Cardiovascular physiology

Poiseuille equation

The factors that determine the resistance of a blood vessel to blood flow are expressed by the Poiseuille equation:

where

The most important concepts expressed in the Poiseuille equation are as follows: First, resistance to flow is directly proportional to viscosity (η) of the blood; for example, as viscosity increases (e.g., if the hematocrit increases), the resistance to flow also increases. Second, resistance to flow is directly proportional to the length (l) of the blood vessel. Third, and most important, resistance to flow is inversely proportional to the fourth power of the radius (r ⁴ ) of the blood vessel. This is a powerful relationship, indeed! When the radius of a blood vessel decreases, its resistance increases, not in a linear fashion but magnified by the fourth-power relationship. For example, if the radius of a blood vessel decreases by one-half, resistance does not simply increase twofold–it increases by 16-fold (2 ⁴ )!

Series and parallel resistances

Resistances in the cardiovascular system, as in electrical circuits, can be arranged in series or in parallel ( Fig. 4.5 ). Whether the arrangement is series or parallel produces different values for total resistance.

• ♦

  Series resistance is illustrated by the arrangement of blood vessels within a given organ. Each organ is supplied with blood by a major artery and drained by a major vein. Within the organ, blood flows from the major artery to smaller arteries, to arterioles, to capillaries, to venules, to veins. The total resistance of the system arranged in series is equal to the sum of the individual resistances, as shown in the following equation and in Figure 4.5 . Of the various resistances in series, arteriolar resistance is by far the greatest. The total resistance of a vascular bed is determined, therefore, in large part by the arteriolar resistance. Series resistance is expressed as follows:

  ${\text{R}}_{\text{total}}\text{=}{\text{R}}_{\text{artery}}\text{+}{\text{R}}_{\text{arterioles}}\text{+}{\text{R}}_{\text{capillaries}}\text{+}{\text{R}}_{\text{venules}}\text{+}{\text{R}}_{\text{vein}}$

  • When resistances are arranged in series, the total flow at each level of the system is the same. For example, blood flow through the aorta equals blood flow through all the large systemic arteries, equals blood flow through all the systemic arterioles, equals blood flow through all the systemic capillaries. For another example, blood flow through the renal artery equals blood flow through all the renal capillaries, equals blood flow through the renal vein (less a small volume lost in urine). Although total flow is constant at each level in the series, the pressure decreases progressively as blood flows through each sequential component (remember Q = ΔP/R or ΔP = Q × R). The greatest decrease in pressure occurs in the arterioles because they contribute the largest portion of the resistance.

• ♦

  Parallel resistance is illustrated by the distribution of blood flow among the various major arteries branching off the aorta (see Figs. 4.1 and 4.5 ). Recall that the cardiac output flows through the aorta and then is distributed simultaneously, on a percentage basis, among the various organ systems. Thus there is parallel, simultaneous blood flow through each of the circulations (e.g., renal, cerebral, and coronary). The venous effluent from the organs then collects in the vena cava and returns to the heart. As shown in the following equation and in Figure 4.5 , the total resistance in a parallel arrangement is less than any of the individual resistances. The subscripts 1, 2, 3, and so forth refer to the resistances of cerebral, coronary, renal, gastrointestinal, skeletal muscle, and skin circulations. Parallel resistance is expressed as follows:

  $\frac{1}{{\text{R}}_{\text{total}}}\text{=}\frac{1}{{\text{R}}_1}\text{+}\frac{1}{{\text{R}}_2}\text{+}\frac{1}{{\text{R}}_3}\text{+}\frac{1}{{\text{R}}_4}\text{+}\frac{1}{{\text{R}}_5}\text{+}\frac{1}{{\text{R}}_6}$

When blood flow is distributed through a set of parallel resistances, the flow through each organ is a fraction of the total blood flow. The effects of this arrangement are that there is no loss of pressure in the major arteries and that mean pressure in each major artery will be the same and be approximately the same as mean pressure in the aorta.

Another predictable consequence of a parallel arrangement is that adding a resistance to the circuit causes total resistance to decrease, not to increase. Mathematically, this can be demonstrated as follows: Four resistances, each with a numerical value of 10, are arranged in parallel. According to the equation, the total resistance is 2.5 (1/R _total = 1/10 + 1/10 + 1/10 + 1/10 = 4/10). If a fifth resistance with a value of 10 is added to the parallel arrangement, the total resistance decreases to 2 (1/R _total = 1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10).

On the other hand, if the resistance of one of the individual vessels in a parallel arrangement increases, then total resistance increases. This can be shown by returning to the parallel arrangement of four blood vessels where each individual resistance is 10 and the total resistance is 2.5. If one of the four blood vessels is completely occluded, its individual resistance becomes infinite. The total resistance of the parallel arrangement then increases to 3.333 (1/R _total = 1/10 + 1/10 + 1/10 + 1/∞).

Pressure profile in the vasculature

Figure 4.8 is a profile of pressures within the systemic vasculature. First, examine the smooth profile, ignoring the pulsations. The smooth curve gives mean pressure, which is highest in the aorta and large arteries and decreases progressively as blood flows from the arteries, to the arterioles, to the capillaries, to the veins, and back to the heart. This decrease in pressure occurs as blood flows through the vasculature because energy is consumed in overcoming the frictional resistances.

Mean pressure in the aorta is high, averaging 100 mm Hg (see Table 4.1 and Fig. 4.8 ). This high mean arterial pressure is a result of two factors: the large volume of blood pumped from the left ventricle into the aorta (cardiac output) and the low compliance of the arterial wall. (Recall that a given volume causes greater pressure when compliance of the vessel is low.) The pressure remains high in the large arteries, which branch off the aorta, because of the high elastic recoil of the arterial walls. Thus little energy is lost as blood flows from the aorta through the arterial tree.

Beginning in the small arteries, arterial pressure decreases, with the most significant decrease occurring in the arterioles. At the end of the arterioles, mean pressure is approximately 30 mm Hg. This dramatic decrease in pressure occurs because the arterioles constitute a high resistance to flow. Since total blood flow is constant at all levels of the cardiovascular system, as resistance increases, downstream pressure must necessarily decrease (Q = ΔP/R, or ΔP = Q × R).

In the capillaries, pressure decreases further for two reasons: frictional resistance to flow and filtration of fluid out of the capillaries (refer to the discussion on microcirculation). When blood reaches the venules and veins, pressure has decreased even further. (Recall that because capacitance of the veins is high, the veins can hold large volumes of blood at this low pressure.) Pressure in the vena cava is only 4 mm Hg and in the right atrium is even lower at 0 to 2 mm Hg.

Arterial pressure in the systemic circulation

Further examination of Figure 4.8 reveals that although mean pressure in the arteries is high and constant, there are oscillations or pulsations of arterial pressure. These pulsations reflect the pulsatile activity of the heart: ejecting blood during systole, resting during diastole, ejecting blood, resting, and so forth. Each cycle of pulsation in the arteries coincides with one cardiac cycle.

Figure 4.9 shows an expanded version of two such cycles of pulsations in a large artery.

• ♦

  Diastolic pressure is the lowest arterial pressure measured during a cardiac cycle and is the pressure in the arteries during ventricular relaxation when no blood is being ejected from the left ventricle.

• ♦

  Systolic pressure is the highest arterial pressure measured during a cardiac cycle. It is the pressure in the arteries after blood has been ejected from the left ventricle during systole. The “blip” in the arterial pressure curve, called the dicrotic notch (or incisura ), is produced when the aortic valve closes. Aortic valve closure produces a brief period of retrograde flow from the aorta back toward the valve, briefly decreasing the aortic pressure below the systolic value.

• ♦

  Pulse pressure is the difference between systolic pressure and diastolic pressure. If all other factors are equal, the magnitude of the pulse pressure reflects the volume of blood ejected from the left ventricle on a single beat, or the stroke volume.

  • Pulse pressure can be used as an indicator of stroke volume because of the relationships between pressure, volume, and compliance. Recall that compliance of a blood vessel is the volume the vessel can hold at a given pressure (C = V/P). Thus assuming that arterial compliance is constant, arterial pressure depends on the volume of blood the artery contains at any moment in time. For example, the volume of blood in the aorta at a given time is determined by the balance between inflow and outflow of blood. When the left ventricle contracts, it rapidly ejects a stroke volume into the aorta, and the pressure rises rapidly to its highest level, the systolic pressure. Blood then begins to flow from the aorta into the rest of the arterial tree. Now, as the volume in the aorta decreases, the pressure also decreases. Arterial pressure reaches its lowest level, the diastolic pressure, when the ventricle is relaxed and blood is returning from the arterial system back to the heart.

  • With aging, the decreased compliance of arterial walls results in increased pulse pressure: the same stroke volume ejected into an “old” artery causes a larger increase in pressure than it does in a “young” artery.

• ♦

  Mean arterial pressure is the average pressure over a complete cardiac cycle and is calculated as follows:

  $\begin{array}{c}\text{Mean arterial pressure}\\ \text{=}\text{Diastolic pressure}\text{+}1/3\text{Pulse pressure}\end{array}$

  • Notice that mean arterial pressure is not the simple mathematical average of diastolic and systolic pressures. This is because a greater fraction of each cardiac cycle is spent in diastole than in systole. Thus the calculation of mean arterial pressure gives more weight to diastolic pressure than systolic pressure.

Interestingly, the pulsations in large arteries are even greater than the pulsations in the aorta (see Fig. 4.8 ). In other words, systolic pressure and pulse pressure are higher in the large arteries than in the aorta. It is not immediately obvious why pulse pressure should increase in the “downstream” arteries. The explanation resides in the fact that, following ejection of blood from the left ventricle, the pressure wave travels at a higher velocity than the blood itself travels (due to the inertia of the blood), augmenting the downstream pressure. Furthermore, at branch points of arteries, pressure waves are reflected backward, which also tends to augment pressure at those sites. (Given that blood flows from the aorta to the large arteries, it may seem odd that systolic pressure and pulse pressure are higher in the downstream arteries. We know that the direction of blood flow must be from high to low pressure and not the other way around! The explanation is that the driving force for blood flow in the arteries is the mean arterial pressure, which is influenced more by diastolic pressure than by systolic pressure (because a greater proportion of each cardiac cycle is spent in diastole). Note in Figure 4.8 that while systolic pressure is higher in the large arteries than in the aorta, diastolic pressure is lower; thus mean arterial pressure is lower downstream.)

Although systolic pressure and pulse pressure are augmented in the large arteries (compared with the aorta), from that point on, there is damping of the oscillations. The pulse pressure is still evident, but decreased, in the smaller arteries; it is virtually absent in the arterioles; and it is completely absent in the capillaries, venules, and veins. This damping and loss of pulse pressure occur for two reasons. (1) The resistance of the blood vessels, particularly the arterioles, makes it difficult to transmit the pulse pressure. (2) The compliance of the blood vessels, particularly of the veins, damps the pulse pressure—the more compliant the blood vessel, the more volume that can be added to it without causing an increase in pressure.

Several pathologic conditions alter the arterial pressure curve in a predictable way ( Fig. 4.10 ). As previously noted, pulse pressure is the change in arterial pressure that occurs when a stroke volume is ejected from the left ventricle into the aorta. Logically, then, pulse pressure will change if stroke volume changes, or if the compliance of the arteries changes.

• ♦

  Arteriosclerosis (see Fig. 4.10 ). In arteriosclerosis, plaque deposits in the arterial walls decrease the diameter of the arteries and make them stiffer and less compliant. Because arterial compliance is decreased, ejection of a stroke volume from the left ventricle causes a much greater change in arterial pressure than it does in normal arteries (C = ΔV/ΔP or ΔP = ΔV/C). Thus in arteriosclerosis, systolic pressure, pulse pressure, and mean pressure all will be increased.

• ♦

  Aortic stenosis (see Fig. 4.10 ). If the aortic valve is stenosed (narrowed), the size of the opening through which blood can be ejected from the left ventricle into the aorta is reduced. Thus stroke volume is decreased, and less blood enters the aorta on each beat. Systolic pressure, pulse pressure, and mean pressure all will be decreased.

• ♦

  Aortic regurgitation (not shown). When the aortic valve is incompetent (e.g., due to a congenital abnormality), the normal one-way flow of blood from the left ventricle into the aorta is disrupted. Instead, blood that was ejected into the aorta flows backward into the ventricle. Such retrograde flow can occur because the ventricle is relaxed (is at low pressure) and because the incompetent aortic valve cannot prevent it, as it normally does.

Venous pressures in the systemic circulation

By the time blood reaches the venules and veins, pressure is less than 10 mm Hg; pressure will decrease even further in the vena cava and the right atrium. The reason for the continuing decrease in pressure is now familiar: The resistance provided by the blood vessels at each level of the systemic vasculature causes a fall in pressure. Table 4.1 and Figure 4.8 show the mean values for venous pressures in the systemic circulation.

Pressures in the pulmonary circulation

Table 4.1 also compares pressures in the pulmonary circulation with pressures in the systemic circulation. As the table shows, the entire pulmonary vasculature is at much lower pressure than the systemic vasculature. The pattern of pressures within the pulmonary circulation is analogous to the systemic circulation, however. Blood is ejected from the right ventricle into the pulmonary artery, where pressure is highest. Thereafter, the pressure decreases as blood flows through the pulmonary arteries, arterioles, capillaries, venules, and veins and back to the left atrium.

An important implication of these lower pressures on the pulmonary side is that pulmonary vascular resistance is much lower than systemic vascular resistance. This conclusion can be reached by recalling that the total flow through the systemic and pulmonary circulations must be equal (i.e., cardiac output of the left and right hearts is equal). Because pressures on the pulmonary side are much lower than pressures on the systemic side, to achieve the same flow, pulmonary resistance must be lower than systemic resistance (Q = ΔP/R). (The pulmonary circulation is discussed in more detail in Chapter 5 .)

Origin and spread of excitation within the heart

The heart consists of two kinds of muscle cells: contractile cells and conducting cells. Contractile cells constitute the majority of atrial and ventricular tissues and are the working cells of the heart. Action potentials in contractile cells lead to contraction and generation of force or pressure. Conducting cells constitute the tissues of the SA node, the atrial internodal tracts, the AV node, the bundle of His, and the Purkinje system. Conducting cells are specialized muscle cells that do not contribute significantly to generation of force; instead, they function to rapidly spread action potentials over the entire myocardium. Another feature of the specialized conducting tissues is their capacity to generate action potentials spontaneously. Except for the SA node, however, this capacity normally is suppressed.

Figure 4.11 is a schematic drawing showing the relationships of the SA node, atria, ventricles, and specialized conducting tissues. The action potential spreads throughout the myocardium in the following sequence:

• 1.

  SA node. Normally, the action potential of the heart is initiated in the specialized tissue of the SA node, which serves as the pacemaker. After the action potential is initiated in the SA node, there is a specific sequence and timing for the conduction of action potentials to the rest of the heart.

• 2.

  Atrial internodal tracts and atria. The action potential spreads from the SA node to the right and left atria via the atrial internodal tracts. Simultaneously, the action potential is conducted to the AV node.

• 3.

  AV node. Conduction velocity through the AV node is considerably slower than in the other cardiac tissues. Slow conduction through the AV node ensures that the ventricles have sufficient time to fill with blood before they are activated and contract. Increases in conduction velocity of the AV node can lead to decreased ventricular filling and decreased stroke volume and cardiac output.

• 4.

  Bundle of His, Purkinje system, and ventricles. From the AV node, the action potential enters the specialized conducting system of the ventricles. The action potential is first conducted to the bundle of His through the common bundle. It then invades the left and right bundle branches and then the smaller bundles of the Purkinje system. Conduction through the His-Purkinje system is extremely fast, and it rapidly distributes the action potential to the ventricles. The action potential also spreads from one ventricular muscle cell to the next, via low-resistance pathways between the cells. Rapid conduction of the action potential throughout the ventricles is essential and allows for efficient contraction and ejection of blood.

The term normal sinus rhythm has a specific meaning. It means that the pattern and timing of the electrical activation of the heart are normal. To qualify as normal sinus rhythm, the following three criteria must be met: (1) The action potential must originate in the SA node. (2) The SA nodal impulses must occur regularly at a rate of 60 to 100 impulses per minute. (3) The activation of the myocardium must occur in the correct sequence and with the correct timing and delays.

Concepts associated with cardiac action potentials

The concepts applied to cardiac action potentials are the same concepts that are applied to action potentials in nerve, skeletal muscle, and smooth muscle. The following section is a summary of those principles, which are discussed in Chapter 1 :

• 1.

  The membrane potential of cardiac cells is determined by the relative conductances (or permeabilities) to ions and the concentration gradients for the permeant ions.

• 2.

  If the cell membrane has a high conductance or permeability to an ion, that ion will flow down its electrochemical gradient and attempt to drive the membrane potential toward its equilibrium potential (calculated by the Nernst equation). If the cell membrane has low conductance or permeability to an ion or is impermeable to the ion, that ion will make little or no contribution to the membrane potential.

• 3.

  By convention, membrane potential is expressed in millivolts (mV), and intracellular potential is expressed relative to extracellular potential; for example, a membrane potential of −85 mV means 85 mV, cell interior negative.

• 4.

  The resting membrane potential of cardiac cells is determined primarily by potassium ions (K ⁺ ). The conductance to K ⁺ at rest is high, and the resting membrane potential is close to the K ⁺ equilibrium potential. Since the conductance to sodium (Na ⁺ ) at rest is low, Na ⁺ contributes little to the resting membrane potential.

• 5.

  The role of Na ⁺ -K ⁺ ATPase is primarily to maintain Na ⁺ and K ⁺ concentration gradients across the cell membrane, although it makes a small direct electrogenic contribution to the membrane potential.

• 6.

  Changes in membrane potential are caused by the flow of ions into or out of the cell. For ion flow to occur, the cell membrane must be permeable to that ion. Depolarization means the membrane potential has become less negative. Depolarization occurs when there is net movement of positive charge into the cell, which is called an inward current. Hyperpolarization means the membrane potential has become more negative, and it occurs when there is net movement of positive charge out of the cell, which is called an outward current.

• 7.

  Two basic mechanisms can produce a change in membrane potential. In one mechanism, there is a change in the electrochemical gradient for a permeant ion, which changes the equilibrium potential for that ion. The permeant ion then will flow into or out of the cell in an attempt to reestablish electrochemical equilibrium, and this current flow will alter the membrane potential. For example, consider the effect of decreasing the extracellular K ⁺ concentration on the resting membrane potential of a myocardial cell. The K ⁺ equilibrium potential, calculated by the Nernst equation, will become more negative. K ⁺ ions will then flow out of the cell and down the now larger electrochemical gradient, driving the resting membrane potential toward the new, more negative K ⁺ equilibrium potential.

  • In the other mechanism, there is a change in conductance to an ion. For example, the resting permeability of ventricular cells to Na ⁺ is quite low, and Na ⁺ contributes minimally to the resting membrane potential. However, during the upstroke of the ventricular action potential, Na ⁺ conductance dramatically increases, Na ⁺ flows into the cell down its electrochemical gradient, and the membrane potential is briefly driven toward the Na ⁺ equilibrium potential (i.e., is depolarized).

• 8.

  Threshold potential is the potential difference at which there is a net inward current (i.e., inward current becomes greater than outward current). At threshold potential, the depolarization becomes self-sustained and gives rise to the upstroke of the action potential.

Action potentials of ventricles, atria, and the purkinje system

The ionic basis for the action potentials in the ventricles, atria, and Purkinje system is identical. The action potential in these tissues shares the following characteristics ( Table 4.2 ):

• ♦

  Long duration. In each of these tissues, the action potential is of long duration. Action potential duration varies from 150 ms in atria, to 250 ms in ventricles, to 300 ms in Purkinje fibers. These durations can be compared with the brief duration of the action potential in nerve and skeletal muscle (1–2 ms). Recall that the duration of the action potential also determines the duration of the refractory periods: The longer the action potential, the longer the cell is refractory to firing another action potential. Thus atrial, ventricular, and Purkinje cells have long refractory periods compared with other excitable tissues.

• ♦

  Stable resting membrane potential. The cells of the atria, ventricles, and Purkinje system exhibit a stable, or constant, resting membrane potential. (AV nodal and Purkinje fibers can develop unstable resting membrane potentials, and under special conditions, they can become the heart’s pacemaker, as discussed in the section on latent pacemakers.)

• ♦

  Plateau. The action potential in cells of the atria, ventricles, and Purkinje system is characterized by a plateau. The plateau is a sustained period of depolarization, which accounts for the long duration of the action potential and, consequently, the long refractory periods.

Figure 4.12 A and B illustrate the action potential in a ventricular muscle fiber and an atrial muscle fiber. An action potential in a Purkinje fiber (not shown) would look similar to that in the ventricular fiber, but its duration would be slightly longer. The phases of the action potential are described subsequently and correspond to the numbered phases shown in Figure 4.12 A and B. The ventricular action potential has also been redrawn in Figure 4.13 to show the ionic currents responsible for each phase. Some of this information also is summarized in Table 4.2 .

• 1.

  Phase 0, upstroke. In ventricular, atrial, and Purkinje fibers, the action potential begins with a phase of rapid depolarization, called the upstroke. As in nerve and skeletal muscle, the upstroke is caused by a transient increase in Na ⁺ conductance (g _Na ) produced by depolarization-induced opening of activation gates on the Na ⁺ channels. When g _Na increases, there is an inward Na ⁺ current (influx of Na ⁺ into the cell), or I _Na , which drives the membrane potential toward the Na ⁺ equilibrium potential of approximately +65 mV. The membrane potential does not quite reach the Na ⁺ equilibrium potential because, as in nerve, the inactivation gates on the Na ⁺ channels close in response to depolarization (albeit more slowly than the activation gates open). Thus the Na ⁺ channels open briefly and then close. At the peak of the upstroke, the membrane potential is depolarized to a value of about +20 mV.

  • The rate of rise of the upstroke is called dV/dT. dV/dT is the rate of change of the membrane potential as a function of time, and its units are volts per second (V/s). dV/dT varies, depending on the value of the resting membrane potential. This dependence is called the responsiveness relationship. Thus dV/dT is greatest (the rate of rise of the upstroke is fastest) when the resting membrane potential is most negative, or hyperpolarized (e.g., −90 mV), and dV/dT is lowest (the rate of rise of the upstroke is slowest) when the resting membrane potential is less negative, or depolarized (e.g., −60 mV). This correlation is based on the relationship between membrane potential and the position of the inactivation gates on the Na ⁺ channel (see Chapter 1 ). When the resting membrane potential is relatively hyperpolarized (e.g., −90 mV), the voltage-dependent inactivation gates are open and many Na ⁺ channels are available for the upstroke. When the resting membrane potential is relatively depolarized (e.g., −60 mV), the inactivation gates on the Na ⁺ channels tend to be closed and fewer Na ⁺ channels are available to open during the upstroke. dV/dT also correlates with the size of the inward current (i.e., in ventricular, atrial, and Purkinje fibers, the size of the inward Na ⁺ current).

• 2.

  Phase 1, initial repolarization. Phase 1 in ventricular, atrial, and Purkinje fibers is a brief period of repolarization, which immediately follows the upstroke. Recall that, for repolarization to occur, there must be a net outward current. There are two explanations for the occurrence of the net outward current during phase 1. First, the inactivation gates on the Na ⁺ channels close in response to depolarization. When these gates close, g _Na decreases and the inward Na ⁺ current (which caused the upstroke) ceases. Second, there is an outward K ⁺ current, caused by the large driving force on K ⁺ ions: At the peak of the upstroke, both the chemical and the electrical driving forces favor K ⁺ movement out of the cell (the intracellular K ⁺ concentration is higher than extracellular K ⁺ concentration, and the cell interior is electrically positive). Because the K ⁺ conductance (g _K ) is high, K ⁺ flows out of the cell, down this steep electrochemical gradient.

• 3.

  Phase 2, plateau. During the plateau, there is a long period (150–200 ms) of relatively stable, depolarized membrane potential, particularly in ventricular and Purkinje fibers. (In atrial fibers, the plateau is shorter than in ventricular fibers.) Recall that for the membrane potential to be stable, inward and outward currents must be equal such that there is no net current flow across the membrane.

  • How is such a balance of inward and outward currents achieved during the plateau? There is an increase in calcium (Ca ²⁺ ) conductance (g _Ca ), which results in an inward Ca ²⁺ current. Inward Ca ²⁺ current is also called slow inward current, reflecting the slower kinetics of these channels (compared with the fast Na ⁺ channels of the upstroke). The Ca ²⁺ channels that open during the plateau are L-type channels and are inhibited by the Ca ²⁺ channel blockers nifedipine, diltiazem, and verapamil. To balance the inward Ca ²⁺ current, there is an outward K ⁺ current, driven by the electrochemical driving force on K ⁺ ions (as described for phase 1). Thus during the plateau, the inward Ca ²⁺ current is balanced by the outward K ⁺ current, the net current is zero, and the membrane potential remains at a stable depolarized value. (See Fig. 4.13 , where during phase 2, the inward Ca ²⁺ current is shown as equal in magnitude to the outward K ⁺ current.)

  • The significance of the inward Ca ²⁺ current extends beyond its effect on membrane potential. This Ca ²⁺ entry during the plateau of the action potential initiates the release of more Ca ²⁺ from intracellular stores for excitation-contraction coupling. This process of so-called Ca ²⁺ -induced Ca ²⁺ release is discussed in the section on cardiac muscle contraction.

• 4.

  Phase 3, repolarization. Repolarization begins gradually at the end of phase 2, and then there is rapid repolarization to the resting membrane potential during phase 3. Recall that repolarization is produced when outward currents are greater than inward currents. During phase 3, repolarization results from a combination of a decrease in g _Ca (previously increased during the plateau) and an increase in g _K (to even higher levels than at rest). The reduction in g _Ca results in a decrease in the inward Ca ²⁺ current, and the increase in g _K results in an increase in the outward K ⁺ current (I _K ), with K ⁺ moving down a steep electrochemical gradient (as described for phase 1). At the end of phase 3, the outward K ⁺ current is reduced because repolarization brings the membrane potential closer to the K ⁺ equilibrium potential, thus decreasing the driving force on K ⁺ .

• 5.

  Phase 4, resting membrane potential, or electrical diastole. The membrane potential fully repolarizes during phase 3 and returns to the resting level of approximately −85 mV. During phase 4, the membrane potential is stable again, and inward and outward currents are equal. The resting membrane potential approaches, but does not fully reach, the K ⁺ equilibrium potential, reflecting the high resting conductance to K ⁺ . The K ⁺ channels, and the resulting K ⁺ current, responsible for phase 4 are different from those responsible for repolarization in phase 3. In phase 4, the K ⁺ conductance is called g _K1 and the K ⁺ current is called, accordingly, I _K1 .

  • The stable membrane potential in phase 4 means that inward and outward currents are equal. The high conductance to K ⁺ produces an outward K ⁺ current (I _K1 ), which has already been described. The inward current that balances this outward current is carried by Na ⁺ and Ca ²⁺ (see Fig. 4.13 ), even though the conductances to Na ⁺ and Ca ²⁺ are low at rest. The question may arise: How can the sum of inward Na ⁺ and Ca ²⁺ currents be the same magnitude as the outward K ⁺ current, given that g _Na and g _Ca are very low and g _K1 is very high? The answer lies in the fact that, for each ion, current = conductance × driving force. Although g _K1 is high, the driving force on K ⁺ is low because the resting membrane potential is close to the K ⁺ equilibrium potential; thus the outward K ⁺ current is relatively small. On the other hand, g _Na and g _Ca are both low, but the driving forces on Na ⁺ and Ca ²⁺ are high because the resting membrane potential is far from the Na ⁺ and Ca ²⁺ equilibrium potentials; thus the sum of the inward currents carried by Na ⁺ and Ca ²⁺ is equal to the outward current carried by K ⁺ .

Action potentials in the sinoatrial node

The SA node is the normal pacemaker of the heart. The configuration and ionic basis for its action potential differ in several important aspects from those in atrial, ventricular, and Purkinje fibers (see Fig. 4.12 C). The following features of the action potential of the SA node are different from those in atria, ventricles, and Purkinje fibers: (1) The SA node exhibits automaticity; that is, it can spontaneously generate action potentials without neural input. (2) It has an unstable resting membrane potential, in direct contrast to cells in atrial, ventricular, and Purkinje fibers. (3) It has no sustained plateau.

The phases of the SA node action potential are described here and correspond to the numbered phases shown in Figure 4.12 C.

• 1.

  Phase 0, upstroke. Phase 0 (as in the other cardiac cells) is the upstroke of the action potential. Note that the upstroke is not as rapid or as steep as in the other types of cardiac tissues. The ionic basis for the upstroke in the SA node differs as well. In the other myocardial cells, the upstroke is the result of an increase in g _Na and an inward Na ⁺ current. In the SA nodal cells, the upstroke is the result of an increase in g _Ca and an inward Ca ²⁺ current carried primarily by L-type Ca ²⁺ channels. There are also T-type Ca ²⁺ channels in SA node, which carry part of the inward Ca ²⁺ current of the upstroke.

• 2.

  Phases 1 and 2 are absent.

• 3.

  Phase 3, repolarization. As in the other myocardial tissues, repolarization in the SA node is due to an increase in g _K . Because the electrochemical driving forces on K ⁺ are large (both chemical and electrical driving forces favor K ⁺ leaving the cell), there is an outward K ⁺ current, which repolarizes the membrane potential.

• 4.

  Phase 4, spontaneous depolarization or pacemaker potential. Phase 4 is the longest portion of the SA node action potential. This phase accounts for the automaticity of SA nodal cells (the ability to spontaneously generate action potentials without neural input). During phase 4, the most negative value of the membrane potential (called the maximum diastolic potential ) is approximately −65 mV, but the membrane potential does not remain at this value. Rather, there is a slow depolarization, produced by the opening of Na ⁺ channels and an inward Na ⁺ current called I _f . The “f,” which stands for funny, denotes that this Na ⁺ current differs from the fast Na ⁺ current responsible for the upstroke in ventricular cells. I _f is turned on by repolarization from the preceding action potential, thus ensuring that each action potential in the SA node will be followed by another action potential. Once I _f and slow depolarization bring the membrane potential to threshold, the Ca ²⁺ channels are opened for the upstroke.

  • The rate of phase 4 depolarization is one determinant of heart rate. If the rate of phase 4 depolarization increases, threshold is reached more quickly, the SA node will fire more action potentials per time, and heart rate will increase. Conversely, if the rate of phase 4 depolarization decreases, threshold is reached more slowly, the SA node will fire fewer action potentials per time, and heart rate will decrease. The effects of the autonomic nervous system on heart rate are based on such changes in the rate of phase 4 depolarization and are discussed later in the chapter.

Latent pacemakers

The cells in the SA node are not the only myocardial cells with intrinsic automaticity; other cells, called latent pacemakers, also have the capacity for spontaneous phase 4 depolarization. Latent pacemakers include the cells of the AV node, bundle of His, and Purkinje fibers. Although each of these cells has the potential for automaticity, it normally is not expressed.

The rule is that the pacemaker with the fastest rate of phase 4 depolarization controls the heart rate. Normally, the SA node has the fastest rate of phase 4 depolarization, and therefore it sets the heart rate ( Table 4.3 ). Recall also that, of all myocardial cells, the SA nodal cells have the shortest action potential duration (i.e., the shortest refractory periods). Therefore SA nodal cells recover faster and are ready to fire another action potential before the other cell types are ready.

When the SA node drives the heart rate, the latent pacemakers are suppressed, a phenomenon called overdrive suppression, which is explained as follows: The SA node has the fastest firing rate of all the potential pacemakers, and impulses spread from the SA node to the other myocardial tissues in the sequence illustrated in Figure 4.11 . Although some of these tissues are potential pacemakers themselves (AV node, bundle of His, Purkinje fibers), as long as their firing rate is driven by the SA node, their own capacity to spontaneously depolarize is suppressed.

The latent pacemakers have an opportunity to drive the heart rate only if the SA node is suppressed or if the intrinsic firing rate of a latent pacemaker becomes faster than that of the SA node. Since the intrinsic rate of the latent pacemakers is slower than that of the SA node, the heart will beat at the slower rate if it is driven by a latent pacemaker (see Table 4.3 ).

Under the following conditions a latent pacemaker takes over and becomes the pacemaker of the heart, in which case it is called an ectopic pacemaker, or ectopic focus. (1) If the SA node firing rate decreases (e.g., due to vagal stimulation) or stops completely (e.g., because the SA node is destroyed, removed, or suppressed by drugs), then one of the latent sites will assume the role of pacemaker in the heart. (2) Or, if the intrinsic rate of firing of one of the latent pacemakers should become faster than that of the SA node, then it will assume the pacemaker role. (3) Or, if the conduction of action potentials from the SA node to the rest of the heart is blocked because of disease in the conducting pathways, then a latent pacemaker can appear in addition to the SA node.

Conduction of the cardiac action potential

In the heart, conduction velocity has the same meaning that it has in nerve and skeletal muscle fibers: It is the speed at which action potentials are propagated within the tissue. The units for conduction velocity are meters per second (m/s). Conduction velocity is not the same in all myocardial tissues: It is slowest in the AV node (0.01–0.05 m/s) and fastest in the Purkinje fibers (2–4 m/s), as shown in Figure 4.14 .

Conduction velocity determines how long it takes the action potential to spread to various locations in the myocardium. These times, in milliseconds, are superimposed on the diagram in Figure 4.14 . The action potential originates in the SA node at what is called time zero. It then takes a total of 220 ms for the action potential to spread through the atria, AV node, and His-Purkinje system to the farthest points in the ventricles. Conduction through the AV node (called AV delay ) requires almost one-half of the total conduction time through the myocardium. The reason for the AV delay is that, of all the myocardial tissues, conduction velocity in the AV node is slowest (0.01–0.05 m/s), making conduction time the longest (100 ms).

Differences in conduction velocity among the cardiac tissues have implications for their physiologic functions. For example, the slow conduction velocity of the AV node ensures that the ventricles do not activate too early (i.e., before they have time to fill with blood from the atria). On the other hand, the rapid conduction velocity of the Purkinje fibers ensures that the ventricles can be activated quickly and in a smooth sequence for efficient ejection of blood.

Mechanism of propagation of cardiac action potential

As in nerve and skeletal muscle fibers, the physiologic basis for conduction of cardiac action potentials is the spread of local currents (see Chapter 1 ). Action potentials at one site generate local currents at adjacent sites; the adjacent sites are depolarized to threshold as a result of this local current flow and fire action potentials themselves. This local current flow is the result of the inward current of the upstroke of the action potential. Recall that, in atrial, ventricular, and Purkinje fibers, this inward current of the upstroke is carried by Na ⁺ , and in the SA node, the inward current of the upstroke is carried by Ca ²⁺ .

Conduction velocity depends on the size of the inward current during the upstroke of the action potential. The larger the inward current, the more rapidly local currents will spread to adjacent sites and depolarize them to threshold. Conduction velocity also correlates with dV/dT, the rate of rise of the upstroke of the action potential, because dV/dT also correlates with the size of the inward current, as discussed previously.

Propagation of the action potential depends not only on the inward current of the upstroke to establish local currents but also on the cable properties of the myocardial fibers. Recall that these cable properties are determined by cell membrane resistance (R _m ) and internal resistance (R _i ). For example, in myocardial tissue, R _i is particularly low because of low-resistance connections between the cells called gap junctions. Thus myocardial tissue is especially well suited to fast conduction.

Conduction velocity does not depend on action potential duration, a point that can be confusing. Recall, however, that action potential duration is simply the time it takes a given site to go from depolarization to complete repolarization (e.g., action potential duration in a ventricular cell is 250 ms). Action potential duration implies nothing about how long it takes for that action potential to spread to neighboring sites.

Autonomic effects on heart rate

The effects of the autonomic nervous system on heart rate are called chronotropic effects. The effects of the sympathetic and parasympathetic nervous systems on heart rate are summarized in Table 4.4 and are illustrated in Figure 4.16 . Briefly, sympathetic stimulation increases heart rate and parasympathetic stimulation decreases heart rate.

Figure 4.16 A shows the normal firing pattern of the SA node. Recall that phase 4 depolarization is produced by opening Na ⁺ channels, which leads to a slow depolarizing, inward Na ⁺ current called I _f . Once the membrane potential is depolarized to the threshold potential, an action potential is initiated.

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  Positive chronotropic effects are increases in heart rate. The most important example is that of stimulation of the sympathetic nervous system, as illustrated in Figure 4.16 B. Norepinephrine, released from sympathetic nerve fibers, activates β ₁ receptors in the SA node. These β ₁ receptors are coupled to adenylyl cyclase through a G _s protein (see also Chapter 2 ). Activation of β ₁ receptors in the SA node produces an increase in I _f , which increases the rate of phase 4 depolarization. In addition, there is an increase in I _Ca , which means there are more functional Ca ²⁺ channels and thus less depolarization is required to reach threshold (i.e., threshold potential decreases). Increasing the rate of phase 4 depolarization and decreasing the threshold potential means that the SA node is depolarized to threshold potential more frequently and, as a consequence, fires more action potentials per unit time (i.e., increased heart rate).

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  Negative chronotropic effects are decreases in heart rate. The most important example is that of stimulation of the parasympathetic nervous system, illustrated in Figure 4.16 C. Acetylcholine (ACh), released from parasympathetic nerve fibers, activates muscarinic (M ₂ ) receptors in the SA node. Activation of muscarinic receptors in the SA node has two effects that combine to produce a decrease in heart rate. First, these muscarinic receptors are coupled to a type of G _i protein called G _K that inhibits adenylyl cyclase and produces a decrease in I _f . A decrease in I _f decreases the rate of phase 4 depolarization. Second, G _K directly increases the conductance of a K ⁺ channel called K ⁺ -ACh and increases an outward K ⁺ current (similar to I _K1 ) called I _K-ACh . Enhancing this outward K ⁺ current hyperpolarizes the maximum diastolic potential so that the SA nodal cells are further from threshold potential. In addition, there is a decrease in I _Ca , which means there are fewer functional Ca ²⁺ channels and thus more depolarization is required to reach threshold (i.e., threshold potential increases). In sum, the parasympathetic nervous system decreases heart rate through three effects on the SA node: (1) slowing the rate of phase 4 depolarization, (2) hyperpolarizing the maximum diastolic potential so that more inward current is required to reach threshold potential, and (3) increasing the threshold potential. As a result, the SA node is depolarized to threshold less frequently and fires fewer action potentials per unit time (i.e., decreased heart rate) ( Box 4.1 ).

  BOX 4.1

  Clinical Physiology: Sinus Bradycardia

  Description of case.

  A 72-year-old woman with hypertension is being treated with propranolol, a β-adrenergic blocking agent. She has experienced several episodes of light-headedness and syncope (fainting). An ECG shows sinus bradycardia: normal, regular P waves, followed by normal QRS complexes; however, the frequency of P waves is decreased, at 45/min. The physician tapers off and eventually discontinues the propranolol and then changes the woman’s medication to a different class of antihypertensive drugs. Upon discontinuation of propranolol, a repeat ECG shows a normal sinus rhythm with a frequency of P waves of 80/min.

  Explanation of case.

  The heart rate is given by the frequency of P waves. During treatment with propranolol, her heart rate was only 45 beats/min. The presence of P waves on the ECG indicates that the heart is being activated in the SA node, which is the normal pacemaker. However, the frequency of depolarization of the SA node is much lower than normal because she is being treated with propranolol, a β-adrenergic blocking agent. Recall that β-adrenergic agonists increase the rate of phase 4 depolarization in the SA node by increasing I _f . β-Adrenergic antagonists, therefore, will decrease phase 4 depolarization and decrease the frequency at which the SA nodal cells fire action potentials.

  Treatment.

  The woman’s sinus bradycardia was an adverse effect of propranolol therapy. When propranolol was discontinued, her heart rate returned to normal.

Autonomic effects on conduction velocity in the atrioventricular node

The effects of the autonomic nervous system on conduction velocity are called dromotropic effects. Increases in conduction velocity are called positive dromotropic effects, and decreases in conduction velocity are called negative dromotropic effects. The most important physiologic effects of the autonomic nervous system on conduction velocity are those on the AV node, which, in effect, alter the rate at which action potentials are conducted from the atria to the ventricles. Recall, in considering the mechanism of these autonomic effects, that conduction velocity correlates with the size of the inward current of the upstroke of the action potential and the rate of rise of the upstroke, dV/dT.

Stimulation of the sympathetic nervous system produces an increase in conduction velocity through the AV node (positive dromotropic effect), which increases the rate at which action potentials are conducted from the atria to the ventricles. The mechanism of the sympathetic effect is increased I _Ca , which is responsible for the upstroke of the action potential in the AV node (as it is in the SA node). Thus increased I _Ca means increased inward current and increased conduction velocity. In a supportive role, the increased I _Ca shortens the ERP so that the AV nodal cells recover earlier from inactivation and can conduct action potentials at the increased firing rate.

Stimulation of the parasympathetic nervous system produces a decrease in conduction velocity through the AV node (negative dromotropic effect), which decreases the rate at which action potentials are conducted from the atria to the ventricles. The mechanism of the parasympathetic effect is a combination of decreased I _Ca (decreased inward current) and increased I _K-ACh (increased outward K ⁺ current, which further reduces net inward current). Additionally, the ERP of AV nodal cells is prolonged. If conduction velocity through the AV node is slowed sufficiently (e.g., by increased parasympathetic activity or by damage to the AV node), some action potentials may not be conducted at all from the atria to the ventricles, producing heart block. The degree of heart block may vary: In the milder forms, conduction of action potentials from atria to ventricles is simply slowed; in more severe cases, action potentials may not be conducted to the ventricles at all.

Mechanisms for changing contractility

Contractility correlates directly with the intracellular Ca ²⁺ concentration, which in turn depends on the amount of Ca ²⁺ released from sarcoplasmic reticulum stores during excitation-contraction coupling. The amount of Ca ²⁺ released from the sarcoplasmic reticulum depends on two factors: the size of the inward Ca ²⁺ current during the plateau of the myocardial action potential (the size of the trigger Ca ²⁺ ) and the amount of Ca ²⁺ previously stored in the sarcoplasmic reticulum for release. Therefore the larger the inward Ca ²⁺ current and the larger the intracellular stores, the greater the increase in intracellular Ca ²⁺ concentration and the greater the contractility.

Effects of the autonomic nervous system on contractility

The effects of the autonomic nervous system on contractility are summarized in Table 4.4 . Of these effects, the most important is the positive inotropic effect of the sympathetic nervous system.

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  Sympathetic nervous system. Stimulation of the sympathetic nervous system and circulating catecholamines have a positive inotropic effect on the myocardium (i.e., increased contractility). This positive inotropic effect has three important features: increased peak tension, increased rate of tension development, and faster rate of relaxation. Faster relaxation means that the contraction (twitch) is shorter, allowing more time for refilling. This effect, like the sympathetic effect on heart rate, is mediated via activation of β ₁ receptors, which are coupled via a G _s protein to adenylyl cyclase. Activation of adenylyl cyclase leads to the production of cyclic adenosine monophosphate (cAMP), activation of protein kinase A, and phosphorylation of proteins that produce the physiologic effect of increased contractility.

  • Two different proteins are phosphorylated to produce the increase in contractility. The coordinated actions of these phosphorylated proteins then produce an increase in intracellular Ca ²⁺ concentration. (1) There is phosphorylation of the sarcolemmal Ca ²⁺ channels that carry inward Ca ²⁺ current during the plateau of the action potential. As a result, there is increased inward Ca ²⁺ current during the plateau and increased trigger Ca ²⁺ , which increases the amount of Ca ²⁺ released from the sarcoplasmic reticulum. (2) There is phosphorylation of phospholamban, a protein that regulates Ca ²⁺ ATPase in the sarcoplasmic reticulum. Unphosphorylated phospholamban inhibits Ca ²⁺ ATPase. When phospholamban is phosphorylated by sympathetic stimulation, this inhibition is removed, Ca ²⁺ ATPase is stimulated, and there is greater uptake and storage of Ca ²⁺ by the sarcoplasmic reticulum. Increased Ca ²⁺ uptake by the sarcoplasmic reticulum has two effects: It causes faster relaxation (i.e., briefer contraction), and it increases the amount of stored Ca ²⁺ for release on subsequent beats.

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  Parasympathetic nervous system. Stimulation of the parasympathetic nervous system and ACh have a negative inotropic effect on the atria . This effect is mediated via muscarinic receptors, which are coupled via a G _i protein called G _K to adenylyl cyclase. Because the G protein in this case is inhibitory, contractility is decreased (opposite of the effect of activation of β ₁ receptors by catecholamines). Two factors are responsible for the decrease in atrial contractility caused by parasympathetic stimulation. (1) ACh decreases I _Ca and inward Ca ²⁺ current during the plateau of the action potential. (2) ACh increases I _K-ACh , thereby shortening the duration of action potential and, indirectly, decreasing the inward Ca ²⁺ current (by shortening the plateau phase). Together, these two effects decrease the amount of Ca ²⁺ entering atrial cells during the action potential, decrease the trigger Ca ²⁺ , and decrease the amount of Ca ²⁺ released from the sarcoplasmic reticulum.