This document describes a fluid-structure interaction (FSI) model developed to simultaneously analyze endothelial shear stress and strain in healthy and atherosclerotic murine arteries. The model incorporates vessel wall elasticity, plaque heterogeneity from 3D histology, and different approaches for including pre-stress of the arterial wall. The results show that including vessel wall properties and plaque composition affects shear stress and strain metrics. Specifically, endothelial strain values depend strongly on the reference state and pre-stress model used. Accounting for the heterogeneous mechanical properties of plaques is important for accurately predicting regional endothelial strain.

1. Considerations for analysis of
endothelial shear stress and strain in
FSI models of Atherosclerosis —
Robert Krams
Robert Krams
Sep 26 · 18 min read
Miten B. Patel1,2,6, Fotios Savvopoulos1,2,6, Caleb C. Berggren3, Lydia Aslanidou4,
Lucas H. Timmins5, Ryan M. Pedrigi3, Ranil de Silva2, Rob Krams6
1Bioengineering and 2NHLI, Imperial College, UK, 3Mechanical & Materials
Engineering, University of Nebraska-Lincoln, USA, 4Institute of Bioengineering, Ecole
Polytechnique Fédérale de Lausanne, Switzerland, 5Bioengineering, University of
Utah, USA, Engineering, 6Queen Mary University, UK
Abstract
Relationship of endothelial shear stress and atherosclerosis has been studied
extensively. The interplay of endothelial strain and plaque development is less well
understood. Inclusion of mechanical heterogeneity in these studies presents a
challenge on accurately predicting endothelial strain. This paper investigates
approaches for including heterogeneity in FSI models on endothelial shear stress and
strain. Difference between reference state (zero strain vs diastolic strain) of strain are
discussed and differences between pre-stress models are evaluated. The shear metrics
appeared to be moderately affected by including vessel wall elasticity and strain
metrics showed strong dependence on the presence of the lipid rich plaque of the
mouse model, the reference state and the pre-stress model.
1.Introduction
Atherosclerosis is a chronic, lipid-driven inflammatory disease that progresses from
simple to advanced plaques composed of a lipid-rich necrotic core and immune cells
within the intima of arteries. Although atherosclerosis is a multifactorial disease,

2. plaque formation tends to localize to regions of the vasculature with high curvature,
side branches or bifurcations. These vessel regions experience disturbed blood flow
and decades of research have demonstrated a correlation between arterial regions with
locally disturbed flow and atherosclerosis(Morbiducci et al., 2016; Yurdagul et al.,
2016). Recent studies, including ours(Pedrigi et al., 2017; Pedrigi et al., 2015; Ryan M.
Pedrigi, 2017; Seneviratne et al., 2017) have demonstrated a causal, not just
correlative, relationship between disturbed flow, and the development of advanced
atherosclerotic plaques(Pedrigi et al., 2017; Pedrigi et al., 2015; Ryan M. Pedrigi,
2017; Seneviratne et al., 2017).
While blood flow derived shear stress has been productive in predicting atherosclerosis
progression and plaque composition, blood vessels and thus endothelial cells are also
exposed to pulsatile blood pressure induced solid stress and strain(Pedrigi et al., 2017;
Pedrigi et al., 2015; Ryan M. Pedrigi, 2017). The effect of endothelial strain has been
far less studied than shear stress, but others and we have shown that disturbed strain
profiles activate pro-atherogenic pathways similarly to shear stress(Chester et al.,
2014; Kwak et al., 2014; Liu et al., 2013; Peters et al., 2015). Atherosclerotic plaques
have highly heterogeneous mechanical properties, with stiff collagen rich areas
juxtaposed to soft lipid rich zones(Alberts-Grill et al., 2013; Chistiakov et al., 2015;
Krams et al., 2005; Tian et al., 2014; Trogan et al., 2002) with the resulting effect on
endothelial strain being unknown. In vitro strain studies often do not consider these
local stress and strain gradients(Liu et al., 2013; Pedrigi et al., 2017).
This paper describes a fluid-structure interaction (FSI) model which incorporates most
complexities of the mechanical environment within the blood and diseased arterial
wall. We incorporate a pre-stress within the wall(Fung, 1991; Taber, 1995), a non-
linear material model which distinguishes healthy and diseased vessel
components(Humphrey et al., 2009), 3D Histology to determine the spatial location of
atherosclerotic plaque constituents, and a correction for pre-existing blood pressure(de
Putter et al., 2007; Speelman et al., 2009).
2.Methods
2.1 Animals,Surgery,Imaging,Histology and mesh
generation
The model geometry, inlet velocity boundary condition and co-registered 3D histology
used to develop the FSI model was based upon a subset (1 female ApoE — / — mouse)

3. of the data available from a prior study(Pedrigi et al., 2016) where the mice, aged 11
weeks, were placed on a high-fat diet and two weeks later instrumented with a blood
flow-modifying tapering cuff. The mice were scanned using micro-CT between eight
and nine weeks later to reconstruct the in vivo geometry of both carotid arteries. STL
defined lumen surfaces were generated using VMTK. Pulsed Doppler ultrasound
measurements of blood velocity at the inlet of each carotid artery were conducted 1–3
days after micro-CT imaging, after which the mouse was euthanized, perfusion fixed,
and the cuff removed from left carotid artery. An extensively validated17 3D histology
method was used to co-register distribution of plaque constituents with finite element
models.
Two vessel wall thicknesses for the cuff vessel were formulated: one with an assumed
nominal wall thickness of 50μm(Campbell et al., 2013; Gregersen et al., 2007) and the
other with wall thickness directly measured from histology. The control vessel assumed
nominal thickness only. The lumen mesh was generated using custom MATLAB code to
produce a structured hexahedral mesh with a three-element boundary layer of 10% of
radius. The mesh density for both meshes were tested for convergence: 0.5% dilatation
for vessel, 0.5% wall-shear for lumen. The study workflow is summarised in Figure 1.
2.2 Material Properties
The choice of the material properties of the arterial wall was based on previously
reported biaxial mechanical testing of arterial specimens which was subsequently
described by a hyperplastic stress-strain response(Humphrey et al., 2009). The axial
and circumferential stress/strain responses were found to be sufficiently similar to
enable fitting to an isotropic Ogden-type model.
with m1=17.41 a1=4.58 m2=15.79 a2=-3.87 m3=0.12 a3=4.46
In areas of lipid uptake, a similar Ogden-type material model was implemented with a
softer stiffness levels(Tracqui et al., 2011), assuming an elastic modulus of 5.5 kPa. A
value of 58.3 kPa was assumed for the normal elastic lamina. The plaque identified
from histology was first separated into three different material types based on the
intensity of lipid staining. The final stiffness of each pixel was based on a weighing
factor based on the relative distribution of lipids over normal tissue.
Density for both the vessel wall and plaque regions was set to 1050 kg/m3 and
Poission’s ratio of 0.49. Blood was modelled as incompressible with a density of

4. 1050kg/m3 and non-Newtonian based on Carreau-Yasuda model(Johnston et al.,
2004)
with h∞= 5.5Pa.s h0 = 3.5Pa.s l=3.313 n= 0.3568 a=2
2.3 ExternalTissue Support
The stability afforded by the surrounding tissue is modelled by adding thicker wall
layer around the vessel outer layer. The thickness and material properties were selected
to ensure a minimal material impact on the vessel wall’s dilatation response to
80mmHg and 120mmHg pressurisation. Density of the vessel wall was n of 0.05 and its
elasticity E of 280Pa.
2.4 Pre-stressing model
Multiple studies(Debes and Fung, 1995; Guo et al., 2005; Matsumoto and Hayashi,
1996; Otoguro et al., 2015; Taber, 2001) indicate that the arterial wall is exposed to
three sources of pre-stress. A circumferential residual stress has been measured(Guo et
al., 2005; Otoguro et al., 2015; Taber, 2001) , and an axial stress noted by recoil after
arterial dissection(Debes and Fung, 1995; Matsumoto and Hayashi, 1996; Otoguro et
al., 2015). In addition, an end-diastolic pre-stress is present.
Residual circumferential stress is determined by simulating the closing of an “open”
vessel model that has been “opened” by 92 degrees(Hansen et al., 2013). Simulation of
the closing of the vessel is performed by bringing the one side of the opening to the
other side which has been held fixed, in order to compute the circumferential residual
stress. Axial pre-stress was determined by applying 100kPa(Gleason et al., 2007) axial
load over 10 steps using backward-incrementation, BI process(de Putter et al., 2007;
Speelman et al., 2009). Lastly, the end-diastolic pre-stress is obtained by the BI
method. Briefly, it utilises the imaged deformed geometry obtained from the microCT
as the initial approximation for the unloaded geometry and incrementally the
geometry is modified with stress obtained from applying pressure to the deformed
vessel geometry. Pressure is incrementally applied to the inner vessel surface up to
80mmHg over 12 steps with first iteration initialised from the stress outcome of the
axial loading BI and closing pre-stress stages.
Prestress was computed for the nominal thickness control vessel. For the instrumented
vessel, three models were formulated:

5. I)“Nominal” — nominal thickness and homogenous wall material with pre-stress
values calculated as above,
II) “Histology” — histology-based wall thickness and heterogeneous wall material
properties with pre-stress values as described above,
III) “Hybrid” — histology based wall thickness and heterogeneous wall material
properties with pre-stress from the “Nominal” model. The rationale of this approach
was that pre-stress was developed during a period when the vessel wall was growing
and still “healthy” and atherosclerosis developed only after cuff placement.
2.5 Boundary condition
Flow waveform measured using Doppler-ultrasound was applied to the inlet of the
model and prescribed as a parabolic profile. Pressure measurements are difficult to
obtain in mice due to their small size. Tail pressure measurements are available
however these are not considered suitable proxies for carotid pressure, due to the
unknown transfer from pressure pulses between both sites(Zhao et al., 2011). In the
absence of direct carotid artery pressure measurements being available, an outlet
boundary model(Pahlevan et al., 2011) was added to the vascular model simulating
the compliance and resistance of the downstream vasculature. The compliance of 2.5E-
14 m4s2/kg was computed using previously published values for compliance and
resistance(Aslanidou et al., 2016). Resistance was optimised to achieve 80mmHg
diastolic pressure.
2.6 FSI modelling
The FSI simulations were performed with Abaqus/Standard 6.14 and Abaqus/CFD
6.14 modules (Dassault Systems) as part of a co-simulation based on Arbitrary
Lagrangian-Euler (ALE) method. The mesh is conservative on the fluid-solid interface
which is the vessel wall inner surface. The pressure and the shear stress are all passed
from this interface face from the blood flow to the vessel wall.
2.7 Shear and Strain metrics
The local wall shear stress (WSS) is calculated from a projection of the shear tensor on
the local wall. From that local WSS the time averaged wall shear stress (TAWSS) was
calculated across one cardiac cycle.

6. In addition, we also calculated endothelial strain. Under physiological conditions, the
circumferential strain is the primary component of the cyclical strain experienced by
the endothelium, but under pathological conditions the entire strain tensor needs to be
incorporated. Hence, to fully capture the effect of strain, we calculated the time
averaged circumferential cyclic strain (TASC), time averaged circumferential radial
strain (TASR) and time averaged axial cyclic strain (TASA). We established diastolic-
strain and not zero-strain as our reference from which to calculate relative strain values
(“cyclic strain’). We propose that this approach is justified as the half-life of endothelial
cells (20–40days) is such that all endothelial cells in our vessels at the moment of
imaging were renewed from adult progenitor cells implying their stress-free length to
be at diastolic length. For comparison, we also calculated cumulative strain, which
used zero-strain as a reference (Figure 4)
3.Results
The entire workflow is summarised in Figure 1. The FSI simulations produced
physiological pressures (88.6/116 mmHg, Figure 2), physiological vessel dilation
through the cardiac cycle ranged 3–10% and physiological wave speeds of 3.9m/s
(Figure 2, (Herold et al., 2017)). Interestingly, Time Average Wall Shear (TAWSS) was
~15% lower in the FSI simulation as compared to CFD results, as expected (Figure 3),
with the hybrid model showing values up to 30% lower (Figure 3).
The choice of reference state (diastolic vs zero strain) determines the outcome of strain
calculations (Figure 4). This was partly due to an increase of strain using the zero-
strain reference and as the material model is non-linear the material becomes so stiff
that the difference between soft plaque and healthy surrounding tissue is lost (Figure
4). Cyclic strain (e.g a diastolic reference) creates more physiological endothelial strain
values especially when a hybrid model is used to calculate the strain values (Figure 4).
Interestingly, in a non-diseased artery the endothelial circumferential strain is
dominant, but in a lipid rich plaque, all three endothelial strain components become
important and as a consequence the dominant strain direction changes (Figure 5).
4.Discussion
We have developed a FSI model for simultaneous determination of endothelial shear
stress and strain in healthy and atherosclerotic murine arteries with co-registered 3D
histology(Cheng et al., 2008; Segers et al., 2007) which enables single time point and

7. longitudinal study of the fluid and solid wall mechanical environment to which
endothelial cells are exposed
4.1 Model is physiologically performing
The control model (Figure 2) produces data which match in-vivo measurements
suggesting the validity of the underlying parameter values used in our simulations.
4.2 Justification of the hybrid model with cyclic strain.
The Backward Integration step aims to find a zero-stress vessel geometry and by doing
so introduces a “pseudo-history” of the vessel wall. As the entire protocol to induce
advanced plaques in the mouse took 9 weeks of which the last 3 weeks were the most
important(Cheng et al., 2008), we calculated two conditions: One where
atherosclerosis was present over the entire history (“Histology model”) and one where
the healthy vessel determined the pre-stress (“Hybrid model”). This assumption of the
latter model seems justified as in the ApoE -/- mouse atherosclerosis does not modify
the opening angle, or the residual strain(Gregersen et al., 2007)
Endothelial cells are turned over in the vessel wall during adult life either through
duplication or differentiation of precursor cells. Therefore, we assume that the shortest
length of endothelial cells is during diastole, and endothelial strain should be defined
as the difference between systolic and diastolic length, which we defined as cyclic
strain.
4.3 Histology heterogeneity compromised by pre-stress
Murine atherosclerosis is often associated with lipid rich plaques, probably due to the
enforced high cholesterol levels used to accelerate atherosclerosis(Tang et al., 2005;
Tracqui et al., 2011). We used a recently developed 3D histology method to co-register
these lipid rich plaques to our material models(Segers et al., 2007). The
circumferential map demonstrates the importance of knowing plaque location as
endothelial circumferential cyclic strain was largely increased over the plaque (Figure
4). Interestingly, the cyclic-strain in the radial (TASR) and axial (TASA) directions
(Figure 4), were also increased over the plaque region, further confirming the softness
of the lipid rich material. Consequently, the direction of the endothelial strain vector
changes and a tensile region is apparent at the interface between the healthy and
diseased areas which may be of interest for evaluation of plaque rupture.

8. 4.4 Decrease in calculated shear from CFD to FSI
Comparison of CFD based TAWSS with the nominal wall thickness FSI model for the
control vessel shows significant difference of ~15% for all FSI models. This is to be
expected as wall displacement was in the order of 10% and under Poiseuille conditions
(low Reynolds number) a 30% decrease in TAWSS was expected. Under a 50/50
duration of systole this reduces to an average effect of 15%, which is close to the
simulated results. While this may not appear to be a large effect, local extremes may
occur (see hybrid model simulations) which might affect low shear stress predictions of
CFD models.
5.Conclusion
A combined analysis of endothelial shear stress and strain in a heterogeneous, diseased
atherosclerotic vessel revealed that shear stress differs when applying flexible walls.
Importantly strain amplitude increased considerably and changed its direction over
lipid rich plaques. High tensile strains can be observed at the interface of healthy-
diseased vessel regions.
6.Images
Figure 1 Framework of reconstructing the vessel and incorporation of histology
heterogeneity (A) Lumen wall geometry is extracted from micro CT and used to create
3D vessel & lumen mesh. (B) Wall material properties using OGDEN model fit to
literature data and softer property to plaque areas based on percentage of lipid present.
© FSI model initialised with diastolic in vivo vessel wall stress computed via solid-only

9. opening angle closing, axial stretch and pressurisation simulations. (D) Outlet
boundary pressure waveform emulated using boundary model formulated based on
typical compliance of murine cerebral vasculature. (E) Flow boundary conditions
prescribed from Ultrasound flow speed measurements at face of inlet extension.
Figure 2 Review of simulation model velocity and displacement vs in-vivo measurements
and the resulting pressure waveform and implied pressure-velocity wave-speed. (A) Inlet
flow velocity closely matches the flow velocity prescribed at the start of the inlet extension
with pressure waveform generated via the outlet boundary model. (B) Vessel dilation
compares well with that observed in the ultrasound measurements. Similarly, © wave
speed (3.9m/s) computed from PV loop closely matches 4.0m/s assumed for the
compliance and resistance measures for defining outlet boundary model.
Figure 3 (A) Time average WSS for the CFD models and (B) reduction in TAWSS vs
CFD in nominal, histology and hybrid model. © Change in TAWSS (actual and %) vs
corresponding CFD model. Change in TAWSS in the FSI as compared to CFD is in line
with that expected (10–15%) due to changes in lumen volume through the cardiac
cycle. Histology model produces same change as the nominal model despite inclusion
of wall heterogeneity due to plaque. Hybrid model demonstrates the dispersion in wall
shear changes expected with wall heterogeneity due to plaque.

10. Figure 4 (A) Stress-strain (s-e) curve for the vessel wall non-linear material model
showing the separation in strain implied by the pre-stress and then additional strain
induced by the cardiac cycle. Key strain points marked to show strain at “zero-stress”,
diastolic and systolic points. (B) Time average circumferential strain (circumferential
“TASCm” and cyclic “TASCc”) for the control vessel with nominal thickness.
Cumulative map has variations due to the irregularity of the vessel wall whereas the
cyclic map demonstrates relatively uniform circumferential strain due to the pulsatile
flow through the cardiac cycle. © Similarly, TASCm and TASCc maps for the respective
models for the instrumented vessel. Though there are material differences between the
nominal and histology TASCm related to the heterogeneity, the TASCc for the two are
almost identical. The hybrid model displays a greater TASCc variation as expected for
the heterogeneity included.

11. Figure 5 Cyclic Time averaged strain in radial,axial directions and strain angle vs shear
angle (A) Cyclic radial strain in the hybrid model shows the material compression of
the plaque areas as expected. This in turn results in a tensile strain in the interface
between the healthy and diseased areas. Similarly, axial strain outcome variation is
significant. (B) Axial and circumferential strain provides the angle at which the
endothelium experiences the strain, enabling comparison with the shear direction. ©
In a healthy vessel this is expected to be 90o. The hybrid model shows the normal
relationship varies materially in plaque areas whist remaining 90o in the healthy areas.
7.Conflict of interest statement
None.
8.Acknowledgments
This work received the support from Thanks to the British Heart Foundation (BHF) for
financial support (RG/11/12/29055 and PG/15/49/31595). Thanks to Clint Davies
Taylor at SIMULA and Imperial College Research Computing Service for their
assistance with Abaqus and computational support.
7.References
Alberts-Grill, N., Denning, T.L., Rezvan, A., Jo, H., 2013. The role of the vascular
dendritic cell network in atherosclerosis. Am J Physiol Cell Physiol 305, C1–21.
Aslanidou, L., Trachet, B., Reymond, P., Fraga-Silva, R.A., Segers, P., Stergiopulos, N.,
2016. A 1D model of the arterial circulation in mice. ALTEX 33, 13–28.
Campbell, I.C., Weiss, D., Suever, J.D., Virmani, R., Veneziani, A., Vito, R.P., Oshinski,
J.N., Taylor, W.R., 2013. Biomechanical modeling and morphology analysis indicates
plaque rupture due to mechanical failure unlikely in atherosclerosis-prone mice. Am J
Physiol Heart Circ Physiol 304, H473–486.
Cheng, C., Tempel, D., Oostlander, A., Helderman, F., Gijsen, F., Wentzel, J., van
Haperen, R., Haitsma, D.B., Serruys, P.W., van der Steen, A.F., de Crom, R., Krams, R.,

12. 2008. Rapamycin modulates the eNOS vs. shear stress relationship. Cardiovasc Res 78,
123–129.
Chester, A.H., El-Hamamsy, I., Butcher, J.T., Latif, N., Bertazzo, S., Yacoub, M.H., 2014.
The living aortic valve: From molecules to function. Glob Cardiol Sci Pract 2014, 52–
77.
Chistiakov, D.A., Revin, V.V., Sobenin, I.A., Orekhov, A.N., Bobryshev, Y.V., 2015.
Vascular Endothelium: Functioning in Norm, Changes in Atherosclerosis and Current
Dietary Approaches to improve Endothelial Function. Mini Rev Med Chem.
de Putter, S., Wolters, B.J., Rutten, M.C., Breeuwer, M., Gerritsen, F.A., van de Vosse,
F.N., 2007. Patient-specific initial wall stress in abdominal aortic aneurysms with a
backward incremental method. J Biomech 40, 1081–1090.
Debes, J.C., Fung, Y.C., 1995. Biaxial mechanics of excised canine pulmonary arteries.
Am J Physiol 269, H433–442.
Fung, Y.C., 1991. What are the residual stresses doing in our blood vessels? Ann
Biomed Eng 19, 237–249.
Gleason, R.L., Wilson, E., Humphrey, J.D., 2007. Biaxial biomechanical adaptations of
mouse carotid arteries cultured at altered axial extension. J Biomech 40, 766–776.
Gregersen, H., Zhao, J., Lu, X., Zhou, J., Falk, E., 2007. Remodelling of the zero-stress
state and residual strains in apoE-deficient mouse aorta. Biorheology 44, 75–89.
Guo, X., Lu, X., Kassab, G.S., 2005. Transmural strain distribution in the blood vessel
wall. Am J Physiol Heart Circ Physiol 288, H881–886.
Hansen, L., Parker, I., Sutliff, R.L., Platt, M.O., Gleason, R.L., 2013. Endothelial
dysfunction, arterial stiffening, and intima-media thickening in large arteries from
HIV-1 transgenic mice. Ann Biomed Eng 41, 682–693.
Herold, V., Herz, S., Winter, P., Gutjahr, F.T., Andelovic, K., Bauer, W.R., Jakob, P.M.,
2017. Assessment of local pulse wave velocity distribution in mice using k-t BLAST PC-
CMR with semi-automatic area segmentation. J Cardiovasc Magn Reson 19, 77.
Humphrey, J.D., Eberth, J.F., Dye, W.W., Gleason, R.L., 2009. Fundamental role of
axial stress in compensatory adaptations by arteries. J Biomech 42, 1–8.

13. Johnston, B.M., Johnston, P.R., Corney, S., Kilpatrick, D., 2004. Non-Newtonian blood
flow in human right coronary arteries: steady state simulations. J Biomech 37, 709–
720.
Krams, R., Verheye, S., van Damme, L.C., Tempel, D., Mousavi Gourabi, B., Boersma,
E., Kockx, M.M., Knaapen, M.W., Strijder, C., van Langenhove, G., Pasterkamp, G., van
der Steen, A.F., Serruys, P.W., 2005. In vivo temperature heterogeneity is associated
with plaque regions of increased MMP-9 activity. European heart journal 26, 2200–
2205.
Kwak, B.R., Back, M., Bochaton-Piallat, M.L., Caligiuri, G., Daemen, M.J., Davies, P.F.,
Hoefer, I.E., Holvoet, P., Jo, H., Krams, R., Lehoux, S., Monaco, C., Steffens, S.,
Virmani, R., Weber, C., Wentzel, J.J., Evans, P.C., 2014. Biomechanical factors in
atherosclerosis: mechanisms and clinical implications. Eur Heart J 35, 3013–3020,
3020a-3020d.
Liu, X.M., Peyton, K.J., Durante, W., 2013. Physiological cyclic strain promotes
endothelial cell survival via the induction of heme oxygenase-1. Am J Physiol Heart
Circ Physiol 304, H1634–1643.
Matsumoto, T., Hayashi, K., 1996. Stress and strain distribution in hypertensive and
normotensive rat aorta considering residual strain. J Biomech Eng 118, 62–73.
Morbiducci, U., Kok, A.M., Kwak, B.R., Stone, P.H., Steinman, D.A., Wentzel, J.J., 2016.
Atherosclerosis at arterial bifurcations: evidence for the role of haemodynamics and
geometry. Thromb Haemost 115, 484–492.
Otoguro, S., Hayashi, Y., Miura, T., Uehara, N., Utsumi, S., Onuki, Y., Obata, Y.,
Takayama, K., 2015. Numerical Investigation of the Residual Stress Distribution of Flat-
Faced and Convexly Curved Tablets Using the Finite Element Method. Chem Pharm
Bull (Tokyo) 63, 890–900.
Pahlevan, N.M., Amlani, F., Hossein Gorji, M., Hussain, F., Gharib, M., 2011. A
physiologically relevant, simple outflow boundary model for truncated vasculature.
Ann Biomed Eng 39, 1470–1481.
Pedrigi, R.M., Mehta, V.V., Bovens, S.M., Mohri, Z., Poulsen, C.B., Gsell, W., Tremoleda,
J.L., Towhidi, L., de Silva, R., Petretto, E., Krams, R., 2016. Influence of shear stress

14. magnitude and direction on atherosclerotic plaque composition. R Soc Open Sci 3,
160588.
Pedrigi, R.M., Papadimitriou, K.I., Kondiboyina, A., Sidhu, S., Chau, J., Patel, M.B.,
Baeriswyl, D.C., Drakakis, E.M., Krams, R., 2017. Disturbed Cyclical Stretch of
Endothelial Cells Promotes Nuclear Expression of the Pro-Atherogenic Transcription
Factor NF-kappaB. Ann Biomed Eng 45, 898–909.
Pedrigi, R.M., Poulsen, C.B., Mehta, V.V., Ramsing Holm, N., Pareek, N., Post, A.L.,
Kilic, I.D., Banya, W.A., Dall’Ara, G., Mattesini, A., Bjorklund, M.M., Andersen, N.P.,
Grondal, A.K., Petretto, E., Foin, N., Davies, J.E., Di Mario, C., Fog Bentzon, J., Erik
Botker, H., Falk, E., Krams, R., de Silva, R., 2015. Inducing Persistent Flow
Disturbances Accelerates Atherogenesis and Promotes Thin Cap Fibroatheroma
Development in D374Y-PCSK9 Hypercholesterolemic Minipigs. Circulation 132, 1003–
1012.
Peters, A.S., Brunner, G., Krieg, T., Eckes, B., 2015. Cyclic mechanical strain induces
TGFbeta1-signalling in dermal fibroblasts embedded in a 3D collagen lattice. Arch
Dermatol Res 307, 191–197.
Ryan M. Pedrigi, M.B.P., Vikram V. Mehta, Fotios Savvopoulos, Avinash Kondiboyina,
Rob Krams, 2017. A Fluid-Structure Interaction analysis in Atherosclerosis indicates
that endothelial strain acts synergistically to disturbed shear stress, The 12th
international symposium on
Biomechanics in Vascular Biology and Cardiovascular Disease
, 02–03–2017 ed, pp. 21–23.
Segers, D., Helderman, F., Cheng, C., van Damme, L.C., Tempel, D., Boersma, E.,
Serruys, P.W., de Crom, R., van der Steen, A.F., Holvoet, P., Krams, R., 2007.
Gelatinolytic activity in atherosclerotic plaques is highly localized and is associated
with both macrophages and smooth muscle cells in vivo. Circulation 115, 609–616.
Seneviratne, A.N., Edsfeldt, A., Cole, J.E., Kassiteridi, C., Swart, M., Park, I., Green, P.,
Khoyratty, T., Saliba, D., Goddard, M.E., Sansom, S.N., Goncalves, I., Krams, R.,
Udalova, I.A., Monaco, C., 2017. Interferon Regulatory Factor 5 Controls Necrotic Core
Formation in Atherosclerotic Lesions by Impairing Efferocytosis. Circulation 136,
1140–1154.

15. Speelman, L., Bosboom, E.M., Schurink, G.W., Buth, J., Breeuwer, M., Jacobs, M.J., van
de Vosse, F.N., 2009. Initial stress and nonlinear material behavior in patient-specific
AAA wall stress analysis. J Biomech 42, 1713–1719.
Taber, L.A., 1995. Biomechanics of Growth, Remodeling, and Morphogenesis. Applied
Mechanics Reviews 48, 487–545.
Taber, L.A., 2001. Stress-Modulated Growth, Residual Stress, and Vascular
Heterogeneity. Journal of Biomechanical Engineering 123, 528–535.
Tang, D., Yang, C., Zheng, J., Woodard, P.K., Saffitz, J.E., Sicard, G.A., Pilgram, T.K.,
Yuan, C., 2005. Quantifying effects of plaque structure and material properties on
stress distributions in human atherosclerotic plaques using 3D FSI models. J Biomech
Eng 127, 1185–1194.
Tian, J., Ren, X., Uemura, S., Dauerman, H., Prasad, A., Toma, C., Jia, H., Abtahian, F.,
Vergallo, R., Hu, S., McNulty, I., Lee, H., Lee, S., Yu, B., Jang, I.K., 2014. Spatial
heterogeneity of neoatherosclerosis and its relationship with neovascularization and
adjacent plaque characteristics: optical coherence tomography study. Am Heart J 167,
884–892 e882.
Tracqui, P., Broisat, A., Toczek, J., Mesnier, N., Ohayon, J., Riou, L., 2011. Mapping
elasticity moduli of atherosclerotic plaque in situ via atomic force microscopy. J Struct
Biol 174, 115–123.
Trogan, E., Choudhury, R.P., Dansky, H.M., Rong, J.X., Breslow, J.L., Fisher, E.A., 2002.
Laser capture microdissection analysis of gene expression in macrophages from
atherosclerotic lesions of apolipoprotein E-deficient mice. Proc Natl Acad Sci U S A 99,
2234–2239.
Yurdagul, A., Jr., Finney, A.C., Woolard, M.D., Orr, A.W., 2016. The arterial
microenvironment: the where and why of atherosclerosis. Biochem J 473, 1281–1295.
Zhao, X., Ho, D., Gao, S., Hong, C., Vatner, D.E., Vatner, S.F., 2011. Arterial Pressure
Monitoring in Mice. Current protocols in mouse biology 1, 105–122.
by Robert Krams

16. Health Robert Krams Fsi Models Atherosclerosis
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