A continuum mathematical model of endothelial layer maintenance and senescence

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Abstract
Background: The monolayer of endothelial cells (ECs) lining the inner wall of blood vessels deteriorates as a person ages due to a complex interplay of a variety of causes including cell death arising from shear stress of blood flow and cellular oxidative stress, cellular senescence, and decreased rate of replacement of dead ECs by progenitor stem cells. Results: A continuum mathematical model is developed to describe the dynamics of large EC populations of the endothelium using a system of differential equations for the number densities of cells of different generations starting from endothelial progenitors to senescent cells, as well as the densities of dead cells and the holes created upon clearing dead cells. Aging of cells is manifested in three ways, namely, losing the ability to divide when the Hayflick limit of 50 generations is reached, decreasing replication rate parameters and increasing death rate parameters as cells divide; due to the dependence of these rate parameters on cell generation, the model predicts a narrow distribution of cell densities peaking at a particular cell generation. As the chronological age of a person advances, the peak of the distribution – corresponding to the age of the endothelium – moves towards senescence correspondingly. However, computer simulations also demonstrate that sustained and enhanced stem cell homing can halt the aging process of the endothelium by maintaining a stationary cell density distribution that peaks well before the Hayflick limit. The healing rates of damaged endothelia for young, middle-aged, and old persons are compared and are found to be particularly sensitive to the stem cell homing parameter. Conclusion: The proposed model describes the aging of the endothelium as being driven by cellular senescence, with a rate that does not necessarily correspond to the chronological aging of a person. It is shown that the age of the endothelium depends sensitively on the homing rates of EC progenitor cells.