External validation of a clinical mathematical model estimating post-operative urine output following cardiac surgery in children.

BACKGROUND: This study aims to externally validate a clinical mathematical model designed to predict urine output (UOP) during the initial post-operative period in pediatric patients who underwent cardiac surgery with cardiopulmonary bypass (CPB). METHODS: Children aged 0-18 years admitted to the pediatric cardiac intensive care unit at Cleveland Clinic Children's from April 2018 to April 2023, who underwent cardiac surgery with CPB were included. Patients were excluded if they had pre-operative kidney failure requiring kidney replacement therapy (KRT), re-operation or extracorporeal membrane oxygenation or KRT requirement within the first 32 post-operative hours or had indwelling urinary catheter for fewer than the initial 32 post-operative hours, or had vasoactive-inotrope score of 0, or those with missing data in the electronic health records. RESULTS: A total of 213 encounters were analyzed; median age (days): 172 (IQR 25-75th%: 51-1655), weight (kg): 6.1 (IQR 25-75th%: 3.8-15.5), median UOP ml/kg/hr in the first 32 post-operative hours: 2.59 (IQR 25-75th%: 1.93-3.26) and post-operative 30-day mortality: 1, (0.4%). The mathematical model achieved the following metrics in the entire dataset: mean absolute error (95th% Confidence Interval (CI)): 0.70 (0.67-0.73), median absolute error (95th% CI): 0.54 (0.52-0.56), mean squared error (95th% CI): 0.97 (0.89-1.05), root mean squared error (95th% CI): 0.99 (0.95-1.03) and R2 Score (95th% CI): 0.29 (0.24-0.34). CONCLUSIONS: This study provides encouraging external validation results of a mathematical model predicting post-operative UOP in pediatric cardiac surgery patients. Further multicenter studies must explore its broader applicability.

Agent-based modeling of nuclear chromosome ensembles identifies determinants of homolog pairing during meiosis.

During meiosis, pairing of homologous chromosomes (homologs) ensures the formation of haploid gametes from diploid precursor cells, a prerequisite for sexual reproduction. Pairing during meiotic prophase I facilitates crossover recombination and homolog segregation during the ensuing reductional cell division. Mechanisms that ensure stable homolog alignment in the presence of an excess of non-homologous chromosomes have remained elusive, but rapid chromosome movements appear to play a role in the process. Apart from homolog attraction, provided by early intermediates of homologous recombination, dissociation of non-homologous associations also appears to contribute to homolog pairing, as suggested by the detection of stable non-homologous chromosome associations in pairing-defective mutants. Here, we have developed an agent-based model for homolog pairing derived from the dynamics of a naturally occurring chromosome ensemble. The model simulates unidirectional chromosome movements, as well as collision dynamics determined by attractive and repulsive forces arising from close-range physical interactions. Chromosome number and size as well as movement velocity and repulsive forces are identified as key factors in the kinetics and efficiency of homologous pairing in addition to homolog attraction. Dissociation of interactions between non-homologous chromosomes may contribute to pairing by crowding homologs into a limited nuclear area thus creating preconditions for close-range homolog attraction. Incorporating natural chromosome lengths, the model accurately recapitulates efficiency and kinetics of homolog pairing observed for wild-type and mutant meiosis in budding yeast, and can be adapted to nuclear dimensions and chromosome sets of other organisms.

Agent-based modeling of nuclear chromosome ensemble identifies determinants of homolog pairing during meiosis.

During meiosis, pairing of homologous chromosomes (homologs) ensures the formation of haploid gametes from diploid precursor cells, a prerequisite for sexual reproduction. Pairing during meiotic prophase I facilitates crossover recombination and homolog segregation during the ensuing reductional cell division. Mechanisms that ensure stable homolog alignment in the presence of an excess of non-homologous chromosomes have remained elusive, but rapid chromosome movements during prophase I appear to play a role in the process. Apart from homolog attraction, provided by early intermediates of homologous recombination, dissociation of non-homologous associations also appears to contribute to homolog pairing, as suggested by the detection of stable non-homologous chromosome associations in pairing-defective mutants. Here, we have developed an agent-based model for homolog pairing derived from the dynamics of a naturally occurring chromosome ensemble. The model simulates unidirectional chromosome movements, as well as collision dynamics determined by attractive and repulsive forces arising from close-range physical interactions. In addition to homolog attraction, chromosome number and size as well as movement velocity and repulsive forces are identified as key factors in the kinetics and efficiency of homologous pairing. Dissociation of interactions between non-homologous chromosomes may contribute to pairing by crowding homologs into a limited nuclear area thus creating preconditions for close-range homolog attraction. Predictions from the model are readily compared to experimental data from budding yeast, parameters can be adjusted to other cellular systems and predictions from the model can be tested via experimental manipulation of the relevant chromosomal features.

Fluid-structure interaction modelling of neighboring tubes with primary cilium analysis.

We have developed a numerical model of two osculating cylindrical elastic renal tubules to investigate the impact of neighboring tubules on the stress applied to a primary cilium. We hypothesize that the stress at the base of the primary cilium will depend on the mechanical coupling of the tubules due to local constrained motion of the tubule wall. The objective of this work was to determine the in-plane stresses of a primary cilium attached to the inner wall of one renal tubule subject to the applied pulsatile flow, with a neighboring renal tube filled with stagnant fluid in close proximity to the primary tubule. We used the commercial software COMSOLⓇ to model the fluid-structure interaction of the applied flow and tubule wall, and we applied a boundary load to the face of the primary cilium during this simulation to produces a stress at its base. We confirm our hypothesis by observing that on average the in-plane stresses are greater at the base of the cilium when there is a neighboring renal tube versus if there is no neighboring tube at all. In combination with the hypothesized function of a cilium as a biological fluid flow sensor, these results indicate that flow signaling may also depend on how the tubule wall is constrained by neighboring tubules. Our results may be limited in their interpretation due to the simplified nature of our model geometry, and further improvements to the model may potentially lead to the design of future experiments.

The space between us: Modeling spatial heterogeneity in synthetic microbial consortia dynamics.

A central endeavor in bioengineering concerns the construction of multistrain microbial consortia with desired properties. Typically, a gene network is partitioned between strains, and strains communicate via quorum sensing, allowing for complex behaviors. Yet a fundamental question of how emergent spatiotemporal patterning in multistrain microbial consortia affects consortial dynamics is not understood well. Here, we propose a computationally tractable and straightforward modeling framework that explicitly allows linking spatiotemporal patterning to consortial dynamics. We validate our model against previously published results and make predictions of how spatial heterogeneity impacts interstrain communication. By enabling the investigation of spatial patterns effects on microbial dynamics, our modeling framework informs experimentalists, helps advance the understanding of complex microbial systems, and supports the development of applications involving them.

Heterogeneous bacterial swarms with mixed lengths.

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming speeds. On the other hand, high fractions of long cells form a bottleneck for efficient swarming. Our results suggest a physical advantage for the spontaneous heterogeneity of bacterial swarm populations.

Interaction of red crabs with yellow crazy ants during migration on Christmas Island.

Invasive species have had a profound impact on ecosystems all over the world. Their presence can lead to fundamental changes in the biodiversity of a given ecosystem as well as the extinction of native species. In particular, this work looks at the effect on the Gecarcoidea natalis (Red Crab) population on Christmas Island due to the presence of vast arrays of supercolonies containing Anoplolepis gracilipes (Yellow Crazy Ant). We primarily study the inter-species interaction occurring during the crab migration to the island coast. We propose a microscopic model for the dynamics of the crabs and ants with the goal of increasing crab survival. Through analysis of the model, we investigate a range of potential preventative measures that could be taken to preserve the native crab population dependent on their locations. The main result of this work is that by considering the locations of ant supercolonies incorporated into Monte Carlo simulations of the model, we can identify the order that the supercolonies need to be removed to provide the greatest chance at survival for the crabs per migration cycle.

Role of hydrodynamic interactions in chemotaxis of bacterial populations.

How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this paper, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a hybrid computational model that incorporates hydrodynamic interactions and adding components from a classical velocity jump model. It is shown that by including hydrodynamic interactions, a suspension with a low initial volume fraction can exhibit locally high concentrations in bacterial aggregates. Also, it is shown that hydrodynamic interactions enhance the merging of the small aggregates into larger ones and lead to qualitatively different aggregate behavior than possible with pure chemotaxis models. Namely, differences in the shape, number, and dynamics of these emergent clusters.

Charged Nanoparticles Quench the Propulsion of Active Janus Colloids.

Active colloidal particles regularly interact with surfaces in applications ranging from microfluidics to sensing. Recent work has revealed the complex nature of these surface interactions for active particles. Herein, we summarize experiments and simulations that show the impact of charged nanoparticles on the propulsion of an active colloid near a boundary. Adding charged nanoparticles not only decreased the average separation distance of a passive colloid because of depletion attraction as expected but also decreased the apparent propulsion of a Janus colloid to near zero. Complementary agent-based simulations considering the impact of hydrodynamics for active Janus colloids were conducted in the range of separation distances inferred from experiment. These simulations showed that propulsion speed decreased monotonically with decreasing average separation distance. Although the trend found in experiments and simulations was in qualitative agreement, there was still a significant difference in the magnitude of speed reduction. The quantitative difference was attributed to the influence of charged nanoparticles on the conductivity of the active particle suspension. Follow-up experiments delineating the impact of depletion and conductivity showed that both contribute to the reduction of speed for an active Janus particle. The experimental and simulated data suggests that it is necessary to consider the synergistic effects between various mechanisms influencing interactions experienced by an active particle near a boundary.

Pulsatile flow through idealized renal tubules: Fluid-structure interaction and dynamic pathologies.

Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of elastohydrodynamic coupling by neighboring tubules. Overall, we are interested in exploring the idea of dynamic pathology to better understand the progression of chronic kidney diseases such as Polycystic Kidney Disease.

Individual based modeling and analysis of pathogen levels in poultry chilling process.

Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp. contamination on broiler carcasses, illustrating how free chlorine (FC) sanitization, organic load in the water, and pre-chill carcass pathogen levels affect pathogen levels of post-chill broilers. In particular, given a uniform distribution of Campylobacter levels on incoming poultry we quantify the efficacy of FC control in not only reducing pathogen levels on average, but also the variation of pathogen levels on poultry exiting the chill tank. Furthermore, we demonstrate that the absence/presence of FC input dramatically influences when, during a continuous chilling operation, cross-contamination will be more likely.

Anomalous Fluctuations in the Orientation and Velocity of Swarming Bacteria.

Simultaneous acquisition of phase-contrast light microscopy and fluorescently labeled bacteria, moving within a dense swarm, reveals the intricate interactions between cells and the collective flow around them. By comparing wild-type and immotile cells embedded in a dense wild-type swarm, the effect of the active thrust generated by the flagella can be singled out. It is shown that while the distribution of angles among cell velocity, cell orientation, and the local flow around it is Gaussian-like for immotile bacteria, wild-type cells exhibit anomalous non-Gaussian deviations and are able to move in trajectories perpendicular to the collective flow. Thus, cells can maneuver or switch between local streams and jets. A minimal model describing bacteria as hydrodynamic force dipoles shows that steric effects, hydrodynamics interactions, and local alignments all have to be taken into account to explain the observed dynamics. These findings shed light on the physical mechanisms underlying bacterial swarming and the balance between individual and collective dynamics.

Curvature-driven foam coarsening on a sphere: A computer simulation.

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution and distribution of cells to the final stationary state.

Effective Rheological Properties in Semi-dilute Bacterial Suspensions.

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally, we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.

A model for collective dynamics in ant raids.

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and the transition from one class of ants to another. Through analysis of an order parameter measuring the orientational order in the system, the model shows self-organization into a collective state consisting of lanes of ants moving in opposite directions as well as the transition back to the individual state once the food source is depleted matching prior experimental results. This indicates that in the absence of direct communication ants naturally form an efficient method for transporting food to the nest/bivouac. The model exhibits a continuous kinetic phase transition in the order parameter as a function of certain system parameters. The associated critical exponents are found, shedding light on the behavior of the system near the transition.

Correlation properties of collective motion in bacterial suspensions.

The study of collective motion in bacterial suspensions has been of significant recent interest. To better understand the non-trivial spatio-temporal correlations emerging in the course of collective swimming in suspensions of motile bacteria, a simple model is employed: a bacterium is represented as a force dipole with size, through the use of a short-range repelling potential, and shape. The model emphasizes two fundamental mechanisms: dipolar hydrodynamic interactions and short-range bacterial collisions. Using direct particle simulations validated by a dedicated experiment, we show that changing the swimming speed or concentration alters the time scale of sustained collective motion, consistent with experiment. Also, the correlation length in the collective state is almost constant as concentration and swimming speed change even though increasing each greatly increases the input of energy to the system. We demonstrate that the particle shape is critical for the onset of collective effects. In addition, new experimental results are presented illustrating the onset of collective motion with an ultrasound technique. This work exemplifies the delicate balance between various physical mechanisms governing collective motion in bacterial suspensions and provides important insights into its mesoscopic nature.

Viscosity of bacterial suspensions: hydrodynamic interactions and self-induced noise.

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system.