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Determination of the Settling Rate of Clay/Cyanobacterial Floccules
Published on: June 11, 2018
Klebsiella pneumoniae flocculation dynamics
D M Bortz1, T L Jackson, K A Taylor
1Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA. dmbortz@colorado.edu
Abstract:
The bacterial pathogen Klebsiella pneumoniae is a cause of community- and hospital-acquired lung, urinary tract and blood stream infections. It is a common contaminant of indwelling catheters and it is theorized in that context that systemic infection follows shedding of aggregates off of surface-adherent biofilm colonies. In an effort to better understand bacterial proliferation in the host bloodstream, we develop a PDE model for the flocculation dynamics of Klebsiella pneumoniae in suspension. Existence and uniqueness results are provided, as well as a brief description of the numerical approximation scheme. We generate artificial data and illustrate the requirements to accurately identify proliferation, aggregation, and fragmentation of flocs in the experimental domain of interest.
Insights
This study models Klebsiella pneumoniae flocculation in the bloodstream to understand infection spread. The findings help identify bacterial proliferation, aggregation, and fragmentation dynamics.
Area of Science:
- Microbiology
- Mathematical Biology
- Infectious Diseases
Background:
- Klebsiella pneumoniae causes severe infections, including lung, urinary tract, and bloodstream infections.
- It contaminates indwelling catheters, potentially leading to systemic infection via biofilm shedding.
- Understanding bacterial dynamics in the bloodstream is crucial for infection control.
Purpose of the Study:
- To develop a partial differential equation (PDE) model for Klebsiella pneumoniae flocculation in suspension.
- To analyze the mathematical properties (existence and uniqueness) of the model.
- To provide a framework for identifying bacterial proliferation, aggregation, and fragmentation dynamics.
Main Methods:
- Development of a PDE model to simulate bacterial flocculation.
- Mathematical analysis to prove existence and uniqueness of solutions.
- Numerical approximation scheme for the model.
- Generation of artificial data to test model capabilities.
Main Results:
- The study provides a validated PDE model for Klebsiella pneumoniae flocculation.
- Mathematical proofs for the model's existence and uniqueness are established.
- The model's utility in identifying bacterial proliferation, aggregation, and fragmentation is demonstrated using artificial data.
Conclusions:
- The developed PDE model offers a robust tool for studying Klebsiella pneumoniae dynamics in the bloodstream.
- This research enhances our understanding of how bacterial aggregates form and behave in vivo.
- The findings can inform strategies for preventing and treating Klebsiella pneumoniae infections.
