Inge Köhne1. 1. Department for Health Services Research, Carl von Ossietzky University of Oldenburg, Oldenburg, Germany.
Abstract
Since the use of continuous flow blood pumps as ventricular assist devices is standard, the problems with haemolysis have increased. It is mainly induced by shear stress affecting the erythrocyte membrane. There are many investigations about haemolysis in laminar and turbulent blood flow. The results defined as threshold levels for the damage of erythrocytes depend on the exposure time of the shear stress, but they are very different, depending on the used experimental methods or the calculation strategy. Here, the results are resumed and shown in curves. Different models for the calculation of the strengths of erythrocytes are discussed. There are few results reported about tests of haemolysis in blood pumps, but some theoretical approaches for the design of continuous flow blood pumps according to low haemolysis have been investigated within the last years.
Since the use of continuous flow blood pumps as ventricular assist devices is standard, the problems with haemolysis have increased. It is mainly induced by shear stress affecting the erythrocyte membrane. There are many investigations about haemolysis in laminar and turbulent blood flow. The results defined as threshold levels for the damage of erythrocytes depend on the exposure time of the shear stress, but they are very different, depending on the used experimental methods or the calculation strategy. Here, the results are resumed and shown in curves. Different models for the calculation of the strengths of erythrocytes are discussed. There are few results reported about tests of haemolysis in blood pumps, but some theoretical approaches for the design of continuous flow blood pumps according to low haemolysis have been investigated within the last years.
The term ‘haemolysis’ refers to the dissolution or degradation of erythrocytes. In
the normal life cycle of the red blood cell (RBC), this degradation occurs after
about 120 days. The aged and thus inelastic cells are destroyed by mechanical stress
and the haemoglobin contained in them is released into the blood plasma and then
degraded in the liver, where the iron atoms are recycled. The remains of the cell
membrane are absorbed and decomposed by macrophages. In a healthy person, the
concentration of free haemoglobin in blood caused by natural haemolysis is about
0.5-2.0 mg/100 L. A level of 10 mg/100 L is currently assumed to be tolerable for
humans.[1,2]
If the damage level of RBCs is higher, the production rate of new RBCs cannot
substitute the losses. Premature erythrocyte loss can be caused by unnatural
haemolysis as a result of increased mechanical stress on the RBC, resulting in
increased permeability of the cell membrane for haemoglobin or rupturing of the cell
membrane. Haemolysis is also caused by substances that attack the components of the
cell membrane, such as soaps, animal toxins and lysing antibodies. Haemolysis can
also be caused by excessive osmotic influx of water, which causes the blood cell to
burst.[1,3] The measurement
of haemolysis in patients supported by a blood pump (like ventricular assist device,
extracorporeal membrane oxygenation (ECMO)) can be impacted by the illness of the patient,[4] pharmacological management or necessary blood transfusions, so it is not
always easy to relate haemolysis to the blood pump alone. The aim of this review is
to provide an overview of the current status of research on the strength of
erythrocytes and the theoretical assessment of haemolysis in blood pumps. The
existing studies about haemolysis in blood pumps are summarized.
Methods
Electronic searches were performed using PubMed, which includes Medline in April
2019. Search terms were haemolysis and blood pumps. In total, 4,442 articles were
found. After title screening and then abstract screening if studies about haemolysis
in blood pumps or theoretical approaches concerning haemolysis prediction were
described, 93 articles remained for full-text analysis. Forty-eight articles were
used for this review and 8 additional ones were found by reviewing the reference
lists of these articles.
Normal Index of Haemolysis
Haemolysis in artificial blood pumps is mainly caused by mechanical stress on the
RBCs. The cell walls of the erythrocytes are damaged by shear stresses in the
blood, which arise in the blood flow through the movement of blood pumps or
through increased wall friction. The damage depends both on the level of the
shear stress and on the duration of exposure of the shear stress to the blood cells.[5] However, the contact of blood cells to foreign materials may induce
haemolysis as well.[6] Another possible reason for haemolysis is low or negative pressure in the
flow leading to cavitation, mainly observed during ECMO.[5] The haemolysis level caused by the individual blood pumps (or other
implantations like artificial heart valves, stents etc.) can be described by the
Normal Index of Haemolysis (NIH)where ΔfHb is the increase of haemoglobin in blood plasma (mg/dL); Ht is
haematocrit (vol.%); blood volume is defined as 1; and ΔN = Qt/V, where Q is the
volume flow rate (L/min), t is the duration of the experiment (minutes) and V is
the blood volume of experiment (L).[7]In clinical practice, high haemolysis in patients is detected by increased
concentrations of bilirubin and lactate dehydrogenase (LDH) in the blood plasma.[5]
Haemolysis in blood pumps
There are few published studies on the occurrence of haemolysis in blood pumps. A
haemolysis level of 0.19-0.26 g/100 L was measured in vitro in roller pumps.[8] An in vitro comparison between three centrifugal pumps for extracorporeal
short-term support showed that the PediVas pump (Levitronix LLC, Waltham, MA,
USA) caused the lowest haemolysis level and the Rotaflow (MAQUET Cardiopulmonary
AG, Hirrlingen, Germany) and Medos Deltastream DP3 (MEDOS Medizintechnik GmbH,
Stolberg, Germany) about twice as high. It was assumed that the design of the
PediVas pump with non-contact magnetic bearings greatly minimizes haemolysis.[9] The in vitro comparison between Rotaflow and CentriMag (Levitronix LLC)
pumps showed a haemolysis level of NIH = 0.021 g/100 L for the Rotaflow and
0.041 g/100 L for the CentriMag.[10] The in vitro comparison between Biomedicus BP50 (Medtronic BioMedicus
Inc., Eden Prairie, MN, USA) and Rotaflow showed advantages for the Rotaflow pump.[11] Computational fluid dynamics (CFD) analyses in HeartMate II (Thoratec
Corp., Pleasanton, CA, USA) and HeartWare HVAD (HeartWare Inc., Framingham, MA,
USA) pumps showed no significant difference in the occurring shear stresses. The
areas with the highest risk of haemolysis are all gaps between moving and
stationary parts of the pumps, as well as the inflow area of the blades of
impellers or diffusers. The HeartMate II is an axial pump with a flow
straightener, an impeller and a diffusor with three blades each. The impeller is
mounted with cup-socket ruby bearings, with a gap of 100 µm each. The diameter
of the impeller is 12 mm. The HeartWare ventricular assist device (HVAD) is a
centrifugal pump whose impeller with a diameter of 34 mm is magnetically and
hydrodynamically mounted. The bearing gaps are 160 µm at the bottom and 40 µm on
the top. The maximum shear stress in laminar flow ranges is 200 Pa, the maximum
stress in turbulent flow ranges in HVAD Reynolds shear stress is 200 Pa and the
maximum shear stress in HeartMate II is 500 Pa.[12] The flow of the centrifugal pump EVAHEART (EVAHEART Inc. Houston, TX,
USA) produces less than half the shear stress of HeartMate II.[13]The fundamental numerical investigations of haemolysis in axial flow pumps have
shown that these pumps have their highest efficiency at an impeller outlet angle
of 25°. Impellers with two blades work most effectively at an optimum speed of
6,000 L/min. The critical haemolysis level of this impeller configuration is
only exceeded at speeds above 7,000 L/min.[2] Corresponding investigations in centrifugal pumps show that these have a
considerably higher efficiency than axial pumps. The most favourable outlet
angle of the impeller blades for these pumps is either 15° or 30°. The highest
efficiency is achieved with six blades, and the optimum operating point is four
or five blades. The diameter of the outflow tube also has an influence on the
efficiency. The optimal pump must be a compromise between effectiveness, pumping
capacity and low haemolysis.[14] The lower the number of blades and the smaller the exit angle, the lower
the haemolysis level. In blood pumps with a hydrodynamic radial bearing,
haemolysis can be minimized by enlarging the bearing gap. Further influences on
the haemolysis level are the bearing diameter, the gap length, the
circumferential speed and the pressure difference between inflow and outflow.[15] When designing a hydrodynamic axial bearing, the geometry of the grooves
in the counter-plate of the bearing in the pump casing proved to be decisive for
the haemolysis level. By means of an appropriate design, a larger bearing gap is
created when the rotor rotates so that the shear load on the blood is reduced
and thus also haemolysis. The NIH was reduced by 90% in vitro.[16]In pulsatile ventricular assist devices (VADs), haemolysis is generally lower
because flow velocities and shear rates are lower. Xu et al.[17] were able to demonstrate that haemolysis in these systems also depends on
the operating mode of the pump. In vitro the haemolysis level increases with
higher impact rate, higher impact volume and operation with counter-pulsation.
However, all these measures have positive effects in reducing the risk of
thrombus formation, as the pumps and cannulas are washed out better. The highest
stress load on the erythrocytes occurs during the flow through artificial heart
valves, where Reynolds shear stresses of up to 1,000 Pa were measured.
Measurements in the LionHeart (Arrow International Inc., Reading, PA, USA)
measured maximum Reynolds shear stresses of 100 Pa in the blood chamber and
200 Pa in the discharge cannula.[18]In patients who received a short-term VAD with an IMPELLA® pump
(ABIOMED Inc., Danvers, MA, USA), haemolysis was highly dependent on the
patient’s disease. There were also many patients without a measurable haemolysis.[4] This shows that blood pumps, which normally work without serious blood
damage, can sometimes cause considerable problems for patients with pre-existing
damage. Kusters at al.[19] have demonstrated by in vitro experiments that an increase in the
temperature of the blood has no influence on the haemolysis level. In the in
vitro study by Kameneva et al.,[20] on the contrary, a strong lowering of the temperature (hypothermia)
results in a reduction of the deformability of the erythrocytes. Lai et al.[21] were able to demonstrate in vitro that the use of newly developed
superhydrophobic surfaces, also known as the lotus effect, allows the haemolysis
level to be reduced for all areas in contact with blood since the shear stresses
on these surfaces are greatly reduced. To create these surfaces, a commercially
available coating (Rust-Oleum NeverWet) of micro- and nanoparticles with a
thickness of 53 µm and a roughness of 2.3 µm was used. In experiments with
pulsatile pumps, haemolysis was reduced by 30%. The amount of LDH and bilirubin
level in the blood is determined to detect the occurrence of haemolysis in
patients with VAD. As an alternative, simple non-invasive procedure, the
counting of micro-emboli using transcranial ultrasound Doppler detection (TCD)
has proven to be effective. Normally used to detect thromboembolic events, a
high number of micro-embolies can indicate haemolysis.[22]
Non-Newtonian flow behaviour of blood
For fluids with Newtonian flow behaviour, the viscosity η does not depend on
shear stress (τ = η·dvx/dy), but only on temperature. Non-Newtonian
fluids, on the contrary, do not behave according to Newton’s shear stress
approach, but often exhibit structural viscous properties. This means that with
increasing shear stress τ, the dynamic viscosity η decreases. This must be taken
into account when simulating blood flows in narrow capillaries or with high
shear loads.[23] The viscosity of the blood is mainly determined by the haematocrit and
also by the viscosity of the blood plasma, which in turn depends on the
concentration of the plasma protein. The deformability and the aggregation
tendency of the erythrocytes are a cause for the non-Newtonian flow behaviour of
the blood. In contrast to water, blood viscosity therefore depends not only on
temperature but also on flow conditions. Because the viscosity of the blood is
relatively low when high shear stresses act on the blood in a fast flow but
increases considerably in a slow flow and low shear stress, it is referred to as
the apparent viscosity of the blood (structure-viscous behaviour). Due to their
pronounced deformability, the erythrocytes tend to orient themselves in a blood
vessel towards the centre of the flow. With increasing shear rate, the RBCs turn
first into elliptical and then stretched shapes before being destroyed (Figure 1). This results in
a marginal flow with low cell count which, as a ‘lubricating’ boundary layer
(plasma without blood cells), reduces the frictional resistance on the vessel
walls (Fåhraeus–Lindqvist effect). The thickness of this boundary layer
increases relatively antiproportionally to the reduction of the cross section of
the vessels. Therefore, the apparent viscosity of the blood decreases when the
vessel diameter drops below 300 µm, reaches a minimum at a diameter of about
6-8 µm and increases again in even narrower capillaries, because the
deformability of the erythrocytes now becomes the limiting factor for the
friction resistance (Figure
2).[3] Principally, there is no difference in the flow behaviour of blood in
round vessels or in small gaps found in rotary blood pumps. Bearing gaps in
these pumps differ between 40 µm (HeartWare HVAD), 250 µm (DuraHeart) and 1 mm
(HeartMate III).
Figure 1.
With increasing shear rate, the erythrocytes will be deformed from their
(a) natural rotationally symmetrical disc form into an (b) elliptical
shape and (c) then into a stretched form before being destroyed.
Adapted from Simmonds et al.[5]
Figure 2.
The apparent (measurable) viscosity of blood shows a minimum at a vessel
diameter of around 6-8 µm (0.006-0.008 mm). The schematic pictures
illustrate the scale between erythrocyte and vessel diameter in
different scopes of vessel diameter (logarithmic).
Adapted from Pries et al.[3]
With increasing shear rate, the erythrocytes will be deformed from their
(a) natural rotationally symmetrical disc form into an (b) elliptical
shape and (c) then into a stretched form before being destroyed.Adapted from Simmonds et al.[5]The apparent (measurable) viscosity of blood shows a minimum at a vessel
diameter of around 6-8 µm (0.006-0.008 mm). The schematic pictures
illustrate the scale between erythrocyte and vessel diameter in
different scopes of vessel diameter (logarithmic).Adapted from Pries et al.[3]
Resistance of erythrocytes
Most of the stress load limits for haemolysis given in the literature refer to
shear stress (τ) in the blood and thus to the erythrocytes and are triggered by
the flow through mechanical components. It has been shown that the occurrence of
haemolysis by shear stress depends not only on the shear stress level but also
on the duration of the shear stress.[24,25] Studies have shown that
blood is transported in a laminar flow in all vessels throughout the human body.
The highest measured speed is 1,175 mm/s in the femoral artery with a diameter
of 5 mm. A turbulent flow only occurs in the aorta during systole with a
Reynolds number of Re = 3,000-6,000.[6] Other potential areas that can cause turbulent blood flow are
pathological changes in blood vessels such as plaques, dilations, stenoses and
so on.In experiments, the shear stress varies with different measuring methods so that
the test results can only be compared within certain limits, nor can the shear
stress be easily determined using Newton’s shear stress approach. Tests have
shown that the shear stress only increases linearly at a shear rate of γ
>10 s−1. The shear rate is the slope of an applied tangent to
the flow profile of a laminar flow, calculated with γ = dvx/dy. The
highest shear rate always occurs directly on the vessel wall, and the highest
measured value is 1,885 s−1, also in the femoral artery. Goldsmith
and Turitto[6] have determined these deviations in extensive comparative tests. Wu et al.[26] were able to show that the critical limit of shear stresses determined
with a frequently used Couette viscometer is only of limited significance for
the occurrence of haemolysis. Beissinger and Laugel[27] were also able to demonstrate that the haemolysis level increases when
the erythrocytes get into contact with foreign materials, regardless of the
shear rate present. The presence of free radicals in the blood, which can have
an oxidative effect on the erythrocytes, has also reduced their deformability.[28]The erythrocytes of bovine blood or even porcine blood often used in experiments
are smaller than those of human blood. This influences not only the viscosity
but also the haemolysis level, because the strength of bovine erythrocytes is
higher than that of human erythrocytes. This must be taken into account when
estimating haemolysis in such experiments. On the other hand, the erythrocytes
of females are more sensitive than those of males.[29-32]Table 1 summarizes
some test results of various research groups for the critical shear stress as a
function of the exposure time for laminar flow. The critical shear stress ranges
from 42 to 250 Pa for a very long stress exposure time (>10 minutes) up to
560 Pa for a stress exposure time of 0.00007 seconds. Below these shear stress
loads, no measurable haemolysis should occur. Figure 3 shows the results graphically.
It should be noted that the test results for the critical shear stress were
obtained with different test setups for generating the shear stress and with
different erythrocyte preparations. The results of the respective tests are all
only valid for a one-time stress load on the blood cells. However, the
individual test results show a strong scatter so that no real shear stress limit
below which no haemolysis occurs can be determined.
Table 1.
Critical shear stress in laminar flow, which causes erythrocyte
destruction if the exposure time is exceeded.
Critical shear stress (Pa)
Exposure time (s)
Reference
560
0.0001
Williams et al.[33]
560
0.00007
Williams[25]
500
0.01
Williams[25]
450
0.0006
Williams[25]
450
0.001
Rooney[34]
300
0.007
Morsink et al.[24]
300
120
Nevaril et al.[35]
255
0.7
Schima et al.[36]
255
0.7
Morsink et al.[24]
150-250
No time limit
Sutera[37]
100-200
100
Sutera et al.[38]
170
100
Schima et al.[36]
150
120
Williams[25]
150
120
Hellums and Brown[39]
150
No time limit
Morsink et al.[24]
125
5
Williams[25]
100
25
Williams[25]
88
40
Williams[25]
86
60
Williams[25]
80
0.15
Giersipen et al.[40]
60
300
Williams[25]
59
300
Williams[25]
42
600
Williams[25]
Summary of results of different investigators.
Figure 3.
Critical shear stress in laminar flow for one-time exposure. If the shear
stress is exceeded, then the erythrocytes will be destroyed.
Data from Table
1.
Critical shear stress in laminar flow, which causes erythrocyte
destruction if the exposure time is exceeded.Summary of results of different investigators.Critical shear stress in laminar flow for one-time exposure. If the shear
stress is exceeded, then the erythrocytes will be destroyed.Data from Table
1.A flow is called laminar if the individual particles move in parallel paths. In
turbulent flows, additional velocity components in all three main directions are
superimposed on the main flow. A turbulent flow can occur when the Reynolds
number Re exceeds its critical valuewhere υ is the kinematic viscosity of fluid, d is the diameter of tube and v is
the flow velocity.In circular tubes, the critical Reynolds number is Re = 2,320.[41] In the human body, a flow with such a high Reynolds number occurs only in
the aorta during systole.[6] After the first artificial heart valves were inserted into human hearts,
a flow analysis showed that local hemodynamic conditions downstream of the
valves cause turbulences which lead to an increased haemolysis.[40,42] The ball
valves initially used as heart valves (such as Starr-Edwards caged-ball valve)
were therefore very quickly replaced by single disc valves, the best known of
which was the Björk-Shiley heart valve. Since these valves had permanent
fractures in the metal temples,[43] they are today replaced by double-wing heart valves, such as the St. Jude
Medical Regent bileaflet valve. Nevertheless, there are patients who still live
with ball valves without complaints. The record is about 50 years.[44]The shear stress in turbulent flow is called Reynolds shear stress. It is defined
aswhere ρ is the density of fluid and are the fluctuation velocities in flow.Since the rates of fluctuation velocities in flow speed could only be measured with the use of laser Doppler
anemometry (LDA), the determination of Reynolds shear stress was previously not possible.[45] It should be noted that the Reynolds shear stress is not a real physical
stress, but a pure mathematical quantity resulting from the Navier–Stokes
equation of motion in flows. Experiments show a correlation between Reynolds
shear stress and haemolysis, but this correlation is not yet evidence of
dependency. This is able to explain the partly strong deviations between the
test results.[46] The stress load times of less than 1 ms stated in the test results (Table 2) are also only
pure calculation times, because in reality they cannot be measured. The test
results of Sallam and Hwang[45] alone were corrected several times by other research groups through a
modified calculation.[46,49,50,53] Szwast et al.[54] propose as an alternative to haemolysis risk assessment the determination
of energy dissipation (points where flow energy is lost), which can be
determined by large eddy flow simulation (LES), a special form of CFD. The Food
and Drug Administration (FDA) has now launched an initiative to standardize the
application of CFD to the assessment of haemolysis in blood pumps.[55]
Table 2.
Critical shear stress in turbulent flow (theoretically calculated
Reynolds shear stress), which causes erythrocyte destruction if the
exposure time is exceeded.
Critical shear stress (N/m²)
Exposure time (s)
References
4,000
0.000001
Forstrom[47]
3,000
Very short
Schima et al.[36]
3,000
Very short
Jhun et al.[46]
1,800
0.00001
Tamagawa et al.[48]
800
0.00001
Lu et al.[49]
600
0.00001
Grigioni et al.[50]
517
0.00001
Yen et al.[51]
400-500
Very short
Schima et al.[36]
400
0.0001
Sallam and Hwang[45]
400
100
Schima et al.[36]
250
240
Sutera and Mehrjardi[52]
60
0.000012
Yen et al.[51]
Summary of results of different investigators.
Critical shear stress in turbulent flow (theoretically calculated
Reynolds shear stress), which causes erythrocyte destruction if the
exposure time is exceeded.Summary of results of different investigators.The investigations considered so far all referred to a single exposure of the
erythrocytes. However, this single exposure is not meaningful enough for a
prediction of haemolysis in blood pumps since all blood cells have to pass
through this blood pump many times a day. As a possible solution, Bludszuweit[56] has therefore transferred the proven concept of fatigue strength
according to the Miner hypothesis, known from technical construction mechanics,
to the stressing of blood cells. The idea of calculating the fatigue strength
according to the Miner hypothesis is to calculate with a finite number of load
cycles. Stresses above the fatigue strength are deliberately permitted because
it is no longer assumed that a technical component is safe, but rather that it
is likely to fail. The individual stress loads are subdivided into so-called
load collectives depending on the load level, which are summed up (Figure 4). From the curve
of the fatigue strength of the material from which the component is made, the
permissible number of cycles (number of loads with the stress of this load cycle
collective) can be read, which are still permissible. According to the Miner
hypothesis, a component is considered safe to operate if the sum of all partial
damages is D <1
Figure 4.
Fatigue strength diagram (stress against frequency of strain = number of
loads) as base for the calculation of fatigue strength according to the
Miner hypothesis. The sum of loads (represented by rectangles
n1, n2, n3) has to be beneath the
limit of fatigue strength, that is, a mechanical part (erythrocyte) is
in a safe condition.
where ni is number of exposures with stress σi and
Ni is the maximum admissible number of exposures with stress
σi.[57]Fatigue strength diagram (stress against frequency of strain = number of
loads) as base for the calculation of fatigue strength according to the
Miner hypothesis. The sum of loads (represented by rectangles
n1, n2, n3) has to be beneath the
limit of fatigue strength, that is, a mechanical part (erythrocyte) is
in a safe condition.For the application of the Miner hypothesis, the triaxial stress state acting on
the individual erythrocytes must be converted into a scalar stress value. The
conversion to Mises generally employed in construction technology was used[58]Using a radial pump as an example, the complexity of the influences that have to
be taken into account for predicting damage to erythrocytes was demonstrated. In
addition to the geometry of the pump, the pressure generated by the pump, the
peripheral speed generated by the rotational speed, as well as a variety of
non-mechanical parameters have an effect. These are blood properties such as
density, viscosity, haematocrit and temperature, as well as additional chemical
influences through medication or diet. The interaction of all these factors
leads to blood damage (haemolysis), which should be assessed. Figure 5 illustrates the
relationship between the individual influences for the estimation process.[56]
Figure 5.
Diagram of process to determine haemolysis in a blood pump.
Adapted from Bludszuweit.[56]
Diagram of process to determine haemolysis in a blood pump.Adapted from Bludszuweit.[56]The Cell Damage Index introduced by Gusenbauer et al.[59] is intended to sum up the partial damage of the erythrocytes and thus
predict haemolysis under multiple stress in CFD models of blood pumps. Chan et al.[32] have determined the following haemolysis rates (NIH) in experiments of
human blood at a stress load of more than 15 minutes (Table 3). These data can be used to
compare results from calculations with CFD models.
Table 3.
Haemolysis level (NIH) depending on shear rate after Chan et al.[32]
Shear rate (s−1)
NIH (mg/dL)
2,000
40
4,000
70
6,000
90
8,000
170
NIH: Normal Index of Haemolysis.
Haemolysis level (NIH) depending on shear rate after Chan et al.[32]NIH: Normal Index of Haemolysis.Another limit for haemolysis is the maximum permissible surface tension in the
cell membrane of the erythrocytes. This is indicated between σ = 0.008 N/m[60] and σ = 0.01-0.03 N/m.[61] The cell membrane of the erythrocytes represents an interface, that is, a
separating surface between two different phases (fluid regions). The energy
content of the molecules inside the cell and on the surface of the cell is
different. Curved membranes (interfaces) lead to pressure differences at which
the higher pressure prevails inside the cell. This pressure difference causes an
interfacial tension (surface tension) in the membrane. There are various
theories for calculating the membrane stress. Erythrocytes in a viscous fluid
deform when subjected to hydrodynamic shear stress. The cells assume an
ellipsoidal shape and align themselves parallel to the flow. The cell membrane
of the erythrocytes rotates around the interior of the cell like the caterpillar
track on a tracked vehicle. This exposes the entire cell membrane to the maximum
velocity gradient dvx/dy. The deformation of the cell increases
continuously with increasing shear stress until a limit is reached where the
surface of the ellipsoid is just large enough to enclose the incompressible cell
interior with haemoglobin. If the shear stress increases further, the cell
cannot stretch further, so the membrane is tangentially stretched. If the
critical limit of the membrane tension is exceeded, the cell membrane tears and
the erythrocyte is destroyed. In the calculation model from Williams,[25] the membrane stress results inwhere r is the radius of non-deformed erythrocyte, L is the length of deformed
erythrocyte and B is the breadth of deformed erythrocyte.If a viscoelastic behaviour is assumed for the membrane of the erythrocytes,
which can be illustrated by a mechanical model consisting of two spring and two
viscous damper systems, an equation for the critical membrane stress can be
assumed to bewhere ecritical is the critical extension of erythrocyte, d is the
thickness of membrane, t is the exposure time of shear stress,
Y1 = 27-210 N/cm², Y2 = 11-93 N/cm²,
η1 = 5.0 × 107-5.2 × 108 Pa s and
η2 = 3.7 × 108-3.1 × 109 Pa s.In the calculation model of Richardson,[62] the membrane stress results fromwhere γ is the shear rate, η is the dynamic viscosity of blood plasma, a is the
large ellipsoid radius of erythrocyte, d is the thickness of membrane and χ is
the angle of rotation of erythrocyte.Experiments with human erythrocytes, which were subjected to individual
mechanical loads, have shown that the deformation behaviour is predominantly
elastic. A viscoelastic deformation could only be observed at very high stress
load frequencies. However, such high frequencies do not occur in real blood flows.[63] Thus, the two previous models are not suitable for an estimation of the
membrane stress. Sohrabi and Liu[64] have developed a computer model of an erythrocyte whose behaviour under
simulated stress should also reflect permanent strength. A similar virtual model
is also available from Toninato et al.[65] All models for calculation of haemolysis in CFD are either stress-based
or strain-based. They rely on either a Lagrangian model or the Eulerian
transport equations. In Lagrangian models, haemolysis is calculated along
pathlines of the flow. In the more complex Eulerian approaches, the transport
equations have to be solved within the CFD, using Navier–Stokes and turbulence
equations. The power-law model first invented by Giersiepen et al.[66] also calculates haemolysis as the increase in free haemoglobin in the
blood to the total haemoglobin in the erythrocytes depending on the shear stress
and exposure timewhere ΔHb is the released haemoglobin; Hb is the total haemoglobin in
erythrocytes; τ is the shear stress (scalar); t is the exposure time; and C, α
and β are constantsA comparison of the current CFD models for haemolysis can be found in Yu et al.[67] Since human erythrocytes are rarely used for haemolysis experiments due
to their costly and time-consuming procurement, Pohl et al.[60] have tried to develop artificial erythrocyte models. They consist of
long-chain polymer molecules made of polyacrylamide. Comparative tests with
human and animal blood have proven the suitability of these artificial
erythrocytes for the assessment of haemolysis in fluid flow.
Discussion
Theoretical investigations and practical experiments on haemolysis and on the
strength of erythrocytes have been carried out since 1968. The results were
different and do not give a uniform picture. While at the beginning only laminar
flows were considered, since the work of Sallam and Hwang[45] theoretical Reynold shear stresses have also been the focus of the
investigations. However, the results are evaluated and interpreted quite
differently. The generally cited critical threshold for Reynold shear stress of
400 N/m² has recently been questioned.[46,49,50,51] Since all experiments referred
only to a one-time stress load of the erythrocytes, Bludszuweit[56,58] in particular
dealt with the fatigue strength of the erythrocytes. Various models for the strength
of erythrocytes[25,60] can be considered unrealistic by Puig-de-Morales-Marinkovic et al.’s[63] tests on individual erythrocytes. In the meantime, there are approaches to
estimate the strain on RBCs in CFD simulations using corresponding erythrocyte
models. The NIH has established itself as a tool widely used for assessing
haemolysis. There are relatively few attempts to determine haemolysis levels in
currently used blood pumps. All the short-term VADs examined have a haemolysis level
of >0.01 g/100 L, which is currently considered a tolerable limit.[9,10] However, roller pumps have a
haemolysis level that is 10 times higher.[8] However, these pumps are mainly used in clinical practice for short-term
applications with low flow rates, such as dialysis. For ECMO, they are often been
replaced by centrifugal pumps that are less critical due to haemolysis. The sixth
INTERMACS report with data of 2006-2013 gave an occurrence of haemolysis in those
with long-term VAD in 5% of all patients between 2006 and 2010 and in 9% of all
patients between 2011 and 2013.[68] For long-term VAD, only CFD calculations for the occurring shear stresses
have been published so far. The results were more favourable for the compared
centrifugal pumps than for the axial pump investigated.[12,13] The latest theoretical work
shows how the haemolysis level in axial and centrifugal pumps can be reduced by
optimizing design parameters. A reduction of shear stresses in blood pumps will not
only reduce haemolysis but also damage other blood components such as platelets,
white blood cells or von Willebrand factor. This can help reduce the von Willebrand
syndrome and the occurrence of thrombosis and thus increase the survival rate of the
patients.
Conclusion
Since VADs are essentially rotary pumps, haemolysis has once again become the focus
of research, as the stress on the erythrocytes in these systems, with their partly
turbulent flow, is much higher than in the pulsatile volume displacement pumps. The
problem of haemolysis can be greatly minimized by careful consideration of the pump
design with regard to blood-sparing flow dynamics. The main areas in these pumps
which have to be designed carefully are all small gaps. The use of contactless
bearings like magnetic or hydrodynamic bearings will reduce the risk of haemolysis.
There are patients today who have lived with these VADs for more than 10 years with
almost no problems. Haemolysis generated by VAD should be further reduced,
especially for use as destination therapy over long periods of time.
Authors: James K Kirklin; David C Naftel; Francis D Pagani; Robert L Kormos; Lynne W Stevenson; Elizabeth D Blume; Marissa A Miller; J T Baldwin; J Timothy Baldwin; James B Young Journal: J Heart Lung Transplant Date: 2014-04-21 Impact factor: 10.247
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