1 / 18

BLOOD FLOW

BLOOD FLOW. Barbara Grobelnik Advisor: dr. Igor Serša. The study of blood flow behavior: Improving the design of implants (heart valves, artificial heart) and extra-corporeal flow devices (blood oxygenators, dialysis machines)

faunus
Download Presentation

BLOOD FLOW

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BLOOD FLOW Barbara Grobelnik Advisor: dr. Igor Serša

  2. The study of blood flow behavior: Improving the design of implants(heart valves, artificial heart) and extra-corporeal flow devices(blood oxygenators, dialysis machines) Understanding the connection between flow characteristics and the development of cardiovascular diseases (atherosclerosis, thrombosis) CONTENTS Cardiovascular physiology Physical properties of blood Viscosity Steady blood flow  Poiseuille’s equation  Entrance effects  Bernoulli’s equation Oscillatory blood flow  Windkessel model  Wommersley equations Introduction Blood Flow

  3. MAIN FUNCTIONS: to deliver oxygen and nutrients to the cells to remove cellular wastes and carbon dioxide to maintain organs at a constant temperature and pH HEART: atrium, ventricles BLOOD VESSELS: aorta, arteries, arterioles, capillaries, veinules, veins Cardiovascular Physiology right ventricle  lungs  left atrium left ventricle  aorta  organs and tissues  right atrium Blood Flow

  4. Poiseuille flow • Steady flow in a rigid cylindrical tube • Pressure gradient • Viscous force The forces are equal and opposite: v(r=R)=0 v(r=0)≠∞ L r r volume flow 2r v average velocity p1 p2 Blood Flow

  5. Newtonian fluid in large blood vessels (at high shear rates) Laminar flow Reynold’s numbers below the critical value of about 2000 No slip at the vascular wall endothelial cells Steady flow pulsatile flow in arteries Cylindrical shape elliptical shape (veins, pulmonary arteries), taper Rigid wall visco-elastic arterial walls Fully developed flow entrance length; branching points, curved sections    x x x x Poiseuille flow - assumptions Blood Flow

  6. Physical properties of blood BLOOD = plasma + blood cells (55%) (45%) electrolyte solution containing 8% of proteins Red blood cells (95%) White blood cells (0.13%) Platelets (4.9%) Reference values RBC: 1 μm 8 μm Blood Flow

  7. Viscosity • Viscosity varies with samples • variations in species • variations in proteins and RBC • Temperature dependent • decrease with increasing T • Blood • a non-Newtonian fluid at low shear rates (the agreggates of RBC) • a Newtonian fluid above shear rates of 50 s-1 • Casson’s equation In small tubes the blood viscosity has a very low value because of a cell-free zone near the wall. Fahraeus-Lindqvist effect Blood Flow

  8. Cell-free marginal layer model  Core regionμc , vc , 0rR-  Cell-free plasma μp , vp , R-r R The Sigma effect theory velocity profile is not continuous small tubes (N red blood cells move abreast) the volume flow is rewritten Fahraeus-Lindqvist Effect R region near the wall μp , vp r μc , vc  the volume flow • N concentric laminae, each of thickness ε 1/μ 1/μ Blood Flow

  9. Entrance length • The flow of fluid from a reservoir to a pipe • flat velocity profile at the entrance point • the fluid in contact with the wall has zero velocity (‘no slip’) • retardation due to shearing adjacent to the wall • boundary layer (where the viscous effects are present) • acceleration in the coreregion to maintain the same volume of flow • parabolic velocity profile  FULLY DEVELOPED FLOW viscous force -boundary layer thickness at z U - free stream velocity inertial force * a=U/t=U/(z/U) Blood Flow

  10. equating the viscous and inertial force k – proportionality constant derived from experiments, approximately 0.06 the boundary layer thickness the entrance length (when =D/2 the flow becomes fully established) Entrance length Pulsatile flow – the entrance length fluctuates The above derivation is valid only for the flow originating from a very large reservoir, where the velocity profile at the entrance point is relatively flat. In other cases, the entrance length is shorter. Blood Flow

  11. Flow trough stenosis v2 > v1 p2 < p1 : caving or closing of the vessel decrease in v2 reopening of the vessel fluttering Flow in aneurysms v2 < v1 p2 > p1 : expansion and bursting of the vessel caused by the weakening of the arterial wall Application of Bernoulli Equation p1 p2, v2, A2 v1 A1p1v1 Bernoulli equation A1 p2, v2, A2 A1v1 = A2v2 Blood Flow

  12. Vascular resistance for Poiseuille flow major drop in the mean pressure in arterioles (60 mmHg) autonomic nervous system controls muscle tension arterioles distend or contract Succesive branching: Increase in the total cross-section area dA1=nA2: Vacular resistance and branching • Mean pressure values [mmHg]: • arteries 100 • capillaries 30-34 at arterial end, 12-15 at venous end velocity decreases, pressure gradient increases n ≥ 2 average d=1.26 Blood Flow

  13. Turbulent Flow • Reynolds number • Flow in the circulatory system is normally laminar • Flow in the aorta can destabilize during the deceleration phase of late systole • too short time period for the flow to become fully turbulent • Diseased conditions can result in turbulent blood flow • vessel narrowing at atherosclerosis, defective heart valves • weakening of the wall, progression of the disease for flow in rigid straight cylindrical pipes critical value Re > 2000 Blood Flow

  14. Unsteady flow models • The pressure pulse: • generated by the contraction of the left ventricle • travels with a finite speed through the arterial wall • change in a shape due to interaction with reflected waves • Windkessel model • the arteries: a system of interconnected tubes with a storage capacity • distensibility Di = dV/dp • Inflow – Outflow = Rate of Storage A typical pressure pulse curve. b systole diastole ts T p0 Blood Flow

  15. The equation for the motion of a viscous liquid in a cylindrical tube (general form): Arterial pulse = periodic function  the sum of harmonics The solution: J0(xi3/2) is a Bessel function of the first kind of order zero and complex argument y=r/R Wommersley number  Wommersley equations The flow velocity pulse and the arterial pressure pulse (femoral artery of a dog). Blood Flow

  16. The role of Wommersley number  - unsteady inertial forces vs. viscous forces (viscous forces dominate when   1) 10-3 18 capillaries aorta The velocity profiles for the first four harmonics resulting from the pressure gradient cos ωt : 3.34 4.72 5.78 6.67 •  Parabolic profile is not formed • The laminae near the wall move first • Solid mass in the centre Increase in :flattening of the central region, reduction of amplitude and reversal of flow at the wall Blood Flow

  17. The sum of harmonics y=r/R • Parabolic shape in the fast systolic rush • Phase lag between the pressure gradient and the movement of the liquid •  The reversal begins in the peripheral laminae (the point of flow reversal: 25° after the pressure The time dependence of velocity at different distances y. gradient) The first four harmonics summed together with a parabola (representing the steady forward flow).  The peak forward and backward velocities: 165 cm/s at 75° 35 cm/s at 165° Back flow: harmonics are out of phase and the profile is flattened Blood Flow

  18. What have we learned? - basic equations of blood flow Why am I interested in blood flow? future experiment: dissolving blood clots under physiological conditions PULSATILE FLOW Conclusion Artificial heart. Blood Flow

More Related