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Related Concept Videos

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
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Microfluidic Model to Mimic Initial Event of Neovascularization
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Model Microvascular Networks Can Have Many Equilibria.

Nathaniel J Karst1, John B Geddes2, Russell T Carr3

  • 1Babson College, Wellesley, MA, 02457, USA. nkarst@babson.edu.

Bulletin of Mathematical Biology
|February 9, 2017
PubMed
Summary
This summary is machine-generated.

Microvascular networks can have multiple steady-state flow configurations, challenging previous assumptions. Understanding these multiple equilibria is crucial for accurately predicting blood flow in human tissues.

Keywords:
Microvascular blood flowMultiple equilibriaNonlinear dynamicsNumerical continuation

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Area of Science:

  • Physiology
  • Biophysics
  • Computational Biology

Background:

  • Previous studies assumed single equilibrium states for microvascular networks.
  • This assumption may not reflect the complexity of real biological systems.
  • Discrepancies exist between observed and predicted flow patterns.

Purpose of the Study:

  • To investigate the potential for multiple steady-state flow configurations in microvascular networks.
  • To challenge the traditional assumption of unique equilibrium states.
  • To explore factors influencing equilibrium discovery in these networks.

Main Methods:

  • Developed computational techniques applicable to general network topologies and geometries.
  • Modeled perturbed honeycomb networks and Voronoi-generated random networks.
  • Analyzed the impact of the pathway effect on equilibrium discovery.

Main Results:

  • Demonstrated that large microvascular networks can exhibit numerous steady-state flow configurations.
  • Identified the pathway effect as significant for discovering multiple equilibria.
  • Showed that previous discrepancies in flow direction prediction may stem from unconsidered equilibria.

Conclusions:

  • Microvascular networks possess multiple equilibrium states, contrary to prior assumptions.
  • The pathway effect is key to understanding equilibrium multiplicity.
  • Further empirical data on plasma skimming could reveal even more equilibria.