Pyramid Science

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Monday, December 01, 2008

Blood Flow Physics

Blood flows from the arteries through capillaries to the veins because the pressure is higher in the arteries. The difference in pressure constitutes the driving force to push the blood from the arteries into the veins (caused by the heart). The greatest fall in pressure in the circulation occurs across the terminal arteries (arterioles) that enter the capillaries and the arterioles offer the greatest resistance to flow.

Pressure difference = flow x resistance

Resistance depends on the radius of the vessel more than its length and for a given pressure difference, doubling the radius will increase flow (decrease resistance) by a factor of 16 since flow is proportional to the fourth power of the radius (2x2x2x2). It is also increased by an increased viscosity. The flow is the same through all sections of the circulatory tree and the section with the greatest pressure drop (across arterioles) has the most resistance to flow. The arterioles make the rate limiting step in the circulation and are at strategic places for regulation. The arterioles appear to be a chief site for regulation of both blood pressure and flow to specific tissues. Smooth muscles are wrapped circularly around the walls of the arterioles and these are controlled by nerves and hormones. When the muscles relax the radius increases. Constriction by contracted muscle will decrease the radius.

The resistance is very sensitive to the changing radius so by controlling the radius of the arterioles the body exercises tight control over the flows and pressures. In the circulation, flow is constant in each total cross-section and the largest fall in pressure occurs in the arterioles. This means that arterioles offer the greatest resistance to flow. Arterioles act like "stopcocks" and by contraction of smooth muscles in the arteriole walls, change the vessel radius and so alter resistance. Resistance to flow occurs because of frictional forces which oppose the motion of the two layers of fluid sliding past each other: a resistance gradient across the vessel. The blood layer immediately adjacent to the vessel wall is held back as it tends to adhere to the stationary wall. This layer retards the next layer which retards the next and so on. This results in telescoping layers of fluid. Fluid in the centre of the vessel moves the fastest, fluid at the wall does not move at all. The overall resistance to flow arises from the frictional interactions of these layers as they slide past one another. The drop in pressure that occurs during flow through the vessel reflects the energy lost to these frictional interactions.

Arterial pressure - the heart pumps blood intermittently. During systole some 70ml blood is thrust into aorta but in diastole no blood leaves the heart. Blood nevertheless flows smoothly and continuously out of the arteries into the capillaries because the aorta and other arteries are not rigid pipes - they have elastic walls which can expand or recoil much like a rubber band. During systole, blood enters the arteries faster than it leaves through the capillary beds. Packing more fluid into the arteries tends to increase the arterial pressure which forces the elastic walls to expand like a balloon force filled with air. The excess fluid is taken up by this expansion so relieving some of the pressure. In diastole, blood still leaves the arteries for the capillaries but none enters from the heart. At this time blood stored in the expanded arteries leaves, propelled in part by the recoil of the arterial walls. It is this stored blood that prevents the pressure from falling so low as it would if the arteries were rigid. The elastic arterial walls buffer changes in pressure and minimise fluctuations that would otherwise occur. A system with rigid walls would change from a very high systolic pressure to a near zero diastolic pressure. Similarly the blood would spurt into the capillary bed with each systole and come to a virtual standstill during diastole.

The elastic arterial system sustains a smooth and continuous flow into the capillaries and relieves the heart of work that would be required to eject blood against the enormous pressure that systolic pressure would develop. Arterial pressure does pulsate from between diastole (80mmHg) to the maximum midway into the systole (120mmHg) - the systolic pressure. The difference (40mmHg) is the pulse pressure. A person with more rigid arteries (older people) will have a higher pulse pressure.

  • To measure human arterial blood pressure an inflatable rubber bag is wrapped around the arm. The bag is inflated and this compresses the blood vessels of the arm. When the pressure in the bag just exceeds the pressure in the artery, the compression will be enough to collapse the artery. If air is then slowly released from the bag, the flow will resume but only for the short time that arterial flow is at its maximum. The pressure at which sounds are first produced (monitored by stethoscope) is the systolic pressure. As gradually more pressure is released, a point is reached where the sound becomes very muffled. This is the diastolic pressure - caused by turbulent blood flow through the narrowed (partially collapsed) artery.

Blood Loss

A tissue can get its nutrients only from the blood supply. During activity it consumes more nutrients and will be able to sustain the increased activity only if it receives more blood. When metabolism increases, its products, potent dilators in the microcirculation, accumulate. The result is an opening of local capillary beds so that the tissue receives more blood. The opposite occurs in quiescence. This will only work if there is a reasonably high pressure in the arteries. Opening or widening blood vessels hardly helps if there is no pressure head to propel the blood.

Further, the blood supply to a particular tissue can increase only by compromising the blood supply to other tissues or by increasing the cardiac output or both. There are no alternatives. Arterial pressure reveals why heart speeds up or stroke volume is increased when necessary. It also explains why smooth muscle in the arterioles of quiescent tissue contracts and constricts vessels so that blood can be shunted to more active areas where it is needed. The nervous system is involved. Pressure difference is the result of flow times resistance. So, when the entire circulation is considered, the flow is simply the cardiac output. The pressure difference (arteries - right atrium) is the pressure in the arteries. The primary resistance in the vascular tree is in the arterioles:

Arterial pressure = cardiac output x arteriolar resistance

Although an approximation, this is a fundamental expression. When a tissue becomes active, metabolic products accumulate and dilate the local microcirculation, which reduces resistance. This reduced resistance should lead to a reduced arterial pressure, but does not happen so clearly the body has a way of increasing the cardiac output to maintain a relatively constant blood pressure. The primary control in sudden changes in blood pressure involves reflexes that originate in special areas (baroreceptors) in the walls of the aortic arch and the internal carotid arteries. Receptors in these areas are sensitive to stretch.

At normal pressure, the walls are stretched and the receptors are active, sending impulses via sensory nerves to centres in the brain that are responsible for coordinating information and regulating the cardiovascular system. These cardiovascular centres control the autonomic nerve supply to the heart and blood vessels. When arterial pressure drops, arterial walls are subjected to less stretch and the sensory nerves coming from the carotid sinus (sinus nerve) and from the aortic arch (depressor nerve) become less active and send fewer impulses. The baroreceptor signals fall in pressure so the cardiovascular centres respond by exciting the sympathetic nerve (part of the autonomic nervous system dealing with the "fight or flight" response) and inhibiting the parasympathetic nerves (ANS dealing with "rest and repair" response). This results in an increased heart rate and strength of contraction (stroke volume) so that cardiac output increases. A general increase in constriction of the arterioles (but not brain or heart) with an increased constriction of the veins, both contribute to raising the blood pressure back toward normal. The heart rate and stroke volume raise cardiac output flow. Constriction of arterioles raises resistance and constriction of veins raises venous return to the heart, shifting it from the venous reservoir to the arterial side of the circulation. When pressure rises the reverse occurs.

Response to sudden blood loss provides a good example of regulation in the cardiovascular system. "Leak" could occur in a vein or artery. When blood is withdrawn from the arteries faster than it is replaced by the heart the mean arterial pressure falls. If it is withdrawn from the veins faster than it is replaced by capillary flow the mean venous pressure falls. A drop in venous pressure results in a decreased venous return and this decreases cardiac output, which in turn decreases mean arterial pressure. In both types of leak, the mean arterial pressure falls unless some regulatory compensation occurs. Reduced stretch of the baroreceptors in the aortic arch and carotid sinus results in reduced frequency of impulses on the sensory nerves (vagus and glossopharyngeal) to the centres in the medulla. This inhibits the parasympathetic nerves but stimulates the sympathetic nerves. By inhibiting the parasympathetic vagus nerve (in this case) the heart is speeded up - the vagus nerve usually acts to slow the heart. Activating the sympathetic nerves also speeds the heart making it beat more forcefully. Additionally, the sympathetic nerves cause intense constriction of the arterioles (raising resistance) and veins (reducing volume of the vascular tree).

All these effects happen in moments after blood is lost and all tend to raise arterial pressure back toward normal. Constriction of veins by sympathetic nerves decreases the proportion of blood held in the veins, shifting it to the arteries. The total vascular volume is decreased so that less blood is needed to fill the system. Constriction of the arterioles increases peripheral resistance to raise blood pressure. It also diminishes flow into the capillary beds so that blood pressure in the capillaries falls. Fluid filters from tissues into the capillaries due to the pressure difference and after several minutes becomes a significant amount. It helps replace blood lost during haemorrhage. Tissue fluid is not blood and doesn't contain plasma proteins and blood cells. Should intense vasoconstriction persist, or more blood is lost, circulatory shock may result.

When the oxygen supply to any organ is inadequate, metabolic (lactic) acids which impair organ function are produced and accumulate and so damage tissues. Vasodilator substances are released allowing protein to leak out through capillary walls into tissue spaces. These vasodilator substances expand the vascular tree, pooling blood in the tissues and veins thus reducing venous return, cardiac output and arterial pressure. Loss of plasma protein into the tissue spaces again upsets fluid balance but this time across the capillary wall in the direction of the tissues. Fluid is lost from the vascular tree and the blood becomes more viscous and may eventually stop as a result of intravascular coagulation. Constriction of blood vessels is most intense in organs (skin, kidneys, liver) but hardly occurs at all in heart, lungs or brain. Nourishment is maintained in organs where continued performance is essential. A new force of gravity is implicated when standing. Lying down gravity is not significant but on standing the weight of blood becomes important. The blood in the foot must support the column of fluid contained in the veins above it onward toward the heart. It is important to realise that this does not directly influence flow within the closed circulatory system. This is because the increase in pressure on the particle tending to push it upward to where there is lower pressure is counterbalanced by the weight of fluid itself. The increased pressures due to gravity are significant because they redistribute fluids Veins are more extensible than arteries.

The increased pressure expands the venous system and blood pools in the systemic veins (as much as 600ml in lower extremities upon quiet standing). The high hydrostatic pressure in the capillaries forces fluid out of the capillaries into the tissue spaces. Sudden changes in position from recumbent to upright resembles haemorrhage because of venous pooling - the subject bleeds into his own vascular system. Activation of sympathetics and inhibition of parasympathetics occur as compensatory responses but in contrast to haemorrhage, filtration of fluid from capillaries to tissue occurs. Venous pooling and oedema can be counteracted by contracting muscles and so compressing veins and lymph vessels to help empty them and relieve local venous pressure. Valves close supporting the weight of blood above them and preventing backflow until the vein refills with blood from the capillaries. This provides temporary relief from high hydrostatic capillary pressure and begins to alleviate oedema. When blood vessels in skin or muscle are dilated due to heat or exercise, the regulatory responses may fail because the intense demands of heat regulation and metabolism have priority.


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