients via Harmonics-Based Orthogonal Projection
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Abstract
In the past, several methods based on iterative solution of pressure-Poisson equation have been developed for measurement of pressure from phase-contrast magnetic resonance (PC-MR) data. In this paper, a non-iterative harmonics-based orthogonal projection method is discussed which can keep the pressures measured based on the Navier-Stokes equation independent of the path of integration.
The gradient of pressure calculated with Navier-Stokes equation is expanded with a series of orthogonal basis functions, and is subsequently projected onto an integrable subspace. Before the projection step however, a scheme is devised to eliminate the discontinuity at the vessel boundaries.
The approach was applied to velocities obtained from computational fluid dynamics (CFD) simulations of stenotic flow and compared with pressures independently obtained by CFD. Additionally, MR velocity data measured in in-vitro phantom models with different degree of stenoses and different flow rates were used to test the algorithm and results were compared with CFD simulations. The pressure results obtained from the new method were also compared with pressures calculated by an iterative solution to the pressure-Poisson equation. Experiments have shown that the proposed approach is faster and is less sensitive to noise.
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References
- 1.Pelc, N.J., Sommer, F.G., Li, K.C.P., Brosnan, T.J., Enzmann, D.R.: Quantitative magnetic resonance flow imaging. Magnetic Resonance Quarterly 10, 125–147 (1994)Google Scholar
- 2.Urchuk, S.N., Fremes, S.E., Plewes, D.B.: In-vivo validations of MR pulse pressure measurement in an aortic flow model: preliminary results. Magn. Res Med. 38, 215–223 (1997)CrossRefGoogle Scholar
- 3.Yang, G.Z., Kilner, P.J., Wood, N.B., Underwood, S.R.: Computation of flow pressure fields from MR velocity mapping. Magn. Res. Med. 36, 520–526 (1996)CrossRefGoogle Scholar
- 4.Tyszka, J.M., Laidlaw, D.H., Asa, J.W., Silverman, J.M.: Three-dimensional time-resolved (4D) relative pressure mapping using MRI. JMRI 12, 321–329 (2000)CrossRefGoogle Scholar
- 5.Song, S.M., Leahy, R.M., Boyd, D.P., Brundage, B.H., Napel, S.: Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images. IEEE Trans. on Medical Imaging 13, 386–397 (1994)CrossRefGoogle Scholar
- 6.Ebbers, T., Wigstrom, L., Bolger, A., Engvall, J., Karlsson, M.: Estimation of relative cardiovascular pressures using time-resolved three-dimensional phase-contrast MRI. Magn. Res. Med. 45, 872–879 (2001)CrossRefGoogle Scholar
- 7.Thompson, R., McVeigh, E.: Fast measurement of intracardiac pressure differences with 2D breath-hold PC MRI. Magn. Res. Med. 49, 1056–1066 (2003)CrossRefGoogle Scholar
- 8.Moghaddam, A.N., Behrens, G., Fatouraee, N., Agarwal, R., Choi, E.T., Amini, A.A.: Factors affecting the accuracy of pressure measurements in vascular stenoses from phase-contrast MRI. Magn. Res. Med. 52, 300–309 (2004)CrossRefGoogle Scholar
- 9.Frankot, R., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. on Pattern Analysis and Machine Intelligence 10(4), 439–451 (1988)zbMATHCrossRefGoogle Scholar
- 10.Currie, I.: Fundamental Mechanics of Fluids. McGraw-Hill, New York (1993)Google Scholar
- 11.Gudbjartsson, H., Paltz, S.: The Rician distribution of noisy MRI data. Magnetic Resonance in Medicine 34, 910–914 (1995)CrossRefGoogle Scholar