  Statistical and mathematical modeling are crucial to describe, interpret,
compare and predict the behavior of complex biological systems including the
organization of hematopoietic stem and progenitor cells in the bone marrow
environment. The current prominence of high-resolution and live-cell imaging
data provides an unprecedented opportunity to study the spatiotemporal dynamics
of these cells within their stem cell niche and learn more about aberrant, but
also unperturbed, normal hematopoiesis. However, this requires careful
quantitative statistical analysis of the spatial and temporal behavior of cells
and the interaction with their microenvironment. Moreover, such quantification
is a prerequisite for the construction of hypothesis-driven mathematical models
that can provide mechanistic explanations by generating spatiotemporal dynamics
that can be directly compared to experimental observations. Here, we provide a
brief overview of statistical methods in analyzing spatial distribution of
cells, cell motility, cell shapes and cellular genealogies. We also describe
cell- based modeling formalisms that allow researchers to simulate emergent
behavior in a multicellular system based on a set of hypothesized mechanisms.
Together, these methods provide a quantitative workflow for the analytic and
synthetic study of the spatiotemporal behavior of hematopoietic stem and
progenitor cells.
