A General Model of Structured Cell Kinetics

Prof Nigel Mottram (University of Glasgow)

Thursday 30th September 14:00-15:00 Room 110/ZOOM (ID: 949 5077 4174)


Many physical systems involve the interaction of micro-scale objects and macro-scale objects within a region. For instance, in biology, the micro-scale objects could be molecules of a particular chemical with the macro-scale-objects being cells and the region a Petri dish or an organ. Within this region we will assume that the micro-scale objects have no volume while the macro-scale objects each have fixed volume. In this talk I will describe a generalised model of the interactions between micro- and macro-scale objects, developing a set of governing equations that include a structured population evolution equation for macro-scale objects (structured by the quantity of micro-scale objects present inside the macro-scale objects) and an evolution equation for the concentration of micro-scale objects in the region outside the macro-scale objects. The micro-scale objects may therefore be present inside or outside the macro-scale objects and we assume that the micro-scale objects can participate in any subset of the following processes: they can be injected into or be removed from the region, they can enter and exit macro-scale objects and they can be produced, processed and destroyed by macro-scale objects. Within this model we allow for the fate of a macro-scale object to be dependent on the amount of micro-scale object that it contains. Examples of the use of this model are: the dynamics of silicosis; Gram-positive bacteria; magnetic ion exchange systems for decontamination.

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