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A Spatiotemporal exploration and 3D modeling of blood flow in healthy carotid artery bifurcation from two modalities: Ultrasound-Doppler and phase contrast MRI.

01 Mar 2020-Computers in Biology and Medicine (Pergamon)-Vol. 118, pp 103644

TL;DR: The measured velocities showed that blood flow keeps a parabolic sectional profile distal from CCA, ECA and ICA, while being quite disturbed in the carotid sinus with a significant decrease in magnitude making this site very prone to atherosclerosis.

AbstractIn the present study, we investigated the velocity profile over the carotid bifurcation in ten healthy volunteers by combining velocity measurements from two imaging modalities (PC-MRI and US-Doppler) and hemodynamic modeling in order to determine the optimal combination for the most realistic velocity estimation. The workflow includes data acquisition, velocity profile extraction at three sites (CCA, ECA and ICA), the arterial geometrical model reconstruction, a mesh generation and a rheological modeling. The results showed that US-Doppler measurements yielded higher velocity values as compared to PC-MRI (about 26% shift in CCA, 52% in ECA and 53% in ICA). This implies higher simulated velocities based on US-Doppler inlet as compared to simulated velocities based on PC-MRI inlet. Overall, PC-MRI inlet based simulations are closer to measurements than US-Doppler inlet based simulations. Moreover, the measured velocities showed that blood flow keeps a parabolic sectional profile distal from CCA, ECA and ICA, while being quite disturbed in the carotid sinus with a significant decrease in magnitude making this site very prone to atherosclerosis.

Summary (3 min read)

1. Introduction

  • Vascular maladies may be caused by thrombi and can lead to stroke [18].
  • Blood flow analysis can confirm the presence of a local vessel anomaly, its impact on the blood flow pattern and its possible evolution [7, 26, 25, 10].
  • Few studies compared velocity measurements in the carotid artery between US-Doppler and PC-MRI [15, 16, 38, 28].
  • Section 2 describes the imaging data sets and the analysis methodology.

2. Material and Methods

  • The arterial geometrical model was extracted from MR anatomical images and the hemodynamic modeling was performed from the obtained models.
  • The velocity waveforms from both PC-MRI and US-Doppler were extracted at three locations: the right CCA, ECA and ICA.

2.1.1. PC-MR imaging

  • The PC-MR images were acquired with a clinical 1.5 T Philips system (Ingenia, Philips medical systems, Best, the Netherlands) using 20 channels phased array head neck spine coil.
  • Fifty 2D anatomical images were acquired in axial orientation to cover cervical region Arij Debbich et al.: Preprint submitted to Elsevier Page 2 of 16 Figure 3: Growing carotid scanning windows size.
  • Key points are located in: CCA at 1.5 cm from the bifurcation, ECA and ICA: at 1 cm from the bifurcation.
  • The ideal velocity encoding (VENC) should be high enough to avoid aliasing and as low as possible to reduce velocity noise [47].
  • The total scan time for an exam was approximately 7 minutes.

2.1.2. US-Doppler imaging

  • All US-Doppler exams were conducted by a radiologist (B.H) with 10 years’ experience in cardiovascular imaging.
  • Clinical General Electric ultrasound systems (LOGIQ E9, GE Healthcare, Milwaukee, WI, USA) with 9 MHz linear probe were used.
  • US-Doppler images were matrices of dimension 720x960.
  • To extract the velocity waveform, the authors chose a profile of one cardiac cycle , fixed the two profile axes and selected 14 feature points on these profiles including PSV and EDV.
  • The USDoppler profile point digitization was performed using the Engauge Digitizer software [29].

2.2. PC-MRI Velocity profile extraction

  • Three velocity waveforms were extracted from PC-MRI at locations CCA, ECA, and ICA during a cardiac cycle which was divided into 14 time points.
  • The following values were deduced from the interpolated waveforms: - Velocity variation at a given pixel VMRIpixel .
  • - Maximum velocity at a given pixel within its eight neighbors VMRImax.-.
  • As the MRI and the US-Doppler examinations were not acquired at the same time, there might be some physiological variations [16].

2.3. Arterial model reconstruction and computational mesh generation

  • The geometrical characteristics of all the vessel segments for the ten subjects are given in Table1.
  • The carotid lumen was separated from the rest of the structures by applying an intensity threshold.
  • The model was further re-meshed using an Octree surface refinement based on prismatic wall [20].
  • Some studies adopted the rheological Newtonian behavior for the carotid artery (stationary viscosity) because it is simpler than the hemodynamic modeling with a non Newtonian behavior and arguing it has aminor impact on the results [33].

2.4. Boundary conditions

  • One of their objectives was to investigate the impact of the inlet boundary conditions on the simulation results.
  • These inlets were pulsed over time and were composed of the two usual physiological phases during a cardiac cycle: systole and diastole.
  • Velocity profile for every subject was matched to VMRImax inthe CCA, 3.3 cm from the carotid bifurcation to conform to the CCA dimension in the geometrical model.
  • (5) where ℎt is the maximal parabolic magnitude matching the VMRImax or VUS at time t. (xc , yc) and R are respectively thecenter coordinates and the radius of the CCA inlet section.
  • All meshes brought velocity profiles close to each other.

2.5. Simulated velocity profiles

  • Simulated velocity profiles Vsim were extracted at threelocations of the carotid bifurcation: 1.5 cm from the bifurcation in the CCA and 1 cm up the bifurcation in ECA and ICA.
  • The values were extracted using CFD-POST from ANSYS software.

3. Results

  • Velocity waveforms were extracted from PC-MRI (VMRImax, VMRIpixel and VMRImean) and Doppler-US (VUS)imaging data for ten volunteers at the three localizations of the carotid artery.
  • The first one, called VSIM_MRI, is based on PC-MRI data VMRImaxprofile used as inlet boundary condition.
  • The authors did not integrate the pixel-based PC-MRI velocity VMRIpixel in the tables since its values werebetween those of VMRImax and VMRImean and were noisier.

3.1. Analysis of PC-MRI velocities

  • Typical measured velocity waveforms from PC-MRI are presented in Figure 4. ECA and ICA relative to V MRImax for PC-MRI (up) and V US for US-Doppler (down).
  • The authors noted that a velocity profile over the CCA diameter at a given location was almost parabolic for all time points . and end diastolic (ED) time points every centimeter from the CCA to the carotid sinus, ICA and ECA .
  • There were significant variations de- tected in the carotid sinus site: a progressive decrease of the maximum velocity and a disruption of the profile shape.

3.2. Analysis of PC-MRI and US velocity measurements

  • Unlike the difference observed by Harloff et al.[15] for ICA, PSV of PC-MRI was on average less than US-Doppler by about 17.6%.
  • The same tendency was observed in CCA PSV (mean difference of 21.8 cm/s), to a much lower extent for CCA EDV .
  • Diastolic velocity profiles are less dissimilar except in ICA for the two modalities.
  • The mean velocity waveforms of the ten volunteers relative to PC-MRI and US-Doppler in CCA, ECA and ICA are plotted in Figure 10.

3.3. Analysis of simulated velocity waveforms

  • Overall, the numerical velocity waveforms were closer to the PC-MRI ones independent of the arterial input function considered (US or MRI).
  • The numerical velocities were compared to in vivo measurements through the global and the local indicators defined in section 3 .
  • The mean difference between measurements and simulation for PSV and EDV was greater.
  • From Tables 2, 3 and 4, it can be noted that the mean PSV of the ten subjects from VSIM_MRImax is lower than that from VSIM_US.

4. Discussion

  • The PC-MRI velocity behavior in the carotid bifurcation was investigated in time and space.
  • It was observed that the velocity estimation increased with the window size up to maximum .
  • This can be difficult to achieve when dealing with a PC-MRI and US-Doppler comparative study like ours for two reasons related to US measurements: i) lack of convenient accessibility for radiologists.
  • The arterial wall pulsatility has not been considered as it would have brought many additional issues with less mastered modeling methods (Fluid Structure Interaction).
  • Locally, the mean difference between VSIM_MRImax and VMRImax varied from 22% to 32% according to the local dif-ference metric at peak systole PSV and from 29% to 37%according to the local difference metric at end diastole EDV.

5. Conclusion

  • The authors investigated blood velocity quantification over the carotid artery bifurcation from PC-MRI and US-Doppler, and 3D velocity modeling from these modalities.
  • PC-MRI data analysis showed velocity across the section of the artery follows a parabolic profile except in the sinus region.
  • Overall, the authors found numerical velocities based on PC-MRI velocity inlet closer to measurements than those based on Doppler-US velocity inlet.
  • Therefore, from their experiments, the PC-MRI-based hemodynamic modeling approach could be reasonably more realistic.

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A Spatiotemporal exploration and 3D modeling of blood
ow in healthy carotid artery bifurcation from two
modalities: Ultrasound-Doppler and phase contrast MRI
Arij Debbich, Asma Ben Abdallah, Mezri Maatouk, Badii Hmida, Monica
Sigovan, Patrick Clarysse, Mohamed Hédi Bedoui
To cite this version:
Arij Debbich, Asma Ben Abdallah, Mezri Maatouk, Badii Hmida, Monica Sigovan, et al.. A Spa-
tiotemporal exploration and 3D modeling of blood ow in healthy carotid artery bifurcation from
two modalities: Ultrasound-Doppler and phase contrast MRI. Computers in Biology and Medicine,
Elsevier, 2020, 118, pp.103644. �10.1016/j.compbiomed.2020.103644�. �hal-02991562�

A Spatiotemporal exploration and 3D modeling of blood flow in
healthy carotid artery bifurcation from two modalities:
Ultrasound-Doppler and phase contrast MRI
Arij Debbich
a,b
, Asma Ben Abdallah
a
, Mezri Maatouk
c
, Badii Hmida
c
, Monica Sigovan
d
,
Patrick Clarysse
d
and Mohamed Hédi Bedoui
a
a
LTIM: Laborator y of Technology and Medical Imaging, Faculty of Medicine, University of Monastir, Tunisia
b
National School of Engineers of Sfax, University of Sfax, Tunisia
c
Medical Imaging Department, CHU Fattouma Bourguiba, Monastir, Tunisia
d
Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621, LYON, France
A R T I C L E I N F O
Keywords:
Computational hemodynamics
Carotid bifurcation
PC-MRI
US Doppler
Normal blood flow
A B S T R A C T
In the present study, we investigated the velocity profile over the carotid bifurcation in ten healthy
volunteers by combining velocity measurements from two imaging modalities (PC-MRI and US-
Doppler) and hemodynamic modeling in order to determine the optimal combination for the most
realistic velocity estimation. The workflow includes data acquisition, velocity profile extraction at
three sites (CCA, ECA and ICA), the arterial geometrical model reconstruction, a mesh generation
and a rheological modeling. The results showed that US-Doppler measurements yielded higher ve-
locity values as compared to PC-MRI (about 26% shift in CCA, 52% in ECA and 53% in ICA). This
implies higher simulated velocities based on US-Doppler inlet as compared to simulated velocities
based on PC-MRI inlet. Overall, PC-MRI inlet based simulations are closer to measurements than
US-Doppler inlet based simulations. Moreover, the measured velocities showed that blood flow keeps
a parabolic sectional profile distal from CCA, ECA and ICA, while being quite disturbed in the carotid
sinus with a significant decrease in magnitude making this site very prone to atherosclerosis.
1. Introduction
Vascular maladies may be caused by thrombi and can
lead to stroke [18]. Nowadays, this pathology represents a
major health challenge since it is one of the leading causes
of mortality all over the world (5.5 million people died of
stroke in 2016) [42]. Hence, the importance of investigating
the blood flow pattern, notably in the carotid artery which
irrigates the brain. This artery is located in the neck. It is
composed of the common carotid artery (CCA) which di-
vides into the external carotid artery (ECA) and the inter-
nal carotid artery (ICA) irrigating the face and the brain re-
spectively. Several in vivo [15, 16, 28, 17, 30] , in vitro
[45, 21, 2], in-silico [23, 19, 49, 33, 11], and mixed image-
CFD (Computational Fluid Dynamics) [22, 36] approaches
have focused on this artery and associated anomalies. The
investigations are mainly aimed at localizing and character-
izing vessel pathologies from velocity distribution.
CFD simulation has received considerable interest ow-
ing to its ability to give access to parameters characteriz-
ing the vascular flow, not easily accessible through direct
measurements, with notably Wall Shear Stress (WSS) pa-
This study was conducted within the framework of the LABEX
PRIMES (ANR-11-LABX-0063 ) project of the University of Lyon, within
the “Investissements d’Avenir ”(ANR-11-IDEX-0 0 07) program operated
by the French National Research Agency (ANR).
arij.debbich@gmail.com (A. Debbich); assoumaba@yahoo.com (A.B.
Abdallah); m.mezri@gmail.com (M. Maatouk); hmidabadii@gmail.com (B.
Hmida); monica.sigovan@creatis.insa-lyon.fr (M. Sigovan);
patrick.clarysse@creatis.insa-lyon.fr (P. Clarysse);
MedHedi.Bedoui@fmm.rnu.tn (M.H. Bedoui)
ORCID(s):
rameters, Oscillatory Shear Index (OSI), Relative Residence
Time (RRT) and helicity. Several studies have pointed the
importance of having an accurate carotid geometry [7, 34].
Some studies investigated the impact of various rheologi-
cal models in CFD modeling [33, 44]. Morbiducci and al.
[33] suggested that if the rheological model was simplified
and blood attributed a constant viscosity (Newtonian fluid)
instead of a variable one (Non Newtonian), the difference
in the simulations would be less than 10%. Other works
[39, 7] have shown that inlet boundary conditions signifi-
cantly affect the numerical simulation of velocity, which also
depends on the carotid artery localization.
Blood flow analysis can confirm the presence of a local
vessel anomaly, its impact on the blood flow pattern and its
possible evolution [7, 26, 25, 10]. Some flow indicators such
as TAWSS (time averaged wall shear stress) and OSI can
help detect and localize abnormal WSS increase leading to
thrombosis formation and stroke [10].
Realistic image-based patient specific CFD modeling re-
quires the extraction of several pieces of information from
medical data with at least: i) the vascular morphology
from medical imaging (Computed tomography Angiography
(CTA) [43] or Magnetic Resonance Imaging (MRI) [41]). ii)
measurements of blood flow velocity (Ultrasound Doppler
(US-Doppler) [46] or phase contrast Magnetic Resonance
(PC-MRI) [41]) to provide at least arterial input functions.
Regarding the anatomy extraction, clinicians generally
use CTA since it offers a higher spatial resolution than MRI
and has proved its reliability [13], especially when determin-
ing a stenosis degree. As for velocity, the most widespread
Arij Debbich et al.:
Preprint submitted to Elsevier Page 1 of 16

A Spatiotemporal exploration and 3D modeling of blood ow in healthy carotid artery bifurcation from two modalities.
Figure 1:
Medical imaging modalities to study the blood ow in the carotid artery for one of the ten subjects. Left: MRI
anatomical slice transverse to the carotid arteries with the region of interest (in red), middle: PC-MRI ow slice showing the
coronal component of the velocity in the carotid, which is vertically oriented, right: US-Doppler measurement showing the peak
systolic velocity (PSV), the end diastolic velocity (EDV), the resistance index (top, left), the Doppler signal in the coronal cut of
the CCA (top right) and the velocity prole variation in six successive cardiac cycles (bottom).
Figure 2:
Reconstructed patient-specic carotid artery models
for the ten subjects.
clinical assessment is based on US-Doppler because of its
accessibility and its ease of use, particularly for the neck.
However, this examination is operator-dependent and getting
velocity values all over the carotid artery bifurcation is a hard
task. This limitation may be overcome with PC-MRI which
can bring both geometric and hemodynamic information si-
multaneously thanks to a compromise between spatial reso-
lution and acquisition time. In this context, few studies com-
pared velocity measurements in the carotid artery between
US-Doppler and PC-MRI [15, 16, 38, 28]. They showed
that there was a significant variation of velocity values in
the CCA and that PC-MRI generally leads to smaller veloc-
ity values compared with US-Doppler. However, these stud-
ies have not considered CFD simulations to complete mea-
surement characteristics in order to obtain an overall carotid
hemodynamic exploration.
In this paper, our objective is to design an optimized pa-
tient specific CFD workflow in terms of quality of velocity
profiles, computational efficiency and clinical applicability.
The anatomical data are obtained from PC-MRI, while ve-
locity data are obtained from both PC-MRI and US-Doppler.
This allows us to address two sub-goals i) comparing ve-
locity measurements from the two imaging modalities im-
plying different acquisition conditions (the widespread US-
Doppler, and less routine PC-MRI) and providing different
velocity quantifications (1D-axial vs 3D). ii) investigating
the optimal combination of velocity measurements and CFD
modeling to provide realistic patient specific flow simula-
tions. We investigated and modeled blood flow velocity from
imaging data in ten healthy volunteers. This work may also
allow deriving PC-MRI and/or US-Doppler measured ve-
locities given numerical velocities. Section 2 describes the
imaging data sets and the analysis methodology. Section 3
presents the obtained results that are discussed in section 4.
2. Material and Methods
The arterial geometrical model was extracted from MR
anatomical images and the hemodynamic modeling was per-
formed from the obtained models. The velocity waveforms
from both PC-MRI and US-Doppler were extracted at three
locations: the right CCA, ECA and ICA.
2.1. Imaging Data
Right carotid artery bifurcations in 10 healthy volunteers
(4 males and 6 females, median age: 35 years, range: 24-
57 years) with no cardiovascular disease history, were ex-
plored at the Radiology Department of Fattouma Bourguiba
University Hospital using both PC-MRI and US-Doppler ac-
cording to the following protocols.
2.1.1. PC-MR imaging
The PC-MR images were acquired with a clinical 1.5
T Philips system (Ingenia, Philips medical systems, Best,
the Netherlands) using 20 channels phased array head neck
spine coil. Two acquisitions (anatomical and flow imag-
ing) were performed (Figure 1). Fifty 2D anatomical images
were acquired in axial orientation to cover cervical region
Arij Debbich et al.:
Preprint submitted to Elsevier
Page 2 of 16

A Spatiotemporal exploration and 3D modeling of blood ow in healthy carotid artery bifurcation from two modalities.
Figure 3:
Growing carotid scanning windows size. Key points
are located in: CCA at 1.5 cm from the bifurcation, ECA and
ICA: at 1 cm from the bifurcation.
with T1 Fast Field Echo (T1 FFE) and the following param-
eters: Repetition time (TR)=13 ms, echo time (TE)=3.6 ms,
NEX (signal average)=1, flip angle=60 deg, pixel size=0.44
x 0.44 mm, slice thickness=3 mm, GAP=2 mm.
The images obtained were then used to acquire four
flow images in oblique sagittal plane (including right carotid
bifurcation with most of CCA and ICA) using 3D Phase
Contrast Angiography (PCA) and the following parameters:
TR=11 ms, TE=7.1 ms, flip angle=15 deg, pixel size=0.73
x 0.73 mm
2
, slice thickness=3 mm, NEX=1, velocity en-
coding (VENC)=90 cm per sec, retrospective cardiac gating
based on pulse oximeterplethysmography was used and 14
phases of cardiac cycle were acquired. The ideal velocity
encoding (VENC) should be high enough to avoid aliasing
and as low as possible to reduce velocity noise [47]. Since
velocity in the carotid artery for normal subjects does not
generally go over 110 cm/s and rarely exceeds 90 cm/s, we
fixed VENC at 90 cm/s.
To minimize the acquisition time, we restricted VENC
to the cranio-caudal direction only. This approach modifies
neither temporal nor spatial resolution. However, it allows
the reduction of acquisition time by a factor of 3. The total
scan time for an exam was approximately 7 minutes.
2.1.2. US-Doppler imaging
All US-Doppler exams were conducted by a radiologist
(B.H) with 10 years experience in cardiovascular imaging.
Clinical General Electric ultrasound systems (LOGIQ E9,
GE Healthcare, Milwaukee, WI, USA) with 9 MHz linear
probe were used. For each subject, velocity profiles of the
right carotid bifurcation were recorded at the following lo-
cations:
CCA: 1.5 cm from the carotid sinus
ECA and ICA: 1 cm from the carotid sinus except the ICA
of volunteer number 5 since his carotid morphology was spe-
cific.
US-Doppler images were matrices of dimension 720x960.
To extract the velocity waveform, we chose a profile of one
cardiac cycle (Figure 1-right-bottom), fixed the two profile
axes and selected 14 feature points on these profiles includ-
ing PSV and EDV. A cubic spline interpolation of these
Figure 4:
CCA velocity waveform extracted from MRI data
(VMRImax, VMRImean and VMRIpixel) for Volunteer 1 (top)
and feature points of CCA velocity waveform extracted from
US data in [17] (bottom).
points provided the US-Doppler velocity profile. The US-
Doppler profile point digitization was performed using the
Engauge Digitizer software [29].
2.2. PC-MRI Velocity profile extraction
Three velocity waveforms were extracted from PC-MRI
at locations CCA, ECA, and ICA during a cardiac cycle
which was divided into 14 time points. The following values
were deduced from the interpolated waveforms:
- Velocity variation at a given pixel 𝑉
MRIpixel
(See Algorithm
in the Appendix).
- Maximum velocity at a given pixel within its eight neigh-
bors 𝑉
MRImax
.
- Mean velocity at a given pixel within its eight neighbors
𝑉
MRImean
Velocity profile processing was performed using
MATLAB R2017 b. The PC-MRI waveforms (𝑉
MRIpixel
,
𝑉
MRImax
, 𝑉
MRImean
) were compared to the US-Doppler ve-
locity waveforms 𝑉
US
and to the CFD simulated waveforms
𝑉
SIM
located at the same sites of the vessel. Comparison of
the measured velocities between US-Doppler and MRI re-
Arij Debbich et al.:
Preprint submitted to Elsevier
Page 3 of 16

A Spatiotemporal exploration and 3D modeling of blood ow in healthy carotid artery bifurcation from two modalities.
quires the two waveforms to be temporally aligned: starting
at the same point of the cardiac cycle and focusing the eval-
uation on the same time interval for both modalities. How-
ever, as the MRI and the US-Doppler examinations were not
acquired at the same time, there might be some physiologi-
cal variations [16]. To minimize this effect, the 14 velocity
values from PC-MRI were temporally aligned to the 14 ex-
tracted points of the US-Doppler curve based on key time
points (where t/T=0, 0.07, 0.15, 0.23, 0.3, 0.38, 0.46, 0.53,
0.65, 0.69, 0.76, 0.84, 0,92, 1).
2.3. Arterial model reconstruction and
computational mesh generation
Out of 50 cross sections of MR imaging data, we selected
32 sections to be segmented: 18 sections before the bifur-
cation related to CCA and 14 sections after the bifurcation
related to ICA and ECA, to obtain a common size for all the
geometrical models with 3.3 cm of CCA length and 2.5 cm
of ECA and ICA length after cutting the wall ends and creat-
ing the inlet/outlet surfaces. The geometrical characteristics
of all the vessel segments for the ten subjects are given in Ta-
ble1. The carotid lumen was separated from the rest of the
structures by applying an intensity threshold. In some cases,
for instance in the case of subject movement, an expert cor-
rected manually the segmentation. The 3D arterial model
was constructed using a Marching Cubes algorithm [27]
leading to a triangular surface mesh which was further re-
meshed if necessary, in order to respect an imposed number
of facets per surface unit [4] and therefore ensure a high mesh
quality for the CFD simulations. Then, we imported the 3D
wall model to create the inlet/outlet surfaces. The model was
further re-meshed using an Octree surface refinement based
on prismatic wall [20]. Next, a volumetric meshing was gen-
erated based on the Delaunay tetrahedral refinement algo-
rithm [53]. The segmentation and the image-based 3D mesh
reconstruction steps were performed using the AMIRA
1
software. The border surface creation was done using DE-
SIGN MODELER software and the mesh refinement was
performed by ICEM, both from ANSYS
2
software. The ob-
tained geometrical models for the 10 subjects are displayed
in Figure 2. Blood flow modeling was based on computa-
tional fluid dynamic (CFD) to solve the governing equations
through the finite volume method (FVM) targeting partial
differential equations solving. As blood is an incompress-
ible fluid with a non-Newtonian behavior and given that all
considered geometries belong to healthy subjects without
anomalies like stenosis or aneurisms, we chose the Navier-
Stokes equation for incompressible fluid with a laminar flow
described by the following equations [1]:
𝜌
𝜕𝑣
𝜕𝑡
+ (𝑣.∇)𝑣
= −∇𝑝 + 𝜇
2
𝑣 (1)
.𝑣 = 0 (2)
1
Thermo Fisher Scientific and Zuse Institute Berlin (ZIB)
2
ANSYS, Inc, Canonsburg, USA
Figure 5:
Localization of extracted velocity proles along the
carotid bifurcation in the coronal orientation of PC-MRI data
(Volunteer 1). One cm of vessel length corresponds to 14
pixels.
where 𝑣 is the velocity, 𝑡 the time, 𝜌 the density, 𝑝 the pres-
sure and 𝜇 the dynamic viscosity.
Some studies adopted the rheological Newtonian behav-
ior for the carotid artery (stationary viscosity) because it is
simpler than the hemodynamic modeling with a non Newto-
nian behavior and arguing it has a minor impact on the results
[33]. In this study, we kept the non-Newtonian property for
blood flow modeling to stay closer to reality. We consid-
ered the Herschal-Bulkley condition, which defines viscos-
ity properties as in [51]:
𝜇 = 𝑘 𝛾
𝑛−1
+
𝜏
0
𝛾
(3)
𝛾 = 𝑣 + (∇𝑣)
𝑇
(4)
where 𝑘 is the consistence index, 𝑛 the power low index, 𝜏
0
the yield stress threshold (𝑘=0.01 Kg/m s, 𝑛=0.68, 𝜏
0
=0.4
Pa) and 𝛾 the rate of strain tensor.
2.4. Boundary conditions
One of our objectives was to investigate the impact of the
inlet boundary conditions on the simulation results. There-
fore, blood flow modeling was studied with two velocity in-
lets: PC-MRI and US-Doppler velocity waveforms extracted
at the CCA location. These inlets were pulsed over time and
were composed of the two usual physiological phases dur-
ing a cardiac cycle: systole and diastole. The PC-MRI inlet
Arij Debbich et al.:
Preprint submitted to Elsevier
Page 4 of 16

Citations
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Journal ArticleDOI
Abstract: Background and objective In a healthy body, the elastic wall of the arteries forms wave-like structures resulting from the continuous pumping of the heart. The systolic and diastolic phases generate a contraction and expansion pattern, which is mimicked in this study by considering a wavy-walled arterial structure. A numerical investigation of the spatio-temporal flow of blood and heat transfer through a porous medium under the action of magnetic field strength is conducted. Method The governing equations of the blood flow in the Darcy model are simulated by applying a vorticity-stream function formulation approach. The transformed dimensionless equations are further discretized using the finite difference method by developing the Peaceman-Rachford alternating direction implicit (P-R ADI) scheme. Results The computational results for the axial velocity, temperature distribution, flow visualization using the streamlines and vorticity contours, isotherms, wall shear stress and the average Nusselt number are presented graphically for different values of the physical parameters. Conclusions The study shows that the axial velocity increases with an increase in the Darcy number, and a similar phenomenon is observed because of an amplitude variation in the wavy wall. Both temperature and wall shear stress decreases with an increase in the Darcy number. The average Nusselt number increases with the magnetic field strength, while it has a reducing tendency due to the permeability of the porous medium.

Journal ArticleDOI
Abstract: The hemodynamics plays a key role in the transport processes, in the blood stream, and thus, on the accumulation and deposition of lipids and medication on the vessel’s wall. Therefore, understanding the hemodynamics of the arterial veins can advance the understanding of transport phenomena and prediction of deposition and buildup of the low-density lipoproteins (LDL) and particulate medication, on the arterial surfaces. Previous studies have showed that for pulsatile flow, laminar-turbulent flow transition may occur, particularly during intense exercises. Experimental and computational studies, of hemodynamics and transport phenomena, pose significant challenges due to the complex aorta’s geometry and arterial fluid dynamics. In the present study, we propose a large-eddy simulation (LES), computational approach, to carry out the hemodynamics and medication dispersion and deposition studies, inside the descending aorta. The analysis reveals that the flow separation causes a preferential deposition and build-up of low-density lipoproteins (LDL) on the arterial surface. Our study also shows that the flow boundary-layer separation is associated with an increase in deposition of the low-density lipoproteins. The analysis reveals the presence of Dean vortices, inside the aorta branches, which contribute to the reduction of the deposition and build-up of low-density lipoproteins on the arterial surfaces. The analysis of medication dispersion and deposition, inside the descending aorta, shows that the total medication deposition increases with the increase of particle size and density. Particles of fiber-like shape are more prone to deposition, and this is due to the fact that fiber-like particles align perfectly with the flow streamlines. Thus, the interaction of complex turbulent eddies with vessel’s wall causes medication deposition. The research shows that LES is a promising tool in the analysis of hemodynamics and medication transport and therefore, it may assist medical planning by providing surgeons with the elements of the blood flow such as, pressure, velocity, vorticity, wall-shear stresses, which cannot be measured in vivo and obtained with imaging techniques.

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Abstract: In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analysed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.

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Abstract: We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

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Journal ArticleDOI
TL;DR: The study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow.
Abstract: Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovascular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley number, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemodynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pockets in which the direction of the wall shear stress oscillates. Atherosclerotic disease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow. This field is rich with challenging problems in fluid mechanics involving three-dimensional, pulsatile flows at the edge of turbulence.

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Journal ArticleDOI
TL;DR: This review intends to introduce currently used 4D flow MRI methods, including Cartesian and radial data acquisition, approaches for acceleratedData acquisition, cardiac gating, and respiration control, and an overview over the potential this new imaging technique has in different parts of the body from the head to the peripheral arteries.
Abstract: Traditionally, magnetic resonance imaging (MRI) of flow using phase contrast (PC) methods is accomplished using methods that resolve single-directional flow in two spatial dimensions (2D) of an individual slice. More recently, three-dimensional (3D) spatial encoding combined with three-directional velocity-encoded phase contrast MRI (here termed 4D flow MRI) has drawn increased attention. 4D flow MRI offers the ability to measure and to visualize the temporal evolution of complex blood flow patterns within an acquired 3D volume. Various methodological improvements permit the acquisition of 4D flow MRI data encompassing individual vascular structures and entire vascular territories such as the heart, the adjacent aorta, the carotid arteries, abdominal, or peripheral vessels within reasonable scan times. To subsequently analyze the flow data by quantitative means and visualization of complex, three-directional blood flow patterns, various tools have been proposed. This review intends to introduce currently used 4D flow MRI methods, including Cartesian and radial data acquisition, approaches for accelerated data acquisition, cardiac gating, and respiration control. Based on these developments, an overview is provided over the potential this new imaging technique has in different parts of the body from the head to the peripheral arteries.

466 citations


Journal ArticleDOI
TL;DR: In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model, and this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.
Abstract: Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.

461 citations


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