Determination of Mechanical Properties of Individual Living Cells

136 Pages·2009·1.89 MB·English

Determination of Mechanical Properties of
Individual Living Cells
Marjan Molavi Zarandi
A Thesis
in
The Department
of
Mechanical and Industrial Engineering
Presented in Partial Fulfillment of the Requirements for
the Degree of Master of Applied Science (Mechanical Engineering) at
Concordia University
Montreal, Quebec, Canada
December 2007
© Marjan Molavi Zarandi, 2007
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ABSTRACT
Determination of Mechanical Properties of Individual Living
Cells
Marjan Molavi Zarandi
In this thesis, a finite element and experimental modal analysis are employed to
determine the mechanical properties of the living cells. Because the determination of
mechanical properties of the living cells and particularly the natural frequencies are
highly important to diagnose the health condition of cells, a comprehensive analysis is
carried out to determine the natural frequencies of individual cells. Since many cells have
a spherical shape, a spherical shape of the cell is considered for this analysis. The natural
frequencies and corresponding mode shapes are determined for specific type of cell
whose elastic properties of cell have been measured experimentally. To validate the
numerical analysis, an experimental set up is designed to measure the natural frequencies
of some scaled up models of cell. In parallel, the numerical method that was used for cell
modal analysis is employed to determine the natural frequencies of scaled up models of
cell to show the agreement between the finite element and experimental analyses. For
then, the FEA model is extrapolated to the biological cell. The results obtained from the
finite element modal analysis of cell are compared to the latest reports available on the
values of natural frequencies of cell.
iii
c
Uhis thesis is dedicatedt om p parents
for their love and to AM for his endless
supports and encouragements.
IV
ACKNOWLEDGEMENTS
It is the most pleasant task where I have the opportunity to express my gratitude to all the
people who have helped me in the path to a Master's degree.
I am deeply indebted to my supervisors, Professor Ion Stiharu and Professor Javad
Dargahi for their invaluable supports. I could not have imagined having a better advisors
and mentors for my Master and without their common sense, knowledge and
perceptiveness, I would never have finished.
I would like to express my special and sincere thanks to my colleague at Concordia
University, Dr. Ali Bonakdar for his assistance and friendly support during the length of
my research work. In addition, I am thankful to Dr. Gino Rinaldi and Mr. Henry
Szczawinski for their assistance during my experiments.
Finally, I would like to express my sincerest gratitude, love to my parents and my family
for their continuous motivation and emotional support. I would like to thank my mother
Mrs. Batool Hadizadeh and my father Mr. Abdolhamid Molavi Zarandi who taught me
the value of patience, hard work and commitment without which I could not have
completed my Master. I am thankful to my sisters Maryam and Mahsa for their love and
being a great source of motivation and inspiration during my education.
v
TABLE OF CONTENTS
I. List of Figures x
I. List of Tables xv
I. List of Symbols xvi
Page
Chapter 1 - Introduction and literature review 1
1.1. Mechanics aplied to biology 1
1.2. Measuring mechanical properties of biological samples 2
1.2.1. Pasive characterization techniques 4
1.2.1.1. Micropipete aspiration 4
1.2.1.2. Atomic force microscopy (AFM) 5
1.2.1.3. Laser optical traping 7
1.2.1.4. Magnetic bead measurement 8
1.2.2. Active stimulation techniques 9
1.2.2.1. Membrane-based stretching 9
1.2.2.2. Flow-induced shear stres 10
1.2.2.3. Substrate stretching 1
1.3. Introduction to cel oscilation 12
1.4. Oscilations of fluid filed elastic spheres 14
1.5. Objective and scope of this research 17
1.6. Thesis overview 17
vi
Chapter 2 - Introduction to ceils and models of living cels 19
2.1. Introduction 19
2.2. Diferent types of cels 20
2.2.1. Kingdom Monera 20
2.2.2. Kingdom Protista 21
2.2.3. Kingdom Plantae 21
2.2.4. Kingdom Fungi 2
2.2.5. Kingdom Animalia 2
2.3. Prokaryotic cels 2
2.4. Eukaryotic cels 23
2.5. Cel structure 27
2.5.1. Membrane 28
2.5.2. Cytoplasm 29
2.5.3. Nucleus 31
2.6. Sumary 31
Chapter 3 - Modeling of living cel and validation of the model 32
3.1. Introduction 32
3.2. Modeling of living cel 35
3.3. Sumary 42
Chapter 4 - Modal analysis for cels 4
4.1. Thre-Dimensional modal analysis for in vacuo spherical cel 4
4.1.1 FEA using ANSYS 4
4.1.2. FEA using COMSOL (FEMLAB) 50
vii
4.2. Thre-Dimensional FE model for fluid filed spherical cel 54
4.2.1. FE model for fluid filled spherical cell using Pelling's data (AFM method) [32]
56
4.2.2. FE model for fluid filed spherical cel using Zinin's data [4] 59
4.3. Sumary 64
Chapter 5 - Experimental works and results 6
5.1. Experimental analysis 6
5.1.1. Experimental setup 67
5.1.2. Tests and results 71
5.2. FEA of fluid filed spheres 80
5.3. Sumary 85
Chapter 6 - Conclusion and proposed future works 86
6.1. Sumary of work 86
6.2. Conclusions 87
6.3. Proposed future works 89
References 91
Apendix I - Other structural parts of cels 9
1.1. Phospholipid bilayer 9
1.2. Proteins 10
1.3. Cytoskeleton 10
1.4. Lysosomes 101
Apendix I - Analysis in ANSYS 102
AI.l. Overview of ANSYS steps 102
viii
AI.2. Preference 103
AI.3. Preprocesor 103
AI.4. Solution 104
AI.5. General Post procesor 104
AI.6. APDL (ANSYS Parametric Design Language) 105
AI.6.2. APDL programing to obtain natural frequencies of spherical cel 105
AII.6.3. APDL programming to obtain natural frequencies of scaled up model of cell
(fluid filed specimen with radius of 29 m) 109
Appendix I - Experimental work for measuring natural frequency of specimens 113
IX
LIST OF FIGURES
Figure 1.1 - Micropipete aspiration for single cel [3] 4
Figurel. 2 — Schematic of atomic force microscope (AFM) [8] 6
Figurel. 3 — Schematic showing optical twezers [8] 8
Figure 1.4 - Magnetic twisting cytometry (MTC) [3] 9
Figure 1.5 — Flow-induced shear stres [3] 1
Figure 1.6 - Substrate stretching [3] 1
Figure 1.7 - Mode shapes of elastic spherical shel, first mode [5] 15
Figure 1.8 ~ Mode shapes of elastic spherical shel, second mode [5] 15
Figure 1.9 — Mode shapes of elastic spherical shel, third mode [5] 15
Figure 1.10 — Mode shapes of elastic spherical shel, forth mode [5] 16
Figure 1.11 — Mode shapes for the n=2 to 6 spheroidal modes of vibration for a fluid-
filed sphere [56] 16
Figure 2.1 — Five kingdoms of cels [59] 20
Figure 2.2 — Diagram of a prokaryotic cel [59] 23
Figure 2.3 ~ Diagram of an animal cel [59] 24
Figure 2.4 — Diagram of a plant cel [59] 24
Figure 2.5 ~ Cel kingdoms [59] 25
Figure 2.6 - Cel diferent shapes in human body [56] 26
Figure 2.7 — Typical animal cel [62] 27
Figure 3.1 ~ Sacharomyces Cerevisiae [67] 32
x