  Background: Analysing tumour architecture for metastatic potential usually
focuses on phenotypic differences due to cellular morphology or specific
genetic mutations, but often ignore the cell's position within the
heterogeneous substructure. Similar disregard for local neighborhood structure
is common in mathematical models.
  Methods: We view the dynamics of disease progression as an evolutionary game
between cellular phenotypes. A typical assumption in this modeling paradigm is
that the probability of a given phenotypic strategy interacting with another
depends exclusively on the abundance of those strategies without regard local
heterogeneities. We address this limitation by using the Ohtsuki-Nowak
transform to introduce spatial structure to the go vs. grow game.
  Results: We show that spatial structure can promote the invasive (go)
strategy. By considering the change in neighbourhood size at a static boundary
-- such as a blood-vessel, organ capsule, or basement membrane -- we show an
edge effect that allows a tumour without invasive phenotypes in the bulk to
have a polyclonal boundary with invasive cells. We present an example of this
promotion of invasive (EMT positive) cells in a metastatic colony of prostate
adenocarcinoma in bone marrow.
  Interpretation: Pathologic analyses that do not distinguish between cells in
the bulk and cells at a static edge of a tumour can underestimate the number of
invasive cells. We expect our approach to extend to other evolutionary game
models where interaction neighborhoods change at fixed system boundaries.
