Skip to main content
SpringerLink
Log in

Stimulus-response method for flows and volumes in slightly perturbed constant parameter systems

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

The area and the first time moment of tracer kinetic data on steady state systems contains information on flows and volumes of distribution in the system. A simple and general method of obtaining such information is given. The method consists of equating the ratio of the time integrals of appropriate stimulus function and response function in an actually performed finite amount tracer experiment to the ratio of stimulus and response that would exist in the tracer steady state. The generality of the method is illustrated by deriving the volume of osmotically exchangeable water in an organ from measurement of its transient bulk water exchange during a small osmotic perturbation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Bergner, P.-E. E. 1964. “Tracer Dynamics and the Determination of Pool-sizes and Turnover Factors in Metabolic Systems.”J. Theoret. Biol.,6, 137–158.

    Article  Google Scholar 

  • —. 1965. “Exchangeable Mass: Determination Without Assumption of Isotopic Equilibrium.”Science,150, 1048–1050.

    Article  Google Scholar 

  • Chinard, F. P., R. Effros, W. Perl and M. Silverman. 1967. “Organ Vascular and Extravascular Compartments in Vivo.” InCompartments Pools and Spaces in Medical Physiology, eds. P.-E. E. Bergner and C. C. Lushbaugh. CONF-661010, Clearinghouse, U.S. Department of Commerce, Springfield, Virginia 22151, 381–422.

    Google Scholar 

  • Meier, P. and K. L. Zierler. 1954. “On the Theory of the Indicator-Dilution Method for Measurement of Blood Flow and Volume.”J. Appl. Physiol.,6, 731–744.

    Google Scholar 

  • Orr, J. S. and F. C. Gillespie. 1968. “Occupancy Principle for Radioactive Tracers in Steady-State Biological Systems.”Science,162, 138–139.

    Article  Google Scholar 

  • —, J. Shimmins and C. F. Speirs. 1969. “Method for Estimating Individual Drug-Dosage Regimens.”Lancet,ii, 771–773.

    Article  Google Scholar 

  • Perl, W. and P. Samuel. 1969a. “Input-Output Analysis for Total Input Rate and Total Traced Mass of Body Cholesterol in Man.”Circulation Res.,25, 191–199.

    Google Scholar 

  • —, R. M. Effros and F. P. Chinard. 1969b. “Indicator Equivalence Theorem for Input Rates and Regional Masses in Multi-Inlet Steady-State Systems With Partially Labeled Input.”J. Theoret. Biol.,25, 297–316.

    Article  Google Scholar 

  • —. 1970. “Input Output Analysis for Osmotically Available Extravascular Water in Organs.”Biophysic. Soc. Abstracts,10, 118a.

    Google Scholar 

  • Stephenson, J. L. 1958. “Theory of Measurement of Blood Flow by Dye Dilution Technique.”IRE Trans. Med. Electron.,PGME-12, 82–88.

    Article  Google Scholar 

  • Zierler, K. L. 1962. “Circulation Times and the Theory of Indicator-Dilution Methods for Determining Blood Flow and Volume.” inHandbook of Physiology, Sec. 2, Vol. 1, eds. W. F. Hamilton and P. Dow. Washington, D.C.: American Physiological Society, 585–615.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Medicine, New Jersey College of Medicine and Dentistry, 07103, Newark, New Jersey

    W. Perl

Authors
  1. W. Perl
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perl, W. Stimulus-response method for flows and volumes in slightly perturbed constant parameter systems. Bulletin of Mathematical Biophysics 33, 225–233 (1971). https://doi.org/10.1007/BF02579475

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579475

Keywords

Search

Navigation