Workshop “Mathematical Modelling, Analysis and Simulation with Applications to Biomedical Processes”

International Advanced Fellowship 2023, Project CNFIS-FDI-2023-F-0214 Prof. Dr.  Maria  Neuss-Radu  (FAU  Erlangen-Nurnberg)  in  collaboration with Centrul de Cercetare Analiza Aplicata al UBB Cluj Napoca


“Mathematical Modelling, Analysis and Simulation with Applications to Biomedical Processes”

UBB Cluj Napoca, October 9-10, 2023

Sala Club a Casei Universitarilor (Str. Em. de Martonne, 1) organized by Prof. Dr. Maria Neuss-Radu and Prof. Dr. Radu Precup

Invited Speakers

Prof.  Dr.  Drs.  h.c.  Willi Jager (IWR, University of Heidelberg)

Dr. Michael Gruber (Clinic of Anesthesiology, Hospital at the University of Regensburg)


10:55-11.20coffee breakcoffee break
19:00Workshop dinner 

Abstracts (in the Order of Presentations)

Modelling, analysis and simulations of layers controling  transi- tions between compartments and of epithelial layers in organisms – Challenges and contributions to mathematical, computational and biomedical research

Willi  Jager  (IWR,  University  of  Heidelberg)

Gaining an integrative understanding of complex interrelationships in biolog- ical and medical systems across all scales is a challenge for interdisciplinary research, especially to mathematics and computational sciences. This be- came particularly evident in the COVID pandemic, where neither sufficient standard knowledge nor data were available and could be used to fight this disease. Covid in its serious phase can develop into viral sepsis, leading to life-threatening multiple organ dysfunction. Sepsis is defined as a life- threatening multiple organ dysfunction, caused by an inadequate host re- sponse to an infection, a disease that can lead to an irreversible collapse of the entire organ system. This lecture will demonstrate with selected ex- amples that mathematical modeling and simulations can qualitatively and quantitatively improve insights into important processes of the infection and the disease, the response of the immune system, the effects on physiological processes on all cellular, tissue and organ level in the body of the host. Our experience is based on research in Sepsis started in 2015. Our research re- sults demonstrate that boundary layers and interfaces are crucial for healthy dynamical processes. The investigation must build on information about the basic structures and functional program of the pathogens and its interactions with the host at the cell and tissue level and at level of the organ system. Of particular importance are the interactions with the immune system, which usually is responding with inflammation as defense against the infection. Dis- ordered responses often occur, especially influenced by a hypoxia, caused by the virus in case of COVID. Since this infection is mainly an air-born, the alveoli in the lungs, which are important for gas exchange, are particularly affected by the virus, which can lead to hypoxia, harmful to the entire body. A main aim of this lecture is to show with selected examples that mathe- matical modelling and simulations of the underlying biochemical – biophysical processes, including the mechanics of fluid and solids, may help to understand arising critical disorders better und develop measures to control them. It will also become clear that the upcoming mathematical and computational prob- lems are exciting both in theory and in application and solutions cannot simply be taken off the shelf. The challenges arise in particular from the difficulties in the considered real systems. Reduction of their complexity and controlling nonlinearities, the arising multi-scales and or randomness, but also the lack of sufficiently good data require new concepts and methods. In particular, the following aspects will be addressed:

  • Epithelial and endothelial layers in parts of organisms, controlling tran- sitions and the coupling of processes in different compartments, are highly important for the dynamics of subsystems and finally of the organ system. Effective model equations for the relevant processes can be derived and sim- ulated using mathematical and computational multiscale
  • Mitochondrial, epithelial, vascular and further dysfunctions, which seriously endanger the supply with crucial substances and the energy, necessary for the functioning of the system, can be identified by setting up and investigating a model system, based on real
  • Coupling biomechanics with biochemistry and fluid dynamics, including poro-elastic media, is a hot topic in mathematical and computational re- search in biosciences and medicine. It is opening up a huge field of future research and transfer to biotechnological and medical

This lecture is based on joint research with Maria Neuss-Radu, Markus Gahn, Jonas Knoch, Gennady Bocharov, Manfred Thiel, Telma Silva, Adelia Sequeira, Yifan Yang, Thomas Richter, Valeria Malieva, Peter Bastian.

Cellular Layers and Neutrophils – A laboratory approximation Michael Gruber (University of Regensburg)

Cellular layers form the most important barriers in organisms. To elucidate their properties a laboratory model is to be implemented using a porous inorganic support plate and tracer substances as possible basis for diffusion investigations. Human Neutrophil Granulocytes are the first line of defense against intruders. A description of these cells as part of the inborn immune system is given in the second half of the presentation. A possible combination of both parts might be the basis for a new observation model of immune responses.

Ill-posed data assimilation problems: analysis and numerics Mihai Nechita (UBB Cluj Napoca)

Numerical analysis for partial differential equations (PDEs) traditionally con- siders problems that are well-posed in the continuum. However, when a part of the boundary is inaccessible for measurements or no information is given on the boundary at all, the problem might be unstable and its numerical approximation more challenging.

In this talk, we discuss ill-posed unique continuation/data assimilation problems in which noisy measurements are given in a subset of the computa- tional domain. We present a framework for stabilized finite element method (FEM) solving such problems based on PDE-constrained optimization with discrete regularization. We consider convection-diffusion equations, for which conditional stability estimates in suitable norms can be used to obtain error estimates in local L2– and H1-norms. We also consider fluid-structure inter- action (FSI) models with velocity measurements given, where such stabilized FEM can be used in applications related to blood flow and medical imagin- ing data (e.g. 4d-flow MRI data measuring the 3d velocity field of a tissue). Numerical results will be presented and analyzed. Based on joint work with Erik Burman, Miguel Fernndez, Lauri Oksanen.

Control of cell evolution after bone marrow transplantation Radu Precup (UBB Cluj Napoca)

We focus on a mathematical model of cell evolution after stem cell trans- plantation. A control problem is formulated to achieve the post-transplant correction of the hematological evolution. To solve the problem, an iterative algorithm based on the idea of lower and upper solution is proposed and used.

Numerical Simulation of Effective Models for Transport Processes in Deformable Porous Media within Mixed Eulerian/Lagrangian Framework

Jonas  Knoch  (FAU  Erlangen-Nurnberg)

We present in this talk an effective model for transport processes in period- ically perforated elastic media, taking into account also cyclic elastic defor- mation as it occurs e.g. in lung tissue due to respiratory movement. The underlying microscopic problem consists of a linear elasticity equation for the displacement within the Lagrangian framework, posed on a fixed domain and a diffusion equation for the concentration within the Eulerian frame- work, posed on the current deformed domain. After a transformation of the diffusion equation onto the fixed domain, we derive the upscaled model by means of a formal asymptotic expansion. The system is nonlinearly coupled through effective coefficients, which also take into account the periodic mi- crostructure. We develop and study numerical methods for our problem and perform simulations that are inspired by a bioengineered microdevice which is able to reconstitute critical lung functions (Lung-On-A-Chip). The sim- ulations shed light into the sensitivity of the model with respect to several experimental parameters such as frequency or magnitude of the cyclic me- chanical strain. This is joint work with Markus Gahn (Heidelberg), Nicolas Neu (Erlangen) and Maria Neuss-Radu (Erlangen).

Derivation of coupled Stokes-Plate-Equations for fluid flow through thin porous elastic layers

Maria  Neuss-Radu  (FAU  Erlangen-Nurnberg)

We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid part. Thickness and periodicity of the layer are of order ϵ, where ϵ is small com- pared to the size of the bulk domains. The fluid flow is described by an instationary Stokes equation and the solid via linear elasticity. We perform the rigorous homogenization of the porous structure in the layer and the reduction of the layer to an interface in the limit ϵ 0 using two-scale con- vergence. The effective model consists of the Stokes equation coupled to a time-dependent plate equation on the interface including homogenized elas- ticity coefficients carrying information about the micro structure of the layer. In the zeroth-order approximation we obtain continuity of the velocities at the interface, where only a vertical movement occurs and the tangential com- ponents vanish. The tangential movement in the solid is of order ϵ and given as a Kirchhoff- Love displacement. Additionally, we derive higher-order cor- rectors for the fluid in the thin layer. This is a joint work with Markus Gahn (Heidelberg) and Willi Jger (Heidelberg).