# A damage-structured PDE model of stem cell hierarchies: The dual role of dedifferentiation in tissue homeostasis and aging

## TL;DR

This paper introduces a mathematical model to study how stem cells manage tissue health and aging through dedifferentiation, showing when it helps or harms.

## Contribution

A novel damage-structured PDE model with a nonlocal δ-function kernel to study dedifferentiation's role in tissue homeostasis and aging.

## Key findings

- Dedifferentiation acts as a detoxification loop by recycling high-damage cells.
- Repair-modulated dedifferentiation reduces damage burden during cell transitions.
- The model shows conditions under which dedifferentiation stabilizes tissue or accelerates aging.

## Abstract

Stem cells maintain tissue integrity through a balance of self-renewal, differentiation, and loss of function due to aging or stress. Recent studies demonstrate that the stem cell hierarchy is not fixed. Transit-amplifying or terminally differentiated cells can dedifferentiate back into stem-like states. Such plasticity supports regeneration but, when combined with damage accumulation, may also accelerate aging and increase cancer risk.

Motivated by these findings, we develop a damage-structured PDE model of a two-compartment lineage consisting of stem and terminally differentiated cells. The model incorporates dedifferentiation, together with a nonlocal δ-function kernel partitioning scheme that conserves total damage and encodes biologically motivated asymmetries. Methodologically, we emphasize reproducibility and robustness on three fronts. First, the δ-kernel partitioning prevents the unbounded drift that arises in local models while preserving conservation. Second, a conservative finite-volume discretization with upwind fluxes and verified first-order accuracy ensures stability and exact mass balance, as confirmed by manufactured-solution tests. Third, distributional metrics and systematic parameter sweeps provide reproducible ways to quantify lineage-level damage dynamics under varying dedifferentiation and repair conditions. These analyses show that threshold-dependent and repair-modulated dedifferentiation both act as protective mechanisms: the former functions as a ‘detoxification loop’ that recycles high-damage cells, and the latter reduces the damage burden imported during dedifferentiation. Together, they mitigate aging-inducing effects. Parameter sweeps further delineate when dedifferentiation stabilizes tissue maintenance versus when it drives aging-like dynamics. Overall, our reproducible framework integrates biological insights on stem-cell plasticity and damage segregation with rigorous mathematical modeling, providing a foundation for experimental validation and therapeutic strategies targeting stem-cell aging and cancer initiation.