# Biomechanical Analysis of Breast Cancer Cells:
A Comparative Study of Invasive and Non-Invasive Cell Lines Using Digital
Holographic Microscopy

1st Hasan Berkay ABDIOGLU1, 2nd Yagmur ISIK1, 3rd Merve SEVGI2, 4th Ufuk
Gorkem KIRABALI1,
5th Caner KARACA3, 6th Yunus Emre MERT1, 7th Defne DEDEHAYIR4, 8th Berke Tuna
BOSTANCI5,
9th Yasemin BASBINAR3, 10th Huseyin UVET1

1Department of Mechatronics Engineering, Yildiz Technical University,
Istanbul, Turkey
2Department of Bioengineering, Yildiz Technical University, Istanbul, Turkey
3Department of Translational Oncology, Dokuz Eylul University, Izmir, Turkey
4Hisar School, Istanbul, Turkey 5The Sezin School, Istanbul, Turkey

###### Abstract

This study investigates the biomechanical properties of breast cancer cells,
focusing on the invasive MDA-MB-231 and non-invasive MCF-7 cell lines, using
phase-shifting digital holographic microscopy and an acousto-holographic
system for non-invasive strain measurement. Findings reveal higher strain
values in MDA-MB-231 cells, indicative of their aggressive, metastatic nature,
compared to lower strain values in MCF-7 cells. This variance in mechanical
properties, potentially linked to distinct metabolic states and responses to
external stimuli, underscores the role of cellular mechanics in cancer
progression. The study advances understanding of breast cancer cell mechanics,
highlighting biomechanical analysis as a crucial tool in cancer research and
potential therapeutic interventions.

###### Index Terms:

Breast Cancer, Biomechanics, Cell Strain, MDA-MB-231, MCF-7, Digital
Holographic Microscopy, Metastasis, Cellular Mechanics.

##  I Introduction

Breast cancer is a malignancy characterized by the abnormal transformation and
uncontrolled proliferation of cells constituting breast tissue [42]. It ranks
among the most prevalent cancer types globally. Breast cancer is prevalent
among women, though it can also occur, albeit rarely, in men [42]. The higher
incidence of breast cancer in women compared to men can be attributed to
several factors, including the continuous exposure of breast tissue to
hormones like estrogen and progesterone, which predispose it to growth [34].
The frequency of breast cancer occurrence in an individual is also influenced
by hormonal factors, genetic predisposition, and lifestyle choices [34].
Breast cancer is categorized into three main types: noninvasive (in situ),
invasive and metastatic breast cancers. Invasive breast cancer has the
potential to metastasize, whereas noninvasive cancer does not exhibit
spreading characteristics [26]. Within the noninvasive category, there are two
subtypes: ductal carcinoma in situ and lobular carcinoma in situ. Lobular
carcinoma in situ involves an increase in lobular cells within the breast
tissue and can elevate the risk of breast cancer [35]. In such cases, close
monitoring and prophylactic treatments, including surgical interventions, may
be considered. The diagnosis and treatment of breast cancer are tailored to
the patient’s individual factors. Early detection plays a crucial role in the
effective treatment of this cancer type [27]. Ductal carcinoma in situ
typically does not present symptoms during examination and possesses the
potential to transition from normal to cancerous cells. It is commonly marked
with wires and radioactive substances during surgical procedures for removal
[39]. Energy metabolism in cancer cells adapts during progression [28, 41].
These metabolic alterations encourage cellular behavior from mitosis to
metastasis. The infamous Warburg effect (aerobic glycolysis) defines that
proliferative cells often run glycolysis and its branched pathways to support
progression, even when oxygen is sufficient [41]. However, not all cancer
cells reorient their metabolism through the Warburg effect. Several mutations
and epigenetic modifications alter oxidative phosphorylation to take advantage
of the Pasteur phenotype [31]. Both Warburg and Pasteur energitic subtypes
could robust some metastatic pathways and phenotypes, but in different ways
[33, 30, 31]. Triple-negative MDA-MB-231 and estrogen-responsive MCF-7 cell
lines adapt their energy metabolism differently. While MCF-7 is a Pasteur
subtype, the more aggressive MDA-MB-231 has a Warburg phenotype. Recent
studies indicate that their metabolic state also influences their metastatic
behavior. Normalization of energy metabolism by site-directed expression of
pyruvate dehydrogenase enzyme provide MDA-MB-231 susceptible to anoikis and
inhibits its metastatic behavior [30]. The energetic subtype may also
influence homing. A recent study suggests that calcification of the OXPHOS
dominant cell line MCF-7 induces TGF-$\beta$ dependent bone metastasis [29].
These different metastatic routes could be related to various cell stiffness
criteria due to cell cytoskeleton reorganization, ROS generation, and membrane
lipid composition [24, 37, 38]. The cytoskeleton, comprising actin filaments,
microtubules, and intermediate filaments, significantly influences cellular
mechanics [36]. Alterations in these cytoskeletal fibers directly impact cell
mechanics. Cellular mechanics, which are crucial in understanding various
cellular functions such as cell migration, adhesion, and division, undergo
significant changes during severe diseases like cancer [32, 36]. One key
mechanical property, cellular strain, is closely linked to cell motility [33].
Cancer cells exhibit higher strain values compared to normal cells, aligning
with their need for movement between tissues [44]. Strain values vary among
cancer cells with different levels of aggressiveness. For instance, MCF-7
cells, which have a lower invasive capability, show different strain values
compared to the highly invasive MDA-MB-231 cancer cells, with MDA-MB-231
exhibiting higher strain [43]. Cell strain, a fundamental parameter in
understanding cellular biomechanics, has been measured using various
techniques for a long time. Although Atomic Force Microscopy (AFM) is
considered the gold standard, its limitations include low resolution, time-
consuming measurements, and an invasive nature. In recent years, digital
holographic microscopy has emerged as a prevalent method in cell imaging.
Varol et al. developed an acousto-holographic system, demonstrating that cell
strain measurements can be conducted in a non-invasive and label-free manner.
In this study, the acoustic wave frequency used by Varol et al. was reduced,
and a higher fps (frames per second) was achieved, thereby increasing the
sample size. This adjustment allows for more detailed and accurate
measurements of cell strain, enhancing the understanding of cellular
biomechanics, particularly in the context of cancer cell behavior and
properties.

##  II MATERIALS AND METHODS

###  II-A Materials

For the invasive breast cancer cell line MDA-MB-231 (ATCC, HTB-22) and the
non-invasive breast cancer cell line MCF-7, DMEM-F12 (Gibco, 21331020)
supplemented with 10% fetal bovine serum and 1% Penicillin-Streptomycin will
be used. The Sylgard 184 Silicone Elastomer Kit (Dow) will be employed for the
production of PDMS chips.

###  II-B Cell Culture

Cells will be passaged when they reach 70-80% confluency. For passaging, cells
will be washed with 2 mL of sterile Phosphate Buffered Saline (PBS) (pH 7.4)
and then treated with 500 $\mu$l of 0.25% Trypsin/EDTA solution. The flask
will be incubated for 5 minutes at 37°C in a 5% CO2 incubator (Thermo
Scientific, Germany). Detached cells will be transferred to a falcon tube and
centrifuged at 1000 rpm for 5 minutes. After centrifugation, the supernatant
will be discarded, and 1 $\mu$l of the cell pellet will be mixed with 49
$\mu$l of trypan blue and added to a Thoma slide for counting under a
microscope. Cell seeding will be performed in each flask to achieve a density
of $1.5×10^{5}$ cells. Seeded cells will be maintained in a 37°C incubator
with 5% CO2 [25].

###  II-C Production of Transducer-Integrated PDMS Chip

The design of the microfluidic chip and channels will be done using 3D design
software. The microfluidic device will be fabricated using
Poly(dimethylsiloxane) (PDMS) with dimensions of 40 mm × 24 mm × 5 mm using UV
lithography. The process includes cleaning of silicon wafers, spinning of SU-8
coating, exposure to UV, and development in Propylene glycol methyl ether
acetate (PGMEA). The microfluidic chip will have a channel designed as 10 mm x
10 mm square for cell seeding. For chip production, silicone elastomer and
curing agent will be mixed in a specified ratio and poured into a mold. To
remove bubbles, the PDMS will be left in a desiccator and then cured at 80°C
for 2 hours. The cured PDMS will be cut from the main mold using a scalpel.
Finally, the PDMS will be exposed to oxygen plasma at 4 mbar for 120 seconds
for bonding with glass.

###  II-D Cell Seeding on Chips

MCF-7 and MDA-MB-231 cells, counted using trypan blue on a Thoma slide after
trypsinization, will be seeded onto the transducer-integrated PDMS chips. The
seeded cells will be incubated in their respective media for 48 hours in a
37°C incubator with 5% CO2.

###  II-E Experimental Setup

In this study, we employed a highly specialized experimental setup centered
around a Mach-Zehnder interferometer with phase-shifting capabilities to
facilitate holographic imaging. We used a consistent light source, a 671 nm,
10 mW DPSSL laser. The system divided incident light into two beams: a
reference beam and an object beam, with phase modulation achieved in the
reference beam through a precision PZT actuator (New Focus, Picomotor 8302). A
microfluidic chamber containing cell culture (or reference microbeads) is
placed in the other arm of the interferometer, and a PZT transducer
(SMBA25W7T05PV, Steiner Martins Inc.) provides acoustic stimulation at
approximately 10 Hz frequency. The light fields are captured by microscope
objective lenses (Newport M-20X, 20x magnification) and recombined at the
second beam splitter of the interferometer after passing through the phase-
shifting device and the microfluidic chamber figure 1. To ensure the system’s
accuracy, meticulous adjustments of mirror angles and beam splitter positions
were made, ensuring optimal interference pattern visibility. Basic calibration
involved the introduction of a matte surface in front of a CMOS camera to
visualize interference patterns, creating distinct brightness differences
between object and reference beams. Further calibration precision was achieved
by aligning the interference pattern’s center onto the camera. Micron-level
focusing of cells was achieved using the Newport HXP50 Hexapod system. For
image processing, interferograms were processed using the least squares
method, allowing for robust handling of potential intensity variations
resulting from diverse measurement methods and conditions. The core of our
research involved the generation of controlled acoustic vibrations applied to
cell surfaces, causing membrane vibrations proportional to the applied force.
Phase-shifting digital holographic microscopy was employed for precise
quantification of cell membrane displacement and elasticity, facilitated by
continuous interferogram acquisition. To subject cells to controlled
vibrations, a specialized acoustic transducer operating at 10 Hz with
thickness modulation was utilized. This systematic process generated a
comprehensive set of interferograms with varying phases, enabling a detailed
characterization of cell responses during vibration [40].

###  II-F Processing of Images

Interferograms are fundamentally photographic images that incorporate optical
interference. Each pixel in an interferogram represents the intensity of the
light beam. This intensity can be mathematically expressed by the
electromagnetic wave equation as
$I^{\prime}+I^{\prime\prime}cos(\phi(x,y)+\delta(t))$. This formula
encompasses three distinct unknown variables. To solve for these unknowns, a
minimum of three equations is required. However, due to potential
discrepancies in the measured intensities arising from the measurement method,
the instrumentation used, and the specific location of measurement, processing
more than three interferograms using the numerical method of least squares can
yield results that are closer to the actual values. Variations in the phase
change intervals will also lead to modifications in the equation that
determines the phase value. The criteria for the least squares method can be
articulated as $\frac{\delta S_{j}}{\delta a_{j}}=0,\quad\frac{\delta
S_{j}}{\delta b_{j}}=0,\quad\frac{\delta S_{j}}{\delta c_{j}}=0.$ This can be
further simplified to $X_{j}=A^{-1}/B_{j}$, where:

$\mathbf{X}_{j}=\begin{pmatrix}{a_{j},b_{j},c_{j}}\end{pmatrix}^{T}$ (1)

$\left[\begin{array}[]{lll}M&\sum\limits_{i=1}^{M}\cos(\delta_{i})&\sum\limits_{i=1}^{M}\sin(\delta_{i})\\\
\sum\limits_{i=1}^{M}\cos(\delta_{i})&\sum\limits_{i=1}^{M}\cos^{2}(\delta_{i})&\sum\limits_{i=1}^{M}\cos(\delta_{i})\sin(\delta_{i})\\\
\sum\limits_{i=1}^{M}\sin(\delta_{i})&\sum\limits_{i=1}^{M}\sin(\delta_{i})\cos(\delta_{i})&\sum\limits_{i=1}^{M}\sin^{2}(\delta_{i})\end{array}\right]$
(2)

$\mathbf{B}_{j}=\begin{pmatrix}\sum_{i=1}^{M}I_{ij}\;\;\sum_{i=1}^{M}I_{ij}\cos(\delta_{i})\;\;\sum_{i=1}^{M}I_{ij}\end{pmatrix}$
(3)

Figure 1: Schematic of the Mach-Zehnder Interferometry Setup. The beam from a
light source is split into two by a beam splitter, with one beam designated as
the reference beam and the other as the object beam. The phase of the
reference beam is shifted using a PZT (lead zirconate titanate) actuator,
creating a phase shift in the interference pattern. An objective lens is used
to magnify both the object and reference beams equally. After the beams
interfere with each other, the resulting pattern is captured by a CMOS
(Complementary Metal-Oxide-Semiconductor) camera.

$\\\ \frac{\delta S_{j}}{\delta a_{j}}=0,\quad\frac{\delta S_{j}}{\delta
b_{j}}=0,\quad\frac{\delta S_{j}}{\delta c_{j}}=0.$ represent the summation
conditions for the least squares criteria. ” $X_{j}=A^{-1}/B_{j}$” denotes the
solution for the unknowns in the system, with $A^{-1}$ representing the
inverse of matrix A, and $Bj$ being a vector in the system of equations. Using
these equations, the values of $a_{j}$ $b_{j}$ and $c_{j}$ can be calculated.
Consequently, the phase value for each pixel can be given by
$\varphi_{j}=arctan((-c_{j})/b_{j})$ . Since the obtained phase values are
based on the arctangent function, divergence is expected at certain values
(multiples of $pi/2$). This divergence can disrupt the continuity of the phase
map. To ensure continuity, phase unwrapping (Phase Unwrapping) should be
performed. Ultimately, the optical path difference (OPD) can be calculated
using the phase map obtained, with the help of the following formula [23]:

$OPD=\frac{\lambda}{2\pi}\\\ \varphi_{j}$ (4)

Here, $\lambda$ represents the wavelength of the light used in the
interferogram, and $\phi_{j}$ is the unwrapped phase value at each pixel. The
optical path difference (OPD) provides crucial information about the optical
properties of the material or the system under investigation.

###  II-G Reconstruction of Strain Maps

In the setup designed for hardness measurement, a wave generator (Siglent
SDG6032X) is used to produce waves. The generated signals are then amplified
using a voltage amplifier (Falco Systems, WMA-300) before being sent to a PZT
(lead zirconate titanate) transducer (Steminc SMBA25W73T05PV) for conversion
into acoustic waves. The generated acoustic waves induce acoustic pressure on
the surface of cells, causing the cell membrane to oscillate in proportion to
the acoustic force. The resulting cell membrane oscillations are observed
using a high-speed camera (CMOS Camera). From these observations, the
displacement of the cell membrane is measured. The strain value of the cell is
determined by calculating the ratio of displacement to the original depth.
This method leverages the principles of acoustics and mechanics to non-
invasively probe the mechanical properties of cells. By analyzing the cell’s
response to the induced acoustic waves, valuable insights into its mechanical
properties, such as strain, can be obtained. This information is crucial in
various fields, including biomedical research and material science, where
understanding the mechanical properties of cells is essential. In this setup,
the vibration of the cell membrane is measured using phase-shift digital
holographic microscopy with a Mach-Zehnder arrangement. This method aims to
continuously obtain interferograms. The different phases of the obtained
interferograms enable the 3D modeling of the cell. To induce vibrations in the
cells, a 10 Hz thickness-mode acoustic transducer is used. The vibration
motion of the transducer generates acoustic waves on PDMS chips, causing the
cells to vibrate. It is assumed that the cell vibrates with a periodic
stimulus at a frequency of $f_{0}$. To capture interferograms at desired
points during the vibration period, the camera is triggered using a periodic
frequency signal of $f_{0}/(1+f_{0}/\delta t)$. After $\delta t/f_{0}$ cycles,
a series of interferograms is obtained for time shifts of $k\delta t$ for
$k=0,1,\ldots,n$ ($n\delta t=\frac{1}{f_{0}}$). This process is repeated for
many time intervals, each yielding a series of interferograms at different
phases [40]. To determine cell strain, a mechanical model that can describe
the mechanical deformation induced on the cell membrane by the vibration of
the piezoelectric transducer is assumed. Strain is defined as relative
deformation, compared to a reference position configuration. For modeling the
small-scale deformations in the membranes of adherent cells, this formula can
be adapted to measure the displacement of the cell membrane due to acoustic
stimulilation. Cell membrane is subjected to a force that causes it to deform,
the strain would be the ratio of the displacement of the membrane (how much it
stretches or compresses) to its original, unstressed length.

$\epsilon=\frac{\Delta L}{L_{0}}$ (5)

In cell biomechanics, strain $\epsilon$ is calculated as $=\frac{\Delta
L}{L_{0}}$ , where $\Delta L$ is the cell membrane’s displacement and $L_{0}$
is its original length. This formula measures how much the membrane stretches
or compresses in response to external forces, providing insights into cellular
responses to acoustic stimuli.

Figure 2: This figure illustrates the distribution of strain values $\epsilon$
in two distinct breast cancer cell lines: MDA-MB-231 (Panel A) and MCF-7
(Panel B). Each cell within the panels represents a specific strain
measurement from individual experiments. The MDA-MB-231 cells, show a range of
strain values, with some cells exhibiting notably higher strain, indicative of
their metastatic potential. In contrast, the MCF-7 cells, display generally
lower strain values.

##  III result

In this study, we conducted a total of 14 separate experiments for each of the
breast cancer cell lines, MDA-MB-231 and MCF-7. The outcomes of these
experiments are detailed in Table 1. figure 2-a presents the strain
measurements of MDA-MB-231 cells, captured through our holographic imaging
setup. These measurements represent the strain values for fourteen distinct
cells over the observation period. In a similar vein, the strain measurements
for MCF-7 cells are depicted in figure 2-b.

TABLE I: Comparative Strain Measurements of Breast Cancer Cell Lines MDA-MB-231 and MCF-7. In this table displays the strain values for each of the 14 experiments conducted on the MDA-MB-231 and MCF-7 breast cancer cell lines. The values are indicative of the biomechanical properties of these cells, with MDA-MB-231 representing a more aggressive phenotype and MCF-7 a less invasive one. No | MDA | MCF | No | MDA | MCF
---|---|---|---|---|---
1 | 0.02321 | 0.01368 | 8 | 0.02755 | 0.01833
2 | 0.02347 | 0.01382 | 9 | 0.02799 | 0.02108
3 | 0.02364 | 0.01453 | 10 | 0.03095 | 0.0212
4 | 0.02389 | 0.01524 | 11 | 0.03348 | 0.02146
5 | 0.02461 | 0.01708 | 12 | 0.03398 | 0.02176
6 | 0.02522 | 0.01732 | 13 | 0.03408 | 0.02517
7 | 0.02568 | 0.01798 | 14 | 0.03612 | 0.02872

Furthermore, the calculated parameters of the strain model are illustrated in
figure 3. An intriguing observation from these results is the apparent
correlation between strain values and the potential for metastasis. The data
indicates that the mean strain value for the MDA-MB-231 cells, which are known
for their more aggressive and metastatic nature, was found to be 0.02813357.
In contrast, the mean strain for the less invasive MCF-7 cells was lower,
recorded at 0.01909786. This variance in strain values between the two cell
lines underscores the potential link between cellular biomechanical properties
and their metastatic capabilities.

Figure 3: This figure presents a comparative analysis of the strain values for
the MDA-MB-231 and MCF-7 breast cancer cell lines. It highlights the average
biomechanical strain exhibited by each cell line, illustrating the distinct
mechanical properties associated with their differing levels of invasiveness
and metastatic potential.

##  IV DISCUSSION

This study has provided significant insights into the biomechanical properties
of breast cancer cells, specifically focusing on the invasive MDA-MB-231 and
the non-invasive MCF-7 cell lines. Through the innovative use of phase-
shifting digital holographic microscopy and a specialized acousto-holographic
system, we have been able to non-invasively measure and compare the strain
values of these two cell lines under acoustic stimulation. Our findings reveal
that the MDA-MB-231 cells, characterized by a Warburg phenotype, exhibit
higher strain values compared to the MCF-7 cells, which align with a Pasteur
subtype. Specifically, the strain values for MDA-MB-231 ranged from 0.02321 to
0.03612, while those for MCF-7 were between 0.01368 and 0.02872. This
difference in strain values is indicative of the distinct mechanical
properties and possibly the metastatic potential of these cell lines. The
higher strain values in MDA-MB-231 cells correlate with their more aggressive
nature and higher invasive capabilities. The study underscores the importance
of cellular biomechanics in cancer research. The differences in strain values
between the two cell lines could be linked to their distinct metabolic states
and their response to external stimuli, such as acoustic waves. This suggests
that cellular mechanics, alongside genetic and molecular profiles, play a
crucial role in the progression and behavior of cancer cells. In conclusion,
our study not only advances the understanding of the mechanical properties of
breast cancer cells but also highlights the potential of biomechanical
analysis as a tool in cancer research and therapy. The differences in strain
values between MDA-MB-231 and MCF-7 cells provide valuable insights into their
respective mechanical properties and behaviors, which could be pivotal in
developing targeted treatments and interventions for breast cancer.

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