Biomedical Engineering Reference
In-Depth Information
However, the global ability to process drugs should scale as the metabolic rate,
M
3/4
, and residence times should scale as the inverse of mass-specific metabolic
rate,
M
1/4
. These 3/4 extrapolations can provide guidelines for drug dosing and
are more appropriate than linear extrapolations. However, factors particular to
the biochemistry of a given species are also important and must be used in tan-
dem with allometric estimates.
To illustrate the problems associated with extrapolations of drug dosing, we
consider the elephant, Tusko. West et al. (63) wanted to determine whether LSD
had the same effect on elephants as a naturally occurring state in male elephants
known as "on musth," which has associated biochemical changes (63). They
cited studies that gave appropriate drug dosing of LSD for cats, rhesus ma-
caques, and humans. Although appropriate drug dosing varies considerably
among these species, their estimate for appropriate drug dosing of an elephant
was a nearly linear extrapolation of the appropriate dosing for cats. Since an
elephant weighs approximately 1000 times as much as a cat, this means Tusko
received approximately 1000 times more LSD than a cat. In contrast, if drug
dosing is scaled according to metabolic rate, the LSD dosing for an elephant is
approximately 180 times that of a cat. While this calculation does not account
for other, possibly important, factors, it naively suggests that Tusko was given
five times more LSD than was appropriate. Tusko died about two hours after
receiving the injection.
3.4. Spread of Infectious Diseases
Epidemiological equations are very similar to those for population growth,
and it is likely that our theory for population growth and mortality rates (17)
could be extended to study the spread of infectious diseases. Certainly, new fac-
tors particular to specific diseases must be considered. For instance, water abun-
dance and biting rates of mosquitoes play an important role in the transmission
rates of malaria (64). Our work on populations demonstrates that the biologi-
cally mediated processing of energy and materials is a direct consequence of the
metabolic rates of the constituent organisms, and therefore, that describing
higher-level phenomena in terms of individual-level interactions is fruitful. A
similar theory could aid studies of the spread of infectious diseases, especially if
combined with previous theoretical models that have already proved useful in
intervention strategies (65,66).
3.5. Cancer Growth
Recently, Deisboeck and his collaborators have published exciting work on
the application of the above growth model (ยง3.1) to tumor growth (8-10). Tak-
ing the ontogenetic growth model described above as a point of departure, they
analyzed growth curves of tumors, both in vivo and in vitro, for rats and hu-
mans. Their results closely matched the form of the ontogenetic growth equa-
