Estimating the irreversible pressure drop across a stenosis by quantifying turbulence production using 4D Flow MRI Hojin Ha 1,2 , Jonas Lantz 1,2 , Magnus Ziegler 1,2 , Belen Casas 1,2 , Matts Karlsson 2,3 , Petter Dyverfeldt 1,2 , Tino Ebbers 1,2 1 Division of Cardiovascular Medicine, Department of Medical and Health Sciences, Linköping University, Linköping, Sweden. 2 Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden. 3 Division of Applied Thermodynamics and Fluid Mechanics, Department of Management and Engineering (IEI), Linköping University, Linköping, Sweden. Corresponding Author: Hojin Ha Phone: +46-762693607 E-mail: [email protected]Running title: Assessment of irreversible pressure drop using 4D flow MRI. Number of words: 5541 words Number of items: 7 Figures, 1 Table
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Estimating the irreversible pressure drop across a … the irreversible pressure drop across a stenosis by quantifying turbulence production using 4D Flow MRI Hojin Ha1,2, Jonas Lantz1,2,
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Estimating the irreversible pressure drop across a stenosis by quantifying
turbulence production using 4D Flow MRI
Hojin Ha1,2, Jonas Lantz1,2, Magnus Ziegler1,2, Belen Casas1,2, Matts Karlsson2,3, Petter Dyverfeldt1,2, Tino Ebbers1,2 1Division of Cardiovascular Medicine, Department of Medical and Health Sciences, Linköping University, Linköping, Sweden.
2Center for Medical Image Science and Visualization (CMIV), Linköping University, Linköping, Sweden.
3Division of Applied Thermodynamics and Fluid Mechanics, Department of Management and Engineering (IEI), Linköping University,
aSeverity is the percentage of area reduction at the stenosis apex. bPost-stenotic dilatation (PSD), defined as a ratio between a diameter at the post-stenosis and upstream diameter.
Table S5. Flow encoding scheme with ICOSA6 sequence
aNA; not-applicable, b θ for the present study is about 31.17º, which corresponds to cosθ = 0.8507 and sinθ = 0.5257
Table S8. Velocity and intravoxel turbulence parameters from ICOSA6 sequence
Number of encoding Velocity component Intravoxel standard deviation
1 V1 = cosθ·u + sinθ·v !12 = cos2θ·(!x
2) + sin2θ·(!y2) + 2·(cosθ)·(sinθ)·(<u'v'>)
2 V2 = cosθ·u - sinθ·v !22 = cos2θ·(!x
2) + sin2θ·(!y2) - 2·(cosθ)·(sinθ)·(<u'v'>)
3 V3 = cosθ·v + sinθ·w !32 = cos2θ·(!y
2) + sin2θ·(!z2) + 2·(cosθ)·(sinθ)·(<v'w'>)
4 V4 = cosθ·v - sinθ·w !42 = cos2θ·(!y
2) + sin2θ·(!z2) - 2·(cosθ)·(sinθ)·(<v'w'>)
5 V5 = sinθ·u + cosθ·w !52 = sin2θ·(!x
2) + cos2θ·(!z2) + 2·(cosθ)·(sinθ)·(<u'w'>)
6 V6 = sinθ·u - cosθ·w !62 = sin2θ·(!x
2) - cos2θ·(!z2) + 2·(cosθ)·(sinθ)·(<u'w'>)
* u,v and w indicate the velocity component in three orthogonal directions along x,y, and z. ** <u’v’>, <v’w’> and <u’w’> indicate the Reynolds stress component