Numerical simulations of stochastic circulatory models.

Area of Science:

• Pharmacokinetics and Mathematical Biology
• Computational modeling of biological systems

Background:

• Stochastic circulatory models offer theoretical insights into biological transport processes.
• Deterministic models, like Bateman and gamma-like functions, are commonly used but may lack stochastic detail.

Purpose of the Study:

• To investigate the properties of two stochastic circulatory models.
• To compare the residence time distributions predicted by deterministic and stochastic models.
• To validate the applicability of deterministic models using stochastic simulation data.

Main Methods:

• Investigated two stochastic circulatory models assuming gamma distribution for cycle time with geometric or Poisson elimination.
• Determined analytical forms of residence time probability density functions (PDFs) for deterministic models.
• Simulated residence time distributions using the stochastic models.
• Employed the Kolmogorov-Smirnov test for model comparison.

Main Results:

• The probability density functions of residence time from deterministic models closely matched simulated distributions from stochastic models.
• This close match was observed even with a relatively small number of simulated particles (1000 xenobiotic particles).
• Model agreement was contingent upon specific parameter conditions being met in the stochastic models.

Conclusions:

• Deterministic models provide a valid and accurate approximation for residence time distributions derived from specific stochastic circulatory models.
• The findings support the continued use of established deterministic models in pharmacokinetic and systems biology research.
• Careful parameter selection is crucial for the accurate application of stochastic models and their comparison with deterministic counterparts.