Performing Cardiac Surgery For Congenital Heart Defects Biology Essay

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The first surgery on the human heat is said to have taken place in 1896, since then cardiac surgery has become a common operation to treat congenital heart defects, valvular heart disease and full heart transplants. The operations are inherently invasive and can be dangerous for the patients, open heart surgery began in the 1950s with the development of an off heart pump (one which is situated outside of the body to allow blood to be pumped whilst undergoing surgery) to allow the heart to be still whilst the blood remained oxygenated. This provided a still heart to allow the operation to take place. Dr. Lillehei utilised a method of 'cross-circulation' where a patient's mother or father were used as an oxygen pump during the operation. Since the 1990san 'off-pump' bypass surgery has been developed that allows the heart to remain beating but is stabilised to allow an almost still work area, some hospitals are now also utilising robotics which allow only small holes to be made in the heart whilst small cameras and robotic arms mimic the surgeons movements to perform the operation.

In with these operations many patients require vein grafts and even artificial valves, patients are now also receiving pumps to replicate the pumping of the heart or to merely assist the heart to pump blood so that there is less pressure on it for the remainder of its life, this is to prevent the occurrence of a heart attack as the heart is on less stress. The emphases on receiving these devices are that they will provide benefits with no additional damage to the patient (other than an altered lifestyle).

A common concern with the use of prosthetic devices in the body is the minimisation of the possible damage that the implant can cause. When artificial devices are added into the bloodstream care must be taken to consider how the device reacts with its surroundings, how the turbine interacts with the blood on a cellular level.

The blood pumps are being used more often and are seen as a viable alternative to a full heart transplant, approximately 20% of children die whilst waiting for a heart transplant, and with these devices being available 'off the shelf' the rate of attrition should reduce, and allow the patient to recover to live a relatively normal life. [Dr Richard Kemp http://www.telegraph.co.uk/health/healthnews/7636208/Teenage-boy-is-youngest-to-receive-artificial-heart-pump.html ]

Assist devices, which take over the majority of the heart's pumping function, allow the heart to rest, heal, and grow stronger. As a result, patients often become healthier and stronger before they undergo transplant surgery.

Sallam and Hwang (1984) are often cited to have quantified the threshold of haemolysis at approximately 400Nm-2

It is often cheaper to utilise CFD techniques to simulate a design rather than test it due to the cost of obtaining correct blood samples, manufacturing costs and health and safety concerns. Although experimental testing should take place before final manufacture, a correctly correlated model can allow for the effect of changes in design to be seen soon after the design has been completed without the need to remanufacture components. This can cut down on the time for the designers to see results and to further optimise the design. By being able to quantify the haemolysis with the use of simulation it can prevent costly experimental tests to be completed to view results.

Blood damage research is often aimed at the red blood cells due to their indispensible role in transporting oxygen and due to the numbers of RBC in the blood.

To date a universal blood damage model is not available due to the complexity of the situation.

In the body blood flow is generally considered laminar, however the use of VAD etc tend to introduce significantly disturbed or turbulent flows [4]

Mechanically induced haemolysis can cause hypercoagulation, bleeding, thrombormebloism, renal damage and neurologic dysfunctions. [4]

Receiving a VAD is a high risk operation can be attached to either the left ventricle, both ventricles, or the aorta. It is often given when with a view to receiving a donor heart. [BHF]

The history of heart pumps

The theory of heart pumps have been around for many years, since the early 1950s mechanical pumps for hearts have been developed. There are different types of pump available, for example centrifugal or axial flow pumps. These are classed as continuous flow pumps - there are no pulsations of blood flow.

In 1999 the NHLBI estimated that 1% of the 250,000 patients receiving cardiac surgery would receive a Ventricular assistance device. This would however be a temporary solution during the operation, with only a small percentage (approximately 2500 patients) being eligible for a total artificial heart. As the development has continued permanent devices have been approved up to a full artificial heart. Although using mechanical technology requires a lot of care, not only on the mechanical side but also the biological side, the damage it can do to the blood (haemolysis) and how the body reacts to the device, it can be much less invasive than a heart transplant of which there is a risk of the body rejecting the donor heart.

What is blood?

Blood consists of red and white blood cells and thrombocytes, and transports vital substances, oxygen and carbon dioxide to and from the cells via links with the respiratory systems; it also transports the waste products of metabolism, nutrients and plasma contents. The flow of blood it used to regulate body temperature and removes toxins from the body through the kidneys.

Blood comprises many constituents, and his approximately 55% Plasma, with the rest being made up of red and white blood cells and blood platelets. Red blood cells contain haemoglobin, and carries oxygen around the extremities of the body. They are approximately 6-8 micrometers in size, whilst the white blood cells form part of the immune system to defend the body against disease. Haemoglobin is the major protein in mature red blood cells, and is the protein that carries the oxygen. It is the release of this protein from the cell membrane that is measured when determining haemolysis levels.

The cell membrane is a biconcave disc, when the cells are young they are very deformable, returning to their original shape rapidly. However as they age they become more rigid the cells survive for approximately 120 days before the spleen eliminates them (Schmaier and Petruzzelli, 2003).

The inner fluid of the red cell is purely viscous and has no elasticity

Platelets can control the viscosity of the blood - too many and clotting can occur where as to few and excessive bleeding can occur, and are vital in the process of haemostasis, which causes the bleeding process to stop. Its viscosity is equal to 1.1-1.2 centipoises (Schmaier and Petruzzelli, 2003).

There are many disorders of blood that can cause issues with VAD's. It is thought that the use of Warifin medication to thin the blood will no longer be needed with the use of VAD's.

The medication is used to ease the pressure on the heart, generally after the patient has a heart attack. This type of medication alters the viscosity of the blood which would have a significant effect on the shear stress effect the blood cells will encounter.

Haemolysis what is it?

Haemolysis in this instance refers to the breaking up of red blood cells than the subsequent release of haemoglobin.

Haemolysis is the phenomenon whereby red blood cells are damaged or age prematurely so that their ability to transport haemoglobin is reduced, which leads to haemolytic anaemia, this can lead to many different medical conditions such as jaundice and pulmonary hypertension, which can significantly increase the risk of heart failure.

It can occur naturally due to defects in glycolysis where the life expectancy of RBC is naturally shorted.

Intravascular haemolysis is the damage of RBC's with in the blood vessels. This can be from mechanical damage, from artificial valves of vascular anomalies. Vascular damage can also be caused by other conditions such as metastatic cancer. Haemolysis can also be caused by RBC defects such as stickle cell anaemia. (Schmaier and Petruzzelli, 2003).

Another disease that can affect blood is Sickle Cell Anaemia, this is where the blood cells are deformed due to abnormal haemoglobin strands, this can cause the blood cells to clump together and cause blockages.

With patients with Sickle cell anaemia now living into their 50s and longer there is a possibility that they may need VAD the difference in the shape and construction of the cells may impact on the cell strength and resistance to shear stress. With stickle cell disease there are haemoglobin deficiencies which ultimately lead to the RBC's becoming irreversibly damaged leading to haemolysis (Schmaier and Petruzzelli, 2003).

Figure http://www.nhlbi.nih.gov/health/dci/Diseases/Sca/SCA_WhatIs.html [15/11/2010]

Cardiovascular disease (CVD) is one of the major causes of mortality/morbidity in the UK, in 2007 CVD was responsible for 34% of deaths in the UK. The most common form of CVD is Coronary Heart Disease (CHD) with 1:5 male and 1:6 female deaths attributed to it. The Department of health (2009) shows that mortality rates are falling as the disease is preventable.

The cardiovascular system incorporates the heart, blood and blood vessels, it enables continuous circulation of blood fulfilling a critical homeostatic need arising from the constant requirement of body cells to take in oxygen and nutrients and excrete waste products such as carbon dioxide. An adequate circulation is essential for all cell activity.

How the heart works

CV system diag

Ht 1

The Cardiac Cycle

The two pulmonary veins carry oxygenated blood from the lungs to the left atrium which pumps it through the mitral valve into the left ventricle then the left ventricle pumps oxygenated blood into the aorta via the aortic valve and to the upper and lower body for exchange of nutrients and gases

Next the deoxygenated blood enters the right atrium of the heart via the superior and inferior vena cava and the blood passes through the tricuspid valve into the right ventricle which then pumps the deoxygenated into the pulmonary artery (PA). The PA divides into the right and left PA's and carries the blood to the lungs for gaseous exchange.

Approximately 5% of oxygenated blood from each heartbeat is diverted from the aorta to the heart muscle to provide oxygen and nutrients. The oxygen rich blood is carried to the heart muscle via the coronary arteries whilst coronary arteries divide into smaller branches forming anastomosis, the cardiac veins via the coronary sinus bring de-oxygenated blood to the right atrium.

Types of heart assistance (blood pump)

History - http://www.hhmi.org/biointeractive/museum/exhibit98/content/h13info.html [heart pump history]

Figure : Intra-Aortic Balloon Pump Schematic. CBF - Coronary Blood Flow.

Figure : A schematic of a Left Heart Assist System. Where silicon tubes are used to draw blood from the Left Atrium (LA) and deposit it to the ascending aorta using the roller pump head.

Figure : Cardiopulmonary Bypass Pump - A schematic presentation of cardio pulmonary bypass pump, utilising a peripheral method of femoral bypass with oxygenation. The pump itself can be a roller head of electromagnetic head. CVP. Central Venous Pressure. PCW Pulmonary Capillary Wedge Pressure. CO Cardiac Output.

Intra-aortic balloon pump is a cylindrical balloon placed within the aorta, and inflated during diastole, thus increasing aortic pressure during diastole and increasing coronary blood flow and balloon deflated prior to and during early left ventricular ejection thus reducing aortic pressure and thus after load.

It is a system that is capable of providing a volume of gas into a pneumatically driven pumping chamber during a given time interval (Bolooki, 1998). It uses a cylinder of helium to power the pneumatic valve mechanism which allows the gas to reach the IABP. The pump must monitor electrocardiogram (ECG), the arterial blood pressure. These signals are processed to open the solenoid valve. The monitoring of the ECG signals allows the determination of the heart beat rate of change to allow for the IABP to react.

Open intra-cardiac operations have become possible since John Gibbon developed the methods for circulatory support (heart-lung machine) in 1951. This allowed total support of the circulation system for short periods whilst operations are carried out (Bolooki, 1998).

The development of these pumps has been ongoing since initial concepts were cited by Clauss et al in 1961. After initial tests in dogs proved successful, human patients began to be fitted with the device. IABP are now one of the most popular ventricular assistance devices due to its relative costs, the ease of installation and removal, minimal discomfort for the patient and the lack of anticoagulation medication needed after fitment. It is also suitable as a long term solution.

Figure : IABP diagram of inflation and deflation. (Bolooki, 1998).

How long does it stay in for?

How is it powered?

Risks involved?

CONTINUOUS FLOW PUMP

NON-CONTINOUS FLOW PUMP

Human heart

Risky procedure, risk of rejection, long lead times for donors. Possible future failure.

Pulsatile blood flow

Design of pumps

What in the design causes haemolysis?

How to better the design.

What is CFD

Computational fluid dynamics (CFD) is used in many industries for a wide variety of simulation tools. The scenario looked at by this thesis is its use to simulate and perform accurate predictions of the levels of damage caused to human blood by a shear device. By observing the levels of 'haemolysis' design changes can be made to minimise damage.

Why is it important?

CFD is an important tool when designing components where the analysis of fluid flow or heat transfer is important. It is used extensively in R&D (Research and Development) to speed up the development of ideas, and to predict the forces, fluid flows in the environment the component will be situated in. It can speed up the design process and can save money by its utilisation to simulate designs with out the need to manufacture and test them.

How have people simulated it?

The simulation of the impact that shear induced stress has on blood cells has been investigated in many studies, Lim has investigated using experiments and mathematical methods (Lim et al., 2001). Using particle image tracking velocity (PIV) to map the velocity vector fields and Reynolds stresses in the downstream of the bio-prosthetic heart valve. This allowed them to use lagrangian techniques to estimate the propensity of the shear induced damage to blood cells. For the experimentation they used aluminium particles to visualise the flow, with the aid of a light beam. The flow was controlled at 72 beats per minute, with a cardiac output of 5litres per minute. By using equations developed by GIERSIEPEN ??? for the estimation of blood damage utilising the exposure time and the shear stress. The exposure time could be accurately interpreted by using the velocities of individual particles in the shear stress fields. The study shows that shear stress under pulsatile flow is greater than steady continuous flow by a factor of 1.2-1.6.

How have they simulated it?

Studies into the computational modelling of blood damage in devices such as the centrifugal pump investigated by Song et al (Song et al., 2003). They used CFD techniques to analyse and track the shear stress history of 388 particle streak lines to evaluate the levels of trauma.

The pump that was simulated is a magnetically suspended centrifugal pump used as a LVAD . The blood has been modelled incompressible, and has been used to find the relationship between haemolysis, shear stress and exposure time.

By using computer simulation the authors were able to determine the percentage of particle streaks that would encounter haemolysis effects and for how long.

How physica works

Application

Creation of geometry

Do medicine/disease alter the blood properties?

How are blood cells modelled.

Henon modelled the shear modulus of blood cells by using optical tweezers. They used them to measure the elastic coefficients of the red blood cell membrane, the use of the optical tweezers allows it to be possible to "trap, manipulate and displace a living cell or a part of it without damage". Henon found that the method used by others such as xxxx deformed the cell by using 3 points to remove the cell and measure the relaxation time would not allow the measurement of the membrane elastic coefficients due to the trapped volume and the exerted force are not well enough defined.(Henon et al., 1999).

The method used by Henon using two silica beads bound to the membrane which seize and deform the cell. The optical tweezers are used to pull the membrane in opposing directions.

The red blood cell may be measured as two independent parallel discs if in a isotonic buffer or as a sphere in hypotonic buffer (Henon et al., 1999).

Image of optical tweezers?

Cell stress

The use of the simple constitutive laws of elasticity are, [[3]in henon]

Cell stress image

For a spherical shell shape with forces applied to its poles, along the equator the stress and deformation will be the same. The membrane is not under tension 5b and there is no pressure difference between the cell interior and exterior. ]

Henon etal have concluded that there is no significant difference in the shear modulus of discotic and spherical red blood cells. The final averaged value for μ found by henon is 2.5±0.4 μN/m.

Below a certain level of stress the subjected cells will not rupture even if exposed indefinitely.

Other techniques to measure red blood cell stress is the use of micropipettes.

(Bélanger et al., 2000) have investigated the impact of different materials used in heart pumps on the haemolysis of blood. Their investigations have shown that the materials used must meet demanding biocompatibility criteria. They were unable to establish one material to use as a membrane that will meet all criteria.

Deformation haemolysis of cells

(Richardson, 1974) have looked into the effect of shear stress on the deformation and haemolysis of red blood cells. In this study Richardson has looked at a single cell in the flow, as the haemolysis is an event which occurs due to local conditions. Previous studies have shown that with a shear rate of less than 100s-1 the cells would lose their biconcave shape and would change to a variety of shapes such as probate ellipsoids. The surface of the cell membrane has been observed to rotate in wave patterns around the cell on a cone plate viscometer whilst in flow, however as flow speed increases this observation ceases to occur. When flow is stopped the cells return to their usual shape. Richardson has assumed that the cells natural shape is a biconcave solid and at low rates of strain the cell membrane is considered elastic. The use of a Hookean or Mooney elastic material is considered. [HOOKEAN TABLE]

After a certain level of stress or strain the cells become viscoelastic and may exhibit a permanent set, however Richardson has not determined stress level at which this happens.

Haemolysis in shear

Below is a diagram to show the strain produced from time dependent stress, where E is young's modulus and μ is poisons ratio.

Figure : Rand's Viscoelastic membrane breakdown model. (Richardson, 1974)

Richardson determines the point at which the maximum stress occurs as this is where the haemolysis is most likely to occur. This is done using equations for the oblate spheroid and calculating the tensions in the equivalent sphere as shown in Figure .

Figure :(Richardson, 1974).

Reynolds number

(Richardson, 1974) has used the data below to determine the Reynolds number of the blood cells, whilst considering only the creeping flow equations as the interest is only with the particle. Richardson believes that the Navier-stokes equations are not necessary for this problem due to the slow flow speeds.

Particle Tracking

Many studies have focused on particle tracking such as (Lim et al., 2001), Lim states that LDA or HFA only provide flow information a point in space and time, and therefore the amount of shear stress observed by the blood cells at an instance in time, and cannot take into account the shear stress observed over a time period of exposure. In this study they have utilised PIV techniques which by utilising a video camera to continuously view flow fields, data can be pooled from a number of frames. This allows for the particle trajectory to be seen along the shear stress map along the instance of time. With this (Lim et al., 2001) were able to obtain an lagrangian description of the stress levels the cells encounter whilst moving over the artificial valve. To visualise the flow they used aluminium particles placed in the blood flow.

By doing this they were able to analyse the shear stress experienced across the artificial valve.

Methods for blood damage prediction

It is largely unknown what degree cells may be damaged by lower mechanical loads as seen by 5,6.

Grigioni et al aimed to develop a power law mathematical model and evaluate the effect of a time varying mechanical loading acting on the blood cell and the effect of the loading history of the blood particle.

ADD TABLE 1 from paper

Grigoni observes the difference between the damage to blood cells when tested in Vitro and when tested in vivo, they found that it is difficult to assess the damage produced by an artificial device without taking into account the time varying load history and the effect of different stress magnitudes. The power law method reported is useful in many situations it does not account for the previous shear stress history of the cell. EQU1

Grigioni has formulated two hypothesis to deal with the accumulation of damage to the cell, the damage accumulated in relation to time and the shear stress damage accumulated over time.

Further research by Grigioni [3] looks at the load histories effect on the blood cell.

Kameneva et al (Kameneva et al., 2004) have studied the effect of turbulent stresses on blood cells. By utilising a capillary tube in a water bath, the blood was driven through a closed loop system with a centrifugal pump and circulated for 90mins with blood tested for haemolysis every 30mins.

Using CFD techniques velocity vector fields were obtained for the blood in the capillary tube. They found that the simulation over predicted the pressure drop for laminar flow and under predicted for the turbulent flows. This was adjusted by scaling the values of the fluid dynamic viscosities with the classic poiseuille pipe flow relationships. Kameneva et al found that when using the capillary tube that the haemolysis had a linear dependence against time at each shear stress for both laminar and turbulent flow.

Add figure 6?

The test results show that turbulence in the blood flow caused a significant increase in the level of haemolysis with wall shear stress between Tw - 200-400Pa (p<0.05) which satisfied their CFD predictions.

Klaus etal [5] have tested for haemolysis using a rotating cylinder in a housing to create the shear stress with a gap of 120μm, the blood flows from one side to the other pumping from a syringe. The flow conditions in the shear gap are laminar and uniform without secondary flow. The flow induced blood damage in the diagram below depends on the applied shear rateY. Shear stress TAO acting on the blood elements and the time period tb of the shear stress [5].

Klaus et al find that by using a mathematical power law approach 100% damage would be cause at 1200ms.

Other mathematical approaches have been used to predict the haemolysis of blood cells in vitro, such as Arora's study (Arora et al., 2005). Arora has used a morphology tensor approach to predict haemolysis levels, this gives the morphology at an instantaneous point and then takes into account the cells rotation when subjected to shear stress. When using this, the authors were able to closely match the experimental results.

Creation of geometry

To simulate the basic shear device the component will be modelled using CAD and meshed according to design with Hypermesh. Once the mesh is created and different 'faces' have been created the design can be simulated with physica using an appropriate inform file.

The faces must be created to separate the moving objects from those that are immobile. By using the correct commands in the inform file the inner rotor can be allowed to spin whilst the stator remains static, this creates the shear force to act on the blood cells. The aim is to simulate the speeds already physically tested to ensure convergence before testing at different speeds to allow for quicker results.

When creating the geometry consideration of how the mesh will be created must be taken into account. Using Autodesk Inventor CAD program the initial sketch was made. To ensure continuity only one sketch is used, and extruded in opposite directions in the Z axis to create the part, each extrusion was made as a separate material, this allows the user to alter the mesh size in Hypermesh software to take into account the different sized channels.

To make this simpler the design was split in two along the Z-axis, this has allowed the number of nodes to be specified across the thin channels.

Once this has been created it has to be exported into Hypermesh, which is the program used for mesh generation.

Firstly a 2D mesh is created on the plain shown in Figure 8. This is done individually for each material segment. Here the element sizes must be specified, to assist with this in lieu of specifying actual size, the number of elements is specified on each surface instead. This makes it simpler to ensure that there are a minimum of 3 elements across any face where there is fluids flow.

F:\2d mesh.JPGFigure : 2D mesh.

Once the 2D mesh is finalised it can then be dragged in the Z-axis to create a 3D mesh. The number of discretization is the number of elements in the Z-axis. Care must be taken when selecting this as if the element sizes are significantly different then the model will not work efficiently, Initially there were very small elements in the blood flow at the base of the stator, and then a sudden increase in size for the sides of the stator as shown in Figure : 3D mesh with no bias. and Figure .

F:\3d non bias.JPG

Figure : 3D mesh with no bias.

F:\3d non bias zoom.JPG

Figure : 3D mesh with no bias. When magnified the significant difference in element size can be seen.

To ease this there is an option to bias the mesh. With this option you can specify the discretization and then bias intensity. This will create a ratio and change the mesh from that above to one where the mesh increases in size by a ratio of the previous elements size. This makes the mesh smoother and allows for more accurate results in the blood flow.

F:\3d bias.JPG

Figure : 3D mesh with bias intensity.

F:\3d bias zoom.JPG

Figure : 3D mesh with bias intensity. As can be seen the element size gradually increases in size from the smallest elements.

When running the simulations it was found to have oscillating pressure fields in the Z-axis around the whole part. The velocity fields were looking correct however.

Under further investigation the mesh was not correct - when imported into Hypermesh from inventor, Hypermesh formed a series of straight lines to form a curve, which when the mesh was created it was read as such, the program was unaware of any curve in the mesh.

Figure : This diagram shows the straightening of the curve when creating the mesh.

Figure : When zoomed in the line of the curve (as shown by arrow) can clearly be seen, and the mesh line at this point is not to that curved line.

Figure : A little further around the curve the mesh generated clearly meets the original curve line drawn.

This restriction as shown in Figure -Figure caused the increase in pressure along the Z-axis.

After further investigation it was found that by creating the mesh in FEMGV the problem was solved.

FEMGV allows the geometry and the mesh to be created without the need to export into another program between the two tasks. Although the issue of 'squaring off' the arch line to form the mesh it does so in equal sizes. The program also knows that the curve exists and accounts for this when creating the mesh. This prevents the mesh from thinking that there are long straight sections in the mesh followed by a sharp corner. By creating them all at equal sizes there are much shorter straight sections with much less significant corners. When Hypermesh created the mesh it did so with slightly different shape and sized elements.

This ensures that there are no areas of the design that are smaller than another area - all the meshes are uniformly thick on its face.

Creation of inform

Navier-Stokes Equasions

The navier stokes equations are used to describe the motion of fluid flows from Newtons second law of fluid flows.

In fluid flows the viscous stresses are functions of the local deformation rate or strain rate.

Discretisation

The process of discretisation solves a system of linear algebraic equations. The method widely used in CFD programming is the Tri-Diagonal Matrix Algorithm (TDMA) developed by Thomas (1949). It is a direct method of solving one-dimensional problems that can be applied iteratively. In 2D situations the TDMA is applied iteratively to solve a system of equations. The system utilises each element of the mesh to create a grid. The TDMA is applied along these lines, for example the next element to the west is assumed to be an unknown, then the equation 7.8 is used in its base form 7.2 which can then solve that point and the points on the same north/south axis. This equation is then moved to the next north south line, the next equation utilises the results of the previous step as its start values. By using this line by line approach the procedure is repeated until convergence occurs. When transferred to a 3d problem the same process occurs, however the TDMA is applied on a selected plane, when the results have been calculated the process moves to the next plane. Each plane is defined by the user when selecting the number of divisions in the Z-axis of the mesh in the shear device case.

Unsteady flows

Boundry conditions

With all cfd problems boundary conditions must be specified. These allow the program to determin the initial conditions by utilising starting temperatures or pressures, and allowing the inlet and outlet ports be shown to show direction of flow.

Difficulties in determining rynolds shear stress

From grigoioni average shear stress

There is not yet a general agreement on the RSS threshold, also on account of the fact that, as for RBCs, haemolysis depends also on the exposure time, besides the shear stress level. Another difficulty in the comparison of results arises from the measurement of the RSS, which depends on the choice of the measurement system (Fontaine et al., 1996; Barbaro et al., 1997), and needs an analysis based on the concept of principal stresses (Malvern, 1977) to provide the maximum

turbulence shear stress exerted on a particle, i.e., the TSSmax; this elaboration has been rarely done, therefore the threshold levels in literature can be the result of an underestimation of the real values.

Actually, in Grigioni et al. (1999) it has been demonstrated that the threshold for haemolysis reported in Sallam and Hwang (1984), i.e., 400 N/m2, was underestimated at least by 50%.

ARORA, D., BEHR, M., CORONADO-MATUTTI, O. & PASQUALI, M. (2005) Estimation of hemolysis in centrifugal blood pumps using morphology tensor approach. . Comutational Fluid and solid mechanics. , Third MIT Conferance, 578-582.

BÉLANGER, M.-C., MAROIS, Y., ROY, R., MEHRI, Y., WAGNER, E., ZHANG, Z., KING, M. W., YANG, M., HAHN, C. & GUIDOIN, R. (2000) Selection of a Polyurethane Membrane for the Manufacture of Ventricles for a Totally Implantable Artificial Heart: Blood Compatibility and Biocompatibility Studies. Artificial Organs, 24, 879-888.

BOLOOKI, H. (Ed.) (1998) Clinical application of the Intra-Aortic Balloon Pump, Miami, Futura Publishing Company.

HENON, S., LENORMAND, G., RICHERT, A. & GALLET, F. (1999) A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophysical Journal, 76, 1145-1151.

KAMENEVA, M. V., BURGREEN, G. W., KONO, K., REPKO, B., ANTAKI, J. F. & UMEZU, M. (2004) Effects of Turbulent Stresses upon Mechanical Hemolysis: Experimental and Computational Analysis. ASAIO Journal, 50, 418-423.

LIM, W. L., CHEW, Y. T., CHEW, T. C. & LOW, H. T. (2001) Pulsatile flow studies of a porcine bioprosthetic aortic valve in vitro: PIV measurements and shear-induced blood damage. Journal of Biomechanics, 34, 1417-1427.

RICHARDSON, E. (1974) Deformation and Haemolysis of Red Cells in Shear Flow. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 338, 129-153.

SCHMAIER, A. & PETRUZZELLI, L. (Eds.) (2003) Hematology for the medical students. , Baltimore, Lippincott Williams and Wilkins.

SONG, X., THROCKMORTON, A. L., WOOD, H. G., ANTAKI, J. F. & OLSEN, D. B. (2003) Computational Fluid Dynamics Prediction of Blood Damage in a Centrifugal Pump. Artificial Organs, 27, 938-941.

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