On the Design of Filters for Fourier and OSVD-based Deconvolution in Bolus Tracking Perfusion MRI

Overview

Journal MAGMA

Publisher Springer

Date 2010 Jun 1

PMID 20512521

Citations 5

Authors

Peter Gall

Philipp Emerich

Birgitte F Kjolby

Elias Kellner

Irina Mader

Valerij G Kiselev

Affiliations

Soon will be listed here.

Abstract

Object: Bolus tracking perfusion evaluation relies on the deconvolution of a tracers concentration time-courses in an arterial and a tissue voxel following the tracer kinetic model. The object of this work is to propose a method to design a data-driven Tikhonov regularization filter in the Fourier domain and to compare it to the singular value decomposition (SVD)-based approaches using the mathematical equivalence of Fourier and circular SVD (oSVD).

Materials And Methods: The adaptive filter is designed using Tikhonov regularization that depends on only one parameter. Using a simulation, such an optimal parameter that minimizes the sum of statistical and systematic error is determined as a function of the first moment difference between the tissue and the arterial curve and the contrast to noise ratios of the input data (CNR( a ) in arteries and CNR( t ) in tissue). The performance of the method is evaluated and compared to oSVD in simulations and measured data.

Results: The proposed method yields a smaller flow underestimation especially for high flows when compared to the oSVD approach with constant threshold. However, this improvement comes to the price of an increased uncertainty of the flow values. The translation of the Tikhonov regularization parameter to an adaptive oSVD-threshold is in good agreement with the literature.

Conclusion: The proposed method is a comprehensive approach for the design of data-driven filters that can be easily adapted to specific needs.

Citing Articles

Evaluation of Siemens Healthineers' StrokeSegApp for automated diffusion and perfusion lesion segmentation in patients with ischemic stroke.

Teichmann L, Khalil A, Villringer K, Fiebach J, Huwer S, Gibson E Front Neurol. 2025; 16:1518477.

PMID: 39926019 PMC: 11804811. DOI: 10.3389/fneur.2025.1518477.

Perfusion magnetic resonance imaging: a comprehensive update on principles and techniques.

Jahng G, Li K, Ostergaard L, Calamante F Korean J Radiol. 2014; 15(5):554-77.

PMID: 25246817 PMC: 4170157. DOI: 10.3348/kjr.2014.15.5.554.

Susceptibility-based analysis of dynamic gadolinium bolus perfusion MRI.

Bonekamp D, Barker P, Leigh R, van Zijl P, Li X Magn Reson Med. 2014; 73(2):544-54.

PMID: 24604343 PMC: 4143505. DOI: 10.1002/mrm.25144.

Deconvolution-Based CT and MR Brain Perfusion Measurement: Theoretical Model Revisited and Practical Implementation Details.

Fieselmann A, Kowarschik M, Ganguly A, Hornegger J, Fahrig R Int J Biomed Imaging. 2011; 2011:467563.

PMID: 21904538 PMC: 3166726. DOI: 10.1155/2011/467563.

Vessel size imaging reveals pathological changes of microvessel density and size in acute ischemia.

Xu C, Schmidt W, Villringer K, Brunecker P, Kiselev V, Gall P J Cereb Blood Flow Metab. 2011; 31(8):1687-95.

PMID: 21468091 PMC: 3170945. DOI: 10.1038/jcbfm.2011.38.

References

Wirestam R, Andersson L, Ostergaard L, Bolling M, Aunola J, Lindgren A . Assessment of regional cerebral blood flow by dynamic susceptibility contrast MRI using different deconvolution techniques. Magn Reson Med. 2000; 43(5):691-700. DOI: 10.1002/(sici)1522-2594(200005)43:5<691::aid-mrm11>3.0.co;2-b. View

Mouridsen K, Christensen S, Gyldensted L, Ostergaard L . Automatic selection of arterial input function using cluster analysis. Magn Reson Med. 2006; 55(3):524-31. DOI: 10.1002/mrm.20759. View

Salluzzi M, Frayne R, Smith M . An alternative viewpoint of the similarities and differences of SVD and FT deconvolution algorithms used for quantitative MR perfusion studies. Magn Reson Imaging. 2005; 23(3):481-92. DOI: 10.1016/j.mri.2004.12.001. View

Ostergaard L, Weisskoff R, Chesler D, Gyldensted C, Rosen B . High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. Part I: Mathematical approach and statistical analysis. Magn Reson Med. 1996; 36(5):715-25. DOI: 10.1002/mrm.1910360510. View

Liu H, Pu Y, Liu Y, Nickerson L, Andrews T, Fox P . Cerebral blood flow measurement by dynamic contrast MRI using singular value decomposition with an adaptive threshold. Magn Reson Med. 1999; 42(1):167-72. DOI: 10.1002/(sici)1522-2594(199907)42:1<167::aid-mrm22>3.0.co;2-q. View

Koh T, Wu X, Cheong L, Lim C . Assessment of perfusion by dynamic contrast-enhanced imaging using a deconvolution approach based on regression and singular value decomposition. IEEE Trans Med Imaging. 2004; 23(12):1532-42. DOI: 10.1109/TMI.2004.837355. View

Calamante F, Morup M, Hansen L . Defining a local arterial input function for perfusion MRI using independent component analysis. Magn Reson Med. 2004; 52(4):789-97. DOI: 10.1002/mrm.20227. View

Liu C, Bammer R, Acar B, Moseley M . Characterizing non-Gaussian diffusion by using generalized diffusion tensors. Magn Reson Med. 2004; 51(5):924-37. DOI: 10.1002/mrm.20071. View

Gall P, Mader I, Kiselev V . Extraction of the first bolus passage in dynamic susceptibility contrast perfusion measurements. MAGMA. 2009; 22(4):241-9. DOI: 10.1007/s10334-009-0170-6. View

10.

Sourbron S, Luypaert R, Van Schuerbeek P, Dujardin M, Stadnik T . Choice of the regularization parameter for perfusion quantification with MRI. Phys Med Biol. 2004; 49(14):3307-24. DOI: 10.1088/0031-9155/49/14/020. View

11.

Kiselev V . On the theoretical basis of perfusion measurements by dynamic susceptibility contrast MRI. Magn Reson Med. 2001; 46(6):1113-22. DOI: 10.1002/mrm.1307. View

12.

Wu O, Ostergaard L, Weisskoff R, Benner T, Rosen B, Sorensen A . Tracer arrival timing-insensitive technique for estimating flow in MR perfusion-weighted imaging using singular value decomposition with a block-circulant deconvolution matrix. Magn Reson Med. 2003; 50(1):164-74. DOI: 10.1002/mrm.10522. View

13.

Yablonskiy D, Haacke E . Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn Reson Med. 1994; 32(6):749-63. DOI: 10.1002/mrm.1910320610. View

14.

Calamante F, Gadian D, Connelly A . Quantification of bolus-tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization. Magn Reson Med. 2003; 50(6):1237-47. DOI: 10.1002/mrm.10643. View