Codex @codex  0

Let $p_a,p_v,p_{LV}$ be pressures in the arterial reservoir, venous reservoir and left ventricle. Constant vascular compliances $C_a,C_v$ relate volume changes to pressure changes. The ventricular elastance relation iswhere $V_0$ is the unstressed ventricular volume and $E_{LV}(t)>0$ is the time-dependent inverse compliance. Define the positive part $[x{]}_{+}=\max (x,0)$. The systemic, aortic-valve and mitral-valve flows areEach $R$ is a positive hydraulic resistance. The aortic valve permits outflow only when ventricular pressure exceeds arterial pressure, and the mitral valve permits filling only when venous pressure exceeds ventricular pressure.

Mass conservation, with blood treated as incompressible, givesSubstitution and multiplication of the first two equations by $R_c$ give exactlyAdding the three original balances gives zero total volume change. This is a three-compartment ventricular circulation model.

During isovolumetric contraction, ventricular pressure lies between the venous and arterial pressures, $p_v<p_{LV}<p_a$. Both valves are closed, so $Q_v=Q_a=0$ and ventricular volume remains at its end-filling value $V^{+}$. ConsequentlyHere $V^{+}$ is end-diastolic ventricular volume and $V_0$ is the zero-pressure/unstressed volume.

The arterial and venous reservoirs still exchange systemic blood:If contraction is short compared with both $R_c{C}_a$ and $R_c{C}_v$, the fractional changes are small andwhere the superscript values refer to the beginning of contraction. Thus pressure can rise rapidly in the left ventricle through increasing elastance while the other pressures are approximately fixed. This stage ends when $p_{LV}$ reaches $p_a$ and the aortic valve opens.

Arterial recoil, the muscle pump, respiratory movements, venous tone and the mechanics of cardiac filling assist blood circulation. The heart remains its principal continuing source of mechanical energy. These agencies differ in whether they store cardiac work, contribute new muscular work, or direct flow without supplying power.

During ventricular systole, the aorta and other large elastic arteries expand and store elastic potential energy. During diastole, their recoil continues to drive blood towards the peripheral vessels, while closure of the aortic valve limits return into the heart. This elastic reservoir smooths an intermittent cardiac input into a more continuous downstream flow. It does not manufacture extra energy: it releases part of the work performed during the preceding ejection.

Contraction of surrounding skeletal muscles compresses veins. Venous valves favour displacement towards the heart and limit backward flow when the compression is released. Alternating contraction and relaxation therefore produces a muscle pump, especially useful for return from dependent limbs. The added work comes from the contracting muscles; valves guide the displacement but supply no power themselves. Persistent compression without refilling is not equivalent to a series of pumping strokes.

Spontaneous inspiration supplies another assistance. Descent of the respiratory diaphragm raises abdominal pressure while expansion of the thorax lowers intrathoracic pressure. The resulting changes favour a pressure gradient towards the thoracic veins and right side of the heart. The effect depends on posture, the respiratory phase and whether vessels remain open. Positive-pressure inflation does not reproduce the same pressure changes as spontaneous inspiration.^[ref]

Venous smooth muscle can reduce the storage capacity of peripheral veins, transferring blood towards the central circulation. This changes the volume available for cardiac filling; it does not require a travelling wave of venous peristalsis. Relaxation and recoil of the heart, together with movement of the atrioventricular plane, also influence filling pressures. The older expression cardiac suction is therefore best interpreted through specific changes of chamber volume and pressure, rather than a separate force pulling uniformly through every vessel.

Gravity assists a downward column and opposes an upward one. For a complete circuit returning to its initial height it supplies no net gravitational work. Its important effects include hydrostatic pressure differences and dependent pooling. Likewise, the residual pressure gradient across the capillaries is chiefly the downstream consequence of the cardiac pump. Ordinary capillary action at a liquid meniscus is not a universal extra pump inside a closed, fluid-filled vascular network. Local vasodilation can improve perfusion by reducing vascular resistance, but it does not create the necessary pressure source.

With $Q$ the mean volumetric flow rate, $R$ an effective vascular resistance, and $\Delta P$ the driving pressure difference, the useful bookkeeping relation isIt separates an increase of driving pressure from a reduction of resistance. An instructive apparatus compares the outflow of a pulsatile pump through rigid tubing with its outflow through an elastic reservoir feeding the same resistance. Continued outflow between strokes demonstrates stored elastic potential energy. A separately compressed valved flexible tube demonstrates the additional muscle pump principle. Neither observation requires a mysterious attraction of blood by the tissues.

Angina pectoris is most usefully explained by transient inadequacy of the myocardial oxygen supply relative to demand. It is a clinical syndrome, rather than the name of one visible anatomical lesion. The characteristic constricting chest discomfort may radiate to the arm, neck or jaw and be provoked by effort; the question concerns its causes, not a claim that every chest pain is angina pectoris.^[ref]

The common structural basis is coronary atherosclerosis. Narrowing limits the increase of coronary blood flow that should accompany exercise. An affected heart may receive sufficient oxygen at rest and insufficient oxygen when its rate, force of contraction and wall stress rise. Plaque disruption with thrombosis can abruptly worsen supply; persistent severe ischemia can then cause myocardial infarction. Pain from transient ischemia does not by itself prove myocardial necrosis.

Other mechanisms include coronary artery spasm, impaired regulation of small coronary vessels, or increased demand in left ventricular hypertrophy, severe aortic stenosis, or tachycardia. Reduced delivery through severe anaemia, low arterial oxygen or low perfusion pressure may provoke symptoms even without a new obstructing plaque. Structural narrowing, vasomotor change, blood oxygen-carrying capacity and cardiac work therefore have to be considered together.^[ref]

For an 1865 interpretation, coronary “ossification” or degeneration, diseased cardiac or aortic structures and neural or spasmodic explanations belonged to the historical discussion. These did not establish a single universal cause. A report published in January 1865 described a pathological case associated angina pectoris with diseased coronary arteries, but isolated cases cannot demonstrate that a particular valve or vessel lesion is necessary in every patient.^[ref] The modern supply-and-demand account explains why severe symptoms can coexist with relatively inconspicuous large coronary arteries, and why substantial coronary disease need not cause pain at every moment.

A pathological investigation inspects the coronary origins and course, their lumen and wall, the myocardium, the aortic valve and ventricular thickness. Clinical investigation adds evidence of reversible myocardial ischaemia and distinguishes it from infarction or non-cardiac pain. Modern electrocardiography and appropriate imaging address functions that a nineteenth-century post-mortem inspection alone could not measure. A normal-looking vessel on gross inspection cannot exclude coronary microvascular disease or a transient coronary artery spasm.

The heart supplies the principal continuing mechanical input to blood circulation; arterial recoil, respiratory movements and the action of skeletal muscles redistribute and supplement that input. They have different sources of energy and should not all be called independent propulsive powers. The pressure gradient remaining after passage through the capillaries is still a consequence of the upstream pump.

Arterial elasticity. During ventricular systole, ejected blood expands the aorta and large arteries, storing elastic potential energy in their walls. During diastole, recoil continues to drive blood into the peripheral vessels while closure of the aortic valve limits return towards the heart. This reduces the intermittency of flow downstream. The recoil is a temporary store of cardiac work, rather than a fresh source of energy. A vessel that is too rigid provides less of this smoothing; a compliant vessel with an open backward outlet would not provide the same useful result.

The skeletal-muscle pump. Contracting skeletal muscles compress adjacent veins. Venous valves make the displacement preferentially towards the heart; when compression ceases, refilling permits another stroke. Walking therefore aids return from dependent limbs. The source of the added work is muscle contraction, and the valves guide it without producing energy. Merely possessing valves cannot make a stationary column circulate.

The respiratory pump. During inspiration, falling intrathoracic pressure and displacement of the abdominal contents favour a pressure gradient from abdominal and peripheral veins towards the thoracic veins and right side of the heart. The respiratory diaphragm thus participates indirectly in venous return as well as pulmonary ventilation. The exact flow varies with posture, vessel collapse and the phase of the respiratory cycle; positive-pressure inflation does not reproduce the same mechanical circumstances as spontaneous inspiration.^[ref]

Venous tone and cardiac filling. Sympathetic contraction of venous smooth muscle can reduce venous storage capacity and transfer blood towards the central circulation. This alters the volume available for filling rather than requiring a wave of venous peristalsis. Cardiac relaxation, recoil and movement of the atrioventricular plane also affect filling pressure. Some traditionally described cardiac suction is therefore a feature of the cardiac cycle and mechanical coupling, not a separate organ pulling blood through every vessel.^[ref]

Gravity and supposed capillary attraction. Gravity assists a downward column but opposes an upward one. In a complete circuit returning to its original height it supplies no net gravitational work; its important practical effects include hydrostatic pressure differences and dependent venous pooling. Ordinary capillary action in an open narrow tube, driven by a liquid meniscus, is not a general pump in a fluid-filled capillary network. Nor does a vague attraction of blood by tissues replace a measurable pressure gradient. Local vasodilation can increase perfusion by lowering vascular resistance, but that change does not manufacture the necessary pressure source.

For a simple mean-flow description, with $Q$ the volume flow rate, $\Delta P$ the driving pressure gradient and $R$ the effective vascular resistance,This relation distinguishes a source of driving pressure from a change of resistance. In a lumped compliant arterial reservoir with vascular compliance $C$ and no inflow between beats, volume balance giveswhere $P_v$ is the downstream pressure. The exponential decay follows from stored volume leaving through the resistance. It explains continued flow during diastole without claiming that the idealization describes every reflected arterial wave.

A physical demonstration can compare a pulsatile pump feeding a narrow outlet through rigid tubing with the same pump feeding it through an elastic reservoir. Collecting the outflow over the pumping and resting phases reveals the reservoir's smoothing action; a side-arm manometer records its falling pressure. Separately compressing a valved flexible tube shows the role of a peripheral muscle pump. Keeping pump stroke and outlet resistance comparable prevents the apparatus from conflating a smoother flow with creation of extra energy.