196
I
nt. J. Medical Engineering and Informatics, Vol. 8, No. 3, 2016
Copyright © 2016 Inderscience Enterprises Ltd.
Cell-free layer analysis in a polydimethysiloxane
microchannel: a global approach
Elmano Pinto, Vera Faustino, Diana Pinho,
Raquel O. Rodrigues, Rui A. Lima and
Ana I. Pereira*
Polytechnic Institute of Bragança, ESTiG/IPB,
C. Sta. Apolónia, 5301-857 Bragança, Portugal
and
ALGORITMI, University of Minho, Guimarães,
Campus Azurém, 4800-058 Guimarães, Portugal
Email: elmano@ipb.pt
Email: verafaustino@ipb.pt
Email: diana@ipb.pt
Email: raquel.rodrigues@ipb.pt
Email: rl@dem.uminho.pt
Email: apereira@ipb.pt
*Corresponding author
Abstract: The cell-free layer (CFL) is a hemodynamic phenomenon that has an
important contribution to the rheological properties of blood flowing in
microvessels. The present work aims to find the closest function describing
RBCs flowing around the cell depleted layer in a polydimethysiloxane (PDMS)
microchannel with a diverging and a converging bifurcation. The flow
behaviour of the CFL was investigated by using a high-speed video microscopy
system where special attention was devoted to its behaviour before the
bifurcation and after the confluence of the microchannel. The numerical data
was first obtained by using a manual tracking plugin and then analysed using
the genetic algorithm approach. The results show that for the majority of the
cases the function that more closely resembles the CFL boundary is the sum of
trigonometric functions.
Keywords: red blood cells; RBCs; cell-free layer; CFL; nonlinear
optimisation; global optimisation.
Reference to this paper should be made as follows: Pinto, E., Faustino, V.,
Pinho, D., Rodrigues, R.O., Lima, R.A. and Pereira, A.I. (2016) ‘Cell-free layer
analysis in a polydimethysiloxane microchannel: a global approach’,
Int. J. Medical Engineering and Informatics, Vol. 8, No. 3, pp.196–209.
Biographical notes: Elmano Pinto received his BS in Biomedical Engineering
from the Polytechnic Institute of Bragança in 2010, and his MS in Biomedical
Technologies from the Polytechnic Institute of Bragança in 2012.
Vera Faustino received her BS in Biomechanics from the Polytechnic Institute
of Leiria in 2009, and her MS in Biomedical Technologies from the
Polytechnic Institute of Bragança in 2012. Currently, she is a PhD student of
Biomedical Engineering at Minho University. Her areas of interest are
microfluidics, microfabrication, separation of cells and particles.
Cell-
f
ree layer analysis in a polydimethysiloxane microchannel 197
Diana Pinho received her BS in Biomedical Engineering from the Polytechnic
Institute of Bragança in 2010, and her MS in Biomedical Technologies from
the Polytechnic Institute of Bragança in 2011. Currently, she is a PhD student
of Mechanical Engineering at Porto University. Her areas of interest are blood
and blood analogues rheology, microfluidics, microfabrication and cell-free
layer development microchannels.
Raquel O. Rodrigues received her BS in Biotechnology Engineering from the
Polytechnic Institute of Bragança in 2007, and her MS in Biomedical
Technologies, in 2012, from the Polytechnic Institute of Bragança. Since
September 2014, she is a PhD student, with a grant of FCT, in Chemical and
Biological Engineering at Porto University. Currently, her work is focused in
the development of magnetic nanoparticles for hyperthermia treatment and also
in the study of their transport in the blood stream using microfluidic devices.
Rui A. Lima is an Assistant Professor at the Department of Mechanical
Engineering, University of Minho (UM), a Research Fellow at the Transport
Phenomena Research Center (CEFT), FEUP, University of Porto and an
external collaborator at the Polytechnic Institute of Bragança (IPB). He
received his PhD in Engineering (2007) from Tohoku University, Japan and
PhD in Biomedical Engineering (equivalence, 2008) from Minho University.
Ana I. Pereira is an Assistant Professor at the Department of Mathematics,
Polytechnic Institute of Bragança, and she is a member of the Algorithm
Research Centre – Minho University. She received her PhD at Minho
University (2006) in Numerical Optimisation area with the thesis ‘A reduction
method to solve semi-infinite programming problems’. She is the author or
co-author of more than 40 journal papers, book chapters and conference
proceedings.
1 Introduction
Blood is a complex fluid composed mainly of suspended red blood cells (RBCs) within
plasma where RBCs are responsible for the supply of oxygen and nutrients to the body
and removal of carbon dioxide and metabolic wastes from tissues. Throughout the years,
several experimental methods were performed in both in vivo (Maeda, 1996; Pries and
Secomb, 1994; Suzuki et al., 1996; Kim et al., 2009) and in vitro (Faustino et al., 2014;
Goldsmith and Turitto, 1986; Lima et al., 2006, 2008, 2009a, 2009b; Rodrigues et al.,
2014) environments, in an attempt to understand the flow behaviour of RBCs in
microchannels and microvessels. These studies have produced significant findings on the
blood rheological properties at a micro-scale level. A hemodynamic phenomenon
observed in both in vivo and in vitro studies is the formation of a marginal cell-free layer
(CFL) at regions adjacent to wall due to the tendency of RBCs to migrate toward the
centre of the microtube (Caro et al., 1978; Garcia et al., 2012; Maeda, 1996). The
existence of a cell depleted layer in microvessels, tend to reduce the apparent viscosity of
blood and by increasing this layer the blood viscosity tend to decrease in both
microchannels and microvessels. Hence, it is important to understand the behaviour of
the CFL in microcirculation as it contributes to the rheological properties of blood
flowing in microvessels, modulates the nitric oxide scavenging effects by RBCs and may
lead to heterogeneous distribution of blood cells in microvascular networks (Fedosov et
198 E. Pinto et al.
al., 2010; Kim et al., 2009). Additionally, several research studies have developed
microfluidic systems able to perform blood separation using the advantage of the CFL
formation in PDMS microchannels with dimensions smaller than 300 µm. Faivre et al.
(2006), Sollier et al. (2010), Yaginuma et al. (2013) and Pinho et al. (2013b) have
demonstrated that the presence of a constriction increases the CFL and as a result they
were able to perform the separation of RBCs from plasma. Therefore, it is also important
to improve our understanding regarding the CFL phenomenon happening in constriction
geometries in order to improve the performance of blood separation microfluidic devices.
Although in vivo and in vitro experiments gives more realistic information on the
flow properties of blood, once validated, physical models and their numerical results are
extremely valuable tools to obtain more insight on the blood rheological properties at a
micro-scale level. Recently due to the advances of the computational techniques and
computing power, several numerical models have been proposed based on a multiphase
approach, in which the blood is considered as a multiphase suspension of deformable
particles and where levels of submodelling for the blood cells behaviour are also taken
into account. Some examples for this type of approach are the boundary element method
(Omori et al., 2011), the immersed boundary method (Bagchi, 2007; Eggleton and Popel,
1998), the lattice Boltzmann method (Dupin et al. 2007) the dissipative particle dynamics
method (Fedosov et al., 2010), the moving particle semi-implicit (MPS) method (Imai
et al., 2010; Tsubota et al., 2006a, 2006b; Gambaruto, 2015) and spring-network model
based on the minimum energy concept (Lima et al., 2009a, 2009b; Nakamura et al.,
2013). Reviews on these numerical methods can be found at Liu et al. (2006), Yamaguchi
et al. (2006) and Lima et al. (2012). Although multiphase approaches are promising
methods, it is still extremely complex to consider the CFL in their numerical models, so
optimisation can be also an important field of study to help in the development of
numerical simulations. In recent years, optimisation algorithms have become increasingly
robust and as a result several researchers have applied this methodology to study
phenomena happening in microfluidic devices. For instance, Bento et al. (2015) have
measured the CFL in a network containing multiple bifurcations and confluences and
they have shown that the function that best fits the CFL was the sum of trigonometric
functions.
The present study tracks RBCs flowing around the CFL and calculates the most
suitable function by using global optimisation technique. The measurements were
performed in a polydimethysiloxane (PDMS) microchannel with a diverging and a
converging bifurcation and all images were obtained by means of a high-speed video
microscopy system.
The paper is organised as follows. Second section shows the materials used in this
work and the methods that were applied in this study. The third section presents the
numerical results and discussion. The last section presents the main conclusions and
some future directions.
2 Materials and methods
2.1 Microchannel geometry
Microchannels were initially developed with a CAD software, where the geometries were
selected taking into account a previous study about the blood flowing through
Cell-
f
ree layer analysis in a polydimethysiloxane microchannel 199
microchannels with bifurcations and confluences fabricated by a soft lithography
technique (Leble et al., 2011). In this study, the parent microchannels have a width of
300, 500 and 1,000 µm and the two branches of the bifurcation and confluence
correspond to 50% of the parent microchannel width. Figure 1 shows the configuration of
the network and the regions where the CFL was measured, where RA and RB are the
upper regions of the microchannel and RC and RD are the lower regions.
Figure 1 Schematic representation of the microchannel geometry and location of the sections
where the images were collected and the CFL was measured
Notes: 1 – Region A (R
A(width)
); 2 – Region B (R
B(width)
); 3 – Region C (R
C(width)
) and
4 – Region D (R
D(width)
).
This geometry was used to fabricate the vinyl master moulds by using a soft xurography
technique (Pinto et al., 2015). The moulds were used for the production of PDMS
microchannels. Briefly, the PDMS was obtained by mixing a curing agent (10:1 ratio)
with PDMS prepolymer. By using a spin coater, a residual amount of PDMS with a ratio
20:1 was dispersed on a slide glass. The PDMS was cured in an oven at 80°C for
20 minutes. Then, by using a blade the microchannels were cutted off and the inlet/outlet
holes were done by using a fluid dispensing tip. Finally, to have a strong adhesion of the
materials, the device was placed in the oven at 80°C for 24 hours. More detailed
information about this process can be found at Pinto et al. (2015).
2.2 Working fluids and experimental set-up
The fabricated microchannels were used to study in vitro blood flow with Dextran 40
containing 10% of RBCs. The blood was collected from a healthy sheep and heparin was
added to prevent clotting. Additionally, the cells were separated from blood by
centrifugation.
A syringe pump (Harvard Apparatus PHD ULTRATM) was used to control the flow
rate of the working fluid. To visualise and measure the flow we have used an inverted
microscope (IX71, Olympus) combined with a high-speed camera (i-SPEED LT).
Figure 2 shows the experimental apparatus used to control the flow and to visualise the
CFL within the microchannels. The microfluidic device containing the microchannels
was placed on the stage of the inverted microscope and a pressure-driven flow was kept
constant by means of a syringe pump. All images have a resolution of 800 × 600 pixels
and were recorded at a frame rate of 200 frames/s.
200 E. Pinto et al.
Figure 2 Experimental apparatus to control and visualise the flow in microchannels produced by
xurography (see online version for colours)
2.3 Image analysis
A manual tracking plugin (MTrackJ), of the image analysis software Image J (NIH), was
used to track individual RBC flowing around the boundary of the RBCs core. By using
MTrackJ plugin, the centroid of the selected RBC was automatically computed. After
obtaining x and y coordinates of the RBC centroids, the data were exported for the
determination of each individual RBC trajectory (Lima et al., 2008; Pinho et al., 2013a).
Figure 3 shows a trajectory of a RBC flowing around the boundary region between the
CFL and RBCs core.
Figure 3 A trajectory of a RBC flowing around the boundary region between the CFL and RBCs
core (see online version for colours)