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what is the equation relating flow to resistance and a pressure gradient

Overview of the Vasculature
      Review the beefcake shown in figures 14.v and fourteen.half-dozen.
Arteries
     Arteries conduct blood away from the eye and toward the body tissues. The larger arteries take more than fibrous tissue in their walls that resist pressure and provide elasticity. The smaller arteries have more smooth muscle in their walls and regulate flow by vasoconstriction and vasodilation.
Arteries Serve as a Pressure Reservoir

     During systole claret is pumped into the arteries under force per unit area. Because of the depression compliance of arteries, the pressure level inside the arteries rises rapidly. During diastole the force per unit area within arteries (held in reserve) is released and contributes to continued flow of blood during diastole.

Arterial Blood Pressure

     The force per unit area of blood in the aorta is the arterial claret pressure. Arterial claret pressure varies during the cardiac bike with maximum pressure chosen systolic pressure level because information technology occurs during systole and minimum force per unit area called diastolic pressure considering information technology occurs during diastole. The boilerplate arterial force per unit area during the cardiac bicycle is the hateful arterial pressure level (MAP).

Extrinsic Control of Arteriole Radius and Mean Arterial Pressure
     Mean arterial pressure is related to arteriole radius by the equation:

MAP = CO x TPR

     Since arteriole radius is the most important factor influencing TPR, agreement the extrinsic command of arteriole radius is of import for understanding the regulation of mean arterial force per unit area.
Sympathetic Control of Arteriole Radius
     Sympathetic neurons innervate the smooth muscle of well-nigh arterioles. The norepinephrine that is released every bit the neurotransmitter binds to a adrenergic receptors and causes vasoconstriction. This increases MAP by increasing TPR.
Epinephrine released by the adrenal medulla demark to both a and 2 adrenergic receptors. Activation of  �2 receptors causes vasodilation. Because a1 receptors outnumber �2 receptors in most locations, epinephrine at high concentration causes vasoconstriction and increases MAP. �2 receptors predominate in the vessels of the centre and skeletal muscle and promote blood flow into these organs during stress by causing vasodilation. Hence, blood catamenia needed past the heart and skeletal muscle during vigorous activities is maintained.
Hormonal Control of Arteriolar Resistance
     In addition to epinephrine two other hormones cause vasoconstriction and increase MAP:
Vasopressin (ADH)

    Vasopressin increases mean arterial force per unit area by promoting vasoconstriction. It also promotes an increase in MAP past limiting urine output and raising blood book. This is why it is likewise called antidiuretic hormone.

Angiotensin Two

    Angiotensin Two is derived from angiotensinogen which is present in the plasma. Angiotensinogen is converted to angiotensin I past renin which is secreted by the kidney. Angiotensin I is converted to angiotensin Two by angiotensin converting enzyme (ACE) which is present on the inner surface of the claret vessels particularly in the lungs.

Capillaries
    Capillaries are the smallest and near numerous of blood vessels. The thin wall of capillaries consist of only an endothelial cell and the supporting basement membrane. The thinness of the capillary wall promotes the rapid and efficient commutation of cloth between the blood and the tissue.
Movement of Materials Across Capillary Walls
    The permeability of capillary walls to water and small solutes allows bulk flow of fluid across the wall. Movement of fluid from the plasma to interstitial fluid is called filtration and movement of fluid from interstitial fluid to plasma is called absorption. A net shift of fluid from plasma to interstitial fluid causes tissue swelling chosen edema.
    The forces that drive motion of fluid into and out of capillaries are called Starling forces and includes:
i. Capillary hydrostatic pressure (Pcap) or the hydrostatic pressure of fluid in the capillaries.
two. Interstitial hydrostatic pressure (Pif) or the hydrostatic pressure of fluid exterior the capillary.
3. Capillary osmotic pressure (Πcap) due to the presence of non-permeating solutes inside the capillaries.
four. Interstitial fluid osmotic pressure (Πif) due to the presence of not-permeating solutes outside the capillaries.
Hydrostatic Pressure Gradient
     The hydrostatic pressure gradient is equal to the difference of the hydrostatic pressure within the capillary and the hydrostatic pressure in the interstitial fluid. The force per unit area inside the capillary is about 38 mm Hg at the arteriolar finish and 16 mm Hg at the venous end. The interstitial hydrostatic pressure is nigh 1 mm Hg. Hence, in that location is a cyberspace hydrostatic pressure pushing fluid out of the capillaries of 37 mm Hg at the arteriolar end and 15 mm Hg at the venous end.
Osmotic Pressure Gradient

     Water flows from a region where the osmotic pressure is lower to a place where information technology is higher when separated by a semipermeable membrane. Osmotic pressure differences between capillaries and the interstitial fluid is due to a  difference in the protein concentration. The osmotic pressure level exerted past the proteins is chosen colloid osmotic pressure or oncotic pressure. Because there is a college concentration of proteins in the capillaries compared to the interstitial  fluid the oncotic pressure gradient is directed in. That is, it drives water into the capillaries. The oncotic pressure gradient across the capillary wall is about 25 mm Hg.

Cyberspace Filtration Pressure
     The direction of h2o motion is determined by internet filtration pressure. Net filtration pressure is determined by the difference betwixt the hydrostatic force per unit area gradient and the oncotic pressure gradient. Filtration is associated with a positive net filtration pressure while absorption is associated with a negative internet filtration force per unit area (see Table 1iv.3).
     Nether normal weather both filtration and absorption are occurring in the capillaries. At the arteriolar end of the capillary where the hydrostatic pressure level exceeds oncotic force per unit area at that place is filtration, at the venous end where hydrostatic pressure is less than oncotic pressure there is absorption.
     Under normal conditions twenty liters of fluid is filtered every mean solar day and about 17 liters are absorbed for a internet filtration of about three liters of fluid. The three liters of fluid that is filtered is returned past the lymphatic system.
 Factors Affecting Filtration and Absorption Across Capillaries
     A nonpathological factor that alters net filtration in the lower extremities occurs every bit the result of standing. Prolonged standing increases capillary hydrostatic pressure and increases net filtration.
   Pathological factors that increase net filtration include:
Tissue injury that results in loss of fluid and plasma proteins associated with capillary damage and the inflammatory response.
Liver disease that results in decrease of plasma protein and a consequent pass up in capillary oncotic pressure.
Kidney illness that results in retention of fluid and/or loss of plasma poly peptide.
Middle affliction that increases hydrostatic pressure in the pulmonary capillaries and causes pulmonary edema.
Veins Lymphatic Organization
     The 3 liters of fluid filtered out of the capillaries returns to the cardiovascular system by the lymphatic system. Fluid enters the lymphatic system by way of blind-ended ducts chosen lymphatic capillaries. The capillaries acquit the fluid by a arrangement of ducts to two big ducts that finally drain into the blood stream. Lymph flows through these ducts by means of skeletal muscle contraction and i-way valves. Larger ducts besides have smooth muscles in their walls.
Lymph nodes are located along the lymph vessels. Foreign organisms (bacteria) and particles are filtered in these lymph nodes where they tin can be phagocytized by macrophages and where lymphocytes tin can react with the foreign substances to stimulate an immune response.

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Source: http://droualb.faculty.mjc.edu/Course%20Materials/Physiology%20101/Chapter%20Notes/Fall%202011/chapter_14%20Fall%202011.htm