Analysis of a semi-Lagrangian numerical method in a cell dwarfism model

Abstract

In this work, we introduce a new semi-Lagrangian numerical method proposed to solve a cell population balance model which describes cell dwarfism, by allowing cell division at any size. We analyse its convergence and derive an optimal rate. Numerical experiments are reported to demonstrate the predicted accuracy of the scheme. Finally, the good behaviour of the numerical method is exhibited in stressed conditions that can provoke lack of smoothness and simulations are included to show how the increase in the division rate of small size-cells promotes dynamics in which nonfunctional dwarf cells are saturating the total cell population.

Keywords:

• Cell population balance model
• dwarfism
• semi-Lagrangian method
• convergence analysis

AMS SUBJECT CLASSIFICATIONS:

• 65M12
• 65M25
• 92D25

Acknowledgments

The authors are very grateful to the anonymous referees for his/her careful reading of the original manuscript and his/her aid to improve it.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was funded in part by project MTM2017-85476-C2-1-P of the Spanish Ministerio de Ciencia e Innovación,and European FEDER funds  [grant numbers PID2020-113554GB-I00/AEI/10.13039/501100011033, RED2018-102650-T] funded by MCIN/AEI/10.13039/501100011033 [research grant number VA193P20] of the Junta de Castilla y León, Spain, and European FEDER funds (EU).