Abstract
Green's function for heat and matter transport is calculated for an infinite medium in which a convection field v(r,t) makes a contribution to the total heat and matter current. It is given by a uniformly and absolutely convergent series in which every term is calculated from the preceding one merely by integration. The solution procedure is interpreted physically and illustrated by a simple problem in which v(r,t)=const. in space and time. Since the solution contains no intrinsic spatial symmetry, it can serve as a starting point for a theory of heat and mass transport in perfused biological tissue.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Aris, R. 1956. “On the Dispersion of a Solute in Fluid Flowing Through a Tube.”Proc. Roy. Soc. London, A,235, 67–77.
Betz, E., D. H. Ingvar and N. A. Lassen. 1966. “Regional Bloodflow in the Cerebral Cortex, Measured Simultaneously by Heat and Inert Gas Clearance.”Acta Physiol. Scand.,67, 1–9.
Chandrasekhar, S. 1943. “Stochastic Problems in Physics and Astronomy.”Rev. Mod. Phys.,15, 1–89.
Doetsch, G. 1956.Handbuch der Laplacetransformation. Basel-Stuttgart: Birkhäuser, Vol. 3.
Giraud, G. 1932. “Sur Certaines Opérations aux Dérivées Partielles du type Parabolique.”Compt. Rend.,195, 98–100.
Golenhofen, K., H. Hensen and G. Hildebrandt. 1963.Durchblutungsmessung mit Wärmeleitelementen. Stuttgart: Thieme.
Hennesy, T. R. 1971. “Inert Gas Diffusion in Heterogeneous Tissue. I: Without Perfusion. II: With Perfusion.”Bull. Math. Biophysics,33, 235–248, 249–257.
Hutten, H. 1970. “Untersuchung nicht-stationärer Austauschvorgänge in gekoppelten Konvektions-Diffusionssystemen.”Ein Beitrag zur theoretischen Behandlung physiologischer Transportprozesse. Akademie der Wissenschaften u.d. Literatur, Mainz. Wiesbaden: Steiner Verlag.
Ingvar, D. H. and N. A. Lassen. 1962. “Regional Bloodflow of the Cerebral Cortex Determined by Krypton 85.”Acta Physiol. Scand.,54, 325–338.
Kety, S. S. and C. F. Schmidt. 1948. “Nitrous Oxide Method for the Quantitative Determination of Cerebral Bloodflow in Man. Theory, Procedure and Normal Values.”J. Clin. Invest.,27, 476–483.
—. 1949. “Measurement of Regional Circulation by the Local Clearance of Radioactive Sodium.”Am. Heart J.,38, 321–328.
Klinger, H. G. 1972. “Untersuchungen zum Wärmetransport in durchströmten biologischen Geweben. Grundlagen zur Bestimmung der Temperaturleitfähigkeit und Durchströmung von biologischen Geweben mit Hilfe einer nichtstationärn Wärmeclearancemethode.” Dissertation, Würzburg.
Perl, W. 1962. “Heat and Matter Distribution in Body Tissues and the Determination of Tissue Bloodflow by Local Clearance Methods.”J. Theor. Biology,2, 201–235.
Pogorzelski, W. 1966. “Integral Equations and their Applications.”Int. Series of Monographs in Pure and Applied Mathematics. Oxford: Pergamon Press, No. 88.
Roulier, A. 1970. “Calculation of Temperature Increase in the Eye Produced by Intense Light.”Bull. Math. Biophysics,32, 403–427.
Schaefer, C. 1958.Einführung in die Theoretische Physik. Berlin: W. de Gruyter, Vol. 2.
Thews, G. 1952. “Über die mathematische Behandlung physiologischer Diffusions-prozesse in zylinderförmigen Objekten.”Acta Biotheoretica Ser. A.,10, 105–137.
—. 1962. “Ein elektrisches Analogrechenverfahren zur Lösung physiologischer Diffusions-probleme. II. Mitteilung: Anwendung des Verfahrens auf Diffusionsprozesse mit konstanten und periodisch veränderlichen Verbrauchsgrößen.”Pflügers Archiv,276, 182–191.
Zierler, K. 1965. “Equations for Measuring Bloodflow by External Monitoring of Radioisotopes.”Circulation Res.,16, 309–321.
Author information
Authors and Affiliations
Additional information
Supported by “Deutsche Forschungsgemeinsc haft”.
Rights and permissions
About this article
Cite this article
Klinger, H.G. Heat transfer in perfused biological tissue—I: General theory. Bltn Mathcal Biology 36, 403–415 (1974). https://doi.org/10.1007/BF02464617
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02464617