Answers to Study Questions

R ∝ 1/r4

Thus,

Rbefore ∝ 1/(rbefore)4

Rafter ∝ 1/(1.1rbefore)4 = [1/(1.1)4][1/(rbefore)4] = (1/1.46)Rbefore = 0.68 Rbefore

Therefore, a 10% increase in vessel radius will reduce its resistance by 32%.

b. Because Q̇ = ΔP/R, and Rafter = 0.68 Rbefore

Q̇after = ΔP/0.68 Rbefore

… and for a given ΔP…

Q̇after = 1/0.68 Rbefore = 1.46 Q̇before

Therefore, for a given ΔP, a 10% increase in vessel diameter will increase flow by 46%.

[Note: One must always use change factors NOT percentage changes in these equations.]

b. Wrong! The right and left hearts are served by a common electrical excitation system and therefore beat at the same rate.

c. Wrong! Although it is true that the right ventricle is less muscular than the left, that fact does not explain why pulmonary pressure is so low. Actually, it is the other way around: because pulmonary arterial pressure is low, the right ventricle does not have to be very muscular to pump blood into the lungs.

d. Right! ΔP = Q̇ × R. Because Q̇ is the same (= CO) through the lungs and the systemic circulation, the only way pulmonary arterial pressure could be relatively low is for pulmonary vascular resistance to be relatively low.

e. Wrong! CO = HR × SV. CO and HR are the same for both the right and left pumps. Therefore, the SV of the right ventricle must be equal to that of the left.

f. This is a complete cop-out for a reasoned explanation!

Ġm = Q̇ × ([G]a − [G]v)

Thus,

Ġm = 60 mL/min × (50 – 30) mg/100 mL = 12 mg/min

1. An electrical arrhythmia would obviously influence heart rate. Depending on the nature of the arrhythmia, HR might be high or low. Because CO = HR × (EDV – ESV) a low HR would tend to reduce CO, whereas a high HR, in and off itself, would do the opposite. In some cases where the HR is extremely high, a counteracting influence of decreased EDV volume may develop because of decreased diastolic filling time. Certain arrhythmias cause the individual ventricular muscle cells not to contract in unison. To develop high pressure in the ventricular chamber, the cells in the ventricular wall must be contracting at the same time. When they do not do so, ventricular ejection is impaired and ESV increases as a result.

2. A “stenotic” valve has an abnormally high resistance to flow when it is supposed to be fully open. A stenotic input valve impedes diastolic filling and reduces EDV. A stenotic output valve impedes ventricular ejection and tends to increase ESV.

3. An “insufficient” valve allows backward flow when it is supposed to be closed. An insufficient inlet valve adversely affects effective SV because some of the volume that the ventricle “pumps” during systole goes backwards into the atria. An insufficient outlet valve adversely affects effective stroke volume because some of the volume that the ventricle pumps out during systole leaks back into the ventricle during diastole.

4. When the heart muscle cells themselves are “failing,” they have diminished ability to generate pressure within the ventricle during systole. This ultimately results in increased ESV.

5. “Inadequate diastolic filling” is just another way of saying, “decreased EDV”. One commonly encountered situation where this occurs is with extreme blood loss.

b. Because the resting membrane is most permeable to K+, the resting membrane potential is always close to the K+ equilibrium potential. Lowering the absolute value of the K+ equilibrium potential will undoubtedly also lower the absolute resting membrane potential (ie, depolarize the cells).

c. Two things can happen when the resting membrane potential is decreased: (1) the potential is closer to the threshold potential, which should increase excitability; and (2) the fast sodium channels become inactivated, making the cell less excitable. Thus, small increases in [K+]o may increase excitability, whereas large increases in [K+]o decrease excitability.

b. Calcium channel blockers slow the firing rate of SA nodal cells by blocking the calcium component of the diastolic depolarization. They will reduce the rate of rise of the AV nodal cell action potential (which is largely due to calcium entry into the cells) and slow the rate of conduction through the AV node. In addition, calcium channel blockers will decrease the amount of calcium made available to the contractile machinery during excitation–contraction coupling and thus will decrease the tension-producing capabilities of the cardiac muscle cell.

c. Potassium channel blockers inhibit the delayed increase in potassium permeability that contributes importantly to the initiation and rate of repolarization of the cardiac myocyte. This prolongs the duration of the plateau phase of the action potential, prolongs the QT interval of the ECG, and prolongs the effective refractory period of the cell.

This is a high resting cardiac output but may be normal during exercise.

b. Pulmonic valve stenosis will increase the right ventricular pressure development during systole, which will promote right ventricular hypertrophy. The increased muscle mass on the right will be reflected as a shift in the net electrical dipole to the right during ventricular depolarization. Tricuspid valve regurgitation does not increase right ventricular pressures or stimulate cardiac muscle hypertrophy.

c. No. Neither pulmonic stenosis nor tricuspid regurgitation will cause elevation in pulmonary vascular pressures or pulmonary edema. If anything, congestion from malfunction of either of these valves on the right side will appear upstream in the systemic system as swollen ankles or as ascites (fluid in the abdominal space).

b. Mitral stenosis produces a significant pressure difference between the left atrium and the left ventricle during diastole (a time when this valve normally should be widely open).

Ḟ = K [(Pc − Pi) − (πc − πi)]

then

Ḟ = K [28 − (−4) − 24 + 0] mm Hg = K × 8 mm Hg

The result is positive, indicating net movement of fluid out of the capillaries.

Then by the series resistance equation,

Rn = Re + Rp = 3 Re/2

b. Since more resistance precedes the junction (Re) than follows it (Re/2), Pj will be closer to Po than to Pi.

c. The flow through the network (which equals the flow through the inlet vessel) is

The pressure drop across the inlet vessel is equal to its resistance times the flow through it

then

and

Therefore,

a decrease in renal resistance must increase 1/TPR and therefore decrease TPR. When the resistance of any single peripheral organ changes, TPR changes in the same direction.

b. Recall that CO = HR × SV. HR increased by a factor of 2 (from 70 to 140 beats/min) during exercise, and because SV increased by a factor of about 1.15, cardiac output must have increased by approximately 130%. [2.0 (1.15) = 2.3 times the original level.]

c. Recall that TPR =

Thus, total peripheral resistance must have decreased by approximately 55% (1.13/2.3 = 0.45 of the original level).

Step 2. The arterial baroreceptor firing rate will decrease, which will increase sympathetic nerve activity from the medullary CV centers.

Step 3. The heart rate and cardiac output will reflexly increase because of the cardiac effects of the increased sympathetic activity on β1-adrenergic receptors. Total peripheral resistance will not be improved by the increase in sympathetic drive because the drug has blocked the α1-adrenergic receptors.

Step 4. The cardiac function curve will shift upward, but the venous return curve will not shift, because the α-receptor blockade blocks the effect of increased sympathetic activity on the veins. Consequently, central venous pressure will be lower than normal (see Figure 8–6).

b and c elicit set point–increasing inputs to the medullary cardiovascular system that result in a higher-than-normal sympathetic output for any given level of input from the arterial baroreceptors. Thus in the presence of these disturbances, the system will operate at higher-than-normal mean arterial pressure and sympathetic activity.

1. The heart rate during exercise is well above the intrinsic rate (≃100 beats/min). This indicates activation of the cardiac sympathetic nerves because withdrawal of cardiac parasympathetic activity cannot increase the heart rate above the intrinsic rate (Chapter 2).

2. Increased arterial pulse pressure and ejection fraction at constant central venous pressure indicate increased stroke volume and cardiac contractility and thus increased activity of cardiac sympathetic nerves (Chapter 3).

3. Decreased renal and splanchnic blood flows in spite of increased mean arterial pressure indicate sympathetic vasoconstriction (Chapter 6).

SV = 6000/70 = 86 mL/beat at rest

SV = 18,000/160 = 113 mL/beat during exercise

[You may recall that, in the absence of other information, changes in SV can be estimated from changes in arterial pulse pressure, Pp. The information in Figure 10–4 indicates that Pp increased 1.75 times (from 40 to 70 mm Hg) as a result of exercise, whereas SV actually increased only 1.32 times (from 86 to 113 mL), as calculated earlier. This discrepancy emphasizes that although SV is a major determinant of Pp, changes in other factors, such as the compliance of arteries (CA), can influence Pp as well (see Appendix C). Part of the increase in Pp that accompanies exercise is due to a decrease in effective arterial compliance. The latter is due to (1) an increase in mean arterial pressure with exercise and (2) the nonlinear nature of the arterial volume–pressure relationship (see Figures 6–8 and 6–10).]

b. Ejection fraction = SV/EDV, therefore EDV = SV/ejection fraction

EDV = 86/0.60 = 143 mL at rest

EDV = 113/0.80 = 141 mL during exercise

[Recall that central venous pressure, PCV, is the cardiac filling pressure or preload and is therefore the primary determinant of EDV. The EDV changed little with exercise because exercise caused little or no change in PCV.]

c. SV = EDV − ESV, therefore ESV = EDV − SV

ESV = 143 − 86 = 57 mL at rest

ESV = 141 − 113 = 28 mL during exercise

[Recall that the primary determinants of ESV are cardiac afterload (mean arterial pressure) and myocardial contractility (see Appendix C). Cardiac afterload increases during exercise and thus goes in the wrong direction to account for a decrease in ESV. Therefore, an increased myocardial contractility, secondary to increased cardiac sympathetic nerve activity, must be primarily responsible for the decrease in ESV that accompanies exercise.]

d.

Key features:

1. End-diastolic volume during both rest and exercise is approximately 140 mL.

2. Ventricular ejection (decreasing ventricular volume) begins when intraventricular pressure reaches the diastolic aortic pressure and the aortic valve opens. Figure 10–4 indicates an arterial diastolic pressure of 80 mm Hg both at rest and during exercise. Thus, ventricular ejection will begin at an intraventricular pressure of 80 mm Hg in both situations.

3 and 4. Peak intraventricular pressure normally equals peak (systolic) arterial pressure. Hence, the systolic arterial pressure values in Figure 10–4 indicate peak intraventricular pressures of 120 and 150 mm Hg during rest and exercise, respectively.

5 and 6. As calculated in c earlier, end-systolic volume is 57 mL at rest and decreases to 28 mL during exercise. The reduction in end-systolic volume accounts for the increase in stroke volume during exercise.

b. Not helpful if carried to an extreme. Cutaneous vasodilation produced by warming adds to the cardiovascular stresses.

c. Helpful if the victim is conscious and can drink because fluid will be rapidly absorbed from the gut to increase circulating blood volume.

d. Might be helpful as an initial emergency measure to prevent brain damage due to severely reduced blood pressure, but prolonged treatment will promote the decompensatory mechanisms associated with decreased organ blood flow.

b. In cardiogenic shock, the hematocrit may decrease because compensatory actions evoked to maintain blood pressure may promote a fluid shift into the vascular space. However, because central venous pressure (and perhaps peripheral venous pressures) may also be elevated, capillary hydrostatic pressures (and thus fluid shifts) are difficult to predict.

c. In septic shock, peripheral vasodilation and peripheral venous pooling may actually promote filtration of fluid out of the vasculature in some beds (which would lead to an increased hematocrit), but the low arterial and central venous pressures may counteract this shift so changes in hematocrits are difficult to predict in this situation.

d. Chronic bleeding disorders are usually associated with low hematocrit and anemia because red blood cell production may not keep pace with red cell losses, whereas the volume-regulating mechanisms may be able to maintain a normal blood volume.