---
title: "The Heart and the Cardiac Cycle"
book: "University Biology — Year 2"
subject: biology
language: en
chapter: 17
exercises: 12
source: https://one-course.com/books/biology/4/en/chapter/17-the-heart-and-the-cardiac-cycle
---

# Chapter 17 — The Heart and the Cardiac Cycle

Cut out a frog’s [heart](#def-b2-heart-anatomy) and drop it into salt solution, and it goes on beating for hours — no nerves, no brain, no [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood), just a muscle that contracts on its own about once a second because a small patch of its cells cannot stay still. A human [heart](#def-b2-heart-anatomy) does this some three billion times in a life, moving on the order of two hundred million litres, without ever being switched off. This chapter is about that pump: its chambers and valves, the cycle of filling and emptying and the pressures that drive it, the electrical system that times it and the trace it leaves on the skin, the law that lets it match its output to its inflow beat by beat, and the nerves and hormones that adjust its pace and force.

## 17.1 The pump

**Definition 17.1 (Chambers and valves).**

The heart is two pumps side by side, each an *atrium* that receives [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) from the [veins](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels) and a *ventricle* that ejects it into an [artery](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels). The right heart takes [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) from the venae cavae and sends it to the lungs through the pulmonary [artery](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels); the left heart takes it back from the pulmonary [veins](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels) and sends it round the body through the aorta. Four valves make the flow one-way: the *atrioventricular valves* (tricuspid on the right, mitral on the left), flaps tethered by cords to papillary muscles so that they cannot be blown back into the atrium; and the *semilunar valves* (pulmonary and aortic), three pockets that fill and seal when the arterial pressure exceeds the ventricle’s. The valves are passive: they open and close on pressure differences alone. The ventricular wall is *myocardium*, striated muscle of branched cells joined end to end by *intercalated discs* full of gap junctions, so that the whole ventricle is electrically one cell and contracts as one; the left ventricle’s wall is three times thicker than the right’s because it pumps against five times the pressure. The heart muscle is fed by its own *coronary arteries*, which fill in diastole, and it runs almost entirely on aerobic metabolism — it cannot borrow.

![The heart in frontal section: two atria above, two ventricles below, the thick left ventricle, the atrioventricular valves with their cords, and the two great arteries leaving the top.](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/img-f93a13916dab.jpg)

*The [heart](#def-b2-heart-anatomy) in frontal section: two atria above, two [ventricles](#def-b2-heart-anatomy) below, the thick left [ventricle](#def-b2-heart-anatomy), the atrioventricular valves with their cords, and the two great arteries leaving the top.*

**Proposition 17.2 (The cardiac cycle).**

One beat at rest lasts about $0.8\,\mathrm{s}$. *Diastole* ($0.5\,\mathrm{s}$): the [ventricles](#def-b2-heart-anatomy) relax, their pressure falls below the atria’s, the atrioventricular valves open and [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) flows in, mostly passively, then with a final push from atrial contraction; the [ventricle](#def-b2-heart-anatomy) ends diastole holding about $120\,\mathrm{mL}$ (the *end-diastolic volume*). *Systole* ($0.3\,\mathrm{s}$): the [ventricles](#def-b2-heart-anatomy) contract; as soon as their pressure exceeds the atrial pressure the atrioventricular valves close (the first [heart](#def-b2-heart-anatomy) sound, “lub”), and for a few hundredths of a second the [ventricle](#def-b2-heart-anatomy) squeezes a closed chamber — *isovolumetric contraction* — until its pressure passes the arterial pressure ($80\,\mathrm{mmHg}$ on the left), when the semilunar valves open and [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) is ejected. The left [ventricle](#def-b2-heart-anatomy) reaches $120\,\mathrm{mmHg}$ and expels about $70\,\mathrm{mL}$ (the *[stroke volume](#prop-b2-heart-cycle)*, an *[ejection fraction](#prop-b2-heart-cycle)* of $60\,\%$); as it relaxes, its pressure falls below the aorta’s, the aortic valve snaps shut (the second sound, “dub”), and an isovolumetric relaxation brings the pressure down to the atrial level, when filling resumes. The right [heart](#def-b2-heart-anatomy) does the same at a fifth of the pressure, ejecting the same volume.

![Pressures in the left heart through one beat. The ventricle squeezes a closed chamber until it exceeds the aortic pressure, ejects while it is above it, relaxes until it falls below the atrial pressure, and fills.](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/fig-203dcb7051bb.svg)

*Pressures in the left [heart](#def-b2-heart-anatomy) through one beat. The [ventricle](#def-b2-heart-anatomy) squeezes a closed chamber until it exceeds the aortic pressure, ejects while it is above it, relaxes until it falls below the atrial pressure, and fills.*

**Theorem 17.3 (The work of the heart).**

Plotted as pressure against volume, one beat of the left [ventricle](#def-b2-heart-anatomy) traces a loop — filling along the bottom, isovolumetric contraction up the right side, ejection along the top from $120\,\mathrm{mL}$ to $50\,\mathrm{mL}$, isovolumetric relaxation down the left — and the area of the loop is the mechanical work of the beat:

$$
W = \oint P\,\mathrm{d}V \approx \bar P_{\text{ejection}}\times \text{stroke volume} \approx 100\,\mathrm{mmHg}\times70\,\mathrm{mL} = 0.93\,\mathrm{J}.
$$

At 72 beats a minute the left [ventricle](#def-b2-heart-anatomy) does about $1.1\,\mathrm{W}$, the right $0.2\,\mathrm{W}$; the [heart](#def-b2-heart-anatomy)’s metabolism is some $8\,\mathrm{W}$, so its mechanical efficiency is near $15\,\%$, the rest being heat and the cost of tension. Raising the pressure the [heart](#def-b2-heart-anatomy) pumps against (hypertension, a narrowed aortic valve) raises the work per beat in proportion, and the muscle thickens in response as any muscle does — until its coronary supply can no longer keep up with its bulk.

**Proof.** Work is force times distance, and for a pressure acting on a moving wall, pressure times swept volume: $\mathrm{d}W = P\,\mathrm{d}V$. Round a closed loop the net work is the enclosed area (filling at low pressure costs little; ejection at high pressure returns much more). $100\,\mathrm{mmHg} = 1.33 \times 10^{4}\,\mathrm{Pa}$ and $70\,\mathrm{mL} =
7 \times 10^{-5}\,\mathrm{m}^{3}$: $1.33\times 10^{4}\times 7\times 10^{-5} =
0.93\,\mathrm{J}$; times $1.2$ beats a second, $1.1\,\mathrm{W}$. ∎

![The pressure–volume loop of the left ventricle. The area enclosed is the work of one beat; a higher arterial pressure raises the top of the loop and the work with it.](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/fig-7adfe4c93ee9.svg)

*The [pressure–volume loop](#thm-b2-heart-work) of the left [ventricle](#def-b2-heart-anatomy). The area enclosed is the work of one beat; a higher arterial pressure raises the top of the loop and the work with it.*

## 17.2 The heart’s own clock

**Proposition 17.4 (Automaticity and conduction).**

The beat originates in the *[sinoatrial node](#prop-b2-heart-conduction)*, a patch of specialised muscle cells in the wall of the right [atrium](#def-b2-heart-anatomy) whose membrane potential never rests: after each action potential it drifts slowly upward (a *pacemaker potential*, driven by a sodium current that switches on at negative potentials and by calcium channels) until it reaches threshold and fires again, about a hundred times a minute if left alone. The impulse spreads through the atrial muscle, cell to cell through the gap junctions, and the atria contract; it reaches the *[atrioventricular node](#prop-b2-heart-conduction)*, the only electrical bridge between atria and [ventricles](#def-b2-heart-anatomy), which conducts slowly and delays it by a tenth of a second — time for the atria to finish filling the [ventricles](#def-b2-heart-anatomy); then it races down the *bundle of His* and the *[Purkinje fibres](#prop-b2-heart-conduction)*, fast-conducting cells that deliver it to the whole ventricular muscle within $30\,\mathrm{ms}$, so that the [ventricles](#def-b2-heart-anatomy) contract from the apex upward, as a unit, and drive the [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) toward the outflow valves. Every part of this system can pace on its own, each more slowly than the last (the node at 100, the AV node at 50, the [Purkinje fibres](#prop-b2-heart-conduction) at 30), so that if the node fails a lower centre takes over — at a slower rate.

**Evidence.** An isolated [heart](#def-b2-heart-anatomy), or a strip of sinoatrial tissue, beats in a dish without nerves; a strip of [ventricle](#def-b2-heart-anatomy) beats too, but more slowly. Cooling or warming the [sinoatrial node](#prop-b2-heart-conduction) alone changes the rate of the whole [heart](#def-b2-heart-anatomy); cutting the AV bundle dissociates the [ventricles](#def-b2-heart-anatomy), which then beat at their own slow rhythm while the atria continue at the node’s ([heart](#def-b2-heart-anatomy) block). Recording from a single node cell shows the slow diastolic depolarisation that no ordinary muscle cell has; blocking the pacemaker current slows it. ∎

![The conduction system. The sinoatrial node fires, the atria depolarise, the atrioventricular node delays the impulse, and the bundle and Purkinje fibres deliver it to the ventricles from the apex upward.](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/fig-c9762662d582.svg)

*The conduction system. The [sinoatrial node](#prop-b2-heart-conduction) fires, the atria depolarise, the [atrioventricular node](#prop-b2-heart-conduction) delays the impulse, and the bundle and [Purkinje fibres](#prop-b2-heart-conduction) deliver it to the [ventricles](#def-b2-heart-anatomy) from the apex upward.*

**Proposition 17.5 (The electrocardiogram).**

The [heart](#def-b2-heart-anatomy) is a large mass of cells depolarising and repolarising in sequence, and the currents that flow in the body around it can be recorded as voltages of a millivolt between electrodes on the limbs: the *electrocardiogram*. Its waves are the events of the conduction system: the *P wave* is atrial depolarisation; the flat *PR interval* ($0.16\,\mathrm{s}$) is the AV delay; the *QRS complex*, sharp and brief ($0.08\,\mathrm{s}$), is ventricular depolarisation — large because the ventricular mass is large, brief because the [Purkinje fibres](#prop-b2-heart-conduction) are fast; the *T wave* is ventricular repolarisation. (Atrial repolarisation is buried in the QRS.) The trace reports timing and conduction, not force: a blocked AV node lengthens the PR interval or dissociates P from QRS, a dead region of [ventricle](#def-b2-heart-anatomy) distorts the QRS, an irregular [atrium](#def-b2-heart-anatomy) (atrial fibrillation) replaces P waves with noise and makes the [ventricles](#def-b2-heart-anatomy) beat irregularly, and an interval between R waves gives the rate.

![A normal electrocardiogram: P (atria), the PR delay at the AV node, QRS (ventricular depolarisation), T (ventricular repolarisation).](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/fig-271f6fb0e164.svg)

*A normal electrocardiogram: P (atria), the PR delay at the AV node, QRS (ventricular depolarisation), T (ventricular repolarisation).*

## 17.3 Regulating the output

**Theorem 17.6 (The Frank–Starling law).**

The force of a ventricular contraction rises with the volume that filled it: within the working range, the more the [ventricle](#def-b2-heart-anatomy) is stretched in diastole (the *preload*), the more it ejects in systole. The [heart](#def-b2-heart-anatomy) therefore pumps out, beat by beat, whatever it receives — a rise in venous return of $20\,\%$ is met by a rise in [stroke volume](#prop-b2-heart-cycle) of $20\,\%$ without any nerve or hormone — and the two [ventricles](#def-b2-heart-anatomy), which must move the same volume, balance each other automatically: if the right [heart](#def-b2-heart-anatomy) delivers more [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) to the lungs, the left [heart](#def-b2-heart-anatomy) receives more and pumps more. The mechanism is in the [sarcomere](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#def-b2-cell-differentiation-fibre): at the short lengths of a poorly filled [ventricle](#def-b2-heart-anatomy) the thick and thin filaments overlap too much and the calcium sensitivity is low; stretching toward the optimal length ($2.2\,\text{µ}\mathrm{m}$) increases both the overlap available for cross-bridges and the sensitivity, so that the same calcium pulse produces more force. Beyond the optimum (an overstretched, failing [heart](#def-b2-heart-anatomy)) the force falls again.

**Evidence.** Frank (1895) recorded the pressure developed by a frog [ventricle](#def-b2-heart-anatomy) filled to different volumes: the peak pressure rose with the filling volume up to a maximum and then fell. Starling (1914), with a dog heart–lung preparation in which venous return and arterial resistance could be set independently, showed that raising the return raised the output stroke by stroke, and that raising the arterial resistance was met, after a few beats of accumulation, by a larger end-diastolic volume and a restored output — the [ventricle](#def-b2-heart-anatomy) answers a load by stretching and a stretch by contracting harder. ∎

![Starling curves. Stroke volume rises with filling; the sympathetic nerves shift the curve upward (more output from the same filling), a failing heart shifts it down.](https://one-course.com/images/onecourse/chapters/biology-4/b2-heart/fig-727fb4b98f74.svg)

*Starling curves. [Stroke volume](#prop-b2-heart-cycle) rises with filling; the sympathetic nerves shift the curve upward (more output from the same filling), a failing [heart](#def-b2-heart-anatomy) shifts it down.*

**Proposition 17.7 (Nerves and hormones).**

The [cardiac output](#thm-b2-heart-starling) is [heart](#def-b2-heart-anatomy) rate times [stroke volume](#prop-b2-heart-cycle), $5\,\mathrm{L}/\mathrm{min}$ at rest and up to $25\,\mathrm{L}/\mathrm{min}$ in a trained athlete’s exercise. Both factors are set by the autonomic nerves. The *vagus* (parasympathetic), releasing acetylcholine onto the [sinoatrial node](#prop-b2-heart-conduction), slows the pacemaker drift and holds the resting rate at 70 rather than the node’s own 100; cut the vagi and the rate rises. The *sympathetic* nerves, releasing noradrenaline, and the adrenal medulla, releasing *adrenaline* into the [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood), speed the drift (more beats), speed conduction, and raise the force of contraction at any filling (a steeper Starling curve, the property called *contractility*), by raising the calcium delivered to the [sarcomeres](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#def-b2-cell-differentiation-fibre) at each beat. In exercise the vagal brake is released first, then the sympathetic accelerator pressed, and a rate of 180 with a [stroke volume](#prop-b2-heart-cycle) of $140\,\mathrm{mL}$ gives $25\,\mathrm{L}/\mathrm{min}$; the signals are relayed through the receptors and second messengers of [Chapter 19](https://one-course.com/books/biology/4/en/chapter/19-chemical-messengers-and-signal-transduction#ch-b2-cell-signalling), and the whole is commanded by the pressure-regulating centres of [Chapter 18](https://one-course.com/books/biology/4/en/chapter/18-regulation-of-blood-pressure-and-exercise#ch-b2-blood-pressure).

**Example 17.8 (Reading a heart).**

Two sounds per beat: lub, the AV valves closing at the start of systole; dub, the semilunar valves closing at its end. A murmur is turbulent flow through a narrowed valve (a stenosis) or back through a leaking one (an insufficiency): a murmur between lub and dub is a leaking mitral valve or a narrowed aortic valve, after dub a leaking aortic valve. A pulse of 70 with a [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) pressure of $120/80$ mmHg means a [stroke volume](#prop-b2-heart-cycle) near $70\,\mathrm{mL}$; a rate of 40 in an athlete is a large [stroke volume](#prop-b2-heart-cycle) and a strong vagal tone; a rate of 40 with a PR interval that lengthens until a beat drops is a diseased AV node. The physiology of this chapter is what a physician hears through a stethoscope in thirty seconds.

## 17.4 Exercises

**Exercise 17.1 ★.**

Trace a drop of [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) from the vena cava to the aorta, naming each chamber, valve and vessel in order.

**Solution of Exercise 17.1.**

Vena cava $\to$ right [atrium](#def-b2-heart-anatomy) $\to$ tricuspid valve $\to$ right [ventricle](#def-b2-heart-anatomy) $\to$ pulmonary valve $\to$ pulmonary [artery](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels) $\to$ lungs $\to$ pulmonary [veins](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels) $\to$ left [atrium](#def-b2-heart-anatomy) $\to$ mitral valve $\to$ left [ventricle](#def-b2-heart-anatomy) $\to$ aortic valve $\to$ aorta.

**Exercise 17.2 ★.**

Give the phases of the [cardiac cycle](#prop-b2-heart-cycle) with the state of each valve in each phase, and the event that causes each of the two [heart](#def-b2-heart-anatomy) sounds.

**Solution of Exercise 17.2.**

Filling (diastole): AV valves open, semilunar closed. Isovolumetric contraction: all four closed. Ejection: semilunar open, AV closed. Isovolumetric relaxation: all closed. First sound: the AV valves closing at the start of systole; second: the semilunar valves closing at its end.

**Exercise 17.3 ★.**

Name the parts of the conduction system in order, with the time the impulse takes to reach each, and the ECG wave each produces.

**Solution of Exercise 17.3.**

[Sinoatrial node](#prop-b2-heart-conduction) ($t = 0$; the P wave as the atria depolarise); [atrioventricular node](#prop-b2-heart-conduction) (reached at about $80\,\mathrm{ms}$, holding the impulse for $100\,\mathrm{ms}$: the PR segment); bundle of His and [Purkinje fibres](#prop-b2-heart-conduction) ($180\text{ to }220\,\mathrm{ms}$; the QRS as the [ventricles](#def-b2-heart-anatomy) depolarise); the T wave later as they repolarise.

**Exercise 17.4 ★.**

State the [Frank–Starling law](#thm-b2-heart-starling) and say why it guarantees that the two [ventricles](#def-b2-heart-anatomy) pump the same volume.

**Solution of Exercise 17.4.**

Within its working range the [ventricle](#def-b2-heart-anatomy) ejects more when it has been filled more. If the right [ventricle](#def-b2-heart-anatomy) pumps more, the left receives more a few beats later and, by the same law, pumps more: any imbalance corrects itself without a signal.

**Exercise 17.5 ★★.**

A [heart](#def-b2-heart-anatomy) has an end-diastolic volume of $130\,\mathrm{mL}$ and an end-systolic volume of $50\,\mathrm{mL}$ at 70 beats a minute. Compute the [stroke volume](#prop-b2-heart-cycle), the [ejection fraction](#prop-b2-heart-cycle) and the [cardiac output](#thm-b2-heart-starling). A failing [heart](#def-b2-heart-anatomy) has $180\,\mathrm{mL}$ and $120\,\mathrm{mL}$: recompute, and say what has happened to the [ejection fraction](#prop-b2-heart-cycle).

**Solution of Exercise 17.5.**

[Stroke volume](#prop-b2-heart-cycle) $80\,\mathrm{mL}$; [ejection fraction](#prop-b2-heart-cycle) $80/130 = 62\,\%$; output $80\times 70 = 5.6\,\mathrm{L}/\mathrm{min}$. Failing: $60\,\mathrm{mL}$, $60/180 = 33\,\%$, $4.2\,\mathrm{L}/\mathrm{min}$ — the dilated [ventricle](#def-b2-heart-anatomy) keeps the output nearly up by working at a large volume, but ejects only a third of what it holds.

**Exercise 17.6 ★★.**

Compute the work of a beat for a [stroke volume](#prop-b2-heart-cycle) of $70\,\mathrm{mL}$ at a mean ejection pressure of $100\,\mathrm{mmHg}$, and the power at 72 beats a minute. Recompute for a hypertensive at $150\,\mathrm{mmHg}$. How much extra oxygen per minute does the second [heart](#def-b2-heart-anatomy) need, if the mechanical efficiency is $15\,\%$ and $1\,\mathrm{mL}$ of oxygen yields $20\,\mathrm{J}$?

**Solution of Exercise 17.6.**

$W = 100\times 133\times 7\times 10^{-5} = 0.93\,\mathrm{J}$; power $0.93\times 1.2 = 1.1\,\mathrm{W}$. At $150\,\mathrm{mmHg}$: $1.4\,\mathrm{J}$, $1.7\,\mathrm{W}$. Extra $0.56\,\mathrm{W}$ mechanical is $3.7\,\mathrm{W}$ metabolic, $0.19\,\mathrm{mL}$ of oxygen a second: $11\,\mathrm{mL}/\mathrm{min}$ more.

**Exercise 17.7 ★★.**

On an ECG the R waves are $0.5\,\mathrm{s}$ apart in one recording and $1.5\,\mathrm{s}$ in another. Give the [heart](#def-b2-heart-anatomy) rates. In a third, P waves come every $0.6\,\mathrm{s}$ and QRS complexes every $1.8\,\mathrm{s}$, with no fixed relation. What has happened?

**Solution of Exercise 17.7.**

$60/0.5 = 120$ beats a minute; $60/1.5 = 40$. Third: complete [heart](#def-b2-heart-anatomy) block — the atria beat at 100 under the node, the [ventricles](#def-b2-heart-anatomy) at 33 under a pacemaker of their own, and the AV node conducts nothing.

**Exercise 17.8 ★★.**

The sinoatrial cell’s potential drifts from $-60\,\mathrm{mV}$ to a threshold of $-40\,\mathrm{mV}$ at $25\,\mathrm{mV}/\mathrm{s}$ before each action potential of $0.15\,\mathrm{s}$. Compute the interval between beats and the rate. Acetylcholine lowers the drift to $18\,\mathrm{mV}/\mathrm{s}$ and the starting potential to $-65\,\mathrm{mV}$; noradrenaline raises the drift to $40\,\mathrm{mV}/\mathrm{s}$. Compute both rates.

**Solution of Exercise 17.8.**

Drift $20/25 = 0.8\,\mathrm{s}$, plus $0.15\,\mathrm{s}$: $0.95\,\mathrm{s}$, 63 beats a minute. Acetylcholine: $25/18 = 1.39\,\mathrm{s}$, plus $0.15$: $1.54\,\mathrm{s}$, 39 a minute. Noradrenaline: $20/40 = 0.5\,\mathrm{s}$, plus $0.15$: $0.65\,\mathrm{s}$, 92 a minute.

**Exercise 17.9 ★★.**

Explain why the AV node’s delay is necessary, what would happen to the output without it, and why a slow AV node (a long PR interval) is harmless up to a point and dangerous beyond it.

**Solution of Exercise 17.9.**

The delay lets the atria finish emptying into the [ventricles](#def-b2-heart-anatomy) before the [ventricles](#def-b2-heart-anatomy) contract; without it atria and [ventricles](#def-b2-heart-anatomy) would contract together, the AV valves would shut on half-filled [ventricles](#def-b2-heart-anatomy) and the [stroke volume](#prop-b2-heart-cycle) would fall by the atrial contribution. A long PR interval merely postpones ventricular systole and costs nothing until the delay grows so long that beats are dropped or conduction fails altogether.

**Exercise 17.10 ★★★.**

An athlete at rest has a rate of 45 and an output of $5\,\mathrm{L}/\mathrm{min}$; in exercise a rate of 180 and $30\,\mathrm{L}/\mathrm{min}$. Compute the [stroke volumes](#prop-b2-heart-cycle) and say what the Starling curve and the sympathetic nerves each contribute. Why can the rate not usefully exceed about 200?

**Solution of Exercise 17.10.**

Rest: $5000/45 = 111\,\mathrm{mL}$; exercise: $30\,000/180 =
167\,\mathrm{mL}$. The Starling law converts the larger venous return of exercise into a larger [stroke volume](#prop-b2-heart-cycle); the sympathetic nerves add rate and contractility (a lower end-systolic volume). Above about 200 the diastole is too short to fill the [ventricle](#def-b2-heart-anatomy) and the [stroke volume](#prop-b2-heart-cycle) falls faster than the rate rises.

**Exercise 17.11 ★★★.**

A narrowed aortic valve leaves an opening of $1\,\mathrm{cm}^{2}$ instead of $3\,\mathrm{cm}^{2}$. Using continuity, compute the velocity of the ejected [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) at $250\,\mathrm{mL}/\mathrm{s}$ through each, and, from Bernoulli ($\Delta P = \tfrac12\rho v^2$), the pressure the [ventricle](#def-b2-heart-anatomy) must generate above the aortic pressure in each case. What does the [ventricle](#def-b2-heart-anatomy) do about it, and what is the eventual cost?

**Solution of Exercise 17.11.**

$v = Q/A$: $250/3 = 83\,\mathrm{cm}/\mathrm{s}$ and $250/1 = 250\,\mathrm{cm}/\mathrm{s}$. $\Delta P = \tfrac12\times 1060\times v^{2}$: $365\,\mathrm{Pa}$ ($2.7\,\mathrm{mmHg}$) and $3300\,\mathrm{Pa}$ ($25\,\mathrm{mmHg}$). The [ventricle](#def-b2-heart-anatomy) generates the extra pressure by thickening its wall; the thick, stiff [ventricle](#def-b2-heart-anatomy) eventually outgrows its coronary supply and fills poorly, and fails.

**Exercise 17.12 ★★★.**

“The [heart](#def-b2-heart-anatomy) is a pump that regulates itself and is only adjusted by the nervous system.” Discuss, distinguishing what automaticity, the [Frank–Starling law](#thm-b2-heart-starling) and the autonomic nerves each provide, and what a transplanted [heart](#def-b2-heart-anatomy) — which has no nerves — can and cannot do.

**Solution of Exercise 17.12.**

Automaticity gives a beat without any input; the Starling law matches output to return and balances the two [ventricles](#def-b2-heart-anatomy) without any input; the nerves and adrenaline only set the rate and contractility around that self-regulated core. A transplanted [heart](#def-b2-heart-anatomy) beats (at about 100, without vagal tone), adjusts its [stroke volume](#prop-b2-heart-cycle) to filling, and can raise its output in exercise by the Starling mechanism and by circulating adrenaline — but slowly, and less than an innervated [heart](#def-b2-heart-anatomy).

## 17.5 Problem: A Heart Under Load

**Problem 17.1.**

Weekend problem — one heart followed from rest to exercise and into disease: its cycle timed, its work computed, its electrocardiogram read, its Starling response and its autonomic control quantified, and a narrowed valve’s cost estimated, ending on the output at rest and in exercise, the work per beat, and the gradient across the stenosis

Data: at rest, rate 70, end-diastolic volume $130\,\mathrm{mL}$, end-systolic $60\,\mathrm{mL}$, mean ejection pressure $100\,\mathrm{mmHg}$ ($1\,\mathrm{mmHg} = 133\,\mathrm{Pa}$), aortic pressure $120/80$ mmHg. Systole lasts $0.3\,\mathrm{s}$ at any rate. Pacemaker: drift from $-60\,\mathrm{mV}$ to $-40\,\mathrm{mV}$, action potential $0.15\,\mathrm{s}$. The [heart](#def-b2-heart-anatomy) consumes $20\,\mathrm{J}$ per millilitre of oxygen with a mechanical efficiency of $15\,\%$; coronary [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) carries $0.2\,\mathrm{mL}$ of oxygen per millilitre and the [heart](#def-b2-heart-anatomy) extracts $70\,\%$ of it. [Blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) density $1060\,\mathrm{kg}/\mathrm{m}^{3}$.

**Part I — The cycle at rest.**

1. Compute the [stroke volume](#prop-b2-heart-cycle) , [ejection fraction](#prop-b2-heart-cycle) and [cardiac output](#thm-b2-heart-starling) .
2. Compute the duration of one cycle and of diastole.
3. Compute the mean ejection rate during systole, in millilitres per second, and the mean velocity through an aortic valve of $3\,\mathrm{cm}^{2}$ .
4. The ventricular pressure rises at $1500\,\mathrm{mmHg}/\mathrm{s}$ during isovolumetric contraction, from 10 to $80\,\mathrm{mmHg}$ . How long does that phase last?
5. Compute the work of one beat and the mechanical power of the left [ventricle](#def-b2-heart-anatomy) .
6. Compute the [heart](#def-b2-heart-anatomy) ’s total power and oxygen consumption (both [ventricles](#def-b2-heart-anatomy) : take the right as a fifth of the left).
7. Compute the coronary [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) flow needed to supply that oxygen.

**Part II — The pacemaker and the trace.**

8. What drift rate ( $\mathrm{mV}/\mathrm{s}$ ) gives a rate of 70?
9. The vagus is cut: the rate becomes 100. What drift rate is that?
10. Compute the drift rate for a rate of 180 in exercise.
11. On the ECG at rest, give the R–R interval, and say what the P, QRS and T waves correspond to.
12. The PR interval is $0.16\,\mathrm{s}$ at rest. Its length is mostly the AV node’s delay: explain what the delay achieves and why a rate of 180 requires the node to speed up too.
13. A patient’s ECG shows QRS complexes every $1.5\,\mathrm{s}$ with P waves every $0.8\,\mathrm{s}$ , unrelated. Diagnose, give the ventricular rate, and say which tissue is pacing the [ventricles](#def-b2-heart-anatomy) .

**Part III — Exercise.** In exercise the rate rises to 180 and the sympathetic nerves raise contractility so that the end-systolic volume falls to $30\,\mathrm{mL}$; venous return raises the end-diastolic volume to $150\,\mathrm{mL}$.

14. Compute the [stroke volume](#prop-b2-heart-cycle) , [ejection fraction](#prop-b2-heart-cycle) and output.
15. Compute the duration of diastole at 180 and explain why the rate cannot usefully go much higher.
16. Compute the power of the left [ventricle](#def-b2-heart-anatomy) at a mean ejection pressure of $120\,\mathrm{mmHg}$ , and the [heart](#def-b2-heart-anatomy) ’s oxygen consumption.
17. Compute the coronary flow needed, and compare with rest. Why is the diastolic shortening a problem for it?
18. Without the sympathetic nerves (a transplanted [heart](#def-b2-heart-anatomy) ) the rate rises only slowly, through adrenaline in the [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) , and contractility less. Predict the output in the first minute of exercise, using the Starling law alone with the same filling.
19. Attribute the rise of output from rest to exercise to its three causes (rate, filling, contractility), in litres per minute each.

**Part IV — A narrowed valve.** The aortic valve narrows to $1\,\mathrm{cm}^{2}$.

20. Compute the ejection velocity at rest through the narrowed valve.
21. Using Bernoulli, $\Delta P = \tfrac12\rho v^{2}$ , compute the pressure the [ventricle](#def-b2-heart-anatomy) must add to push [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood) through it, in mmHg.
22. Recompute both in exercise.
23. What must the [ventricle](#def-b2-heart-anatomy) ’s peak pressure be in each case to keep the aortic pressure normal, and by what factor is its work per beat raised at rest?
24. The [ventricle](#def-b2-heart-anatomy) wall thickens in response. Explain why this helps and why it eventually fails (think of the coronary supply and of diastolic filling).
25. State the result: the output at rest and in exercise, the work per beat at rest, and the gradient across the narrowed valve at rest and in exercise.

**Solution of Problem 17.1.**

**1.** $70\,\mathrm{mL}$; $70/130 = 54\,\%$; $70\times 70 =
4.9\,\mathrm{L}/\mathrm{min}$. **2.** $60/70 = 0.86\,\mathrm{s}$; diastole $0.86 - 0.3 =
0.56\,\mathrm{s}$. **3.** $70/0.3 = 233\,\mathrm{mL}/\mathrm{s}$; $233/3 = 78\,\mathrm{cm}/\mathrm{s}$. **4.** $70/1500 = 0.047\,\mathrm{s}$, about $50\,\mathrm{ms}$. **5.** $100\times 133\times 7\times 10^{-5} = 0.93\,\mathrm{J}$; $0.93\times 70/60 = 1.1\,\mathrm{W}$. **6.** Both [ventricles](#def-b2-heart-anatomy) $1.1\times 1.2 = 1.3\,\mathrm{W}$; at $15\,\%$, $8.7\,\mathrm{W}$ metabolic; $8.7/20 = 0.43\,\mathrm{mL}$ of oxygen a second, $26\,\mathrm{mL}/\mathrm{min}$. **7.** Extracting $0.14\,\mathrm{mL}$ per millilitre of [blood](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-blood): $26/0.14 = 190\,\mathrm{mL}/\mathrm{min}$. **8.** Interval $0.86\,\mathrm{s}$, drift time $0.71\,\mathrm{s}$: $20/0.71 = 28\,\mathrm{mV}/\mathrm{s}$. **9.** Interval $0.6\,\mathrm{s}$, drift $0.45\,\mathrm{s}$: $44\,\mathrm{mV}/\mathrm{s}$. **10.** Interval $0.33\,\mathrm{s}$, drift $0.18\,\mathrm{s}$: $110\,\mathrm{mV}/\mathrm{s}$. **11.** R–R $0.86\,\mathrm{s}$; P: atrial depolarisation; QRS: ventricular depolarisation; T: ventricular repolarisation. **12.** The delay lets the atria empty into the [ventricles](#def-b2-heart-anatomy) before they contract; at 180 the whole cycle is $0.33\,\mathrm{s}$, so an unchanged $0.16\,\mathrm{s}$ delay would consume half of it — the sympathetic nerves speed the node’s conduction as well. **13.** Complete [heart](#def-b2-heart-anatomy) block: the [ventricles](#def-b2-heart-anatomy) at 40 a minute, paced by the bundle or [Purkinje fibres](#prop-b2-heart-conduction), the atria at 75 under the [sinoatrial node](#prop-b2-heart-conduction). **14.** $120\,\mathrm{mL}$; $120/150 = 80\,\%$; $120\times 180 =
21.6\,\mathrm{L}/\mathrm{min}$. **15.** $0.33 - 0.3 = 0.03\,\mathrm{s}$: almost no time to fill; faster still and the [stroke volume](#prop-b2-heart-cycle) collapses. **16.** $W = 120\times 133\times 1.2\times 10^{-4} = 1.9\,\mathrm{J}$, $\times 3$ a second: $5.7\,\mathrm{W}$; both [ventricles](#def-b2-heart-anatomy) $6.9\,\mathrm{W}$; metabolic $46\,\mathrm{W}$; oxygen $2.3\,\mathrm{mL}/\mathrm{s}$, $140\,\mathrm{mL}/\mathrm{min}$. **17.** $140/0.14 = 1000\,\mathrm{mL}/\mathrm{min}$, five times the resting flow, to be delivered in a diastole shrunk to a tenth of the cycle: the coronary [arterioles](https://one-course.com/books/biology/4/en/chapter/16-blood-and-the-circulatory-system#def-b2-blood-circulation-vessels) must dilate to their limit. **18.** Rate about 100 without vagal tone, end-systolic volume unchanged at $60\,\mathrm{mL}$: [stroke volume](#prop-b2-heart-cycle) $150 - 60 = 90\,\mathrm{mL}$, output $9\,\mathrm{L}/\mathrm{min}$. **19.** Rate alone ($70 \to 180$ at $70\,\mathrm{mL}$, i.e. $12.6\,\mathrm{L}/\mathrm{min}$): $+7.7$; filling ($20\,\mathrm{mL}$ more at 180): $+3.6$; contractility ($30\,\mathrm{mL}$ less residual at 180): $+5.4$ — from 4.9 to $21.6\,\mathrm{L}/\mathrm{min}$, the three contributions totalling exactly $+16.7$. **20.** $233/1 = 233\,\mathrm{cm}/\mathrm{s}$, $2.3\,\mathrm{m}/\mathrm{s}$. **21.** $\tfrac12\times 1060\times 2.33^{2} = 2900\,\mathrm{Pa}$, $22\,\mathrm{mmHg}$. **22.** $120/0.3 = 400\,\mathrm{mL}/\mathrm{s}$, $4\,\mathrm{m}/\mathrm{s}$; $\tfrac12\times
1060\times 16 = 8500\,\mathrm{Pa}$, $64\,\mathrm{mmHg}$. **23.** Peak $120 + 22 = 142\,\mathrm{mmHg}$ at rest, about $140 +
64 = 204\,\mathrm{mmHg}$ in exercise; the mean ejection pressure at rest rises from 100 to 122: work per beat $\times 1.22$. **24.** A thicker wall generates more force and lowers the stress per fibre; but the mass to be perfused grows while the coronary flow, squeezed by the thick wall in systole and given a shorter diastole, does not keep pace, and a thick wall relaxes poorly and fills less: ischaemia and failure follow. **25.** $4.9\,\mathrm{L}/\mathrm{min}$ at rest, $21.6\,\mathrm{L}/\mathrm{min}$ in exercise; $0.93\,\mathrm{J}$ per beat; gradient $22\,\mathrm{mmHg}$ at rest and $64\,\mathrm{mmHg}$ in exercise.