Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 15

3

2

1

0

25 50 75 100 125 150

Cell diameter ( µ m)

Fig. 2 Evolution of adipose cell-size distribution under positive and negative energy
balance. C56BL/6 mich were fed with a high-fat diet for 7 weeks, then with a regular diet for
following 12 weeks. Cell-size distributions in epididymal fat depots were measured at initial time
(3 months old; black), after 7-week high-fat diet (red), and after 7-week high-fat diet plus
12-week regular diets (blue). Mean SD (n = 6). Note that we estimated absolute frequencies of
cell sizes from their relative frequencies by using the measured depot mass of epididymal fat

4 Adipose Tissue Dynamics

The Bayesian method can infer adipose tissue dynamics from changes of static
snapshots of adipose cell-size distributions under positive and negative energy
balance (Fig. 2 ). Possible physical processes in adipose tissue dynamics are
recruitment of new cells, growth, shrinkage, size fluctuation, and death of existing
cells. They can be mathematically summarized in a model described by the fol-
lowing partial differential equation:

2 n
os 2 k ð s Þ n :

o n

ot ¼ bd ð s s 0 Þ o os ½v ð s Þ n þ D o

ð 11 Þ

The equation describes the whole life of adipose cells from birth to death. Here,
model parameters represent birth rate b at minimal cell size s 0 , size-dependent
growth/shrinkage rate v ð s Þ , size fluctuation rate D, and size-dependent death rate
k ð s Þ . Note that we replaced the frequencies n i at discrete ith size bins with a
frequency function n ð s Þ for continuous size s as a continuum limit. Hereafter we
examine each process inferred from changes of adipose cell-size distribution under
positive and negative energy balance.