Mechanical models for malaria infected erythtocytes 7

Finite element analysis was done to simulate the cell deformation in micropipette aspiration and optical tweezers stretching.. The effect of bending stiffness on the cell deformability w

Chapter 7 Conclusions and Future Work

140

Chapter 7 Conclusions and Future Work

This thesis focused on the modeling of malaria (P.f) infected erythrocytes One of the main objectives was to propose computational models for the malaria (P.f)

infected erythrocytes at their different stages of parasite maturation, in particular at the mid and late stages, for which no accurate models had been proposed currently The other was to relate the loss of cell deformability to the change in mechanical properties of the cell membrane and structural changes occurred within the cell

The major contributions and findings of this thesis are summarized as follows:

1 A two-component model was developed to study the malaria (P.f.) infected

erythrocyte deformation Finite element analysis was done to simulate the cell deformation in micropipette aspiration and optical tweezers stretching The simulation was done using finite element program ABAQUS The model was able to predict the cell deformation in both of these two experiments

2 The effect of initial membrane shear modulus µ0 on the malaria (P.f.)

infected erythrocyte deformability was studied using the two-component model The values of initial membrane shear modulus were obtained by comparing the finite element simulation result with that of experiments Considering the decreasing cell sizes and data deviation, the analysis

Chapter 7 Conclusions and Future Work

141

provided the range of initial membrane shear modulus for each parasite maturation stage The increase in membrane shear modulus with the progression of disease state was quantified

3 The effect of bending stiffness on the cell deformability was studied by simulating the cell deformation in both micropipette aspiration and optical tweezers stretching Parametric studies were done by varying the initial

bending stiffness D 0 in the range of 3.3 x 10 -20 J to 1.5 x 10 -18 J The bending stiffness was found to have little effect on the cell deformation

4 The hemispherical cap model was commonly used for analyzing cell deformation in micropipette aspiration, due to its simplicity in calculating membrane shear modulus However, with the wide range of micropipette sizes used in the experiments, this model may not be valid for all pipette sizes The model and method proposed in this thesis allowed us to test the validity of hemispherical cap model by applying the model to analyze the simulation curves with known values of membrane shear modulus Using

this method, the range of 0.1 ≤ p

cell

R

R ≤ 0.4 was proved valid for using hemispherical cap model in micropipette aspiration For cells that can be assumed as a liquid enclosed by incompressible membrane, it is easier to apply hemispherical cap model due to its simplicity in calculation, and the

results will be valid as long as 0.1 ≤ p

cell

R

R ≤ 0.4

5 It may not be suitable to use hemispherical cap model and two-component model to analyze the infected cells in the middle to late stages, since the parasite occupies more than 40% of the host cell’s volume An advanced

Chapter 7 Conclusions and Future Work

142

multi-component model was developed to study the effect of parasite inclusion on the host cell deformation Finite element simulations were done using ABAQUS to simulate the deformation in both micropipette aspiration and optical tweezers stretching This advanced model was able

to simulate mechanical probing at the different locations of the host cell and explain the difference in shear modulus given by hemispherical cap model for the same cell The multi-component model also allowed us to quantify the effect of PVM stiffness and sizes

6 Using the multi-component model, it was found that compared to the PVM sizes and the stiffness of PVM and host cell membrane, the interaction between PVM and host cell membrane did not significantly play an important role in the cell deformation induced by optical tweezers Even if they were stuck to each other after contact, it would not affect the cell deformation as much as the change in membrane stiffness, PVM sizes and PVM stiffness would

The work in this thesis indicated interesting directions of studying the malaria infected erythrocytes The future work can include the following:

1 The current multi-component model can be further developed to include not only the hemoglobin but also the food vacuole and the parasite itself within the parasitophorous vacuole membrane (PVM) If the experimental techniques allow us to probe the PVM and its internal structure directly, a

Chapter 7 Conclusions and Future Work

143

more complete model can be established If the current experimental techniques are not able to probe them directly, a more complex multi-component model is still a good tool to analyze the heterogeneity within the host cell

2 These models can also be used in studying the mechanical properties of

malaria P.vivax, which is believed to become softer instead of stiffer with

the progression of infection stage Due to the limitation of culturing techniques, we cannot conduct micropipette aspiration and optical

tweezers stretching on P.vivax in our lab If the experiment data of these two experiments are available for P.vivax cells, the models used in this

thesis can be applied in studying their mechanical properties

3 These models proposed in this thesis may also be used to evaluate the drug treatments on the mechanical properties of the cells Since the severity of malaria can be regarded as a function of capillary blockage caused by the decrease in deformability of the infected erythrocytes, drugs can be developed to recover the natural deformability of the cell These computational models can be used to quantify the effectiveness of these drugs This can contribute to better understanding, diagnosis and treatment

of malaria, as well as other diseases that induce similar effects on the living cells

References

144

References

ABAQUS (v6.4) "ABAQUS Analysis User's Manual."

Ashkin, A and J M Dziedzic (1985) "Observation of radiation-pressure trapping of

particles by alternating light beams." Physical Review Letters 54(12): 1245-1248

Ashkin, A., J M Dziedzic and T Yamane (1987) "Optical trapping and

manipulation of single cells using infrared laser beams." Nature 330(6150): 769-71

Barjas-Castro, M L., M M Brandao, A Fontes, F F Costa, C L Cesar and S T Saad (2002) "Elastic properties of irradiated RBCs measured by optical tweezers."

Transfusion 42(9): 1196-9

Brandao, M M., A Fontes, M L Barjas-Castro, L C Barbosa, F F Costa, C L Cesar and S T Saad (2003) "Optical tweezers for measuring red blood cell elasticity:

application to the study of drug response in sickle cell disease." Eur J Haematol 70(4):

207-11

Bustamante, C., Z Bryant and S B Smith (2003) "Ten years of tension:

single-molecule DNA mechanics." Nature 421(6921): 423-7

Cokelet, G R., R Soave, G Pugh and L Rathbun (1993) "Fabrication of in Vitro Microvascular Blood Flow Systems by Photolithography." Microvascular Research

46(3): 394-400

Dao, M., J Li and S Suresh (2006) "Molecularly based analysis of deformation of spectrin network and human erythrocyte." Materials Science and Engineering: C

Proceedings of the First TMS Symposium on Biological Materials Science 26(8):

1232-1244

Dao, M., C T Lim and S Suresh (2003) "Mechanics of the human red blood cell

deformed by optical tweezers." J Mech Phys Solids 51(11-12): 2259-2280

Derganc, J., B Bozic, S Svetina and B Zeks (2000) "Stability analysis of

micropipette aspiration of neutrophils." Biophys J 79(1): 153-62

Dobbe, J G., M R Hardeman, G J Streekstra, J Strackee, C Ince and C A

Grimbergen (2002) "Analyzing red blood cell-deformability distributions." Blood

Cells Mol Dis 28(3): 373-84

Dong, C., R Skalak and K L Sung (1991) "Cytoplasmic rheology of passive

neutrophils." Biorheology 28(6): 557-67

Dong, C., R Skalak, K L Sung, G W Schmid-Schonbein and S Chien (1988)

"Passive deformation analysis of human leukocytes." J Biomech Eng 110(1): 27-36

References

145

Duffy, D C., J C McDonald, O J A Schueller and G M Whitesides (1998)

"Rapid Prototyping of Microfluidic Systems in Poly(dimethylsiloxane)." Anal Chem

70(23): 4974-4984

Evans, E and Y C Fung (1972) "Improved measurements of the erythrocyte

geometry." Microvasc Res 4(4): 335-47

Evans, E and A Yeung (1989) "Apparent viscosity and cortical tension of blood

granulocytes determined by micropipet aspiration." Biophys J 56(1): 151-60

Evans, E A (1983) "Bending elastic modulus of red blood cell membrane derived

from buckling instability in micropipet aspiration tests." Biophys J 43(1): 27-30

Evans, E A and R Skalak (1979) "Mechanics and thermodynamics of

biomembranes: part 1." CRC Crit Rev Bioeng 3(3): 181-330

Ferko, M C., A Bhatnagar, M B Garcia and P J Butler (2007) "Finite-element stress analysis of a multicomponent model of sheared and focally-adhered endothelial

cells." Ann Biomed Eng 35(2): 208-23

Fung, Y C (1990) Biomechanics : motion, flow, stress, and growth New York ; London, Springer-Verlag

Fung, Y C (1993) Biomechanics : mechanical properties of living tissues New York ; London, Springer-Verlag

Fung, Y C (1997) Biomechanics : circulation New York ; London, Springer

Fung, Y C and P Tong (1968) "Theory of the sphering of red blood cells." Biophys

J 8(2): 175-98

Glenister, F K., R L Coppel, A F Cowman, N Mohandas and B M Cooke (2002)

"Contribution of parasite proteins to altered mechanical properties of malaria-infected

red blood cells." Blood 99(3): 1060-3

Gregersen, M I., C A Bryant, W E Hammerle, S Usami and S Chien (1967)

"Flow Characteristics of Human Erythrocytes through Polycarbonate Sieves

10.1126/science.157.3790.825." Science 157(3790): 825-827

Guest, M M., T P Bond, R G Cooper and J R Derrick (1963) "Red Blood Cells:

Change in Shape in Capillaries." Science 142: 1319-21

Guilak, F and V C Mow (2000) "The mechanical environment of the chondrocyte:

a biphasic finite element model of cell-matrix interactions in articular cartilage." J

Biomech 33(12): 1663-73

Haldar, K., N Mohandas, B U Samuel, T Harrison, N L Hiller, T Akompong and

P Cheresh (2002) "Protein and lipid trafficking induced in erythrocytes infected by

malaria parasites." Cell Microbiol 4(7): 383-95

References

146

Henon, S., G Lenormand, A Richert and F Gallet (1999) "A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers."

Biophys J 76(2): 1145-51

Hill, M (2002) "Hole's Human Anatomy & Physiology, 9th Edition."

Ho, M and N J White (1999) "Molecular mechanisms of cytoadherence in malaria."

Am J Physiol 276(6 Pt 1): C1231-42

Hochmuth, R M (2000) "Micropipette aspiration of living cells." J Biomech 33(1):

15-22

Hochmuth, R M., R N Marple and S P Sutera (1970) "Capillary blood flow I

Erythrocyte deformation in glass capillaries." Microvasc Res 2(4): 409-19

Hochmuth, R M., H P Ting-Beall, B B Beaty, D Needham and R Tran-Son-Tay (1993) "Viscosity of passive human neutrophils undergoing small deformations."

Biophys J 64(5): 1596-601

Huang, H., R D Kamm and R T Lee (2004) "Cell mechanics and

mechanotransduction: pathways, probes, and physiology." Am J Physiol Cell Physiol

287(1): C1-11

Kyes, S A., J A Rowe, N Kriek and C I Newbold (1999) "Rifins: a second family

of clonally variant proteins expressed on the surface of red cells infected with

Plasmodium falciparum." Proc Natl Acad Sci U S A 96(16): 9333-8

Lenormand, G., S Henon, A Richert, J Simeon and F Gallet (2003) "Elasticity of

the human red blood cell skeleton." Biorheology 40(1-3): 247-51

Leterrier, J F (2001) "Water and the cytoskeleton." Cell Mol Biol (Noisy-le-grand)

47(5): 901-23

Li, J., M Dao, C T Lim and S Suresh (2005) "Spectrin-level modeling of the

cytoskeleton and optical tweezers stretching of the erythrocyte." Biophys J 88(5):

3707-19

Lim, C T., M Dao, S Suresh, C H Sow and K T Chew (2004) "Large deformation

of living cells using laser traps." Acta Materialia 52(7): 1837-1845

Lim, C T., E H Zhou, A Li, S R K Vedula and H X Fu (2006) "Experimental techniques for single cell and single molecule biomechanics." Materials Science and Engineering: C

Proceedings of the First TMS Symposium on Biological Materials Science 26(8):

1278-1288

Lim, C T., E H Zhou and S T Quek (2006) "Mechanical models for living cells a

review." J Biomech 39(2): 195-216

References

147

Litvinov, R I., H Shuman, J S Bennett and J W Weisel (2002) "Binding strength and activation state of single fibrinogen-integrin pairs on living cells." Proc Natl Acad

Sci U S A 99(11): 7426-31

Lu , M and X Luo (2001) Foundations of Elasticity

Magowan, C., W Wollish, L Anderson and J Leech (1988) "Cytoadherence by Plasmodium falciparum-infected erythrocytes is correlated with the expression of a

family of variable proteins on infected erythrocytes." J Exp Med 168(4): 1307-20

Marcelli, G., K H Parker and C P Winlove (2005) "Thermal fluctuations of red

blood cell membrane via a constant-area particle-dynamics model." Biophys J 89(4):

2473-80

Marti, M., J Baum, M Rug, L Tilley and A F Cowman (2005) "Signal-mediated export of proteins from the malaria parasite to the host erythrocyte." J Cell Biol

171(4): 587-92

McDonald, J C and G M Whitesides (2002) "Poly(dimethylsiloxane) as a material

for fabricating microfluidic devices." Acc Chem Res 35(7): 491-9

Merkel, R (2001) "Force spectroscopy on single passive biomolecules and single

biomolecular bonds." Physics Reports 346(5): 343-385

Miller, L H., D I Baruch, K Marsh and O K Doumbo (2002) "The pathogenic

basis of malaria." 415(6872): 673-679

Miller, L H., S Usami and S Chien (1971) "Alteration in the rheologic properties of Plasmodium knowlesi infected red cells A possible mechanism for capillary

obstruction." J Clin Invest 50(7): 1451-5

Mills, J P., L Qie, M Dao, C T Lim and S Suresh (2004) "Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers." Mech

Chem Biosyst 1(3): 169-80

Missirlis, Y F and A D Spiliotis (2002) "Assessment of techniques used in

calculating cell-material interactions." Biomolecular Engineering 19(2-6): 287-294

Parker, K H and C P Winlove (1999) "The deformation of spherical vesicles with permeable, constant-area membranes: application to the red blood cell." Biophys J

77(6): 3096-107

Pasloske, B L., D I Baruch, M R van Schravendlijk, S M Handunnetti, M

Aikawa, H Fujioka, T F Taraschi, J A Gormley and R J Howard (1993) "Cloning and characterization of a Plasmodium falciparum gene encoding a novel

high-molecular weight host membrane-associated protein, PfEMP3." Molecular and

Biochemical Parasitology 59(1): 59-72

Rand, R P and A C Burton (1964) "Mechanical Properties of the Red Cell

Membrane I Membrane Stiffness and Intracellular Pressure." Biophys J 4: 115-35

References

148

Sato, M., D P Theret, L T Wheeler, N Ohshima and R M Nerem (1990)

"Application of the micropipette technique to the measurement of cultured porcine

aortic endothelial cell viscoelastic properties." J Biomech Eng 112(3): 263-8

Schmid-Schonbein, G W., K L Sung, H Tozeren, R Skalak and S Chien (1981)

"Passive mechanical properties of human leukocytes." Biophys J 36(1): 243-56

Secomb, T W and R Hsu (1989) "Motion of nonaxisymmetric red blood cells in

cylindrical capillaries." J Biomech Eng 111(2): 147-51

Shao, J Y., G Xu and P Guo (2004) "Quantifying cell-adhesion strength with

micropipette manipulation: principle and application." Front Biosci 9: 2183-91

Shelby, J P., J White, K Ganesan, P K Rathod and D T Chiu (2003) "A

microfluidic model for single-cell capillary obstruction by Plasmodium

falciparum-infected erythrocytes." Proc Natl Acad Sci U S A 100(25): 14618-22

Shieh, A C and K A Athanasiou (2002) "Biomechanics of single chondrocytes and

osteoarthritis." Crit Rev Biomed Eng 30(4-6): 307-43

Shieh, A C and K A Athanasiou (2003) "Principles of cell mechanics for cartilage

tissue engineering." Ann Biomed Eng 31(1): 1-11

Shu, C., S Kuo-Li Paul, R Skalak, S Usami and A Tozeren (1978) "Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane."

Biophysical Journal 24(2): 463-87

Simo, J C and K S Pister (1984) "Remarks on rate constitutive equations for finite deformation problems: computational implications." Computer Methods in Applied

Mechanics and Engineering 46(2): 201-215

Skalak, R and P I Branemark (1969) "Deformation of red blood cells in capillaries."

Science 164(880): 717-9

Skalak, R., A Tozeren, R P Zarda and S Chien (1973) "Strain energy function of

red blood cell membranes." Biophys J 13(3): 245-64

Sleep, J., D Wilson, R Simmons and W Gratzer (1999) "Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study." Biophys

J 77(6): 3085-95

Strey, H., M Peterson and E Sackmann (1995) "Measurement of erythrocyte

membrane elasticity by flicker eigenmode decomposition." Biophys J 69(2): 478-88

Suresh, S., J Spatz, J P Mills, A Micoulet, M Dao, C T Lim, M Beil and T

Seufferlein (2005) "Connections between single-cell biomechanics and human

disease states: gastrointestinal cancer and malaria." Acta Biomater 1(1): 15-30

Suresh, S., J Spatz, J P Mills, A Micoulet, M Dao, C T Lim, M Beil and T

Seufferlein (2005) "Supplementary material S5: computational modeling of optical

tweezers stretching of malaria-infected human red blood cells." Acta Biomater 1(1):

15-30

References

149

Sutton, N., M C Tracey, I D Johnston, R S Greenaway and M W Rampling (1997) "A Novel Instrument for Studying the Flow Behaviour of Erythrocytes

through Microchannels Simulating Human Blood Capillaries." Microvascular

Research 53(3): 272-281

Theret, D P., M J Levesque, M Sato, R M Nerem and L T Wheeler (1988) "The application of a homogeneous half-space model in the analysis of endothelial cell

micropipette measurements." J Biomech Eng 110(3): 190-9

Ting, B P (2007) Probing the elasticity change in breast cancer cells Division of

Bioengineering, National University of Singapore Bachelor of Engineering

Tsai, M A., R S Frank and R E Waugh (1993) "Passive mechanical behavior of

human neutrophils: power-law fluid." Biophys J 65(5): 2078-88

Van Vliet, K J., G Bao and S Suresh (2003) "The biomechanics toolbox:

experimental approaches for living cells and biomolecules." Acta Materialia

The Golden Jubilee Issue Selected topics in Materials Science and Engineering: Past,

Present and Future 51(19): 5881-5905

Weed, R I (1970) "The importance of erythrocyte deformability." The American

Journal of Medicine 49(2): 147-150

World-Health-Organization (2000) "Severe falciparum malaria." Transactions of the

Royal Society of Tropical Medicine and Hygiene 94(Supplement 1): 1-90

World-Health-Organization (2008) World Malaria Report 2008

Yeoh, O H (1990) "Characterization of Elastic Properties of Carbon-Black-Filled

Rubber Vulcanizates." Rubber Chem Technol 63: 792-805

Zarda, P R., S Chien and R Skalak (1977) "Elastic deformations of red blood cells."

J Biomech 10(4): 211-21

Zhou, C., P Yue and J J Feng (2007) "Simulation of Neutrophil Deformation and Transport in Capillaries using Newtonian and Viscoelastic Drop Models." Ann

Biomed Eng 35(5): 766-80

Zhou, E H., C T Lim, T K.S.W and Q S.T (2004) "Finite element modeling of the micropipette aspiration of malaria-infected red blood cells." The 3rd international conference on experimental mechanics, Singapore, 2004

Zhou, E H., C T Lim, T K.S.W and Q S.T (2004) "Proceedings of the 2nd world congress for Chinese biomedical engineers, Beijing, China."