MEASUREMENT AND COMPUTATION OF
LYMPHOCYTE DEFORMATION BY USING MICROCHANNEL FLOW
AND THE COMPOUND DROP MODEL
Kazuya Tatsumi, Kyohei Haizumi, Kosuke Sugimoto and Kazuyoshi Nakabe
Kyoto University, JapanABSTRACT
The aim of this study was to examine the physical properties of lymphocytes and to develop a numericalmodel to predict their motion and deformation. Measurements were made using microchannels with acontraction region and numerical computations were carried out using the compound drop model describedin this study, which considers the shear-thinning effects of the cytoplasm and the presence of the nucleus.
The results of computational and experimental efforts to study the non-linear effects of elongational flow on
the lymphocyte deformation showed excellent agreement.
KEYWORDS: Drop model, Lymphocyte characteristics, Deformation, Microchannel
INTRODUCTION
Micro technologies have been used to gain a better understanding of physical aspects such as
properties, motion and deformation of single blood cells during flow, with the aim to provide novel
biological insights that may have potential medical applications. While red blood cells have been the main
subject of these previous studies, little attention has been paid to lymphocytes and other white blood cells.
Further, lymphocyte deformability has mostly been measured using the micropipette aspiration, theaccuracy of which may be low because of wall friction and limited number of samples.
In this study, microchannel flow was used to directly measure the shape of each lymphocyte, quicklyand continuously. The contraction region shown in Figure 1 produced an elongational flow, which
deformed the lymphocyte with time, thus allowing us to measure the viscoelastic properties of the cell.
On the bases of these results, we present a compound drop model which considers the shear-thinningeffects and the presence of the nucleus to precisely match the properties and deformation characteristics.
NUMERICAL MODEL
The present model is based on the drop model which consists of the membrane with zero thickness andthe cytoplasm only (the fluid inside). Surface tension is applied to the membrane. The ND model is themodel with the Newtonian fluid properties applied to the cytoplasm. The shear-thinning drop (STD) model considers the shear-thinning effect of the cytoplasm as Eq. (1).
−β γ (1)µ c = max  µ c 0 1 +  ,6.25 [Pa⋅s]  γc µc0 is the zero-shear viscosity. Note that a lower limit 6.25Pa⋅s is applied to µc in order to prevent asignificant decrease of the viscosity. In addition to this, the STCD model considers the nucleus placed in
the cytoplasm by applying another drop of much higher viscosity.
Table 1 shows the physical properties and parameters of each model. For the coupling the lymphocyte
and the flow field, Immersed Boundary method was employed to the boundary.
EXPERIMENTAL SETUP
Figure 1 shows the schematic of the microchannel together with the dimensions. The contraction partis located at the middle. The microchannel was made of PDMS (poly-dimethylsiloxane) with a coverglass attached to the bottom. The motion and shape of the lymphocytes were measured by a high speed
video camera (Vision Research Co. Inc., Phantom V7.3). The image recoded by the camera had the sizeof 800×600pixels with the resolution of 0.217µm/pixel.
978-0-9798064-7-6/µTAS 2014/$20©14CBMS-0001 1308

18th International Conference on Miniaturized
Systems for Chemistry and Life Sciences
October 26-30, 2014, San Antonio, Texas, USA(a) Schematic of lymphocytes(b) Computational domain(c) Microchannel

Figure 1: Schematic illustrations of the lymphocyte, and contraction region; dimensions are in micrometers
Table 1. Lymphocyte properties of each drop modelParameters
Cell membrane tension τc [µN/m]
Apparent viscosity [Pa⋅s]
Zero shear viscosity µc0 [Pa⋅s]
Shear-thinning parameter β [−]Characteristic shear rate γc [1/s]
Nuclear membrane tension τn [Pa⋅s]
Nucleoplasm viscosity µn [µN/m]10−−−ModelsSTDSTCD
3030−−250
250
0.50.50.05−−−−−

ND
30300250

Jurkat cells (ATCC, CRL-2570) was used as lymphocytes in the experiment. The collected cell wasthen suspended in PBS to which PVP (MW=3.6×105, Nakalai tesque, K-90) was mixed. PVP 8wt% and12wt% solutions were used to obtain solutions of different viscosity.
RESULTS AND DISCUSSION
Figure 4 (a) shows the relationship between deformation index (DI) and flow rate (Q). DI is the value
measured at the inlet of the contraction region, x=0. In the case of ND model, the DI remained constant orgradually decreased with Q. This is due to the fact that under simple elongational flow condition, the deformation rate becomes linear to time when the cell property is viscous dominant. Therefore, although theenlongational force increases with the flow rate, the DI at x=0, which is the integrated value, remained
constant against Q.
On the other hand, the DI of the STD and STCD models increased, corresponding with the experimental measurements. Figure 3 shows the influence of the nucleus and its position on deformation characteristics. The results of STCD model ((a)-(c)) shows that the rigid nucleus suppressed cell deformationand that a slight deviation in its position markedly affected the deformation rate. Further, the shape of thelymphocyte predicted by the computation were in close agreement with the experimental results. As
shown in Fig. 4 (a), the results of STCD model show a better agreement with the experiment than theSTD model particularly in the small Q region. These results indicate the validity of the model and how
important it is to include the nucleus in the computation.
Further analysis of deformation characteristics allowed us to predict the fluid properties of the cytoplasm. Figure 4 shows the relationship between shear rate and viscosity, as measured by the present model. µc is the viscosity considering the shear-thinning effect, and is defined as Eq. (2).
0.74σ ext 0(2)µc =f (γ0 )⋅DI
f is an adjusting function obtained by a preliminary computation for elongational flow, and σexp0 is thestress applied to the cell by the surrounding fluid. Although the present measurement of the viscosity islower than that predicted by the empirically derived formula of Drury et al., the results show a reasonable
match with the distribution.
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(a) ∆xn = −1.5 µm (b) ∆xn = 0 µm(d)Nucleus located at the trailing end(c) ∆xn = 1.5 µm(e)Nucleus located at the leading end

Figure 3: (a)~(c)Effects of the nucleus position on the lymphocyte deformation and flow pattern of the cytoplasm in the computation: the position is moved ±1.5 µm in the streamwise direction. (d) & (e) snapshots ofthe measurements showing identical effects of nucleus.

(a) DI and Q(b) shear rate and visocity
Figure 4: (a) Relationship between deformation index (DI) measured at the contraction region, and flowrate (Q): comparison of the results obtained from the experiment (scattering symbols) and computation using different models (lines), and (b) Relationship between the shear rate and viscosity predicted from thecomputation (filled symbols) and experiments (outlined symbol), and the results obtained by Dury et al.

CONCLUSION
The nucleus showed significant effects on the deformation characteristic of the lymphocyte. STCD
model considering this effect showed a good agreement with the measurement result in the flow rate andDI relationship. Further, by comparing the experimental results with the simulation, the shear-thinning effect of the lymphocyte could be estimated with a simplified model.
ACKNOWLEDGEMENTS

This work was financially supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan.

REFERENCES[1] G. Schade-Kampmamm, A. Hebeisen, M. Hessler, T. and M. D. Berardino, “Flow Cytometry and Cell Sorting of Heterogeneous Microbial Populations: the Importance of Single Cell Analysis,” Cell Proliferation, 41, 830 (2008).
[2] A. Yeung and E. Evans, “Cortical Shell-liquid Core Model for Passive Flow of Liquid-like Spherical Cells into Micropipettes,” Biophysical Journal, 56, 139 (1989).
[3] J. L. Drury and M . Dembo, “Aspiration of Human Neutrophils: Effects of Shear Thinning and Cortical Dissipation,” Biophysical Journal, 81, 3166 (2001).

CONTACT* Kazuya Tatsumi; phone: +81-75-383-3606; tatsumi@me.kyoto-u.ac.jp1310