A two-fluid model for tissue growth within a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.

Intelligent pipeline control - a simulation study in the automotive sector

Automotive producers are aiming to make their order fulfilment processes more flexible. Opening the pipeline of planned products for dynamic allocation to dealers/ customers is a significant step to be more flexible but the behaviour of such Virtual-Build-To-Order systems are complex to predict and their performance varies significantly as product variety levels change. This study investigates the potential for intelligent control of the pipeline feed, taking into account the current status of inventory (level and mix) and of the volume and mix of unsold products in the planning pipeline, as well as the demand profile. Five ‘intelligent’ methods for selecting the next product to be planned into the production pipeline are analysed using a discrete event simulation model and compared to the unintelligent random feed. The methods are tested under two conditions, firstly when customers must be fulfilled with the exact product they request, and secondly when customers trade-off a shorter waiting time for compromise in specification. The two forms of customer behaviour have a substantial impact on the performance of the methods and there are also significant differences between the methods themselves. When the producer has an accurate model of customer demand, methods that attempt to harmonise the mix in the system to the demand distribution are superior.