Computational fluid dynamics,
usually abbreviated as CFD, is a
branch of fluid mechanics that uses numerical methods and algorithms to solve
and analyze problems that involve fluid flows. The human body fluid has complex
behavior and its study is very difficult. Experiments to understand the fluid
behavior might be time consuming and costly. CFD complement experimental and analytical approaches by providing an alternative cost-effective means of
simulating real fluid flow, particularly in human body fluids. CFD has the
capacity to simulate flow conditions that are not reproducible during
experimental tests found in geophysical and biological fluid dynamics, such as
scenarios that are too huge, too remote, or too small to be simulated
experimentally.
This
report discusses about the components of CFD and its application in various bio- medical field. All CFD processes contain three main components to provide
useful information, such as pre-processing (pre-processor), solving
mathematical equations (solver), and post-processing (post processor). Initial
accurate geometric modeling and boundary conditions are essential to achieve
adequate results. Medical imaging, such as ultrasound imaging, computed
tomography, and magnetic resonance imaging can be used for modeling, and
Doppler ultrasound, pressure wire, and non-invasive pressure measurements are
used for flow velocity and pressure as a boundary condition.
Many
simulations and clinical results have been used to study congenital heart
disease, heart failure, ventricle function, aortic disease, work of heart,
coronary artery disease and carotid and intra-cranial cardiovascular diseases.
With decreasing hardware costs and rapid computing times, researchers and
medical scientists may increasingly use this reliable CFD tool to deliver
accurate results. A realistic, multidisciplinary approach is essential to
accomplish these tasks. Indefinite collaborations between mechanical engineers
and clinical and medical scientists are essential.
The aim of this report
is to survey the state of CFD technology in the biomedical field and discuss
the development and current scenario of CFD tool in the biomedical field. Approximately 80% of the human body mass
consists of water. The vascular system (arteries and veins) delivers nutrients
and retrieves waste products. The respiratory system delivers oxygen and
retrieves carbon dioxide. These vital transport systems are mainly tubular in
nature, and are powered by the heart and lung respectively. Any kind of damage
or obstruction of these transport systems will, in all likelihood, result in a
variety of diseases than can have a profound effect on wellness and quality of
life. Vessel damage or obstruction may be treated by a variety of surgical and
interventional procedures: stenting, balloon angioplasty, in situ drug delivery
for unclotting, bypass surgery, artificial organ implantation, etc. Many of
these procedures are performed daily on thousands of patients, and have led to
an impressive empirical knowledge database. Some of these procedures have
statistically significant failure rates, indicating a need to study in depth
the aid dynamics before and after the intervention. As in the manufacturing
industries, it would be highly desirable to predict the outcome of an
intervention before 'cutting tissue', particularly for complex cases where a
detailed empirical database is lacking.
The
basic steps required for any type of flow
simulation are the following:
Ø Pre-Processing
or Problem Definition:
Ø Geometry
(Surface);
Ø Boundary
and Initial Conditions;
Ø Grid
Generation;
Ø Fluid-Structure
Solver; and
Ø Visualization
and Data Reduction.
Any
type of interventional simulation will require accurate modeling of
patient-specific anatomy and physiologic conditions. It is here where the
biggest obstacle to routine simulations lies. Typically, only the anatomy is
imaged. Flows may be measured non-invasively by PCMRA or ultrasound (US).
However, the accuracy for these measurements can be problematic due to imaging
artifacts and noise. The compliance of an arterial wall is difficult to obtain,
and its pressure/dilatation may be highly nonlinear.
Nevertheless,
recent advances in:
Ø Radiology
(high contrast imaging);
Ø Image-to-surface
definition tools;
Ø Automatic
grid generation;
Ø Fast in compressible flow solvers and realistic boundary conditions;
Ø Fluid-structure
interaction techniques;
Ø Insightful
visualization;
Ø Validation
in the form of in vitro/vivo studies; and
Ø Increased
compute and graphics power have led to a favorable confluence of techniques
that have made predictions on the living human being possible, and in some
cases, routinely so.
In
the sequel, we focus on recent advances, outstanding issues and obstacles for
each one of these areas. Thereafter, we show several examples to demonstrate
that what a vision was several years ago is maturing rapidly and may indeed
lead to medical tools in the near future.
Computational fluid
dynamics (CFD) is a mechanical engineering field for analyzing fluid flow, heat
transfer, and associated phenomena, using computer-based simulation. CFD is a
widely adopted methodology for solving complex problems in many modern engineering
fields. The merit of CFD is developing new and improved devices and system
designs, and optimization is conducted on existing equipment through
computational simulations, resulting in enhanced efficiency and lower operating
costs.
The technique is very
powerful and spans a wide range of areas. In the beginning, CFD was primarily
limited to high-technology engineering areas-, but now it is a widely adopted
methodology for solving complex problems in many modern engineering fields. CFD
is becoming a vital component in the design of industrial products and systems.
Examples are aerodynamics and hydrodynamics of vehicles, power plants including
turbines, electronic engineering, chemical engineering, external and internal
environmental architectural design, marine and environmental engineering,
hydrology, meteorology, and bio-medical engineering.
The study of fluid
mechanics includes the study of fluids either in motion (fluid in dynamic mode)
or at rest (fluid in stationary mode). CFD is usually dedicated to fluids that
are in motion, and how the fluid flow behavior influences processes.
Additionally, the physical characteristics of fluid motion can usually be
described through fundamental mathematical equations, usually in partial
differential form, which govern the process of interest and are often called
governing equations. These mathematical equations are solved by being converted
by computer scientists using high-level computer programming languages. The
computations reflect the study of fluid flow through numerical simulations,
which involves employing programs performed on high-speed digital computers to
attain numerical solutions.
Computational fluid
dynamics is usually performed with use of commercial CFD codes. CFD codes are
structured by numerical algorithms that consider fluid-flow problems. All CFD
codes must contain three main components to provide useful information; 1) a
pre-processor, 2) a solver, and 3) a post-processor.
Pre-processing consists
of inputting a fluid flow problem into a CFD program. This includes defining
the geometry of the region of interest, grid or mesh generation, selection of
the physical and chemical phenomena that need to be modeled, a definition of fluid
properties, and specification of appropriate boundary conditions at the inlet
and outlet. The larger the number of cell grids the better the solution
accuracy. The accuracy of a solution and the required time for computational
problem solving are dependent on grid fineness. Most of the time spent is
devoted to this process.
In cardiovascular
systems, computational imaging tools may confer the grid generation
information, but limitations are that the resolution of current imaging tools
is still low and geometry varies according to the cardiac cycle. Blood acts as
a non-Newtonian fluid, because blood has varying viscosity according to its
shear rate. Fig -shows the correlation between blood viscosity and shear
rate.Thus, the correct viscosity model using a mathematical equation should be
selected according to the range of shear rates. The energy conservation law of
fluid motion is an important consideration for basic concepts. Boundary
conditions, such as blood pressure, blood flow velocity, and temperature are
readily available from invasive and non-invasive measurements based on the
region of interest. Another essential consideration is that these boundary
conditions also vary according to the cardiac cycle and the unique conditions
of coronary circulation. Fig- 2 shows a sample of these pressure and
velocity profiles during cardiac cycles for modeling and CFD.
Numerical solution
techniques are available such as finite difference, finite element, finite
volume, and spectral methods. Each has a distinct numerical technique, but the
basis of the solver is to perform an approximation of unknown flow variables by
means of simple functions, discretionary by substitution of the approximations
into the governing flow, and an algebraic solution. If the user uses a solution
technique, the time spent depends upon the calculating capacity of the
computer. Usually, the finite volume method is adopted for cardiovascular
systems.
The object of this
process is to visualize the computational results. Many visualization tools
have been developed, including domain geometry and grid display, vector plots,
line and shaded contour plots, two-dimensional and three-dimensional surface
plots, particle tracking, and color postscript outputs. After this process, the
researcher can easily understand the simulation results. For example, the
changes in blood flow profiles, pressure distribution, wall shear stress (WSS),
oscillating shear index (OSI), and shear rate can be visualized using color
rendering techniques. Furthermore, a cyclic motion view can be obtained during
cardiac cycles.
In the biomedical field,
CFD is still emerging. The main reason why CFD in the biomedical field has
lagged behind is the tremendous complexity of human body fluid behavior.
Recently, CFD biomedical research is more accessible, because high performance
hardware and software are easily available with advances in computer science.
All CFD processes contain three main
components to provide useful information, such as pre-processing, solving
mathematical equations, and post-processing. Initial accurate geometric
modeling and boundary conditions are essential to achieve adequate results.
Medical imaging, such as ultrasound imaging, computed tomography, and magnetic
resonance imaging can be used for modeling, and Doppler ultrasound, pressure
wire, and non-invasive pressure measurements are used for flow velocity and
pressure as a boundary condition.
Many simulations and
clinical results have been used to study congenital heart disease, heart
failure, ventricle function, aortic disease, and carotid and intra-cranial
cerebrovascular diseases. With decreasing hardware costs and rapid computing
times, researchers and medical scientists may increasingly use this reliable
CFD tool to deliver accurate results. A realistic, multidisciplinary approach
is essential to accomplish these tasks. Indefinite collaborations between
mechanical engineers and clinical and medical scientists are essential.
CFD may be an important
methodology to understand the pathophysiology of the development and progression
of disease and for establishing and creating treatment modalities in the
cardiovascular field.
Recently, medical researchers have used
simulation tools to assist in predicting the behavior of circulatory blood flow
inside the human body. Computational simulations provide invaluable information
that is extremely difficult to obtain experimentally and is one of the many CFD
sample applications in the biomedical area in which blood flow through an
abnormal artery can be predicted. CFD analysis is increasingly performed to
study fluid phenomena inside the human vascular system. Medical simulations of
circulatory function offer many benefits. They can lower the chances of
postoperative complications, assist in developing better surgical procedures,
and deliver a good understanding of biological processes, as well as more
efficient and less destructive medical equipment such as blood pumps.
Furthermore, medical applications using CFD have expanded not only into the
diseased clinical situation, but also into health life supportives, such as
sport medicine and rehabilitation. Several examples are discussed as follows.
Although many systemic risk factors predispose
development of atherosclerosis, it preferentially affects certain regions of
circulation, suggesting developing coronary atherosclerosis.
Information regarding
the spatial distribution of intraluminal hemodynamics of the coronary that
lesion-prone areas may at least in part be due to biomechanically related
factors. Furthermore, luminal hemodynamics, such as flow velocity, pressure
changes, and WSS have been suggested as other risk factors for vascular tree
are available using CFD.
Fig-3 shows an
example of performing CFD from pre-processing to post-processing. At first, a
mesh or grid of region of interest is generated from the coronary extract
images of computerized tomogram. The researchers might use any three
dimensional medical images. The Digital Imaging and Communications in Medicine
(DICOM) files should be converted into a file which can be used in a soft ware
analyzing three dimensional vector information. All the digitalized data, such
as velocity and pressure information according as cardiac cycle as a boundary
condition were selected to put into an appropriate algebraic solution. And, the
next step is mathematic solving process by the computer. At this process,
mechanical engineers and medical scientists should discuss about all the
clinical situations for selecting an appropriate viscosity models due to
non-Newtonian fluid analysis, governing equations. Final step is visualization
process for user. There are so many representative processing results, such as
pressure profiles, velocity profiles, particle tracing, time-averaged wall
shear stress (TAWSS), OSI, etc. This figure shows high TAWSS, OSI at
bifurcation. TAWSS shows higher at bifurcation apex, but OSI shows higher at
lateral side of side branch.
Fontan circulation,
first described by Fontan and Baudet, is
characterized by the absence of a right ventricle and functions under unique
hemodynamics. The key targets of geometric correction of Fontan procedure are
the separation of systemic and pulmonary venous return and establishing the
pathway of a passive, direct, and unobstructed connection between the systemic
venous return and the pulmonary artery (PA) for treating single ventricle
physiology, as one example of congenital heart disease.
While the Fontan
procedure is a classic treatment procedure for a functional single ventricle in
patients with congenital heart diseases, it has a potentially harmful effect
for normal circulation. The absence of a right ventricle induces a pressure
elevation in the venous system. The basic pathophysiological mechanisms
originate from increased central venous pressure and the superior vena cava
(SVC) and inferior vena cava (IVC).
Elevated central venous
pressure is poorly tolerated over time, particularly in the IVC, and has
deleterious effects on liver and splanchnic circulation. Protein-losing
enteropathy and plastic bronchitis characterize the worst outcomes. At the liver
level, elevated central venous pressure may induce complex liver dysfunction
and stimulate angiogenesis factors favoring a venovenous anastomosis, pulmonary
venous fistula, and, potentially, aortopulmonary collateral anastomoses. At the
lung level, the upper PA branches are poorly or not perfused, and the lymphatic
circulation is globally impaired. The single ventricle faces a significant
increase in total systemic resistance because it needs to "push"
against not only the usual systemic resistance but also lung resistance. As a
consequence, the systemic ventricle becomes hypertrophied, with elevated
end-diastolic pressure, which diminishes diastolic performance.Several studies
have focused on solving these problems.
Computational fluid
dynamics was performed after artificially modeling the Fontan circulation using
medical information. Fig-5 shows the velocity profiles at maximal
flow among cardiac cycle time periods. Significantly increased flows were
driven from the SVC, particularly during inspiration, indicating that unmixed
blood flow to the PA and blood flow in the IVC may be more congested during
inspiration than during expiration. During standing and inspiration, blood flow
profiles aggravate the stagnation of systemic venous blood flow return and
failure of the blood mixing function, suggesting that an artificial pumping
device is essential for correcting Fontan circulation failure.
This is another example
of using CFD as a diagnostic tool for evaluating heart function. Work of the
heart (WHO) is calculated using a pressure-volume curve. Some new indirect
diagnostic tools are available to evaluate the WOH. The modified Windkessel
model was used with blood viscosity models to develop a mathematical model for
estimating WOH utilizing the pulse waves between two points of a vessel. The
human arterial system is a network of vessels that converts intermittent flow
of the heart into steady flow through the capillaries and venous system. The
modified Windkessel model is a type of lumped parameter model that allows
simulation of blood flow in the entire circulatory system as an electrical
circuit (Fig-6).
In this figure, Qin, Q1,
and Q1 are defined as the flow rate exiting from the left ventricle during
systole, the flow rate passing through the peripheral system, and the flow rate
passing through the distal system, respectively. Similarly, p1 and p2 are the
pressures measured at the proximal and distal locations, representatives of
central and peripheral blood pressure, respectively. Moreover, C1 and C2 are
proximal and distal compliances, where L corresponds to the inertia of blood
(L=0.017 mmHgs2/mL). Flow rate in the left ventricle can be
calculated with the mathematical fluid analysis shown in Fig-7 by
measuring blood pressure curves at two points in the peripheral arteries
(brachial and radial arteries).
The blood viscosity model is essential to solve
the problem of an increased burden of work on the heart, so further study will
be needed to verify which viscosity model results are similar compared to in
vivo results. However, this type of study might suggest the
possibility of developing non-invasive devices for measuring WHO. Fig-7
Proximal (Q1) and distal (Q2) flow rates in the
left ventricle calculated with the Herschel-Bulkley equation.
CFD is being
increasingly employed to understand carotid stenosis and its biological
properties according to geometric risks, or via virtual prototyping to Physiology and diseases of the aorta,
carotid, and cerebral arteries are also studied with recommend the best design
for surgical reconstruction during a carotid endarterectomy, and conjunctional research magnetic resonance images. Furthermore, CFD is being used to better understand blood flow
through an aneurysm in the abdominal artery, and the development and
progression of aortic dissection.
There are many
advantages when considering CFD. Theoretical development in the computational
sciences focuses on the construction and solution of governing equations and
the study of various approximations to these equations. CFD complements
experimental and analytical approaches by providing an alternative
cost-effective means of simulating real fluid flow, particularly in human body
fluids. CFD has the capacity to simulate flow conditions that are not
reproducible during experimental tests found in geophysical and biological
fluid dynamics, such as scenarios that are too huge, too remote, or too small
to be simulated experimentally. Furthermore, CFD provides rather detailed
visual and comprehensive information when compared to analytical and
experimental fluid dynamics.
Although CFD is
advantageous, it cannot easily replace experimental testing as a method to
gather information for design purposes. Despite its many advantages, the
researcher must consider the inherent limitations of applying CFD. Numerical
errors occur during computations; therefore, there will be differences between
the computed results and reality. Visualizing numerical solutions using
vectors, contours, or animated movies of unsteady flow are the most effective
ways to interpret the huge amount of data generated from numerical
calculations. Wonderfully bright color pictures may provide a sense of realism
to the actual fluid mechanics inside a flow system, but they are worthless if
they are not quantitatively correct. Thus, numerical results must always be
thoroughly examined before they are believed; therefore, a CFD user needs to
learn how to properly analyze and make critical judgments about the computed
results.
Another important
comment is collaboration between mechanical engineers and medical scientists.
Not any one department can deliver a result. Each discipline should provide
feedback on the results at each step.
This report has
identified current four applications of CFD in Biomedical field. Rapid advances
of many industrial applications in computer science are outstanding, which
requires changes in CFD. This changing situation is partly attributed to the
rapid evolution of CFD techniques and models. Excellent creative models for
simulating complex fluid mechanics problems in the human body and therapeutic
models are now being progressively applied, particularly with the availability
of commercial CFD computer programs. The increasing use of these programs in
medicine might reveal how demanding the practical problems analyzed by CFD are.
With decreasing hardware costs and rapid computing times, researchers and
medical scientists may be relying increasingly on this reliable CFD tool to
deliver accurate results. However, a realistic multidisciplinary approach is
essential to accomplish these tasks. Indefinite collaborations between
mechanical engineers and clinical and medical scientists are essential. CFD may
be an important methodology for understanding the pathophysiology of developing
and progressing cardiovascular disease and for establishing creative treatment moralities in the cardiovascular field.
With regards,
Rabin
