Multi-scale modelling and analysis is becoming increasingly important and relevant. Analysis
of the emergent properties from the interactions between scales of multi-scale systems is
important to aid in solutions. There is no universally adopted theoretical/computational
framework or language for the construction of multi-scale models. Most modelling approaches
are specific to the problem that they are addressing and use a hybrid combination of modelling
languages to model specific scales. This thesis addresses if process algebra can offer a unique
opportunity in the definition and analysis of multi-scale models.

In this thesis the generic Process Algebra with Layers (PAL) is defined: a language for
multi-scale integration modelling. This work highlights the potential of process algebra to
model multi-scale systems. PAL was designed based on features and challenges found from
modelling a multi-scale system in an existing process algebra. The unique features of PAL
are the layers: Population and Organism. The novel language modularises the spatial scales
of the system into layers, therefore, modularising the detail of each scale. An Organism can
represent a molecule, organelle, cell, tissue, organ or any organism. An Organism is described
by internal species. An internal species, dependent on the scale of the Organism, can also
represent a molecule, organelle, cell, tissue, organ or any organism. Populations hold specific
types of Organism, for example, life stages, cell phases, infectious states and many more. The
Population and Organism layers are integrated through mirrored actions.

This novel language allows the clear definition of scales and interactions within and between
these scales in one model. PAL can be applied to define a variety of multi-scale systems. PAL
has been applied to two unrelated multi-scale system case studies to highlight the advantages
of the generic novel language. Firstly the effects of ocean acidification on the life stages of the
Pacific oyster. Secondly the effects of DNA damage from cancer treatment on the length of a
cell cycle and cell population growth.