Biomedical Engineering Reference
In-Depth Information
Figure 5
. Plot of the logarithm of sleep cycle time, the period between REM and non-REM
sleep, in minutes versus the logarithm of body size in Kg, ln(Mass(Kg)). The slope computed
using OLS regression is 0.19 (
p
< 0.0001,
n
= 32, 95% CI: 0.14, 0.23). Note that the confi-
dence intervals exclude the naive expectation of 1/4. This is because the scaling of sleep cycle
time should scale as brain mass to the 1/4, and since brain mass scales as body mass to the 3/4
(93), the predicted exponent is actually 3/16 = 0.1875, which is in close agreement with the
measured exponent. This figure will appear in Savage and West GB (to be published) (7).
3.7. Lifespan
The lifespan,
L
, of animals scales as
L
=
L
0
M
1/4
e
E
/
kT
, reflecting the fact that
larger, colder animals generally live longer than smaller, warmer ones (1,2). The
scaling exponent is the same for all species, but among different taxa of mam-
mals
L
0
varies by more than a factor of two. Furthermore, birds live a factor of
ten longer than mammals of similar mass. There is evidence that these variations
may be due to differences in the rates of radical production by mitochondria and
rates of DNA repair of different species (80-82). Consequently, combining theo-
ries of aging and empirical findings (83-87) with the theory of biological scaling
may give new insights into the process of aging.
4.
DISCUSSION AND CONCLUSIONS
The paradigm and principles developed here suggest novel ways of using
quantitative analytic thinking to attack many fundamental problems in the bio-
medical sciences. This work has enormous potential at all scales and in a variety
of different contexts, ranging from the highly practical (such as pharmacology,
cancer growth, and aging as well as immunology; see this volume, Part III,
