# Transit and lifespan in neutrophil production: implications for drug intervention

## TL;DR

This paper compares different mathematical models for neutrophil production, extending existing models with new parameters and techniques, and analyzes their stability and implications for drug response predictions.

## Contribution

It introduces a generalized transit compartment model with decoupled maturation time and applies linear chain techniques to reformulate models as distributed delay DDEs.

## Key findings

- Incorrect mean maturation time definitions in existing models
- Reformulation as distributed delay DDEs enhances model analysis
- Stability and bifurcation analyses inform pharmacological modeling

## Abstract

We compare and contrast the transit compartment ordinary differential equation modelling approach with distributed and discrete delay differential equation models. We focus on Quartino's extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. We extend the Quartino model by considering a general number of transit compartments and introduce an extra parameter which allows us to decouple the maturation time from the production rate of cells, and review the well established linear chain technique from the delay differential equation (DDE) literature which can be used to reformulate transit compartment models with constant transit rates as distributed delay DDEs. We perform a state-dependent time rescaling of the Quartino model in order to apply the linear chain technique and rewrite the Quartino model as a distributed delay DDE, which yields a discrete delay DDE model in a certain parameter limit. We then perform stability and bifurcation analyses on the models to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension model incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment, which can have far reaching consequences on the development of future models of myelosuppression in PK/PD.