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Patient-Speci�c Velocity Boundary
Conditions from Phase Contrast
Magnetic Resonance Imaging
Andrea Torti
Università degli Studi di Pavia
February 26, 2014
Supervisor: Simone Morganti, PhD
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 1 / 22
Outline
Computational Fluid Analysis in the Biomedical Field
Goal of the thesis
From PC MRI data to patient-speci�c velocity pro�les
Conclusions and Future Works
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 2 / 22
Outline
Computational Fluid Analysis in the Biomedical Field
Goal of the thesis
From PC MRI data to patient-speci�c velocity pro�les
Conclusions and Future Works
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 3 / 22
Outline
Computational Fluid Analysis in the Biomedical Field
Goal of the thesis
From PC MRI data to patient-speci�c velocity pro�les
Conclusions and Future Works
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 4 / 22
Outline
Computational Fluid Analysis in the Biomedical Field
Goal of the thesis
From PC MRI data to patient-speci�c velocity pro�les
Conclusions and Future Works
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 5 / 22
Computational Fluid Analysis
Computational Fluid Analysis (FSI/CFD) is:
non-invasive
potentially very accurate
predictive
Therefore very useful in the Biomedical �eld
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 6 / 22
Computational Fluid Analysis (FSI/CFD)
A widely investigated issue for practical purposes:
Gerbeau and Vidrascu, 2003 �> Algorithms for FSI
Papaharilaou et al., 2006 �> FSI for Abdominal Aortic Walls Stress
Bluestein et al., 2008 �> FSI for Abdominal Aortic Aneurysm
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 7 / 22
FSI/CFD Recipe
...What is needed?
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 8 / 22
Geometrical Domain - Patient-Speci�c Approach
Nealand and Kerckho�s, 2009 �> Progress in Patient-Speci�c Approaches
Auricchio et al., 2014 �> CFD for TEVAR evaluation
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 9 / 22
Aim of the thesis
GOAL
De�nition of a time and space-dependent Aortic In�ow using Patient-Speci�c Data from PhaseContrast Magnetic Resonance Imaging
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 10 / 22
Available Data - PC MRI
PC-MRI: physical principles
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 11 / 22
PC MRI
Two kinds of data
Unlike standard MRI, PC-MRI also employs information from phase maps
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 12 / 22
Clinical Data
30 phase maps (ascending aorta slice) extracted via PC MRI at I.R.C.C.S. San Donato, Milan
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 13 / 22
Image Cropping and Segmentation
1) Rectangular, Automatic Cropping with ImageJ
2) Elliptical, Semi-Automatic Segmentation with Matlab
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 14 / 22
From Images to Matrices
Once in Matlab, each image is related to a matrix, whose cells contain values in Houns�eld units(HU, from 0 to 255, measuring tissue density).
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 15 / 22
From Houns�el Units to Velocities
In PC-MRI, mid-gray represents steady tissues (HU0 = 127)
HUmax = 255 �> MRI Venc (in this case, 200 cm/s)
Being R = Venc/HUmax , we can use the following relation:
v(i,j) = (HU(i,j)-HU0)R
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 16 / 22
Mean Velocities Calculations
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 17 / 22
Comparing Datasets
Our Data vs Machine-provided Data
In blue, our plot representing mean velocity vs time, compared to the data provided by I.R.C.C.S.San Donato (in red)
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 18 / 22
Results
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 19 / 22
Conclusions
In the present work:
literature review on computational �uid analysis
collection of patient-speci�c PC MRI data
elaboration of the provided data to obtain time- and space-dependant velocity pro�les
Obtained patient-speci�c aortic in�ow from PC MRI is in good agreement with machine-provideddata
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 20 / 22
Future Work: Data interpolation
Data are represented on a �ner grid (but still discrete!)
We would need an interpolant function �> (LIFE V)
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 21 / 22
Patient-Speci�c Velocity Boundary
Conditions from Phase Contrast
Magnetic Resonance Imaging
Andrea Torti
Università degli Studi di Pavia
February 26, 2014
Supervisor: Simone Morganti, PhD
Andrea Torti (unipv) Boundary Conditions from PC-MRI February 26, 2014 22 / 22
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