Modelling shared space users via rule-based social force model

The promotion of space sharing in order to raise the quality of community living and safety of street surroundings is increasingly accepted feature of modern urban design. In this context, the development of a shared space simulation tool is essential in helping determine whether particular shared space schemes are suitable alternatives to traditional street layouts. A simulation tool that enables urban designers to visualise pedestrians and cars trajectories, extract flow and density relation in a new shared space design and achieve solutions for optimal design features before implementation. This paper presents a three-layered microscopic mathematical model which is capable of representing the behaviour of pedestrians and vehicles in shared space layouts and it is implemented in a traffic simulation tool. The top layer calculates route maps based on static obstacles in the environment. It plans the shortest path towards agents' respective destinations by generating one or more intermediate targets. In the second layer, the Social Force Model (SFM) is modified and extended for mixed traffic to produce feasible trajectories. Since vehicle movements are not as flexible as pedestrian movements, velocity angle constraints are included for vehicles. The conflicts described in the third layer are resolved by rule-based constraints for shared space users. An optimisation algorithm is applied to determine the interaction parameters of the force-based model for shared space users using empirical data. This new three-layer microscopic model can be used to simulate shared space environments and assess, for example, new street designs

Effects of non-linear GJ channels on the AP propagation : a modelling insight

International audienceBackground: Velocity and pattern of propagation of cardiac AP depends on structural andfunctional properties of the tissue, such as conductivity, dynamics of transmembrane ionicchannels and gap junctions (GJ). Gap junctions are clusters of channels that connect adjacent cells. A gap junction channel(GJC) is made of proteins named ­ connexins. Electrical behavior of GJCs depend on the typeand arrangement of their connexin composition. The dominating connexins in cardiacmyocytes are Cx43, Cx45 and Cx40. Methods and results: In current mathematical models, GJCs are considered to be passive.But, the experimental results, obtained by the dual­voltage clamp technique, show that GJCs display biophysical electrical properties such as voltage gating,i.e. a time and voltage dependence. Here we model Cx43 GJCs. We use the Hodgkin­Huxley formalism to describe GJCsconductance via one gating variable g j = g j (t, V j ). From our experimental results we obtain model parameters: the normalisedsteady state conductance and the time constant to reach the steady state, both voltagedependent. Once we have described the behavior of the single GJC, we write the mathematical model ofthe tissue, where we apply GJ current on specific parts of the cells’ membranes. Numerics and outlook: Some 3D numerical experiments are currently being performed on athin strip of cells, in order to compare the model’s results with the experimental ones. We use a monolayer of 50 × 3 cells, represented by cylinders of 100μm lengthand 10μm radius, with 2μm inter­cellular distance. We model GJCs on the cross sections of the cylinders. Finally, we apply an external stimulus on the border of the domain, and observe the propagation of theAP. Our goal is to make a mathematical model of the heterogeneous GJCs, including Cx45channels, as these have been shown to play a role in arrythmogenesis