Page 73 - Computational Modeling in Biomedical Engineering and Medical Physics

60 Computational Modeling in Biomedical Engineering and Medical Physics

that the airways are very narrow and U 1 is sufficient small for the flow to be laminar
(n 5 1), t 1,opt B (9/16)K 22 , yielding the optimal expiration time t 2,opt B (3/16)K 22
The theoretical high point that the respiration intervals are of the same scale

2
1=2
AD ΔC
22
t 1 ; t 2 Þ BK 5 ;
ð opt ð2:21Þ
_ m
is in good concordance with a significant body of observation archived and correlated
in biology literature (Schmidt-Nielsen, 1972). This theoretical time of respiration
increases with the size of the animal’s body as a power law with the exponent B0.25,
again, in excellent agreement with the data correlated in biology.

Heart beating
Relying on the minimization of the mechanical power constrained by a global mass
transfer limit the constructal principle may predict the existence of an eigen heartbeats
frequency, finely adjusted, that is inverse proportional with the body size. The two-
chamber piston model of the circulatory system, Fig. 2.11, feeds the pulmonary

Figure 2.11 The human circulatory system model with two chambers heart model.