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Speaker: **Christophe Sotin**

Title: **Modeling challenges in planetary science**

Abstract: Numerical simulations become increasingly more important in helping scientists explore the solar system and understand its formation and evolution. I will use three examples illustrating the challenges: deep drilling in the icy crust of ocean world to search for biosignatures, hyper velocity sampling of Venus atmosphere to measure noble gases abundances that inform on why Venus and Earth have had such a divergent geological evolution, and two-phase convective models to interpret observations made by spacecraft.

]]>Speaker: **Václav Klika**

Title: **Implications of tissue heterogeneity in cartilage modelling**

Abstract: Current models targeting mechanobiology of cartilage are

becoming increasingly refined and complex by the inclusion of ever more

details such as heterogeneous distribution of solid matrix within

cartilage, fixed charged density, heterogeneous Darcy’s law with

preferential directions of flow determined by deformation, fibres,

compaction effects (the closing of pores), and complex 3D geometries.

Despite the undoubted benefit of having a finer description of the

cartilage tissue and hence the prospect of capturing its behaviour in a

wider context there is at the same time the issue of model verification as

the amount of data necessary for parameter estimation and subsequent

independent model validation rapidly increases.

In this talk we follow a different path to minimise the problem of

overestimation by revisiting the 1D experimentally relevant (confined

compression with rotational symmetry) biphasic model which allows for

qualitative insight and more reliable parameter estimation. Particularly

we shall see that the inclusion of heterogeneity in the initial solid

volume fraction corresponding to the presence of proteoglycans in

cartilage matrix has profound implications on both bulk equations, and

initial and boundary conditions. This influence is mediated by swelling

pressure being a consequence of achieving electroneutrality in the

system.

We shall rederive the 1D biphasic model carefully, as the linear

bihpasic model previously used that allows for an analytical solution has

some limitations in its presentation and derivation and is a special case

of the model formulated here with the swelling pressure contribution. Then

we continue with exploring the fundamental consequences of heterogeneous

distribution of initial volume fraction via the swelling pressure term

noting that compactification (pores closing) is naturally reflected in the

swelling pressure term.

If time permits, we shall discuss possible replacement of the

classically used Donnan theory for swelling pressure by a model reflecting

some of the microscopic natures of the cartilage tissue: a macroscale

model for swelling pressure that is an upscaled version of

Poisson-Nernst-Planck microscopic description. To this end we use the

method of multiple scales which is suitable even for systems with slowly

varying periodicity.

Speaker: **Marco Ellero**

Title: **GENERIC-compliant particle-discretizations of stochastic differential equations: applications to complex fluids**

Speaker: **Charlotte Perrin**

Title: **Macroscopic systems with maximum packing constraint**

Abstract:

This talk addresses the mathematical analysis of fluid models including a maximum packing constraint. These equations arise naturally for instance in the modeling of mixtures like suspensions. I will present recent results on two classes of PDEs systems which correspond to two modeling approaches: the “soft” approach based on compressible equations with singular constitutive laws (pressure and/or viscosities) close to the maximal constraint; and the “hard” approach based on a free boundary problem between a congested domain with incompressible dynamics and a free domain with compressible dynamics.

]]>Speaker: **Radomír Chabiniok**

Title: **Cardiac modeling in clinical practice: Physiology, biophysics & patient-specific management**

Abstract:

Biophysical modeling of cardiovascular system has been a very active research field in the past decades [1]. A number of sophisticated models based on physiological and physical assumptions have been created. A diligent work on mathematical analysis of complex problems, creation of efficient numerical schemes and development of computational resources allowed to conduct some significant model-validation studies. Efficient data assimilation techniques allowed to incorporate clinical data to extend the information included in the data but without modeling not accessible, and to increase the predictive capabilities of the models. Translating existing models into clinical practice is the next, and ultimately crucial step.

This task strongly depends on the interaction between clinical and modeling teams. While the clinical team characterizes the problem typically by targeting an important component in diagnosis or decision making for optimal management of a given patient the modeling team contributes by proposing the most suitable techniques to address the given question. The modeling ingredients selected must be compatible with the accuracy requested in the given problem, and the modeling framework must be in line with the time-constraint given by the clinical question. This talk will demonstrate a few examples of clinical modeling topics run between the research group M?DISIM of Inria Saclay Ile-de-France and various clinical partners.

First, the clinical application of modeling for monitoring purposes in patients under general anesthesia or at intensive care units will be presented. A direct collaboration with the Department of Anesthesia, Lariboisiere hospital in Paris, France, with two anesthetists directly included in the Inria modeling team (A. le Gall, MD full-time during his 3-year PhD project, and F. Vallee, MD, half-time) allows to advance this research towards first proof-of-concept works.

Secondly, augmenting the interpretation of clinical exams will be demonstrated on single- ventricle patients in an early-stage heart failure (HF). Such patients undergo a combined cardiovascular magnetic resonance (CMR) and heart catheterisation exam under pharmacological stress. Even such a complex data acquisition may not, however, uncover the underlying major component of their HF. Modeling shows a greatly promising tool to assist in refining the diagnosis the step prior to target the optimal treatment option. This project is pursued in the collaboration of Inria with Biomedical engineering department directly incorporated within St Thomas’ Hospital, King’s College of London, UK. A regular weekly work of an Inria researcher at St Thomas’ hospital and additional visits of a PhD candidate in the Inria lab is another example of a mode of function? of such a translational interdisciplinary research.

Finally, the problem of the optimal timing for a valve replacement therapy in patients with chronically overloaded ventricle will be discussed. It represents an example of addressing a question whether to and when to perform the intervention, and ultimately leads to a need to extend the modeling framework to capture the long-term progress of the pathology. This project is a part of an Associated research team? ToFMOD between Inria and University of Texas Southwestern Medical Center Dallas, with additional contributing partners being King’s College London, Institute for Clinical and Experimental Medicine (IKEM) and Czech Technical University in Prague. The decision was taken to confront and extend the existing long-term models with the patients with repaired Tetralogy of Fallot (rToF) as: 1) ToF is the most common complex congenital heart disease; 2) rToF patients are being followed with regular CMRs every 2-5 years (i.e. the longitudinal data of changes of the heart dilatation prior to intervention, an reverse- remodel-shrinking afterwards are possible to obtain). We believe that the knowledge gathered from the specific congenital heart disease cohort might be in addition to directly impacting the management of rToF patients partially applied in other more common acquired diseases.

All together, such presented modes of interdisciplinary work might lead to increasing a number of successful clinical applications of modelling with the ultimate goal in advancing healthcare.

Inria, M?DISIM research team, Paris-Saclay University, France

LMS, Ecole Polytechnique, CNRS, Paris-Saclay University, France

School of Biomedical Engineering and Imaging Sciences, St Thomas’ Hospital, King’s College London, UK

Literature: [1] R. Chabiniok et al.: Multi-physics and multiscale modelling, data?model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics, Interface Focus 6, 2016

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Speaker: **Ondřej Pejcha**

Title: **Catastrophic interactions of binary stars and the associated transients**

Abstract:

In this project, we plan to employ two numerical methods not commonly used in this subfield of astronomy. First, we will use low-Mach number (magneto)-hydrodynamics, which filters out sound waves in order to not be limited by the CFL condition. We will need to include realistic equation of state, energy transport by radiative diffusion, cylindrical or custom coordinates to capture non-spherical objects, complicated boundary conditions (stellar surface and excised cores of the stars), and eventually magnetic fields. Small regions of the domain might become supersonic. On the other hand, we will likely not need adaptive mesh refinement, nuclear burning or radiation transport beyond simple diffusion/conduction.

Second task aims to build moving-mesh radiation-hydrodynamics in 2D and 3D to study aspherical shock collisions and instabilities. The idea is to combine many essentially 1D Lagrangian spherical cones with transverse fluxes. For radiation, flux-limited diffusion will be sufficient (implicit update to explicit hydrodynamics), but detailed microphysics is important: realistic equation of state, opacities, and potential complications like small chemical reaction networks and growth of dust.

]]>*Speaker*: **Petr Zeman**

*Title*: **Vysokoteplotní chování nových tenkovrstvých materiálů**

*Abstract*:

Pokrok v oblasti nových technologií je úzce spojen s vývojem nových pokročilých materiálů. Pro vysokoteplotní aplikace jsou klíčové materiály, které jsou schopny odolávat nejen vysokým teplotám, ale i současnému vlivu okolního prostředí. Důležitou roli v tomto ohledu sehrávají vysokoteplotní tenkovrstvé materiály schopné modifikovat a ochránit povrch základního materiálu.

Přednáška uvede posluchače do problematiky vysokoteplotních materiálů s důrazem na tenkovrstvé materiály a metody charakterizace jejich vysokoteplotního chování. Významná pozornost bude věnována studiu oxidační odolnosti a teplotní stability struktury, složení a vlastností nových tenkovrstvých materiálů na bázi multiprvkových neoxidových a oxidových keramik a kovových skel připravených na pracovišti přednášejícího.

*Speaker*: **Eduard Rohan**

*Title*: **Homogenization of hierarchically arranged porous media **

*Abstract*:

The talk is aimed as an itroduction to the homogenization-based modelling of the so-called double-porosity media. Two situations can be distinguished: A) media described by the Biot-Darcy system of equations with highly heterogeneous permeability coefficients and other poroelastic coefficients, or B) media constituted by nested periodic structures. We focus on the second type of porous media formed by a microporous elastic skeleton with mesoscopic channels (cracks, or fissures). At the microscale level, the linearized fluid-structure interaction problem is treated, so that the first level of homogenization leads to the Biot continuum model describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model describing flow at the micro and meso-scopic pores coupled with the overall equilibrium equation respecting the hierarchical structure of the two-phase medium. Applications in the tissue perfusion modelling are shown.