Properties and modelling of the venous blood flow. 1111, Budapest, Műegyetem rkp. 3. D ép. 3. em Tel: Fax:

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1 Properties and modelling of the venous blood flow 1111, Budapest, Műegyetem rkp. 3. D ép. 3. em Tel: Fax:

2 Overview of the lectures Introduction Properties of the venous system The phenomenon of collapsible tubes, modelling methods Viscoelastic material model Demonstration of some calculations

3 Introduction Why is it useful to model venous blood flow? In Hungary 52% of the mortalities due to illness are caused by the diseases of the circulatory system (Source: WHO Mortality Database 2005) In order to understand the development several diseases (e.g. varicose veins, thrombosis), the blood flow mechanisms have to be further investigated. Modelling (venous) blood flow might help the medicine in the treatment and therapy of these diseases.

4 Introduction Venous circulatory system: Small veins (venules) (~10 9 branches, ~25 μm) Veins (less then mm) vena cava inferior ( )/superior ( ) ( 2 db, 32 mm) o o o Complex, looped network Huge diameter differences The blood flow mechanisms are also complex

5 Structure of the veins

6 Function of the venous system According to the definition: Returning blood to the heart Role of blood storing In normal state 75% of the whole blood volume is stored in the veins The contraction and relaxation of the smooth muscles in the venous wall influence the distribution of the blood ( vasoconstriction ) The power of the heart is also influenced (+/- 20% CO) (cardiac output: CO = stroke volume*heart rate)

7 Classification of the veins According to their position: Superficial veins (near to the body surface, no surrounding arteries) Deep veins (deeper in the tissues, mostly surrounded by arteries) According to their function: Systemic veins (deoxygenated blood is transported from the capillaries to the right atrium of the heart) Pulmonary veins (blood enriched in oxygen is transported from the lungs to the left atrium of the heart)

8 Properties Differences compared to the arteries: Lower transmural pressure Thinner vessel walls (collapsing vessels!) Elliptic cross section in the unloaded state Opposite flow direction (i.e. capillaries -> heart) Presence of venous valves Exceptions: Vena cava superior/inferior Pulmonary arteries

9 Definitions Compliance C Volume change regarding to the pressure It characterizes the V(p) relationship Not constant along the vessels Distensibility dv dp ml mmhg D 1 V dv dp C V 1 mmhg

10 Definitions Mean filling pressure It can be defined for any arbitrary organ In- and outflow is stopped, the pressure is equalized Venous resistance R p Q Pas m 3 Hagen-Poiseuille law: (laminar flow) R 8L 4 R wall 4v R

11 Definitions Inertia ( Inertance ) I L A Pas m 3 2 What pressure gradient is required for the unit change in volumetric flow rate? p I dq dt

12 Venous vessel wall C vein 20-40C artery (but it might be two hundred times larger) The large compliance causes the remarkable storage capacity The storage volume reduces in case of emergency (see vasoconstriction ) In case of acute bleeding the body uses this storage capacity

13 Venous vessel wall Effect of various physiological states: Permanent physical work increases compliance Raising the environmental temperature increases compliance Effect of aging: the distensibility (i.e. compliance) of the forearm decreases with time The shape and geometrical properties of the veins depend on the body height

14 Venous vessel wall The vessel walls show a so called bioviscoelastic property (Emil Monos: The biomechanics of the vessel wall (in hungarian)) The deformation is pressure and time dependent /ε(p,t)/ Repetitive loading and unloading of the vessel wall results in hysteresis A.N. Nicolaides et al. A proper material model is needed to describe these phenomena

15 Phlebology Deals with the disorders of the venous system Varicose veins (venous insufficiency) Disorder of the venous valves Deep vein thrombosis Blood clots are formed, embolia or chronic venous insufficiency can occur Inflammation caused by blood clots (thrombophlebitis)

16 Blood flow inducing mechanisms Mechanisms inducing venous blood flow: Pressure difference generated by the heart (less than in the arteries, approx.15 mmhg) Contraction of the skeletal muscles ( Venous muscle pump ) Pulsation of the arteries Abdominal overpressure caused by inhalation

17 Venous muscle pump Periodical contraction and relaxation of the muscles causes the venous vessels to collapse Due to the collapse blood is extruded from the vessel section Reverse flow is prevented by venous valves Operates similar to a volumetric pump

18 Venous muscle pump Properties of the venous muscle pump: Average volume of the calf: ml Stored blood volume by the calf: ml Continuous muscle exercise: the blood content reduces by 1,5-2,0 ml/100ml in the calf In case of intense muscle work the blood flow: ~20-30 ml/min

19 Venous valves The valves play a role in the limitation of hydrostatic pressure A few footsteps reduce the blood pressure in the ankle from ~100 mmhg to ~ 20 mmhg Lack of movement can cause fainting (ortostatic intolerance) -> baroreflexes are activated Long lasting standing position causes the valves to open, continuous fluid column is formed Increasing infiltration in the capillaries Edemas are formed inside the tissues

20 Properties of the blood Pulmonary veins: oxygenated blood Vivid red colour Systemic veins: blood rich in CO 2 Dark red colour (not blue!) non-newtonian, heterogeneous fluid Viscosity depends on: Velocity (if v then μ ) Shear stress (if τ then μ )

21 Pressure conditions in the veins In lying position: Postcapillar venules: mmhg Small veins: mmhg Large veins: mmhg Pressure in the right atrium: 3 5 mmhg CVP central venous pressure pressure of the right atrium (usually measured using a venous catheter)