The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete elem...The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.展开更多
A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been deve...A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.展开更多
A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forwar...A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.展开更多
Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coa...Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of展开更多
It aims to investigate the protective effects of sodium hyaluronate,panthenol,Portulaca oleracea L.and Calendula officinalis L.on hyperosmotic dehydration-induced injury of human immortalized keratinocytes(HaCaT).The ...It aims to investigate the protective effects of sodium hyaluronate,panthenol,Portulaca oleracea L.and Calendula officinalis L.on hyperosmotic dehydration-induced injury of human immortalized keratinocytes(HaCaT).The safety mass concentrations of four raw materials were screened by detecting cell viability,and the secretion of hyaluronic acid(HA)was determined using the ELISA method.The expression of HaCaT barrier function related genes(OVOL1,EREG,TGM1,TGM2,IVL,IRF6,THBS1,CASP14)was detected at the mRNA level to explore the regulatory effect of four raw materials on these genes.The results demonstrate that pretreatment with the four kinds of raw materials could increase the cell viability after hyperosmotic dehydration,promote the secretion of HA,and improve the expression of barrier function related genes after hyperosmotic dehydration,among which panthenol and Calendula officinalis L.are better.The results show that the four raw materials have a certain protective effect on the hyperosmotic dehydration cell model,which provides data support for its application in cosmetics.展开更多
This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume e...This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.展开更多
A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-indu...A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-induced volume loss effects.The numerical model was verified based on the results of a centrifuge test and a set of parametric studies was implemented based on this model.There is good agreement between the trend of the results of the centrifuge test and the present model.The results of parametric studies show that the tunnelling-induced pile internal force and deformation depend mainly on the pile?tunnel distance,the pile length to tunnel depth ratio and the volume loss.Two different zones are separated by a 45° line projected from the tunnel springline.Within the zone of influence,the pile is subjected to tensile force and large settlement;whereas outside the zone of influence,dragload and small settlement are induced.It is also established that the impact of tunnelling on a pile group is substantially smaller as compared with a single pile in the same location with the rear pile in a group,demonstrating a positive pile group effect.展开更多
The objective of this work is to develop a novel feature for traffic flow models, when traffic queues on two-way arterials periodically extend until then they block an upstream signal in oversaturated conditions. The ...The objective of this work is to develop a novel feature for traffic flow models, when traffic queues on two-way arterials periodically extend until then they block an upstream signal in oversaturated conditions. The new model, proposed as conditional cell transmission model （CCTM） has been developed with two improvements. First, cell transmission model （CTM） is expanded for two-way arterials by taking account of all diverging and merging activities at intersections. Second, a conditional cell is added to simulate periodic spillback and blockages at an intersection. The results of experiments for a multilane, two-way, three-signal sample network demonstrate that CCTM can accommodate various traffic demands and accurate representation of blockages at intersections. The delay of left turns is underestimated by 40 % in moderate conditions and by 58% in oversamrated condition when using the CTM rather than CCTM. Finally, the consistency between HCS 2000 and CCTM shows that CCTM is a reliable methodology of modeling traffic flow in oversaturated condition.展开更多
A water balance has a significant impact on the overall system performance in proton exchange membrane fuel cell.An actual fuel cell application has a dynamic electrical load which means also dynamic electrical curren...A water balance has a significant impact on the overall system performance in proton exchange membrane fuel cell.An actual fuel cell application has a dynamic electrical load which means also dynamic electrical current.Therefore,since this electrical current is known,the water production from the fuel cell reaction is also able to be predicted.As long as the fuel cell water transportation model is provided,the present liquid water inside the porous medium is also able to be modeled.A model of the liquid water saturation level in a fuel cell in unsteady load condition was proposed.This model is a series of the water transportation model of water saturation level for the final output of proton exchange membrane(PEM) fuel cell to predict the flooding or drying of PEM fuel cell.The simulation of vehicle fuel cell in different dynamic load profiles and different inlet air conditions was done using this model.The simulation result shows that PEM fuel cell with different dynamic load profiles has different liquid water saturation level profiles.This means that a dynamic load fuel cell requires also a dynamic input air humidification.展开更多
A novel conditional cell transmission model （CCTM） is a potential simulation tool because it accommodates all traffic conditions from light condition to oversaturated condition. To test the performance of the CCTM, ...A novel conditional cell transmission model （CCTM） is a potential simulation tool because it accommodates all traffic conditions from light condition to oversaturated condition. To test the performance of the CCTM, a series of experiments for sensitivity analysis were designed and performed for a multilane, two-way, three-signal sample network. Experiment 1 shows that the model is performed in a logical and expected manner with variations in traffic demand with time and direction. Experiment 2 shows when the possibility of the occurrence of a useful gap increases to 60% and 100%, the delays in left rams decrease by 5% and 15%, respectively. In Experiment 3, comparing the possibility of a conditional cell of 0 with 100%, delay of left turn and delay of the entire network were underestimated by 58% and 11%, respectively. Hence, sensitivity analysis demonstrates that by reflecting local drivers＇ behaviors properly, the CCTM provides an accurate representation of traffic flow in simulating oversaturated traffic conditions.展开更多
In order to investigate enhancements to cell transmission model (CTM) as a tool for traffic signal timing in oversaturated conditions, randomly distributed saturation flow rates and arrival rates were used instead of ...In order to investigate enhancements to cell transmission model (CTM) as a tool for traffic signal timing in oversaturated conditions, randomly distributed saturation flow rates and arrival rates were used instead of constant values to simulate traffic flow movement, estimate the average delay of the network and search for an optimal traffic signal timing plan. A case study was given to demonstrate that the proposed methodology can capture unique phenomena in oversaturated conditions such as forward wave, spillback and lane entrance blockage. The results show that CTM underestimates travel time by 25% when compared to Simtraffic, while the enhanced CTM underestimates by only 3%. A second case study shows that a dynamic signal timing plan is superior to a fixed signal timing plan in the term of average delay.展开更多
Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and th...Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and theoretical models. Micropipette aspiration (MPA) is one of common techniques in determining mechanical properties of the living cells. The halfspace model (HSM) is employed in MPA technique. However,in the conditions of linear constitutive relations and small deformations,the HSM is inadequate for characterizing the MPA of a spherical cell in two respects. Firstly,the cell size is fairly finite other than semi-infinite to the inner radius of a micropipette;Secondly,cells are compressible,with a Poisson’s ratioνvarying from 0. 2 to 0. 4 (23-25) instead of incompressible (ν=0. 5). Thus,a more accurate model is necessary.In this study,the viscoelastic expressions were derived from our previous MPA test. Then,a sphere model (SM) employed to analyze mechanical properties of rabbit chondrocytes combined with the experimental data. Differences in mechanical properties estimated by different mechanical models were evaluated.Methods A sphere model (SM) was employed. The relative dimension of cell to micropipette and the compressibility of the cell were taken into account,as shown in Fig. 1a.■Fig.1 Sphere model of the MPA of a single cell employing different constitutive relationships The approximate expression for the aspirated length was obtained from our previous study as follows:■Furthermore,assuming that the cell behaves as a homogeneous and isotropic standard linear solid (Fig. 1b),two viscoelastic creep expressions of the aspirated length for incompressible sphere model (ICSM) and for compressible sphere model (CSM) were derived by elastic-viscoelastic correspondence principle and integral transformation as Eqs.(2) and (3)respectively.■Results(1) Comparisons of models The elastic modulus from the ICSM was 47. 4%higher than that of the half-space model (HSM)(P<0. 001). For the CSM,the percentage increase in E over the value for the HSM was 87. 7%,78. 9%,and 64. 9%when the Poisson’s ratio was set to 0. 2,0. 3,and 0. 4,respectively.For the viscoelasticity,the parameters for the ICSM and CSM were significantly larger than those of the HSM (P <0. 001). The k1,k2,andμfor the ICSM were 37. 8%,37. 9%,and 39. 0%higher,respectively,than those of the HSM. For the CSM,the viscoelastic parameters decreased with the increase ofν. Whenν=0. 3,k1,k2,andμincreased by 71. 0%,200%,and 157%,respectively,compared to those of the ICSM (P<0. 001);For the cases ofν=0. 2 andν=0. 4,the above parameters were respectively 102%,243%,and 209%and 35. 3%,97. 5%,and 79%higher than those of the ICSM.(2) Predictions for the relative errors of mechanical parameters caused by HSM e is defined as the relative change of elastic moduli (or relative error) between the HSM and SM. As shown in Fig. 2,when Poisson’s ratioνis 0. 3,in order to let the e less than 30%,relative dimension between the cell and the micropipetteξneeds to be at least 5. 0. Whenνequals 0. 5 (ICSM),ξis about 3. 3 to make the e reach 20%. However,ξis rarely larger than 5. 0 in general MPA experiments,thus the relative error of modulus will exceed 30%. The above results are independent of cell types,thus they are applicable to other spherical solid-like cells.■Fig.2 Thresholds ofξvarying withνwhen e was 10%,20%,and 30%,respectively Another parameter VR was introduced to represent the relative errors of viscoelastic parameters between HSM and SM.With regard to ICSM (Fig. 3a),whenξis 3,VRis nearly 22%. If theξis larger than 8. 0,the relative error will be reduced to less than 10%. For the CSM,the viscoelastic parameters of a typical chondrocyte varying withξandνwere obtained,as shown from Figs. 3b to 3d. Whenνtends to 0. 5,the parameters tend to those of ICSM. When theξexceeds 10,each parameter changes very little. For a certain Poisson’s ratio (ν=0. 3),whenξis 3,the VR of k1,k2,andμare 47. 1%,70. 8%,and 68. 2%,respectively. Whenξequals 5 and 10,the above values are 42. 3%,68. 8%,65%,and 38. 4%,66. 0%,63. 2%,respectively. For a givenξ(ξ=3),whenνis 0. 2,the VR of k1,k2,andμare 53. 6%,73. 3%,and 75. 0%,respectively.Whenνis taken as 0. 3 and 0. 4,the above errors are 47. 7%,71. 1%,68. 2%,and 38. 4%,58. 8%,54. 8%,respectively.Thus,the VR also decreases with the increase ofξandν.Conclusions The effects of the relative dimension between the cell,and micropipette and the Poisson’s ratio of cell were remarkable and should be taken into consideration in the pursuit of more accurate mechanical parameters of cells.展开更多
基金Project(51378006) supported by National Natural Science Foundation of ChinaProject(141076) supported by Huoyingdong Foundation of the Ministry of Education of China+1 种基金Project(2242015R30027) supported by Excellent Young Teacher Program of Southeast University,ChinaProject(BK20140109) supported by the Natural Science Foundation of Jiangsu Province,China
文摘The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.
基金Projects(41674080,41674079)supported by the National Natural Science Foundation of China
文摘A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.
基金Project(60672042) supported by the National Natural Science Foundation of China
文摘A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.
文摘Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of
文摘It aims to investigate the protective effects of sodium hyaluronate,panthenol,Portulaca oleracea L.and Calendula officinalis L.on hyperosmotic dehydration-induced injury of human immortalized keratinocytes(HaCaT).The safety mass concentrations of four raw materials were screened by detecting cell viability,and the secretion of hyaluronic acid(HA)was determined using the ELISA method.The expression of HaCaT barrier function related genes(OVOL1,EREG,TGM1,TGM2,IVL,IRF6,THBS1,CASP14)was detected at the mRNA level to explore the regulatory effect of four raw materials on these genes.The results demonstrate that pretreatment with the four kinds of raw materials could increase the cell viability after hyperosmotic dehydration,promote the secretion of HA,and improve the expression of barrier function related genes after hyperosmotic dehydration,among which panthenol and Calendula officinalis L.are better.The results show that the four raw materials have a certain protective effect on the hyperosmotic dehydration cell model,which provides data support for its application in cosmetics.
文摘This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.
文摘A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-induced volume loss effects.The numerical model was verified based on the results of a centrifuge test and a set of parametric studies was implemented based on this model.There is good agreement between the trend of the results of the centrifuge test and the present model.The results of parametric studies show that the tunnelling-induced pile internal force and deformation depend mainly on the pile?tunnel distance,the pile length to tunnel depth ratio and the volume loss.Two different zones are separated by a 45° line projected from the tunnel springline.Within the zone of influence,the pile is subjected to tensile force and large settlement;whereas outside the zone of influence,dragload and small settlement are induced.It is also established that the impact of tunnelling on a pile group is substantially smaller as compared with a single pile in the same location with the rear pile in a group,demonstrating a positive pile group effect.
基金Project(51108343) supported by the National Natural Science Foundation of ChinaProject(06121) supported by University of Transportation Center for Alabama,USA
文摘The objective of this work is to develop a novel feature for traffic flow models, when traffic queues on two-way arterials periodically extend until then they block an upstream signal in oversaturated conditions. The new model, proposed as conditional cell transmission model （CCTM） has been developed with two improvements. First, cell transmission model （CTM） is expanded for two-way arterials by taking account of all diverging and merging activities at intersections. Second, a conditional cell is added to simulate periodic spillback and blockages at an intersection. The results of experiments for a multilane, two-way, three-signal sample network demonstrate that CCTM can accommodate various traffic demands and accurate representation of blockages at intersections. The delay of left turns is underestimated by 40 % in moderate conditions and by 58% in oversamrated condition when using the CTM rather than CCTM. Finally, the consistency between HCS 2000 and CCTM shows that CCTM is a reliable methodology of modeling traffic flow in oversaturated condition.
文摘A water balance has a significant impact on the overall system performance in proton exchange membrane fuel cell.An actual fuel cell application has a dynamic electrical load which means also dynamic electrical current.Therefore,since this electrical current is known,the water production from the fuel cell reaction is also able to be predicted.As long as the fuel cell water transportation model is provided,the present liquid water inside the porous medium is also able to be modeled.A model of the liquid water saturation level in a fuel cell in unsteady load condition was proposed.This model is a series of the water transportation model of water saturation level for the final output of proton exchange membrane(PEM) fuel cell to predict the flooding or drying of PEM fuel cell.The simulation of vehicle fuel cell in different dynamic load profiles and different inlet air conditions was done using this model.The simulation result shows that PEM fuel cell with different dynamic load profiles has different liquid water saturation level profiles.This means that a dynamic load fuel cell requires also a dynamic input air humidification.
基金Project(51108343)supported by the National Natural Science Foundation of ChinaProject(06121)supported by University of Transportation Center for Alabama,USA
文摘A novel conditional cell transmission model （CCTM） is a potential simulation tool because it accommodates all traffic conditions from light condition to oversaturated condition. To test the performance of the CCTM, a series of experiments for sensitivity analysis were designed and performed for a multilane, two-way, three-signal sample network. Experiment 1 shows that the model is performed in a logical and expected manner with variations in traffic demand with time and direction. Experiment 2 shows when the possibility of the occurrence of a useful gap increases to 60% and 100%, the delays in left rams decrease by 5% and 15%, respectively. In Experiment 3, comparing the possibility of a conditional cell of 0 with 100%, delay of left turn and delay of the entire network were underestimated by 58% and 11%, respectively. Hence, sensitivity analysis demonstrates that by reflecting local drivers＇ behaviors properly, the CCTM provides an accurate representation of traffic flow in simulating oversaturated traffic conditions.
基金Project(51108343) supported by the National Natural Science Foundation of ChinaProject(06121) supported by University of Transportation Center for Alabama, USA
文摘In order to investigate enhancements to cell transmission model (CTM) as a tool for traffic signal timing in oversaturated conditions, randomly distributed saturation flow rates and arrival rates were used instead of constant values to simulate traffic flow movement, estimate the average delay of the network and search for an optimal traffic signal timing plan. A case study was given to demonstrate that the proposed methodology can capture unique phenomena in oversaturated conditions such as forward wave, spillback and lane entrance blockage. The results show that CTM underestimates travel time by 25% when compared to Simtraffic, while the enhanced CTM underestimates by only 3%. A second case study shows that a dynamic signal timing plan is superior to a fixed signal timing plan in the term of average delay.
文摘Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and theoretical models. Micropipette aspiration (MPA) is one of common techniques in determining mechanical properties of the living cells. The halfspace model (HSM) is employed in MPA technique. However,in the conditions of linear constitutive relations and small deformations,the HSM is inadequate for characterizing the MPA of a spherical cell in two respects. Firstly,the cell size is fairly finite other than semi-infinite to the inner radius of a micropipette;Secondly,cells are compressible,with a Poisson’s ratioνvarying from 0. 2 to 0. 4 (23-25) instead of incompressible (ν=0. 5). Thus,a more accurate model is necessary.In this study,the viscoelastic expressions were derived from our previous MPA test. Then,a sphere model (SM) employed to analyze mechanical properties of rabbit chondrocytes combined with the experimental data. Differences in mechanical properties estimated by different mechanical models were evaluated.Methods A sphere model (SM) was employed. The relative dimension of cell to micropipette and the compressibility of the cell were taken into account,as shown in Fig. 1a.■Fig.1 Sphere model of the MPA of a single cell employing different constitutive relationships The approximate expression for the aspirated length was obtained from our previous study as follows:■Furthermore,assuming that the cell behaves as a homogeneous and isotropic standard linear solid (Fig. 1b),two viscoelastic creep expressions of the aspirated length for incompressible sphere model (ICSM) and for compressible sphere model (CSM) were derived by elastic-viscoelastic correspondence principle and integral transformation as Eqs.(2) and (3)respectively.■Results(1) Comparisons of models The elastic modulus from the ICSM was 47. 4%higher than that of the half-space model (HSM)(P<0. 001). For the CSM,the percentage increase in E over the value for the HSM was 87. 7%,78. 9%,and 64. 9%when the Poisson’s ratio was set to 0. 2,0. 3,and 0. 4,respectively.For the viscoelasticity,the parameters for the ICSM and CSM were significantly larger than those of the HSM (P <0. 001). The k1,k2,andμfor the ICSM were 37. 8%,37. 9%,and 39. 0%higher,respectively,than those of the HSM. For the CSM,the viscoelastic parameters decreased with the increase ofν. Whenν=0. 3,k1,k2,andμincreased by 71. 0%,200%,and 157%,respectively,compared to those of the ICSM (P<0. 001);For the cases ofν=0. 2 andν=0. 4,the above parameters were respectively 102%,243%,and 209%and 35. 3%,97. 5%,and 79%higher than those of the ICSM.(2) Predictions for the relative errors of mechanical parameters caused by HSM e is defined as the relative change of elastic moduli (or relative error) between the HSM and SM. As shown in Fig. 2,when Poisson’s ratioνis 0. 3,in order to let the e less than 30%,relative dimension between the cell and the micropipetteξneeds to be at least 5. 0. Whenνequals 0. 5 (ICSM),ξis about 3. 3 to make the e reach 20%. However,ξis rarely larger than 5. 0 in general MPA experiments,thus the relative error of modulus will exceed 30%. The above results are independent of cell types,thus they are applicable to other spherical solid-like cells.■Fig.2 Thresholds ofξvarying withνwhen e was 10%,20%,and 30%,respectively Another parameter VR was introduced to represent the relative errors of viscoelastic parameters between HSM and SM.With regard to ICSM (Fig. 3a),whenξis 3,VRis nearly 22%. If theξis larger than 8. 0,the relative error will be reduced to less than 10%. For the CSM,the viscoelastic parameters of a typical chondrocyte varying withξandνwere obtained,as shown from Figs. 3b to 3d. Whenνtends to 0. 5,the parameters tend to those of ICSM. When theξexceeds 10,each parameter changes very little. For a certain Poisson’s ratio (ν=0. 3),whenξis 3,the VR of k1,k2,andμare 47. 1%,70. 8%,and 68. 2%,respectively. Whenξequals 5 and 10,the above values are 42. 3%,68. 8%,65%,and 38. 4%,66. 0%,63. 2%,respectively. For a givenξ(ξ=3),whenνis 0. 2,the VR of k1,k2,andμare 53. 6%,73. 3%,and 75. 0%,respectively.Whenνis taken as 0. 3 and 0. 4,the above errors are 47. 7%,71. 1%,68. 2%,and 38. 4%,58. 8%,54. 8%,respectively.Thus,the VR also decreases with the increase ofξandν.Conclusions The effects of the relative dimension between the cell,and micropipette and the Poisson’s ratio of cell were remarkable and should be taken into consideration in the pursuit of more accurate mechanical parameters of cells.
