Analytical Studies on the Dye Dilution Curves in Normal Subjects

Abstract

1 It is important to secure the mathematical model of indicator dilution curves for the theoretical investigation of the dilution method. [numerical formula] Formula (1) reported by E. V. Newman in 1951, give us a clear explanation for the formation of dye dilution curves. But due to the insufficiency of its experimental proof in human subjects and the difficulty of the treatment of exponential equations, this formula has not been so available. For the purpose of the experimental proof of Newman's theory, we tried to decide the values of constants in formula (1), and to compose the dilution curve from the formula. In experiments, we used 1-2cc of 2% Coomasie blue solution, and after the injection into the Basilic vein, added the flashing by physiological NaCl solution. The dilution curves were recorded by ear-piece method. For Newman's theory, the assumption of instantaneous injection is the most important premise. When this assumption is satisfied, the author named such dilution curves the simple dilution curves. As we set the injection site on the Basilic vein, that condition was only approximately satisfied. And in such cases, adequate values of V1, V2, v3 can not be found. Hence, the dilution curve required to be corrected at analysis. From Newman's formula, following simultaneous equations (2), (3), (4) have been led. [numerical formula] From these simultaneous equations, we may find easily the following relations with geometrical considerations on λ-μ plane. Suppose tanα=C^-p/A^^, the equations mean that λ1, λ2, λ3 are the λ-ordinates of three intersections of the curve μ=e-tap/λ with a straight line, which makes an angle α with λ-axis. Simultaneously, three points on the curve μ=e-ti/λ of which λ-ordinates are λ-1, λ2, λ3, stand on a straight line. Having known the values of C^-1, A^-, tgt ti by the clinical experiment, we may obtain the values of λ1, λ2, λ3 with graphical method, using the above-mentioned relations.