Appendix 1: Physical Quantities for Selected Arteries
6.2 Electrical Excitation
Myocytes are also composed of striated myofibrils (Fig.6.3b). Each myofibril consists of chains of sarcomeres, each about 2μm long, which are terminated at each end by a Z-disc. These Z discs provide an anchor for the thinfilaments, which engage with thick filaments to generate tension (Fig.6.3c). The mechanism of tension generation is described in more detail in Sect.6.3.
A valve plane separates the electrically excitable atria and ventricles. It is composed of connective tissue and provides a mechanical anchor for the valves.
The connective tissue is electrically inexcitable, and is penetrated only by the atrioventricular node (see below).
6.1.3 Myocardial Perfusion and Metabolism
The heart itself requires a supply of oxygenated blood in order for its metabolic needs to be met, and has its own system of arteries and veins. A branching network of coronary arteries is perfused from left and right branches, which connect to the aorta very close to the aortic valve. The main branches of the coronary arteries remain on the epicardial surface, and smaller vessels penetrate the myocardium. If a coronary artery develops a significant stenosis, then the region of myocardium perfused by that artery may become ischaemic. Ischaemia describes the changes in cell metabolism resulting from a reduction or interruption of the supply of oxy- genated blood. These changes include altered electrical excitability, and reduced contractility. Prolonged or severe ischaemia resulting from complete blockage of a coronary artery will result in a myocardial infarction. Unless bloodflow is restored quickly, the ischaemic region of myocardium will undergo irreversible cell death.
Ultimately the region will become scar tissue, with impaired mechanical function.
Venous blood collects in the coronary sinus, which is located around the pos- terior of the heart, close to the valve plane. The coronary sinus drains into the right atrium.
permeability or conductance that depends on the potential difference across the membrane. An example of an ion channel embedded in the cell membrane is shown in Fig.6.4. These ion channels, pumps and exchangers act to regulate the intra- cellular concentration of Na+, Ca2+and K+.
At rest, the concentrations of Na+ and Ca2+ outside the cell exceed the con- centration inside the cell, and the concentration of K+ inside the cell exceeds the concentration outside the cell (Table6.1). At rest, the cell membrane is permeable to K+. A single K+ion is therefore exposed to a concentration gradient, and so K+ ions tend to diffuse out of the cell. The effect of this diffusion is to establish a gradient in electrical potential because the K+ions that diffuse out of the cell carry an excess positive charge. At equilibrium, the tendency to diffuse out of the cell is balanced by the opposing effect of potential difference. The corresponding voltage across the cell membrane at equilibrium is given by the Nernst equation
E¼RT
zFloge ½Kþo
½Kþi
;
where R is the gas constant (8.316 J K−1mol−1), T is absolute temperature (body temperature is 310 K), z the valency of K+ions (1), F the Faraday constant (charge carried by one mole of K+ions, 96,484 C mol−1), [K+] concentration of K+outside Fig. 6.4 Cartoon of myocyte cell membrane, showing lipid biplayer, with embedded ion channel (elongated ellipsoids) admitting a single ion
Table 6.1 Typical equilibrium concentrations of cations involved in the cardiac action potential Ionic
species
Intracellular concentration (mM)
Extracellular concentration (mM)
Nernst potential (mV)
Na+ 10 140 +70
Ca2+ 0.0001 1.2 +124
K+ 140 5 −90
(o) and inside (i) the cell. For normal concentrations of K+, the Nernst potential is
−90 mV, with the inside of the cell negatively charged relative to the outside. This is close to the resting potential of cardiac myocytes, which are polarised to a voltage typically between−80 and−90 mV. The K+Nernst potential is not exactly equal to the resting potential because the membrane retains a very small permeability to Na+ ions, which acts to slightly reduce the resting potential.
When the potential difference across the cell membrane is perturbed so that it decreases below a threshold of around−65 mV (for example by an action potential in a neighbouring cell), voltage-gated ion channels open to admit Na+. There is a large gradient not only in Na+concentration but also in electrical potential, which results in an influx of Na+into the cell and a rapid depolarisation of the membrane potential towards the Nernst potential for Na+ions, which is around +70 mV.
Almost immediately, the Na+ion channels inactivate, shutting off further influx of Na+ ions. However, the change in membrane potential has two further conse- quences. First, the change opens voltage-gated Ca2+ ion channels, which admit Ca2+ into the cell. Second, the change also opens voltage-gated K+ion channels, which results in an outwardflow of K+ ions. Initially the influx of Ca2+tends to balance the outflow of K+, but then the Ca2+ion channels begin to close and the outflow of K+ dominates, leading to repolarisation of the cell to the resting potential. Computational and mathematical models have played an important role alongside experimental work in the discovery of these detailed physiological mechanisms, and this story is recounted by Noble and Rudy (2001).
The action potential is an all or nothing response, once the cell is depolarised to its threshold it will respond with a complete action potential. Once a cell begins an action potential, it will not respond to a further stimulus until is has repolarised. The cell is said to be refractory, and the interval between depolarisation and the time at which the cell can produce another action potential is called the refractory period.
Typically, the refractory period is around the same as the action potential duration.
Figure6.5shows time series generated from a computer model of the human atrial action potential, and includes both the action potential and the main currents that flow throughout the different phases.
In cardiac tissue, cells are electrically connected by gap junctions, which enable the action potential to be passed from one cell to its neighbours. Since gap junctions are part of the intercalated discs, the action potential propagates faster along the long axis of cells than across the short axis.
6.2.2 Activation Sequence for Normal Beats
A normal heartbeat begins with the spontaneous depolarisation of pacemaking cells in the sinus node, located in the right atrium. In these specialised cells, there a small inward current gradually brings the membrane potential to threshold during the resting phase. The result is a series of spontaneous beats, and the interval between these beats is modulated by neural activity.
The normal beat initiated in the sinus node propagates through the left and right atrium, and into a further specialised region of tissue called the atrioventricular node. In the normal heart, the atrioventricular node provides the only pathway for an action potential to propagate through thefibrous tissue that separates the atria and ventricles, and acts as a mechanical support for the valves.
The atrioventricular node is linked to Purkinjefibres, which conduct the action potential very rapidly, and terminate throughout the ventricular tissue. The rapid propagation of the action potential through the Purkinje system ensures synchro- nised contraction of the ventricular chambers.
This sequence of electrical activation is shown in Fig.6.6, which includes a representation of the action potential shape in each region.
6.2.3 Origin of the Electrocardiogram
The sequence of electrical activation and recovery that acts to initiate and syn- chronies the mechanical activity of the heart can be observed on the torso surface as the electrocardiogram (ECG). The local electrical potential produced by action potentials in the tissue act to generate currentflow within the torso, which behaves as a volume conductor. In turn, this currentflow produces a potential on the body surface, and the time course of the potential reflects the sequence of activation and recovery in different parts of the heart.
Since it provides a non-invasive way to assess the function of the heart, the ECG is a powerful and widely used diagnostic tool. The ECG is recorded from electrodes
Upstroke
Plateau
RepolarisaƟon Notch
Rest
-200 0
0 100 200 300 400 500 600
-400 Ca2+ current (pA)
Time (ms)
0 100 200 300 400 500 600
Time (ms)
0 100 200 300 400 500 600
Time (ms)
0 100 200 300 400 500 600
Time (ms) 0
10
-10 -20
60 40 20 0 40
20 0 -20 -40 -60 Membrane Voltage (mV) -80
-100
K+ current (pA)Na+ current (nA)
Fig. 6.5 Cardiac action potential, with principal inward (Na+ and Ca2+), and outward (K+) currents shown
places on the torso, and the ECG arising from each complete cardiac cycle is composed of three types of deflection, as shown in Fig.6.7. The size and shape of these deflections depends on the electrode placement.
Electrical activation of the sinus node and atria is inscribed on the ECG as the P wave. The electrical activation the ventricles is then inscribed as the QRS complex.
The Q wave is thefirst downward deflection, the R wave the upward deflection, and the S wave the second downward deflection. The configuration of the QRS complex is strongly influenced by the location of recording electrodes, and one or more of
Sino-atrial node (pacemaker)
Atrial tissue
Atrio-ventricular node (delay)
Purkinje fibre (fast)
Ventricular tissue
300-400 ms 150-200 ms
Fig. 6.6 Cardiac action potentials in different regions of the heart
PQ interval (150 ms) P wave duration (100 ms)
QT interval (400 ms) QRS
duration (100ms)
ST segment
Q S R
P
T
Atrial depolarisation
Ventricular depolarisation
Atrial repolarisation
Ventricular repolarisation
Fig. 6.7 The normal electrocardiogram
the Q, R and S waves may be very small. The QRS complex typically obscures any deflection arising from repolarisation of the atria, but repolarisation of the ventricles is inscribed as the T wave. The duration of each deflection, as well as intervals between the deflections, can convey important diagnostic information.
The P wave duration reflects conduction of the action potential through the atria, and the PQ interval (usually referred to, incorrectly, as the PR interval) indicates atrial activation time plus slow conduction through the atrioventricular node.
A short PQ interval can indicate an additional and abnormal activation pathway from atria to ventricles, which results in early activation of the ventricles and can provide a substrate for re-entrant arrhythmia (see below). A prolonged PR interval can indicate delays in conduction through the atrioventricular node.
The QRS duration reflects electrical activation of the specialised Purkinjefibres and both left and right ventricles. A prolonged QRS duration indicates slower than normal conduction in the Purkinje system.
The portion of the ECG between the end of the QRS complex and the start of the T wave is the ST segment, and reflects the state of the ventricles between the end of the activation sequence and the start of recovery. When this segment is displaced above or below the ECG baseline, it is indicative of myocardial ischaemia.
The QT interval reflects the time between the start of ventricular activation, and then end of ventricular recovery. The QT interval duration shortens at elevated heart rates, and may be expressed as a corrected value (denoted QTC) calculated using Bazett’s formula, which gives QTCas the measured QT divided by the square root of the RR interval. The QT interval is prolonged by any change that acts to increase the action potential duration, or the range of action potential durations, in ven- tricular myocytes.
6.2.4 Arrhythmias and Conduction Defects
Cardiac arrhythmias disturb the normal activation of the heart, and so influence the ability of the heart to propel blood around the circulation. An arrhythmia can arise from spontaneous action potential formation outside of the sino-atrial node, from abnormal conduction of the action potential, or from a combination of the two.
Spontaneous depolarisation can arise in the atria, the atrioventricular node, or the ventricles, and produces an ectopic beat that usually precedes the next natural beat.
These extra beats are seen on the ECG, and usually have a different morphology to normal beats because they arise in a different location and produce a different activation sequence. Ectopic beats are often felt as a ‘missed beat’, and are a commonfinding in otherwise normal individuals.
Abnormal propagation of the action potential can be more serious. During a normal beat, the cardiac tissue does not begin to recover until all of the tissue has been activated. However, if the duration of electrical activation is short, or the activation wave propagates slowly, then it is possible for the activation to propagate into regions of tissue that have recovered. This leads to circulating waves of
electrical activation that are termed re-entry, and are similar to a‘Mexican wave’in a sports stadium. The period of re-entry is usually faster than the normal heart rate, and so an arrhythmia sustained by re-entry will suppress beats arising naturally in the sinus node. The increase in activation rate is referred to as tachycardia.
Three types of arrhythmia are shown in Fig.6.8. In atrioventricular node re-entrant tachycardia, activation propagates from the atria to the ventricles through the atrioventricular node. Re-entry occurs because the activation is then able to propagate back into the atria, before re-entering the ventricles. In some individuals, an abnormal region of excitable tissue between atria and ventricles exists, and provides an alternative pathway alongside the atrioventricular node. This condition is called Wolff—Parkinson–White syndrome, and activation of the atrioventricular node and then alternative pathway (or vice versa) provides the substrate for re-entry. Each activation produces a series of deflections on the ECG.
In the ventricles, damaged tissue following a myocardial infarction can provide a region of slow conduction, which acts as a substrate to set up a re-entrant circuit for ventricular tachycardia. Each activation produces a deflection on the ECG. If the single activation wave breaks up into several re-entrant waves, then ventricular tachycardia can degenerate to ventricularfibrillation.
Multiple re-entrant waves in the atria the mechanism that underlies atrial fib- rillation. The turbulent activity in the atria produces an undulating baseline on the ECG, with no regular and discernible P waves. Activation of the atrioventricular node is irregular, and so ventricular beats occur at irregular intervals.
Normal (sinus) rhythm
Atrial fibrillation
Ventricular tachycardia
Atrio-ventricular node re-entrant tachycardia
Fig. 6.8 Electrocardiogram of normal beat, atrial fibrillation, atrioventricular node re-entrant tachycardia, and ventricular tachycardia