This numerical model assesses white blood cell (WBC) damage caused by shear flow within ventricular assist devices (VADs). The model relates WBC deformation and surface area to tensor theory and fluid mechanics. Analysis of two key parameters showed the model is sensitive to changes in parameters, validating the model. Under three simplified cases, critical values for circulatory volume and relaxation time were identified. Further experiments should consider complex stress flows rather than simple shearing.

1. Academic Year 2015/16
Xianqi Yuan Supervisor: Dr Katharine Fraser
Numerical Modelling of White
Blood Cell Damage
Final Year Engineering Project of B.Eng.
Mechanical Engineering
Conclusions
This numerical model constructed to assess the white blood cell damage done by the
shear flow within the VAD pump body provides with the direct relationships on the
deformation and surface area model. The model relies mainly on the tensor theory
and fluid mechanics.
The change in two dominant parameters in the model suggest significant
characteristics on the sensitivity of the model to the parameters, the parameters’
sensitivity contributes to the validity of the model.
Loops under three types of simplified case, the critical value for the circulatory volume
and relaxation time were found. The further experimental device should be considered
on the application of complex stress flow rather than merely under simple shearing.
Introduction
This project focused on the white blood cell (WBC) damage done by ventricular assist device (VAD) within corresponding patients’ body. The numerical model is constructed
to assess the damage on white blood cells on a basis of strain tensor theory. The model analogizes the existing numerical model on damage prediction for red blood cells
(RBCs). Data were collected from the experimental analysis done to the device under the simulation of computational fluid dynamics (CFD) analysis. The outcome provides a
numerical modelling method on white blood cell damage mode by selecting viable parameters to define the damage.
Background
As an essential component in human immune system, white blood cells
exist mainly in blood and lymphatic system. Leukocytes are fragile when
being exposed under artificial mechanical environment. Clinically,
ventricular assist device implants have been applied to patients with
heart failure for many years, which have been proved in achieving the
prolongation of patients’ life. They can easily cause side effects by
damaging blood cells. Most previous studies focused on the damage
done to RBCs and platelets, but the damage done to WBCs has been
seldom assessed, though it can further weaken the immune system, due
to which patients would suffer immunologic derangement.
Results
Different deformation mode can be seen under different conditions.
Original normal droplet, also the proportional shape of the deformed droplet under
uniaxial extensional stress. The stress is exerted on two poles.
Orients at 45°. The simple shear stress expresses the shearing effects.
The deformation is biaxial due to the shear flow is biaxial. Under both the pole-
pole direction and the normal direction shown in the figure.
The damage done to blood cells under the same equivalent stress should rank top
down as planar hyperbolic stress, uniaxial extensional stress and simple shear
stress
Experimental test data indicate that as increasing the rotation speed of the pump,
which is to increase the magnitude of the shear stress the damage appears to be
accumulated with the loops.
0
10
20
30
40
5 120 240 360
Foldchangefrombaseline
Time (min)
1L/min, 2200
rpm (n=4)
5L/min, 2200
rpm (n=4)
5 L/min 3300
rpm (n=5)
(Chan 2013)
Results
A certain proportion of blood cells re-entre into the pump with an insufficient recovered
form.
Total Volume
of the Loop (L)
Percentage of
D<0.1
Percentage of
D<0.01
Percentage of
D<0.0001
0.25 90.8% 84.3% 58.9%
0.5 94.5% 91.1% 87.6%
Table 1 Percentage of Deformation with Different Loop Volumes
Method
Euler method: step forward at each time to compute further on the path line.
Lagrangian fluid computation method: The WBC deformation is computed along path lines;
focuses on the particle within the flow field, and regards the motion as the function of its
coordinates and time.
Blood cells regarded as neutrally buoyant liquid droplet in general flow, the oil drop in viscous flow
model RBCs under shear stress condition.
Oil drop: incompressible to keep a constant volume; the shape should remain ellipsoidal at all time.