Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 21

Fig. 4 Adipose cell-size distributions depending on age

1 þ tanh s s k
g k

;

k m
1 þ exp ð a k ð S c S v ÞÞ

k ð s Þ ¼ ð 18 Þ

where S v ¼ R ds s 4 ð s Þ= R ds s 3 n ð s Þ is the volume weighted average radius, and k m ,
a k , s k , and g k are kept constant. (3) The growth/shrinkage rate is defined as

r v tanh s s þ
0 : 5s þ

tanh s s
g

;

v ð s ; t Þ ¼v m

ð 19 Þ

for a constant v m and r v ¼ v þ = v m .
Table 3 shows the E SA and E PT results for the reduced (model 2) and non-
reduced (model 1) models with g ð t Þ . The non-reduced model, model 1, shows a
better fit than the reduced model, model 2, as indicated by the E SA values in
Table 3 and Figs. 5 and 6 . However, model 2 is more likely as it has much lower
E PT values.