Dynamic Computational Model of Symptomatic Bacteremia to Inform Bacterial Separation Treatment Requirements

Abstract

The rise of multi-drug resistance has decreased the effectiveness of antibiotics, which has led to increased mortality rates associated with symptomatic bacteremia, or bacterial sepsis. To combat decreasing antibiotic effectiveness, extracorporeal bacterial separation approaches have been proposed to capture and separate bacteria from blood. However, bacteremia is dynamic and involves host-pathogen interactions across various anatomical sites. We developed a mathematical model that quantitatively describes the kinetics of pathogenesis and progression of symptomatic bacteremia under various conditions, including bacterial separation therapy, to better understand disease mechanisms and quantitatively assess the biological impact of bacterial separation therapy. Model validity was tested against experimental data from published studies. This is the first multi-compartment model of symptomatic bacteremia in mammals that includes extracorporeal bacterial separation and antibiotic treatment, separately and in combination. The addition of an extracorporeal bacterial separation circuit reduced the predicted time of total bacteria clearance from the blood of an immunocompromised rodent by 49%, compared to antibiotic treatment alone. Implementation of bacterial separation therapy resulted in predicted multi-drug resistant bacterial clearance from the blood of a human in 97% less time than antibiotic treatment alone. The model also proposes a quantitative correlation between time-dependent bacterial load among tissues and bacteremia severity, analogous to the well-known 'area under the curve' for characterization of drug efficacy. The engineering-based mathematical model developed may be useful for informing the design of extracorporeal bacterial separation devices. This work enables the quantitative identification of the characteristics required of an extracorporeal bacteria separation device to provide biological benefit. These devices will potentially decrease the bacterial load in blood. Additionally, the devices may achieve bacterial separation rates that allow consequent acceleration of bacterial clearance in other tissues, inhibiting the progression of symptomatic bacteremia, including multi-drug resistant variations.

Fig 1. Bacterial burden decreased over time in tissue compartments of healthy rodents.

Immunonormal rodents intratracheally inoculated with (A) A. baumannii (10⁷ CFU/mL) or (B) K. pneumoniae (10⁷ CFU/mL) were modeled. The median numbers of bacteria in each compartment observed experimentally were used as the initial conditions for these simulations[,–27], and trajectories were generated using the parameter estimates described in the Materials and Methods.

Fig 2. Bacterial time in neutropenic rodents until reaching a lethal A. baumannii concentration.

The median numbers of bacteria in each compartment observed experimentally in previous literature were used as the initial conditions for these simulations[25,35], and trajectories were generated using the parameter estimates shown in Materials and Methods.

Fig 3. A. baumannii burden decreased post inoculation in immunocompromised rodents treated with colistin methanosulfate (3 mg/kg).

The associated parameters are shown in Materials and Methods.

Fig 4. Bacterial separation (100% efficiency) combined with antibiotic administration improved A. baumannii clearance rate.

A. baumannii cleared from the blood compartment of the immunocompromised rodent model in 28 h when implementing bacterial separation (100% efficiency) and antibiotic treatment. Antibiotic administration alone resulted in bacterial clearance from the blood compartment in 55 h.

Fig 5. Bacterial separation (100% and 60% efficiency) improved A. baumannii clearance rates from the blood compartment.

20% bacterial separation efficiency was not efficient enough to impact the overall bacterial clearance rate and resulted in the same clearance rates as antibiotic treatment alone.

Fig 6. Bacterial separation (100% efficiency) with antibiotic treatment improved A. baumannii clearance from human blood compartment.

This combination treatment resulted in A. baumannii clearance (≤1 CFU/mL) from the blood compartment in 1 h. The time required for A. baumannii to be cleared to a negligible concentration (≤ 1 CFU/mL) from the blood compartment of the human model with antibiotic administration alone was 15 h.

Fig 7. Treatment of MDR A. baumannii human model using 100% efficient bacterial separation with antibiotic treatment.

Using this combination therapy, MDR A. baumannii clearance (≤ 1 CFU/mL) from the blood compartment of the human mathematical model occurred in 1 h. The time required for MDR A. baumannii to be cleared to a negligible concentration (≤1 CFU/mL) from the blood compartment with antibiotic administration alone was 29 h.

Fig 8. The five-compartment kinetic model describing bacterial pathogenesis.

Intratracheal instillation of a Gram-negative bacteria bolus initially occurred in the lung compartment, with initial concentration L₀ (CFU mL^-1). Bacterial proliferation rates (p, h⁻¹), clearance rates (c, h⁻¹), and transport rates between compartments were included in the model schematic. The rate of bacterial transport between compartments was represented as a function of blood flow rate per compartment volume (Q/V, mL h^-1), modified by an experimentally determined partitioning coefficient (x, dimensionless).

Fig 9. Magnetic separation efficiency, f(r_f), of Gram-negative bacteria incubated with bacteria-targeting magnetic nanoparticles in whole blood.

In the model predictions, the maximum magnetic separation efficiency occurred using magnetic nanoparticles with a radius of 25nm. The theoretical model prediction was verified by comparison to results published by Kang et al.[13].