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.


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

T. Christian Gasser, KTH Royal Institute of Technology, Sweden

Alain Goriely, University of Oxford, UK

Georges Limbert, University of Southampton, UK

Gustavo Orozco, Lund University, Sweden

Hanna Isaksson, Lund University, Sweden

Stéphane Avril, Ecole des Mines de Saint-Etienne, France

Svein Kleiven, KTH Royal Institute of Technology, Sweden


  • 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


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.

Biaxial testing

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

COMSOL Modeling

Computational models report results comparable to the analytical solutions.


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.

The video is speeded up and because of this the image seems to be jerky. The real duration is greater than 7 minutes.

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