Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Good health and well-being

Academic Year 2020/2021

Learning outcomes

The aim of the course is to provide the student the basic knowledge and competence for the biomechanics modelling of the musculoskeletal and the cardio-circulatory systems and sub-systems. In particular, the student will be able to identify the key variables for the modelling of the main anatomical structures, and for the characterisation of their mechanical behaviour in physiological and pathological conditions.

Course contents


What is a model
Fundamentals of geometry
Fundamentals of trigonometry
Coordinate transformations
Kinematics of the material point and rigid body
Continuous deformable media



Lagrangian and Eulerian coordinates
Infinitesimal deformations of Cauchy
Deformations and main axes (invariants)


Euler-Cauchy principle
Deformation tensor
Undefined equilibrium equations
Boundary equilibrium conditions
Coordinate transformations
Main tensions and axes
Deformation energy

Constituent equations:

Strain and Strain Rate (Compatibility Equations)
Constituent equation (non-viscous fluid, Newtonian viscous fluid, linear elastic solid)
Examples (deflection of a beam: demonstration)


Linear (Maxwell, Voight, Kelvin models; General formulation; Response of a viscoelastic body to harmonic stress; Electrical analogy)
Response to a generic deformation history
Use of viscoelastic models

The muscle:

Fundamentals of physiology and morphology
Hill equations and model
Skeletal muscle: basic equations (3-element model)

Fluid dynamics:

Material and spatial description of the motion of a continuous medium (material derivative)
Continuity equation (Recall: Gauss theorem)
Kirchoff's law
Euler equations of motion
Navier Stokes equations for an incompressible and isotropic Newtonian viscous fluid
Examples (motion of a fluid in a circular tube with rigid walls and variable section; pulsatile bulb; stationary flow of an incompressible fluid in a horizontal channel; stationary flow of an incompressible fluid in a horizontal cylindrical tube with rigid walls)
Reynolds number
Energy balance

The cardiovascular system:

Fundamentals of physiology and morphology
Laminar flow of blood in a cylindrical vessel (Poiseuille's law)
Arterial fluid dynamics (models with distributed and concentrated parameters)
Propagation of a flat elastic wave

The heart muscle:

Fundamentals of physiology and morphology
Left ventricle models
Examples (cylindrical model of ventricle: demonstration)
Characterization of the pulsatile heart coupled to its load
Starling's law


Pdf material available on-line

- Yuan-Cheng Fung "A first course in continuum mechanics"

- Yuan-Cheng Fung "Biomechanics: Mechanical Properties of Living Tissues"

- Yuan-Cheng Fung "Biomechanics: Circulation"

- Yuan-Cheng Fung "Biomechanics: Motion, Flow, Stress, and Growth"

Teaching methods

Class lessons, latoratory activity

Assessment methods

Written and oral test.
The test aims at evaluating the theoretical knowledge of the student and his/her abilities in facing design problems. Moreover, the analysis and synthesis capacities, correctness of language, clearness of concepts and exposition will be evaluated too.

Teaching tools

Study material provided on-line.

Office hours

See the website of Rita Stagni