I finished my experience in the Summer School entitled “Computational Tissue Biomechanics: From in-vitro experiment to computational analysis“.

The course introduces and applies state-of-the-art tools in the continuum mechanical analysis of biological tissues. It is designed for master students and PhD students having a decent background in mechanical engineering and solid mechanics.

Furthermore, the course integrates theoretical, numerical, and experimental concepts in the description and analysis of biological tissues. Lectures (18 hours) are combined with hands-on laboratory (4 hours) and Finite Element Method (FEM) modeling work (4 hours) towards the integration of theoretical and practical knowledge. Also practical tasks are carried out in groups of students and are supervised by PhD students.

## Biomechanics

Several biomechanics experts from different parts of Europe spoke at the conference.

He holds a Master of Mechanical Engineering (1997) and a PhD in Civil Engineering (2001), both from Graz University of Technology, Austria. In 2008 Gasser accomplished his Habilitation in Solid Mechanics/Biomechanics at KTH. The development and application of advanced numerical techniques to solve realistic (bio)engineering and clinical problems, is Dr. Gasser’s main research objective.

He currently holds the chair of Mathematical Modelling and to become Director of the Oxford Centre for Collaborative Applied Mathematics (OCCAM).

He holds a Master in Engineering Mechanics (Toulouse, France) and a Research Master in Theoretical Mechanics (Bordeaux, France). He obtained a PhD in Computational Biomechanics from the University of Southampton in 2002 and is a Chartered Engineer and Member of the Institution of Mechanical Engineers (IMechE) since 2005. Dr. Limbert also sits on the board of the Engineering in Medicine and Health Division of the IMechE since 2004.

He holds a PhD in applied Physics with specialization in biomechanics from the University of Eastern Finland, Kuopio, Finland, where he also worked as a postdoctoral researcher (2020-2021). His research interest covers numerical drug delivery into brain tissue, musculoskeletal modeling of knee joint, and mechanobiological modeling of cartilage degeneration.

Prior to joining Lund University, Dr Isaksson spend three years as a post-doctoral researcher at the Biophysics of Bone and Cartilage research group at the University of Eastern Finland. Isaksson’s research area is primarily bone biomechanics and mechanobiology, focusing on functional imaging and statistical shape modeling of bone, characterization of bone damage and fracture mechanisms as well as on improvement of bone quality during fracture repair. She also has ongoing research in cartilage and tendon biomechanics and mechanobiology.

He holds several visiting professorship, such as at Technical University Graz (2022), Technical University Vienna (2021), Yale University (2018, 2019). Dr. Avril’s research interest covers the mechanics of soft biological tissues, inverse problems and mechanobiology of the thoracic aorta. The goal of his research is to improve the treatment of cardiovascular diseases by assisting physicians and surgeons with biomechanical numerical simulation.

He is Director of the Doctoral Programs in Technology and Health and Applied Medical Engineering at KTH, and the Director of a Joint Doctoral Program between Karolinska Institute and KTH in Medical Technology. Dr. Kleiven’s research primarily focuses on head and neck injury prevention and improving the clinical neuro-surgery treatment results with simulations and innovations.

## Calendar

• Gasser: Computational Continuum Biomechanics
• In vitro tissue testing
• FEM modeling
• KTH guided tour
• Goriely: tissue testing
• Isaksson: bone tissue
• In vitro tissue testing
• Limbert: skin tissue
• Orozco/Isaksson:tendon/ligament, cartilage
• Kleiven: brain tissue
• Gasser: blood vessel
• Avril: blood vessels
• Nobel Prize Museum tour

## Venue

The Summer School takes place at KTH main campus in the north of Stockholm city.

### FEM modeling

The modeling course involves the computational analysis of the biaxial test. By using COMSOL Multhiphysics it is possibile to create geometry for a quarter of the samples and apply prescribed displacement at the attacchment point.

A Yeoh strain energy model with vascular tissue parameter it is used.

Computational models report results comparable to the analytical solutions.

### Laboratory

Laboratory works provides biaxaxial testing and fracture test for tissue from a pig aorta.

Experimental data must be fitted with the selected strain energy to describe the model and constitutive parameters.

The straing energy models of Yeoh and Fung were used. The data fitting was completed by minimizing the differences between the data and the corresponding model results.

\min\to\left[\sum_{k=1}^N\left(P_{k,j}(c_1,c_2)-P_{k,j}^{\mathrm{exp}} \right)\right]

Where P is the first Piola Kirchoff stresses for each protocol:

P_a^{\mathrm{exp}}={F_a\over H_0\cdot L_i};\quad P_c^{\mathrm{exp}}={F_c\over H_0\cdot L_i}

And analytical with plane stress conditions:

P_j={\partial \Psi\over \partial \lambda_i}-{\partial \Psi\over \partial \lambda_r}

And the index vary over direction.

Numerical minimization was performed with Matlab.

The second experiment was a fracture test for the same tissue. A uniaxial tensile test was conducted until the fracture of the aorta.

Also DIC (digital image corelation) was used to evaluated strain over the sample surface.