Mathematical Models of Adipose Tissue Dynamics - The Mechanobiology of Obesity and Related Diseases - page 25

Fig. 7 Gaussian approximation: Most fat mass is in bigger cells

distribution. We therefore used only this component of the adipose cell size dis-
tribution to model adipocyte dynamics, using the height, mean, and variance from
the patient data. Apart from cell number changing processes, the rest of the model
we used is the same as given in the previous sections [ 16 , 17 ], with a diffusive
component with parameter D and a convective component with parameter v m0 . The
adipose cell size distribution in most individuals is approximated well by a
mathematical model composed of two decaying exponentials and one Gaussian
distribution [ 12 ]. Each distribution was normalized to the total number of cells to
account for differences in fat cell number between individuals based on weight.
The body composition models predicted change in fat mass was compared to
the prediction from diffusion and convective drift acting on the adipose cell size
distribution. A cost function equal to the sum of square differences between the
non-transient body composition data from week 1-2 and the adipose tissue models
normalized fat mass from week 1-2, computed from the density of fat and the
number of cells at each diameter in the distribution. The cost was evaluated for
each of the six groups, insulin sensitive (IS), insulin resistant (IR), IS males (ISM),
IS females (ISF), IR males (IRM), and IR females (IRF), at different combinations
of D and v m0 to determine the combination that minimized the cost function. The
number of subjects are 15, 13, 4, 11, 4, and 9, for IS, IR, ISM, ISF, IRM, IRF,
respectively. Nevertheless, the cost surfaces show that requiring agreement
between the predictions of the two models specifies lipid turnover and lipid uptake
or release magnitudes.
Cost surfaces show that lipolysis or lipogenesis v m0 has a much greater effect on
the goodness of fit than the lipid turnover D (Fig. 8 ). Lipogenesis and lipolysis,
represented by convective velocity, have the greater effect since they move the