Allometric laws

Field of determining the parameters of the model, in which all parameters have physiological meaning depends on allometric parameters of the organism. A quantitative description of these dependencies is currently a discussion on science. The greatest recognition of this theory has received universal power dependencies of parameters of biological systems on body mass [21], [22], [23], [24]. It is based on a situation that many of the fundamental characteristics of the organism associated with the size of the body power dependence in the form of:

(72)

where c_i - scaling constants, m - body mass, b_i - allometric exponents. We accept this theory as a first approximation to express the allometric dependence of the parameters of mathematical models of circulation. List of allometric exponents of main variables of the circulatory system, built on the basis of data from [15], [21], [22], [23], [24] are listed in the table.

Physiological variable	Allometric exponent
Duration of the cardiac cycle and the value dimension of time	1/4
Heart rate	-1/4
Total blood volume and other quantities dimension of volume	1
Heart output	3/4
Blood pressure	0
Oxygen debt	1
Volumetric blood flow	3/4
Volume elasticity	-1
Conductivity	3/4

On the basis of these data by analyzing the dimensions are calculated allometric exponents for all the parameters of a mathematical model of the circulatory system.

Equation (72) in the model used in the formula allometric scaling to the values of the parameters

(73)

through the average value of normal body mass m₀, taken equal to 70 kg, and the experimentally established average normal value for a_i⁰.

Mathematical model > Allometric laws

References on the topic:

Modelling > Blood circulation parameters > Other parameters > Body mass