Title :
Unified proportionality equation for modeling biological and pharmacological data
Author :
Lai, Ralph W. ; Lai, Melisa W. ; Richardson, Alec G.
Author_Institution :
The Toshi Co., Pittsburgh, PA, USA
Abstract :
Introduces the modeling of biological and pharmacological data using a new mathematical concept. A wide variety of sigmoidal and bell-shaped batch data curves in the life sciences can be described by the unified proportionality equation: ±d(qmω1)=K(qnω2 ), where d is the notation of the differential and q is the notation of the logarithm, K is a proportionality constant, and m and n are the logarithmic dimensions of the geometric variables ω1 and ω2. The geometric values are defined as the linear distance in a linear measurement and the non-linear distance between an asymptote and the asymptotic curve in a non-linear measurement. The parameters m and n are non-negative integers. Proportionality graphs and characteristics of equation parameters are illustrated with simulated data in plant growth, oxygen dissociation in hemoglobin and myoglobin, and the drug action of an agonist
Keywords :
biocybernetics; equations; medicine; modelling; O2 dissociation; antagonist drug action; asymptotic curve; bell-shaped batch data curves; biological data modelling; geometric variables; haemoglobin; life sciences; linear distance; linear measurement; logarithmic dimensions; myoglobin; nonlinear distance; nonlinear measurement; pharmacological data modelling; plant growth; proportionality graphs; sigmoidal curves; simulated data; unified proportionality equation; Biological system modeling; Differential equations; Drugs; Integral equations; Mathematical model; Nonlinear equations;
Conference_Titel :
Computer-Based Medical Systems, 1998. Proceedings. 11th IEEE Symposium on
Conference_Location :
Lubbock, TX
Print_ISBN :
0-8186-8564-6
DOI :
10.1109/CBMS.1998.701288