Biomedical Engineering Reference
In-Depth Information
Figure 3
. Effects of temperature,
T
-1
(1000/(K), on mass-corrected lifespan, ln(
LM
-1/4
(days/g
1/4
)). Data are for fish and aquatic invertebrates held at different constant temperatures in
the laboratory. This figure is reproduced with permission from Gillooly et al. (2000) (1).
chapter, we provide a general theory for the origin of these scaling relationships
based on previously published work (1,12). In the third section we focus on the
development of subsequent theories that apply biological scaling to biomedical
problems. In the final section we summarize the findings presented in this chap-
ter and speculate about future work in these areas.
2.
MODEL DESCRIPTION
:
THEORY FOR THE
ORIGIN OF SCALING RELATIONSHIPS
Metabolic rate sets the pace of life. By modeling the dynamics of the car-
diovascular system based on some general assumptions, which are independent
of the detailed dynamics and design, the body size dependence for metabolic
rate,
B
r
M
3/4
, can be derived. The temperature dependence is given by a Boltz-
mann factor,
B
r
e
-E/kT
, and is a direct consequence of the kinetics of the underly-
ing biochemical reactions responsible for the production of ATP. As mentioned
above, these two variables alone explain a surprising amount of the variation in
metabolic rate and set a baseline for analyzing biological organisms. It is likely
that the residual variation points to interesting biological differences between
organisms and gives clues as to what these differences are.
