<p>The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.</p> / Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology

No description available.

The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model. / Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology

Dans ce travail, nous nous intéressons à l’interaction champ électrique-particule diélectrique dans les phénomènes diélectrophorétiques, aussi bien d’un point de vue théorique que numérique. L’application à long terme concerne l’électro- manipulation des cellules biologiques. La compréhension de ces phénomènes nécessite une modélisation complète des mécanismes de polarisation qui régissent l’interaction champ-particule, et met en oeuvre des modèles électromécanique et électroci- nétique. Après avoir introduit les différents phénomènes et notions nécessaires, nous abordons la modélisation de la polarisation à l’aide de la théorie du potentiel et proposons une approche pour déterminer numériquement les coefficients de polarisation identifiés. Nous montrons que, si le développement multipolaire peut se réduire au premier ordre pour le cas d’une particule sphérique plongée dans un champ uniforme, les ordres supérieurs sont nécessaires pour les particules non sphériques. Nous montrons également comment un processus d’homogénéisation permet d’étudier les configurations de particules multicouches avec cette approche. Dans le cadre de l’étude électromécanique des phénomènes diélectrophorétiques, nous mettons ensuite en œuvre cette approche multipolaire. Deux applications traitées numériquement sont présentées. Nous y montrons la pertinence de cette approche pour calculer la force et le couple exercés sur une particule dans des situations où le champ appliqué présente de fortes non-uniformités, l’approche dipolaire classique se révélant beaucoup moins performante dans ce cas. La particule et son milieu de suspension étant en réalité deux milieux en contact mais non-indépendants, des phénomènes électrocinétiques se produisent à l’interface. Ces effets interfaciaux sont abordés en vue de les prendre en compte dans le phénomène d’électrorotation d’une cellule biologique. Nous modélisons le problème complet d’une particule sphérique chargée plongée dans un milieu de suspension et soumise à un champ tournant en prenant en compte les effets électroosmotiques. La résolution par éléments finis de ce problème couplé montre la pertinence de l’approche développée, notamment pour les basses fréquences. / In this work, we investigate about the interaction between electrical fields and dielectric particles in the dielectrophoretic phenomena, in theorical and numerical ways. The long-term application are related to electromanipulation and caracterisation of biological cells. Understanding these phenomena requires a complete modeling of polarization mechanisms governing the field-particle interaction and implements electromechanical and electrokinetic models. After introducing the necessary concepts and phenomena, we address polarization modeling using potential theory and suggest an approach for a numerical determination of polarization coefficients. We show that if the multipolar expansion can be reduced to the first order for the case of a spherical particle immersed in a uniform field, the higher orders are needed for nonspherical particles. We show also how a homogenization process allows the study of multilayered particles configurations using this approach. As part of the electromechanical study of dielectrophoretic phenomena, we implement the multipolar approach for two applications numerically treated. We show the relevance of this approach to calculate the force and torque exerted on a particle in situations where the applied field has strong non-uniformities, where the classical dipole approach turn out to be much less efficient. The particle and the suspending medium are in reality two media in contact but not independent as some electrokinetic phenomena occur at the interface. These interfacial effects are addressed in order to be taken into account in the electrorotation phenomenon of a biological cell. The model dealing with the whole problem of a charged spherical particle immersed in a suspension medium and subjected to a rotating field and taking into account the electroosmotic effects is treated. The resolution of the corresponding coupled problem using the finite element method shows the relevance of this approach.

No description available.

There is an increasing need for accurate models describing the electrical behaviour of individual biological cells exposed to electromagnetic fields. In this area of solving linear problem, the most frequently used technique for computing the EM field is the Finite-Difference Time-Domain (FDTD) method. When modelling objects that are small compared with the wavelength, for example biological cells at radio frequencies, the standard Finite-Difference Time-Domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD, based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating the Hodgkin and Huxley membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900MHz, 1800MHz and 2450MHz. This method will facilitate deeper investigation of the phenomena in the interaction between EM fields and biological systems. Moreover, the nonlinear response of biological cell exposed to a 0.9GHz signal was discussed on observing the second harmonic at 1.8GHz. In this, an electrical circuit model has been proposed to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with known nonlinear device. Meanwhile, the first and second harmonic responses of the cavity due to the loading of the cavity with the lossy material will also be demonstrated. The results from proposed mathematical model, give good indication of the input power required to detect the weakly effects of the second harmonic signal prior to perform the measurement. Hence, this proposed mathematical model will assist to determine how sensitivity of the second harmonic signal can be detected by placing the required specific input power.

No description available.

yes / There is an increasing need for accurate models describing the electrical behaviour of individual biological cells exposed to electromagnetic fields. In this area of solving linear problem, the most frequently used technique for computing the EM field is the Finite-Difference Time-Domain (FDTD) method. When modelling objects that are small compared with the wavelength, for example biological cells at radio frequencies, the standard Finite-Difference Time-Domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD, based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating the Hodgkin and Huxley membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900MHz, 1800MHz and 2450MHz. This method will facilitate deeper investigation of the phenomena in the interaction between EM fields and biological systems. Moreover, the nonlinear response of biological cell exposed to a 0.9GHz signal was discussed on observing the second harmonic at 1.8GHz. In this, an electrical circuit model has been proposed to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with known nonlinear device. Meanwhile, the first and second harmonic responses of the cavity due to the loading of the cavity with the lossy material will also be demonstrated. The results from proposed mathematical model, give good indication of the input power required to detect the weakly effects of the second harmonic signal prior to perform the measurement. Hence, this proposed mathematical model will assist to determine how sensitivity of the second harmonic signal can be detected by placing the required specific input power.

Miniature compliant grippers are designed and developed to manipulate biological cells and characterize them. Apart from grippers, other compliant mechanisms are also demonstrated to be effective in manipulation and characterization. Although scalability and force-sensing capability are inherent to a compliant mechanism, it is important to design a compliant mechanism for a given application. Two techniques based on Spring-lever models and kinetoelastostatic maps are developed and used for designing compliant devices. The kinetoelastostatic maps-based technique is a novel approach in designing a mechanism of a given topology and shape. It is also demonstrated that these techniques can be used to tune the stiffness of a mechanism for a given application. In situations where any single mechanism is incapable of executing a specific task, two or more mechanisms are combined into a single continuum with enhanced functionality. This has led to designs of composite compliant mechanisms. Biological cells are manipulated using compliant grippers in order to study their mechanical responses. Biological cells whose size varies from 1 mm (a large zebrafish embryo) to 10 µm (human liver cells), and which require the grippers to resolve forces ranging from 1 mN (zebrafish embryo) to 10 nN (human cells), are manipulated. In addition to biological cells, in some special cases such as tissue-cutting and cement-testing, inanimate specimens are used to highlight specific features of compliant mechanisms. Two extreme cases of manipulation are carried out to demonstrate the efficacy of the design techniques. They are: (i) breaking a stiff cement specimen of stiffness 250 kN/m (ii) gentle grasping of a soft zebrafish embryo of stiffness 10 N/m. Apart from manipulation, wherever it is viable, the mechanisms are interfaced with a haptic device such that the user’s experience of manipulation is enriched with force feedback. An auxiliary study on the characterization of cells is carried out using a micro¬pipette based aspiration technique. Using this technique, cells existing in different conditions such as perfusion, therapeutic medicines, etc., are mechanically characterized. This study is to qualitatively compare aspiration-based techniques with compliant gripper-based manipulation techniques. A compliant gripper-based manipulation technique is beneficial in estimating the bulk stiffness of the cells and can be extended to estimate the distribution of Young’s modulus in the interior. This estimation is carried out by solving an inverse problem. A previously reported scheme to solve over specified boundary conditions of an elastic object—in this case a cell—is improved, and the improved scheme is validated with the help of macro-scale specimens.

Les travaux présentés dans ce manuscrit de thèse concernent le développement d’une méthode de caractérisation électrique de cellules biologiques, sans marquage, basée sur la diélectrophorèse Ultra Haute Fréquence (DEP-UHF). Sous l’action d’un champ électrique alternatif non uniforme, les cellules biologiques sont soumises à des forces de déplacement essentiellement liées à leurs propriétés diélectriques. En particulier, aux hautes fréquences, le champ électrique pénètre à l’intérieur de la cellule et interagit donc avec son contenu intracellulaire. Il est donc possible d’accéder à une «signature diélectrophorétique» de la cellule représentative de ses propriétés biologiques internes mais aussi de mécanismes physiologiques tels que l’apoptose ou encore la différenciation. Ce manuscrit présente le développement d’un microsystème innovant, implémenté à partir des couches passives d’une puce BiCMOS et couplé à un réseau microfluidique, pour la caractérisation, à l’échelle cellulaire, par DEP-UHF. Le microsystème développé permet une analyse fine et précise du comportement DEP haute fréquence d’une cellule. Un banc expérimental dédié aux caractérisations cellulaires, capable de générer des signaux hautes fréquences dans la gamme 10 MHz – 1 GHz pour des amplitudes allant jusqu’à 18 Vpp, a été développé. Ces travaux exploratoires ont pour but de démontrer le potentiel de discrimination de cette méthode entre différentes lignées cellulaires cancéreuses humaines à des stades tumoraux différents, dans l’objectif de développer de nouveaux outils d’aide au diagnostic. L’existence de différences significatives entre les signatures de certains types cellulaires ouvre des perspectives très intéressantes notamment pour le développement d’outils de tri cellulaire originaux basés uniquement sur les propriétés diélectriques intracellulaires. / The work presented in this dissertation concerns the development of an original label-free electrical characterization method dedicated to biological cells based on Ultra High Frequency dielectrophoresis (DEP-UHF). Under the action of a non-uniform alternative electric field, the biological cells are subjected to displacement forces related to their own dielectric properties. In particular, at high frequencies, the electric field penetrates inside the cell and thus interacts with its intracellular content. Therefore, it is possible to access to a «dielectrophoretic signature» of the cell that it is representative of its internal biological properties but also of physiological mechanisms such as apoptosis or differentiation. This dissertation presents the development of an innovative microsystem, implemented in the passive layer stack of a BiCMOS chip and associated with microfluidic, dedicated to biological characterization, at the cellular level. The developed microsystem allows an accurate analysis of a single cell DEP-UHF behaviour. An experimental bench, dedicated to cell characterization, and able to generate high frequency signals from 10 MHz to 1 GHz up to 18 Vpp magnitude, has been also developed accordingly. Actually, the led exploratory work achieved was focused on evaluating the discrimination potential of this method between different human cancer cells at different tumor stages with the objective to envision new kind of diagnostic tools. Finally, the existence of significant differences between the signatures of different cell types leads to very interesting perspectives, particularly for the development of new cell sorting tools based especially on the intracellular dielectric properties.