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Circulatory Correlates: Vascular Impedance, Resistance, and Capacity

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Windkessel Vessels
1.1 Arterial Diameter Measurement
1.2 Caliber Changes and Hemodynamic Consequences in Windkessel Vessels
1.3 Arterial Elasticity and Hemodynamics
1.4 Effects of Alterations in Vasomotor Tone on Arterial Elasticity
1.5 Effects of Alterations in Transmural Pressure on Arterial Elasticity
1.6 Vasomotor Changes and Vascular Impedance
1.7 Smooth Muscle and Baroreceptor Areas
2 Resistance Vessels
2.1 Blood Flow, Pressure Gradient, Vascular Caliber, and Viscosity
2.2 Critical Closure
2.3 Vasomotor Changes in Microcirculation and Capillary Fluid Dynamics
2.4 Integrated Responses
3 Capacitance Vessels
3.1 Venoconstriction and Venous Capacity
3.2 Mobilization of Volume by Systemic Circulation: Venomotor Changes and Mean Circulatory Pressure
3.3 Mobilization by Regional Circulations
3.4 Changes in Compliance and Hemodynamic Consequences
3.5 Venomotor Changes and Cardiac Output
3.6 null
Figure 1. Figure 1.

effect of section of lumbar sympathetic trunk at L3−L4 on outside diameter (D) of dog femoral artery.

effect of stimulation of the lumbar sympathetic trunk at a level of L3−L4 on the outside diameter of a dog femoral artery. Stimulus parameters: 4.2 V, 5 ms, at 15 Hz. [From Gerová and Gero , by permission of the American Heart Association, Inc.]

Figure 2. Figure 2.

Equilibrium between internal (Pi) and external (Po) pressures and mean wall tension (T), which would have to be applied to both halves of longitudinally split, hollow cylinder to hold halves together.

Figure 3. Figure 3.

Elastic moduli (E) of relaxed and constricted carotid artery as function of strain and pressure, derived by Dobrin and Rovick from pressure‐circumference curves. At any pressure, E (constricted) < E (relaxed). “Unstressed” circumference of constricted vessel was used to compute strain for both constricted and relaxed vessels, leading to erroneous conclusion that at comparable strain, constricted vessels have lower elastic moduli. Compare this to same data plotted in Fig. using appropriate “unstressed” circumferences to compute strain.

From Dobrin and Rovick
Figure 4. Figure 4.

Stress‐strain relationships of relaxed and constricted carotid artery derived from data of Dobrin and Rovick . Strain was calculated for each by using appropriate “unstressed” circumferences obtained at pressures of approximately 5 mmHg. At most strain and stress values and at comparable distending pressures, slope of stress‐strain curve is lower, that is, elastic modulus is lower for constricted vessel.

Figure 5. Figure 5.

Dependence of dynamic elastic modulus on arterial pressure. DTA, descending thoracic aorta; ABA, abdominal aorta; BCA, brachiocephelic artery; LSC, left subclavian artery; CA, carotid artery; FA, femoral artery. Note relatively greater pressure dependence of elasticity in peripheral arteries.

From Cox
Figure 6. Figure 6.

Pressure‐radius relationships for rabbit ear artery, showing little change in ΔP/Δro within normal range of arterial pressure despite very different degrees of vascular smooth muscle contraction. Curves are fully constricted (closed circles), intermediately constricted (closed squares), and fully relaxed (open and closed triangles). Epinephrine and a 60‐min period of electrical stimulation at 4 Hz were used to produce full or partial constriction. Open circles show response of artery to increasing pressure after electrical stimulation but without added epinephrine.

Figure 7. Figure 7.

Vascular input impedance (modulus and phase) of systemic circulation of dog plotted against frequency. Note relatively stable impedance modulus at frequencies above that of resting heart rate (2 Hz). This should be compared to higher values between 0 and 2 Hz and modulus of input impedance of simple elastic tube terminated by hydraulic resistance (Fig. A). (Coherence is a measure of association between the variables and is akin to a correlation coefficient.

From Taylor , by permission of the American Heart Association, Inc
Figure 8. Figure 8.

Top: input impedance of branching assembly of elastic tubes (solid line) compared with that of single “equivalent” tube (broken line). Reflection coefficient is 0.6 in both cases, so that |Z0|0 at zero frequency is 11.5. Note reduction of modulus spikes, hence a greater stability of |Z0|0 when multiple tubes are present in model. Bottom: input impedance of random‐length, branching assembly as in Top, showing stabilizing effects on both modulus and phase of viscous properties (largely of smooth muscle) of vessel walls. Solid line shows no viscosity, dashed line represents phase angle of 10° for viscoelastic modulus, and dotted line shows phase angle of 20°. Results of wall viscosity are similar to fluid viscosity, except that latter elevates impedance modulus at zero frequency (i.e., input resistance).

From Taylor
Figure 9. Figure 9.

Mean systemic input impedance modulus and phase for 12 unanesthetized dogs before (open circles) and following (closed circles) carotid sinus hypotension produced by occlusion of brachiocephalic artery. Note increase in characteristic impedance, part of which may be due to elevated systemic pressure and its effect on elasticity, and part due to reduction cross‐sectional area of arterial tree.

From Cox et al.
Figure 10. Figure 10.

Effect of elevated blood pressure induced by norepinephrine injection on systemic vascular input impedance. Note shift to right of minima of modulus from roughly 3 and 8 Hz to 5 and 10 Hz, respectively. Failure of characteristic impedance to rise suggests that pressure‐induced increases in elasticity of arterial tree were offset by increases in its cross‐sectional area.

From O'Rourke and Taylor , by permission of the American Heart Association, Inc
Figure 11. Figure 11.

Vascular impedance of dog femoral artery showing effects of vasodilatation on modulus and phase. Reduction in reflection coefficient flattens undulations in modulus and phase. Shift to left of impedance modulus minimum is not completely explained by the random tube model , but such a disparity might be expected to arise from geometric dissimilarities between model and femoral vascular bed. Intercept of phase on frequency axis was variable—intercept during dilatation occurred at lower frequencies and supported model , whereas in later study it occurred at a higher frequency than the control.

From Taylor , by permission of the American Heart Association, Inc
Figure 12. Figure 12.

Changes in contour and timing of peaks of simultaneously recorded femoral pressure waves and flow waves following vasodilatation induced by close arterial injection of acetylcholine. Note close correspondence of pressure and flow during dilatation, which can be anticipated when reflections are substantially reduced. Mean blood pressure: 107 mmHg (control), 94 mmHg (vasodilated). Mean flow: 1.08 ml/s (control), 6.93 ml/s (vasodilated).

From O'Rourke and Taylor , by permission of the American Heart Association, Inc
Figure 13. Figure 13.

Modulus of vascular impedance of systemic circulation and impedance of renal, celiac, and femoral vascular beds under control conditions (open circles), reflex constriction (solid squares), and reflex dilatation (solid triangles) before and after bilateral vagotomy. In renal and celiac beds, vasoconstriction elevated impedance and vasodilatation reduced impedance at all frequencies, although this was true only for first four harmonies in femoral bed.

From Cox and Bagshaw , by permission of the American Heart Association, Inc
Figure 14. Figure 14.

Changes in relative contribution of oscillatory power to total cardiac power (oscillatory power fraction) as function of heart frequency, and influence on control relationship (open circles) of isoproterenol (uppermost curve, open squares), norepinephrine (solid circles), and angiotensin (lowest curve, closed squares). Isoproterenol elevated cardiac output and total cardiac power but increased pulsatile losses, thereby reducing cardiac efficiency.

From Cox
Figure 15. Figure 15.

Profile of pressure drops through systemic circulation, demonstrating major site of vascular resistance in precapillary vessels and showing increase and decrease in capillary pressure, which occurs during precapillary vasodilatation and vasoconstriction, respectively.

From Keele and Neil
Figure 16. Figure 16.

Equilibrium relationships of mean wall stress [(Piri − Poro/(rori)] and inside radius at five levels of distending pressure (6–60 mmHg). Passive elastic behavior of dilated arteriole (inset) is seen as solid squares. Hypothetical elastic diagram (open circles) assumes maintained shortening of vascular smooth muscle. Actual effects of reduction in pressure and hence stress in constricted vessel is seen in inset and is represented by line linking inverted triangles.

Data in inset redrawn from Gore
Figure 17. Figure 17.

Maximum decrease in mean diameter [(Do − Di)/2] as percentage of control (elicited by 250 nA · s dose of norepinephrine) expressed as function of initial tangential stress.

From Gore
Figure 18. Figure 18.

Relationship of constrictor responses (percent of maximum) of capacitance vessels (continuous line) and resistance vessels (broken line) to stimulation frequency in isolated hindquarters of a cat. Calculated fluid influx shown as fine broken line.

From Mellander
Figure 19. Figure 19.

Simplistic model of capacitance system consisting of an adjustable reservoir (screw) representing venomotor tone and a spring representing total venous compliance.

Figure 20. Figure 20.

Graphic solution of two equations: 1) dependence of right atrial pressure on cardiac output (venous return curve, c and d), and 2) dependence of cardiac output on right atrial pressure (Starling cardiac function curve, a and b). Point of intersection of a and c (t), which in an intact animal occurs at a right atrial pressure of about 0 mmHg, represents the stable operating point for the cardiovascular system at rest. Curve b represents an increased myocardial contractility, and curve d shows a decreased resistance to venous return. At zero cardiac output, pressure within all parts of circulation is same and is defined as mean circulatory filling pressure (mcfp).

Adapted from Guyton et al.
Figure 21. Figure 21.

Effect of prevailing venous pressure on magnitude of total active and passive blood mobilization following vasoconstrictor nerve stimulation of isolated cat hindquarters preparation. At low pressures of about 2 mmHg, active and passive contributions are equal, whereas at higher pressures active emptying predominates.

From Öberg
Figure 22. Figure 22.

Hypothetical relationship of volume to pressure within one or more veins before active venoconstriction (curve I) and after active venoconstriction (curve II), in which no change in compliance occurred within observed pressure range of P1−P2. Change in compliance accompanying venoconstriction is represented by curve III. A loss of volume equal to ΔV1 + ΔV2 is partly compensated by active venoconstriction (ΔV1), but results in fall in pressure to P2 along curve II if no change in compliance occurs, or to P4 if compliance is decreased. Effects of fall in venous pressure is to mobilize passively volume ΔV1. In addition, venoconstriction with no changes in compliance adds further volume ΔV2 to total. If compliance is reduced, however, as seen in curve III, additional volume (ΔV3) mobilized is less than that given by curve II.

Figure 23. Figure 23.

Electrical analogue characterizing relationship of pressure changes and total capacity of systemic circulatio.

From Shoukas and Sagawa , by permission of the American Heart Association, Inc
Figure 24. Figure 24.

Time dependence of total systemic vascular compliance. P values indicate statistical significance of the difference in compliances between intact and vagotomized dogs. Triangles indicate lumped data for intact and vagotomized dogs.

From Shoukas and Sagawa , by permission of the American Heart Association, Inc
Figure 25. Figure 25.

Mean pressure‐volume relationships (“effective” compliance) calculated from data obtained from 8 subjects by measuring changes in central venous pressure resulting from infusion and removal of dextran/blood. Because all recorded relationships showed hysteresis, above points at each value of volume were obtained as mean of two volumes at corresponding pressure values, one on ascending limb, the other on descending limb. NE and LBPP denote norepinephrine and lower body positive pressure, the latter produced by enclosing lower half of subject in a box up to level of xiphoideus sterni.

From Echt et al. , by permission of the American Heart Association, Inc
Figure 26. Figure 26.

Simple series‐coupled resistive and capacitative models of circulation.

two‐reservoir model after Guyton et al. .

two‐reservoir model of Berne and Levy .

3‐reservoir model.

Figure 27. Figure 27.

Parallel reservoir model of circulation. C1 and C2, compliances; , and , arterial resistances; and , venous resistances; Pra, right atrial pressure.

From Caldini et al. , by permission of the American Heart Association, Inc
Figure 28. Figure 28.

Semilog plot of ratio of blood volume (Vt − Vss) still to change at time t, to total volume change between two steady states V1 and Vss as function of time following step decrease in right atrial pressure while maintaining constant flow.

From Caldini et al. , by permission of the American Heart Association, Inc
Figure 29. Figure 29.

Relationships of flow () and right atrial pressure (Pra) before and during epinephrine infusion calculated for isovolumic conditions. Broken line represents effect of epinephrine on elastic and resistive properties alone.

From Caldini et al. , by permission of the American Heart Association, Inc


Figure 1.

effect of section of lumbar sympathetic trunk at L3−L4 on outside diameter (D) of dog femoral artery.

effect of stimulation of the lumbar sympathetic trunk at a level of L3−L4 on the outside diameter of a dog femoral artery. Stimulus parameters: 4.2 V, 5 ms, at 15 Hz. [From Gerová and Gero , by permission of the American Heart Association, Inc.]



Figure 2.

Equilibrium between internal (Pi) and external (Po) pressures and mean wall tension (T), which would have to be applied to both halves of longitudinally split, hollow cylinder to hold halves together.



Figure 3.

Elastic moduli (E) of relaxed and constricted carotid artery as function of strain and pressure, derived by Dobrin and Rovick from pressure‐circumference curves. At any pressure, E (constricted) < E (relaxed). “Unstressed” circumference of constricted vessel was used to compute strain for both constricted and relaxed vessels, leading to erroneous conclusion that at comparable strain, constricted vessels have lower elastic moduli. Compare this to same data plotted in Fig. using appropriate “unstressed” circumferences to compute strain.

From Dobrin and Rovick


Figure 4.

Stress‐strain relationships of relaxed and constricted carotid artery derived from data of Dobrin and Rovick . Strain was calculated for each by using appropriate “unstressed” circumferences obtained at pressures of approximately 5 mmHg. At most strain and stress values and at comparable distending pressures, slope of stress‐strain curve is lower, that is, elastic modulus is lower for constricted vessel.



Figure 5.

Dependence of dynamic elastic modulus on arterial pressure. DTA, descending thoracic aorta; ABA, abdominal aorta; BCA, brachiocephelic artery; LSC, left subclavian artery; CA, carotid artery; FA, femoral artery. Note relatively greater pressure dependence of elasticity in peripheral arteries.

From Cox


Figure 6.

Pressure‐radius relationships for rabbit ear artery, showing little change in ΔP/Δro within normal range of arterial pressure despite very different degrees of vascular smooth muscle contraction. Curves are fully constricted (closed circles), intermediately constricted (closed squares), and fully relaxed (open and closed triangles). Epinephrine and a 60‐min period of electrical stimulation at 4 Hz were used to produce full or partial constriction. Open circles show response of artery to increasing pressure after electrical stimulation but without added epinephrine.



Figure 7.

Vascular input impedance (modulus and phase) of systemic circulation of dog plotted against frequency. Note relatively stable impedance modulus at frequencies above that of resting heart rate (2 Hz). This should be compared to higher values between 0 and 2 Hz and modulus of input impedance of simple elastic tube terminated by hydraulic resistance (Fig. A). (Coherence is a measure of association between the variables and is akin to a correlation coefficient.

From Taylor , by permission of the American Heart Association, Inc


Figure 8.

Top: input impedance of branching assembly of elastic tubes (solid line) compared with that of single “equivalent” tube (broken line). Reflection coefficient is 0.6 in both cases, so that |Z0|0 at zero frequency is 11.5. Note reduction of modulus spikes, hence a greater stability of |Z0|0 when multiple tubes are present in model. Bottom: input impedance of random‐length, branching assembly as in Top, showing stabilizing effects on both modulus and phase of viscous properties (largely of smooth muscle) of vessel walls. Solid line shows no viscosity, dashed line represents phase angle of 10° for viscoelastic modulus, and dotted line shows phase angle of 20°. Results of wall viscosity are similar to fluid viscosity, except that latter elevates impedance modulus at zero frequency (i.e., input resistance).

From Taylor


Figure 9.

Mean systemic input impedance modulus and phase for 12 unanesthetized dogs before (open circles) and following (closed circles) carotid sinus hypotension produced by occlusion of brachiocephalic artery. Note increase in characteristic impedance, part of which may be due to elevated systemic pressure and its effect on elasticity, and part due to reduction cross‐sectional area of arterial tree.

From Cox et al.


Figure 10.

Effect of elevated blood pressure induced by norepinephrine injection on systemic vascular input impedance. Note shift to right of minima of modulus from roughly 3 and 8 Hz to 5 and 10 Hz, respectively. Failure of characteristic impedance to rise suggests that pressure‐induced increases in elasticity of arterial tree were offset by increases in its cross‐sectional area.

From O'Rourke and Taylor , by permission of the American Heart Association, Inc


Figure 11.

Vascular impedance of dog femoral artery showing effects of vasodilatation on modulus and phase. Reduction in reflection coefficient flattens undulations in modulus and phase. Shift to left of impedance modulus minimum is not completely explained by the random tube model , but such a disparity might be expected to arise from geometric dissimilarities between model and femoral vascular bed. Intercept of phase on frequency axis was variable—intercept during dilatation occurred at lower frequencies and supported model , whereas in later study it occurred at a higher frequency than the control.

From Taylor , by permission of the American Heart Association, Inc


Figure 12.

Changes in contour and timing of peaks of simultaneously recorded femoral pressure waves and flow waves following vasodilatation induced by close arterial injection of acetylcholine. Note close correspondence of pressure and flow during dilatation, which can be anticipated when reflections are substantially reduced. Mean blood pressure: 107 mmHg (control), 94 mmHg (vasodilated). Mean flow: 1.08 ml/s (control), 6.93 ml/s (vasodilated).

From O'Rourke and Taylor , by permission of the American Heart Association, Inc


Figure 13.

Modulus of vascular impedance of systemic circulation and impedance of renal, celiac, and femoral vascular beds under control conditions (open circles), reflex constriction (solid squares), and reflex dilatation (solid triangles) before and after bilateral vagotomy. In renal and celiac beds, vasoconstriction elevated impedance and vasodilatation reduced impedance at all frequencies, although this was true only for first four harmonies in femoral bed.

From Cox and Bagshaw , by permission of the American Heart Association, Inc


Figure 14.

Changes in relative contribution of oscillatory power to total cardiac power (oscillatory power fraction) as function of heart frequency, and influence on control relationship (open circles) of isoproterenol (uppermost curve, open squares), norepinephrine (solid circles), and angiotensin (lowest curve, closed squares). Isoproterenol elevated cardiac output and total cardiac power but increased pulsatile losses, thereby reducing cardiac efficiency.

From Cox


Figure 15.

Profile of pressure drops through systemic circulation, demonstrating major site of vascular resistance in precapillary vessels and showing increase and decrease in capillary pressure, which occurs during precapillary vasodilatation and vasoconstriction, respectively.

From Keele and Neil


Figure 16.

Equilibrium relationships of mean wall stress [(Piri − Poro/(rori)] and inside radius at five levels of distending pressure (6–60 mmHg). Passive elastic behavior of dilated arteriole (inset) is seen as solid squares. Hypothetical elastic diagram (open circles) assumes maintained shortening of vascular smooth muscle. Actual effects of reduction in pressure and hence stress in constricted vessel is seen in inset and is represented by line linking inverted triangles.

Data in inset redrawn from Gore


Figure 17.

Maximum decrease in mean diameter [(Do − Di)/2] as percentage of control (elicited by 250 nA · s dose of norepinephrine) expressed as function of initial tangential stress.

From Gore


Figure 18.

Relationship of constrictor responses (percent of maximum) of capacitance vessels (continuous line) and resistance vessels (broken line) to stimulation frequency in isolated hindquarters of a cat. Calculated fluid influx shown as fine broken line.

From Mellander


Figure 19.

Simplistic model of capacitance system consisting of an adjustable reservoir (screw) representing venomotor tone and a spring representing total venous compliance.



Figure 20.

Graphic solution of two equations: 1) dependence of right atrial pressure on cardiac output (venous return curve, c and d), and 2) dependence of cardiac output on right atrial pressure (Starling cardiac function curve, a and b). Point of intersection of a and c (t), which in an intact animal occurs at a right atrial pressure of about 0 mmHg, represents the stable operating point for the cardiovascular system at rest. Curve b represents an increased myocardial contractility, and curve d shows a decreased resistance to venous return. At zero cardiac output, pressure within all parts of circulation is same and is defined as mean circulatory filling pressure (mcfp).

Adapted from Guyton et al.


Figure 21.

Effect of prevailing venous pressure on magnitude of total active and passive blood mobilization following vasoconstrictor nerve stimulation of isolated cat hindquarters preparation. At low pressures of about 2 mmHg, active and passive contributions are equal, whereas at higher pressures active emptying predominates.

From Öberg


Figure 22.

Hypothetical relationship of volume to pressure within one or more veins before active venoconstriction (curve I) and after active venoconstriction (curve II), in which no change in compliance occurred within observed pressure range of P1−P2. Change in compliance accompanying venoconstriction is represented by curve III. A loss of volume equal to ΔV1 + ΔV2 is partly compensated by active venoconstriction (ΔV1), but results in fall in pressure to P2 along curve II if no change in compliance occurs, or to P4 if compliance is decreased. Effects of fall in venous pressure is to mobilize passively volume ΔV1. In addition, venoconstriction with no changes in compliance adds further volume ΔV2 to total. If compliance is reduced, however, as seen in curve III, additional volume (ΔV3) mobilized is less than that given by curve II.



Figure 23.

Electrical analogue characterizing relationship of pressure changes and total capacity of systemic circulatio.

From Shoukas and Sagawa , by permission of the American Heart Association, Inc


Figure 24.

Time dependence of total systemic vascular compliance. P values indicate statistical significance of the difference in compliances between intact and vagotomized dogs. Triangles indicate lumped data for intact and vagotomized dogs.

From Shoukas and Sagawa , by permission of the American Heart Association, Inc


Figure 25.

Mean pressure‐volume relationships (“effective” compliance) calculated from data obtained from 8 subjects by measuring changes in central venous pressure resulting from infusion and removal of dextran/blood. Because all recorded relationships showed hysteresis, above points at each value of volume were obtained as mean of two volumes at corresponding pressure values, one on ascending limb, the other on descending limb. NE and LBPP denote norepinephrine and lower body positive pressure, the latter produced by enclosing lower half of subject in a box up to level of xiphoideus sterni.

From Echt et al. , by permission of the American Heart Association, Inc


Figure 26.

Simple series‐coupled resistive and capacitative models of circulation.

two‐reservoir model after Guyton et al. .

two‐reservoir model of Berne and Levy .

3‐reservoir model.



Figure 27.

Parallel reservoir model of circulation. C1 and C2, compliances; , and , arterial resistances; and , venous resistances; Pra, right atrial pressure.

From Caldini et al. , by permission of the American Heart Association, Inc


Figure 28.

Semilog plot of ratio of blood volume (Vt − Vss) still to change at time t, to total volume change between two steady states V1 and Vss as function of time following step decrease in right atrial pressure while maintaining constant flow.

From Caldini et al. , by permission of the American Heart Association, Inc


Figure 29.

Relationships of flow () and right atrial pressure (Pra) before and during epinephrine infusion calculated for isovolumic conditions. Broken line represents effect of epinephrine on elastic and resistive properties alone.

From Caldini et al. , by permission of the American Heart Association, Inc
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Barry S. Gow. Circulatory Correlates: Vascular Impedance, Resistance, and Capacity. Compr Physiol 2011, Supplement 7: Handbook of Physiology, The Cardiovascular System, Vascular Smooth Muscle: 353-408. First published in print 1980. doi: 10.1002/cphy.cp020214