Mechanical models for malaria infected erythtocytes 6

Chapter A Multi-component Model of Malaria Infected Erythrocyte Chapter A Multi-component Model for the Malaria Infected Erythrocyte 6.1 Introduction As introduced in Chapter 1, the human erythrocyte is generally believed to behave like an elastic body, consisting of haemoglobin and erythrocyte membrane, but structural changes occur within the host erythrocyte after the invasion of malaria (P.f) parasite. In the ring stage, the parasitophorous vacuole (PV) encloses the parasites and forms a ring-like structure. The parasitophorous vacuole membrane (PVM) is semi-permeable allowing the parasite to secrete and gain nutrient. In the trophozoite stage, the parasite continue growing and occupy nearly 40% of the host erythrocyte’s volume. The membranous extensions of PVM form erythrocyte membrane-tethered Maurer’s clefts (MCs) (Haldar et al. 2002) and a tubulovesicular network (TMN). The hemozoin crystals deposit in the food vacuole (FV), making the hemoglobin digestion products visible. Knobs (K) are induced on the cell surface. In the schizont stage. The parasite divides itself and forms 16-32 daughter merozoites surrounded by the PVM. These daughter merozoites will burst out and invade uninfected erythrocytes. In Chapter 3, a two-component finite element model was developed to study the effect of initial membrane shear modulus on the deformation of malaria infected erythrocytes in micropipette aspiration and optical tweezers stretching experiments, and quantified the initial shear modulus of erythrocytes at the different infection 114 Chapter A Multi-component Model of Malaria Infected Erythrocyte stages. In this chapter, a multi-component model will be developed to account for the structural changes occurring within the host cell due to the parasite invasion. Parametric studies will be done to investigate the effect of parasite inclusion on the cell deformation during micropipette aspiration and optical tweezers stretching experiments. 6.2 Material Constitutive Relations Different from earlier chapters, a multi-component model was used. The haemoglobin was also modeled as an incompressible or nearly incompressible fluid with a hydraulic fluid model within a fluid-filled cavity. The constitutive relation of the materials used to model the erythrocyte’s membrane and PVM was expressed in the form of strain energy potential. The strain energy potential was defined in Yeoh’s form (Yeoh 1990), which was given in Equation 3.8. As derived in the Chapter (Eq. 3.1 ~ 3.13), if we assume that the material is incompressible and has a constant surface area, the initial shear modulus of the material was given in Equation 3.13. As in the previous chapter, the material used for modelling the cell membrane and PVM was simplified, so that we could reduce the parameters in defining material properties and focus more on the effect of parasite inclusion. We reduced the parameters by setting C20 = C30 = 0, where C20, C30 are the temperature-dependent material parameters. The strain energy potential was therefore simplified as 115 Chapter U A Multi-component Model of Malaria Infected Erythrocyte 0 2h0   22  32  3 (6.1) where λ1 , λ2, λ3 are the principal stretch ratios corresponding to principal axes x1 , x2, x3 , µ is the initial shear modulus of the material, h0 is the initial thickness of the membrane. 6.3 Simulation of Micropipette Aspiration In this section, simulation of micropipette aspiration will be done using the finite element multi-component model. The geometric description, boundary and loading conditions and finite element mesh will be introduced. The simulations were done using the finite element analysis program ABAQUS. The effect of parasite location, PVM size and rigidity and the inclusion of cytoplasm on the erythrocyte deformation during micropipette aspiration will be introduced. 6.3.1 Geometric Description of Micropipette Aspiration Figure 6.1. The geometric sketch of the simulation of cell deformation during micropipette aspiration using multi-component model. 116 Chapter A Multi-component Model of Malaria Infected Erythrocyte In this section, we focus on the mid to late stage of infection. Severe structural changes occur in this period and the cell becomes spherical. In this malaria infected erythrocyte model, the outer layer is a cortical shell representing the host erythrocyte membrane. The inner shell represents the semipermeable PVM of the infected erythrocyte. The whole cell is filled with incompressible fluid. Both the cell membrane and PVM are assumed to be spherical. Figure 6.1 is an illustration of the model’s basic geometry. The radius of the host cell, PVM and pipette will be measured and resized for each specific experiment. The location of PVM also varies from case to case. The fillet radius of the pipette is 0.4 µm. 6.3.2 Boundary and Loading Conditions Similar to the two-component model, due to the axisymmetric loading condition and cell geometry, the simulation was simplified as an axisymmetric problem. The finite element model was created in the x-y plane. The nodes located on the symmetric axis were only allowed to move in y-direction. A constantly increasing aspiration pressure was uniformly applied on the part of cell surface that was within the aspiration area of the rigid and fixed pipette. The interaction between membrane and PVM will be discussed later in the chapter. 117 Chapter 6.3.3 A Multi-component Model of Malaria Infected Erythrocyte Finite Element Mesh Similar to the two-component model, the membrane was represented by 449 plane stress axisymmetric elements (SAX1), and the fluid cavity was represented by 449 2-node linear hydrostatic fluid elements (FAX2). The PVM was also represented by 449 plane stress axisymmetric elements (SAX1). 6.3.4 Finite Element Analysis Using ABAQUS The model was analyzed in ABAQUS 6.4. Similar to what was described in Chapter 3, the aspiration pressure started with an initial value of Pa, and increased uniformly to 200 Pa in the simulation. When the membrane of the host cell deformed, the relative position of the PVM to the membrane was fixed. A method was introduced in Chapter (Figure 3.7) to determine whether the experiment data can be fitted with the simulation curve. Figure 6.2 shows the comparison between experiment image and simulation using ABAQUS. A trophozoite stage malaria (P.f) infected erythrocyte with a radius of 3.83 µm were aspirated into a pipette with Rp = 0.61 µm. Its shear modulus µ0 was 33.75 µN/m, calculated using hemispherical cap model. The relationship between projection length Lp and pressure difference ∆P is plotted in Figure 6.3 for both experimental data and simulation curve. The simulation was done by assuming that µ0 of the host cell membrane was equal to the value given by hemispherical cap model. The µ0 of PVM varied from µN/m to nearly rigid, and the results showed that the 118 Chapter A Multi-component Model of Malaria Infected Erythrocyte PVM with this size and location did not affect the deformation of the host erythrocyte in micropipette aspiration. ∆P=40Pa ∆P=70Pa ∆P=140Pa ∆P=160Pa ∆P=190Pa Figure 6.2. Comparison between experiment image and simulation image of a trophozoite stage malaria (P.f) infected erythrocyte with a radius of 3.83 µm being aspirated into a pipette with Rp = 0.61 µm. Figure 6.3. Relationship between projection length Lp and pressure difference ∆P of a trophozoite stage malaria (P.f) infected erythrocyte with a radius of 3.83 µm being aspirated into a pipette with Rp = 0.61 µm, analyzed using multi-component model. 119 Chapter A Multi-component Model of Malaria Infected Erythrocyte Similarly, a schizont stage malaria infected erythrocyte (Figure 6.4) was analyzed using ABAQUS, as shown in Figure 6.5. The host cell with a radius of 3.43 µm were aspirated into a pipette with Rp = 0.73 µm. Its shear modulus µ0 was 39.72 µN/m, calculated using the hemispherical cap model. The relationship between projection length Lp and pressure difference ∆P is plotted in Figure 6.6 for both experimental data and simulation curve. Figure 6.4. Experiment Image of a schizont stage malaria erythrocyte obtained from experiment, Rp = 0.73 µm, Rcell = 3.43 µm, RPVM = 2.52 µm. Figure 6.5. Finite element model of a schizont stage malaria erythrocyte being aspirated into a micropipette, Rp = 0.73 µm, Rcell = 3.43 µm, RPVM = 2.52 µm. 120 Chapter A Multi-component Model of Malaria Infected Erythrocyte The simulation was done by assuming that the µ0 of the host cell membrane was equal to the value given by hemispherical cap model. The initial shear modulus µ0 of PVM also varied from µN/m to nearly rigid, which all resulted in the same simulation curve of Lp vs. ∆P. Therefore, the results showed that the PVM with this size and location had little influence on the deformation of the host erythrocyte in micropipette aspiration. Similar tests were done for early-stage infected cells with smaller parasites. It was found that with small parasite at this location, the results of multi-component model agreed with the results of two-component model, with all other parameter values remaining constant. The effect of probing location on the cell deformation would be discussed in section 6.3.6. Figure 6.6. Relationship between projection length Lp and pressure difference ∆P of a trophozoite stage cell, analyzed using multi-component model. 121 Chapter 6.3.5 A Multi-component Model of Malaria Infected Erythrocyte Effect of Enclosed Fluid The enclosed fluid in the multi-component model also affects the model’s deformation in the simulation of the micropipette aspiration. An example is shown in Figure 6.7. Assuming that the experiment started at the same initial aspiration pressure, the deformation of the cell without enclosed fluid was bigger than the one with enclosed fluid. In the given example, the shear modulus of PVM did not affect the deformation of the host cell in micropipette aspiration. Figure 6.7. Effect of enclosed fluid on a trophozoite stage cell’s deformation in micropipette aspiration (Rp = 0.61 µm, Rcell = 3.83 µm, RPVM = 1.92 µm). 122 Chapter 6.3.6 A Multi-component Model of Malaria Infected Erythrocyte Effect of Parasite Location Figure 6.8. Illustration of probing position: section A and section B defined for micropipette aspiration. Increasing Aspiration Pressure Figure 6.9. Movement and deformation of PVM within the host cell as the aspiration pressure increased. In the previous sections, the experimental images we chose to analyze using multi-component model and hemispherical cap model all had a parasite located away from the micropipette. 123 Chapter A Multi-component Model of Malaria Infected Erythrocyte In this section, the multi-component model will be used to study the deformation of the cells that had a parasite located near to the pipette. To discuss this problem clearly, we define the section of the membrane that is very close to the PVM as section B, and the section away from the PVM as section A, as illustrated in Figure 6.8. From the experiments, it can be observed that if we probe section B of the host cell surface, with increase in aspiration pressure, the PVM also deformed within the host cell. An example is shown in Figure 6.9. Noticing the PVM’s deformation in micropipette aspiration, we did a series of tests to probe the trophozoite and schizont stage cells at both section A and section B. The results calculated using hemispherical cap model are shown in Figure. 6.10. Figure 6.10. The effect of probing positions on the calculated shear modulus using the hemispherical cap model in micropipette aspiration. 124 Chapter A Multi-component Model of Malaria Infected Erythrocyte Every cell was probed at both section A and section B. The results showed that if we probe the same cell at section B, the shear modulus of the host cell membrane given by hemispherical cap model was always higher than the ones probed at section A. One possible contributing factor was that the PVM was also aspirated into the pipette and affected the deformation of the host erythrocytes, which can be proven by Figure 6.9. Figure 6.11. The effect of probing locations on studying the same trophozoite stage malaria infected erythrocyte. The cell radius was measured as 3.09 µm. The radius of the PVM was measured as 1.67 µm. The initial shear modulus of the host cell µ0 (cell) = 15.78 µN/m. 125 Chapter A Multi-component Model of Malaria Infected Erythrocyte To study the effect of probing location of the cell surface on studying the same cell, the multi-component model was used to simulate this process, as shown in Figure 6.11. The example was given for a trophozoite stage malaria infected erythrocyte. The cell radius was measured as 3.09 µm. The radius of the PVM was measured as 1.67 µm. The inner and outer radius of the micropipette was measured as 0.71 µm and 1.41 µm, respectively. When we probed this cell at section A, the hemispherical cap model gave a shear modulus value of 15.78 µN/m. When we probe the same cell at section B, the hemispherical cap model gave a shear modulus value of 26.11 µN/m. In this graph, the preset initial shear modulus of the host cell µ0 (cell) = 15.78 µN/m, given by calculation using hemispherical cap model at section A. The initial shear modulus of the PVM µ0 (PVM) changed from ~ 10 times of µ0 (cell). In this simulation, all the four curves obtained by simulation of probing section A overlapped each other, and the simulation agreed well with that of the experimental probing the same section. This implied that the initial shear modulus of the host cell µ (cell) obtained by probing section A was suitable for describing the host cell membrane stiffness. Therefore, we applied this value obtained by probing section A to the finite element simulation of probing the host cell at section B. Similar as in Chapter 5, a hemispherical cap model was used to push the host cell ( probing section A) or PVM ( probing section B) into the pipette until Lp = Rp. The PVM and host cell membrane elements did not separate after contact. The simulation results showed that if the host cell was probed at section B, the PVM affect the deformation of the host cell. The black solid curve and red dashed curve shared the same mechanical properties of the host cell membrane and PVM, but 126 Chapter A Multi-component Model of Malaria Infected Erythrocyte they differed from each other due to their different probing location during the simulation. When the µ0 (PVM) value ranged from ~ times of µ0 (cell), the simulation curves can be fitted with the experimental data. When the µ0 (PVM) is or 10 times of the µ0 (cell), there was no obvious cell deformation in the simulation. From these results, we can see that if the cell was probed at section B, the PVM affected the cell deformation, and thus affected the validity of using the hemispherical cap model, which assumed the cell to be a fluid enclosed by membrane only. But if the cell was probed at section A, hemispherical cap model was still able to predict the shear modulus of the host cell membrane. 6.3.7 Effect of PVM Rigidity Figure 6.12. The experimental and simulation images of the micropipette aspiration of a trophozoite stage malaria infected erythrocyte (Rp = 0.67 µm, Rcell = 4.23 µm, RPVM = 2.52 µm). In section 6.3.6, it was shown that with different probing locations on the host cell surface, the PVM affected the cell deformation, and thus affected the validity of using hemispherical cap model. When we probed the host cell membrane at where the 127 Chapter A Multi-component Model of Malaria Infected Erythrocyte membrane and PVM were very close to each other (defined as section B), the PVM had an influence on the host cell’s deformation, and the deformation would be changed with different µ0 (PVM) value. Therefore, in this section, more computational tests would be done to study the effect of PVM stiffness on the cell’s deformation in micropipette aspiration. The cell radius was measured as 4.23 µm. The radius of the PVM was measured as 2.52 µm. The inner and outer radius of the micropipette was measured as 0.67 µm and 1.63 µm, respectively, as shown in Figure 6.12. When we probed this cell at section A, the hemispherical cap model gave a shear modulus value of 23.33 µN/m, and this value will be used for µ0 (cell) in this parametric study. The simulation data or probing section B of this cell was plotted in the form of Lp as a function of 0 ( PVM ) . The data shown the projection length obtained when 0 (cell ) the aspiration pressure reached 100 Pa. Since the µ0 (cell) was fixed with the value we obtained probing section A, only µ0 (PVM) was changed in this parametric study. In Figure 6.13 (a), 0 ( PVM ) varied from 1~100. The projection length 0 (cell ) (aspiration pressure = 110 Pa) decreased with the shown in Figure 6.13 (b). When 0 ( PVM ) at the range of 1~5, as 0 (cell ) 0 ( PVM ) equals to and 100, the cell deformation 0 (cell ) reached an Lp of 0.76 µm and 0.71 µm, respectively. The decreasing rate of projection length as a function of 0 ( PVM ) dropped as shown in Figure 6.13. 0 (cell ) 128 Chapter A Multi-component Model of Malaria Infected Erythrocyte (a) (b) Figure 6.13. Effect of μ0(PVM) on the host cell deformation, with a fixed μ0(cell) value, (a) μ0(PVM)/μ0(cell) varied from 1~100, (b) an enlarged plot of μ0(PVM)/μ0(cell) varied from 1~5. 6.4 Simulation of Optical Tweezers Stretching In this section, simulation of optical tweezers stretching will be done using the finite element multi-component model. The geometric description, boundary and 129 Chapter A Multi-component Model of Malaria Infected Erythrocyte loading conditions, finite element mesh will be introduced. The simulations were done using the finite element analysis program ABAQUS. The effect of PVM size and rigidity, and the interaction between host cell membrane and PVM on the erythrocytes’ deformation during micropipette aspiration will be introduced. 6.4.1 Geometric Description of Optical Tweezers Stretching Similar with earlier chapters, the finite element model was reduced and represented by only one-eighth of the cell, because of the erythrocyte’s plane symmetric geometry and the axial loading conditions. However, PVM was added into the multi-component model. z yx Contact Area Figure 6.14. The three-dimensional multi-component model of erythrocytes in the simulation of optical tweezers stretching experiments. 130 Chapter A Multi-component Model of Malaria Infected Erythrocyte As shown in Figure 6.14 (b), the three-dimensional model for trophozoite and schizont stage cells was estimated to be 3.38 μm in direction x and 3.5 μm in direction z. The contact surface where the cell attached to the silica micro beads is modelled as a flat region of μm in width and 0.55 μm in height. The cell and PVM shapes were assumed to be spherical. A parametric study on the radius of PVM would be introduced in later sections. 6.4.2 Boundary and Loading Conditions Similar to that in the Chapter (Figure 3.13), the initial boundary conditions of the erythrocyte and PVM are as follows: the edge in y-z plane: U1=UR 2=UR3=0, the edge in z-x plane: U2=UR 3=UR1=0, the edge in x-y plane: U3=UR1=UR2=0. where U1 , U2, U3 are the displacement in x, y, z direction, respectively, and UR1 , UR2, UR3 are the rotation to x, y, z axes. The coordinates are illustrated in Figure 6.14. The displacement in direction x was applied on the flat surface to stretch the erythrocyte. 131 Chapter 6.4.3 A Multi-component Model of Malaria Infected Erythrocyte Finite Element Mesh The model was analyzed in ABAQUS. The erythrocyte’s membrane was represented by three thousand S4R shell elements (4-node doubly curved shell finite membrane strains elements) on the outer surface of the model. The cytoplasm was represented by three thousand F3D4 elements (4-node linear 3-dimensional quadrilateral hydrostatic fluid element) on the inner surface of the model. The flat surface composed of 100 S4R shell elements. Two different element types were used in modelling the PVM for different purposes. When the PVM was assumed to be rigid, R3D4 (4-node, 3-dimensional bilinear quadrilateral rigid element) was used. When the PVM was assumed to be deformable, S4R (4-node doubly curved shell finite membrane strains elements) was used. There were 1500 elements used in both cases. 6.4.4 Finite Element Analysis using ABAQUS for Optical Tweezers Stretching Figure 6.15. Finite element analysis of the multi-component model’s deformation undergoing optical tweezers stretching. 132 Chapter A Multi-component Model of Malaria Infected Erythrocyte To study the effect of PVM on the erythrocyte deformation in optical tweezers stretching, we used ABAQUS to conduct finite element analysis, and obtained the axial and transverse diameter change of the erythrocyte as a function of stretching force. When the transverse diameter of the cell membrane did not decrease to the radius of PVM, as shown in Figure 6.15, the simulation results were consistent with the results obtained using two-component model. Similar test was done for biconcave shaped ring stage infected erythrocytes, and the deformation of the biconcave shaped cell was not affected by the inclusion of PVM. The results obtained from multi-component model for healthy and early-stage infected erythrocytes agreed with those obtained from two-component model. Figure 6.16. Finite element simulation of the multi-component model deformation undergoing optical tweezers stretching, when the membrane contact with PVM. 133 Chapter A Multi-component Model of Malaria Infected Erythrocyte However, if the transverse diameter of the cell membrane decreased to the radius of PVM, as shown in Figure 6.16, they contacted with each other and lead to different force-displacement relationships. The effect of PVM radius, rigidity and interaction properties on the force-displacement relationships would be discussed in detail in later sections. 6.4.5 Effect of Erythrocyte Membrane Stiffness, Interaction between Erythrocyte Membrane and PVM, and PVM Sizes on the Cell Deformation Undergoing Optical Tweezers Stretching A parametric study was done with two fixed initial shear modulus µ0 = 7.6 µN/m and µ0 = 32.8 µN/m for the host cell’s membrane. The purpose was to compare the effect of host cell membrane stiffness to other parameters like PVM radius and interaction properties between cell membrane and PVM. These two values of initial shear modulus were chosen according to the average membrane shear modulus of normal erythrocytes and trophozoite stage malaria infected erythrocytes calculated in Chapter 3. It should be noted that different from the two-component model in Chapter 3, the number of parameters used in calculating constitutive relations was reduced (Eq. 6.3), and the model was assumed to be spherical with a radius of 3.5 µm in this Chapter. The effect of PVM stiffness would be discussed in the next section, while in this section, the PVM was modelled as a rigid shell. Therefore, this parametric study was done with three changing parameters. 134 Chapter A Multi-component Model of Malaria Infected Erythrocyte As shown in Figure 6.17, the simulation curves obtained using the same membrane stiffness overlapped with each other before the axial diameter reached 7.4 µm and then branched out due to different PVM sizes. The PVM radii R 1, R2, R3, R4 and R5 shown in the figure were 2.5 µm, µm, 3.3 µm, 3.4µm, and 3.48µm, respectively. They were chosen because they could display the trend of PVM’s size effects well. When the PVM radius was smaller than 2.5 µm, the simulation result was consistent with the results obtained with PVM radius equal to 2.5 µm. Figure 6.17. Effect of membrane stiffness, interaction between PVM and cell membrane, and PVM sizes on the erythrocyte deformation in optical tweezers stretching. The PVM radii R1, R2, R3, R4 and R5 shown in the figure were 2.5 µm, µm, 3.3 µm, 3.4µm, and 3.48µm, respectively. 135 Chapter A Multi-component Model of Malaria Infected Erythrocyte The two line styles represented different interaction properties between PVM and host cell membrane. The solid lines assumed that the interaction between PVM and host cell membrane was frictionless and they were allowed to separate after contact. The dashed lines assumed that the host cell membrane was stuck to the PVM and would not separate from each other after contact. It is known that the enclosed parasite may result in an increased internal viscosity of the host erythrocyte and derive proteins such as PfEMP2 and KAHRP of PfHrP1 on the inner surface of the erythrocyte membrane (Miller et al. 1971; Magowan et al. 1988; Ho and White 1999). So the PVM and host erythrocyte membrane might bond to each other in a certain level. The simulation curves shown in solid lines did not consider the stickiness between the PVM and host erythrocyte membrane, while the curves shown in dashed lines assumed that the stickiness between PVM and cell membrane were so high that they were stuck to each other after contact. From the results, we can see that the paired solid and dashed lines did not differ from each other in most cases. Compared to the effect of membrane stiffness and PVM sizes, the interaction properties between PVM and host cell membrane stiffness played an insignificant role in the deformation of the cell stretched by optical tweezers. The stickiness between the cell membrane and PVM did not have significance influence on the cell deformation induced by optical tweezers stretching. Comparatively, the host cell membrane stiffness and PVM sizes played a bigger role in the cell deformability. With the increase in membrane stiffness and PVM radius, the axial diameter change decreased obviously. 136 Chapter 6.4.6 A Multi-component Model of Malaria Infected Erythrocyte Effect of PVM Stiffness on the Erythrocyte Deformation undergoing Optical Tweezers Stretching Figure 6.18. Effect of host cell membrane and PVM initial shear modulus on the cell deformation in the simulation of optical tweezers stretching. The host erythrocyte radius was 3.5 µm for all the simulation curves. In the last section, PVM was assumed to be rigid. In this section, PVM was assumed to be deformable. A parametric study was done with different PVM sizes, and initial shear modulus of both host cell membrane and PVM. The simulations were done using two different radii of PVM. The green and blue curves represented the RPVM value of 3.4µm, and 3.48µm, respectively. The host cell radius was 3.5 µm for 137 Chapter A Multi-component Model of Malaria Infected Erythrocyte all the simulation curves. The line styles corresponded to different combinations of host cell membrane shear modulus and PVM shear modulus, as listed in the legend. Similar to the last section, we chose initial shear modulus µ0 = 7.6 µN/m as a preset value, according to the average initial shear modulus of normal erythrocyte calculated in Chapter 3. A parametric study was done with different combinations of initial shear modulus for the host cell’s membrane and the PVM. The initial membrane shear modulus µ0(cell) was assumed to be and times of the preset value µ0 = 7.6 µN/m, while the initial shear modulus of PVM µ0 (PVM) was assumed to be and times of the µ0(cell). The results were shown in Figure 6.18. It can be observed that with the same RPVM value and µ0(cell), the increase in µ0(PVM) would lead to smaller deformation of the cell stretched by optical tweezers at equal stretching force. When the µ0(PVM) and µ0(cell) both became times bigger, the simulation curve significantly differed from the one obtained by assuming µ0(PVM) = µ0(cell) = 7.6 µN/m. The PVM radius had an influence on the cell deformation undergoing optical tweezers stretching, but the membrane and PVM stiffness seems to play a more important role in the deformation of malaria (P.f.) infected erythrocytes. 6.5 Conclusions In this chapter, the multi-component model was introduced to study the effect of parasitophorous vacuole membrane (PVM) size, stiffness and its interaction properties with the host cell membrane. The simulation was done using the finite element analysis program ABAQUS to simulate the malaria infected erythrocyte 138 Chapter A Multi-component Model of Malaria Infected Erythrocyte deformation in micropipette aspiration and optical tweezers stretching. The numerical results were found to be insensitive to the mesh parameter changes. In micropipette aspiration, parametric studies were done to study the effect of PVM on the cell deformation. The simulation also allowed us to study the effect of cytoplasm on the cell deformation. In the experiments, probing different locations on the same cell would lead to different shear modulus calculated using hemispherical cap model. The multi-component model was able to model the mechanical probing of different locations on 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 by conducting a parametric study on 0 ( PVM ) . 0 (cell ) In optical tweezers stretching, the multi-component model was also applied to study the effect of PVM on the cell deformation. Parametric studies were done with different host cell membrane stiffness, PVM stiffness, PVM sizes and different interactions between PVM and host cell membrane. The finite element analysis allowed us to quantify these effects. 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 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 significantly as in the changes in membrane stiffness, PVM sizes and PVM stiffness. 139 [...]... change decreased obviously 1 36 Chapter 6 6.4 .6 A Multi-component Model of Malaria Infected Erythrocyte Effect of PVM Stiffness on the Erythrocyte Deformation undergoing Optical Tweezers Stretching Figure 6. 18 Effect of host cell membrane and PVM initial shear modulus on the cell deformation in the simulation of optical tweezers stretching The host erythrocyte radius was 3.5 µ for all the simulation curves... model Figure 6. 16 Finite element simulation of the multi-component model deformation undergoing optical tweezers stretching, when the membrane contact with PVM 133 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte However, if the transverse diameter of the cell membrane decreased to the radius of PVM, as shown in Figure 6. 16, they contacted with each other and lead to different force-displacement... affected the deformation of the host erythrocytes, which can be proven by Figure 6. 9 Figure 6. 11 The effect of probing locations on studying the same trophozoite stage malaria infected erythrocyte The cell radius was measured as 3.09 µm The radius of the PVM was measured as 1 .67 µm The initial shear modulus of the host cell µ (cell) = 15.78 0 µ N/m 125 Chapter 6 A Multi-component Model of Malaria Infected. .. modulus of the host cell membrane 6. 3.7 Effect of PVM Rigidity Figure 6. 12 The experimental and simulation images of the micropipette aspiration of a trophozoite stage malaria infected erythrocyte (Rp = 0 .67 µ Rcell = 4.23 µ RPVM = 2.52 m, m, µ m) In section 6. 3 .6, it was shown that with different probing locations on the host cell surface, the PVM affected the cell deformation, and thus affected the... the 127 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte membrane and PVM were very close to each other (defined as section B), the PVM had an influence on the host cell’s deformation, and the deformation would be changed with different µ (PVM) value 0 Therefore, in this section, more computational tests would be done to study the effect of PVM stiffness on the cell’s deformation in micropipette... length as a function of 0 ( PVM ) dropped as shown in Figure 6. 13 0 (cell ) 128 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte (a) (b) Figure 6. 13 Effect of μ0(PVM) on the host cell deformation, with a fixed μ0(cell) value, (a) μ0(PVM)/μ0(cell) varied from 1~100, (b) an enlarged plot of μ0(PVM)/μ0(cell) varied from 1~5 6. 4 Simulation of Optical Tweezers Stretching In this section,... program ABAQUS to simulate the malaria infected erythrocyte 138 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte deformation in micropipette aspiration and optical tweezers stretching The numerical results were found to be insensitive to the mesh parameter changes In micropipette aspiration, parametric studies were done to study the effect of PVM on the cell deformation The simulation also... radius of PVM, as shown in Figure 6. 15, the simulation results were consistent with the results obtained using two-component model Similar test was done for biconcave shaped ring stage infected erythrocytes, and the deformation of the biconcave shaped cell was not affected by the inclusion of PVM The results obtained from multi-component model for healthy and early-stage infected erythrocytes agreed with... contact The simulation results showed that if the host cell was probed at section B, the PVM affect the deformation of the host cell The black solid curve and red dashed curve shared the same mechanical properties of the host cell membrane and PVM, but 1 26 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte they differed from each other due to their different probing location during the simulation... section, while in this section, the PVM was modelled as a rigid shell Therefore, this parametric study was done with three changing parameters 134 Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte As shown in Figure 6. 17, the simulation curves obtained using the same membrane stiffness overlapped with each other before the axial diameter reached 7.4 µ and then branched out due to different . erythrocytes at the different infection Chapter 6 A Multi-component Model for the Malaria Infected Erythrocyte Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte 115 stages. In. = 0 .61 µm, analyzed using multi-component model. Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte 120 Similarly, a schizont stage malaria infected erythrocyte (Figure 6. 4). Chapter 6 A Multi-component Model of Malaria Infected Erythrocyte 123 6. 3 .6 Effect of Parasite Location Figure 6. 8. Illustration of probing position: section A and section B defined for micropipette