Biomedical Engineering Reference
In-Depth Information
tion, but the parameters were determined by fitting the data and not from first
principles. Although the basic ideas behind our growth model should apply to
tumors, the theory does not include the presence of necrotic tissue. As such, the
derived parameters might be misleading.
Concurrently, Alex Herman and we have been developing a theory for tu-
mor growth that includes necrosis, with the initial goal of predicting the effects
of tumor size and host size on the tumor's metabolic rate. Using the network
theory for the cardiovascular system, we intend to make predictions that apply to
both avascular and vascular tumors. For the latter, we are combining the mecha-
nism of angiogenesis with the network theory (§2.1) to describe, or possibly to
predict, the structure and dynamics of the tumor vascular system. Predictions
about which properties of cancer vasculature allow cancer cells to grow quickly
and at the expense of the rest of the body will be made. Preliminary results sug-
gest that a substantial amount of tumor data can be parsimoniously explained
and that disparate empirical findings for tumors can be interrelated in a novel
way. We have a manuscript in preparation in which we provide a theory for the
allometry of asymptotic tumor sizes and doubling times and derive tumor
growth trajectories in a mechanistic fashion (11).
3.6. Sleep
Sleep is one of the most noticeable and widespread phenomena in multicel-
lular animals, occurring in mammals, birds, amphibians, reptiles, and insects
(67). Recent neurobiological studies have uncovered a great deal of information
about the mechanisms involved in sleep, but a convincing demonstration of the
function of sleep is considered one of the most important, unsolved problems in
science. Some of the most-studied and best-known hypotheses for the function
of sleep are related to metabolic rate. These include rest for the body or brain
(6,68), cortical reorganization associated with memory and learning (69-73),
and cellular repair in the body or brain (74-79). However, there is a remarkable
absence of quantitative theories to elucidate or distinguish between these metab-
olically based theories for sleep.
We have developed a quantitative theory for mammalian sleep that relates
fundamental parameters of sleep to metabolic rate and thus, to body size. This
theory is based on the hypothesis that processes related to metabolism or meta-
bolic damage, most notably cortical reorganization and cellular repair, occur
during sleep. For example, sleep cycle time—the time between the endings of
periods of REM sleep, i.e., the amount of REM sleep plus non-REM sleep in a
single cycle—increases with body size in a systematic way (see Figure 5). Using
this theory we are also able to derive previously unknown relationships between
sleep time, awake time, and body size, and these relationships are supported by
available data for mammals (7). These findings suggest that a metabolic theory
for sleep is well founded and is possibly the dominant explanation for why ani-
mals sleep the amounts that they do.
