arXiv subjects

Sarah D. Olson

Publications and source records attributed to Sarah D. Olson.

9 recordsLinked to original sources

arXiv2026

A geometry-dependent, force balance-driven model of Staphylococcus epidermidis biofilm cell cluster detachment

Biofilms, bacteria cells surrounded by a self-produced polymeric matrix, are common on medical devices and lead to many hospital infections. The biofilm lifecycle includes disassembly and dispersion, where bacteria clusters detach from the biofilm, circulate in the bloodstream, and potentially colonize secondary infection sites. Existing models often simplify detachment to a function of biofilm thickness or extracellular polymeric substance (EPS) density, without tracking properties of detached clusters that impact their biological fate, including cluster size and morphology. Addressing this gap, our detachment model accounts for drag and adhesion in tagged sections of the biofilm determined by the cluster geometry and local arrangement of bacteria and EPS. A stickiness parameter controls local EPS adhesion strength, which is modulated to disrupt (or compromise) EPS biomass. We specifically model the detachment of clusters from a Staphylococcus epidermidis biofilm grown for 24 hours. Experimental data for biofilm microstructural features are utilized to benchmark the simulated biofilm, which is then subjected to different EPS disruption levels. We examine parameters that influence detached biofilm cell cluster frequency, size, and shape, providing mechanistic insights into how compromised EPS influences detachment dynamics. This integrated modeling framework is a significant advance in the predictive capabilities for biofilm detachment processes.

q-bio.QM↗

arXiv2025

Analysis of the stability of an immersed elastic surface using the method of regularized Stokeslets

A linear stability analysis of an elastic surface immersed in a viscous fluid is presented. The coupled system is modeled using the method of regularized Stokeslets (MRS), a Lagrangian method for simulating fluid-structure interaction at zero Reynolds number. The linearized system is solved in a doubly periodic domain in a 3D fluid. The eigenvalues determine the theoretical critical time step for numerical stability for a forward Euler time integration, which are then verified numerically across several regularization functions, elastic models, and parameter choices. New doubly periodic regularized Stokeslets are presented, allowing for comparison of the stability properties of different regularization functions. The stability results for a common regularization function are approximated by a power law relating the regularization parameter and the surface discretization for two different elastic models. This relationship is empirically shown to hold in the different setting of a finite surface in a bulk fluid.

physics.flu-dyn↗

arXiv2019

Emergent three-dimensional sperm motility: Coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signaling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the three-dimensional motion of the flagellum in a viscous, Newtonian fluid with the evolving calcium concentration. The flagellum is modeled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a one-dimensional reaction-diffusion model on a moving domain, the centerline of the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

math.NA↗

arXiv2019

Global Density Analysis for an Off-Lattice Agent-Based Model

Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational model is often counterbalanced by the difficulty of performing rigorous analysis to determine emergent behaviors. In addition, without precise definitions of cell interactions, calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially thousands of simulations. Through developing a precise definition of an off-lattice CA or AB model with a specified interaction neighborhood, we develop a general method to determine a Global Recurrence Rule (GRR). This allows estimates of the state densities in time, which can be easily calculated for a range of parameters in the model. The utility of this framework is tested on an Epidemiological Cellular Automata (E-CA) model where agents or cells correspond to people that are in the susceptible, infected, or recovered states. The interaction neighborhoods of cells are determined in a mathematical formulation that allows the GRR to accurately predict the long term behavior and steady states. The modeling framework outlined will be generally applicable to many areas and can be easily extended.

math.DS↗

arXiv2019

Computational framework to capture the spatiotemporal density of cells with a cumulative environmental coupling

Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel computational framework to describe and simulate stochastic cellular processes that are coupled to the environment. Specifically, through upscaling, we derive a continuum governing equation that considers the cell density as a function of time, space, and a cumulative variable that is coupled to the environmental conditions. For this new governing equation, we consider the stability through an energy analysis, as well as proving uniqueness and well-posedness. To solve the governing equations in free-space, we propose a numerical method using fundamental solutions. As an application, we study a cell moving in an infinite domain that contains a toxic chemical, where a cumulative exposure above a critical value results in cell death. We illustrate the validity of this new modeling framework and associated numerical methods by comparing the density of live cells to results from the corresponding agent-based model.

math.NA↗

arXiv2018

A hybrid cellular automaton model of cartilage regeneration capturing the interactions between cellular dynamics and scaffold porosity

To accelerate the development of strategies for cartilage tissue engineering, models are necessary to study the interactions between cellular dynamics and scaffold (SC) porosity. In experiments, cells are seeded in a porous SC where over a month, the SC slowly degrades while cells divide and synthesize extracellular matrix (ECM) constituents. We use an off-lattice cellular automaton framework to model the individual behavior of cells within the SC. The movement of cells and the ability to reproduce is determined by the nutrient profile and local porosity. A phenomenological approach is used to capture a continuous profile for SC and ECM evolution, which will then change the local porosity. We parameterize the model by matching total cell counts to chondrocytes seeded in a polyglycolic acid SC. We investigate the total cell count and location of various cell populations for different initial SC porosities. Similar to experiments, we observe cell counts that level off around day 15 with higher values in SCs of lower initial porosity. Cell clustering is observed in regions at the edge of the construct that are close to the nutrient-rich medium in the fluid bath. Model results show that a bias in motion due to sensitivity to porosity allows cells to move in a more optimal arrangement. We investigate the distribution of cells as the cell reproduction rate, cell movement distance, and sensitivity to porosity is varied. We observe non monotonic changes in total cell counts within different regions of the construct due to the interplay between porosity and cellular movement. We also analyze the emergent average cell speed for different initial SC porosities, observing an higher average for the lowest initial SC porosity. This model provides a framework to further investigate how changes in biological parameters can change the cellular count and distribution in SCs of different initial porosity

q-bio.TO↗

arXiv2016

Accelerating the Uzawa Algorithm

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson acceleration (also known as Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleration on several steady Stokes and Oseen problems for incompressible flows. For perspective, we include in our comparison several other iterative methods that have appeared in the literature. The results indicate that the accelerated preconditioned Uzawa algorithm converges significantly faster than the algorithm without acceleration and is competitive with the other methods considered.

math.NA↗

arXiv2015

Swimming Speeds of Waving Cylindrical Tails in Viscous Fluids with Resistance

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an infinite-length cylinder propagating lateral or spiral displacement waves. For fixed bending kinematics, we find that swimming speeds are enhanced due to the added resistance from the fibers. In addition, we examine the work and the torque exerted on the cylinder in relation to the resistance. The solutions for the torque, swimming speed, and work of an infinite-length cylinder in a Stokesian fluid are recovered as the resistance is reduced to zero. Finally, we compare the asymptotic solutions with the numerical results obtained from the Method of Regularized Brinkmanlets. The swimming speed of a finite-length filament decreases as its length decreases and planar bending induces an angular velocity that increases linearly with added resistance. The comparisons between the asymptotic analysis and computation give insight on the effect of the length of the filament, the permeability, and the thickness of the cylinder in terms of the overall performance of planar and helical swimmers

physics.flu-dyn↗

arXiv2015

Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study Spherical Basis Function (SBF), Radial Basis Function (RBF) and Lagrange-Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, are given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange-Chebyshev interpolants for modeling twice-differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method.

math.NA↗