Biomedical Engineering Reference
In-Depth Information
evolution of adipose cell-size distributions. Oscillation of adipose cell-size dis-
tributions has been observed in rats with a period of about 50 days [
30
]. This
dynamic scenario can also explain the bimodal shape of adipose cell-size distri-
butions. The accumulation of small adipose cells below the lower critical size for
size-dependent growth could explain the lower peak in the adipose cell-size
distribution.
5 Adipose Tissue Development
Adipose tissue dynamics varies depending on many factors including age and
genetic makeup. To account for age-dependent variations, we propose adding a
time dependent factor to Eq. (
11
) as follows:
2
n
os
2
k
ð
s
Þ
n
:
o
n
ot
¼ b
ð
t
Þ
d
ð
s
s
0
Þ
o
os
½v
ð
s
;
t
Þ
n
þ
D
o
ð
16
Þ
The controversy of whether adipose tissues can recruit new cells after a certain
development stage or not might be due to a decrease in the birth rate after a critical
age. We propose that the birth rate increases with age before adulthood but starts
decreasing again after reaching a critical age:
(
2
ð
b
max
b
1
Þ
1
þ
exp
ð
A
t
Þ=
a
1
b
ð
t
Þ
¼
b
1
þ
if t
A
;
ð
17
Þ
2
ð
b
max
b
2
Þ
1
þ
exp
ð
t
A
Þ=
a
2
b
2
þ
if t [ A
:
where A is the critical age, b
max
is the maximum birth rate at the critical age A, b
1
is the birth rate at the start, and b
2
is the minimal birth rate reached at older age
(Fig.
3
).
5.1 Parallel Tempering as a Model Selection Method
Figure
4
shows the change in adipose cell-size distribution over time taken from a
Zucker fatty rat under a regular chow diet.
The aim is to find the simplest model that can best fit the experimental data. In
the section above we already included age dependency for the birth rate. To do so
for v
ð
s
Þ
is, however, less intuitive. v
ð
s
Þ
has six parameters that can change with
age, v
þ
, s
þ
, g
þ
, v
m
, s
, and g
. If we use different values for each of the six
parameters at each time step, we end up with too many parameters and thus over-
fitting the data. For example, in the above case, this will lead to 66 additional
parameters.
To decide which of the six parameters shows the most relevant variation, we
compare six models, in each of which only one of the parameters is time-dependent,
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