Some nutritional and excretional interactions and the growth of an organ or colony

Following the general form for the differential equation of organism and colonial growth, there is derived a rational formulation for the growth of a bounded cell community (e.g., an organ) equipped with a food supply and a waste removal mechanism. It is shown how, from the integral form and an empirical curve, the vital coefficients of the equation can be derived. Changes to be expected in these coefficients are discussed, and the analytic methods for assessing them are set forth. It is hoped that these equations and similar ones will make it possible to relate empirical curves to the mathematico-biophysical theory of the cell. The opinions or assertions contained herein are the private ones of the writers, and are not to be construed as official or reflecting the views of the Navy Department or the Naval Service at large.     

On the theory of blood-tissue exchanges: II. Applications

The application of a previously developed theory of inert gas absorption is here outlined. Interpretation of uptake curves and the method of obtaining tissue constants from such curves is discussed, together with illustrations from actual experiment. A critique of previous analytic procedures is included. The material in this article should be construed only as the personal opinion of the writers and not as representing the opinion of the Navy Department officially.     

A note on the physiological arrangement of tissues

Presented are the kinetics of uptake of an inert solute by tissues arranged in series, distinct parallel and competitive parallel, with respect to the circulation. The uptake in all cases can be described by a series of exponentials, but the number of these terms and the character of the constants is specific for each arrangement. This fact can be of value in deducing tissue arrangement from uptake data. The material in this article is the opinion of the writers, and should not be construed as representing the policies of the Navy Department or the Naval Service at large.     

The physiological factors which govern inert gas exchange

The decay constants (k _j ) of the equation of inert gas exchanges are the roots of an algebraic equation of degreen+1, wheren is the number of distinct absorbing tissues. The coefficients of this equation can be obtained numerically by certain independent experiments to measure the tissue parameters. Graphical solution of this equation yields theoretical values of thek _j . Combining these constants with the numerical values for the partial derivatives of thek _j then gives the per cent rate of change of thek _j as any one tissue parameter varies by a given fraction of its normal range. A numerical example of these calculations shows good conformity with experiment, and permits a quantitative estimate of variations in the speed of gas exchange from a knowledge of changes in the physiological state. The opinions expressed in this article are the private ones of the writers, and are not to be construed as reflecting the policies of the Navy Department or the Naval Service at large.     

On the theory of blood-tissue exchanges: III. Circulation and inert-gas exchanges at the lung with special reference to saturation

The results of a simple analysis of the situation in the lungs with regard to the uptake of inert gases is presented. It is shown that the gas transfer at the lung governs the early stages of gas uptake by a body region so that the latter conceivably could be used as an index of lung function. It is shown that the so-called Fick Principle, which serves as the basis of most indirect cardiac output methods, is an approximation to a more general equation. When the latter equation is applied to a slowly permeating gas, it offers the possibility of determining functional lung surface. The material in this article should be construed only as the personal opinion of the writers and not as representing the opinion of the Navy Department officially.     

On the theory of blood-tissue exchanges: I. Fundamental equations

A mathematical analysis of the absorption of an inert gas by a heterogeneous system ofn phases, e.g., a limb consisting ofn tissues, is presented. The total uptake of gas, ϕ(t), up to timet is given in terms of arterial concentration, cardiac delivery, blood volume, and the volume, permeability, and partition coefficient of each tissue. The theory predicts how the uptake curve should change in shape under a variety of physiological conditions, and how from the numerical values of the constants the values of certain tissue constants, e.g. permeabilities, may be obtained. The material in this article should be construed only as the personal opinion of the writers and not as representing the opinion of the Navy Department officially.