INTRODUCTION
When is a piece of matter said to be alive? When it goes on "doing something," moving, exchanging material with its environment.
Erwin Schrodinger
The adult human being has an estimated 100 trillion cells that must go on exchanging material with the external environment to stay alive. To accomplish this, the circulatory system includes a vascular network that stretches more than 60,000 miles (more than twice the circumference of the Earth), and an average of 8000 liters of blood is pumped through this vascular network every day (1). This chapter describes the flow of blood through the circulatory system, and includes a description of flow through the heart (cardiac output) and flow through distant regions of the vascular circuit (peripheral blood flow). Most of these concepts are old friends from the physiology classroom, but this chapter applies them to actual practice at the bedside.
CARDIAC OUTPUT
Circulatory flow originates in the muscular contractions of the heart. Because blood is an incompressible fluid that flows through a closed hydraulic loop, the volume of blood ejected by the left side of the heart (in a given time period) must equal the volume of blood returning to the right side of the heart (over the same period of time). This reflection of the conservation of mass (volume) in a closed hydraulic system is known as the principle of continuity (2). It predicts that the volume flow of blood (volumetric flow rate), which is determined by the stroke output of the heart, will be the same at all points along the circulatory system. Therefore, the forces that determine cardiac stroke output also determine volumetric blood flow. The determinants of cardiac stroke output that can be measured or derived in a clinical setting are shown in Table 1.1. Each of these is described briefly in the paragraphs that follow.
PRELOAD
When a weight is attached to one end of a resting muscle, the muscle stretches to a new length. The weight in this situation represents a force called the preload, that is, the load imposed on a muscle before the onset of contraction. The preload force acts indirectly to augment the force of muscle contraction. That is, the preload force stretches the muscle to a new resting length and (according to the length-tension relationship of muscle) the increase in muscle length then leads to a more forceful muscle contraction.
Pressure-Volume Curves
In the intact heart, the stretch imposed on the cardiac muscle at rest is a function of the volume in the ventricles at the end of diastole. Therefore, ventricular end-diastolic volume (EDV) is used as a reflection of the preload force for the intact heart (3). The pressure-volume curves in Figure 1.1 describe the influence of preload on the mechanical performance of the left ventricle during diastole (lower curves) and systole (upper curves). The solid curves represent the normal pressure-volume relationships for diastole and systole. Note that the uppermost curve in the figure has a rapid ascent, indicating that small changes in diastolic volume are associated with large changes in systolic pressure. The normal relationship between diastolic volume (preload) and the strength of ventricular contraction was described independently by Otto Frank and Ernest Starling, and is commonly known as the Frank-Starling phenomenon (3). This relationship can be restated as follows:
In the normal heart, the diastolic volume (preload) is the principal force that governs the strength of ventricular contraction.
This indicates that the stroke output of the normal heart is primarily a reflection of the diastolic volume. Therefore, the most effective measure for preserving the cardiac output is to maintain an adequate diastolic volume. This emphasizes the value of avoiding hypovolemia and correcting volume deficits when they exist.
Ventricular Function Curves
Ventricular end-diastolic volume is not easily measured at the bedside, and the ventricular end-diastolic pressure (EDP) is more commonly used as a reflection of ventricular preload in clinical practice (see Chapter 11 for more information on end-diastolic pressure). The relationship between end-diastolic pressure (preload) and stroke volume (systolic performance) is used to monitor the Frank-Starling relationship in the clinical setting. The curves that define this relationship, known as ventricular function curves (4), are shown in Figure 1.2. Unfortunately, the interpretation of ventricular function curves can be misleading, as is demonstrated in the sections that follow.
Ventricular Compliance
The stretch imposed on cardiac muscle is determined not only by the volume of blood in the ventricular chambers, but also by the tendency of the ventricular wall to distend or stretch at any given chamber volume. This latter property is described as the compliance (distensibility) of the ventricle. Compliance is defined by the following relationship between changes in EDP and volume (EDV) (5):
Compliance= change EDV/change EDP
(1.1)
The lower curves in Figure 1.1 show the end-diastolic pressure-volume relationships for the normal ventricle and a noncompliant (stiff) ventricle. As the ventricle becomes less compliant (e.g., when the ventricle hypertrophies), there is less of a change in diastolic volume relative to the change in diastolic pressure. Early in this process, the EDV remains normal, but the EDP increases above normal. As the compliance decreases further, the increase in EDP eventually reduces venous inflow into the heart, thereby causing a reduction in EDV. The decrease in EDV then leads to a decrease in the force of ventricular contraction. This illustrates how changes in ventricular compliance can lead to changes in cardiac stroke output, and how changes in cardiac stroke output can be independent of changes in systolic function.
The decrease in stroke output that accompanies a decrease in ventricular compliance is known as diastolic heart failure (6). The difference between heart failure caused by systolic and diastolic dysfunction is presented in Chapter 16.
The Preload Measurement
Changes in ventricular compliance also influence the reliability of EDP as a reflection of EDV. For example, a decrease in ventricular compliance results in a higher-than-expected EDP at any given EDV. Therefore, the EDP overestimates the actual preload (EDV) when the ventricle is noncompliant. The following points are important to remember when EDP is used as an index of ventricular preload:
EDP provides an accurate reflection of preload only when ventricular compliance is normal. Changes in EDP provide an accurate reflection of changes in preload only when ventricular compliance is constant.
The influence of ventricular compliance on the assessment of preload surfaces again in Chapter 11. Chapter 16 describes the importance of an accurate preload measurement in distinguishing systolic from diastolic forms of heart failure.
AFTERLOAD
When a weight is attached to one end of a contracting muscle, the force of muscle contraction must overcome the opposing force of the weight before the muscle begins to shorten its length. The weight in this situation represents a force called the afterload, the load imposed on the muscle after the onset of contraction. The afterload is an opposing force that determines the force of muscle contraction needed to initiate muscle shortening (i.e., isotonic muscle contraction). In the intact heart, the afterload force is equivalent to the tension developed across the wall of the ventricles during systole (3).
The determinants of ventricular wall tension are derived from observations on soap bubbles made by the Marquis de Laplace in 1820. These observations were the basis for the law of Laplace, which states that the tension across a thin-walled sphere is directly related to the internal pressure and radius of the sphere: T = Pr. Because the ventricles are not thin-walled spheres, the Laplace relationship for the intact heart incorporates a factor that reflects the average thickness of the ventricular wall (5). The law of Laplace applied to the intact heart is then expressed as T = Pr/t, where T represents the tension across the wall of the ventricle during systole, P represents the transmural pressure across the ventricle at the end of systole, r represents the chamber radius at the end of diastole, and t represents the average thickness of the ventricular wall. The forces that contribute to ventricular wall tension are shown in Figure 1.3.
Pleural Pressures
Because afterload is a transmural force, it is influenced by the pleural pressures at the outer surface of heart. Negative pleural pressures increase transmural pressure and increase ventricular afterload, whereas positive pleural pressures have the opposite effect. Negative pressures surrounding the heart can impede ventricular emptying by opposing the inward displacement of the ventricular wall during systole (7). This action is responsible for the decrease in systolic blood pressure (reflecting a decrease in stroke volume) that occurs during the inspiratory phase of spontaneous breathing. When this inspiratory-related drop in pressure is greater than 15 mm Hg, the condition is called pulsus paradoxus (which is a misnomer, because the response is not paradoxical, but is an exaggerated version of the normal response).
Positive pleural pressures can promote ventricular emptying by facilitating the inward displacement of the ventricular wall during systole (7). Rapid and forceful rises in positive pressure surrounding the heart might also produce a massagelike action to expel blood from the heart and great vessels in the thorax. This is the proposed explanation for the success of cough CPR, which uses forceful coughing to maintain circulatory flow in patients with ventricular tachycardia (8). In fact, positive pleural pressure swings may be responsible for the hemodynamic effects of closed chest cardiac massage, as discussed in Chapter 18 (8).
Impedance versus Resistance
A major component of afterload is the resistance to ventricular outflow in the aorta and large, proximal arteries. The total hydraulic force that opposes pulsatile flow is known as impedance (9). This force is a combination of two forces: (a) a force that opposes the rate of change in flow, known as compliance, and (b) a force that opposes mean or volumetric flow, known as resistance. Vascular compliance is not easily measured at the bedside (10). On the other hand, vascular resistance is derived by assuming that hydraulic resistance is analogous to electrical resistance. That is, Ohm's law predicts that resistance to flow of an electric current (R) is directly proportional to the voltage drop across a circuit (E) and inversely proportional to the flow of current (I); R = E/I. The hydraulic analogy then states that resistance to the flow of fluid through a tube is directly proportional to the pressure drop along a tube (Pin - Pout), and inversely proportional to the flow of volume (Q):
R=Pin-Pout/
(1.2)
This relationship is applied to the systemic and pulmonary circulations, creating the following derivations:
SVR=(MAP-CVP)/C
(1.3)
Pulmonary vacular resistance (PVR) = (MAP - LAP)/C
(1.4)
where MABP is mean arterial blood pressure, CVP is central venous pressure, MPAP is mean pulmonary artery pressure, LAP is left-atrial pressure, and CO is the cardiac output. Vascular resistance is expressed in units of pressure and flow. Because the pressures are measured in mm Hg, the units would be mm Hg per mL/second. However, the dislike for expressing pressures in mm Hg has led to the common practice of expressing vascular resistance in CGS (centimeter-gram-second) units, or dynes ´ second/cm5. The conversion is dynes second/cm5 = 1333 ´ mm Hg/mL/second.
Clinical Monitoring
Although afterload is a combination of several forces that oppose ventricular emptying, most of the component forces of afterload cannot be measured easily or reliably at the bedside. As a result, the vascular resistance, derived as shown above, is often used as the sole measure of ventricular afterload. However, as might be expected, vascular resistance is not an accurate measure of total ventricular afterload (11).
A shift in the height and slope of the ventricular function curve could be an indirect marker of changes in afterload, as shown in Figure 1.2. However, shifts in the ventricular function curve can also be caused by changes in the contractile state of the myocardium, and because it is not possible to determine whether myocardial contractility is constant using bedside measurements, a shift in the position of ventricular function curves cannot be used as a marker of changes in afterload.
CONTRACTILITY
The contraction of striated muscle is attributed to interactions between contractile proteins arranged in parallel rows in the sarcomere. The number of bridges formed between adjacent rows of contractile elements determines the contractile state or contractility of the muscle fiber. The contractile state of a muscle is reflected by the force and velocity of muscle contraction (3).
The contractile state of cardiac muscle in the intact heart is reflected in the systolic performance of the ventricles. This is demonstrated in the upper curves in Figure 1.1. The systolic pressures in this figure reflect isovolumetric contraction (i.e., the pressures are generated before the aortic valve opens), which eliminates the influence of outflow impedance (afterload) on systolic pressure. Therefore, the changes in systolic pressure at any given diastolic volume (preload constant) reflect changes in the contractile state of the myocardium.
Clinical Monitoring
Changes in myocardial contractility alter the height and slope of the ventricular function curve, as demonstrated in Figure 1.2. However, as just mentioned, changes in the position of ventricular function curves can also be the result of changes in ventricular afterload. Therefore, because it is not possible to monitor afterload to determine whether it is constant, a shift in the ventricular functions curve is not a reliable method for detecting changes in myocardial contractility (4).
PERIPHERAL BLOOD FLOW
The cardiac stroke output travels through a vast array of vascular channels that can differ markedly in size. The focus of the remainder of the chapter is the factors that govern flow through these vascular channels.
Caution: The determinants of flow through vascular conduits are derived from idealized hydraulic models that differ considerably from the conditions that exist in the intact circulatory system. For example, the flow in small tubes usually is steady or nonpulsatile flow, and does not represent the continually changing pulsatile pattern of flow that occurs in many regions of the native circulation. Because of discrepancies like this, the description of blood flow that follows should be used more as a qualitative than quantitative description of the hydraulics of vascular flow.
FLOW IN RIGID TUBES
The hydraulic analogy of Ohm's law, as mentioned previously, states that steady volumetric flow (Q) through a rigid tube is proportional to the pressure gradient between the inlet and outlet of the tube (Pin - Pout), and the constant of proportionality is the hydraulic resistance to flow (R):
Q=(Pin-Pout) x 1/
(1.5)
The flow of fluids through small tubes was described independently by a German engineer (G. Hagen) and a French physician (J. Poiseuille), and their observations are combined in the equation shown below, called the Hagen-Poiseuille equation (12,13).
Q=(Pin-Pout) x (PiR4/8uL
(1.6)
This equation identifies the components of hydraulic resistance as the inner radius (r) and length of the tube (L), and the viscosity of the fluid (u). Because the final term in the Hagen-Poiseuille equation is the reciprocal of resistance (i.e., 1/R), the hydraulic resistance to steady, volumetric flow is expressed as
R=8uL/Pir
(1.7)
The components of the Hagen-Poisseuille equation are shown in the diagram in Figure 1.4. Note that flow varies according to the fourth power of the inner radius of the tube.
Thus, a twofold increase in the inner radius of the tube will result in a sixteenfold increase in flow: (2r)4 = 16 r. Flow varies much less with the other determinants of resistance; that is, a twofold increase in the length of the tube or the viscosity of the fluid results in a 50% decrease in flow rate. The influence of tube dimensions on flow rate has more practical applications as determinants of flow through vascular catheters, as presented in Chapter 4.
FLOW IN TUBES OF VARYING DIAMETER
The Hagen-Poisseuille equation predicts that as blood moves away from the heart and encounters vessels of decreasing diameter, the resistance to flow should increase and flow rate should decrease. However, the principle of continuity described earlier predicts that blood flow will be the same at all points along the vascular circuit. This apparent dilemma can be resolved by considering the relationship between flow velocity and cross-sectional area of a tube. For a rigid tube of varying diameter, the velocity of flow (v) at any point along the tube is directly proportional to the volumetric flow rate (Q) and inversely proportional to the cross-sectional area of the tube (A). These relationships are described below (2).
v=Q/
(1.8)
If flow is constant, a decrease in the cross-sectional area of a tube results in an increase in the velocity of flow. This is how the nozzle on a garden hose works, and is the rationale for jet ventilation.
Equation 1.8 can be rearranged to yield the relationship Q = v ´ A. This relationship indicates that proportional changes in velocity and cross-sectional area in opposite directions result in a constant volume flow rate. This means that blood flow can remain unchanged in blood vessels of diminishing diameter if there are equal and opposite changes in the velocity of flow and the cross-sectional area of the vessels. The trick here is to use the total cross-sectional area of the vessels in a region rather than the cross-sectional area of individual vessels. This resolves the discrepancy between the principle of continuity and the Hagen-Poiseuille relationships.
Circulatory Design
The graph in Figure 1.5 shows the changes in flow velocity and cross-sectional area in different regions of the circulation (13). As expected, when blood moves toward the periphery, there are proportionate and reciprocal changes in cross-sectional area and velocity of flow. The high velocity of flow in the proximal arteries seems well suited for delivering blood quickly to the microcirculation, to allow more time for diffusional exchange with the tissues. The low velocity and large cross-sectional area in the capillaries are also well-suited for diffusional exchange. These features show a rational design in the circulatory system.
FLOW IN COLLAPSIBLE TUBES
The hydraulic relationships described above apply to flow through rigid tubes, but blood vessels are not rigid tubes. The determinants of flow in collapsible tubes are explained with the aid of the apparatus shown in Figure 1.6 (14). The apparatus shows a tube with collapsible walls passing through a fluid reservoir. The height of the fluid in the reservoir can be adjusted to vary the external pressure on the tube. As mentioned earlier, flow in a rigid tube is proportional to the pressure difference between the inlet and outlet of the tube (Pin - Pout). This is also the case in collapsible tubes as long as the external pressure is not high enough to compress the tube. However, as shown in Figure 1.6, when the external pressure exceeds the outlet pressure (Pext > Pout) and compresses the tube, the driving force for flow is pressure difference between the inlet pressure and the external pressure (Pin - Pext). In this situation, the driving pressure for flow is independent of the pressure gradient along the tube.
The Pulmonary Circulation
Vascular compression has been demonstrated in the cerebral, pulmonary, and systemic circulations. Extravascular compression is a particular concern in patients who require positive-pressure mechanical ventilation (14). In this situation, pressures in the alveoli can exceed pressures in the underlying pulmonary capillaries, and the resultant capillary compression changes the driving force for flow across the lungs, as illustrated in Figure 1.6. Thus, whereas the normal driving pressure for flow across the lungs is the difference between the mean pulmonary artery pressure and the left-atrial pressure (PAP - LAP), the driving pressure for flow when pulmonary capillaries are compressed is the difference between the pulmonary artery pressure and the alveolar pressure (PAP - Palv). The pulmonary vascular resistance (PVR) will then differ as follows:
Normal: PVR=PAP-LAP/C
(1.9)
when Palv>LAP: PVR=PAP-Palv/C
(1.10)
The problems created by vascular compression in the lungs are discussed in Chapters 11 and 26.
VISCOSITY
Solids resist being deformed (changing shape), whereas fluids deform continuously (i.e., flow) but resist changes in the rate of deformation (i.e., the flow rate). The inherent resistance of a fluid to changes in flow rate is expressed as the viscosity of the fluid (12,15). When a force is applied that changes flow rate (i.e., a shear force), the change in flow rate varies inversely with the viscosity of the fluid. Thus, as the viscosity of a fluid increases, the fluid flows less rapidly in response to a shear force. The influence of viscosity is easily demonstrated by comparing the flow of molasses (high viscosity) and the flow of water (low viscosity) when the force of gravity is applied (i.e., when both are spilled).
Blood Viscosity
The viscosity of whole blood is determined by the number and strength of interactions between plasma fibrinogen and the circulating erythrocytes (15,16). The concentration of circulating erythrocytes (i.e., the hematocrit) is the principal determinant of whole blood viscosity. The relationship between hematocrit and blood viscosity is shown in Table 1.2. Note that viscosity is expressed in absolute units (centipoise) and also as a relative value (the ratio of blood viscosity to the viscosity of water). Whole blood with a normal hematocrit (i.e., 40%) has a viscosity that is three to four times higher than that of water. Thus, to move whole blood with a normal hematocrit, the circulatory system must generate a pressure that is three to four times higher than the pressure needed to move water the same distance. The acellular blood (zero hematocrit) in Table 1.2 is equivalent to plasma, and has a viscosity that more closely approximates the viscosity of water. Thus, moving plasma does not require nearly the work involved in moving whole blood. This difference in work load can have significant implications in the patient with coronary disease or limited cardiac reserve.
Other factors that influence viscosity are body temperature and the flow rate (16). Viscosity rises in response to decreases in temperature and flow rate. The increase in blood viscosity in low flow states might represent an adaptive response aimed at promoting coagulation at sites of hemorrhage (15). However, the rise in viscosity can also serve to further reduce blood flow and thereby provoke ischemic injury. The tendency of viscosity to increase with decreases in blood flow is a potential problem in the ICU patient population, and deserves further study.
Hemodynamic Effects
The Hagen-Poisseuille equation predicts that (all other variables constant) blood flow will change in the same proportion as the change in blood viscosity; that is, if viscosity is reduced by one-half, blood flow will double (15).
The graph in Figure 1.7 demonstrates the hemodynamic effects of a progressive decrease in blood viscosity. In this case, the subject was an elderly male with secondary polycythemia, and the reduction in viscosity was achieved by progressive (isovolemic) hemodilution. As shown in the graph, the progressive reduction in hematocrit was associated with a progressive rise in cardiac output. The disproportionate improvement in cardiac output may be caused by the fact that low flow rates can increase viscosity, and thus an increase in flow could itself produce a further increase in flow. The ability to modulate blood flow by manipulating the hematocrit is presented in more detail in Chapter 44.
Clinical Monitoring
Viscosity is measured by placing a fluid sample between two parallel plates that are sliding past each other, and recording the resistance or "stickiness" in the movement of the plates. The instrument that performs this task is called a viscometer. The units of measurement for viscosity are the poise (or dyne ´ second/cm2) in the CGS system, and the pascal second (Pa s) in the SI system. To convert units, use the relationship 1 poise = 0.1 Pa s. Viscosity is also expressed in relative terms (relative to the viscosity of water), a method that may be preferred for its simplicity.
The major drawback in monitoring viscosity is the tendency of viscosity to vary with changes in temperature, hematocrit, and flow rate. As a result, local conditions in the microcirculation can produce changes in blood viscosity that will go undetected in the in vitro (viscometer) measurement of viscosity. In states of adequate blood flow, the measurement is considered to be reasonably accurate. However, for the critically ill patient with suspected low flow who might benefit from measurements of blood viscosity, the reliability of the measurement is likely to be uncertain. A more feasible application of the viscosity measurement would be to monitor the effects of packed cell transfusions on blood viscosity to determine the point at which hemoconcentration can be counterproductive in individual patients.
When is a piece of matter said to be alive? When it goes on "doing something," moving, exchanging material with its environment.
Erwin Schrodinger
The adult human being has an estimated 100 trillion cells that must go on exchanging material with the external environment to stay alive. To accomplish this, the circulatory system includes a vascular network that stretches more than 60,000 miles (more than twice the circumference of the Earth), and an average of 8000 liters of blood is pumped through this vascular network every day (1). This chapter describes the flow of blood through the circulatory system, and includes a description of flow through the heart (cardiac output) and flow through distant regions of the vascular circuit (peripheral blood flow). Most of these concepts are old friends from the physiology classroom, but this chapter applies them to actual practice at the bedside.
CARDIAC OUTPUT
Circulatory flow originates in the muscular contractions of the heart. Because blood is an incompressible fluid that flows through a closed hydraulic loop, the volume of blood ejected by the left side of the heart (in a given time period) must equal the volume of blood returning to the right side of the heart (over the same period of time). This reflection of the conservation of mass (volume) in a closed hydraulic system is known as the principle of continuity (2). It predicts that the volume flow of blood (volumetric flow rate), which is determined by the stroke output of the heart, will be the same at all points along the circulatory system. Therefore, the forces that determine cardiac stroke output also determine volumetric blood flow. The determinants of cardiac stroke output that can be measured or derived in a clinical setting are shown in Table 1.1. Each of these is described briefly in the paragraphs that follow.
PRELOAD
When a weight is attached to one end of a resting muscle, the muscle stretches to a new length. The weight in this situation represents a force called the preload, that is, the load imposed on a muscle before the onset of contraction. The preload force acts indirectly to augment the force of muscle contraction. That is, the preload force stretches the muscle to a new resting length and (according to the length-tension relationship of muscle) the increase in muscle length then leads to a more forceful muscle contraction.
Pressure-Volume Curves
In the intact heart, the stretch imposed on the cardiac muscle at rest is a function of the volume in the ventricles at the end of diastole. Therefore, ventricular end-diastolic volume (EDV) is used as a reflection of the preload force for the intact heart (3). The pressure-volume curves in Figure 1.1 describe the influence of preload on the mechanical performance of the left ventricle during diastole (lower curves) and systole (upper curves). The solid curves represent the normal pressure-volume relationships for diastole and systole. Note that the uppermost curve in the figure has a rapid ascent, indicating that small changes in diastolic volume are associated with large changes in systolic pressure. The normal relationship between diastolic volume (preload) and the strength of ventricular contraction was described independently by Otto Frank and Ernest Starling, and is commonly known as the Frank-Starling phenomenon (3). This relationship can be restated as follows:
In the normal heart, the diastolic volume (preload) is the principal force that governs the strength of ventricular contraction.
This indicates that the stroke output of the normal heart is primarily a reflection of the diastolic volume. Therefore, the most effective measure for preserving the cardiac output is to maintain an adequate diastolic volume. This emphasizes the value of avoiding hypovolemia and correcting volume deficits when they exist.
Ventricular Function Curves
Ventricular end-diastolic volume is not easily measured at the bedside, and the ventricular end-diastolic pressure (EDP) is more commonly used as a reflection of ventricular preload in clinical practice (see Chapter 11 for more information on end-diastolic pressure). The relationship between end-diastolic pressure (preload) and stroke volume (systolic performance) is used to monitor the Frank-Starling relationship in the clinical setting. The curves that define this relationship, known as ventricular function curves (4), are shown in Figure 1.2. Unfortunately, the interpretation of ventricular function curves can be misleading, as is demonstrated in the sections that follow.
Ventricular Compliance
The stretch imposed on cardiac muscle is determined not only by the volume of blood in the ventricular chambers, but also by the tendency of the ventricular wall to distend or stretch at any given chamber volume. This latter property is described as the compliance (distensibility) of the ventricle. Compliance is defined by the following relationship between changes in EDP and volume (EDV) (5):
Compliance= change EDV/change EDP
(1.1)
The lower curves in Figure 1.1 show the end-diastolic pressure-volume relationships for the normal ventricle and a noncompliant (stiff) ventricle. As the ventricle becomes less compliant (e.g., when the ventricle hypertrophies), there is less of a change in diastolic volume relative to the change in diastolic pressure. Early in this process, the EDV remains normal, but the EDP increases above normal. As the compliance decreases further, the increase in EDP eventually reduces venous inflow into the heart, thereby causing a reduction in EDV. The decrease in EDV then leads to a decrease in the force of ventricular contraction. This illustrates how changes in ventricular compliance can lead to changes in cardiac stroke output, and how changes in cardiac stroke output can be independent of changes in systolic function.
The decrease in stroke output that accompanies a decrease in ventricular compliance is known as diastolic heart failure (6). The difference between heart failure caused by systolic and diastolic dysfunction is presented in Chapter 16.
The Preload Measurement
Changes in ventricular compliance also influence the reliability of EDP as a reflection of EDV. For example, a decrease in ventricular compliance results in a higher-than-expected EDP at any given EDV. Therefore, the EDP overestimates the actual preload (EDV) when the ventricle is noncompliant. The following points are important to remember when EDP is used as an index of ventricular preload:
EDP provides an accurate reflection of preload only when ventricular compliance is normal. Changes in EDP provide an accurate reflection of changes in preload only when ventricular compliance is constant.
The influence of ventricular compliance on the assessment of preload surfaces again in Chapter 11. Chapter 16 describes the importance of an accurate preload measurement in distinguishing systolic from diastolic forms of heart failure.
AFTERLOAD
When a weight is attached to one end of a contracting muscle, the force of muscle contraction must overcome the opposing force of the weight before the muscle begins to shorten its length. The weight in this situation represents a force called the afterload, the load imposed on the muscle after the onset of contraction. The afterload is an opposing force that determines the force of muscle contraction needed to initiate muscle shortening (i.e., isotonic muscle contraction). In the intact heart, the afterload force is equivalent to the tension developed across the wall of the ventricles during systole (3).
The determinants of ventricular wall tension are derived from observations on soap bubbles made by the Marquis de Laplace in 1820. These observations were the basis for the law of Laplace, which states that the tension across a thin-walled sphere is directly related to the internal pressure and radius of the sphere: T = Pr. Because the ventricles are not thin-walled spheres, the Laplace relationship for the intact heart incorporates a factor that reflects the average thickness of the ventricular wall (5). The law of Laplace applied to the intact heart is then expressed as T = Pr/t, where T represents the tension across the wall of the ventricle during systole, P represents the transmural pressure across the ventricle at the end of systole, r represents the chamber radius at the end of diastole, and t represents the average thickness of the ventricular wall. The forces that contribute to ventricular wall tension are shown in Figure 1.3.
Pleural Pressures
Because afterload is a transmural force, it is influenced by the pleural pressures at the outer surface of heart. Negative pleural pressures increase transmural pressure and increase ventricular afterload, whereas positive pleural pressures have the opposite effect. Negative pressures surrounding the heart can impede ventricular emptying by opposing the inward displacement of the ventricular wall during systole (7). This action is responsible for the decrease in systolic blood pressure (reflecting a decrease in stroke volume) that occurs during the inspiratory phase of spontaneous breathing. When this inspiratory-related drop in pressure is greater than 15 mm Hg, the condition is called pulsus paradoxus (which is a misnomer, because the response is not paradoxical, but is an exaggerated version of the normal response).
Positive pleural pressures can promote ventricular emptying by facilitating the inward displacement of the ventricular wall during systole (7). Rapid and forceful rises in positive pressure surrounding the heart might also produce a massagelike action to expel blood from the heart and great vessels in the thorax. This is the proposed explanation for the success of cough CPR, which uses forceful coughing to maintain circulatory flow in patients with ventricular tachycardia (8). In fact, positive pleural pressure swings may be responsible for the hemodynamic effects of closed chest cardiac massage, as discussed in Chapter 18 (8).
Impedance versus Resistance
A major component of afterload is the resistance to ventricular outflow in the aorta and large, proximal arteries. The total hydraulic force that opposes pulsatile flow is known as impedance (9). This force is a combination of two forces: (a) a force that opposes the rate of change in flow, known as compliance, and (b) a force that opposes mean or volumetric flow, known as resistance. Vascular compliance is not easily measured at the bedside (10). On the other hand, vascular resistance is derived by assuming that hydraulic resistance is analogous to electrical resistance. That is, Ohm's law predicts that resistance to flow of an electric current (R) is directly proportional to the voltage drop across a circuit (E) and inversely proportional to the flow of current (I); R = E/I. The hydraulic analogy then states that resistance to the flow of fluid through a tube is directly proportional to the pressure drop along a tube (Pin - Pout), and inversely proportional to the flow of volume (Q):
R=Pin-Pout/
(1.2)
This relationship is applied to the systemic and pulmonary circulations, creating the following derivations:
SVR=(MAP-CVP)/C
(1.3)
Pulmonary vacular resistance (PVR) = (MAP - LAP)/C
(1.4)
where MABP is mean arterial blood pressure, CVP is central venous pressure, MPAP is mean pulmonary artery pressure, LAP is left-atrial pressure, and CO is the cardiac output. Vascular resistance is expressed in units of pressure and flow. Because the pressures are measured in mm Hg, the units would be mm Hg per mL/second. However, the dislike for expressing pressures in mm Hg has led to the common practice of expressing vascular resistance in CGS (centimeter-gram-second) units, or dynes ´ second/cm5. The conversion is dynes second/cm5 = 1333 ´ mm Hg/mL/second.
Clinical Monitoring
Although afterload is a combination of several forces that oppose ventricular emptying, most of the component forces of afterload cannot be measured easily or reliably at the bedside. As a result, the vascular resistance, derived as shown above, is often used as the sole measure of ventricular afterload. However, as might be expected, vascular resistance is not an accurate measure of total ventricular afterload (11).
A shift in the height and slope of the ventricular function curve could be an indirect marker of changes in afterload, as shown in Figure 1.2. However, shifts in the ventricular function curve can also be caused by changes in the contractile state of the myocardium, and because it is not possible to determine whether myocardial contractility is constant using bedside measurements, a shift in the position of ventricular function curves cannot be used as a marker of changes in afterload.
CONTRACTILITY
The contraction of striated muscle is attributed to interactions between contractile proteins arranged in parallel rows in the sarcomere. The number of bridges formed between adjacent rows of contractile elements determines the contractile state or contractility of the muscle fiber. The contractile state of a muscle is reflected by the force and velocity of muscle contraction (3).
The contractile state of cardiac muscle in the intact heart is reflected in the systolic performance of the ventricles. This is demonstrated in the upper curves in Figure 1.1. The systolic pressures in this figure reflect isovolumetric contraction (i.e., the pressures are generated before the aortic valve opens), which eliminates the influence of outflow impedance (afterload) on systolic pressure. Therefore, the changes in systolic pressure at any given diastolic volume (preload constant) reflect changes in the contractile state of the myocardium.
Clinical Monitoring
Changes in myocardial contractility alter the height and slope of the ventricular function curve, as demonstrated in Figure 1.2. However, as just mentioned, changes in the position of ventricular function curves can also be the result of changes in ventricular afterload. Therefore, because it is not possible to monitor afterload to determine whether it is constant, a shift in the ventricular functions curve is not a reliable method for detecting changes in myocardial contractility (4).
PERIPHERAL BLOOD FLOW
The cardiac stroke output travels through a vast array of vascular channels that can differ markedly in size. The focus of the remainder of the chapter is the factors that govern flow through these vascular channels.
Caution: The determinants of flow through vascular conduits are derived from idealized hydraulic models that differ considerably from the conditions that exist in the intact circulatory system. For example, the flow in small tubes usually is steady or nonpulsatile flow, and does not represent the continually changing pulsatile pattern of flow that occurs in many regions of the native circulation. Because of discrepancies like this, the description of blood flow that follows should be used more as a qualitative than quantitative description of the hydraulics of vascular flow.
FLOW IN RIGID TUBES
The hydraulic analogy of Ohm's law, as mentioned previously, states that steady volumetric flow (Q) through a rigid tube is proportional to the pressure gradient between the inlet and outlet of the tube (Pin - Pout), and the constant of proportionality is the hydraulic resistance to flow (R):
Q=(Pin-Pout) x 1/
(1.5)
The flow of fluids through small tubes was described independently by a German engineer (G. Hagen) and a French physician (J. Poiseuille), and their observations are combined in the equation shown below, called the Hagen-Poiseuille equation (12,13).
Q=(Pin-Pout) x (PiR4/8uL
(1.6)
This equation identifies the components of hydraulic resistance as the inner radius (r) and length of the tube (L), and the viscosity of the fluid (u). Because the final term in the Hagen-Poiseuille equation is the reciprocal of resistance (i.e., 1/R), the hydraulic resistance to steady, volumetric flow is expressed as
R=8uL/Pir
(1.7)
The components of the Hagen-Poisseuille equation are shown in the diagram in Figure 1.4. Note that flow varies according to the fourth power of the inner radius of the tube.
Thus, a twofold increase in the inner radius of the tube will result in a sixteenfold increase in flow: (2r)4 = 16 r. Flow varies much less with the other determinants of resistance; that is, a twofold increase in the length of the tube or the viscosity of the fluid results in a 50% decrease in flow rate. The influence of tube dimensions on flow rate has more practical applications as determinants of flow through vascular catheters, as presented in Chapter 4.
FLOW IN TUBES OF VARYING DIAMETER
The Hagen-Poisseuille equation predicts that as blood moves away from the heart and encounters vessels of decreasing diameter, the resistance to flow should increase and flow rate should decrease. However, the principle of continuity described earlier predicts that blood flow will be the same at all points along the vascular circuit. This apparent dilemma can be resolved by considering the relationship between flow velocity and cross-sectional area of a tube. For a rigid tube of varying diameter, the velocity of flow (v) at any point along the tube is directly proportional to the volumetric flow rate (Q) and inversely proportional to the cross-sectional area of the tube (A). These relationships are described below (2).
v=Q/
(1.8)
If flow is constant, a decrease in the cross-sectional area of a tube results in an increase in the velocity of flow. This is how the nozzle on a garden hose works, and is the rationale for jet ventilation.
Equation 1.8 can be rearranged to yield the relationship Q = v ´ A. This relationship indicates that proportional changes in velocity and cross-sectional area in opposite directions result in a constant volume flow rate. This means that blood flow can remain unchanged in blood vessels of diminishing diameter if there are equal and opposite changes in the velocity of flow and the cross-sectional area of the vessels. The trick here is to use the total cross-sectional area of the vessels in a region rather than the cross-sectional area of individual vessels. This resolves the discrepancy between the principle of continuity and the Hagen-Poiseuille relationships.
Circulatory Design
The graph in Figure 1.5 shows the changes in flow velocity and cross-sectional area in different regions of the circulation (13). As expected, when blood moves toward the periphery, there are proportionate and reciprocal changes in cross-sectional area and velocity of flow. The high velocity of flow in the proximal arteries seems well suited for delivering blood quickly to the microcirculation, to allow more time for diffusional exchange with the tissues. The low velocity and large cross-sectional area in the capillaries are also well-suited for diffusional exchange. These features show a rational design in the circulatory system.
FLOW IN COLLAPSIBLE TUBES
The hydraulic relationships described above apply to flow through rigid tubes, but blood vessels are not rigid tubes. The determinants of flow in collapsible tubes are explained with the aid of the apparatus shown in Figure 1.6 (14). The apparatus shows a tube with collapsible walls passing through a fluid reservoir. The height of the fluid in the reservoir can be adjusted to vary the external pressure on the tube. As mentioned earlier, flow in a rigid tube is proportional to the pressure difference between the inlet and outlet of the tube (Pin - Pout). This is also the case in collapsible tubes as long as the external pressure is not high enough to compress the tube. However, as shown in Figure 1.6, when the external pressure exceeds the outlet pressure (Pext > Pout) and compresses the tube, the driving force for flow is pressure difference between the inlet pressure and the external pressure (Pin - Pext). In this situation, the driving pressure for flow is independent of the pressure gradient along the tube.
The Pulmonary Circulation
Vascular compression has been demonstrated in the cerebral, pulmonary, and systemic circulations. Extravascular compression is a particular concern in patients who require positive-pressure mechanical ventilation (14). In this situation, pressures in the alveoli can exceed pressures in the underlying pulmonary capillaries, and the resultant capillary compression changes the driving force for flow across the lungs, as illustrated in Figure 1.6. Thus, whereas the normal driving pressure for flow across the lungs is the difference between the mean pulmonary artery pressure and the left-atrial pressure (PAP - LAP), the driving pressure for flow when pulmonary capillaries are compressed is the difference between the pulmonary artery pressure and the alveolar pressure (PAP - Palv). The pulmonary vascular resistance (PVR) will then differ as follows:
Normal: PVR=PAP-LAP/C
(1.9)
when Palv>LAP: PVR=PAP-Palv/C
(1.10)
The problems created by vascular compression in the lungs are discussed in Chapters 11 and 26.
VISCOSITY
Solids resist being deformed (changing shape), whereas fluids deform continuously (i.e., flow) but resist changes in the rate of deformation (i.e., the flow rate). The inherent resistance of a fluid to changes in flow rate is expressed as the viscosity of the fluid (12,15). When a force is applied that changes flow rate (i.e., a shear force), the change in flow rate varies inversely with the viscosity of the fluid. Thus, as the viscosity of a fluid increases, the fluid flows less rapidly in response to a shear force. The influence of viscosity is easily demonstrated by comparing the flow of molasses (high viscosity) and the flow of water (low viscosity) when the force of gravity is applied (i.e., when both are spilled).
Blood Viscosity
The viscosity of whole blood is determined by the number and strength of interactions between plasma fibrinogen and the circulating erythrocytes (15,16). The concentration of circulating erythrocytes (i.e., the hematocrit) is the principal determinant of whole blood viscosity. The relationship between hematocrit and blood viscosity is shown in Table 1.2. Note that viscosity is expressed in absolute units (centipoise) and also as a relative value (the ratio of blood viscosity to the viscosity of water). Whole blood with a normal hematocrit (i.e., 40%) has a viscosity that is three to four times higher than that of water. Thus, to move whole blood with a normal hematocrit, the circulatory system must generate a pressure that is three to four times higher than the pressure needed to move water the same distance. The acellular blood (zero hematocrit) in Table 1.2 is equivalent to plasma, and has a viscosity that more closely approximates the viscosity of water. Thus, moving plasma does not require nearly the work involved in moving whole blood. This difference in work load can have significant implications in the patient with coronary disease or limited cardiac reserve.
Other factors that influence viscosity are body temperature and the flow rate (16). Viscosity rises in response to decreases in temperature and flow rate. The increase in blood viscosity in low flow states might represent an adaptive response aimed at promoting coagulation at sites of hemorrhage (15). However, the rise in viscosity can also serve to further reduce blood flow and thereby provoke ischemic injury. The tendency of viscosity to increase with decreases in blood flow is a potential problem in the ICU patient population, and deserves further study.
Hemodynamic Effects
The Hagen-Poisseuille equation predicts that (all other variables constant) blood flow will change in the same proportion as the change in blood viscosity; that is, if viscosity is reduced by one-half, blood flow will double (15).
The graph in Figure 1.7 demonstrates the hemodynamic effects of a progressive decrease in blood viscosity. In this case, the subject was an elderly male with secondary polycythemia, and the reduction in viscosity was achieved by progressive (isovolemic) hemodilution. As shown in the graph, the progressive reduction in hematocrit was associated with a progressive rise in cardiac output. The disproportionate improvement in cardiac output may be caused by the fact that low flow rates can increase viscosity, and thus an increase in flow could itself produce a further increase in flow. The ability to modulate blood flow by manipulating the hematocrit is presented in more detail in Chapter 44.
Clinical Monitoring
Viscosity is measured by placing a fluid sample between two parallel plates that are sliding past each other, and recording the resistance or "stickiness" in the movement of the plates. The instrument that performs this task is called a viscometer. The units of measurement for viscosity are the poise (or dyne ´ second/cm2) in the CGS system, and the pascal second (Pa s) in the SI system. To convert units, use the relationship 1 poise = 0.1 Pa s. Viscosity is also expressed in relative terms (relative to the viscosity of water), a method that may be preferred for its simplicity.
The major drawback in monitoring viscosity is the tendency of viscosity to vary with changes in temperature, hematocrit, and flow rate. As a result, local conditions in the microcirculation can produce changes in blood viscosity that will go undetected in the in vitro (viscometer) measurement of viscosity. In states of adequate blood flow, the measurement is considered to be reasonably accurate. However, for the critically ill patient with suspected low flow who might benefit from measurements of blood viscosity, the reliability of the measurement is likely to be uncertain. A more feasible application of the viscosity measurement would be to monitor the effects of packed cell transfusions on blood viscosity to determine the point at which hemoconcentration can be counterproductive in individual patients.
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