(Properties of vascular system (hemodynamic

2- Properties of vascular system (hemodynamics)
1-Blood flow, conductance and Ohm s law:
Blood flow is volume of blood per unit of time (eg. cm3 /s). The blood flow from area of high pressure to area of low pressure.
Blood Flow (Q) = ? Pressure (P) / Resistance (R).
? Pressure (P) = P 1 – P 2. P1 represent the pressure at the origin of the vessel; P2 represent the pressure at end of the vessel. The blood flow through the vessel can be calculated by above formula which is called Ohm s law. Conductance is a measure of the blood flow through a vessel for a given pressure difference. It is expressed in terms of milliliters per second per millimeter of mercury pressure.
Methods of measuring blood flow:
A- Electromagnetic flow-meter.
B- Doppler ultrasonic (e.g. peripheral blood flow).
C- Fick principle (e.g. renal blood flow).
D- Plethysmograph (e.g. forearm blood flow).
Laminar blood flow:
Within the blood vessels, thin layer of blood in contact with the wall of the vessel does not move next layer has low velocity; the next has a higher velocity and so forth, the velocity being greatest in the center of the stream. See figure6. Laminar flow occurs at critical velocity, flow is silent, above this velocity, flow is turbulent. Turbulent flow creates sound..


Figure (6): Laminar blood flow (Guyton & Hall 2006).

2- Blood velocity:
It is displacement of blood per unit of time (eg. cm/s). The blood velocity (V) is directional proportion to blood flow (Q) divided by the area of the conduit (A).
Velocity (cm / s) = Flow (ml /s) / Area (cm²). V = Q/ A
The average velocity of fluid movement at any point in a system is inversely proportionate to the total sectional area at that point. Therefore, the average velocity of the blood is higher in aorta (small cross sectional area) and lower in the capillaries (large cross sectional area), which have 1000 times the total cross-section area of the aorta. The mean velocity of the blood in the proximal portion of the aorta is 40 cm / s. Table (1) shows characteristics of aorta and capillaries in humans.

Table (1): The characteristics of aorta and capillary in humans.
Vessel
Lumen diameter Wall thickness Sectional area (cm²) Blood volume %
Aorta 2.5 cm 2 mm 4.5 2
Capillary 5 µm 1 µm 4500 5

The flow in aorta is aphasic, ranges from 120 cm / s during systole to a negative value at the time of the transient backflow before the aortic valve closes in diastole. In distal portions of aorta and large arteries, velocity is also greater in systole than in diastole. The vessels walls are elastic, stretched during systole and recoil during diastole, so forward flow is continuous.
Clinically the velocity of the circulation can be measured by injecting a bile salt preparation into an arm vein and timing the first appearance of the bitter taste it produces. The average normal arm-to-tongue circulation time is 15 seconds.
3- Resistance:
Resistance is internal friction to blood flow. It is directly proportional to the viscosity of blood, and length of the vessel. It is inversely proportional to the forth power of the vessel radius. The below equation is called Poiseuille s equation.
R = 8?L/ (22/7)r4
? = Viscosity of blood.
L = Length of vessel.
r = radius of vessel.
The unit of resistance is pressure unit divided by flow unit which is expressed in R unit. For example, when the mean aortic pressure is 90 mmHg and the left ventricular output is 90 ml/s, the total peripheral resistant is 90 mmHg/90 ml/s = 1 R unit,
Factors affecting resistance:
A-Radius. Resistance proportions inversely with forth power of radius. The rate of blood flow is directly proportional to the forth power of the radius of the vessel.
B-Viscosity. The resistance varies directly with viscosity; the viscosity of the plasma is about 1.8 times as viscosity of water. Whole blood is 3 -4 times as viscous of water.
The blood viscosity depends on:
A- Hematocrit: It is the percentage of red blood cells volume to whole volume of blood. If a person has a hematocrit of means 40 that 40% of blood volume is blood cells and the remainder is plasma. Increase the number of RBC causes increase in hematocrit as in polycythemia while in anemia, peripheral resistance is decreased. Variation in the hematocit is the major factor that changes the viscosity of blood. In sever polycythemia, the increase in resistance does increase the work of the heart.
B- Composition of plasma: The plasma proteins such as the immunoglobulin which is elevated in some diseases that leads to increase viscosity.
4- Capacitance & compliance:
Capacitance is a degree of blood vessels to distensible (ability of vessel to stretch). It is inversely related to elastance. Arteries have more elastic tissues in them, so the capacitance is less. While the veins have less elastic tissue, so they are more capacitance vessels in the body. Normally, the veins collapsed and oval in cross-section. A large amount of blood can be added to the venous system before the veins become distended to the point where further in volume produce a large rise in venous pressure. At rest, more than half of circulating blood (60%) is located within veins, Compliance is ability of vessel to stretch and hold volume. Veins have thinner, less muscular walls than do arteries; thus, the arteries have a higher compliance. This means that a given amount of pressure will cause more distension in vein than in arteries, so that the veins can hold more blood.
C = V/P C = Compliance (ml/mmHg).
V = Volume (ml).
P = pressure (mmHg).
5- Law of Laplace:
The relation between distending pressure (P) and tension (T) is shown in figure7. The tension in the wall is necessary to balance the distending pressure. The law of Laplace is an important physical principle with several applications in physiology. This law states that tension in the wall of a cylinder (T) is equal to the product of the transmural pressure (P) and the radius (r) divided by the wall thickness (w). In thin walled structures, w is very small and can be ignored. The wall tension (T) is force that squeezes down on the contained volume.
P = T/r P = dynes/cm2. T = dynes/cm. r = cm. T = P X r
The smaller radius of blood vessel leads to the lower tension in the wall. In the human aorta, the tension at normal pressure is about 170.000 dynes/cm, and in the vena cava is 21.000 dyne/cm, but in the capillaries is approximately 16 dynes/cm. When the cardiac chamber is increased (dilated heart), a greater tension must be developed in myocardium to produce any given pressure. In the lung, the radii of curvature of the alveoli become smaller during expiration, and these structures would tend to collapse, if the tension were not reduced by the surface –tension- lowering agent (surfactant). Another example of this law is seen in urinary bladder.

Figure (7): Relation between distending pressure (P) and wall tension (T) in hollow viscous (Ganong s review of medical physiology 2010).
6- Starling forces:
The rate of filtration at any point along a capillary depends upon a balance of Starling forces. Starling is physiologist who first described them. There are four forces that determine fluid movement through the capillary membrane. They vary from one organ to another.
1- The capillary hydrostatic pressure (Pc): It tends to force fluid outward the capillary membrane. Mean capillary pressure is about 30 – 40 mmHg in arterial end of capillaries, 10 – 15 mmHg in the venous end.
2- The interstitial hydrostatic pressure (Pi): It tends to force fluid inward through capillary membrane.
3- The plasma colloid osmotic pressure (pc): It tends to force osmosis of fluid inward through the capillary membrane. About 80 % of total colloid osmotic pressure of plasma results from the albumin fraction, 20 % from the globulin, non from the fibrinogen.
4- The interstitial colloid osmotic pressure (pi): It tends to force osmosis of fluid outward through the capillary membrane. See figure 8.
Fluid movement = K (Pc + ?i) – (Pi + ?c)

Figure (8): Starling forces (Fox 2006).
7- Reynold s number (Re):
It predicts whether blood flow will be laminar or turbulent. When Re is increased, there is a greater tendency for turbulence. It is increased by decrease blood viscosity e.g anemia and narrowing of vessels.
8- Arterial pulse:
The blood forced into the aorta during systole not only to move the blood in the vessels forward but also to set up a pressure wave that travels along the arteries. The pressure wave expands the arterial walls as it travels, and the expansion is palpable as the pulse. The wave travels much higher than the velocity of blood flow. It is about 4 m/s in aorta, 8 m/s in the large arteries and 16 m/s in the small arteries of young adults. Consequently, the pulse is felt in the radial artery at wrist about 0.1 s after the peak of systolic ejection into the aorta. With advancing age, the arteries become more rigid, and the pulse wave move faster. The strength of the pulse is determined by the pulse pressure and little to the mean pressure. The pulse is weak (thread) in shock and strong when stroke volume is large during exercise. When aortic valve is incompetent (aortic insufficiency), the pulse is particularly strong. The pulse is called collapsing pulse.