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MINI REVIEW
published: 12 May 2020
doi: 10.3389/fphys.2020.00454
Frontiers in Physiology | www.frontiersin.org 1 May 2020 | Volume 11 | Article 454
Edited by:
James B. Hoying,
Cardiovascular Innovation Institute
(CII), United States
Reviewed by:
Jessica E. Wagenseil,
Washington University in St. Louis,
United States
Jingyan Han,
Boston University, United States
*Correspondence:
Craig J. Goergen
cgoergen@purdue.edu
†These authors have contributed
equally to this work
Specialty section:
This article was submitted to
Vascular Physiology,
a section of the journal
Frontiers in Physiology
Received: 03 February 2020
Accepted: 09 April 2020
Published: 12 May 2020
Citation:
Lipp SN, Niedert EE, Cebull HL,
Diorio TC, Ma JL, Rothenberger SM,
Stevens Boster KA and Goergen CJ
(2020) Computational Hemodynamic
Modeling of Arterial Aneurysms: A
Mini-Review. Front. Physiol. 11:454.
doi: 10.3389/fphys.2020.00454
Computational Hemodynamic
Modeling of Arterial Aneurysms: A
Mini-Review
Sarah N. Lipp 1†, Elizabeth E. Niedert 1†, Hannah L. Cebull 1, Tyler C. Diorio 1, Jessica L. Ma 1,
Sean M. Rothenberger 1, Kimberly A. Stevens Boster 1,2 and Craig J. Goergen 1*
1 Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States, 2 School of Mechanical
Engineering, Purdue University, West Lafayette, IN, United States
Arterial aneurysms are pathological dilations of blood vessels, which can be of clinical
concern due to thrombosis, dissection, or rupture. Aneurysms can form throughout
the arterial system, including intracranial, thoracic, abdominal, visceral, peripheral, or
coronary arteries. Currently, aneurysm diameter and expansion rates are the most
commonly used metrics to assess rupture risk. Surgical or endovascular interventions
are clinical treatment options, but are invasive and associated with risk for the patient.
For aneurysms in locations where thrombosis is the primary concern, diameter is also
used to determine the level of therapeutic anticoagulation, a treatment that increases
the possibility of internal bleeding. Since simple diameter is often insufficient to reliably
determine rupture and thrombosis risk, computational hemodynamic simulations are
being developed to help assess when an intervention is warranted. Created from subject-
specific data, computational models have the potential to be used to predict growth,
dissection, rupture, and thrombus-formation risk based on hemodynamic parameters,
including wall shear stress, oscillatory shear index, residence time, and anomalous
blood flow patterns. Generally, endothelial damage and flow stagnation within aneurysms
can lead to coagulation, inflammation, and the release of proteases, which alter
extracellular matrix composition, increasing risk of rupture. In this review, we highlight
recent work that investigates aneurysm geometry, model parameter assumptions, and
other specific considerations that influence computational aneurysm simulations. By
highlighting modeling validation and verification approaches, we hope to inspire future
computational efforts aimed at improving our understanding of aneurysm pathology and
treatment risk stratification.
Keywords: hemodynamic modeling, computational fluid dynamics, aneurysm, validation, fluid-structure
interaction
1. INTRODUCTION
Arterial aneurysms are pathological focal dilations of arteries that can have life-threatening
consequences. Aneurysms are commonly classified as saccular (asymmetric outpouchings) or
fusiform (circumferential dilations). Other distinct vascular pathologies include pseudoaneurysms,
which are partial thickness dilations of the blood vessel wall, and arterial dissections, which occur
when medial layers separate and pressurized blood extravasates into a false lumen (Kumar et al.,
2018). Aneurysm complications include rupture, hypovolemic shock (Dawson and Fitridge, 2013;
published: 12 May 2020
doi: 10.3389/fphys.2020.00454
Frontiers in Physiology | www.frontiersin.org 1 May 2020 | Volume 11 | Article 454
Edited by:
James B. Hoying,
Cardiovascular Innovation Institute
(CII), United States
Reviewed by:
Jessica E. Wagenseil,
Washington University in St. Louis,
United States
Jingyan Han,
Boston University, United States
*Correspondence:
Craig J. Goergen
cgoergen@purdue.edu
†These authors have contributed
equally to this work
Specialty section:
This article was submitted to
Vascular Physiology,
a section of the journal
Frontiers in Physiology
Received: 03 February 2020
Accepted: 09 April 2020
Published: 12 May 2020
Citation:
Lipp SN, Niedert EE, Cebull HL,
Diorio TC, Ma JL, Rothenberger SM,
Stevens Boster KA and Goergen CJ
(2020) Computational Hemodynamic
Modeling of Arterial Aneurysms: A
Mini-Review. Front. Physiol. 11:454.
doi: 10.3389/fphys.2020.00454
Computational Hemodynamic
Modeling of Arterial Aneurysms: A
Mini-Review
Sarah N. Lipp 1†, Elizabeth E. Niedert 1†, Hannah L. Cebull 1, Tyler C. Diorio 1, Jessica L. Ma 1,
Sean M. Rothenberger 1, Kimberly A. Stevens Boster 1,2 and Craig J. Goergen 1*
1 Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States, 2 School of Mechanical
Engineering, Purdue University, West Lafayette, IN, United States
Arterial aneurysms are pathological dilations of blood vessels, which can be of clinical
concern due to thrombosis, dissection, or rupture. Aneurysms can form throughout
the arterial system, including intracranial, thoracic, abdominal, visceral, peripheral, or
coronary arteries. Currently, aneurysm diameter and expansion rates are the most
commonly used metrics to assess rupture risk. Surgical or endovascular interventions
are clinical treatment options, but are invasive and associated with risk for the patient.
For aneurysms in locations where thrombosis is the primary concern, diameter is also
used to determine the level of therapeutic anticoagulation, a treatment that increases
the possibility of internal bleeding. Since simple diameter is often insufficient to reliably
determine rupture and thrombosis risk, computational hemodynamic simulations are
being developed to help assess when an intervention is warranted. Created from subject-
specific data, computational models have the potential to be used to predict growth,
dissection, rupture, and thrombus-formation risk based on hemodynamic parameters,
including wall shear stress, oscillatory shear index, residence time, and anomalous
blood flow patterns. Generally, endothelial damage and flow stagnation within aneurysms
can lead to coagulation, inflammation, and the release of proteases, which alter
extracellular matrix composition, increasing risk of rupture. In this review, we highlight
recent work that investigates aneurysm geometry, model parameter assumptions, and
other specific considerations that influence computational aneurysm simulations. By
highlighting modeling validation and verification approaches, we hope to inspire future
computational efforts aimed at improving our understanding of aneurysm pathology and
treatment risk stratification.
Keywords: hemodynamic modeling, computational fluid dynamics, aneurysm, validation, fluid-structure
interaction
1. INTRODUCTION
Arterial aneurysms are pathological focal dilations of arteries that can have life-threatening
consequences. Aneurysms are commonly classified as saccular (asymmetric outpouchings) or
fusiform (circumferential dilations). Other distinct vascular pathologies include pseudoaneurysms,
which are partial thickness dilations of the blood vessel wall, and arterial dissections, which occur
when medial layers separate and pressurized blood extravasates into a false lumen (Kumar et al.,
2018). Aneurysm complications include rupture, hypovolemic shock (Dawson and Fitridge, 2013;
Lipp et al. Hemodynamic Modeling of Arterial Aneurysms
Wanhainen et al., 2019), tissue compression (Thompson et al.,
2015), dissection initiation or progression (Czerny et al., 2019),
or thromboembolism and ischemia (Dawson and Fitridge, 2013;
McCrindle et al., 2017). Aneurysm pathophysiology can involve
endothelial changes, damage resulting in an inflammatory
cascade, release of proteases, extracellular matrix remodeling,
and smooth muscle cell apoptosis, all of which can propagate
aneurysm growth and rupture (Chalouhi et al., 2012; Hendel
et al., 2015) requiring surgical repair, coiling, and flow diverting
stents (Table S1). Because there is abnormal blood flow and
endothelial cell damage in aneurysms, coagulability can be
pharmacologically altered to lower thrombus risk (McCrindle
et al., 2017).
Current guidelines for aneurysm intervention consider
diameter, expansion rate, symptoms, and other risk factors as
summarized in Table S1. Since risk factors for aneurysm rupture
prediction are imperfect considering that some small, growing
aneurysms still rupture, it is likely that some large or rapidly
growing aneurysms do not require surgical treatment (UCAS
Japan Investigators et al., 2012; Dawson and Fitridge, 2013;
Kontopodis et al., 2016; Saeyeldin et al., 2019). Similarly, the
risk assessment of thromboembolism from aneurysms based
on diameter has relatively poor sensitivity and specificity
(Grande Gutierrez et al., 2019). However, assessing aneurysm
hemodynamics with computational models may help identify
more accurate predictors of vessel rupture or thrombosis
formation, improving risk stratification that can guide clinical
decision-making. This mini-review highlights recent literature
that describes computational modeling of aneurysms and
pseudoaneurysms using patient-specific geometries, boundary
conditions, and model validation and verification.
2. FROM IMAGES TO SIMULATIONS
2.1. Imaging
Medical imaging can be used to acquire patient-specific
information for computational fluid dynamics (CFD) and fluid-
structure interaction (FSI) simulations. Vessel geometry
information is often obtained using digital subtraction
angiography (DSA), computed tomographic angiography
(CTA), or magnetic resonance angiography (MRA). Recent
efforts have also utilized volumetric ultrasound or optical
coherence tomography to acquire vessel geometry (Jia et al.,
2012; Van Disseldorp et al., 2019), but their application to CFD
remains limited to animal studies (Phillips et al., 2017).
Every imaging technique has trade-offs. Most notably, DSA
and CTA subject the patient to ionizing radiation, which can
Abbreviations: AAAs, abdominal aortic aneurysms; BAV, bicuspid aortic valve;
CAAs, coronary artery aneurysms; CFD, computational fluid dynamics; CTA,
computed tomographic angiography; DSA, digital subtraction angiography;
FSI, fluid-structure interactions; IAs, intracranial aneurysms; KD, Kawasaki
disease; MI, myocardial infarct; MRA, magnetic resonance angiography; MRI,
magnetic resonance imaging; OSI, oscillatory shear index; PAAs, peripheral artery
aneurysms; PDA, pancreaticoduodenal artery; PDAA, pancreaticoduodenal artery
aneurysm; PC-MRI, phase contrast-magnetic resonance imaging; SMA, superior
mesenteric artery; RT, residence time; TAAs, thoracic aortic aneurysms; WSS, wall
shear stress; WSSG, wall shear stress gradient; VAAs, visceral artery aneurysms;
VVUQ, verification, validation, and uncertainty quantification.
increase cancer incidence, limiting use for longitudinal studies
(Einstein et al., 2007). Even so, the high resolution, low cost,
and fast scan time have made CTA a common clinical imaging
modality for aneurysms. While MRA does not subject patients to
radiation, this technique requires expensive equipment, consists
of longer scan times, and produces relatively low resolution
images compared to CTA (Sailer et al., 2014).
In addition to aneurysm geometry, some imaging
techniques provide subject-specific boundary conditions
for hemodynamic simulations. Velocity information acquired
non-invasively via pulsed wave Doppler ultrasound and
phase contrast-magnetic resonance imaging (PC-MRI) can
estimate two-dimensional velocity-based inlet boundary
conditions (Boussel et al., 2009; Enevoldsen et al., 2012).
PC-MRI provides time-resolved velocity measurements in
either a single direction (2D PC-MRI) or throughout an
entire volume (4D flow MRI) (Boussel et al., 2009; Eker et al.,
2015), but is limited by lower spatio-temporal resolution.
While each imaging modality has limitations, imaging data
is key to provide the subject-specific information regarding
aneurysm geometry and boundary conditions necessary for
hemodynamic modeling.
2.2. Modeling
Three-dimensional computational simulations of the vasculature
can be used to estimate hemodynamic metrics. If the walls of
the model are rigid, only the fluid domain is considered. If the
walls are compliant, both solid and fluid domains are considered,
often referred to as FSI simulations. The fluid domain model
can be created by segmenting the vessel lumen from medical
imaging data (Figure 1). The entire volume is then typically
broken into discrete elements, creating a mesh of individual
nodes (Figure 1, third panel). The conservation of mass and
momentum equations for pressure and velocity can then be
solved at each spatial location within the domain (Figure 2). This
process varies depending on the study, software, and methods
used. The most common parameters, inputs, as well as how they
are obtained are listed in Table S2. Hemodynamic parameters
that may influence aneurysm formation, growth, rupture, and
thrombosis can be calculated based on the simulation results
(Table S3). For example, wall shear stress (WSS) is the tangential
stress blood exerts on vessel walls and has been linked to
rupture risk (Figure 2B; Table S3; Meng et al., 2014). For
risk stratification studies, WSS-related parameters have been
investigated (Liang et al., 2019), such as WSS gradient (WSSG)
(Table S3; Longo et al., 2017) and oscillatory shear index
(OSI). OSI represents the change in direction of the shear
forces during the cardiac cycle, and elevated OSI is associated
with pro-inflammatory markers (Figure 2C; Sei et al., 2017).
Complex flow patterns are frequently observed in aneurysms
(Xiang et al., 2011). Flow stagnation in an aneurysm can be
quantified by the residence time (RT), which is the average time a
particle remains within the aneurysm (Reza and Arzani, 2019).
Higher RT indicates flow stagnation and retention of platelets
and inflammatory cells, which may contribute to thrombus
formation (Figure 2D; Rayz et al., 2010; Reza and Arzani,
2019).
Frontiers in Physiology | www.frontiersin.org 2 May 2020 | Volume 11 | Article 454
Wanhainen et al., 2019), tissue compression (Thompson et al.,
2015), dissection initiation or progression (Czerny et al., 2019),
or thromboembolism and ischemia (Dawson and Fitridge, 2013;
McCrindle et al., 2017). Aneurysm pathophysiology can involve
endothelial changes, damage resulting in an inflammatory
cascade, release of proteases, extracellular matrix remodeling,
and smooth muscle cell apoptosis, all of which can propagate
aneurysm growth and rupture (Chalouhi et al., 2012; Hendel
et al., 2015) requiring surgical repair, coiling, and flow diverting
stents (Table S1). Because there is abnormal blood flow and
endothelial cell damage in aneurysms, coagulability can be
pharmacologically altered to lower thrombus risk (McCrindle
et al., 2017).
Current guidelines for aneurysm intervention consider
diameter, expansion rate, symptoms, and other risk factors as
summarized in Table S1. Since risk factors for aneurysm rupture
prediction are imperfect considering that some small, growing
aneurysms still rupture, it is likely that some large or rapidly
growing aneurysms do not require surgical treatment (UCAS
Japan Investigators et al., 2012; Dawson and Fitridge, 2013;
Kontopodis et al., 2016; Saeyeldin et al., 2019). Similarly, the
risk assessment of thromboembolism from aneurysms based
on diameter has relatively poor sensitivity and specificity
(Grande Gutierrez et al., 2019). However, assessing aneurysm
hemodynamics with computational models may help identify
more accurate predictors of vessel rupture or thrombosis
formation, improving risk stratification that can guide clinical
decision-making. This mini-review highlights recent literature
that describes computational modeling of aneurysms and
pseudoaneurysms using patient-specific geometries, boundary
conditions, and model validation and verification.
2. FROM IMAGES TO SIMULATIONS
2.1. Imaging
Medical imaging can be used to acquire patient-specific
information for computational fluid dynamics (CFD) and fluid-
structure interaction (FSI) simulations. Vessel geometry
information is often obtained using digital subtraction
angiography (DSA), computed tomographic angiography
(CTA), or magnetic resonance angiography (MRA). Recent
efforts have also utilized volumetric ultrasound or optical
coherence tomography to acquire vessel geometry (Jia et al.,
2012; Van Disseldorp et al., 2019), but their application to CFD
remains limited to animal studies (Phillips et al., 2017).
Every imaging technique has trade-offs. Most notably, DSA
and CTA subject the patient to ionizing radiation, which can
Abbreviations: AAAs, abdominal aortic aneurysms; BAV, bicuspid aortic valve;
CAAs, coronary artery aneurysms; CFD, computational fluid dynamics; CTA,
computed tomographic angiography; DSA, digital subtraction angiography;
FSI, fluid-structure interactions; IAs, intracranial aneurysms; KD, Kawasaki
disease; MI, myocardial infarct; MRA, magnetic resonance angiography; MRI,
magnetic resonance imaging; OSI, oscillatory shear index; PAAs, peripheral artery
aneurysms; PDA, pancreaticoduodenal artery; PDAA, pancreaticoduodenal artery
aneurysm; PC-MRI, phase contrast-magnetic resonance imaging; SMA, superior
mesenteric artery; RT, residence time; TAAs, thoracic aortic aneurysms; WSS, wall
shear stress; WSSG, wall shear stress gradient; VAAs, visceral artery aneurysms;
VVUQ, verification, validation, and uncertainty quantification.
increase cancer incidence, limiting use for longitudinal studies
(Einstein et al., 2007). Even so, the high resolution, low cost,
and fast scan time have made CTA a common clinical imaging
modality for aneurysms. While MRA does not subject patients to
radiation, this technique requires expensive equipment, consists
of longer scan times, and produces relatively low resolution
images compared to CTA (Sailer et al., 2014).
In addition to aneurysm geometry, some imaging
techniques provide subject-specific boundary conditions
for hemodynamic simulations. Velocity information acquired
non-invasively via pulsed wave Doppler ultrasound and
phase contrast-magnetic resonance imaging (PC-MRI) can
estimate two-dimensional velocity-based inlet boundary
conditions (Boussel et al., 2009; Enevoldsen et al., 2012).
PC-MRI provides time-resolved velocity measurements in
either a single direction (2D PC-MRI) or throughout an
entire volume (4D flow MRI) (Boussel et al., 2009; Eker et al.,
2015), but is limited by lower spatio-temporal resolution.
While each imaging modality has limitations, imaging data
is key to provide the subject-specific information regarding
aneurysm geometry and boundary conditions necessary for
hemodynamic modeling.
2.2. Modeling
Three-dimensional computational simulations of the vasculature
can be used to estimate hemodynamic metrics. If the walls of
the model are rigid, only the fluid domain is considered. If the
walls are compliant, both solid and fluid domains are considered,
often referred to as FSI simulations. The fluid domain model
can be created by segmenting the vessel lumen from medical
imaging data (Figure 1). The entire volume is then typically
broken into discrete elements, creating a mesh of individual
nodes (Figure 1, third panel). The conservation of mass and
momentum equations for pressure and velocity can then be
solved at each spatial location within the domain (Figure 2). This
process varies depending on the study, software, and methods
used. The most common parameters, inputs, as well as how they
are obtained are listed in Table S2. Hemodynamic parameters
that may influence aneurysm formation, growth, rupture, and
thrombosis can be calculated based on the simulation results
(Table S3). For example, wall shear stress (WSS) is the tangential
stress blood exerts on vessel walls and has been linked to
rupture risk (Figure 2B; Table S3; Meng et al., 2014). For
risk stratification studies, WSS-related parameters have been
investigated (Liang et al., 2019), such as WSS gradient (WSSG)
(Table S3; Longo et al., 2017) and oscillatory shear index
(OSI). OSI represents the change in direction of the shear
forces during the cardiac cycle, and elevated OSI is associated
with pro-inflammatory markers (Figure 2C; Sei et al., 2017).
Complex flow patterns are frequently observed in aneurysms
(Xiang et al., 2011). Flow stagnation in an aneurysm can be
quantified by the residence time (RT), which is the average time a
particle remains within the aneurysm (Reza and Arzani, 2019).
Higher RT indicates flow stagnation and retention of platelets
and inflammatory cells, which may contribute to thrombus
formation (Figure 2D; Rayz et al., 2010; Reza and Arzani,
2019).
Frontiers in Physiology | www.frontiersin.org 2 May 2020 | Volume 11 | Article 454
Lipp et al. Hemodynamic Modeling of Arterial Aneurysms
FIGURE 1 | Pipeline used for computational modeling. Imaging data is acquired for the vessel of interest. The angiography images are segmented to identify the
geometry of the vessel. Surface and volumetric meshes are created using available meshing software packages. Boundary conditions are defined and parameters are
set in order to run simulations and analyze hemodynamic parameters, such as WSS, OSI, and others. Figure modified from Numata et al. (2016).
It is important to note that all models require assumptions,
which can influence simulation results and model fidelity. This
is especially important when estimating vessel wall properties,
the inflow boundary conditions, and the outflow boundary
conditions (Steinman and Pereira, 2019). While simulations
are useful for calculating hemodynamic parameters linked
to aneurysm progression, assumptions should be carefully
considered to maintain reasonable model fidelity.
3. ANEURYSMS
3.1. Intracranial Aneurysm
Intracranial aneurysms (IAs) are present in 3.2% of the
general population (Thompson et al., 2015). IAs are generally
asymptomatic, but IA rupture can lead to subarachnoid
hemorrhage (Thompson et al., 2015). While the management
and risk stratification of IAs remains controversial (Cebral et al.,
2011b) and there are no consensus guidelines with a diameter
cut off (Thompson et al., 2015), a clinical standard for surgical
intervention is defined as an aneurysm diameter ≥7–10 mm
(Bederson et al., 2000; Thompson et al., 2015).
Patient-specific CFD simulations are now being used to
identify hemodynamic parameters that may trigger IA growth
or rupture (Etminan and Macdonald, 2015) (Figures 2A–D).
Studies considering thrombosis often report RT, recirculation
zones, and/or WSS as these are of interest for growth and rupture
analyses (Vali et al., 2017). Initial conflicting results were reported
for IA suggesting that aneurysm progression is related to both
low WSS (Boussel et al., 2008; Miura et al., 2013) and high WSS
(Cebral et al., 2009, 2011b). A unified theory by Meng et al.
(2014) proposes two independent progression pathways. The first
suggests that high WSS and a positive WSSG make a region prone
to dilation, while the other suggests low WSS and high OSI are
the driving forces. More recent work has correlated aneurysm
growth and rupture to high OSI (Kawaguchi et al., 2012), high
WSSG (Shojima et al., 2010; Machi et al., 2017), and larger areas
of low WSS (Zhang et al., 2016; Qiu et al., 2017). Given that
abnormally low WSS is related to endothelial cell damage, areas
of low WSS may also correlate to areas of further vascular wall
damage. Cebral et al. (2011b) identified additional qualitative
risk factors within the aneurysmal region, including complex
flow, unstable flow structures, concentrated inflows, and small
impingement regions. Recent advancements in IA modeling have
yielded the ability to aid in surgical planning and improve patient
outcomes in several case studies (Vali et al., 2017). The ultimate
aim to predict IA rupture risk on a patient-specific basis remains
a work in progress (Saqr et al., 2019).
Unique challenges exist for modeling IAs. The small size
of the cerebral vasculature makes accurate vessel segmentation
and velocity measurements difficult. Although the cerebral
vasculature is less elastic than proximal elastic arteries, a
rigid wall assumption can alter WSS values and increase flow
instability (Torii et al., 2007; Yamaguchi, 2016). Finally, a
Newtonian blood flow assumption may be insufficient in some
IA cases (Saqr et al., 2019). Similar to aneurysms in other
parts of the body, relevant assumptions and approximate error
bounds should be reported to improve reproducibility when
modeling IAs.
3.2. Thoracic Aortic Aneurysms
Thoracic aortic aneurysms (TAAs) are pathological dilations of
the thoracic aorta, most commonly occurring in the ascending
region (Isselbacher, 2005; Ramanath et al., 2009). Hypertension,
aging, and smoking all contribute to risk of aortic aneurysm
development, and single gene mutations have greater influence
on TAA development than any other region of the aorta
(Milewicz et al., 2008; Hiratzka et al., 2009; Pinard et al., 2019).
Current clinical guidelines suggest that rupture risk outweighs
surgical risk for non-familial cases when TAA diameter is ≥55
mm or expands at a rate ≥5 mm/year (Hiratzka et al., 2009;
Erbel et al., 2014). However, dissection and rupture occasionally
occur below these thresholds, demonstrating a critical need for
improved risk assessment (Pape et al., 2007; Zafar et al., 2018).
Since the ascending thoracic aorta sits directly above the left
ventricle, it typically experiences the highest blood velocities,
wall forces, and wall displacements of any artery. Computational
modeling can be used to simulate these forces either using a rigid
wall assumption or FSI methods to incorporate the effects of wall
elasticity–a critical aspect in highly deformable vessels like the
aorta (Reymond et al., 2013; Trachet et al., 2015) (Figures 2E–H).
Studies using a rigid wall often focus on geometric effects using
patient-specific parameters without the additional computational
Frontiers in Physiology | www.frontiersin.org 3 May 2020 | Volume 11 | Article 454
FIGURE 1 | Pipeline used for computational modeling. Imaging data is acquired for the vessel of interest. The angiography images are segmented to identify the
geometry of the vessel. Surface and volumetric meshes are created using available meshing software packages. Boundary conditions are defined and parameters are
set in order to run simulations and analyze hemodynamic parameters, such as WSS, OSI, and others. Figure modified from Numata et al. (2016).
It is important to note that all models require assumptions,
which can influence simulation results and model fidelity. This
is especially important when estimating vessel wall properties,
the inflow boundary conditions, and the outflow boundary
conditions (Steinman and Pereira, 2019). While simulations
are useful for calculating hemodynamic parameters linked
to aneurysm progression, assumptions should be carefully
considered to maintain reasonable model fidelity.
3. ANEURYSMS
3.1. Intracranial Aneurysm
Intracranial aneurysms (IAs) are present in 3.2% of the
general population (Thompson et al., 2015). IAs are generally
asymptomatic, but IA rupture can lead to subarachnoid
hemorrhage (Thompson et al., 2015). While the management
and risk stratification of IAs remains controversial (Cebral et al.,
2011b) and there are no consensus guidelines with a diameter
cut off (Thompson et al., 2015), a clinical standard for surgical
intervention is defined as an aneurysm diameter ≥7–10 mm
(Bederson et al., 2000; Thompson et al., 2015).
Patient-specific CFD simulations are now being used to
identify hemodynamic parameters that may trigger IA growth
or rupture (Etminan and Macdonald, 2015) (Figures 2A–D).
Studies considering thrombosis often report RT, recirculation
zones, and/or WSS as these are of interest for growth and rupture
analyses (Vali et al., 2017). Initial conflicting results were reported
for IA suggesting that aneurysm progression is related to both
low WSS (Boussel et al., 2008; Miura et al., 2013) and high WSS
(Cebral et al., 2009, 2011b). A unified theory by Meng et al.
(2014) proposes two independent progression pathways. The first
suggests that high WSS and a positive WSSG make a region prone
to dilation, while the other suggests low WSS and high OSI are
the driving forces. More recent work has correlated aneurysm
growth and rupture to high OSI (Kawaguchi et al., 2012), high
WSSG (Shojima et al., 2010; Machi et al., 2017), and larger areas
of low WSS (Zhang et al., 2016; Qiu et al., 2017). Given that
abnormally low WSS is related to endothelial cell damage, areas
of low WSS may also correlate to areas of further vascular wall
damage. Cebral et al. (2011b) identified additional qualitative
risk factors within the aneurysmal region, including complex
flow, unstable flow structures, concentrated inflows, and small
impingement regions. Recent advancements in IA modeling have
yielded the ability to aid in surgical planning and improve patient
outcomes in several case studies (Vali et al., 2017). The ultimate
aim to predict IA rupture risk on a patient-specific basis remains
a work in progress (Saqr et al., 2019).
Unique challenges exist for modeling IAs. The small size
of the cerebral vasculature makes accurate vessel segmentation
and velocity measurements difficult. Although the cerebral
vasculature is less elastic than proximal elastic arteries, a
rigid wall assumption can alter WSS values and increase flow
instability (Torii et al., 2007; Yamaguchi, 2016). Finally, a
Newtonian blood flow assumption may be insufficient in some
IA cases (Saqr et al., 2019). Similar to aneurysms in other
parts of the body, relevant assumptions and approximate error
bounds should be reported to improve reproducibility when
modeling IAs.
3.2. Thoracic Aortic Aneurysms
Thoracic aortic aneurysms (TAAs) are pathological dilations of
the thoracic aorta, most commonly occurring in the ascending
region (Isselbacher, 2005; Ramanath et al., 2009). Hypertension,
aging, and smoking all contribute to risk of aortic aneurysm
development, and single gene mutations have greater influence
on TAA development than any other region of the aorta
(Milewicz et al., 2008; Hiratzka et al., 2009; Pinard et al., 2019).
Current clinical guidelines suggest that rupture risk outweighs
surgical risk for non-familial cases when TAA diameter is ≥55
mm or expands at a rate ≥5 mm/year (Hiratzka et al., 2009;
Erbel et al., 2014). However, dissection and rupture occasionally
occur below these thresholds, demonstrating a critical need for
improved risk assessment (Pape et al., 2007; Zafar et al., 2018).
Since the ascending thoracic aorta sits directly above the left
ventricle, it typically experiences the highest blood velocities,
wall forces, and wall displacements of any artery. Computational
modeling can be used to simulate these forces either using a rigid
wall assumption or FSI methods to incorporate the effects of wall
elasticity–a critical aspect in highly deformable vessels like the
aorta (Reymond et al., 2013; Trachet et al., 2015) (Figures 2E–H).
Studies using a rigid wall often focus on geometric effects using
patient-specific parameters without the additional computational
Frontiers in Physiology | www.frontiersin.org 3 May 2020 | Volume 11 | Article 454
Lipp et al. Hemodynamic Modeling of Arterial Aneurysms
FIGURE 2 | Hemodynamic parameters assessed by computational modeling for aneurysms at different anatomical locations. Velocity (m/s) (A), velocity during peak
systole (m/s) (E,I), velocity during diastole (cm/s) (M), wall shear stress (WSS) magnitude (B), WSS in peak systole (Pa) (F), WSS (Pa) (J), WSS in diastole (dynes/sq
cm) (N), oscillatory shear index (OSI) (C,G,K,O), relative residence time (RT) (D,H,L), and particle RT gradient (s/m) (P) were assessed for intracranial aneurysms (IAs)
of the internal carotid artery (A), paraclinoid aneurysm in a segment of internal carotid artery (B,C), and middle cerebral artery (D), distal arch thoracic aortic aneurysm
(TAA) (E–G), thoracic aortic aneurysm dissection (H), abdominal aortic aneurysm (AAA) (I–L), and coronary artery aneurysms (CAAs) (M–P). Figures modified from
Tian et al. (2016) (A), Wan et al. (2019) (B–C), Sugiyama et al. (2013) (D), Numata et al. (2016) (E–G), Shi et al. (2016) (H), Qiu et al. (2018) (I–L), Sengupta et al.
(2012), Sengupta (2013) (M–O), and Sengupta et al. (2014) (P).
expense and required material properties needed for FSI. For
example, studies using rigid walls revealed that patients with
bicuspid aortic valve (BAV) have complex blood flow patterns
that cause higher and uneven wall shear stresses, increasing the
potential for TAA formation (Youssefi et al., 2017; Condemi
et al., 2018; Edlin et al., 2019). Mendez et al. (2018) simulated
blood flow in BAV TAAs using both rigid walls and FSI, finding
non-significant differences in helical flow, but significantly lower
estimated pressure in CFD simulations. In particular, they
found the largest differences between rigid and deformable wall
Frontiers in Physiology | www.frontiersin.org 4 May 2020 | Volume 11 | Article 454
FIGURE 2 | Hemodynamic parameters assessed by computational modeling for aneurysms at different anatomical locations. Velocity (m/s) (A), velocity during peak
systole (m/s) (E,I), velocity during diastole (cm/s) (M), wall shear stress (WSS) magnitude (B), WSS in peak systole (Pa) (F), WSS (Pa) (J), WSS in diastole (dynes/sq
cm) (N), oscillatory shear index (OSI) (C,G,K,O), relative residence time (RT) (D,H,L), and particle RT gradient (s/m) (P) were assessed for intracranial aneurysms (IAs)
of the internal carotid artery (A), paraclinoid aneurysm in a segment of internal carotid artery (B,C), and middle cerebral artery (D), distal arch thoracic aortic aneurysm
(TAA) (E–G), thoracic aortic aneurysm dissection (H), abdominal aortic aneurysm (AAA) (I–L), and coronary artery aneurysms (CAAs) (M–P). Figures modified from
Tian et al. (2016) (A), Wan et al. (2019) (B–C), Sugiyama et al. (2013) (D), Numata et al. (2016) (E–G), Shi et al. (2016) (H), Qiu et al. (2018) (I–L), Sengupta et al.
(2012), Sengupta (2013) (M–O), and Sengupta et al. (2014) (P).
expense and required material properties needed for FSI. For
example, studies using rigid walls revealed that patients with
bicuspid aortic valve (BAV) have complex blood flow patterns
that cause higher and uneven wall shear stresses, increasing the
potential for TAA formation (Youssefi et al., 2017; Condemi
et al., 2018; Edlin et al., 2019). Mendez et al. (2018) simulated
blood flow in BAV TAAs using both rigid walls and FSI, finding
non-significant differences in helical flow, but significantly lower
estimated pressure in CFD simulations. In particular, they
found the largest differences between rigid and deformable wall
Frontiers in Physiology | www.frontiersin.org 4 May 2020 | Volume 11 | Article 454
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