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Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis

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Abstract

An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:

$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$

whereB 1(t) is the first order initial entry function for the tracer material,P(t1) the perturbation function.T(t 2) is the tracer input function, andB 1(t−t 2 ,t 1 −t 2 ) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system.

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Authors and Affiliations

  1. Department of Physics, City College of the, City University of New York, New York, New York

    H. E. Hart

  2. Medical Physics Laboratory, Division of Neoplastic Medicine, Montefiore Hospital, New York, New York

    H. E. Hart

Authors
  1. H. E. Hart
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Additional information

This research was supported in part under grant NIH GM 11044-03.

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Hart, H.E. Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis. Bulletin of Mathematical Biophysics 27, 417–429 (1965). https://doi.org/10.1007/BF02476846

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  • DOI: https://doi.org/10.1007/BF02476846

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