Figure 1. Force measurement during microinjection of mouse oocytes. (a) Schematic of the working principle. (b) SEM im-

age of a PDMS cell holding device. (c) Indentation forces deform the mouse oocyte and deflect three supporting posts. Post

deflections were measured by visually tracking the displacements of the post top circles (blue).

CHARACTERIZING ELASTIC AND VISCOELASTIC PROPERTIES OF

YOUNG AND AGED MOUSE OOCYTES USING A PDMS MICRODEVICE Xinyu Liu

1*, Jiayi Shi

2, Zong Zong

2, Roxanne Fernandes

3, Robert F. Casper

3,

Andrea Jurisicova3, Kai-Tak Wan

2, and Yu Sun

3

1McGill University, Canada

2Northeastern University, United States

3University of Toronto, Canada

ABSTRACT

This paper presents the characterization of elastic and viscoelastic properties of young and aged mouse oocytes us-

ing a polydimethylsiloxane (PDMS) microdevice that we previously reported. Nanonewton-level forces applied to the

oocytes are measured by visually tracking the deformation of low-stiffness PDMS supporting posts. In this work,

stress-relaxation test of the oocytes is performed using the microdevice, and a two-step, large-deformation mechanical

model is developed to extract the mechanical properties of the oocytes from the measured force-deformation data. It

was found that the aged oocytes are significantly softer (elastic modulus: 2.2 kPa vs. 5.2 kPa in young oocytes) but more

viscous (relaxation time: 4.1 s vs. 2.3 s in young oocytes).

KEYWORDS: Mechanical characterization; vision-based force measurement; PDMS microdevice; oocyte; aged mouse;

elastic and viscoelastic properties; cell mechanics

INTRODUCTION

Ageing alters various biological functions of cells. For instance, aged females tend to have more fertility problems

due to multiple cellular defects in their oocytes. Assisted reproduction technologies require the reproductive quality of

oocytes to be evaluated for selecting healthy cells for in vitro fertilization (IVF). One possibility is to measure subtle

mechanical differences between healthy and defective oocytes during intracytoplasmic sperm injection (ICSI, a typical

procedure used in the IVF treatment for inserting a sperm cell into an oocyte).

Existing techniques for single-cell mechanical characterization, such as micropipette aspiration [1], AFM indenta-

tion [2], magnetic bead measurement [3], optical tweezers [4], and MEMS-based measurement [5] require sophisti-

cated equipment [1-4] or delicate devices [5], and are difficult to operate simultaneously during ICSI. We recently de-

veloped a PDMS microdevice [6], which can be seamlessly integrated into an ICSI system, and is capable of

measuring cellular forces during ICSI without requiring a separate characterization process. We demonstrated the fea-

sibility of mechanically differentiating healthy and defective mouse oocytes by examining the measured force-

deformation curves. In this paper, we describe the use of this microdevice for performing stress-relaxation test of oocytes

from young (healthy) and aged (defective) mice, and therefore, characterizing elastic and viscoelastic properties of these cells.

EXPERIMENTAL

The measurement of forces applied to an oocyte was realized by visually tracking structural deformations of PDMS posts

that support the oocyte, and subsequently, transforming material deformations into forces. Figure 1(a) illustrates the working

principle of the technique. While a micropipette injects an oocyte inside a device cavity, applied forces are transmitted to low-

stiffness supporting posts. In real time, a sub-pixel computer vision tracking algorithm measures post deflections that are input

into an analytical mechanics model [6] to determine the force exerted on the oocyte. Figure 1(b) shows a scanning electron

978-0-9798064-4-5/µTAS 2011/$20©11CBMS-0001 467 15th International Conference onMiniaturized Systems for Chemistry and Life Sciences

October 2-6, 2011, Seattle, Washington, USA

Figure 2. Stress-relaxation test. (a)

Displacement of the micropipette vs.

time during the stress-relaxation test.

(b) Schematic of the expected cellular

force response vs. time.

Figure 3. A two-step large-deformation model of the oocyte. (a) Schematic diagram of the two-step deformation, including

an initial plate compression (Step 1) and a subsequent flat-punch indentation with the half-space assumption. (b)

A meshed 2D axisymmetric model of the oocyte for finite element analysis. (c) The distribution of displacement (left) and

Von-Mises stress (right) in an oocyte after compression.

microscopy (SEM) picture of the device, fabricated using standard soft lithography

[6]. The supporting posts are 45µm high and 12µm in diameter. Young’s modulus

of the posts was calibrated to be 524.7±22.1kPa (n=5) using nanoindentation. A

computer vision algorithm was developed to track post deflections at 30Hz with a

resolution of 0.5 pixel. The force measurement resolution was 2nN. Figure 1(c)

shows an indented mouse oocyte and deflected posts that are tracked and labeled

by circles.

We conducted stress-relaxation test to quantify the elastic and viscoelastic

properties of oocytes. As shown in Figure 2, the micropipette was controlled to

indent an oocyte at a constant speed of 60 µm/s (Stage I in Figure 2), stopped at a

displacement of 40 µm, and then held the micropipette’s position for 45 s (Stage II

in Figure 2), during which the indentation force, as schematically shown in Figure

2(b), was measured by visually tracking the deflections of the supporting posts.

While holding the micropipette’s position, the local deformation d2 (Figure 1(c)),

increased due to the effect of cell relaxation; however, this relaxation-induced

deformation change can be safely ignored, and the total cell deformation, d=d1+d2,

can be regarded as a constant value since d1>>d2 (Figure 1(c)). The gradual

decrease in measured force indicates viscoelastic properties of the oocyte.

We developed a mechanical model to extract the elastic and viscoelastic

properties of the oocytes. The cell is modeled as an incompressible, isotropic,

axisymmetric and continuum sphere with an elastic modulus, E, and Poisson’s

ratio, γ= 0.5. Due to the large deformation of the oocyte during indentation (maximum deformation is close to 40% of the oo-

cyte diameter), finite element analysis (FEA) does not lead to a converged solution. Therefore, we adopted a two-step defor-

mation approach (Figure 3(a)). Firstly, the oocyte is compressed by a rigid top plate with a force, F, resulting in an ap-

proached distance, y1, and a planar contact circle with radius, c. Secondly, the top plate is then replaced by a central load with

the same magnitude, F, distributed over the micropipette tip. The original planar region is treated as an infinite half continuum

and the central load a cylindrical punch indenter with radius, a, thus forming an indentation dimple with depth, y2. The overall

indentation depth is y= y1+ y2.

The constitutive equation in Step 1, F1(y) where y ≤ y1, was found by FEA with large deformation. Figure 5 shows a 2D

structured element mesh of the oocyte and Figure 6 a typical deformation-stress distribution inside the cell. The constitutive

relation in Step 2, F2(y) where y1 < y ≤ y2, was solved using a classical mechanics model for the problem of indenting an infi-

nite half space by a cylindrical flat-end punch [7]. The viscoelastic properties of the occyte were quantified using the linear

elastic model above. At the stage of cell relaxation (stage-II in Figure 2), the apparent elastic modulus as a function of time is

reflected by the constitutive equation F2(y).

EXPERIMENTAL RESULTS

We performed the stress-relaxation test on eight young oocytes and eight aged oocytes. During the test, the indentation

force and cell deformation were simultaneously recorded. Figure 4 shows the force-deformation data at Stage I (Figure 4(a)),

and the force-time data at Stage II (Figure 4(b)). Most of the curves from young and aged oocytes separate themselves dis-

tinctly with a slight overlap of a few curves. We fitted the force-deformation data at Stage I (Figure 4(a)) into the calculated

constitutive equation, and obtained the oocyte’s elastic modulus (Table 1). During cell relaxation (Stage II), we calculated the

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Figure 4. Experimental results of the stress-relaxation test of young and aged oocytes. (a) Force-deformation data

from the young (blue) and aged (red) oocytes at Stage I. (b) Force-time data from the young (blue) and aged (red) oo-

cytes at Stage II. The black lines are typical curve fits to single sets of experimental data. (c) Example data of appar-

ent elastic modulus as a function of time.

Table 1. Elastic and viscoelastic properties of young (n=8) and aged (n=8) oocytes (*p<0.001).

Elastic property Viscoelastic properties

Oocyte type Elastic modulus

E (kPa)

Instantaneous modulus

E0 (kPa)

Relaxed modulus

ER (kPa)

Relaxation time

τ (s)

Young oocyte 5.2 ± 0.5 5.2 ± 0.5 2.7 ± 0.4 2.3 ± 0.2

Aged oocyte 2.2 ± 0.6* 2.2 ± 0.6* 1.0 ± 0.3* 4.1 ± 0.6*

elastic modulus as a function of time, and fitted the modulus-time data into a standard three-parameter viscoelastic model:

RR Et

EEtE +

−−=

τexp)()( 0 (1)

where E0 is the instantaneous elastic modulus at t = 0, ER is the relaxed modulus at t → ∞, and τ is the relaxation time. The

viscoelastic parameters of the oocytes are summarized in Table 1. We found that the aged oocytes are significantly softer

(with lower modulus values) but more viscous (with longer relaxation time) than the young oocytes.

CONCLUSION

This study represents the first quantitative comparison of the elastic and viscoelastic properties of young and aged mouse

oocytes. The results quantitatively demonstrated that young and aged mouse oocytes are mechanically different, which is at-

tributed to the structural differences of the biomembrane (zona pellucida, or ZP) and cytoskeleton. Our previous study on the

structures of ZP and F-actin from young and aged mouse oocytes has shown that the aged oocytes have significantly lower

density in ZP glycoproteins and F-actin [6]. The experimental data and modeling results in the present work further support

our conclusion that the measured mechanical properties of oocytes could be useful as a mechanical cue to assist the selection

of healthy oocytes for IVF.

REFERENCES

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[3] A.R. Bausch, F. Ziemann, A.A. Boulbitch, K. Jacobson, and E. Sackmann, “Local measurements of viscoelastic parame-

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optical tweezers,” Biophys. J., vol. 68, pp. 988-996, 1995.

[5] Y. Sun, K.T. Wan, K.P. Roberts, J.C. Bischof, and B.J. Nelson, “Mechanical property characterization of mouse zona

pellucida,” IEEE Trans. Nanobiosci., vol. 2, pp. 279-86, 2003.

[6] X.Y. Liu, R. Fernandes, A. Jurisicova, R. F. Casper, and Y. Sun, “In situ mechanical characterization of mouse oocytes

using a cell holding device,” Lab Chip, vol. 10, pp. 2154-61, 2010.

[7] D. Maugis, Contact, Adhesion and Rupture of Elastic Solids. New York, Springer, 2000.

CONTACT

*X.Y. Liu, tel: +1-514-398-1526; xinyu.liu@mcgill.ca

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