Solution (source code)

= Solution

\b[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.<Anatomy and Physiology 2e by J. Gordon Betts and others/20.2 Blood Flow, Blood Pressure, and Resistance>[Venous System; Skeletal Muscle Pump; Respiratory Pump]{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 is
$$
\boxed{Q=\frac{\Delta P}{R}}.
$$
It 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>.