TY - JOUR

T1 - About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia

AU - Gaudiano, Marcos E.

AU - Lenaerts, Tom

AU - Pacheco, Jorge M.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can – on average – easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system.

AB - Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can – on average – easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system.

KW - Chronic Myeloid Leukemia

KW - Discrete-continuous model

KW - Hematopoiesis

KW - Moran's process

KW - Peto's paradox

UR - http://www.scopus.com/inward/record.url?scp=84994010506&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2016.11.001

DO - 10.1016/j.mbs.2016.11.001

M3 - Article

C2 - 27816533

AN - SCOPUS:84994010506

VL - 282

SP - 174

EP - 180

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -