Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 11

Therefore, whenever adipose tissues meet the expansion demands, they have to
make a decision whether to enlarge existing resources or to recruit new resources
that have flexible expansion potential, but cannot be removed without possibly
inflammatory processes such as necrosis and apoptosis once they have appeared.
There may not be a universal strategy since different fat depots have different
cellularity; epididymal fat depot rely on hypertrophy, while subcutaneous fat
depots rely on both hypertrophy and hyperplasia [ 4 ]. People in developed countries
rarely experience uncertainties in future food intake, but animal models can be
used to probe the regulatory response of adipose tissue to ensure energy homeo-
stasis under changes in food availability.
Unfortunately, currently available experimental techniques are not capable of
direct measurements of the complicated dynamic processes of adipose tissues. In
this Chapter, we introduce a Bayesian method that infers the dynamic processes
from changes of static snapshots of adipose cell-size distributions. The mathe-
matical modeling explains detailed physical processes of adipose tissue expansion/
shrinkage, and suggests microscopic origins of metabolic disorders in obesity and
diabetes.
2 Bimodal Size Distribution
The size of adipose cells is usually observed by microscopes with the histological
preparation of adipose tissue sections. This conventional method has the well-
known limitations of small sample number and uncertainties in diameter mea-
surements as the locations of the centers of the cut cells relative to the tissue section
are unknown. To address the latter issue, isolated suspension of adipose cells has
been used for microscopic observations [ 10 ]. Another popular and powerful method
is the automatic counting and sizing of adipose cells fixed by osmium tetroxide
[ 11 ]. The Coulter multi-sizer determines sizes of such fixed cells by measuring
conductivity changes due to the obstruction produced by cells going through an
aperture. This allows fast unbiased measurement of large numbers of fixed adipose
cells. The precise histograms of adipose cell sizes measured by the multi-sizer
always give bimodal size distributions of adipose cells (Fig. 1 ), while the con-
ventional microscopic measure frequently produces unimodal size distributions that
ignore the left peak of small cells in the bimodal size distribution. The lower peak,
measured by the multi-sizer, has been criticized on the grounds that it may have
originated from particles broken from fixed adipose cells. However, computerized
measurements with higher microscopic resolution have also observed the bimodal
size distribution in the isolated suspension of adipose cells [ 10 ]. Therefore, the
lower peak seems to be real, although the multi-sizer observation may somewhat
exaggerate it.
As suggested in McLaughlin et al. [ 12 ], the bimodal distribution can be
approximately fitted with two exponentials and one Gaussian function. Therefore,
it is tempting to interpret the origin of the bimodality as two cell populations of