Three-Dimensional Numerical Modeling of Acoustic Trapping in Glass Capillaries

Acoustic traps are used to capture and handle suspended microparticles and cells in microfluidic applications. A particular simple and much-used acoustic trap consists of a commercially available, millimeter-sized, liquid-filled glass capillary actuated by a piezoelectric transducer. Here, we present a three-dimensional numerical model of the acoustic pressure field in the liquid coupled to the displacement field of the glass wall, taking into account mixed standing and traveling waves as well as absorption. The model predicts resonance modes well suited for acoustic trapping, their frequencies and quality factors, the magnitude of the acoustic radiation force on a single test particle as a function of position, and the resulting acoustic retention force of the trap. We show that the model predictions are in agreement with published experimental results, and we discuss how improved and more stable acoustic trapping modes might be obtained using the model as a design tool.Comment: 13 pages, 15 pdf figures, pdfLatex/Revte

Collective motion of cells: from experiments to models

Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems having been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals therefore the study of collective motion of cells is likely to reveal some specific important features which are overviewed in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is both presenting the related experimental observations and treating them in the light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.Comment: 24 pages, 25 figures, 13 reference video link

The motion of a deforming capsule through a corner

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner

Numerical and experimental analysis of a hybrid material acoustophoretic device for manipulation of microparticles.

Acoustophoretic microfluidic devices have been developed for accurate, label-free, contactless, and non-invasive manipulation of bioparticles in different biofluids. However, their widespread application is limited due to the need for the use of high quality microchannels made of materials with high specific acoustic impedances relative to the fluid (e.g., silicon or glass with small damping coefficient), manufactured by complex and expensive microfabrication processes. Soft polymers with a lower fabrication cost have been introduced to address the challenges of silicon- or glass-based acoustophoretic microfluidic systems. However, due to their small acoustic impedance, their efficacy for particle manipulation is shown to be limited. Here, we developed a new acoustophoretic microfluid system fabricated by a hybrid sound-hard (aluminum) and sound-soft (polydimethylsiloxane polymer) material. The performance of this hybrid device for manipulation of bead particles and cells was compared to the acoustophoretic devices made of acoustically hard materials. The results show that particles and cells in the hybrid material microchannel travel to a nodal plane with a much smaller energy density than conventional acoustic-hard devices but greater than polymeric microfluidic chips. Against conventional acoustic-hard chips, the nodal line in the hybrid microchannel could be easily tuned to be placed in an off-center position by changing the frequency, effective for particle separation from a host fluid in parallel flow stream models. It is also shown that the hybrid acoustophoretic device deals with smaller temperature rise which is safer for the actuation of bioparticles. This new device eliminates the limitations of each sound-soft and sound-hard materials in terms of cost, adjusting the position of nodal plane, temperature rise, fragility, production cost and disposability, making it desirable for developing the next generation of economically viable acoustophoretic products for ultrasound particle manipulation in bioengineering applications

Multi-physics interactions drive VEGFR2 relocation on endothelial cells.

Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM). We develop a mathematical model in order to simulate the relocation of VEGFR2 on the cell membrane during the mechanical adhesion of cells onto a ligand-enriched substrate. Co-designing the in vitro experiments with the simulations allows identifying three phases of the receptor dynamics, which are controlled respectively by the high chemical reaction rate, by the mechanical deformation rate, and by the diffusion of free receptors on the membrane. The identification of the laws that regulate receptor polarization opens new perspectives toward developing innovative anti-angiogenic strategies through the modulation of EC activatio

Cell traction forces in 3-D microenvironments

Las células son capaces de sentir y responder activamente frente a los estímulos mecánicos de su entorno. Los estímulos mecánicos que provienen de la matriz extracelular, tales como la rigidez, la topología de la superficie o la deformación, son traducidos en señales bioquímicas a través de las interacciones entre la célula y la matriz. Para poder sobrevivir y crecer las células necesitan adherirse y propagarse sobre el sustrato que las rodea. Una vez adheridas, las células generan fuerzas contráctiles a través de la interacción actina-miosina, ejerciendo de este modo tracción sobre el sustrato subyacente. Es por ello, que las fuerzas de tracción ejercidas por las células son reguladores críticos de la adhesión, la señalización y la función celular, y por tanto son muy importantes en numerosos procesos biológicos tales como la inflamación, la cicatrización de heridas, la angiogénesis e incluso la metástasis. Pese a su importancia, la medición de las fuerzas celulares en un contexto fisiológico así como entender su contribución en los procesos biológicos sigue siendo todavía un reto. Además, debido a que las interacciones célula-matriz varían considerablemente entre ambientes bidimensionales y tridimensionales, entender su influencia sobre las respuestas celulares normales y patológicas en sistemas tridimensionales es esencial para poder traducir de manera eficiente dichos conocimientos en terapias médicas. El principal objetivo de esta Tesis es, por tanto, el desarrollo de modelos computacionales enfocados al estudio de diferentes aspectos de las interacciones célula-matriz, que permitan entender mejor los fenómenos específicos y que sirvan como referencia para el desarrollo de nuevos experimentos y de técnicas de modelado in vitro. Además, todos los modelos y experimentos contenidos en esta tesis se centran en el estudio de células individuales. En primer lugar, debido a la complejidad y a las grandes diferencias que presentan con respecto a la migración celular colectiva, y en segundo lugar debido a la importancia que supone el estudio de la migración celular individual en procesos tan importantes como es la invasión de células tumorales. Además, debido a la relevancia que suponen fisiológicamente los entornos tridimensionales, en la mayoría de los modelos in silico desarrollados en esta Tesis, se han considerado aproximaciones tridimensionales para poder así imitar mejor las condiciones in vivo de células y tejidos.En primer lugar, se ha investigado la dinámica de unión de los sitios de adhesión célula-matriz, más en particular cómo las células transmiten las fuerzas a través de estas uniones a la matriz extracelular. Para ello, se ha desarrollado un modelo numérico mediante el uso del método de los elementos finitos [1]. En segundo lugar, se ha desarrollado un modelo in vitro para el estudio de las interacciones célula-matriz tanto a nivel celular como a nivel de tejido. En particular, se presentan diferentes dispositivos de microfluídica, los cuales están siendo utilizados en la actualidad para el estudio de diferentes procesos biológicos. Estos han sido utilizados para estudiar los procesos de formación de gradientes químicos a través de una matriz tridimensional [2]. Investigaciones recientes han indicado que las fuerzas de tracción celular son reguladores críticos de la invasión de las células tumorales, las cuales dependen en gran medida de las propiedades mecánicas tanto de las células como de la matriz que las rodea. Debido a que surge la necesidad de tener un conocimiento mucho más profundo sobre este mecanismo, la segunda parte de esta Tesis se ha centrado en el desarrollo de diferentes experimentos para cuantificar las fuerzas celulares, así como en el desarrollo de un modelo in silico basado en elementos finitos para reconstruir las fuerzas ejercidas por las células durante su migración, permitiendo de este modo estudiar la dependencia de las propiedades mecánicas de las células sobre la solución de fuerzas obtenida [3]. En resumen, una mejor comprensión de los mecanismos subyacentes a las interacciones célula-matriz, aportados en parte por la aparición de nuevas tecnologías para estudiar la mecánica celular a alta resolución espacial y temporal, no sólo resulta en una mejor comprensión del comportamiento de células normales, sino que también conduce al desarrollo de terapias novedosas para tratar enfermedades relacionadas con los defectos en las interacciones mecánicas celulares.<br /

A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell

Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Cell mechanics in flow: algorithms and applications

The computer simulations are pervasively used to improve the knowledge about biophysical phenomena and to quantify effects which are difficult to study experimentally. Generally, the numerical methods and models are desired to be as accurate as possible on the chosen length and time scales, but, at the same time, affordable in terms of computations. Until recently, the cell mechanics and blood flow phenomena on the sub-micron resolution could not be rigorously studied using computer simulations. However, within the last decade, advances in methods and hardware catalyzed the development of models for cells mechanics and blood flow modeling which, previously, were considered to be not feasible. In this context, a model should accurately describe a phenomenon, be computationally affordable, and be flexible to be applied to study different biophysical changes. This thesis focuses on the development of the new methods, models, and high-performance software implementation that expand the class of problems which can be studied numerically using particle-based methods. Microvascular networks have complex geometry, often without any symmetry, and to study them we need to tackle computational domains with several inlets and outlets. However, an absence of appropriate boundary conditions for particle- based methods hampers study of the blood flow in these domains. Another obstacle to model complex blood flow problems is the absence the highperformance software. This problem restricts the applicability of the of particlebased cell flow models to relatively small systems. Although there are several validated red blood cell models, to date, there are no models for suspended eukaryotic cells. The present thesis addresses these issues. We introduce new open boundary conditions for particle-based systems and apply them to study blood flow in a part of a microvascular network. We develop a software demonstrating outstanding performance on the largest supercomputers and used it to study blood flow in microfluidic devices. Finally, we present a new eukaryotic cell model which helps in quantifying the effect of sub-cellular components on the cell mechanics during deformations in microfluidic devices