This journey started several years ago when I decided to enjoy the Medical Engineering course at the University of Rome Tor Vegata. More concretely, it started several months ago, moving to Stockholm and starting my traineeship at KTH as described in the previous chapter of this diary. Now, the end has come with my master’s graduation with a 110 cum laude as a Master’s Doctor in Engineering.

What’s the thesis about?

The impact of residual strains on the stress analysis of atherosclerotic carotid vessels – predictions based on the homogenous stress hypothesis

Cardiovascular disease

Have you ever been asked how many people die from cardiovascular disease?


Sadly, the number is very high and the majority is related to atherosclerotic processes. The stenosis formation is due to a systemic pathology leading to the thickening of the vessel internal wall with the deposition of material. This leads to atherosclerotic plaque formation with the consequent risk of rupture leading to thrombus and ischaemic events or stroke, and then the patient’s death.

Atherosclerotic plaque progression


This thesis project introduces an innovative computational framework to include the description of residual stresses and strains in patient-specific carotid stenosis due to atherosclerotic plaque following the homogenous stress hypothesis.

Generic workflow for the model. It starts with a conversion from medical images into a mesh, segmenting the images to distinguish between the properties of the different tissues. The STL mesh models are imported into Comsol material properties assigned through a Matlab procedure. Finite element simulation routines in Comsol are employed to compute the finite element solution and investigate the stress state and residual strains. * @Windows11 i7-10850H – 32 GB RAM 2933 MHz

Thesis foundation

It was Galileo Galileo, more than 400 years ago, to introduce the idea of seeing tensions as a growth limiter. Which is why all living beings have finite size. But only in the 19th century, a concrete theory was formulated in Davis’s law relating soft tissue growth and remodeling to environmental stimuli.

In 1966 Wolinski and Galcov introduced new experimental evidence highlighting how it is possible to observe a constant tensile state in vascular tissue. There exists tensional homeostasis where homeostasis is a dynamic sequence of equilibrium status in which the vascular tissue goes against a continuous remodeling to respond to the mechanical environment and the blood pressure. Then, in the early 90s, Fung introduced the homogenous stress hypothesis relating the vascular tissue growth & remodeling to the maintaining of a homogenous stress state reducing the stress gradient across the wall.

Wolinsky – Glacov, 1966. Fung,1991

This hypothesis leads to the introduction of the computational framework proposed in this thesis works to include residual stresses and strains in complex geometries such as patient-specific carotid diseased vessels.

Thesis outcomes

The introduced numerical framework allows the vascular tissue to growth and remodeling. Results show a general homogenization of the stress state as well as a reduction of the peak stress.

Standard FEM analysis
Growth & remodelling

Carotid arteries

Clearly, it is applied to several patient-specific geometries of diseased carotid vessels. These structures include tissue distribution information discriminating between lipid-rich necrotic core, calcification, intra-plaque hemorrhage, and healthy tissues.

It is a numerical framework based on finite elasticity revisiting the deformation gradients as a multiplicative composition of two parts. The first one is due to growth and remodeling and the elastic part is due to tissue properties and compatibility requirements.

I will describe it better in the following publications.

Peak stress analysis

As biomedical engineers, in the lately 20 years we introduce a new biomechanical approach to analyze the atherosclerotic plaque and the stress state in order to estimate a rupture risk index. This is created in aid to the current medical guidelines relying on lumen narrowing and patient anamnesis that however understates rupture risk in 30% of the asymptomatic patients leading to great risk for health or patient’s death.

Localization of the peak stress near to the plaque fibrous cap with higher rupture risk

Growth & remodeling

This thesis work shows how it is not only possible to include residual stress is such complex geometries, but it became necessary if we want to estimate the rupture risk.

Loading of the vessel followed by the growth & remodeling process and then the unloading to see the residual strains.

It was a very long journey giving to me a lot of experience in computational analysis and hyperelasticity to describe biological tissue such as their growth and remodeling processes. At the same time, I know a lot of interesting people and experts in this field that became a continuous source of inspiration for both life and academic continuous improving.


You can find a dairy of the months for the preparation of the thesis abroad at the following links: