Stochasticity and Determinism in Models of Hematopoiesis

Abstract

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Predicting time to relapse in acute myeloid leukemia through stochastic modeling of minimal residual disease based on clonality data

“…Two types of modeling are commonly used: deterministic and stochastic [10]. Opinions are split as to whether the stochastic models of leukemogenesis and evolution of leukemia preand post-treatment are more relevant than deterministic ones [10,18,19]. Deterministic models do not account for the unpredictability of clonal heterogeneity in the genomic landscapes [9], although some assign different parameters to each individual [14].…”

Visualizing hematopoiesis as a stochastic process

“…Fifty percent generate the full spectrum of observations. Additionally, stochastic models are more versatile than deterministic models in that they provide quantification of uncertainty or variability (reviewed in Ogawa, 15 Guttorp,16 and Kimmel 17 ). Figure 1, HSC behavior in our model is described by 3 parameters: l, the mean replication (self-renewal) rate; a, the mean apoptosis rate; and n, the mean rate of differentiation to a multipotent progenitor (short-term repopulating) cell.…”

Towards Quantitative Systems Pharmacology Models of Chemotherapy‐Induced Neutropenia

“…Most authors who have studied hematopoietic models with random dynamics have done so with the focus being the development of cancers (with detailed review in Ref. ). However, as previously mentioned, the Loeffler group has published a hybrid deterministic/stochastic model incorporating the effects of G‐CSF, GM‐CSF, and chemotherapy to incorporate the cell cycle‐dependent effects of chemotherapy .…”