Mohamed Yacin Sikkandar,
Natteri M. Sudharsan,
S. Sabarunisha Begum, E. Y. K. Ng
WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
Computational Fluid Dynamics: A Technique to Solve Complex
Biomedical Engineering Problems - A Review
MOHAMED YACIN SIKKANDARa*, NATTERI M SUDHARSANb,
S. SABARUNISHA BEGUMc, E.Y.K. NGd
*a
Department of Medical Equipment Technology, College of Applied Medical Sciences,
Majmaah University, Al Majmaah 11952, SAUDI ARABIA
b
Department of Mechanical Engineering, Rajalakshmi Engineering College, Chennai, INDIA
c
Department of Chemical Engineering, Sethu Institute of Technology, Kariapatti, INDIA
d
School of Mechanical & Aerospace Engineering, College of Engineering, Nanyang
Technological University, SINGAPORE
*corresponding author email: m.sikkandar@mu.edu.sa
Abstract: - Fluid flows play a major role in everyday life, such as thunderstorms, environmental disasters,
in engineering fields, applied biosciences to understand complex processes such as blood flow, breathing
and renal flow in living systems. Understanding of flow physics is important to execute detailed
engineering and healthcare product development. Mathematical modelling can solve the physics of fluid
dynamics using partial differential equations (PDE) built on conservation laws. This model can be solved
numerically by Computational Fluid Dynamics (CFD) to yield quantitative results. CFD has attracted
significant interest in the biomedical engineering area, from researchers to study the complex human
anatomical and physiological processes, response to diseases and its effectiveness to develop prosthetics.
The introductory sections of the review explain the basics of CFD and its use in biomedical engineering
research. The review then focuses on the applications of CFD in biomedical problems, including
cardiovascular diseases, airflow pattern and aerosol deposition in lungs, cerebrospinal fluid flow in brain
and for artificial organ design analysis. The widespread adoption of CFD will dramatically accelerate the
improvement of healthcare soon with patient specific customization. Moreover, contextual evidence is
also provided for beginners to better understand of the topic.
Key-Words: - Navier-Stokes equations, cardiac disease, aneurysm, stenosis, cerebrospinal fluid, lung air
flow, patient-specific design
set of rules to visualize, unravel and examine
problems that involve fluid and/or heat flow [4].
CFD modelling is governed by underlying fluid
dynamic equations: Mass, momentum and energ
y conservation at the same time. CFD helps
predict the fluid flow characteristics using
software tools based on mathematical modelling.
CFD is performed sequentially or in parallel
with a set of procedures through classical
equations of fluid motion and auxiliary relations
with approximations by huge sets of algebraic
equations followed by numerically solving using
computers [5]. Initially, CFD was restricted to
high-tech engineering applications and now it is
widely accepted for resolving complex design
challenges in contemporary appliances [6].
Modern computerized systems are used to carry
out highly complex computations to numerically
simulate the interface of liquids and gasses with
different boundary conditions. Better solutions /
results can be achieved with high - speed
supercomputers. Various modern engineering
1 Introduction
Investigation on quantitative analysis of
temperature in human forearm tissue and arterial
blood in resting state during 1948 was
considered as the pioneer in the field of bioheat
equations and mathematical modelling of blood
flow in biological systems [1]. It is a generally
accepted fact that human anatomy and
physiology are enormously complex system in
nature because of its highly interconnected
numerous subsystems [2, 3]. Most of the
physiological processes (including chi or qi,
cupping therapies of Traditional Chinese
Medicine) in the human body are found to be
unclear; the flow of blood and gas in vital organs
is as yet not understood well enough by medical
science as they could not measure directly. Thus,
there is need to address such problems using
advanced engineering tools by applying complex
engineering concepts in biomedical engineering.
Computational fluid dynamics (CFD) is such a
domain which utilizes numerical approaches and
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Natteri M. Sudharsan,
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numerical analyses of cardiovascular diseases,
aneurysm and stenosis in abdominal and renal
arteries, ophthalmology, airflow and aerosol
deposition in lungs, cerebrospinal fluid flow in
brain and artificial organ design analysis are
highlighted to demonstrate the widespread
successful use of the highly efficient
computational tool in biomedical engineering
core areas. Section 4 finally summarises the
applications of CFD, limitations and further
scope of research. The idea of the paper is not to
relate one methodology of approach across
various problems. Each method of approach is
unique to the problem at hand. The paper aims
to bring out the power of CFD across major
biomedical problems.
domains use the exemptional potential of CFD
simulations and are increasing year by year.
Biomedical research using CFD analysis has
become more accessible with readily available
high performance in software and hardware
systems. In recent years, many biomedical
researchers have demonstrated their potential in
CFD to study complex physiological flow
dynamics. There is increasing interest to apply
CFD modelling in usage of cardiovascular and
neurovascular medicine, enhancing diagnostic
assessment, device design by incorporating
novel features and clinical trials. CFD based
technologies are broadened to construct complex
computer representations (in silico models) of
human to understand and monitor health and
disease. These technologies can envisage
physiological responses to clinical interventional
therapies and figure out hitherto unmeasurable
hemodynamic parameters. CFD modelling
techniques are being used to analyze and help in
extracting the geometrical parameters of major
arteries such as abdominal aorta for graft
designing in treating aneurysms etc.[7-10].
Thus, the contribution of CFD to biomedical
engineering research application is found to be
immense. A few typical applications of CFD are
shown in Fig. 1.
2 Background of CFD
It is a part of fluid mechanics and uses
mathematical evaluation and data structure
method to analyse and solve challenges that
include flow of fluid. In the modern era, interest
in quantified numerical techniques have
increased drastically subsequent to the
recognition of the computational power of
computers. The role of numerical analysis is
Fig.1: Various applications of CFD (a) Gas turbine (b) Post Curing Oven (c) Supersonic flow (d)
Microfluidics and (e) human thoracic aorta with plaque
vital that it has been accepted as an emerging
subject, it is concerned with numerical analysis
which has its own standing based on analytical
and experimental knowledge of engineering
disciplines [4]. Fluid Mechanics can be defined
as the science which deals with the study of
behaviour of fluids either at rest(fluid in
stationary mode) or in motion(fluid in dynamic
Section 2 of this article discusses the
background of CFD technology, CFD processes,
boundary conditions, and discussions on various
software and solvers used for pre-processing and
post processing in CFD simulations and
analysis. Section 3 of this article reviews the
various biomedical applications of CFD in
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found to be more appropriate in predicting wall
shear stress in comparison to Newtonian model
[13].
mode). Computer solution to equation of fluid
mechanism has captured the attention of one
third of researchers and its steadily increasing
[5]. CFD numerically stimulates the flow field
by approximating hydrodynamic variables such
as pressure and velocity by solving full NervierStokes (N-S) equation with finite element or
finite volume methods.
The equations that govern fluid flow are the
continuity (mass transport) equation mentioned
below (1) and equation of momentum
(momentum field of the flow), which is under
investigation, has to be applied together, where
𝑢𝑢 is the fluid velocity vector, p is the pressure, 𝜌𝜌
is the density of the fluid and 𝑓𝑓 is the body force
acting on the fluid [6,11].
2.3 Bioheat Equation
In 1948, Penne’s measured the tissue
temperature profile in forearm and compared
with the Governing equation presented as
equation (2).
𝑘𝑘∇2 𝑇𝑇 − 𝑐𝑐𝑏𝑏 𝑤𝑤𝑏𝑏 (𝑇𝑇 − 𝑇𝑇𝑎𝑎 ) + 𝑞𝑞𝑚𝑚 = 0
There are three terms in the equation, the first
accounts for the conservation of heat flux
through conduction, the second accounts for the
heat supplied due to the arterial volumetric
blood perfusion rate, whose strength depends on
the temperature gradient among the artery and
vein that acts as the counter current heat
exchanger, and the last accounts for the
metabolic rate of the tissue [1].
Though several investigators have questioned
the assumption made on the temperature
maintained in the arterial and venous path, a
detailed survey by Sudharsan et al (1998)
concluded that for tissues perfused with large
arteries the Penne’s equation provides a
reasonable approximation of the local tissue
temperature [14].
The physical behaviour of fluid motion is
referred by an equation that governs the process
of interest and so-called governing equation.
Super-computers using advanced computing
languages, resolves the study via numerical
simulations that performs hi-tech digital
processing to arrive at numerical solutions [11].
Current trend of advanced technology is helpful
to resolve highly complex problems using
advanced simulation techniques. Engineers are
shifting more towards numerical stimulation for
testing, optimizing and calibration of
preliminary design as computing is cost
effective and less time consuming than physical
experiments and experimental database has high
degree accuracy with numerical predictions in
many complex applications [15].
As of today, CFD is recognised as one of
computer-aided engineering (CAE) spectrum of
tools applied across all engineering domains and
its method of fluid transport modelling enables
the power of stimulated virtual equipment. CFD
software has gone beyond the representations of
Navier– Stokes or Da Vinci equations and
become a vital part of aerodynamic and
∇ ⋅u = 0
u t = −(u ⋅ ∇ )u + ν∇ 2 u −
1
∇p + f
ρ
(1)
2.1 Laminar – Turbulent
Laminar and turbulent is determined using
Reynolds number, the flow in the pipe is laminar
if the Reynolds number (based on the diameter
of the pipe) is less than 2300 and turbulent if it is
greater. The effect of turbulence is accounted in
equation 1 by replacing the velocity u to a time
averaged velocity 𝑢𝑢�
replacing kinematic
viscosity term 𝑣𝑣 𝑎𝑎𝑎𝑎 𝑣𝑣𝑒𝑒𝑓𝑓𝑓𝑓 .
The effective viscosity accounts for
turbulence by using various mathematical
models such as one equation model, Prandtl
mixing length model, K epsilon, k omega, RNG
kε, realisable kε etc. However, the major portion
of the pulse is laminar in nature and assuming
the blood flow as laminar provides a reasonable
approximation for flow through larger vessels, in
capillaries the diameter is very small and thus
𝑅𝑅𝑒𝑒 values are laminar in nature. But capillary
flow has different problems in terms of obeying
in Newtonian.
2.2 Newtonian and Non-Newtonian
A fluid is considered Newtonian when a
viscose stress is proportional to local strain rate,
e.g. when a fluid is conveyed through a circular
tube, stresses develop due to the adjoining layers
of fluid continuum, this is because the fluid
velocity is not constant throughout or near
parabolic in nature. However, in a micro vessel
the viscosity varies with haematocrit and shear
rate in accordance with the Quemada rheological
relation [12]. The non-Newtonian models are
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Mohamed Yacin Sikkandar,
Natteri M. Sudharsan,
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WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
hydrodynamic process for the design of various
automotive crafts or manufacturing operations
that this world has invented. Using CFD,
medical research world has gained an extensive
knowledge on the different ways body fluids and
components will perform, that will help achieve
greater scale of developments for bio-fluid
physiology research and to invent advanced
medical devices. It also offers, simulation
opportunities that will help to understand the
suggested alteration and confirm that medical
intervention is moving on the right direction at
every stage [16]. It is essential to have a detailed
understanding of the problem under analysis,
step by step approach and continuous
questioning to execute a successful simulation
and provide meaningful end results. Though
every case of simulation varies based on various
requirements, it is an unavoidable fact the three
will be almost no change in the execution steps.
2.5.2 Solver
After identification of nature of physics, it is
the stage to set boundary conditions based on
fluid material properties, flow physics model
(compressible vs incompressible, viscous vs
inviscid, laminar vs turbulent, steady vs transient
and more importantly, in blood flow if it is to be
treated as Newtonian or Non-Newtonian), and
solved using a computer. The general
commercial software exist in the market
includes: ANSYS FLUENT, ANSYS CFX, Star
CCM, CFD++, OpenFOAM etc. All these
separate software system tools have unique
capabilities. All complex equations related to the
flow physics problem can be solved using the
selected software.
2.5.3 Post-Processing
Post-processing is the step to analyze the
results to obtain appropriate graphical
representations and visualized reports. Some of
the commonly used post-processing software
include:
ANSYS
CFD-Post,
EnSight,
FieldView, ParaView, Tecplot 360 etc.
Defining the boundary condition specification is
considered as a critical step in the CFD analysis.
In this process, adequate information must be
provided on the flow, pressure and potential
dynamics of the vessel wall at the geometry
boundaries. Presently this is an interesting
research
domain
and
most
advanced
methodologies depend on combining lowerorder mathematical models of proximal/distal
circulation to the inlet(s)/outlet(s) of the model
[4,5].
2.4 Verification and Validation
It is necessary to verify the used governing
equations with actual physic and mechanics.
Validation is a key priority in the development
of any CFD codes. Many validations must be
done as blind tests and it is a continuous process
including validation database (large scale and
laboratory), proper model evaluation protocol
(simple tests, sensitivity studies, experimental
test
geometries,
experimental
realistic
geometries, testing of models), model system
and documentation.
2.5 CFD processes
Numerical algorithms for CFD codes are
structured by contemplating the fluid-flow
problems. There are three important stages in
CFD processes to deliver practical information;
a pre-processor, a solver and a post-processor.
3
Prominent
Applications
CFD is a widely used technique in many
biomedical engineering domains as can be seen
in Table 1 discusses the detailed review of
papers published on CFD applications on
biomedical engineering.
2.5.1 Pre-Processing
This process helps in diligently portraying the
realistic geometry and at this stage the
researcher must be capable of identifying the
interested fluid domain. Smaller segments called
meshes will be generated for the geometry
which holds the fluid of interest. There is
various well known Pre-Processing software
available in the market including: Gridgen,
CFD-GEOM, ANSYS Meshing, ANSYS ICEM
CFD, TGrid, Hypermesh Femap, to name a few.
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used to study the effect of pulsatile flow and
regularly excited wall on pulsatile type of blood
vessel wall shear stress (WSS) [22,23]. In this
study, the authors numerically established an
unsteady Navier-Stokes (N-S) solver using
operator splitting and simulated compressibility
for the changing boundary problem in order to
study compliant vessel blood flow. CFD was
3.1 Cardiovascular Diseases
Human cardiovascular system (CVS)
interconnects many vital organs in the body and
is accountable for transferring nutrients to
tissues/organs, releasing waste products,
supplying hormones, as well as thus retaining a
suitable atmosphere for existence with the
natural operation of organs/tissues [35]. Several
Table 1. Various applications of CFD modelling
Biomedical Study (with year)
Evaluation of biomechanical aspects in the atherosclerotic
process (1998, 2002)
Pulsatile flow in a compliant curved tube model of coronary
artery (2000)
Unsteady flow of fluids through arterial stenosis (2000)
Unsteady viscous flow model on moving domain through
stenotic artery (2001)
Simulation of oscillatory wall shear stress in channel with
moving indentation (2002)
Modelling of fluid-wall interactions for viscous flow in
stenotic elastic artery (2002)
Fluid dynamic analysis in a human left anterior descending
coronary artery with arterial motion (2004)
Wall pressure gradient in normal left coronary artery tree
(2005)
Computational model of blood flow in the aorta-coronary
bypass graft (2005)
Evaluation of a novel Y-shaped extra cardiac fontan baffle
(2009)
Study on fluid-dynamics modelling of the human left ventricle
(2012)
Abdominal aortic aneurysm on hemodynamic loads using a
realistic geometry with CT (2013)
Translate the biomechanical rupture risk of abdominal aortic
aneurysms to their equivalent diameter risk: method and
retrospective validation (2014)
Deposition of particles in the alveolar airways: Inhalation and
breath-hold with pharmaceutical aerosols (2015)
Spiral blood flow in aorta-renal bifurcation models (2016)
Evaluation of sedentary lifestyle effects on carotid
hemodynamics and atherosclerotic events incidence (2017)
Wall shear stress estimation of thoracic aortic aneurysm with
computational fluid dynamics (2018)
CFD and echocardiography method to simulate blood flow in
the single right ventricle (2018)
Reference
[17,18]
FASTFLO as PDEs calculator
[22]
[19]
[20]
[21]
In-house code
Not mentioned
[22]
[24]
Not mentioned
[25]
ANSYS Fluent Gambit
[26]
Not mentioned
[27]
ANSYS-CFX 12
[28]
BioDyn, Tdyn
[29]
A4clinics (VASCOPS GmbH,
Graz, Austria)
[30]
Fluent 14, ANSYS, Inc.
[31]
ANSYS CFX (v14.5, ANSYS,
Inc., Canonsburg, PA, USA)
COMSOL 5.0 (COMSOL,
Inc, Stockholm, Sweden)
Star CCM+ (Siemens, USA)
[32]
ANSYS-FLUENT
17.0
[34]
[33]
[13]
used to study the coronary arteries pulsatile flow
and pressure characteristic using 3 dimensional
(3D) finite element model (FEM) in conjunction
with transient flow and changing boundaries
[19]. Advanced CFD model was used to
describe local flow dynamics in both 3D spatial
and four-dimensional (4D) spatial and temporal
numerical models and medical outcomes have
been applied to examine heart failure, congenital
heart disease, ventricle malfunction, aortic
disease, carotid and intra-cranial cerebrovascular
diseases. Acquaintance of blood flow patterns in
such diseases is a crucial element in research
and accurate diagnosis [36]. CFD method was
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CFD Tools used
CFDS-Flow 3D package
program, AEA Company,
Britain
FIDAP7.62, FLUENT, Inc.,
Evanston, IL
In-house code
In-house code
125
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Mohamed Yacin Sikkandar,
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WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE
[39]. A review paper on various methodologies
to generate anatomic and physiologic models
with different properties, boundary conditions,
governing equations to blood flow and vessel
wall dynamics were discussed [40]. CFD-based
modelling techniques are being used to quantify
the dynamic growth of atherosclerotic plaque
and arterial remodelling was studied in coronary
artery disease patients [41]. A review paper on
CFD simulations specifically on heart blood
flow was published [15]. The researchers
contributed impressive research findings
remarkably in this area by providing solutions to
cardiovascular diseases. [7,28,42,43]. Left
ventricular (LV) blood flow pattern was
simulated for myocardial infarction (MI)
patients’ cardiac MRI using CFD. LV
characteristics were quantified before and after
surgical ventricular restoration (SVR) adjusting
intraventricular blood flow during clinical
coronary artery bypass grafting (CABG)
procedure [7,28,42,43]. The CFD results
revealed that SVR improves ventricular function
with modified intraventricular blood flow (Fig
3).
domains [24]. This analysis was carried out by
reconstruction of intravascular ultrasound
(IVUS) and bi-plane angiographic fusion images
in the left anterior descending (LAD) coronary
artery segment. Their model was used to
compare left anterior descending coronary artery
hemodynamics, before and after angioplasty.
Normal human left coronary artery (LCA) tree
model with 3D wall pressure gradient (WPG)
was analysed quantitatively, extracted from
angiographies (averaged human data set); it was
effectively fitted (adopted) for FEA [36]. Results
of geometrical bypass models (aorta-left
coronary bypass graft model and aorta-right
coronary bypass graft model) based on real-life
situations were developed using CFD [26].
The variations in local vascular geometry was
investigated using 3D CFD modelling which
were influenced by distributions of wall shear
stress (WSS) in a bent coronary artery through
theoretical stent implantation [37] and is shown
in Fig.2.
Fig.2: Time-dependent changes in spatial WSS
across the cardiac cycle in computational vessels
implanted with 12 mm stents that conform to
(flexible, left) or cause straightening of
(inflexible, right) an idealized and curved
coronary artery using CFD (LaDisa et al;
BioMed Central Ltd. 2006).
Fig.3: After surgery blood flow patterns during
diastole at (a) t D 0:033 s, (b) t D 0:1 s, (c) t D
0:2 s, (d) t D 0:301 s, (e) t D 0:401 s, and (f) t D
0:435 s. (This figure is reproduced with
permission from “3D CFD/MRI modelling
reveals that ventricular surgical restoration
improves ventricular function by modifying
intraventricular blood flow”, S. S. Khalafvand,
L. Zhong and E. Y. K. Ng, Int J Numer Method
Biomed Eng. 2014 Oct;30(10):1044-56. doi:
10.1002/cnm.2643. Epub 2014.
Authors computed WSS by assuming plaque
thickness as the variance between the lumen
(3D) and outer arterial wall [38]. An unusual Yshaped extra cardiac Fontan baffle was studied
and its hemodynamic performance was
evaluated at rest and during exercise states with
a patient-specific (MRI) data using CFD model
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Table 2. Summary of CFD modelling for cardiac abnormalities
Clinical applications
Data and evidence
To evaluate biomechanical
factors in the atherosclerotic
process.
3D spatial patterns of steady
and pulsatile flows in the left
coronary artery were simulated,
using a finite volume method.
Characteristics of coronary
arteries is represented by
accelerating flow with
physiological pressure and
flow wave and it play a vital
role in its localization.
Using a 3D FEM with transient
flow and moving boundaries to
simulate pulsatile flow with
physiological pressure and flow
wave forms characteristic of
the coronary arteries.
Study the behaviour of the
arterial motion and
mathematical patterns on the
hemodynamics of coronary
artery of a left anterior
descending (LAD) and
compare the scale of the
disease before and after the
treatment.
To inspect the left coronary
artery (LCA) tree of the 3D
wall pressure gradient
(WPG) in quantity.
3D arterial segments were
reconstructed at 10 phases of
the cardiac cycle for both preand post-intervention based on
the fusion of intravascular
ultrasound (IVUS) and biplane
angiographic images.
For patients with severe
coronary artery disease
bypass grafting surgery is an
effective treatment
A model LCA tree, based on
averaged human data set
extracted from angiographies
was adopted. The WPG was
calculated with 44,452 nodes
and a validated numerical code.
CFD is used for 3D coronary
bypass models of the aortoright coronary bypass and the
aorta-left coronary bypass
systems.
Exam the stent-induced
regional geometry influence
distributions of WSS with
3D coronary artery.
Compute WSS at several
intervals during the cardiac
cycle, time averaged WSS, and
WSS gradients via
conventional techniques.
To study the association of
plaque thickness with
endothelial shear stress.
3D luminal model using CFD.
Three patients affected by
MI and 3 normal subjects
were assessed on their
throbbing blood flow
patterns in the left
ventricular.
Patients with intermediate
coronary stenosis.
Compute velocity and pressure
fields for patient specific 2D
geometries with the
combination of non-invasive
MRI and CFD.
Effect of Cardiac Motion on
Aortic Valve Flow for
Computational Simulations
of the Thoracic Aorta.
Approved IRB database of
patients with congenital
cardiovascular disease who had
clinically indicated cardiac
MRI studies in Children's
Hospital of Wisconsin.
WSS Estimation of Thoracic
Aortic Aneurysm with CFD.
3D aneurysm model was
reconstructed from the CT scan
slices using MIMICS. The
original CT image file format
was DICOM
Full-volume 3D and 2D echo
image loops were acquired
with a S5-1 transducer at > 60
frames per second.
CFD and echocardiography
method to simulate blood
flow in the single right
ventricle
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Quick computational time of
myocardial fractional flow
reserve (FFR).
Potential clinical impact
Limitations and
challenges
Hemodynamic variables, include There are marked
flow velocity, pressure and shear individual variations in
vascular structure and
stress of the left anterior
descending coronary bifurcation hemodynamics.
site were calculated.
It focused on the WSS and
Computational mesh
circumferential strain (CS)
density resulted in
dynamic behaviour in a
acceptable errors
compliant model of a coronary
in WSS.
artery including the curvature of
the bending artery and
physiological radial wall motion.
Study the left anterior
Assumed same flow ratedescending coronary artery
time data at the inlet to
hemodynamics before and after the arterial segment,
angioplasty.
ignored the branches
effect in the imaged
segments as the IVUS
images were only
available in main vessel.
Ref.
Spatial WPG differentiation
indicates that locally low
values of this physical
parameter probably correlate to
atherosclerosis localization.
Simulation findings have
not been validated with a
chronic model of left
coronary artery.
[36]
To alleviate or delay the
occurrence of vein graft
disease. Also dimensions of the
aorta, saphenous vein and the
coronary artery to simulate the
actual configurations at
surgery.
Better understand the regional
geometry obtained at once after
stent implantation. Evaluate the
effect of stented vessel to a
higher risk of neointimal
hyperplasia and then
restenosis.
Study the relationship of
hemodynamic parameters with
plaque thickness in the critical
coronary region.
Found some useful information
on intra-LV flow patterns with
heart diseases for the flow
patterns and pressure drop in
the
LV chamber.
Quick computer model in
quantifying the functional
significance of moderately
obstructed coronary arteries.
More precise measurements of
hemodynamic variables via
cardiac motion in AoV blood
flow that are associated with
long-term morbidity for the
thoracic aorta, such as TKE
and WSS.
Omit low WSS region
near heel region of the
anastomosis domain, and
high WSS in toe region
of the domain, resulting it
prone to intimal
hyperplasia.
Simulation is not
compared with a chronic
model of coronary artery
restenosis.
[26]
Simulation findings have
not been benchmarked
with a chronic model.
[38]
2-D model are limited.
Study exclude the mitral
valve motion in the LV
flow processes. Limited 6
cases only.
[15]
Limited sample size.
Only validated de novo
lesions. Selection bias is
likely.
The images used were of
relatively low-pixel
resolution (∼1.75 mm)
and hence introduce noise
in relatively stationary
periods in cardiac cycle
despite the smoothing
algorithm.
Findings are based on
limited population (i.e.,
one particular case)
[44]
suffers some spatial and
temporal resolutions and
muscles and values were
smoothing out to
optimize CFD modelling
[34]
model can be tested for varying
stresses that an artery may be
subjected (to) in day to day
life.
Qualitative comparisons
demonstrated good
concordance between the CFDsimulated results and Echo
measured values
127
[17,18]
[19]
[24]
[37]
[10]
[13]
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'Computational Biomechanics in Thoracic
Aortic Dissection (AOD)' discussed about the
importance of using CFD and their study to help
doctors in improving their decision–making
process in two types of Aortic disorders such as
Type A (ascending aorta) and Type B
(descending
aorta)[46].
Computational
techniques had been used to assess the
movement of pulsatile displacement forces
acting on thoracic Aortic endografts (Fig 4 and
5) and the study enhanced the understanding of
power and relative position of the loads
experiences in-vivo by thoracic aortic endografts
to improve their design and performance [40].
In the normal left ventricle, blood flow
characteristics were studied using MRI, workenergy and N-S equations. They found that the
2D results' dynamic and energy characteristics
were comparable to a 3D model. Through
numerical analysis based on MRI of cardiac
motion, 3D blood flow in a human left ventricle
was further studied during myocardial dilation,
the formation, growth and decay of vortices
were analysed with flow patterns on different
diametric planes [8]. Numerical proof-ofconcept method was developed to study blood
flow field under the influence of direct phasecontrast PC-MRI measurements and fluid
physics model, permitting both the accuracy of
PC-MRI and the high spatial resolution of CFD.
This approach allowed data from fractional or
comprehensive quantities to be merged into an
advanced CFD solver, to enhance the accuracy
of the subsequent flow approximations. The
authors claimed that this filtered approach could
reduce scan time, increase spatial resolution,
and/or filtering the noises of PC-MRI
measurements [9].
Numerical methods were developed to evaluate
the impact of cardiac motion on blood flow
measurements through the aortic valve so as to
determine its effect on patient-specific localized
hemodynamics [10, 11]. A CFD model was
developed to study the vortex formation pattern
and flow reversals in single right ventricle
(SRV) and their results were considered as
promising [13]. Use of CFD modelling in
cardiac abnormalities numerical simulations are
listed in Table 2.
3.2 Atherosclerosis
Stenosis)
(Aneurysm
Fig.4: Flow and pressure waveforms in selected
vessels obtained in the CFD analysis of a
proximal descending thoracic aortic aneurysm
(TAA) model. Note the physiologic range of the
waveforms, presenting features such as
retrograde flow in the descending aorta during
early systole, and forward flow through the
cycle in the common carotid artery. (This figure
is reproduced with permission from Figueroa,
C.A., Taylor, C.A., Chiou, A.J., Yeh, V., Zarins,
C.K.: Magnitude and direction of pulsatile
displacement forces acting on thoracic aortic
endografts. J. Endovasc. Ther. 16(3), 350–358
(2009).
and
Atherosclerosis
is
a
predominant
cardiovascular disease, where fatty material is
accumulated in the intima (inner layer) of
arteries that supplies fluid to brain, heart, other
vital organs including lower extremities [40]. An
abnormal swelling of an artery due to the
weakness in the arterial wall is termed as
aneurysm; this could affect varieties of artery
including the peripheral arteries and aorta. Book
titled “Biomechanics and Mechanobiology of
Aneurysms” covers the clinical context of
aneurysm and CFD technique of endovascular
repair of abdominal aortic aneurysms (AAA).
These AAAs are irreversible dilation of
infrarenal aorta which if untreated could grow
and rupture [45]. The
review article on
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Fig.5: Wall shear (left) and pressure (right)
stresses representing the actions of the blood on
the endograft. These stresses are integrated over
the surface of the endograft to calculate the total
3D force exerted by the pulsatile flow. Note that
the pressure is several orders of magnitude
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larger than the shear stress. Reproduced from
Figueroa et al,[5].
pressure (RADP). Convincing CFD models were
built from magnetic resonance (MR)
angiography and phase-contrast [48].
Preliminary study was done on hyper
dynamic analysis of renal artery stenosis (RAS),
using CFD technique based on non-improved
steady-state free slow-moving magnetic
resonance angiography. Their study showed that
non-improved-MRA-based CFD could be used
to unsystematically assess hemodynamic
measurable factors of RAS, and the obtained
variables would yield useful details related to
stratification of the stenosis and more
therapeutic treatment [49]. The effect of the
renal artery ostium flow diverter on
hemodynamic
and
atherogenesis
was
investigated using CFD modelling techniques
[50].
The effects of spiral form of flow on
hemodynamic
changes
in
aorta-renal
bifurcations were studied and the results showed
that the spirality effects causes an evident
variation in blood velocity distribution by
creating only slight changes in fluid shear stress
patterns, and indicated that spiral nature of blood
flow has atheroprotective effects in renal arteries
and hence to be considered in the analysis of
aorta and renal arteries [32]. To study the
behaviours of tracers flowing through the kidney
CFD compartmental modelling was used to
validate its accuracy [51].
The pathogenesis of AAA is multi-factorial
and their development results in highly rated
stresses and disturbed hemodynamic [30]. A
CFD modelling paper presented the differences
between healthy and the diseased cases mainly
in the presence of highly raised up wall stresses
and aggressive flow disturbances [47]. A study
revealed a link or association between the AAA
geometric parameters, abdominal flow patterns,
wall stress shear (WSS), intraluminal thrombus
(ILT), and AAA arterial wall rupture with CFD
[29]. Appropriate viscosity models can be
selected to compute non-Newtonian fluids and
to solve fluid flow equation to obtain desired
results. According to Fig 6 (a and b), the WSS,
velocity and pressure of fluid flow can be
visualised to predict the reason and identify the
best method of intervention for atherosclerosis.
Fig.6: (a) Main geometrical parameters: 𝐿𝐿AAA
aneurysm length, 𝐷𝐷MAX maximum diameter of
the aneurysm𝑑𝑑proximal neck beginning of the
AAA sac, 𝑑𝑑distal neck ending of the AAA sac,
𝑑𝑑abdominal aorta nondeformed abdominal aorta
diameter, 𝐿𝐿 is the absolute length of the tortuous
vessel, and 𝜏𝜏 is the imaginary straight line. (b)
Schematic visualization of a cross-sectional
AAA section, where 𝑟𝑟 and 𝑅𝑅 are defined as the
radii measured at the midsection of the AAA sac
from the longitudinal z-axis to the posterior and
anterior walls.
3.3 Ophthalmology
Usage of CFD in ophthalmology studies have
been increased in recent years. For minimizing
inaccuracies researchers while developing
retinal mathematical models always try to
construct the model that best resemble the actual
system [52]. An article published in the
American Academy of Ophthalmology website
gives a brief summary of CFD use in
ophthalmological diseases [53]. The process
which damages the optic nerve by increasing the
intraocular pressure and blocking the outflow is
called Glaucoma, there are lot of complex
question regarding the brittle balance between
the inflow and the outflow of aqueous humour in
normal human eye which is yet to be completely
understood [54]. It was mentioned by Sultan et
al, that the IOP (intraocular pressure) though
excluded from the glaucoma definition remains
as a casual risk factor [55]. IOP is related with
increased resistance to aqueous humour outflow
and it is not different from normal (non-
A detailed study was made on the effects of a
periodically excited wall on the oscillatory
nature of flow structures and WSS [21-23].
Recent study was conducted on CFD analysis of
a saccular shaped aneurysm, that resulted in
marking the pulsatile blood flow as laminar is
correct and WSS values did not go over the
prediction. Using magnetic resonance imaging,
Yim et al, (2004) put forth a methodology for
the calculation of renal artery differential
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glaucomatous individual and these remarks have
led to a better understanding of the aqueous
humour properties and the support of CFD.
Many researchers have tried to demonstrate the
elements of aqueous humour outflow with
reference to different parameters of the human
eye in the anterior chamber [56-59]. A
Newtonian fluid was modelled for the aqueous
humour and a linear elastic solid for the iris and
it was to compute the iris contour in the eyes.
Ooi and Ng (2008) developed a 2-D model of
human eye to understand the presence of natural
flow of aqueous humour and to investigate the
flow effects inside the anterior chamber [60]. In
Ooi et al, (2011) using the above model research
was conducted to learn about the natural
convection in the anterior chamber on the ocular
heat transfer as shown in Fig 7. CFD is used to
investigate the crystalline lenses and ciliary
body structures. John et al, (1996) defined lens
as a clear biconvex form in the eyes that in co–
occurrence with the cornea helps to refract light
that needs to be focused on the retina, lens is
used to change the focal distance of the eye so it
can correctly focus on objects to indulge various
focal length distances. For analysing catalase
activities, lens epithelial samples were taken,
and analysts tried to apply CFD to stimulate heat
and its exposure caused damage to lens. Sharon
et al 2008 led analyst group showed that bakery
heat exposure can cause damage to the eye lens
depending on its length of the exposure [58].
Heys et al, (2003) stated that through
tremendous effort they were able to include
computational assessment in the role of
accommodation in pigmentary glaucoma.
3.4 Fluid and Air Flow in Lungs
Incompressible flow equation by NavierStokes well predicts the air flow through lungs
at low speeds [61]. CFD plays as a powerful tool
to predict the transport and deposition of gases
and particles in the respiratory tract system. It is
limited to relatively small regions due to the
complexity of airways at respiratory path.
Numerous studies were carried out to simulate
the lungs with CFD approach. The process needs
an accurate CAD model using MRI and CT
scans to generate mesh model for the geometry
[62]. This helps physicians to develop medical
devices and necessary treatments methods.
A study on numerical simulation to visualize
the flow characteristics in an empty Rochester
style inhalation chamber during steady-state and
transient pollutant concentrations was employed
with commercial CFD program [63]. To
evaluate the turbulent effects, polydisperse
aerosol size distribution, and multiple lung lobes
deposition in the mouth–throat (MT) and entire
tracheobronchial (TB) airways, a new CFD
approach was established [63, 64]. The authors
developed CFD modelling of the stochastic
individual pathway (SIP) to simulate the
transport and deposition of whole lung aerosols.
This CFD approach simulates the upper airways
through the lobar bronchi using characteristic
models derived from Computed Tomography
(CT) scan images. These models are also rapidly
prototyped for generating corresponding in-vitro
deposition data. SIP approach also simulates the
transport and deposition in the remainder of the
tuberculosis (TB) airways which ensembles to
create and compute individual pathways. Several
recent studies from this group provide detailed
in-vitro deposition data from realistic inhalers
using characteristic models of MT, nasal airways
and upper TB region [64, 65]. Very good
agreement was achieved between the in-vitro
deposition data and CFD predictions for
pharmaceutical aerosols based on numerical
model refinements implemented through userdefined functions (UDFs). The SIP approach
was found to be a reliable method for simulating
lung deposition of pharmaceutical aerosols with
a computational multiple order of magnitude
compared
with
simulating
all
the
tracheobronchial airways.
An
investigation
on
patient-specific
respiratory pathway under physiological
boundary conditions using a CFD model of a
healthy, a stenotic and a post-operatory stented
Fig.7: A typical temperature distribution of the
eye with and without AH flow in the vertical
orientation. (This figure is reproduced from Simulation of aqueous humour hydrodynamics
in human eye heat transfer, EH Ooi, EYK Ng,
Computers in Biology and Medicine 38 (2008)
252 – 262).
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based on 2D phase contrast (PC) MRI
measurements and additional anatomical data.
These models and simulations allow noninvasive analysis of the CSF flow environment
in healthy and patient cases [70-72]. However, it
is difficult to quantify 3D complexities using the
unidirectional encoding 2D phase contrast MRI
CSF flow measurements within the CSF flow
field.
CFD studies of CSF flow in the cervical
spine have been conducted under geometrically
simplified subject-specific 3D models without
fine anatomical structures and with idealized
spinal cord nerve rootlets and denticulate
ligaments [68-72].
Yiallourou et al (2012) used time-resolved 3D
velocity encoded phase-contrast MRI (4D PC
MRI) in 3 healthy volunteers and 4 CM patients
and compared the 4D PC MRI measurements to
subject-specific 3D CFD computations [72].
They considered rigid-walled geometry and
didn’t include small anatomical structures like
denticulate ligaments, nerve roots and arachnoid
trabeculae. They then 4D PC MRI flow
measurements and T2-weighted anatomy MRI
images at the cervical-medullary junction of a
single healthy volunteer and obtained CFD
simulations considering the fluid to be
incompressible and Newtonian. These results
support the use of CFD modelling in CSF flow
for subject specific MRI within the cervical
spine also provide consistent quantitative
geometric and hydrodynamic parameters to
potential clinical diagnostic and assessment
purposes.
human trachea estimated outflow pressure
waveforms which allows the computation of
peripheral impedance of truncated bronchial
generation and modelling the lungs as fractal
networks [66]. Recently, a CFD transient
simulation of the cough clearance process was
analysed with Eulerian wall film model [67]. In
this research, a methodology was proposed to
predict cough mucus clearance which
successfully enabled the simulation and
quantification of the overall performance of
cough. Researchers proved that CFD can be
used to model and predict fluid and air flow in
lungs which are considered clinically as very
complex.
3.5 Cerebrospinal Fluid Flow
Brain, blood and cerebrospinal fluid (CSF)
co-exist and preserve a constant volume in
intracranial space. The role of CSF is very
crucial as it protects the brain from injury and
delivers nutrients to and from the brain along
with the removal of waste products. CSF
dynamics in the cervical spinal subarachnoid
space (SSS) are useful to help diagnose and
assess craniospinal disorders like Chiari
malformation [68]. CSF fluctuation is a complex
phenomenon in fluid dynamics as it flows inside
the craniospinal cavities in a pulsatile manner
which results from the systolic expansion and
contraction of cerebral blood vessels. Clinically,
it is still unclear the complex multifactorial
processes of the development, progression, and
rupture of cerebral aneurysms. In recent years,
many researchers have focused on brain
aneurysm research. Contributions were made
using patient-specific CFD models for brain
aneurysm and highlighted the mechanisms of
computational models for patient-specific
assessment on brain aneurysm rupture risk and
patient management [68]. It is also clinically
accepted that hemodynamics plays a major role
in brain aneurysm. However, there is no
consensus among researchers and clinicians on
implication of any hemodynamic variable in
these mechanisms. Hemodynamics strongly
depends on the vascular geometry and it requires
investigations to better understand the
interaction between mechano-biological wall
responses and hemodynamic loading. These
govern the natural history of cerebral aneurysms
and it is needed to study well on the in-vivo
aneurysmal hemodynamic environment [69].
CFD simulations and in-vitro flow models are
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3.6 Artificial Organ Design
Artificial organs are engineered devices that
are implanted or integrated into human body to
replace non-functional natural organ and helps
patient to return to normal life. Prototype
development stage of artificial organs involves
many numerical simulations on hemodynamics
with optimal geometry to make devices
clinically viable. Simulated flow permit
information on the size and location of
stagnation zones and thus the local shear rate.
These parameters can be used to correlate to the
extent of thrombus formation and haemolysis
which are important to establish the success of a
blood pump [73]. Ventricular assist devices
(VADs) are mechanical pumps to augment or
replace the function of one or more chambers of
failing heart. Satisfactorily blood damage
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abnormalities.
Biomedical
engineering
researchers now could gain knowledge on flow
behaviour of body fluids and understand how the
system components are expected to perform.
Thus, it makes possibilities to improve bio-fluid
physiology studies and to better designed
medical treatments and devices. Computational
modelling tools provide an opportunity to
evaluate multiple situations for an extremely
difficult condition to setup experimental system.
Several laboratories work on numerical
modelling of human circulatory system for
improving abnormality risk-prediction. The
usage of CFD is being consistently stretched for
many biomedical applications including nose
and sinus flows, vocal tract analysis, joint
lubrication, spinal fluid flows etc. Apart from
the
above
applications,
computational
techniques are also applied in developing
medical devices in surgical procedures. The
reducing cost of computational time, memory
and development of improved mathematical
models, biomedical applications are further
expected in extending the implementation of
versatile CFD techniques and allow in saving
human lives. In near future, it would be possible
for a physician to compile CT of a patient with
digital captured computational model. The
properties and boundary conditions would be
enforced, and the physician can visually see the
flow phenomenon simulated inside. Moreover,
this can be integrated with a bio 3D printer to
tailor-make prosthesis like heart valves, stents,
etc., based on the CT and computational results,
ensuring that it is patient specific and with an inbuilt fail-safe mechanism. Overall, this review
adequately describes the detail of state-of-the-art
in terms of “horizontal” technology (CFD) or
provide sufficient detail to understand the
implications of application of the technology to
specific “vertical” biomedical problems. In
coming years use of CFD in biomedical and its
related field is likely to surge.
models are lacking in numerical analysis of
VADs despite much efforts, that limit the full
potential of CFD. Implantable VADs have been
regarded as a promising instrument in the
clinical treatment of patients with severe heart
failures. Chua et al. 2006, illustrated, a 3D
model of the Kyoto-NTN magnetically
suspended centrifugal blood pump and provide
CFD solution of the inner flow field of the pump
including the velocity profiles, static pressure
distributions and the shear stress distributions of
the blood [74].
Katharine et al. (2011) reviewed the use of
CFD in the development of VADs and listed
state-of-the-art CFD analysis of blood pumps,
with a practical critical review of the studies.
Also, the paper presented a summary of blood
damage models and their difficulties in CFD
implementation, explained the gaps in
knowledge with future work [75]. Farag et al.
(2014) published a review article presenting
results on patients receiving mechanical assist
devices using CFD simulations for end-stage
heart failure [76].
The use of CFD extends in evaluating the
performance of artificial organs such as to
predict the physiological behaviour of a
prosthetic heart valve. Claudio Capelli et al.
(2017) investigated the differences in
hemodynamic performances using different
anchoring systems with the help of CFD
analysis [77]. They adopted a combined
approach
of
commercially
available
experimental and computational tools for bioprosthetic aortic valves. Numerical computations
allow identification of useful information on the
locations of high shear rates in the flow which
damage the blood cells and needs proper
boundary conditions. The use of CFD technique
is being consistently extended for many other
biomedical applications like vocal tract analysis,
nose and sinus flows, joint lubrication, spinal
fluid flows etc. In addition to these biomedical
applications, the use of CFD is also employed in
developing medical devices for surgical
procedures.
Nomenclature
c Specific heat capacity [J/kg. oC]
h Heat transfer coefficient [W/m2 oC]
k Thermal conductivity [W/m2 oC]
L length [m]
q Volumetric heat generation [W/m3]
T Temperature [oC]
w Blood perfusion rate [kg/(s.m3)]
Subscripts: a- Artery, b- Blood, e- Environment,
m- Metabolic
4 Summary
With the advancement of high-speed
computers and newer generation computational
software, CFD has been a more economical and
feasible alternative high-end technology-based
tool to diagnose and predict circulatory
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