Mathematical Hemodynamics

Teacher: dr. Josip Tambańća, professor
Semester: second or third
ECTS: 4
Elective course

  1. To introduce students to the application of mathematical modelling in the analysis of cardio vascular systems.
  2. To introduce students to the basic tools from mathematics, fluid dynamics, mechanics and human cardiovascular anatomy and physiology, necessary to study problems in cardiovascular fluid dynamics.
  3. To show how mathematics, especially continuum mechanics and computing can be used in an integrated way to analyse biomedical systems and devices, like blood flow or stents.

Students are going to be able:

  1. To have an enhanced knowledge and understanding of mathematical modelling and mathematical methods using continuum mechanics for the analysis of problems in hemodynamics.
  2. To be able to formulate model using continuum mechanics for a particular problem in circulatory system.
  3. To be aware of the use of partial differential equations and computers to assist them in studying biological/medical systems.
  4. To use numerical methods to get qualitative conclusions for problems in hemodynamics.
  1. Basic anatomy and physiology of the cardiovascular system. The heart and coronary arteries, blood vessels, blood.
  2. Introduction to continuum mechanics. Equations of motion, stress, strain. Constitutive equations.
  3. Blood flow modelling. The incompressible Navier-Stokes equations. Nondimensional form of the equations, Reynolds number, Poiseuille and Womersley flow. Weak formulation of the equations.
  4. Arterial wall models. Three-dimensional models. Membrane and Koiter type models. Simplified models.
  5. Stent models. Three-dimensional models. One-dimensional models of curved elastic rods. Simplified one-dimensional stent models.
  6. Fluid-structure interaction models. Mathematical formulation, mathematical and physical properties, numerical schemes.
  • Course objectives

    1. To introduce students to the application of mathematical modelling in the analysis of cardio vascular systems.
    2. To introduce students to the basic tools from mathematics, fluid dynamics, mechanics and human cardiovascular anatomy and physiology, necessary to study problems in cardiovascular fluid dynamics.
    3. To show how mathematics, especially continuum mechanics and computing can be used in an integrated way to analyse biomedical systems and devices, like blood flow or stents.
  • Expected learning outcomes

    Students are going to be able:

    1. To have an enhanced knowledge and understanding of mathematical modelling and mathematical methods using continuum mechanics for the analysis of problems in hemodynamics.
    2. To be able to formulate model using continuum mechanics for a particular problem in circulatory system.
    3. To be aware of the use of partial differential equations and computers to assist them in studying biological/medical systems.
    4. To use numerical methods to get qualitative conclusions for problems in hemodynamics.
  • Course content

    1. Basic anatomy and physiology of the cardiovascular system. The heart and coronary arteries, blood vessels, blood.
    2. Introduction to continuum mechanics. Equations of motion, stress, strain. Constitutive equations.
    3. Blood flow modelling. The incompressible Navier-Stokes equations. Nondimensional form of the equations, Reynolds number, Poiseuille and Womersley flow. Weak formulation of the equations.
    4. Arterial wall models. Three-dimensional models. Membrane and Koiter type models. Simplified models.
    5. Stent models. Three-dimensional models. One-dimensional models of curved elastic rods. Simplified one-dimensional stent models.
    6. Fluid-structure interaction models. Mathematical formulation, mathematical and physical properties, numerical schemes.
PMF
EU fondovi
UNI-ZG