title: 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.
authors.affiliation: Division of Applied Mathematics, Brown University, 182 George St., Providence, RI, 02912, USA. Gabriel_provencher_langlois@brown.edu.
authors.forename: Gabriel P
authors.initials: GP
authors.lastname: Langlois
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA, 02138, USA.
authors.forename: Morgan
authors.initials: M
authors.lastname: Craig
authors.affiliation: Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 0B9, Canada.
authors.forename: Antony R
authors.initials: AR
authors.lastname: Humphries
authors.affiliation: Department of Mathematics, Physics, and Physiology, McGill University, Montreal, QC, H3G 1Y6, Canada.
authors.forename: Michael C
authors.initials: MC
authors.lastname: Mackey
authors.affiliation: Department of Mathematical Sciences, San Diego State University, San Diego, CA, 92182-7720, USA.
authors.forename: Joseph M
authors.initials: JM
authors.lastname: Mahaffy
authors.affiliation: Département de mathématiques et de statistique, Université de Montréal, Montreal, QC, H3C 3J7, Canada.
authors.forename: Jacques
authors.initials: J
authors.lastname: Bélair
authors.affiliation: Laboratoire Chrono-Environnement, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030, Besançon, France.
authors.forename: Thibault
authors.initials: T
authors.lastname: Moulin
authors.affiliation: Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 0B9, Canada.
authors.forename: Sean R
authors.initials: SR
authors.lastname: Sinclair
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada.
authors.forename: Liangliang
authors.initials: L
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D001792:Blood Platelets / Q000473:pathology* / Q000502:physiology*; D003198:Computer Simulation; D064368:Healthy Volunteers; D006801:Humans; D055641:Mathematical Concepts; D008533:Megakaryocytes / Q000473:pathology / Q000502:physiology; D008938:Mitosis; D008954:Models, Biological; D010976:Platelet Count; D013921:Thrombocytopenia / Q000097:blood / Q000209:etiology; D034061:Thrombopoiesis / Q000502:physiology*; D013926:Thrombopoietin / Q000502:physiology
chemical_list: D013926:Thrombopoietin
keywords: Cyclic thrombocytopenia; Delay differential equations; Dynamic diseases; Megakaryopoiesis; Platelet regulation dynamics; Thrombopoiesis