Ivan Cimrák

Modelling and simulation of processes in microfluidic devices for biomedical applications

We investigate a mathematical model describing the flow of a liquid in a microchannel. The model incorporates immersed objects in the fluid as well as fixed obstacles and boundaries of the microchannel. Objects can have different elastic properties, including solid objects and deformable objects. The flow description accounts for all types of mechanical interactions: fluid-object, object-object, fluid-walls, and object-walls interactions.

An ESPResSo implementation of elastic objects immersed in a fluid

Abstract We review the Lattice-Boltzmann (LB) method coupled with the immersed boundary (IB) method for the description of combined flow of particulate suspensions with immersed elastic objects. We describe the implementation of the combined LB–IB method into the open-source package ESPResSo . We present easy-to-use structures used to model a closed object in a simulation package, the definition of its elastic properties, and the interaction between the fluid and the immersed object. We also present the test cases with short examples of the code explaining the functionality of the new package.

Simulation study of rare cell trajectories and capture rate in periodic obstacle arrays

Abstract Microfluidic devices that contain periodic obstacle arrays are frequently used for capture of rare cells such as circulating tumour cells (CTC). Detailed computational analysis can give valuable insights into understanding of fluidic processes inside such devices. Using our previously developed Object-in-fluid framework, we investigate characteristics of a single CTC in a suspension of red blood cells. In this work, we describe a new model for evaluation of cell capture probability that includes the surface area of the cell-obstacle contact. We analyze individual trajectories of CTCs and their distribution between the obstacles during the transport through the device. We vary two parameters – hematocrit and column radius of the cylindrical obstacles. While the hematocrit has a slight influence on the CTC trajectories and the cell capture rate computed by the newly developed model, the effect of column radius is much more pronounced. We observe that increase in column radius increases the capture rate quadratically. And secondly, with the exception of the very small column radius, increase in hematocrit slightly decreases the capture rate linearly.

Energy contributions of different elastic moduli in mesh-based modeling of deformable objects

One of the topics in biomedical engineering that is rapidly gaining interest, is modeling blood flow for various applications. We present a mesh-based model of elastic objects that can be used in such applications and a new approach to evaluation of energy contributions that correspond to different types of elastic forces in this model. We validate the new metric by looking at simulation experiments that focus on particular deformations of the object. The simulations are performed using our object-in-fluid framework as a part of extensible simulation package ESPResSo.

Recent advances in mesh-based modeling of individual cells in biological fluids

The problem of modeling blood flow can be approached on different levels of accuracy. We investigate a model consisting of two major components: the fluid representing blood plasma and the elastic objects representing all types of cells in blood, e.g. red blood cells. The elastic objects are immersed in the fluid and they interact with each other. Our research is focused on spring-network models of elastic objects. We present the results concerning the scalability of meshes. We investigate the relation between mechanical properties of physical cells and the stiffness parameters of underlying meshes. Further, we present new metric that supplements energy-based approaches in cases when the energy is difficult to calculate. To demonstrate the abilities of our software implementation, we provide tests concerning the computational complexity. We show the significant speed-up caused by using templates when generating many cells with the same elastic properties. We also demonstrate the quadratic dependence of the computational time on increasing number of simulated cells. We suggest several directions for further model enhancements, such as better implementation of cell-cell collisions, inclusion of adhesion processes, monitoring the rupture of cells, and development of physically more relevant implementation of forces for some cells elastic moduli.

Non‐uniform force allocation for area preservation in spring network models†

In modeling of elastic objects in a flow such as red blood cells, white blood cells, or tumor cells, several elastic moduli are involved. One of them is the area conservation modulus. In this paper, we focus on spring network models, and we introduce a new way of modeling the area preservation modulus. We take into account the current shape of the individual triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. The analysis shows that this approach tends to regularize the triangulation. We demonstrate this effect on individual triangles as well as on the complete triangulations. Copyright

A novel approach with non-uniform force allocation for area preservation in spring network models1)

One of the most important characteristics of red blood cells is their elasticity and ability to return to original biconcave shape after external forces stop acting on them. There are several conservation laws that together govern this return and one of them is the area conservation. In this paper, we focus on local area conservation and introduce a new way of modeling it using a spring network model. We take into account the current shape of the network triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. Since the force contributions in each node are combined from all adjacent triangles, the final resulting shape might not be the same, but overall effect on the triangulations is positive in the sense that this approach tends to regularize them.

Collision rates for rare cell capture in periodic obstacle arrays strongly depend on density of cell suspension.

Recently, computational modelling has been successfully used for determination of collision rates for rare cell capture in periodic obstacle arrays. The models were based on particle advection simulations where the cells were advected according to velocity field computed from two dimensional Navier–Stokes equations. This approach may be used under the assumption of very dilute cell suspensions where no mutual cell collisions occur. We use the object-in-fluid framework to demonstrate that even with low cell-to-fluid ratio, the optimal geometry of the obstacle array significantly changes. We show computational simulations for ratios of 3.5, 6.9 and 10.4% determining the optimal geometry of the periodic obstacle arrays. It was already previously demonstrated that cells in periodic obstacle arrays follow trajectories in two modes: the colliding mode and the zig–zag mode. The colliding mode maximizes the cell-obstacle collision frequency. Our simulations reveal that for dilute suspensions and for suspensions with cell-to-fluid ratio 3.5%, there is a range of column shifts for which the cells follow colliding trajectories. However we showed, that for 6.9 and 10.4%, the cells never follow colliding trajectories.

Mesh-Based Modeling of Individual Cells and Their Dynamics in Biological Fluids

This text is aimed at providing both basic and advanced knowledge on the individual cell modeling in a flow. Besides the overview of various existing approaches, it is focused on mesh-based model and on its capabilities to cover complex mechano-elastic properties combined with adhesion and magnetic phenomena. We also describe validation procedures, offer an example of use of the model for better understanding of cell behavior and a short overview of future research directions.

PDMS microfluidic structures for LOC applications

We described a new technology for a fabrication of microfluidic components for lab on a chip application based on polydimethylsiloxane (PDMS). The combination of direct laser writing (DLW) lithography for patterning a microstructures and PDMS replica molding process were used. The microfluidic path was formatted after putting final chip on the top of glass slide. The prepared PDMS based microfluidic structure can be used in lab on a chip applications in sensing and biological measurements. Surface of the final chip structure was study by confocal microscope.