Equations correctly relates flow pressure and resistance relationship

Venous Return - Control of Cardiac Output - NCBI Bookshelf

equations correctly relates flow pressure and resistance relationship

Venous return refers to the flow of blood from the periphery back to the right pressure in controlling venous return, and measuring both accurately proved to be very difficult. mean systemic pressure minus the right atrial pressure, and resistance is the Several of its characteristics are significant: first, the relationship is. Under these circumstances, phase IV sounds more accurately predict The mean arterial pressure (MAP) is calculated by the formula: TPR is the resistance to flow in dynes · sec · cm−5 and clinically represents 8 . Related information. This equation results in a large resistance (and no flow) while the valve is The parameter a (mmHg/cm3) is related to elastance during relaxation, .. that the correct mean arterial blood pressure is obtained for pa = 1, i.e.

If, however, they are widely separated, the blood pressure may be written to signify both e. Under these circumstances, phase IV sounds more accurately predict diastolic pressures.

equations correctly relates flow pressure and resistance relationship

Considerable controversy exists concerning prediction of the diastolic blood pressure using Korotkoff sounds. Systolic pressure normally varies with respirations.

Cardiac Equations

During inspiration, the negative intrathoracic pressure causes pooling of blood in expanding pulmonary vessels and a delay of flow to the left ventricle. Thus, systolic pressure falls as cardiac output falls momentarily. The following procedure checks for a paradoxical pulse.

equations correctly relates flow pressure and resistance relationship

During normal respirations, the pressure is noted at which Korotkoff sounds are first heard. Commonly, these first sounds are audible only during expiration. Cuff pressure is slowly lowered until Korotkoff sounds are heard continually. If the difference between these two pressures exceeds 10 mm Hg, a pulsus paradoxus exists. A paradoxical pulse occurs most commonly with clinical situations involving large negative intrathoracic pressures like heavy breathing, asthma, or emphysema.

Pulsus paradoxus also occurs in pericardial tamponade, but the mechanisms are more complex and not as well understood. The blood pressure is usually taken with the patient seated. Additional information may be gained by checking the patient in the lying and standing positions.

equations correctly relates flow pressure and resistance relationship

A supine blood pressure should be compared to that obtained after the patient has been standing for a sufficient time to allow the pulse to stabilize. Normally, systolic blood pressure should not drop more than 10 mm Hg, and diastolic pressure should remain unchanged or rise slightly.

equations correctly relates flow pressure and resistance relationship

Significant orthostatic changes in blood pressure may indicate dehydration or an adverse drug reaction. When correlated with an inadequate rise in pulse, it may indicate autonomic nervous system dysfunction.

All patients should have the blood pressure checked in the left and right arm at least once to detect anatomical abnormalities. Pressure differences greater than 15 mm Hg may indicate obstruction of flow to one of the brachial arteries, such as occurs in coarctation of the aorta.

Basic Science The overall blood pressure as measured in the brachial artery is maintained by the cardiac output and the total peripheral resistance TPR to flow.

The mean arterial pressure MAP is calculated by the formula: Mean arterial pressure is a useful concept because it can be used to calculate overall blood flow, and thus delivery of nutrients to the various organs. Blood flow is defined by Poiseuille's law: This formula is commonly restated in a more clinically useful expression: In this example the TPR demonstrated can be used as a standard in evaluating pathologic conditions.

Normal cardiac output of 5. In this example of a typical hypertensive, the cardiac output is normal and the elevated blood pressure is thought to occur as a direct result of increased TPR. The TPR is maintained by resistance vessels, small precapillary muscular arterioles that regulate the rate of diastolic runoff in the arterial tree.

These resistance vessels regulate blood flow by changes in vascular tone that adjust the radius r of the vessel.

Since radius appears in the formula to the fourth power i. This example is representative of septic shock. Lax vasomotor tone causes a low TPR, and blood pressure can be maintained only by a substantial rise in cardiac output. Cardiac output is calculated by multiplying heart rate by stroke volume.

In intrinsic cardiac disease the stroke volume may be decreased, but cardiac output can be maintained by a compensatory rise in heart rate. For a given TPR, the blood pressure is maintained unless there is a relative bradycardia or a further fall in stroke volume. During systole, the volume of blood ejected from the left ventricle must enter the aorta and major arterial branches.

The distensibility of the arteries compensates this volume and stores energy in order to perfuse the capillary beds during diastole. If, for example, the aorta is stiff from atherosclerotic disease, the left ventricle generates a higher pressure to eject a given quantity of blood, and so the systolic pressure is higher. With each heartbeat there are minor adjustments in these factors that are all intricately controlled to provide perfusion of the organs. Baroreceptors in the aorta and carotid body are stretched by the blood pressure and send feedback information to autonomic nervous system centers in the brainstem.

Autonomic outflow then controls heart rate, vascular tone, and contractile state of the myocardium to adjust blood pressure accordingly. When vascular tone increases, unstressed volume decreases and mean systemic pressure increases for each level of blood volume. Conversely, totally blocking the sympathetic nervous system or otherwise reducing vasomotor tone has been shown to shift the curve to the right in a parallel manner.

The vessels on the arterial side have much less capacity and are much less distensible than the veins, and consequently, the characteristics of their volume—pressure relationship differ markedly from those of the venous side; the unstressed arterial vascular volume is approximately 0. In addition, the arterial vessel wall is more responsive to sympathetic nervous system innervation and vasoactive hormones.

Several sites in the vascular system have large reservoir capacities. Portions of the vascular system have a large capacitance, that is, they can gain or lose large volumes of blood with little change in pressure.

Therefore, as pressure within other portions of the venous system increases or decreases, large volumes of blood can move into or out of these reservoirs, buffering changes in pressure throughout the vascular system. Smooth muscle of the vascular walls of some of the vessels in these sites can contract in response to sympathetic stimulation and circulating vasoconstrictor substances, significantly decreasing their capacitance and causing additional blood to be translocated to other portions of the circulation.

Large veins in the abdomen and thorax are especially effective reservoirs, as are the sinuses of the spleen and liver. The vascular plexuses of the skin can also function as reservoirs. Blood flow into the skin is highly responsive to catecholamines released from the sympathetic nerves innervating the resistance vessels of the skin, the constriction of which decreases blood volume stored in the veins of the skin.

All of these reservoir functions can significantly affect mean systemic pressure, as their effective capacitance is altered, and blood is transferred to or from other portions of the vascular system. The vasopressor hormone angiotensin II is implicated as a causative factor in many forms of hypertension. The renal sodium-retaining effects of angiotensin II are the primary mechanisms contributing to sustained blood pressure elevation, although the peptide has other significant vascular actions.

Its effects on mean systemic pressure were analyzed in a series of studies in dogs in which angiotensin II was infused intravenously for 7 days, raising mean arterial blood pressure from the normal level of to mm Hg [ 5 ]. Blood volume remained unchanged, while mean systemic pressure rose from 9.

The effect of the hormone was to increase the vascular tone, causing an increase in filling pressure at a constant blood volume. Right atrial pressure is normally approximately 0 mm Hg or atmospheric pressure. At a normal level of right atrial pressure, venous return will be normal as long as mean systemic pressure and resistance are normal.

Each additional 1 mm Hg increase resulted in a similar decrease in venous return, until atrial pressure reached 7 mm Hg, the mean systemic pressure, at which point flow into the heart ceased. The results of their study are plotted in Figure 2. As atrial pressure is raised from the normal value of 0 to 7 mm Hg, venous return falls from the normal level to 0.

The slope of the relationship is the inverse of the more When right atrial pressure is reduced below the normal value of 0 mm Hg, a different venous return response pattern is observed. But with subsequent 1 mm Hg increments in pressure reduction, the rate of rise in venous return falls progressively less until it reaches a steady level at pressures below —4 mm Hg. Further right atrial pressure reductions below —4 mm Hg will not increase venous return further.

The negative right atrial pressure and venous return data are presented in Figure 2. The relationship becomes curved as pressure falls to approximately —2 to —3 mm Hg as the slope decreases progressively with additional reductions in atrial pressure.

At approximately —4 mm Hg, the slope becomes 0, and further reductions do not cause additional increases in venous return. The relationship is curvilinear between —2 and —4 mm Hg due to progressively increasing resistance to venous return resulting from collapse of more The explanation for the nonlinear nature of the relationship in the negative pressure range of the right atrial pressure and the plateau below —4 mm Hg is the progressive collapse of veins as the luminal pressure falls below extramural pressure.

Within the chest, the pressure averages approximately —4 mm Hg but cycles between values more negative during inspiration to slightly positive during expiration. As right atrial pressure, which is equal to venous pressure anywhere within the thorax, falls below atmospheric pressure, some veins just outside their point of entry into the thorax may collapse during inspiration, as their intraluminal pressure falls below atmospheric pressure.

As central venous pressure falls lower, more veins may collapse for longer portions of the respiratory cycle, while below —4 mm Hg, essentially, all veins in the chest remain collapsed until the buildup of upstream blood increases their intraluminal pressure to —4 mm Hg or greater. The collapse of the veins increases resistance to venous return, which is the inverse of the slope of the relationship between flow and right atrial pressure.

Ultimately, resistance becomes infinite below —4 mm Hg, preventing any increase in flow above that present at —4 mm Hg. The resistance increases progressively as right atrial pressure falls from approximately —2 to —4 mm Hg, causing the plotted relationship between pressure and flow to be curvilinear in this range. The pulsations of the right atrium cause a retrograde pressure wave that may progress through the central veins to varying distances.

These pulses contribute to the fluctuations in venous closure that occur in the negative right atrial pressure range that are reflected in the curve or splay of the pressure—flow relationship.

Changes in arterial as well as venous resistances affect venous return. In Chapter 1the progressive blood pressure reductions throughout the vascular system were presented in Table 1. The greatest segmental pressure reduction occurs at the arterioles, indicating that arterioles contribute the largest portion of total systemic vascular resistance.

Furthermore, the resistance of the arterioles is highly dynamic, capable of increasing or decreasing several folds in a few seconds. The smooth muscle in the arteriole walls responds rapidly to changes in concentrations of circulating vasoactive hormones, local metabolically linked mediators, and input from fibers of the sympathetic nervous system. Angiotensin II and catecholamines in the blood and locally produced endothelin are powerful arteriolar smooth muscle agonists, significantly affecting resistance to venous return.

In the experiment referred to above, in which angiotensin II was infused into dogs for 7 days, venous return remained unchanged while mean systemic pressure increased from 9. During this period, right atrial pressure increased slightly from 1. Calculating resistance to venous return during the control period from the pressure gradient for venous return mean systemic pressure—right atrial pressure and the rate of venous return cardiac output yields a value of 2.

After 7 days of angiotensin infusion, resistance to venous return increased to 3. In a study on dogs, after a 7-day control period, angiotensin II was infused intravenously for an additional 7 days.

Locally produced and circulating nitric oxide, prostacyclin, and prostaglandin E2 are vascular smooth muscle antagonists, producing arteriolar dilation and reduction of resistance to venous return. Local tissue metabolism, in particular, aerobic metabolism, strongly affects arteriolar resistance. Activity that reduces tissue pO2 especially elicits significant arteriolar dilation and reduction in resistance to venous return.

The linkage between total body tissue oxygen demand and resistance to venous return is a fundamental mechanism governing control of cardiac output.

equations correctly relates flow pressure and resistance relationship

This is the basic mechanism by which the cardiovascular system responds to changes in demand for cardiac output as metabolic rate changes. Other means of cardiovascular control may take part in responses to metabolic changes, but this connection of tissue oxygen demand to resistance to venous return is of overriding significance.

Pressure and Blood Flow

Oxygen demand is a strong determinant of resistance to venous return over periods ranging from seconds to hours and in long-term and steady-state conditions. If demand is elevated for extended periods of days or weeks, new microvascular vessels grow through the tissue in need, decreasing local vascular resistance and increasing blood flow.

Conversely, if blood flow exceeds demand for periods of several days or more, microvascular vessels will degenerate, reducing vascular density and increasing resistance. This process is termed rarifaction and normally normally takes place in tissues whose use and metabolic activity are reduced. Rarifaction also may occur if arterial blood pressure increases. For example, in the angiotensin II infusion experiment, the infusion resulted in a steady-state increase in arterial blood pressure of 60 mm Hg by affecting renal function, and the peptide had an immediate direct constrictor effect on the arterioles throughout the body.

But during the 7-day course of the study, the sustained increase in arterial pressure may have induced microvascular rarifaction throughout the body. The immediate and delayed increases in tissue resistance throughout the body may both have contributed to the increase in observed resistance to venous return during the infusion period.

The relatively large diameter of central veins presents little resistance to flowing blood, although they are easily compressed and flattened by surrounding tissue.

When they are compressed, they create significant resistance. For example, many veins entering the thorax over the first ribs are partially compressed by the sharp angle of the path over the bone. In the abdomen, the weight of the viscera may flatten the great veins, and in the neck, atmospheric pressure prevents the jugular veins from assuming a rounded shape when a person is upright. Within the thorax, the veins may collapse if central venous pressure falls much lower than the atmospheric pressure.

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Even considering these impediments to blood flow, venous resistance is a relatively minor component of resistance to venous return. Arterial resistance, especially that portion resulting from the arterioles, makes up the greatest portion of total vascular resistance. It is this portion that is most actively regulated in response to changes in demand of the circulatory system.

The Venous Return Curve If right atrial pressure were changed in steps over the entire range of possible atrial pressures and venous return were measured at each point, plotting the data set would yield a complete venous return curve, which is presented in Figure 2. As mentioned earlier, such measurements would have to be made during total blockade of the autonomic nervous system so that circulatory reflexes would be normal.

Venous return falls progressively as right atrial pressure increases, until right atrial pressure reaches 7 mm Hg, the normal value for mean systemic pressure.

At that point, venous return is 0 because the pressure gradient for venous return is 0. As right atrial pressure falls below 0, the venous return curve increases at a progressively declining rate until flow reaches a plateau at approximately —4 mm Hg. As discussed above, the reason for the curvilinear nature in this portion of the relationship, termed the transition zone, is the progressive increase in vascular resistance due to the collapse of increasing numbers of veins as right atrial pressure becomes more negative.

Venous return values are for humans. Such a function curve can reveal important characteristics of the circulation. First, the value of cardiac output or venous return at a given level of right atrial pressure can be read directly from the curve. Similarly, the value of mean systemic pressure is easily determined from the value of the x-axis intercept.

For a given level of right atrial pressure, the pressure gradient for venous return can be calculated from the difference between the mean systemic pressure and the value of right atrial pressure.

The resistance to venous return can also be calculated from the pressure gradient for venous return and rate of venous return at any level of right atrial pressure. Finally, the lower limit of right atrial pressure that will affect venous return, the plateau pressure, can be determined from inspection of the graph. These circulatory characteristics are key elements in understanding the regulation of cardiac output.

Alterations of the Venous Return Curve The characteristics of the venous return curve can be altered dramatically within seconds by rapidly acting physiological mechanisms and for indefinitely extended periods by long-acting responses of the circulatory control system.