Numerical evaluation of incresed blood pressure due to arterial stenoses and

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
10
NUMERICAL EVALUATION OF INCRESED BLOOD PRESSURE DUE TO
ARTERIAL STENOSES AND ATROPHY OF END ORGAN
Vishal V. Shukla1
, Promad M. Padole2
1
Research Scholar, Visvesvaraya National Institute of Technology, Nagpur, M.S., India, 440011
2
Professor, Visvesvaraya National Institute of Technology, Nagpur, M.S., India, 440011
ABSTRACT
This paper explains and demonstrates that flow through Venturimeter is comparable to flow
through stenotic artery, discarding other complicated physiological factors. In this study systolic blood
pressure 120 mm of mercury is set as standard baseline in non-stenotic artery. The increasing pressure
rise is found for increasing blockages. A FE Model was analysed to obtain the values of corresponding
blood pressures. For 80 % Stenosis, rise of about 64% in blood pressure and about 55 % reduction of
blood flow to end organ was found.The study concludes that without using any pressure or flow
measuring devices, a couple of simple and handy charts can be obtained. They can be used as as a
primary diagnostic tool. CFD study of blood flow through stenotic models provides easy-to-use
information to doctors dealing with patients of high Blood Pressure.
Keywords: Blood pressure, Blood Flow Rate, Computational Fluid Dynamics (CFD), Stenotic artery
1. INTRODUCTION
Human body is a complex combination of bio-structures & bio-fluids systems. Kidney is a one
of the complex organ in human body with multifarious chemical, biological and physiological
mechanisms. There are two Kidneys in human body, located just below the rib cage, one on each side
of the spine. The main function of kidney is to filter the blood separating impurities in the form of
urine. Narrowing of blood vessels due to deposition of fatty substance or cholesterol on the inner side
of arterial wall is called stenosis. Stenosis acts as an obstruction to blood flow due to reduced cross
section area of blood vessel. Moreover, due to stenosis the upstream blood pressure also increases.
The most common cause of secondary hypertension (blood pressure) is Renal Artery Stenosis
(RAS). Hypertension is complex disorder that affects the heart, brain, blood vessels and kidneys. RAS,
as shown in Fig. 1, is narrowing of the major arteries that supply blood to the kidneys, due to build up
of fatty substance called plaque. The narrowing of the renal artery diminishes the blood supply to the
kidney. When the kidney is deprived of normal blood supply, it shrinks in size due to atrophy. Thus
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
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ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 5, September - October (2013), pp. 10-20
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11
RAS may ultimately lead to kidney failure [1, 2]. RAS reduces the blood flow through the renal artery
to kidney and causes the kidney to release increased amount of the hormone renin. Renin is a powerful
blood pressure regulator, initiates a series of chemical events that result in hypertension
Hypertension due to RAS is known as Reno Vascular Hypertension (RVH). Based on the
extent of RAS, RVH can be very severe and mostly difficult to control by medication. Elevated blood
pressure in one renal artery can cause loss of filtering function and therefore damage the other kidney
as well [3, 4].
Figure 1: Renal Artery Stenosis (RAS)
RAS reduces efficient functioning of kidney. The deteriorated kidney function may be reversed
by correcting stenosis. It is now known that many cases of RAS are under diagnosed and may present
as a spectrum of other diseases based on secondary hypertension. RVH is an important consequence of
RAS. Antihypertensive medical therapy fails to control RVH [5, 6]. Restoring of narrowed blood
vessel with a spring like device called stent is one of the efficient mechanisms to down regulate RVH.
Several investigators have reported that renal artery revascularization can stabilize or improve renal
function. Over 1 to 4 years of time, stenosis often redevelops (restenosis). RAS is associated with loss
of renal size. Clinical investigations till date are unable to demonstrate a relationship between severity
of stenosis and renal function.
Fundamentally, the kidneys require continuous flow of blood to function. Clearly, there are
some biological or chemical factors that influence functioning of kidneys. But the mechanical factors
like length & diameter of stenosis and intrarenal pressure also affect the renal blood flow. Several
modern test procedures based on imaging techniques are available at the speciality hospitals. Some of
them are: Angiography, Magnetic resonance angiography (MRA), Ultrasound etc. The machines and
tooling required to one or more of the above test procedures are costly. Therefore these diagnostic test
procedures are expensive. The radiologists use one of the above diagnostic test procedures at specialty
hospitals for finding the exact location and severity of RAS. The general physician can predict the
existence of RAS but cannot quantify the extent (percent blockage). Management of RAS consists of
three possible strategies: medical management, surgical management and percutaneous therapy with
balloon angioplasty and stent implantation.
2. MATERIALS AND METHODS
One of the investigation [7], in their experiments on hemodynamic effects in elastic silicon
rubber models, have shown that geometry, hemodynamics and vessel wall structure have a strong
influence on creation of stenoses. Pressure and velocity gradients, flow behavior, velocity distribution

12
and shear stress on the wall are very important parameters in blood flow analysis. Plaque deposits are
found predominantly at arterial bends and bifurcations. Another study [8] based on the cardiovascular
electronic system and crude forms of CFD model. The pressure drop of each section due to the stenosis
was computed by means of an electrical circuit and a simple CFD model. Arterial stenoses in the range
of 0–78% have been investigated to estimate plaque progression and wall stresses, both numerically
and experimentally. However, the study presents very elementary CFD models and does not quantify
the reduction in blood flow to kidney due to RAS.
Blood is not a fluid but rather a suspension of particles. Blood can be assumed to be Newtonian.
This is because the velocity and shear rates in the larger arteries are high. The shear rate of blood flow
is found to be about 1000 sec−1
in large vessels. In large arteries, the shear stress (τ) exerted on blood
elements is linear with the rate of shear, and blood behaves as a Newtonian fluid. In this range, the
elastic behavior of blood becomes insignificant. The nonnewtonian behaviour is important only in
small vessels (veins) and not in large size blood vessels like renal arteries. Therefore, the effect of
nonnewtonian behavior of blood in renal arteries is small and negligible [9, 10, and 11]. The
turbulence is not present in the cardiovascular system in physiological situations. Hence, blood flow is
laminar. The viscosity of blood is patient specific but varies in the range of 3-4 mPa-s at a temperature
of 370
C. the value of viscosity for blood can be taken as 3.5 mPa-S Therefore, blood is considered to
be an isotropic, incompressible and homogeneous fluid with a density value of 1050 kg/m3
.
2.1 Geometric and finite element modeling
Geometric modeling of object domain followed by finite element solution of respective
physical phenomenon provides the better understanding of the problem at hand. It eliminates the
difficulty of complex analytical problem solving procedures and hence adopted frequently by many
researchers. Modeling, in combination with experimental data and analytical approach, often yields
logical scientific conclusions.
Two-dimensional (2-D) geometrical section of healthy and stenotic renal artery models are
created, with the FEM general purpose CFD code ANSYS v 13.0 (ANSYS® Inc., USA). ANSYS is a
Finite Element Analysis (FEA) system with multiple pre and post processing codes for structural,
thermal and fluid flow.
Finite Element Method (FEM) based and not Finite Volume Method (FVM) based CFD is used to
investigate the effect of RAS on the increase in blood pressure. This is because of the inherited
advantages of FEM as enlisted below:
It caters to the needs of geometric flexibility.
It allows applying physical boundary conditions easily and accurately.
It satisfies global physical (linear) conservation laws automatically especially quadratic
quantities and even for which divergence theorems are not applicable.
Laplacian, divergence and gradient operators are ad-joint to each other in continuum in FEM
and not in FVM.
Phase speed of FEM is always more accurate than that of FVM.
Based on the data collected from various sources like books and research papers, it is known
that the geometry of a healthy renal artery is almost tubular (cylindrical) and symmetrical. Therefore,
only a section of length (g = 16 mm), diameter (h = 8 mm) and the length of stenotic wall length (f = 8
mm), as shown in Fig. 2, is modeled. About 10 numbers of symmetrical stenotic models are created at
the middle portion of geometry by creating arcs with three key points. The minimum diameter at the
site of stenoses and percentage of stenoses based on diameters and areas are calculated as shown in
TABLE 1.

13
Figure 2: Sections of stenotic renal artery: a-23 %, b-44 %, c-61%, d-80 %, and e-92 % (major
dimensions of section of stenotic artery; f = 8 mm; g = 16 mm; h = 8 mm).
Table 1: Percentage of stenosis on the basis of area
Inside diameter (mm) 8.0 7.0 6.0 5.0 4.3 4.0 3.5 3.3 3.0 2.3
% Stenosis based on the cross
sectional area
0 23 44 61 71 75 80 83 86 92
In general, stenoses are specified relative to percentage of blocked areas; therefore, henceforth
in this study, stenoses based on percent areas shall be followed. The mesh is built with 2-D Fluid 141
elements, each having four nodes and 4 degrees of freedom (two translational velocities: Vx & Vy) and
two pressures: Px & Py). The numbers of iterations are determined by using different meshes, from
coarse to progressively fine, until the inlet pressure distribution is mesh convergent within a prescribed
tolerance. The total numbers of nodes are about 1374 and elements about 1301 for the healthy artery
configuration i.e. with 0 % stenosis, which slightly differs for the stenotic configurations due to local
mesh adaptations. The mesh for 92% stenotic section is shown magnified in the inset in Fig. 2. While
meshing the artery walls are set for desired number of mesh divisions. Blood is modeled as an
incompressible, homogeneous, Newtonian viscous fluid, with a specific mass of 1050 kg/m3
and a
constant dynamic viscosity of 3.5X10-3
Pa-s (J.R. Torii et al., 2006; K. Hassani et al, 2007). The flow is
assumed to be steady state, Laminar and adiabatic (K. Hassani et al, 2007). The rise in the pressure
depends not only on the viscosity and density of the fluid but also on the extent of the stenosis.
Therefore simulation of flow of water (ρ=1000Kg/m3
and µ=0.798X10-3
Pa-s) through various
stenoses have also been carried out.
A normal renal artery has a blood flow of about 1 LPM. Therefore to impose boundary
conditions, the axial inlet velocity of 0.33 cm/s (as flow is 1 LPM through 8 mm dia. artery) is assigned
in X-direction ( Vx = 0.33 cm/s) and zero transverse velocity components ( Vy = 0 cm/s)at the entrance
of the vessel. The inlet velocity profile is assumed to be laminar. No slip boundary conditions are
imposed on the impermeable, rigid vessel walls. Vessel walls are assumed to be rigid to simplify and
analysis and also there shall be a very minor changes on the output quantities under consideration like
pressure drop (∆P), frictional head loss (Hf) etc.
At the outlet zero gauge pressure (equivalent to 1 atm. pressure) as a reference pressure is
imposed to determine the pressure difference (∆P) between the inlet and outlet. Identical geometric
models, Finite Element mesh and boundary conditions (Pressure, Velocity, Velocity-Profile and Flow

14
Rate) are used in both the CFD investigations of water as well as blood; however viscosities and
densities differ as mentioned above. The external forces, such as those due to gravity or human motion
are assumed to be not significant and are neglected.
Considering symmetric pressure distribution and steady state 2-D fluid flow, fluid shear
stresses due to RAS are numerically analyzed. Both the fluids (blood & water) are treated as
incompressible and Newtonian fluid. Two CFD analyses one each for water & blood and one
experimental analysis, only for water, have been carried out to investigate the effect of blockage on the
rise of pressure. The overall approach can be justified on the basis of following logic:
1. Experimental analysis of blood flow through stenotic arterial sections is not practicable; therefore,
computer simulation is the only option to investigate the case of blood flow through stenotic section.
2. If the CFD results of water flow matches with the experimental results of water flow, then FE model
is validated. And hence CFD results of blood flow shall be quite reliable.
On the basis of the above logic, the objectives are set. (i) To establish a FEM based mathematical blood
pressure model and (ii) To formulate kidney atrophy model based on stenosis.
2.2 Experimental set up
Simple experimental setup was designed to investigate the effect of stenoses on the rise of
pressure. The experimental setup as shown in Fig. 3 consists of a positive displacement gear pump
with torque of 1.6 Nm. The outlet of the pump is connected to a polyethylene tube resembling the renal
artery of diameter 8 mm and length 0.3 m connected by means of a Tee joint. One end of the Tee is
attached to the polyethylene tube while the other end is connected to a vertical tube of diameter 12 mm
and length 2 meters. The vertical tube acts as both a piezometer-cum-surge tank in the experiment. The
experiment was carried out simply to validate the CFD model created and analysed on computer. Once
the results are for water both experimental and that of computational model are found close enough,
the computational model was called be satisfactorily validated [12].
Figure 3: Experimental setup to determine the effect of stenosis on rise in blood pressure: (a) nine
numbers of specimens are cut from a nylon bar; (b) length of each specimen is 10 mm; (c) specimens
are drilled through using various sizes of drill bits; and (d) top view of specimen (countersunk at distal
ends).
Following a standard Finite Element Method procedure of Modeling, meshing, assigning the
material properties and applying boundary conditions, the FE model was solved.

15
3. RESULTS AND DISCUSSION
The solution was smoothly converged without any warnings and error. It is mainly because of
all the parameters in the preprocessing phase were correctly attributed. Fig. 4, shows the iteration
convergence of CFD solution run for blood flow through the computational model.
The flow of blood through renal artery model without stenosis is Laminar (max. Re = 1003).
The velocity profile as shown in Fig 5 (a) indicates highest velocity of 36.7 cm/s at middle section of
artery. The velocity profile in the stenotic section with maximum blockage (92%) is shown in Fig. 5
(b). The highest velocity of 136 cm/s (Re = 938) is observed at 0.25 mm from the wall.
Figure 4: CFD solution convergence for blood flow
(a) (b)
Figure 5: Laminar velocity profiles for blood flow through normal and blocked artery: (a)
velocity profile in the section of model artery for blood flow (0% stenosis, healthy artery) and (b)
velocity profile in the section of model artery for blood flow (92% stenosis, blocked artery).

16
And as shown in Fig. 6 (a), velocity distribution fairly remains the same within the core of the
renal artery. One of the important things noticed in the study is little reduction in velocities near the
wall and downstream of the stenosis region and can be verified from Fig. 6 (b).
(a) (b)
Figure 6 (a): velocity distribution of blood flow within the tube model with maximum blockage (92%
stenosis); (b): distribution of blood flow velocity vectors with recirculation zones shown near the entry
and exit of 92% stenotic sections
The CFD models of blood flow through renal artery with increasing size of stenoses are then
sequentially solved in the similar fashion. The trends for increasing velocity, increasing pressure
drops, increasing fluid shear stress near wall and increasing pressure coefficients are observed, they
are listed in TABLE 2.
Table 2: CFD results of investigated parameters for blood flow
%
Stenosis
Pressure
diff.
(N/m2
)
% Press.
rise ∆P
Pressure in mm
Hg (120 mm
baseline)
Max.
Velocity
(mm/s)
Shear Stress
MPa
0 125 0 120 367 3.85
23 132 6 127 409 3.95
44 153 19 143 480 4.80
61 203 39 167 587 6.74
71 261 52 183 690 8.94
75 285 56 188 735 9.08
80 361 65 199 819 13.30
83 460 73 208 975 14.77
86 534 77 212 1114 16.26
92 725 83 219 1360 20.24
The distribution of blood pressure loss (∆P) is shown in Fig. 7 (a). It shows there is a loss of
about 124.5 N/m2
(0.94 mm of Hg) between the entry and exit of the artery for 0 % stenosis (healthy
artery model) case. This means that if there is gauge pressure of 15892.2 N/m2
(120 mm of Hg) at
outlet, the gauge pressure at the inlet would be 160017.055 N/m2
(120.94 mm of Hg). The distribution
of pressure loss for 92% stenotic renal artery is shown in Fig. 7 (b). It shows that there is a pressure
difference of about 725.194 N/m2
(5.47 mm of Hg) between the entry and exit of the 92 % stenotic
renal artery, which is almost 83 % higher than the ∆P in case of healthy artery. The values of ∆P
obtained from CFD analysis for increasing stenosis and corresponding % ∆P rise to healthy artery
case are listed in TABLE 2.

17
(a) (b)
Figure 7 (a): The distribution of pressure loss (∆P), for blood flow, within the section of modeled
artery without blockage (0% stenosis) — this value of pressure loss (∆P) is used as reference; (b) The
distribution of pressure loss (∆P), for blood flow, within the section of modeled artery with 92%
stenosis; compared to ∆P of healthy section (124 N/mm2
), ∆P in this case is about (725N/mm2);
therefore, change in ∆P (from 0% to 92%) is about 83%
Maximum blood shear stress of 20.24 MPa is found at the stenotic wall in 92 % stenotic artery
whereas the shear stress was found merely to be about 5 MPa for 0 % Stenosis. Shear stresses in both
cases are shown in Fig. 8 (a and b).
(a) (b)
Figure 8: (a) Maximum fluid shear stress of 20.4 MPa in blood flow near the stenotic vessel wall in
92% stenosis; the maximum shear stress in blood flow, as expected, is more than that of water; (b)
Maximum fluid shear stress of 3.9 MPa, in blood flow near the stenotic vessel wall in 0% stenosis, is
concentrated at the artery wall near entry; this is the favorable location for plaque deposition.
If 120 mm of mercury column (systolic blood pressure) is considered as standard baseline
reference in non-stenotic renal artery, the incremental blood pressure rise is found because of the
presence of increasing extent of stenoses. And hence to obtain the values of corresponding secondary
hypertension in column number 4 of TABLE 2. The respective % increase in ∆P (converting to
mmHg), is simply added to 120 mm of Hg baseline pressure. Referring TABLE 2, Pressure difference
(∆P) increases and therefore, if pressure at outlet is maintained constant, the pressure at inlet rises.
TABLE 3, CFD study also revealed that there is loss of blood flow to kidney due to stenotic renal
artery. Further, it is found that the increasing extent of stenoses reduces the downstream blood flow to
kidney.

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6340(Print), ISSN 0976 – 6359(Online)
Table 3: CFD results indicating reduction in Blood flow to Kidney due to RAS
%
stenosis
Area (mm2
)
0 50.24
23 38.46
44 28.26
61 19.62
71 14.51
75 12.56
80 10.04
83 8.54
86 7.06
92 4.15
4. QUANTIFICATION TOOL TO RELATE RAS & RVH
Considering the first determined flow of 18438.08 (mm
and possibly 100 % blood flow to kidney (T
of increasing stenosis section. Mapping the CFD results of reduced blood flow to kidney, shown in
TABLE 3, by standard curve fitting techniques, mathematical mod
Quadratic Polynomial Fit: y=a+bx+cx
mathematic model of blood pressure rise based on varied extents of stenotic arterial sections now can
be expanded by interpolation. Model thus developed can be shown as a simple graph as shown in Fig.
9. Similarly, a typical and convenient graph can also be presented as shown in
how much less flow would be available for kidney for a specific extent o
be very much helpful in determining the shrinkage to kidney and possible atrophy.
Fig 9: A ready utility tool to diagnose probable Renal Artery Stenosis based on measured Blood
6359(Online) Volume 4, Issue 5, September - October
18
CFD results indicating reduction in Blood flow to Kidney due to RAS
Max
velocity
(mm/s)
Flow to Kidney
(mm3
/s)
%
Reduction
in flow
% Blood
flow finally
available to
kidney
367 18438 0
409 15732 15
480 13564 26
587 11519 38
690 10015 46
735 9231 50
819 8226 55
975 8334 55
1114 7870 57
1360 5647 69
QUANTIFICATION TOOL TO RELATE RAS & RVH
Considering the first determined flow of 18438.08 (mm3
/s), for healthy section, as reference
% blood flow to kidney (TABLE 3); the % reduction can be easily computed for rest
, by standard curve fitting techniques, mathematical model is researched to fit the data.
Quadratic Polynomial Fit: y=a+bx+cx2
, appreciably maps the data and is found suitable. Expanded
of blood pressure rise based on varied extents of stenotic arterial sections now can
interpolation. Model thus developed can be shown as a simple graph as shown in Fig.
Similarly, a typical and convenient graph can also be presented as shown in Fig
how much less flow would be available for kidney for a specific extent of stenosis. These results could
be very much helpful in determining the shrinkage to kidney and possible atrophy.
A ready utility tool to diagnose probable Renal Artery Stenosis based on measured Blood
Pressure
(2013) © IAEME
CFD results indicating reduction in Blood flow to Kidney due to RAS
% Blood
flow finally
available to
kidney
100
85
74
62
54
50
45
45
43
31
/s), for healthy section, as reference
); the % reduction can be easily computed for rest
el is researched to fit the data.
, appreciably maps the data and is found suitable. Expanded
of blood pressure rise based on varied extents of stenotic arterial sections now can
interpolation. Model thus developed can be shown as a simple graph as shown in Fig.
Fig 10 to understand
These results could
A ready utility tool to diagnose probable Renal Artery Stenosis based on measured Blood

6340(Print), ISSN 0976 – 6359(Online)
Fig 10: A derived quantification tool to determine probable reduction in blood flow
To read and understand Fig.
about 64% blood pressure (Secondary Hypertension 198 mm of Hg),
about 55 % reduction of blood flow to kidney. It can be seen in
receives only 45% of otherwise normal blood supp
supplied to kidney. Therefore even without using any pressure measuring deice or flow measuring
devices, a couple of simple and handy charts as given in Fig. 9 and Fig. 10 can be used as as a primary
diagnostic tool. Some of research reviewed and a few medical experts when consulted
and accepted the utility of the presented mathematical models.
5. CONCLUSION
The CFD study of blood flow through stenotic models of RAS provides easy
information to doctors dealing with patients of high BP. It is sort of handy clini
general medical practitioners to diagnose RAS. The information could be used in the tabular or
graphical form to conjecture the likelihood of RAS based on measured blood pressure of the patient.
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6359(Online) Volume 4, Issue 5, September - October
19
on tool to determine probable reduction in blood flow
known percentage of RAS.
Fig. 9 and Fig. 10, consider example of 80 % RAS, there is rise of
about 64% blood pressure (Secondary Hypertension 198 mm of Hg), as seen in Fig. 9
duction of blood flow to kidney. It can be seen in Fig. 10. This demonstrates
receives only 45% of otherwise normal blood supply i.e. instead of 1 LPM only 250 ml of blood is
even without using any pressure measuring deice or flow measuring
diagnostic tool. Some of research reviewed and a few medical experts when consulted
and accepted the utility of the presented mathematical models.
The CFD study of blood flow through stenotic models of RAS provides easy
information to doctors dealing with patients of high BP. It is sort of handy clinical information to the
S. Lai, Atherosclerotic ischemic renal, Diagnosis and prevalence in a
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(2013) © IAEME
on tool to determine probable reduction in blood flow Kidney based on
, consider example of 80 % RAS, there is rise of
9 and also there is
10. This demonstrates kidney
ly i.e. instead of 1 LPM only 250 ml of blood is
even without using any pressure measuring deice or flow measuring
diagnostic tool. Some of research reviewed and a few medical experts when consulted have confirmed
The CFD study of blood flow through stenotic models of RAS provides easy-to-use
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