# Normal and pathological dynamics of platelets in humans

## Abstract

We develop a mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this information to investigate both normal and pathological platelet production, specifically cyclic thrombocytopenia. Carefully estimating model parameters from laboratory and clinical data, we then argue that a subset of parameters are involved in the genesis of cyclic thrombocytopenia based on clinical information. We provide model fits to the existing data for both platelet counts and thrombopoietin levels by changing four parameters that have physiological correlates. Our results indicate that the primary change in cyclic thrombocytopenia is an interference with, or destruction of, the thrombopoietin receptor with secondary changes in other processes, including immune-mediated destruction of platelets and megakaryocyte deficiency and failure in platelet production. This study contributes to the understanding of the origin of cyclic thrombocytopenia as well as extending the modeling of thrombopoiesis.

### Keywords

Platelet regulation dynamics Thrombopoiesis Megakaryopoiesis Cyclic thrombocytopenia Dynamic diseases Delay differential equations### Mathematics Subject Classification

37N25 92B99 92C30 37G15## Notes

### Acknowledgements

This research was supported by the NSERC (National Sciences and Engineering Research Council) of Canada through Discovery grants to JB, ARH, and MCM, and PGS-D program to MC. SRS thanks McGill University for a Science Undegraduate Research Award. GPL and MCM are especially grateful to Dr. Jayson Potts (UBC) for his initial contact that prompted the initiation of this research. We thank Prof. Jiguo Cao (SFU) for introducing us to LW.

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