Biological Fluid Mechanics

Data is displayed for academic year: 2024./2025.

Lecturers

Prof.
Ivo Džijan
Assoc. Prof.
Severino Krizmanić

Course Description

The content of the course is divided into four parts:1) Basic equations of fluid mechanics2) Anatomy and physiology of the cardiovascular system3) Principles and levels of cardiovascular system modeling4) A lumped parameter model of the cardiovascular system

Study Programmes

University graduate
[FER3-HR] Biomedical Engineering - study
Elective Courses (2. semester)

Learning Outcomes

  1. Interpret the basic laws of fluid mechanics for control volume
  2. Derive a model of unsteady, one-dimensional fluid flow in pipes
  3. Formulate the cardiac cycle and blood vessel characteristics
  4. Analyze the propagation of pressure and flow waves in the arterial tree
  5. Reconstruct the parameters in the constitutive equation of the viscoelastic arterial wall from the measurement of arterial pressure and diameter
  6. Calculate time variations of blood pressure and flow rate in viscoelastic arterial tree by transmission line method
  7. Formulate a lumped parameter model of the whole cardiovascular system
  8. Analyze the influence of parameters in the lumped parameter model of cardiovascular system

Forms of Teaching

Lectures

Seminars and workshops

Independent assignments

Week by Week Schedule

  1. Lectures: Introductory overview: course content, mathematical and computer tools used in the course., Seminar: Determination of parameters in a model of blood viscosity by the Least Squares Method
  2. Lectures: Fundamentals of fluid mechanics: Lagrange and Euler description of fluid flow, material derivation, strain rate tensor, vortex tensor, strain tensor, relative volume rate of change of fluid particle and particle volume deformation. Mass and surface forces in fluid., Seminar: Identification of the Carreau-Yassuda model parameters
  3. Lectures: Fundamental laws of fluid dynamics. Newton's law of viscosity, Navier-Stokes equations. Hagen-Poiseuille's law for laminar stationary flow in a pipe, Womersley's solution for pulsating flow in a pipe., Seminar: Application of Fourier transform to aortic valve flow and aortic root pressure profiles
  4. Lectures: The concept of control volume. Basic equations for one-dimensional fluid flow in blood vessels. Hydraulic-electrical-mechanical analogy., Seminar: Solving ordinary differential equations in the time and frequency domain
  5. Lectures: Fundamentals of the theory of elasticity: Hooke's law, equilibrium equations. Stresses of stress states in thick-walled pipes. Models of viscoelastic materials., Seminar: Identification of the parameters of the viscoelastic model of the arterial wall
  6. Lectures: Analysis of wave propagation in long tubes: speed of propagation of weak pressure perturbations, D'Alambert's solution for progressive waves, propagation of finite intensity waves. Applicability of lumped parameter models., Seminar: Numerical simulation of static creep and relaxation tests
  7. Lectures: Blood and blood flow: blood viscosity, blood flow functions, anatomy of blood vessels (arteries, arterioles, capillaries, and veins)., Seminar: Analysis of Womersley's solution for pulsating flow in a pipe
  8. Lectures: Anatomy of the heart: heart muscle, heart valves, pulmonary and systemic circulation., Seminar: Parameter Identification of a three parameter Windkessel model of the arterial tree
  9. Lectures: Physiology of blood flow: heart function, Frank-Starling's law, analysis of heart period - Wiggers diagram., Seminar: Parameter Identification of a Windkessel model of an arterial tree with more parameters
  10. Lectures: Modeling of blood flow in arteries: transmission line model, analysis of wave reflection on artery branches. Solution methods in the time and frequency domain., Seminar: Application of the Transmission Line Method for the analysis of wave phenomena in the arterial tree
  11. Lectures: Lumped parameter models of an arterial tree, basic characteristics of input impedance for systemic and pulmonary arteries, model of veins., Seminar: Computer program for solving a lumped parameter model of cardiovascular system
  12. Lectures: Parameters identification of a lumped parameter model., Seminar: Analysis of blood flow simulation results in a lumped parameter model
  13. Lectures: Modeling of heart and heart valve functions: passive and active characteristics of ventricles and atria, models of heart valves., Seminar: Sensitivity analysis of blood flow simulation results to changes in cardiac input parameters
  14. Lectures: Numerical solution of lumped parameter model of whole circulation, presentation of simulation results., Seminar: Sensitivity analysis of blood flow simulation results in changes in venous and arterial input parameters
  15. Lectures: Analysis of the impact of input model parameters on flow and pressure time profiles., Seminar: Display of Wiggers diagram from blood flow simulation results

Literature

(.), Virag, Z., Mehanika bioloških strujanja, materijali za predavanja, Fakultet strojarstva i brodogradnje, Zagreb, 2010.,
(.), Caro, C.G.; Pedley, T.J.; Schroter, R.C.; Seed, W.A.:The Mechanics of Circulation, Cambridge University Press, New York, 2012.,
(.), 1. Westerhof, N.; Stergiopulos, N.; Noble, M.I.M: Snapshots of Hemodynamics, An Aid for Clinical Research and Graduate Education, drugo izdanje, Springer Science+Business Media, 2010. 2. Aaronson, P.I.; Ward, J.P.T; Wiener C.M.; Schulman S.P.; Gill, J.S.: The Cardiovascular System at a Glance, Blackwell Science Ltd., London, 1999.,

For students

General

ID 261434
  Summer semester
5 ECTS
L3 English Level
L2 e-Learning
30 Lectures
15 Seminar
0 Exercises
0 Laboratory exercises
0 Project laboratory
0 Physical education excercises