Research School: Digital Twins of the Human Body

Dec 10, 2025, 9:00 AM → Dec 11, 2025, 7:00 PM Europe/Rome

Room 128-129 (SISSA Main Building)

Cangiani, Andrea (SISSA)

Research School: Digital Twins of the Human Body

Join us for an intensive 2-day school on biomedical modeling and high-performance computing. This event will focus on advanced topics in the modeling and simulation of human organs using the deal.II finite element library, combining theory with real-world applications.

What we offer

• Presentations on key challenges in biomedical modeling
• In-depth sessions on algorithmic and implementation aspects
• Practical hands-on tutorials
   

Whether you are a student, researcher, or professional, this program will equip you with the tools and insights to advance your work at the intersection of life sciences and computing.

Scientific program

Biomedical modeling sessions

• Mechanobiology of cell motility
• Poro-viscoelasticity of brain tissue
• Vascularized tissues modeling
• Computational cardiac models

In-depth algorithmic sessions

• Model reduction with scientific and physics-informed machine learning
• Finite element algorithms with matrix-free implementations
• Sparse linear equation solvers
• Preconditioners for coupled multiphysics problems
• Polytopic mesh methods

Hands-on tutorials

• Modeling alveolar structures and surfactant
• Mechanobiology of cell motility
• PSCToolkit
• Cardiac simulations

 

Wednesday, December 10

9:00 AM → 9:30 AM Registration

9:30 AM → 9:45 AM Welcome

9:45 AM → 10:30 AM BIOMEDICAL MODELING SESSION: The Mechanobiology of Cell Motility

Convener: Salvadori, Alberto (University of Brescia)

9:45 AM The Mechanobiology of Cell Motility

While the biochemistry of blood coagulation is well understood, less is known about how the mechanobiology of platelets influences clot remodeling and thus initiates tissue repair. Platelets not only release biochemical components needed to rapidly form fibrin-rich thrombi but also initiate wound site contraction. Research has shown that platelets are responsible for assembling the initial fibronectin fibers, preceding the infiltration of other cells. It is now well established that cellular motility results from the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone around the nucleation loci, which ultimately results in cellular or bacterial motility. To investigate the mechanobiology of these processes, state-of-the-art microscopy has been combined with a novel theory, leading to advanced modeling and simulations. With respect to most published mixture theories, we abandoned the assumption of incompressibility of all constituents and extended the classical theory of Larché-Cahn chemo-transport-mechanics. The theory appears to suit well in modeling cell motility and might also work well in other mechanobiological areas of interest for our project dealii-X.

Speaker: Salvadori, Alberto (University of Brescia)

10:30 AM → 11:00 AM Coffee break

11:00 AM → 11:45 AM BIOMEDICAL MODELING SESSION: Poro-viscoelasticity of brain tissue: modeling and inverse parameter identification

Convener: Greiner, Alexander (FAU)

11:00 AM Poro-viscoelasticity of brain tissue: modeling and inverse parameter identification

The brain is arguably the most complex human organ and modeling its mechanical behavior has challenged researchers for decades. There is still a lack of understanding on how this tissue responds to mechanical loading and how material parameters can be reliably calibrated. The Theory of Porous Media combined with finite viscoelasticity provides a theoretical framework to explore the underlying physical mechanisms, including interactions between solid matrix and free-flowing interstitial fluid and corresponding viscous and porous effects. By comparing finite element simulations with experimental data of cyclic compression–tension loading and compression–relaxation experiments, we show that the solid volumetric stress proves to be a crucial factor for the overall biphasic tissue behavior, as it strongly interferes with porous effects controlled by the permeability. An inverse parameter identification (PI) reveals that poroelasticity alone is insufficient to capture the time-dependent material behavior, but a poro-viscoelastic formulation captures the response of brain tissue well. Including the lateral displacement of specimens during testing into the inverse PI, results in more accurate parameters. Taken together, our analyses provide valuable insights into the individual contributions of viscous and porous effects. They can help identify more reliable poro-viscoelastic parameters for brain finite element simulations in the future.

Speaker: Greiner, Alexander (FAU)

11:45 AM → 12:45 PM HANDS-ON TUTORIAL: Modeling Alveolar Structures and Surfactant: Hands-On Session with ExaDG

Convener: Temür, Bugrahan (TU München)

11:45 AM Modeling Alveolar Structures and Surfactant: Hands-On Session with ExaDG

Mechanical ventilation is a critical method for patients with impaired pulmonary function, but it can cause ventilator-induced lung injury. Clinicians must balance effective respiration with strategies that protect lung tissue. However, the local effects of mechanical ventilation are challenging to measure or observe by medical imaging. Computational models promise physics-based forecasts on the impact of different ventilation maneuvers on patient-specific geometries. Yet, most models fail to incorporate many crucial effects in respiratory mechanics, surfactant being among the most notable. Surfactant molecules in the fluid lining of the alveoli reduce surface tension, thereby increasing lung compliance. To understand surfactant effects and integrate them into patient-specific reduced-order or homogenized models, we require numerous highly resolved simulations of delicate and complex alveolar structures. We perform these simulations using the open-source ExaDG software project. ExaDG is based on deal.II and provides highly efficient solvers for problems in fluid mechanics, solid mechanics, and fluid-structure interaction. The extensible software architecture enables us to implement surfactant dynamics in the matrix-free hyperelasticity solver. The exceptional performance allows us to handle the high resolution and the large number of different setups required to extract information from the fine-scale alveolar structure simulations.

Speaker: Temür, Bugrahan (TU München)

12:45 PM → 2:00 PM Lunch break

2:00 PM → 2:45 PM IN-DEPTH ALGORITHMIC SESSION: Accelerating Numerical Simulations in CFD by Model Reduction with Scientific and Physics-Informed Machine Learning for Digital Twin(s)

Convener: Prof. Rozza, Gianluigi (SISSA, International School for Advanced Studies)

2:00 PM Accelerating Numerical Simulations in CFD by Model Reduction with Scientific and Physics-Informed Machine Learning for Digital Twin(s)

Partial differential equations (PDEs) are invaluable tools for modeling complex physical phenomena. However, only a limited number of PDEs can be solved analytically, leaving the majority of them requiring computationally expensive numerical approximations. To address this challenge, reduced order models (ROMs) have emerged as a promising field in computational sciences, offering efficient computational tools for real-time simulations, suited to manage digital twins. In recent years, deep learning techniques have played a pivotal role in advancing efficient ROM methods with exceptional generalization capabilities and reduced computational costs, especially for parametric settings and turbulent flows. In this talk we explore how classical ROM techniques can be elevated through the integration of some deep learning models. We will introduce hybrid approaches, which consider both physics-based and purely data-driven techniques, as well as aggregated ones, where the model is built as a combination of different pre-trained models. Examples will deal with parametric flows also with turbulence.

Speaker: Prof. Rozza, Gianluigi (SISSA, International School for Advanced Studies)

2:45 PM → 3:30 PM IN-DEPTH ALGORITHMIC SESSION: Polytopic mesh methods: recent developments and deal.II-based implementation

Conveners: Africa, Pasquale Claudio, Cangiani, Andrea (SISSA)

2:45 PM Polytopic mesh methods: recent developments and deal.II-based implementation

The efficient and accurate resolution of multiphysics problems posed on intricate geometries typically requires time-consuming meshing, and the accurate representation of the geometry and solutions features with standard meshes may require excessive computational power.
Polytopic meshes can be used for complexity reduction for multi-physics problems posed on intricate geometries. For instance, the possibility of using general shape elements permits the exact representation of very general domains and interfaces, or the accurate representation of such domains without the need of overly refined meshes. Another example is the possibility to use hierarchies of nested agglomerated meshes, which can be used to design efficient multigrid solvers.
The Polydeal library extends deal.II with robust support for polygonal and polyhedral discretizations, integrating smoothly with its existing framework. We will demonstrate how these new features can be used in practice, offering greater flexibility for complex geometries while preserving the familiar deal.II workflow.
As proof of concept, we will demonstrate the use within Polydeal of a novel multilevel agglomeration and preconditioning strategy designed to solve the monodomain equation in cardiac electro-physiology using high-order discontinuous Galerkin (DG) methods.

Speakers: Cangiani, Andrea (SISSA), Africa, Pasquale Claudio

3:30 PM → 4:00 PM Coffee break

4:00 PM → 6:00 PM HANDS-ON TUTORIAL: Hands-on Mechanobiology of Cell Motility

Convener: Serpelloni, Mattia (University of Brescia)

4:00 PM Hands-on Mechanobiology of Cell Motility

This contribution reviews recent advancements in mechanobiology at the University of Brescia (UNIBS), with particular emphasis on the development of advanced computational models—built on the deal.II finite element library—for investigating cell motility.
Controlling cell motility remains a major scientific challenge, as it underpins key biological processes such as metastasis, embryogenesis, angiogenesis, and hemostasis. These phenomena depend on the dynamics of sometimes transient, force-bearing cytoskeletal networks, regulated and activated by the molecular activity of adhesive proteins (receptors) on the cell membrane.
Accordingly, our research focuses on two central aspects:
(i) the role of actin cytoskeleton dynamics in the mechanobiology of cell motility, and
(ii) the role of cell mechanics in receptor activity.
For (i), we propose a multiphysics model extending the Larché–Cahn framework for chemo-mechanical coupling. It captures the interaction between actin transport, polymerization, and mechanical forces driving membrane protrusion and cell migration.
For (ii), we introduce a model exploring how cell mechanics influences the chemo-diffusive behavior of adhesive receptors and their interactions with extracellular molecules called ligands. In this context, the cell membrane is idealized as the boundary of a deformable body, with its morphology governed by intracellular dynamics.
Simulations for both models (i) and (ii) are obtained using a Lagrangian perspective.
Numerical studies based on model (i) demonstrate the code’s ability to generate force-bearing domains through monomer polymerization—an approach particularly suited for simulating fibrin network formation in hemostasis. In silico experiments relying on model (ii) provide insights into the mechanobiology of adhesive protein relocation in advecting cells.
We conclude by outlining future developments and offering hands-on sessions, where participants will have the opportunity to run mechanobiological simulations using our computational tools.

Speaker: Serpelloni, Mattia (University of Brescia)

Thursday, December 11

9:00 AM → 9:45 AM IN-DEPTH ALGORITHMIC SESSION: High-performance finite element algorithms with matrix-free implementations

Convener: Kronbichler, Martin (Ruhr University Bochum)

9:00 AM High-performance finite element algorithms with matrix-free implementations

The objective of my talk is the efficient implementation of solvers for linear systems arising from the discretization of partial differential equations (PDEs) with higher-order finite element methods. The classical workflow is to first construct a sparse matrix and a right-hand side through the evaluation of element integrals in one part of the code. The matrix and vector are then passed to a specialized solver software, which usually employs an iterative method of the Krylov family combined with some sophisticated preconditioner. While this abstraction has been highly successful for many problems, research on performance optimizations of this parts reveals that all steps are characterized by a low arithmetic intensity, i.e., a low ratio of arithmetic operations compared to memory access of loading all matrix entries repeatedly into the compute units. Due to the continuous hardware evolution of the last decades, computations have actually become very cheap in comparison to memory access. In fact, modern CPUs and GPUs can sustain more than 100 arithmetic operations for each data element loaded from main (RAM) memory. It is therefore natural to seek for algorithms that avoid storing the big sparse matrices altogether, and rather apply the operator action on the fly within iterative solvers. This leads to matrix-free solvers.
The talk will present the main design characteristics of fast matrix-free operator evaluation for PDEs based on computing the cell and face integrals on the fly with the deal.II finite element library. I will consider both memory access and efficiency of arithmetic work, such as sum-factorization techniques, with respect to modern hardware of the exascale era, with the goal to minimize the time-to-solution. In the talk, applications in computational fluid dynamics will be shown, comparing both classical H1 and L2 conforming methods against H(div) conforming Raviart-Thomas operators. While these methods show large speedups for matrix-vector products in isolation, the overall solver strategy crucially depends on efficient preconditioners that balance low iteration counts with fast operator evaluation, for which either matrix-free and matrix-based ingredients can be attractive. In our research, we consider both multigrid techniques with polynomial or geometric mesh coarsening, block-Jacobi methods with local solvers based on the fast diagonalization method and approximate incomplete matrix factorizations. Finally, the talk will look into the node-level performance optimizations of these algorithms and scalability to large supercomputers.

Speaker: Kronbichler, Martin (Ruhr University Bochum)

9:45 AM → 10:30 AM IN-DEPTH ALGORITHMIC SESSION: Scalable and optimal preconditioners for coupled multiphysics problems

Convener: Heltai, Luca (University of Pisa)

9:45 AM Scalable and optimal preconditioners for coupled multiphysics problems

We introduce augmented Lagrangian preconditioning strategies for solving linear systems arising from coupled problems. In particular we explore in details finite element discretizations of fictitious domain formulations with Lagrange and distributed Lagrange multipliers. The presentation focuses on two- and three-block structures appearing in Poisson, Stokes, and elliptic interface problems, and on their efficient solution with Flexible GMRES. We discuss both exact and inexact augmented Lagrangian preconditioners, including a computationally cheaper block-triangular variant. A spectral analysis is provided to explain the observed convergence behavior. Numerical experiments in two and three dimensions demonstrate the robustness and scalability of the proposed preconditioners, even in the presence of strong coefficient jumps.

Speaker: Heltai, Luca (University of Pisa)

10:30 AM → 11:00 AM Coffee break

11:00 AM → 11:45 AM IN-DEPTH ALGORITHMIC SESSION: Recent advances on MUMPS: MUltifrontal Massively Parallel Solver for the direct solution of sparse linear equations

Convener: Amestoy, Patrick (MUMPS Technologies)

11:00 AM Recent advances on MUMPS: MUltifrontal Massively Parallel Solver for the direct solution of sparse linear equations

The scientific library MUMPS (for MUltifrontal Massively Parallel Solver) solves large systems of sparse linear equations, AX=B, in a robust and efficient way on high performance computers. The matrix A is a large square matrix and X and B are vectors or matrices whose sparsity can also be exploited. MUMPS is an open source software, distributed under the CeCILL C licence which can be downloaded from http://mumps-solver.org.
In many areas of numerical simulation, the solution of sparse linear systems is a critical and expensive part of the simulation and numerically difficult problems often lead to longer calculation times, memory used and power consumption. Today, we want to solve linear systems of increasingly large sizes (several hundred million unknowns) allowing complex problems to be addressed while maintaining performance and numerical stability.
In the recent years, we have worked on a low-rank method called Block Low-Rank (BLR) to exploit data sparsity and proved that we can reduce the complexity of sparse solvers in terms of the number of floating-point operations and memory usage of the numerical phases. We have also show that low- rank approximations exhibit remarkable properties that allow for the use of mixed precision arithmetic without loss of accuracy. We also describe recent work done with XKblas library (CeCILL-C free license) to address GPU-based architectures such as NVIDIA Grace Hopper, AMD MI250 and AMD MI300.

Speaker: Amestoy, Patrick (MUMPS Technologies)

11:45 AM → 12:45 PM HANDS-ON TUTORIAL: Tutorial on PSCToolkit

Convener: Filippone, Salvatore (University of Rome Tor Vergata)

11:45 AM Tutorial on PSCToolkit

We present a tutorial on PSCToolkit, a set of libraries for high-performance linear solvers on parallel computers. The toolkit provides many advanced features besides the usual Krylov solvers, such as support for Algebraic Multigrid (AMG) preconditioning techniques based on the aggregation of unknowns, employing both standard strength-of-connection measures and graph-matching strategies. Moreover, it includes a variety of highly parallel smoothers, such as polynomial accelerators for weighted Jacobi methods, Additive Schwarz schemes, and block-Jacobi variants of Gauss–Seidel iterations and approximate inverse approaches. The toolkit provides easy mechanisms to run on GPUs supporting the CUDA programming environment; it is currently being integrated into dealii.X framework for use in the project; it has been tested for scaling on the Leonardo platform up to 8192 GPUs with linear systems of size up to 10^11.

Speaker: Filippone, Salvatore (University of Rome Tor Vergata)

12:45 PM → 2:00 PM Lunch break

2:00 PM → 2:45 PM BIOMEDICAL MODELING SESSION: Modelling vascularized tissues: coupling 3D elastic matrix and 1D vascular tree

Convener: Belponer, Camilla (WIAS Berlin)

2:00 PM Modelling vascularized tissues: coupling 3D elastic matrix and 1D vascular tree

A key aspect of vascularized tissues is the fact that their properties are heavily influenced by the presence of the vascular tree. On one hand vessels are expanding and contracting due to systemic circulation on the other hand the surrounding matrix reacts with a counter-active (elastic) response. This means that neither the circulation at the capillaries, nor the elastic properties of the matrix can be studied and modeled on their own. Here we present a computational model for the efficient simulation of such tissues. Our model is based on a geometrical multiscale 3D (elastic) -1D (fluid) coupled formulation, handling the effect of the vasculature on the elastic matrix with an immersed method. This allows us to treat fluid inclusions at a lower dimensionality and thus to capture the interaction between the two phases of the material without requiring the discretization of the fluid-solid interface within the computational mesh. In order to study the effect of complex vessel networks, we explore the relationship between the coupled system and parameters that can be estimated at larger scale (macroscale). This goes in the direction of solving inverse problems in the context of tissue imaging, as available medical data usually have a limited resolution, typically at the scale of an effective - macro scale - tissue, and cannot resolve the microscale. We will present a brief mathematical background, as well as key aspects of the coupling and its applications.

Speaker: Belponer, Camilla (WIAS Berlin)

2:45 PM → 3:30 PM BIOMEDICAL MODELING SESSION: Computational Cardiac Models in the iHEART Simulator

Convener: Dedè, Luca (Politecnico di Milano)

2:45 PM Computational Cardiac Models in the iHEART Simulator

In this talk, we review mathematical and numerical models of the human heart that are able to capture both its physiology and pathological conditions. We focus on the differential models underlying cardiac electrophysiology, mechanics, and blood flow dynamics, including those that describe the fiber bundles characteristic of cardiac tissue. We then present an overview of the numerical methods implemented in the finite element library lifex for simulating these core models, as well as the multiscale and multiphysics integrated models upon which the iHEART simulator is built. This presentation provides the foundation for the hands-on tutorial session on the lifex library.

Speaker: Dedè, Luca (Politecnico di Milano)

3:30 PM → 4:00 PM Coffee break

4:00 PM → 6:00 PM HANDS-ON TUTORIAL: Hands-on cardiac simulations with life^x

Convener: Bucelli, Michele (Politecnico di Milano)

4:00 PM Hands-on cardiac simulations with life^x

We present an overview of life^x, a library designed for multiphysics simulations for cardiovascular applications, based on deal.ii. In this session, we will describe the structure and general-purpose features of the library, focusing on the multiphysics coupling capabilities that the it offers. Additionally, we will illustrate the planned future developments and improvements. Finally, attendees will have the opportuninty to familiarize with life^x through hands-on cardiovascular simulations, focusing in particular on cardiac muscular fibers reconstruction, electrophysiology and cardiovascular hemodynamics.

Speaker: Bucelli, Michele (Politecnico di Milano)