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Computationally efficient algorithms for convection-permeation-diffusion models for blood-tissue exchange.

J B Bassingthwaighte1, I S Chan, C Y Wang

  • 1Center for Bioengineering, University of Washington, Seattle 98195.

Annals of Biomedical Engineering
|January 1, 1992
PubMed
Summary

A novel numerical method significantly accelerates the analysis of tissue data from imaging and tracer studies. This fast, accurate approach enhances understanding of capillary-tissue exchange and substrate transport in organs.

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Area of Science:

  • Physiology
  • Biophysics
  • Medical Imaging

Background:

  • Accurate modeling of tissue data from imaging and tracer studies is crucial for understanding physiological processes.
  • Existing analytical solutions for capillary-tissue exchange models are computationally intensive.
  • Heterogeneities in organ blood flow and solute exchange present significant modeling challenges.

Purpose of the Study:

  • To develop a computationally efficient numerical method for analyzing tissue deposition and tracer outflow data.
  • To accurately model multisolute exchange and flow heterogeneities in capillary-tissue units.
  • To improve the speed and accuracy of pharmacokinetic modeling for in vivo studies.

Main Methods:

  • A sliding fluid element algorithm was developed for capillary convection.

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  • Radial and axial transport across capillary and cell barriers were calculated analytically within each time step.
  • The numerical method was validated against analytical solutions for multi-region models.

    • Main Results:

    • The numerical method achieved high accuracy (within 0.5%) for 2-barrier, 3-region models.
    • Solutions were 100-1000 times faster than purely analytical methods for 3-region models.
    • For 4-region models, the speedup exceeded 10,000 times compared to analytical solutions.

    Conclusions:

    • The developed numerical method offers a significant speed advantage for complex capillary-tissue exchange modeling.
    • This approach enhances the feasibility of analyzing positron emission tomographic and multiple indicator dilution studies.
    • The method provides a powerful tool for investigating substrate transport and transcapillary exchange kinetics in vivo.