L13 CVS Physiology 6 Haemodynamics

Overview

This lecture covers haemodynamics: the physical factors that govern blood flow. It works through the relationship between flow, pressure gradient and resistance (Darcy’s Law), the three patterns blood flow can take and how turbulence is predicted by the Reynolds number, Poiseuille’s Law and how resistance combines in series and parallel, why flow is distributed unequally across organs at rest and shifts markedly during exercise, how the elastic arteries and pulse pressure shape arterial blood pressure and what changes it, and finally how venous pressure is generated and returned to the heart via the skeletal muscle and respiratory pumps.

Flow, pressure and resistance

• The vascular system’s major function is to maintain blood pressure; the heart pumps, but the vessels carry the flow to the organs.
• Blood flow is the quantity of blood passing a given point in the circulation per unit time, normally expressed in mL/min. Overall blood flow in the total circulation of an adult at rest is about 5000 mL/min, i.e. the cardiac output.
• Darcy’s Law: flow depends on the pressure gradient and the resistance to flow.
  $F=\Delta P/RF\propto \Delta PF\propto 1/R$
• Two pipes can have very different absolute pressures but the same flow if their pressure difference ($\Delta P$) is the same (e.g. $P_1=100$, $P_2=10$ mmHg vs $P_1=500$, $P_2=410$ mmHg, both $\Delta P=90$ mmHg, both flow $=10$ mL/min). Flow tracks the pressure gradient, not absolute pressure.
• Applying Darcy’s law to the systemic circulation: flow = cardiac output (CO), pressure difference = mean aortic pressure ($P_{AO}$) minus central venous pressure (CVP), resistance = total peripheral resistance (TPR).
  $CO=(P_{AO}-CVP)/TPR\approx P_{AO}/TPR$
  (CVP is treated as negligible relative to $P_{AO}$.)

Patterns of blood flow

Three patterns:

• Laminar - most arteries, arterioles, venules and veins. Layers of fluid flow at different rates, producing a parabolic velocity profile (maximum at the centre, zero at the wall, with a marginal plasma layer near the wall). Viewed end-on, flow forms nested cylindrical laminae.
  • The sliding of one laminar layer over another is shear; shear stress arises from friction between molecules. Normal shear stress is 0.5-1.5 Pa.
  • High shear stress can tear the endothelium. It is increased in hypertension, atheroma and Marfan’s syndrome; high shear stress at the proximal aorta specifically can result in a dissecting aortic aneurysm (blood tracks within a split in the vessel wall, separate from the true lumen).
• Turbulent - normally in the ventricles, and sometimes the aorta (e.g. in pregnancy) or over atheroma (heard as a bruit).
  • As driving pressure rises, flow stops increasing linearly with pressure and instead rises as the square root of pressure ($F\propto \sqrt{\Delta P}$ once turbulent, vs $F\propto \Delta P$ while laminar) - this marks the transition from laminar to turbulent flow.
  • Turbulence is predicted by the Reynolds number ($Re$), directly proportional to velocity ($v$), vessel diameter ($D$) and blood density ($\rho$), and inversely proportional to blood viscosity ($\eta$):
    $Re=vD\rho /\eta$
    Demonstrated by Sir Osborne Reynolds (1883) using dye visualisation.
  • Critical $Re\approx 2000$; most vessels sit below this. $Re$ is physiologically high in: the left ventricle (mixes blood for uniform gas content), the aortic root during peak ejection (increased $D$), exercise (increased $v$), and pregnancy or anaemia (both reduce $\eta$). It is pathologically increased in atherosclerotic vessels. Detected by stethoscope as a murmur (heart) or bruit (vessels).
• Bolus - capillaries. Red blood cells move in single file through the narrow vessel, each carrying a “plasma bolus”.

Resistance: Poiseuille’s law and series/parallel arrangement

• Poiseuille’s Law: resistance is governed by tube length ($L$), fluid viscosity ($\eta$) and tube radius ($r$):
  $R=8\eta L/\pi r^4$

  The lecture's key for this equation labels "R" as radius while separately showing radius as "r" in the diagram and formula; this looks like a labelling inconsistency in the source. $R$ = resistance, $r$ = radius (raised to the 4th power) as used in the formula itself.

• Because resistance depends on radius to the 4th power, the radius of arterioles is a hugely powerful regulator of peripheral resistance. Arterioles and the smallest arteries are the main site of resistance to flow; the proof is that the biggest pressure drop in the systemic circulation occurs across the arterioles (pressure falls from a pulsatile ~80-120 mmHg through the arterial segments to near 0 mmHg by the venous side).
• Series resistance (e.g. successive segments along one path): $R_t=R_1+R_2+R_3$.
• Parallel resistance (e.g. branch circuits supplying different organs): $1/R_t=1/R_1+1/R_2+1/R_3$.
• The pulmonary and systemic circuits are arranged in series with each other (blood flows sequentially: lungs -> heart -> systemic organs -> heart). Within the systemic circuit, organ branches are arranged in parallel.
• Parallel arrangement of the systemic circulation: (1) guarantees all tissues receive fresh oxygenated blood, (2) allows independent variation of blood flow through different organs according to their need.

Distribution of blood flow across organs

• Flow is not the same in all organs. At rest (total ~5000 mL/min): brain 650 mL/min (13%), heart 215 (4%), skeletal muscle 1030 (20%), skin 430 (9%), kidneys 950 (20%), abdominal organs 1200 (24%), other 525 (10%).
• Rest vs moderately vigorous exercise (L/min, % of CO): cardiac output rises from 5.8 (100%) to 20 (100%). Brain 0.75 (13% -> 4%), heart 0.25 (4%) -> 0.85 (4%), gut 1.5 (26%) -> 0.6 (3%), kidney 1.0 (17%) -> 0.5 (3%), skeletal muscle 1.2 (21%) -> 15 (75%), skin 0.5 (7%) -> 1.95 (10%), other 0.6 (10%) -> 0.35 (2%).
• Key point: skeletal muscle’s share of cardiac output rises dramatically during exercise (21% to 75%), while the gut’s and kidney’s shares fall sharply, illustrating that parallel circulation allows organ flow to be independently redirected according to need.

Arterial blood pressure

• The aorta and large arteries reduce the fluctuations in flow and pressure created by intermittent ventricular ejection, via their highly elastic walls: during systole, energy is stored in the stretched vessel wall; during diastole this energy is released. This prevents large swings in arterial BP between beats and produces more steady flow into the smaller arteries.
• Pulse pressure = systolic pressure - diastolic pressure (e.g. 120 mmHg - 80 mmHg = 40 mmHg). The arterial pressure waveform rises from diastolic baseline to a systolic peak, shows a dicrotic notch on the downstroke, then declines back toward diastolic.
• Pulse pressure is determined by (1) stroke volume of the left ventricle and (2) arterial stiffness (reduced compliance): $Pulsepressure=Strokevolume/Compliance$.
  • On the pressure-volume curve for the elastic arteries, a given increase in stroke volume produces a disproportionately larger rise in pulse pressure when starting from a higher baseline pressure/volume (the curve steepens at higher volumes).
  • Increased arterial stiffness (a steeper pressure-volume slope = elastance; $1/slope$ = compliance) produces a bigger pulse pressure for the same stroke volume.
  • Ageing “hardens” arteries (arteriosclerosis), reducing compliance, so pulse pressure can double with age.
• Clinically, pulse pressure provides information about stroke volume: reduced in congestive heart failure, severe haemorrhage and aortic stenosis; increased in well-trained athletes, aortic valve regurgitation and arteriosclerosis.
• Blood pressure is not stable through the day: it is variable (spiky) during waking hours (e.g. a sharp spike with a pain stimulus), and runs lower and less variable during sleep.
• Effect of age (example values): 20-30 years, 120/80 mmHg, mean 93 mmHg, pulse pressure 40 mmHg. 60-70 years, 170/90 mmHg, mean 117 mmHg, pulse pressure 80 mmHg. Population data (brachial artery, English cohort) show systolic, mean and diastolic pressures all rising with age in both sexes; diastolic pressure plateaus and slightly declines after about age 50-60, while systolic and mean pressure continue to rise.

) and disease, specifically hypertension. One value is legible: during sleep, BP falls to an example reading of 80/50 mmHg.

Venous system and venous pressure

• Veins have all three vessel tunics but thinner walls than arteries (so they often appear collapsed in histological slides), and less smooth muscle and elastin than arteries.
• Veins are highly distensible and are called capacitance vessels, acting as blood reservoirs: their high compliance at normal operating pressures lets them release or store blood in response to small pressure changes.
• Blood volume distribution: systemic circuit - aorta 2%, arteries 10%, arterioles 3%, capillaries 6%, venules 10%, veins 40%, venae cavae 4%. Pulmonary circuit - right heart 4%, arteries and arterioles 5%, capillaries 3%, venules and veins 8%, left heart 4%. Taking the whole circulation together: pulmonary circulation 12%, heart 9%, arteries 11%, arterioles and capillaries 7%, veins and venules 61% - the majority of total blood volume resides in the venous system.
• Four determinants of venous pressure: (1) sympathetic innervation, (2) blood volume, (3) respiratory pump, (4) skeletal muscle pump. (The lecture also flags a distinction between arterial and venous constriction as a topic heading, but [slide does not elaborate] on the mechanism.)
• Venous-return pathway: increased sympathetic activity to veins, increased blood volume, increased skeletal muscle pump activity, and increased inspiratory movements each raise venous pressure, which raises venous return, which raises atrial pressure, which raises end-diastolic ventricular volume, which (via the Frank-Starling mechanism) raises cardiac stroke volume.
• Skeletal muscle pump: veins run between skeletal muscles and contain one-way valves. Muscle contraction compresses the vein, opening the valve and driving blood toward the heart; the valve closes to prevent backflow when the muscle relaxes.
• Fainting (vasovagal syncope) was illustrated with an example of a guardsman collapsing after prolonged standing; [slide does not elaborate further mechanism].
• Varicose veins: venous valves normally prevent backflow. If valves become leaky (incompetent), the veins dilate and become tortuous, i.e. varicose veins. About 15% of adults are affected, mainly in the lower limbs.

Self-test

1. Define haemodynamics and state the two physical factors that flow depends on.
2. State Darcy’s law and explain what the two-pipe example demonstrates about pressure gradient versus absolute pressure.
3. Starting from Darcy’s law, give the simplified equation relating cardiac output, mean aortic pressure and total peripheral resistance, and state the assumption that allows the simplification.
4. Describe the three patterns of blood flow and name where in the circulation each normally occurs.
5. Define shear stress in laminar flow, give its normal range, and explain how excessive shear stress can lead to a dissecting aortic aneurysm.
6. Describe how the flow-pressure relationship changes as flow transitions from laminar to turbulent.
7. State the Reynolds number equation and list four situations in which it is physiologically increased and one in which it is pathologically increased.
8. State Poiseuille’s law and explain why arteriolar radius has such a powerful effect on peripheral resistance.
9. Distinguish resistance in series from resistance in parallel, giving the formula for each and identifying where in the circulation each arrangement occurs.
10. List two advantages of the parallel arrangement of the systemic circulation.
11. Describe how the distribution of cardiac output to skeletal muscle, gut and kidney changes between rest and exercise.
12. Explain how the elastic walls of the aorta and large arteries convert the heart’s intermittent ejection into steadier downstream flow.
13. Define pulse pressure and state the two factors that determine it.
14. Predict the effect of reduced arterial compliance (as in ageing) on pulse pressure and explain why.
15. Give one clinical condition in which pulse pressure is reduced and one in which it is increased.
16. Describe how systolic, diastolic and mean arterial pressure each change with age, based on the lecture’s data.
17. List the four determinants of venous pressure given in the lecture.
18. Describe how the skeletal muscle pump and venous valves promote venous return, and explain what happens if the valves become incompetent.
19. Explain why veins are called capacitance vessels and state approximately what proportion of total blood volume resides in the veins and venules.
20. Integrative: trace the pathway by which increased skeletal muscle pump activity during exercise could increase cardiac stroke volume, linking venous pressure, venous return, atrial pressure, end-diastolic volume and the Frank-Starling mechanism.

Answers

Reveal answers

1. Haemodynamics is the physical factors that govern blood flow. Flow depends on the pressure gradient and the resistance to flow.
2. Darcy’s law: $F=\Delta P/R$, so flow is proportional to the pressure gradient and inversely proportional to resistance. The two-pipe example shows that pipes with very different absolute pressures but the same $\Delta P$ (90 mmHg in both) have identical flow (10 mL/min), showing flow tracks the pressure gradient, not absolute pressure.
3. $CO=(P_{AO}-CVP)/TPR\approx P_{AO}/TPR$; the simplification assumes CVP is negligible relative to mean aortic pressure.
4. Laminar (most arteries, arterioles, venules, veins), turbulent (ventricles; sometimes the aorta, e.g. in pregnancy; over atheroma), and bolus (capillaries, single-file red cells with a plasma bolus).
5. Shear stress is the frictional stress from one laminar layer sliding over another; normal range is 0.5-1.5 Pa. Excessively high shear stress (as in hypertension, atheroma or Marfan’s syndrome) can tear the endothelium, and at the proximal aorta specifically this can cause a dissecting aortic aneurysm.
6. While laminar, flow rises linearly with pressure ($F\propto \Delta P$); once turbulence develops, flow instead rises as the square root of pressure ($F\propto \sqrt{\Delta P}$), i.e. progressively less flow increase per unit pressure increase.
7. $Re=vD\rho /\eta$. Physiologically increased in: the left ventricle, the aortic root during peak ejection, exercise, and pregnancy or anaemia. Pathologically increased in atherosclerotic vessels.
8. $R=8\eta L/\pi r^4$. Because resistance is inversely proportional to radius to the 4th power, small changes in arteriolar radius produce large changes in resistance, making arterioles the dominant site of control of peripheral resistance.
9. Series: resistances add directly, $R_t=R_1+R_2+R_3$ (e.g. pulmonary and systemic circuits relative to each other). Parallel: reciprocals add, $1/R_t=1/R_1+1/R_2+1/R_3$ (e.g. organ branches within the systemic circulation).
10. Parallel arrangement guarantees all tissues receive fresh oxygenated blood, and allows independent variation of blood flow to each organ according to its need.
11. Skeletal muscle’s share of cardiac output rises sharply from about 21% at rest to about 75% during exercise, while gut and kidney shares fall (gut from about 26% to 3%, kidney from about 17% to 3%).
12. During systole the elastic vessel walls stretch and store energy from the ejected stroke volume; during diastole that stored energy is released as the walls recoil, maintaining forward flow and preventing large pressure swings, so flow into smaller arteries stays more steady.
13. Pulse pressure = systolic pressure - diastolic pressure. It is determined by left ventricular stroke volume and arterial stiffness (compliance): $Pulsepressure=Strokevolume/Compliance$.
14. Reduced compliance increases pulse pressure for a given stroke volume, because the pressure-volume curve is steeper (higher elastance); this is why pulse pressure can double with the arterial stiffening of ageing.
15. Reduced in congestive heart failure, severe haemorrhage, or aortic stenosis (any one). Increased in well-trained athletes, aortic valve regurgitation, or arteriosclerosis (any one).
16. Systolic and mean arterial pressure rise progressively with age; diastolic pressure rises initially but plateaus and slightly declines after about age 50-60 (English population data).
17. Sympathetic innervation, blood volume, the respiratory pump, and the skeletal muscle pump.
18. Contraction of skeletal muscle compresses veins running between them, opening one-way valves and driving blood toward the heart; the valves close on muscle relaxation to prevent backflow. If the valves become incompetent (leaky), veins dilate and become tortuous, producing varicose veins.
19. Veins are highly distensible/compliant, letting them store or release blood with small pressure changes, functioning as a reservoir; veins and venules together hold about 61% of total blood volume.
20. Increased skeletal muscle pump activity raises venous pressure, which raises venous return to the heart, raising atrial pressure, which raises end-diastolic ventricular volume; by the Frank-Starling mechanism this increased end-diastolic volume increases cardiac stroke volume.