Abstract
Remyelination is a regenerative process that aims to repair damaged regions of the central nervous system, caused by demyelinating diseases, like multiple sclerosis. This process fails to completely repair the demyelinated lesions in many cases and the causes of the failures are not clear. Since many factors and complex mechanisms regulate the process, it is helpful to use high-level modelling languages to describe it and model checking techniques to perform the analysis. They allow us to describe and simulate this stochastic process, and to analyse its behaviour in different scenarios. This study will support neurologists to reason about the different factors that influence this complex process and to create new hypotheses to test through lab experiments. In this chapter, we introduce a novel process algebra called MELA that we used for modelling the remyelination process. We present a number of MELA models capturing different hypotheses about the functioning of remyelination, and their comparison. We perform the analysis of the spatio-temporal evolution of remyelination using Signal Spatio-Temporal Logic and Statistical Model Checking.
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Notes
- 1.
A random variable T has exponential distribution with parameter \(\lambda \) \((0 \le \lambda < \infty )\) if \(P(T > t) = e^{- \lambda t}\), for all \(t \ge 0\). The mean, or expected value, of an exponentially distributed random variable T with rate parameter \(\lambda \) is given by \(E[T] = \frac{1}{\lambda }\).
- 2.
The external boundary of a subset of locations A is defined as \(B^+(A) :=\{l \in \mathscr {L} \mid l \notin A \; \wedge \; \exists l' \in A \text{ such } \text{ that } (l,l') \in E\}\).
- 3.
The average size of the lesion is taken to be 0.5 mm in all dimensions. This was chosen as it is the size of an average lesion produced in a commonly used mouse model of demyelination and remyelination in the mouse corpus callosum, as explain in Sect. 11.5.1.
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Luisa Vissat, L., Hillston, J., Williams, A. (2019). Stochastic Spatial Modelling of the Remyelination Process in Multiple Sclerosis Lesions. In: Liò, P., Zuliani, P. (eds) Automated Reasoning for Systems Biology and Medicine. Computational Biology, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-17297-8_11
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