Biomedical Engineering Reference
In-Depth Information
Stahl (6) found that spleen mass scaled with body mass as ~
M
1.02
across di-
verse mammal species, or as ~
M
0.85
when limited to primates only. More re-
cently, Nunn (7) found that spleen mass scaled with body mass as ~
M
1.17
across
primates, based on an analysis that included some of the data used in (6), but
which used mean mass values for species as data points, rather than values for
individual animals.
Estimates for the number of lymph nodes in dogs, humans, horses, and
cows are available (8), and in Figure 1 are plotted against adult body masses
typical for these species. While there is some suggestion of an increase in the
number of lymph nodes with mass, it is difficult to evaluate the slope reliably
with data for so few species, and where body masses and lymph node counts
were not available for the same individuals.
Concentrations of lymphocytes in the blood have been compared among
primate species, using data compiled by the International Species Information
System (9,10). Using a similar database (11), we find that among diverse mam-
mal species, adult blood lymphocyte concentrations scale with adult body mass
as ~
M
-0.07
(
n
= 138,
F
= 18.53,
p
< 0.001,
r
2
= 0.12), and as ~
M
-0.1
(
n
= 45,
F
=
18.78,
p
< 0.001,
r
2
= 0.30) when limited to primates. This implies that if blood
volume scales with mass as ~
M
1.02
(12), total number of lymphocytes will scale
as ~
M
1.0
M
-0.1
~
M
0.9
.
Data are also available for lymphocyte output from the thoracic duct (13),
which is the major lymphatic vessel through which lymph enters the circulatory
system (14). Among nine species of mammals, concentration of lymphocytes in
the lymph decreases with body mass as ~
M
-0.16
(though this relationship is not
significant at the
p
= 0.05 level;
n
= 9,
F
= 3.49,
p
= 0.10,
r
2
= 0.33), while flow
from the thoracic duct increases with body mass as ~
M
0.89
(
n
= 9,
F
= 85.10,
p
<
0.001,
r
2
= 0.92). It then follows that total lymphocyte output per unit time
scales with body mass as ~
M
0.73
(
n
= 9,
F
= 44.40,
p
< 0.001,
r
2
= 0.86; Figure 2),
which is intriguingly similar to the
M
3/4
scaling laws found in the WBE theory
(2,3).
3.
CONCLUSIONS
The use of scaling laws in immunology is a field in its infancy. We have
tried here to show that scaling laws can provide insights into the properties of
immune systems in animals of different sizes. Although we focused our atten-
tion on the number and size of lymphocyte clones needed to provide protection
to animals of different mass, there is a great need to also understand the ana-
tomical features of immune systems in different mammals. The lymphatic sys-
tem, with its chains of lymph nodes, is organized to some extent as an inverse
branching network, with collecting lymphatics joining together to form larger
vessels. Along the way are lymph nodes that filter the fluid as it returns to the
circulation. The scaling relations that govern the operation of the circulatory
