Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 29

We have provided here a proof of principle that requiring the mathematical
consistency of two physiological models of fat mass at different scales and
incorporating different elements of subject data gives insight into changes in
physiological processes in adipose tissue associated with insulin resistance.

7 Summary and Discussion

Adipose cell-size distributions represent traces of physical processes that indi-
vidual adipose cells experience during their life. In the Chapter, we introduced
how to infer dynamical processes from changes of static cell-size distributions
using Bayesian inference. Given experimental data, mathematical modeling gen-
erally proposes possible hypothetical models that can explain the data. Bayesian
inference plays a crucial role in obtaining the likelihood parameter values for
given models, and quantitatively selecting the best model among them [ 21 ].
Therefore, this can serve as a general framework to infer underlying dynamics
given data. For example, we have applied this to understand the development of
pancreatic islets, the critical micro-organs for glucose metabolism [ 41 ].
Adipose cell-size distributions have long been measured in obesity research.
However, mean cell size, obtained from the size distribution, was the single
information practically used to examine hypertrophy and hyperplasia of adipose
cells [ 4 , 5 ]. Unlike these classic studies, the mathematical modeling of adipose
cell-size distributions can provide substantially more information on adipose tissue
dynamics. We could determine the cell-size dependency of adipose cell growth or
shrinkage and death under positive/negative energy balance. In addition, cell-size
fluctuations (lipid turnover) and cell turnover in adipose tissue are difficult to
obtain experimentally. Therefore, mathematical modeling plays dual roles for
integrating given data and for predicting physiological mechanisms that are not
directly observable. The modeling is only as good as uncertainties in data allow.
For example, the correct estimation of total cell number is critical because it
affects the inference of cell recruitment and death. Although we deduced total cell
number in adipose tissues from the tissue mass divided by the average mass of
adipose cells, the number estimation could be erroneous due to an inaccurate
measurement of the average cell mass. This uncertainty can ultimately be avoid-
able with direct measure of total cell number in adipose tissues. As another
example, a fixed cell-size distribution can be explained alternatively as a stationary
distribution exactly balancing cell recruitment, special growth, and death. Here
direct measurements of one of these physical processes can easily check or rule out
alternative possibilities. Therefore, for a better understanding of adipose tissue
dynamics, theoretical modeling and experiment should complement each other.
This Chapter has focused on explaining the mechanistic building blocks of
physical processes in modeling of adipose tissue dynamics. To complete the
modeling, physiology of energy homeostasis needs to be incorporated into the
present

model so that each physical process is automatically controlled by