A Lifshitz-Slyozov type model for adipocyte size dynamics: limit from Becker-Döring system and numerical simulation

Area of Science:

• Mathematical Biology
• Cell Biology
• Partial Differential Equations

Background:

• Adipose cell size distribution is biologically bimodal.
• Existing models like the Becker-Döring system describe cell dynamics.
• Understanding adipose cell size dynamics is crucial for metabolic research.

Purpose of the Study:

• To introduce and analyze a Lifshitz-Slyozov type model for adipose cell size distribution dynamics.
• To establish a convergence result from the Becker-Döring model to the Lifshitz-Slyozov model.
• To propose and investigate a novel second-order diffusive Lifshitz-Slyozov model for improved experimental data fitting.

Main Methods:

• Development of a transport partial differential equation model.
• Application of distribution tail techniques to prove convergence from the Becker-Döring model.
• Numerical simulations using a well-balanced scheme for the diffusive Lifshitz-Slyozov model.

Main Results:

• A new convergence result is proven between the Becker-Döring and Lifshitz-Slyozov models.
• The second-order diffusive Lifshitz-Slyozov model is proposed, potentially fitting experimental data better.
• Numerical simulations demonstrate that asymptotic profiles can be bimodal or unimodal, depending on parameters.

Conclusions:

• The second-order diffusive Lifshitz-Slyozov model offers a promising approach to modeling adipose cell size distribution.
• Asymptotic profiles generated by the second-order model are independent of initial conditions, a key advantage.
• This work bridges theoretical modeling with biological data, advancing the understanding of adipose tissue dynamics.