New Discrete Formulation for Reduced Population Balance Equation: An Illustration to Crystallization

In this paper, we focus on providing a discrete formulation for a reduced aggregation population balance equation. The new formulation is simpler, easier to code, and adaptable to any type of grid. The presented method is extended to address a mixed-suspension mixed-product removal (MSMPR) system where aggregation and nucleation are the primary mechanisms that affect particle characteristics (or distributions). The performance of the proposed formulation is checked and verified against the cell average technique using both gelling and non gelling kernels. The testing is carried out on two benchmarking applications, namely batch and MSMPR systems. The new technique is shown to be computationally less expensive (approximately 40%) and predict numerical results with higher precision even on a coarser grid. Even with a revised grid, the new approach tends to outperform the cell average technique while requiring less computational effort. Thus the new approach can be easily adapted to model the crystallization process arising in pharmaceutical sciences and chemical engineering.

Modeling and analysis of melanoblast motion

Melanoblast migration is important for embryogenesis and is a key feature of melanoma metastasis. Many studies have characterized melanoblast movement, focusing on statistical properties and have highlighted basic mechanisms of melanoblast motility. We took a slightly different and complementary approach: we previously developed a mathematical model of melanoblast motion that enables the testing of biological assumptions about the displacement of melanoblasts and we created tests to analyze the geometric features of cell trajectories and the specific issue of trajectory interactions. Within this model, we performed simulations and compared the results with experimental data using geometric tests. In this paper, we developed the associated mathematical model and the main focus is to study the crossings between trajectories with new theoretical results about the variation of number of intersection points with respect to the crossing times. Using these results it is possible to study the random nature of displacements and the interactions between trajectories. This analysis has raised new questions, leading to the generation of strong arguments in favor of a trail left behind each moving melanoblast.

A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails

The Michaelis-Menten reaction scheme is among the most influential models in the field of biochemistry, since it led to a very popular expression for the rate of an enzyme-catalysed reaction. After the realisation that this expression is valid in a limited region of the parameter space, two additional expressions were later introduced. The range of validity of these three expressions has been studied thoroughly, since the significance of a reliable rate is not based only on the accuracy of its predictive abilities but also on the physical insight that is acquired in the process of its construction. Here a new expression for the rate is introduced that is valid in practically the full parameter space and reduces to the expressions in the literature, when considering appropriate limits. The new expression is produced by employing algorithmic tools for asymptotic analysis, so that its construction is not hindered by the dimensional form and the complexity of the full model or by a wide parameter range of interest. These tools can be employed for the derivation of enzyme rate expressions of much more complex kinetics mechanisms.

Multifidelity-CMA: a multifidelity approach for efficient personalisation of 3D cardiac electromechanical models

Personalised computational models of the heart are of increasing interest for clinical applications due to their discriminative and predictive abilities. However, the simulation of a single heartbeat with a 3D cardiac electromechanical model can be long and computationally expensive, which makes some practical applications, such as the estimation of model parameters from clinical data (the personalisation), very slow. Here we introduce an original multifidelity approach between a 3D cardiac model and a simplified "0D" version of this model, which enables to get reliable (and extremely fast) approximations of the global behaviour of the 3D model using 0D simulations. We then use this multifidelity approximation to speed-up an efficient parameter estimation algorithm, leading to a fast and computationally efficient personalisation method of the 3D model. In particular, we show results on a cohort of 121 different heart geometries and measurements. Finally, an exploitable code of the 0D model with scripts to perform parameter estimation will be released to the community.