Abstract

The artificial neural network (ANN) based models have shown the potential to provide alternate data-driven solutions in disease diagnostics, cell sorting and overcoming AFM-related limitations. Hertzian model-based prediction of mechanical properties of biological cells, although most widely used, has shown to have limited potential in determining constitutive parameters of cells of uneven shape and nonlinear nature of force-indentation curves in AFM-based cell nano-indentation. We report a new artificial neural network-aided approach, which takes into account, the variation in cell shapes and their effect on the predictions in cell mechanophenotyping. We have developed an artificial neural network (ANN) model which could predict the mechanical properties of biological cells by utilizing the force versus indentation curve of AFM. For cells with 1 μm contact length (platelets), we obtained a recall of 0.97 ± 0.03 and 0.99 ± 0.0 for cells with hyperelastic and linear elastic constitutive properties respectively with a prediction error of less than 10%. Also, for cells with 6–8 μm contact length (red blood cells), we obtained the recall of 0.975 in predicting mechanical properties with less than 15% error. We envisage that the developed technique can be used for better estimation of cells' constitutive parameters by incorporating cell topography into account.

References

1.
di Carlo
,
D.
,
2012
, “
A Mechanical Biomarker of Cell State in Medicine
,”
J. Lab. Autom.
,
17
(
1
), pp.
32
42
.10.1177/2211068211431630
2.
Suresh
,
S.
,
2007
, “
Biomechanics and Biophysics of Cancer Cells
,”
Acta Biomater.
,
3
(
4
), pp.
413
438
.10.1016/j.actbio.2007.04.002
3.
Xu
,
W.
,
Mezencev
,
R.
,
Kim
,
B.
,
Wang
,
L.
,
McDonald
,
J.
, and
Sulchek
,
T.
,
2012
, “
Cell Stiffness is a Biomarker of the Metastatic Potential of Ovarian Cancer Cells
,”
PLoS One
,
7
(
10
), p.
e46609
.10.1371/journal.pone.0046609
4.
Nematbakhsh
,
Y.
,
Pang
,
K. T.
, and
Lim
,
C. T.
,
2017
, “
Correlating the Viscoelasticity of Breast Cancer Cells With Their Malignancy
,”
Convergent Sci. Phys. Oncol.
,
3
(
3
), p.
034003
.10.1088/2057-1739/aa7ffb
5.
Maciaszek
,
J. L.
, and
Lykotrafitis
,
G.
,
2011
, “
Sickle Cell Trait Human Erythrocytes Are Significantly Stiffer Than Normal
,”
J. Biomech.
,
44
(
4
), pp.
657
661
.10.1016/j.jbiomech.2010.11.008
6.
Raj
,
A.
, and
Sen
,
A. K.
,
2018
, “
Microfluidic Sensors for Mechanophenotyping of Biological Cells
,”
Energy, Environ., Sustainability
, pp.
389
408
.10.1007/978-981-10-7751-7
7.
González-Bermúdez
,
B.
,
Guinea
,
G. V.
, and
Plaza
,
G. R.
,
2019
, “
Advances in Micropipette Aspiration: Applications in Cell Biomechanics, Models, and Extended Studies
,”
Biophys. J.
,
116
(
4
), pp.
587
594
.10.1016/j.bpj.2019.01.004
8.
Lee
,
L. M.
, and
Liu
,
A. P.
,
2015
, “
The Application of Micropipette Aspiration in Molecular Mechanics of Single Cells
,”
ASME J. Nanotechnol. Eng. Med.
,
5
(
4
), p.
040902
.10.1115/1.4029936
9.
Arbore
,
C.
,
Perego
,
L.
,
Sergides
,
M.
, and
Capitanio
,
M.
,
2019
, “
Probing Force in Living Cells With Optical Tweezers: From Single-Molecule Mechanics to Cell Mechanotransduction
,”
Biophys. Rev.
,
11
(
5
), pp.
765
782
.10.1007/s12551-019-00599-y
10.
Tanase
,
M.
,
Biais
,
N.
, and
Sheetz
,
M.
,
2007
, “
Magnetic Tweezers in Cell Biology
,”
Methods Cell Biol.
,
83
(
07
), pp.
473
493
.10.1016/S0091-679X(07)83020-2
11.
Weber
,
A.
,
Zbiral
,
B.
,
Iturri
,
J.
,
Benitez
,
R.
, and
Toca-Herrera
,
J. L.
,
2021
, “
Measuring (Biological) Materials Mechanics With Atomic Force Microscopy. 2. Influence of the Loading Rate and Applied Force (Colloidal Particles)
,”
Microsc. Res. Tech.
,
84
(
5
), pp.
1078
1088
.10.1002/jemt.23643
12.
Krieg
,
M.
,
Fläschner
,
G.
,
Alsteens
,
D.
,
Gaub
,
B. M.
,
Roos
,
W. H.
,
Wuite
,
G. J. L.
,
Gaub
,
H. E.
, et al.,
2018
, “
Atomic Force Microscopy-Based Mechanobiology
,”
Nat. Rev. Phys.
,
1
(
1
), pp.
41
57
.10.1038/s42254-018-0001-7
13.
Kiss
,
R.
,
Bock
,
H.
,
Pells
,
S.
,
Canetta
,
E.
,
Adya
,
A. K.
,
Moore
,
A. J.
,
de Sousa
,
P.
, and
Willoughby
,
N. A.
,
2011
, “
Elasticity of Human Embryonic Stem Cells as Determined by Atomic Force Microscopy
,”
ASME J. Biomech. Eng.
,
133
(
10
), p.
101009
.10.1115/1.4005286
14.
Petit
,
C.
,
Karkhaneh Yousefi
,
A. A.
,
Guilbot
,
M.
,
Barnier
,
V.
, and
Avril
,
S.
,
2022
, “
Atomic Force Microscopy Stiffness Mapping in Human Aortic Smooth Muscle Cells
,”
ASME J. Biomech. Eng.
,
144
(
8
), p.
081001
.10.1115/1.4053657
15.
Liu
,
Y.
,
Wang
,
K.
,
Sun
,
X.
,
Chen
,
D.
,
Wang
,
J.
, and
Chen
,
J.
,
2020
, “
Development of Microfluidic Platform Capable of Characterizing Cytoplasmic Viscosity, Cytoplasmic Conductivity and Specific Membrane Capacitance of Single Cells
,”
Microfluid. Nanofluid.
,
24
(
6
), pp.
1
11
.10.1007/s10404-020-02350-6
16.
Raj
,
A.
,
Dixit
,
M.
,
Doble
,
M.
, and
Sen
,
A. K.
,
2017
, “
A Combined Experimental and Theoretical Approach Towards Mechanophenotyping of Biological Cells Using a Constricted Microchannel
,”
Lab Chip
,
17
(
21
), pp.
3704
3716
.10.1039/C7LC00599G
17.
Sajeesh
,
P.
,
Raj
,
A.
,
Doble
,
M.
, and
Sen
,
A. K.
,
2016
, “
Characterization and Sorting of Cells Based on Stiffness Contrast in a Microfluidic Channel
,”
RSC Adv.
,
6
(
78
), pp.
74704
74714
.10.1039/C6RA09099K
18.
Wang
,
X.
, and
Zhang
,
X.
,
2019
, “
Biomechanical Study on Elastic and Viscoelastic Properties of Osteoblasts Using Atomic Force Microscopy
,”
Proceedings of 2019 IEEE International Conference on Mechatronics and Automation, ICMA 2019
, Tianjin, China, Aug. 4–7, pp.
1377
1381
.10.1109/ICMA.2019.8816579
19.
Ding
,
Y.
,
Xu
,
G. K.
, and
Wang
,
G. F.
,
2017
, “
On the Determination of Elastic Moduli of Cells by AFM Based Indentation
,”
Sci. Rep.
,
7
(
1
), pp.
1
8
.10.1038/srep45575
20.
Liang
,
X.
,
Shi
,
X.
,
Ostrovidov
,
S.
,
Wu
,
H.
, and
Nakajima
,
K.
,
2016
, “
Probing Stem Cell Differentiation Using Atomic Force Microscopy
,”
Appl. Surf. Sci.
,
366
, pp.
254
259
.10.1016/j.apsusc.2016.01.082
21.
Dintwa
,
E.
,
Tijskens
,
E.
, and
Ramon
,
H.
,
2008
, “
On the Accuracy of the Hertz Model to Describe the Normal Contact of Soft Elastic Spheres
,”
Granul. Matter
,
10
(
3
), pp.
209
221
.10.1007/s10035-007-0078-7
22.
el Kennassi
,
E.
,
el Kennassi
,
F.
,
Dirhar
,
M. A.
,
Azelmad
,
E.
, and
Janati
,
K. I.
,
2020
, “
Nano-Mechanical Eukaryotic Cell Behavior by Finite Element Modeling
,”
Int. J. Anal., Exp. Finite Element Anal. (IJAEFEA)
,
7
(
3
), pp.
61
67
.10.26706/ijaefea.3.7.20200803
23.
Chen
,
J.
,
2014
, “
Nanobiomechanics of Living Cells: A Review
,”
Interface Focus
,
4
(
2
), p.
20130055
.10.1098/rsfs.2013.0055
24.
Boccaccio
,
A.
,
Fiorentino
,
M.
,
Manghisi
,
V. M.
,
Monno
,
G.
, and
Uva
,
A. E.
,
2020
, “
Effect of Cell Shape on Nanoindentation Measurements
,”
Design Tools and Methods in Industrial Engineering
,
C.
Rizzi
,
A. O.
Andrisano
,
F.
Leali
,
F.
Gherardini
,
F.
Pini
, and
A.
Vergnano
, eds.,
Springer International Publishing
,
Cham
, pp.
37
44
.
25.
Guz
,
N.
,
Dokukin
,
M.
,
Kalaparthi
,
V.
, and
Sokolov
,
I.
,
2014
, “
If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments
,”
Biophys. J.
,
107
(
3
), pp.
564
575
.10.1016/j.bpj.2014.06.033
26.
Beicker
,
K.
,
O'Brien
,
E. T.
,
Falvo
,
M. R.
, and
Superfine
,
R.
,
2018
, “
Vertical Light Sheet Enhanced Side-View Imaging for AFM Cell Mechanics Studies
,”
Sci. Rep.
,
8
(
1
), pp.
1
12
.10.1038/s41598-018-19791-3
27.
Li
,
M.
,
Dang
,
D.
,
Liu
,
L.
,
Xi
,
N.
, and
Wang
,
Y.
,
2017
, “
Atomic Force Microscopy in Characterizing Cell Mechanics for Biomedical Applications: A Review
,”
IEEE Trans. Nanobioscience
,
16
(
6
), pp.
523
540
.10.1109/TNB.2017.2714462
28.
Sun
,
W.
,
Yin
,
P.
,
Wang
,
C.
,
Ren
,
Y.
,
Han
,
X.
,
Wu
,
C.
, and
Zhang
,
W.
,
2021
, “
Determination of the Elastic Modulus of Adherent Cells Using Spherical Atomic Force Microscope Probe
,”
J. Mater. Sci.
,
56
(
32
), pp.
18210
18218
.10.1007/s10853-021-06445-5
29.
Cao
,
G.
, and
Chandra
,
N.
,
2010
, “
Evaluation of Biological Cell Properties Using Dynamic Indentation Measurement
,”
Phys. Rev. E Stat., Nonlinear Soft Matter Phys.
,
81
(
2
), pp.
1
9
.https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.021924
30.
Qian
,
L.
, and
Zhao
,
H.
,
2018
, “
Nanoindentation of Soft Biological Materials
,”
Micromachines (Basel)
,
9
(
12
), pp.
1
24
.10.3390/mi9120654
31.
Wang
,
L.
,
Tian
,
L.
,
Wang
,
Y.
,
Zhang
,
W.
,
Wang
,
Z.
, and
Liu
,
X.
,
2020
, “
Determination of Viscohyperelastic Properties of Tubule Epithelial Cells by an Approach Combined With AFM Nanoindentation and Finite Element Analysis
,”
Micron
,
129
, p.
102779
.10.1016/j.micron.2019.102779
32.
Tang
,
G.
,
Galluzzi
,
M.
,
Zhang
,
B.
,
Shen
,
Y. L.
, and
Stadler
,
F. J.
,
2019
, “
Biomechanical Heterogeneity of Living Cells: Comparison Between Atomic Force Microscopy and Finite Element Simulation
,”
Langmuir
,
35
(
23
), pp.
7578
7587
.10.1021/acs.langmuir.8b02211
33.
Ferrazzi
,
G.
,
2011
, “
Numerical Modeling of Atomic Force Microscopy (AFM) Towards Estimation of Material Parameters From Fibroblast Cells
,”
Degree Project in Solid Mechanics Second Level
, Stockholm, Sweden, p.
44
.https://www.divaportal.org/smash/get/diva2:562186/FULLTEXT01.pdf
34.
Wang
,
L.
,
Wang
,
L.
,
Xu
,
L.
, and
Chen
,
W.
,
2019
, “
Finite Element Modelling of Single Cell Based on Atomic Force Microscope Indentation Method
,”
Comput. Math. Methods Med.
,
2019
, pp.
1
10
.10.1155/2019/7895061
35.
Müller
,
S. J.
,
Weigl
,
F.
,
Bezold
,
C.
,
Bächer
,
C.
,
Albrecht
,
K.
, and
Gekle
,
S.
,
2021
, “
A Hyperelastic Model for Simulating Cells in Flow
,”
Biomech. Model. Mechanobiol.
,
20
(
2
), pp.
509
520
.10.1007/s10237-020-01397-2
36.
Haga
,
J. H.
,
Beaudoin
,
A. J.
,
White
,
J. G.
, and
Strony
,
J.
,
1998
, “
Quantification of the Passive Mechanical Properties of the Resting Platelet
,”
Ann. Biomed. Eng.
, 26(2), pp.
268
277
.10.1114/1.118
37.
Sachs
,
L.
,
Denker
,
C.
,
Greinacher
,
A.
, and
Palankar
,
R.
,
2020
, “
Quantifying Single-Platelet Biomechanics: An Outsider's Guide to Biophysical Methods and Recent Advances
,”
Res. Pract. Thromb. Haemost.
,
4
(
3
), pp.
386
401
.10.1002/rth2.12313
38.
Li
,
M.
,
Liu
,
L. Q.
,
Xi
,
N.
,
Wang
,
Y. C.
,
Dong
,
Z. L.
,
Xiao
,
X. B.
, and
Zhang
,
W. J.
,
2012
, “
Atomic Force Microscopy Imaging and Mechanical Properties Measurement of Red Blood Cells and Aggressive Cancer Cells
,”
Sci. China Life Sci.
,
55
(
11
), pp.
968
973
.10.1007/s11427-012-4399-3
39.
Abbasi
,
A. A.
,
Ahmadian
,
M. T.
,
Alizadeh
,
A.
, and
Tarighi
,
S.
,
2018
, “
Application of Hyperelastic Models in Mechanical Properties Prediction of Mouse Oocyte and Embryo Cells at Large Deformations
,”
Sci. Iran.
,
25
(
2B
), pp.
700
710
.10.24200/sci.2017.4321
40.
Graybill
,
P. M.
,
Bollineni
,
R. K.
,
Sheng
,
Z.
,
Davalos
,
R. V.
, and
Mirzaeifar
,
R.
,
2021
, “
A Constriction Channel Analysis of Astrocytoma Stiffness and Disease Progression
,”
Biomicrofluidics
,
15
(
2
), p.
024103
.10.1063/5.0040283
41.
Park
,
K.
, and
Desai
,
J. P.
,
2017
, “
Machine Learning Approach for Breast Cancer Localization
,”
International Conference on Manipulation, Automation and Robotics at Small Scales, MARSS 2017-Proceedings
, Montreal, QC, Canada, July 17–21, pp.
1
6
.10.1109/MARSS.2017.8001925
42.
Minelli
,
E.
,
Ciasca
,
G.
,
Sassun
,
T. E.
,
Antonelli
,
M.
,
Palmieri
,
V.
,
Papi
,
M.
,
Maulucci
,
G.
,
Santoro
,
A.
,
Giangaspero
,
F.
,
Delfini
,
R.
,
Campi
,
G.
, and
de Spirito
,
M.
,
2017
, “
A Fully-Automated Neural Network Analysis of AFM Force-Distance Curves for Cancer Tissue Diagnosis
,”
Appl. Phys. Lett.
,
111
(
14
).10.1063/1.4996300
43.
Nyberg
,
K. D.
,
Bruce
,
S. L.
,
Nguyen
,
A. V.
,
Chan
,
C. K.
,
Gill
,
N. K.
,
Kim
,
T. H.
,
Sloan
,
E. K.
, and
Rowat
,
A. C.
,
2018
, “
Predicting Cancer Cell Invasion by Single-Cell Physical Phenotyping
,”
Integr. Biol. (United Kingdom)
,
10
(
4
), pp.
218
231
.10.1039/C7IB00222J
44.
Lin
,
J.
,
Kim
,
D.
,
Tse
,
H. T.
,
Tseng
,
P.
,
Peng
,
L.
,
Dhar
,
M.
,
Karumbayaram
,
S.
, and
di Carlo
,
D.
,
2017
, “
High-Throughput Physical Phenotyping of Cell Differentiation
,”
Microsyst. Nanoeng.
,
3
(
1
), pp.
1
7
.10.1038/micronano.2017.13
45.
Darling
,
E. M.
, and
Guilak
,
F.
,
2008
, “
A Neural Network Model for Cell Classification Based on Single-Cell Biomechanical Properties
,”
Tissue Eng. Part A
,
14
(
9
), pp.
1507
1515
.10.1089/ten.tea.2008.0180
46.
Rodriguez
,
M. L.
,
McGarry
,
P. J.
, and
Sniadecki
,
N. J.
,
2013
, “
Review on Cell Mechanics: Experimental and Modeling Approaches
,”
ASME Appl. Mech. Rev.
,
65
(
6
), p.
060801
.10.1115/1.4025355
47.
Na
,
S.
,
Sun
,
Z.
,
Meininger
,
G. A.
, and
Humphrey
,
J. D.
,
2004
, “
On Atomic Force Microscopy and the Constitutive Behavior of Living Cells
,”
Biomech. Model. Mechanobiol.
,
3
(
2
), pp.
75
84
.10.1007/s10237-004-0051-x
48.
Bansod
,
Y. D.
,
Matsumoto
,
T.
,
Nagayama
,
K.
, and
Bursa
,
J.
,
2018
, “
A Finite Element Bendo-Tensegrity Model of Eukaryotic Cell
,”
ASME J. Biomech. Eng.
,
140
(
10
), p.
101001
.10.1115/1.4040246
49.
Demchenkov
,
E. L.
,
Nagdalian
,
A. A.
,
Budkevich
,
R. O.
,
Oboturova
,
N. P.
, and
Okolelova
,
A. I.
,
2021
, “
Usage of Atomic Force Microscopy for Detection of the Damaging Effect of CdCl2 on Red Blood Cells Membrane
,”
Ecotoxicol. Environ. Saf.
,
208
, pp.
1
7
.10.1016/j.ecoenv.2020.111683
50.
Sergunova
,
V.
,
Leesment
,
S.
,
Kozlov
,
A.
,
Inozemtsev
,
V.
,
Platitsina
,
P.
,
Lyapunova
,
S.
,
Onufrievich
,
A.
,
Polyakov
,
V.
, and
Sherstyukova
,
E.
,
2022
, “
Investigation of Red Blood Cells by Atomic Force Microscopy
,”
Sensors
,
22
(
5
), p.
2055
.10.3390/s22052055
51.
Diez-Silva
,
M.
,
Dao
,
M.
,
Han
,
J.
,
Lim
,
C.-T.
, and
Suresh
,
S.
,
2010
, “
Shape and Biomechanical Characteristics of Human Red Blood Cells in Health and Disease
,”
MRS Bull.
,
35
(
5
), pp.
382
388
.10.1557/mrs2010.571
52.
Peters
,
M. D.
, and
Iber
,
D.
,
2017
, “
Simulating Organogenesis in COMSOL: Tissue Mechanics
,” arXiv [Preprint].
arXiv:1806.04138
.10.48550/arXiv.1710.00553
53.
Ding
,
Y.
,
Wang
,
J.
,
Xu
,
G. K.
, and
Wang
,
G. F.
,
2018
, “
Are Elastic Moduli of Biological Cells Depth Dependent or Not? Another Explanation Using a Contact Mechanics Model With Surface Tension
,”
Soft Matter
,
14
(
36
), pp.
7534
7541
.10.1039/C8SM01216D
54.
Barns
,
S.
,
Balanant
,
M. A.
,
Sauret
,
E.
,
Flower
,
R.
,
Saha
,
S.
, and
Gu
,
Y. T.
,
2017
, “
Investigation of Red Blood Cell Mechanical Properties Using AFM Indentation and Coarse-Grained Particle Method
,”
Biomed. Eng. Online
,
16
(
1
), pp.
1
21
.10.1186/s12938-017-0429-5
55.
COMSOL,
2008
, “
Fluid-Structure Interaction in a Network of Blood Vessels Fluid-Structure Interaction in a Network of Blood Vessels
,”
COMSOL
, pp.
1
7
.https://www.comsol.com/model/fluid-structureinteraction-in-a-network-of-blood-vessels-660
56.
Barreto
,
S.
,
Perrault
,
C. M.
, and
Lacroix
,
D.
,
2014
, “
Structural Finite Element Analysis to Explain Cell Mechanics Variability
,”
J. Mech. Behav. Biomed. Mater.
,
38
, pp.
219
231
.10.1016/j.jmbbm.2013.11.022
57.
Muh Ibnu Choldun
,
R.
,
Santoso
,
J.
, and
Surendro
,
K.
,
2019
, “
Determining the Neural Network Topology: A Review
,”
ACM International Conference Proceeding Series
, Association for Computing Machinery, New York, Feb., pp.
357
362
.10.1145/3316615.3316697
58.
Kontomaris
,
S. V.
,
Malamou
,
A.
, and
Stylianou
,
A.
,
2022
, “
The Hertzian Theory in AFM Nanoindentation Experiments Regarding Biological Samples: Overcoming Limitations in Data Processing
,”
Micron
,
155
, p.
103228
.10.1016/j.micron.2022.103228
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