Hemodynamics and tissue blood flow

Blood flow through any vessel or organ equals the pressure difference across it divided by its resistance, Q = ΔP/R, the circulatory form of Ohm law. For the whole systemic circulation the pressure difference is mean arterial pressure minus right atrial pressure and the flow is the cardiac output, so total peripheral resistance is about 100 mmHg divided by 5 L/min. Poiseuille law shows what sets resistance in a long straight tube: it rises with length and blood viscosity and falls with the fourth power of the radius, so a small change in arteriolar calibre produces a large change in flow, and arterioles account for about half of total resistance. Viscosity depends mostly on haematocrit; polycythaemia raises resistance and anaemia lowers it. Vessels in series add their resistances, vessels in parallel add their conductances, so adding capillaries in parallel lowers the resistance of an organ. Flow is normally laminar: layers slide over one another with the fastest stream in the centre, and it is silent. When velocity is high, the vessel wide or the viscosity low, the Reynolds number passes about 2000 and flow becomes turbulent, dissipating energy as eddies and sound; this is the basis of murmurs across narrowed valves, bruits over stenosed arteries and the Korotkoff sounds heard under a sphygmomanometer cuff. Flow can be measured with electromagnetic or ultrasound Doppler flowmeters, and cardiac output by the Fick principle or indicator dilution.

Laplace law states that the tension in a vessel wall equals the transmural pressure multiplied by the radius, so a capillary with a radius of a few micrometres withstands its pressure with a wall one cell thick, whereas the aorta needs a thick elastic wall, and a dilated ventricle or an aneurysm must generate more wall tension for the same pressure and so tends to dilate further. Each ejection distends the aorta and produces a pressure pulse; the pulse pressure (systolic minus diastolic, about 40 mmHg) rises with a larger stroke volume and with a stiffer aorta, which is why it widens in the elderly and in aortic regurgitation and narrows in aortic stenosis and heart failure. The pulse wave travels along the arteries at 3 to 15 m/s, much faster than the blood itself, and is damped by the resistance of the small vessels until it disappears in the capillaries; peripheral arteries show a higher systolic peak because of wave reflection. The veins hold about two thirds of the blood volume, with a compliance about twenty-four times that of arteries, and act as a reservoir that sympathetic venoconstriction can mobilise. Venous pressure at the right atrium (central venous pressure) is close to 0 mmHg and rises when the right heart fails or blood volume expands. In the standing adult gravity adds about 90 mmHg to venous pressure at the feet; the valves in the limb veins and the muscle pump, which squeezes blood toward the heart with each contraction, keep the venous pressure in the walking foot below 25 mmHg, and the respiratory pump adds flow with each inspiration.

Each tissue controls its own flow in proportion to its metabolic need. In the acute metabolic mechanism a rise in activity lowers local oxygen and raises carbon dioxide, hydrogen ions, potassium, adenosine and lactate, all of which relax arteriolar smooth muscle and open more precapillary sphincters; this explains active hyperaemia during exercise and the reactive hyperaemia after a period of occlusion. The myogenic mechanism responds to stretch: a sudden rise in pressure distends the arteriole, which then constricts, and a fall lets it relax. Together these mechanisms give autoregulation, the near constancy of flow between about 70 and 175 mmHg of arterial pressure in the kidney, brain, heart and skeletal muscle. Endothelial cells add their own signals: shear stress releases nitric oxide, which dilates, and injury or angiotensin releases endothelin, which constricts. Over weeks the long-term mechanism changes the vasculature itself: chronic hypoxia or increased demand stimulates vascular endothelial growth factor and new capillaries grow, and when a large artery is blocked slowly, collateral vessels enlarge, which is why a gradual coronary occlusion may cause no infarct while a sudden one does. Circulating agents override local control when the whole body needs it: noradrenaline and adrenaline, angiotensin II, vasopressin and endothelin constrict; bradykinin, histamine, prostacyclin and atrial natriuretic peptide dilate. Ions matter too: a high calcium level constricts, high potassium and magnesium dilate, and acidosis dilates.

About ten billion capillaries with a total surface near 500 square metres exchange substances with the interstitial fluid, and precapillary sphincters open and close intermittently (vasomotion) so that only a fraction are perfused at rest. Exchange is mainly by diffusion: lipid-soluble gases cross the whole endothelial surface, while water and small solutes cross through the intercellular clefts, which are narrow in muscle, wide and fenestrated in the kidney and gut, absent in the brain and open in the liver sinusoids. Bulk fluid movement follows the Starling forces. Capillary hydrostatic pressure (about 30 mmHg at the arterial end, 10 mmHg at the venous end) and interstitial oncotic pressure (about 8 mmHg) push fluid out; plasma oncotic pressure (about 28 mmHg, mostly albumin) and the slightly negative interstitial hydrostatic pressure (about -3 mmHg) pull it in. Filtration slightly exceeds reabsorption over the whole capillary, and the lymphatics return the excess 2 to 3 litres a day together with the protein that leaked. Oedema forms when capillary pressure rises (heart failure, venous obstruction), when plasma oncotic pressure falls (nephrotic syndrome, liver failure, malnutrition), when capillary permeability rises (inflammation, burns) or when lymph drainage is blocked (filariasis, node dissection). The interstitial gel and the negative interstitial pressure form a safety factor of about 17 mmHg before free fluid accumulates.

Resting coronary flow is about 225 ml/min, roughly 4 to 5 percent of cardiac output, and can rise three- to fourfold in exercise. Flow to the left ventricle is phasic: during systole the contracting muscle compresses the intramuscular vessels, especially the subendocardial ones, so left coronary flow falls and most of it occurs in diastole; the right ventricle, working at lower pressure, is perfused through both phases. This is why the subendocardium is the first to suffer in ischaemia and why tachycardia, which shortens diastole, threatens coronary supply. Control is overwhelmingly local and metabolic: the myocardium extracts about 70 percent of the oxygen delivered even at rest, so any increase in work must be met by more flow, and adenosine released when oxygen falls short, together with potassium, carbon dioxide, hydrogen ions and nitric oxide, dilates the coronary arterioles. The autonomic nerves act mostly indirectly through the change in cardiac work; directly, alpha receptors on the epicardial vessels constrict slightly and beta receptors on the intramuscular vessels dilate, and the metabolic dilatation from increased work normally dominates any sympathetic constriction. The heart uses fatty acids for most of its energy at rest and switches toward glucose and lactate during ischaemia; when coronary flow stops, the myocardium exhausts its reserves within minutes and infarcts if flow is not restored.