Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics

We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the oscillations with respect to fluctuations and noise.Comment: 19 pages, 2 figures, 4 table

Lattice Kinetic Monte Carlo Simulations of Platelet Aggregation and Deposition

Platelet aggregation is an essential process in forming a stable clot to prevent blood loss. The response of platelets to a complex signal of pro-clotting agonists determines the stability and size of the resulting clot. An underdeveloped clot represents a bleeding risk, while an overdeveloped clot can cause vessel occlusion, which can lead to heart attack or stroke. A multiscale model was developed to study the integration of platelet signaling within the complex phenomena driven by flow. The model is built upon a lattice kinetic Monte Carlo algorithm (LKMC) to track platelet motion and binding. First, a new method for including flow-driven particle motion in LKMC was derived from a timescale analysis of particle motion. Simple methods for simulating flow-driven motion were found to exhibit concentration dependent velocities violating the assumptions in the model. The nature of the error was analyzed mathematically and resolved by considering the chain length distribution on the lattice. The accuracy of the method was found to scale linearly with the lattice spacing. Second, the LKMC method was extended to study particle aggregation in complex flows. The LKMC results for simple flows were compared directly to a continuum population balance equation (PBE) approach. A contact time model was introduced to capture nonideal collisions in the LKMC model and a connection to the continuum collision efficiency was derived. The particle size distribution for a baffled geometry with regions of standing vortices and squeezing flows was determined using the LKMC method for varying baffle heights. Finally, the LKMC method was incorporated within a multiscale model to simulate platelet aggregation including platelet signaling (neural network model), blood flow (lattice Boltzmann method), and the release of soluble platelet agonists (finite element method). The neural network model for platelet signaling was trained on patient-specific, experimental measurements of intracellular calcium enabling patient-specific predictions of platelet function in flow. The model accurately predicted the order of potency for three antiplatelet therapies, donor-specific aggregate size, and donor-specific response to antiplatelet therapy as compared to microfluidic experiments of platelet aggregation

Hydrodynamics

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics