TY  - JOUR
A1  - Gomez, Christophe
A1  - Hartung, Niklas
T1  - Stochastic and deterministic models for the metastatic emission process
BT  - Formalisms and Crosslinks
JF  - Cancer Systems Biology
N2  - Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.
KW  - Poisson process
KW  - Structured population equation
KW  - Metastasis
KW  - Mathematical modeling
Y1  - 2018
SN  - 978-1-4939-7493-1
SN  - 978-1-4939-7492-4
U6  - https://doi.org/10.1007/978-1-4939-7493-1_10
SN  - 1064-3745
SN  - 1940-6029
VL  - 1711
SP  - 193
EP  - 224
PB  - Humana Press Inc.
CY  - Totowa
ER  -