Velocity and Flow in the Cardiovascular System

Velocity and flow The Poiseuille–Hagen equation can be applied to describe the factors involved in total aorta blood flow or that to individual organs (Q = volume/time): where Q represents flow (volume/time), PA – PB change in pressure (mmHg, where 1 mmHg = 133 Pa) over the measured length, π = 3....

Velocity and flow The Poiseuille–Hagen equation can be applied to describe the factors involved in total aorta blood flow or that to individual organs (Q = volume/time): where Q represents flow (volume/time), PA – PB change in pressure (mmHg, where 1 mmHg = 133 Pa) over the measured length, π = 3.14, r is vessel radius (cm), L vessel length (cm), η blood viscosity [Pascal second (Pa⋅s), equivalent to kg/(m⋅s)] and 8 is a predetermined constant for rigid tube measurements. The major factors affecting the flow of blood in the vascular system are blood pressure, vessel length and radius, and the viscosity of the blood. From the equation, flow is directly proportional to the difference in the inflow and outflow pressure, inversely proportional to the length of the vessel, and directly proportional to the radius raised to the fourth power. Note that if the vessel radius is decreased slightly, the flow decreases tremendously. Viscosity inversely affects flow and viscosity is increased by cellular components, as exemplified by what happens in greyhounds and horses when the hematocrit increases from about 40% to 55 or 60% during a race. Blood with a normal hematocrit has a viscosity about two to three times that of water or saline. From the above equation, one notes that when flow is decreased by the increased blood viscosity, a greater driving pressure (ΔP) is required to return the flow to normal.  Laminar Flow vs Streamlined flow Laminar (streamlined) flow is characterized by layers of fluid moving in series, with each layer having a different velocity of flow (Figure 30.8). The laminar flow profile within a vessel is parabolic, with the maximum (Vm) near the center of the vessel and a progressive decrease toward the vessel walls where it falls to zero (V0). When the laminar or streamline flow pattern is disrupted and develops irregular motion within a tube, the flow is termed turbulent and is usually accompanied by audible vibrations. Sound due to turbulence is associated with high blood velocity and is more prominent around arterial bifurcations, stenotic vessels and near valves, where there are major changes in diameter of the conducting vessel. When Re is greater than 3000, turbulence will usually produce a sound sufficient to hear. One only needs to understand that the magnitude of the number predicts whether turbulence or sound will be heard from the vessel. The viscosity will usually remain relatively constant under normal conditions. However, during excitement, especially in greyhounds, the viscosity may increase to 1.5 times the normal value and because of the inverse relationship of viscosity to Re, the number will decrease. Vascular resistance Another major factor that controls organ blood flow is the diameter of the distributing vessels. The major components of a blood vessel are collagen and elastin, which expand and contract during each beat of the heart. The primary control of the systemic vascular resistance and ultimately the systemic blood pressure is the responsibility of the smaller muscular arteries and arterioles. These vessels contain more smooth muscle and are controlled by the organ’s metabolic needs, autonomic nervous system, and the endocrine system. The smaller arterioles can be controlled by local metabolites such as adenosine, pH, K+, Ca2+, O2, CO2, nitric oxide, and local cytokines. The vascular resistance can be evaluated with reference to Ohm’s law of electricity. Ohm’s law states that volts (V) are equal to the current (I) times the resistance (R) or V = IR. When solved for R the equation becomes V/I. To relate this to the biological system, volts (V) will equal the hydrostatic pressure (ΔP), current (I) will equal flow (Q), and vascular resistance will equal the hydrostatic pressure (PA – PB) divided by flow (Q ). Hence the Poiseuille–Hagen equation becomes: From this equation, the major controlling factor is the vessel radius to the fourth power. If the vessel radius is doubled, the resistance is decreased by 16 times; similarly, if the vessel radius is halved, the resistance is increased by 16 times. An increase in vessel radius occurs in the venous system where small vessels converge into larger vessels, thus causing a decrease in the resistance. The diverging effect of the arterial system (larger to smaller vessels) causes the resistance to increase. However, there is a decrease in blood pressure because of the great increase in the blood distribution area. The vascular smooth muscle cells control the radius of the smaller vessels. In the larger arterial vessels the radius is controlled primarily by the amount of collagen and elastin. Collagen and elastin can maintain vessel structure without an energy requirement and can actually act as a support pump to move blood into the vessels during diastole. Vascular compliance The term compliance (C) is used to describe the elastic nature of blood vessels and is the change in vascular volume (ΔV) with a given change in internal pressure (ΔP), thus C = ΔV/ΔP. The compliance of the vascular system varies considerably. The arterial system, which structurally contains mostly collagen and elastin, has little compliance. The vessels will not expand easily and thus resist the flow of blood producing the systemic blood pressure required for tissue perfusion. However, the venous system is structurally different, because the vessel walls contain less collagen and elastin than the arteries The venous system is able to expand easily and hold larger volumes of blood. Thus, the arterial system has been defined as the resistance system and the venous system as the compliance system of the vascular system. If vessel walls are more compliant, they can hold more blood per increment of distending pressure (i.e., ΔV/ΔP). The heart Gross structure The four‐chambered mammalian heart consists of the right and left atria and the right and left ventricles (Figure 30.9). This muscular pump circulates the blood throughout the body. The size of the mammalian heart (0.3–1.0% of body weight) correlates with the degree of physical activity characteristic of the species or breed. For example, the relatively sedentary pig’s heart is approximately 0.3% of body weight while the athletic greyhound dog and thoroughbred horse heart is 1.2% of body weight. Atria The thin‐walled, low‐pressure atria serve three functions: (i) as an elastic reservoir and conduit from the venous bed to the ventricle; (ii) as a booster pump, enhancing ventricular filling; and (iii) assisting atrioventricular (AV) valve closure before ventricular systole. Cardiac valves The four sets of fibrous cardiac valves are oriented to maintain a unidirectional flow of blood through the heart. The passive opening and closing of these valves occurs in response to pressure changes produced by contraction and relaxation of the four muscular chambers. The atrioventricular (AV) valves separate the atria from the ventricles and the semilunar valves are positioned between the ventricles and the great arteries (pulmonary artery and aorta). Ventricles The ventricular myocardial mass comprises most of the heart’s weight. During contraction a decrease in transverse diameter and some shortening in the base–apex direction reduce the volume of the left ventricle. The former is particularly effective, owing to the constrictor action of the mid‐wall circumferential fibers. The right ventricle has much thinner walls and only about one‐ third the mass of the left ventricle. During systole, its free wall moves toward the interventricular septum due to the contraction of the spiral muscles. Systole in the left ventricle also functions to assist ejection from the right ventricle by the curvature of the septum, pulling the right ventricular free wall toward the septum (called left ventricular aid). Pericardium The heart is surrounded by two layers of pericardium, with the relationship between the two being compared to pushing a clenched fist (representing the heart) into the middle of a partly inflated balloon (representing the pericardium). The clenched fist (heart) would then be surrounded by two layers (pericardium) but would not be within the lumen of the balloon (pericardial cavity). The inner layer or visceral pericardium is firmly attached to the external surface of the heart forming the epicardium. Between the visceral and parietal pericardium is a small amount of serous fluid that gives a lubricated surface for the heart movements. The outer layer or parietal pericardium is slightly larger than the heart in diastole (relaxation) and is reinforced by an external layer of inelastic collagen‐rich fibrous connective tissue. The surface of the fibrous pericardium is covered by the parietal pleura of the mediastinum. The pericardium is relatively inelastic and thus protects against acute expansion of the heart. Because of this inelasticity, the acute accumulation of intrapericardial fluid under pressure will tend to collapse the veins that enter the atria and impede or halt cardiac filling (cardiac tamponade). When cardiac enlargement develops gradually, as in hypertrophy, or when there is slow accumulation of fluid (pericardial effusion), the pericardium will enlarge to accommodate the increased contents. Congenital absence or surgical removal of the pericardium ordinarily does not disturb cardiac function. The restraining effect of the pericardium promotes mechanical interplay between the cardiac chambers, so that the volume and pressure effect of distension of one chamber will be transmitted to the other chambers. For example, enlargement of the right ventricle due to obstructed blood flow through the lungs will lead to displacement of the interventricular septum and reduction in volume of the left ventricular chamber. Myocardial cell Although the pacemaker, conduction, and working cells account for the majority (>70%) of the heart’s mass, they only constitute one‐third of the total number of cells in the heart. The remaining cells are fibroblasts, endocardial cells, endothelial cells, and vascular smooth muscle cells. The working myocardial cells or myocardium are striated muscle surrounded by a plasma membrane (sarcolemma) and do not form a morphological syncytium. They do, however, form a functional syncytium because of the presence of tight (gap) junctions that have low electrical resistance and allow passage of ions and small molecules between adjacent cells. The atrial functional syncytium is separated (insulated) from the ventricular functional syncytium by the annulus fibrosi. The working myocardial cells are specialized for contraction and impulse conduction, but most cells do not initiate impulses. The contractile cells of smaller mammals (rat, guinea pig) are somewhat thinner than those of larger mammals. Each myocardial cell has a centrally located nucleus, is packed with contractile myofibrils, and contains numerous mitochondria. The working myocardial cells are organized in series and connected end to end by intercalated disks to form myocardial fibers. The term “fiber” is applied to individual cells as well as to a chain of cells connected by intercalated disks. Parallel groups of fibers are separated into bundles that are surrounded by connective tissue sheaths. The heart wall contains layers of muscle fibers that characteristically show a smooth change in orientation across the wall. The superficial layers of fibers spiral around the heart after arising from the annulus fibrosi. They seem to spiral toward the apex just beneath the epicardium. At the apex these fibers traverse the myocardial wall and spiral back to the heart’s base just beneath the endocardium and form the papillary muscles. Within each cell or fiber are myofibrils consisting of sarcomeres joined end to end at their Z lines. Each myofibril extends the entire length of the cell and is anchored at each end to the intercalated disk. The sarcomere is the fundamental contractile unit between two cross ‐striations (Z lines) (Figure 30.11). The sarcomeres of parallel myofibrils are aligned in transverse register across the cell, giving the cross ‐banded appearance. The sarcomeres, in turn, are composed of still finer structures, the myofilaments, which are strands of the contractile proteins myosin and actin. Dark transverse bands called Z lines form the boundaries of each sarcomere. Light (I band) and dark (A band) zones exist within the sarcomere because of the overlapping arrangement of actin and myosin. At least two other proteins, tropomyosin and troponin, modulate the contractile process. Intercalated disks Intercalated disks are specialized paired membrane junctions that interdigitate and connect the ends of adjacent cells in series. The transverse portions of these disks are at right angles to the fibers. They are always located at the level of a Z line but frequently run longitudinally the length of a sarcomere to the next Z line, forming a zig‐zag or step‐like pattern. The intercalated disks have three types of functional specializations. 1 The fascia adherens occupies the major part of the transverse segment of the disk and forms a strong connection between adjacent fibers and a locus for insertion of actin myofilaments. 2 Desmosomes are round bodies in the transverse segment of the disk that appear to weld the sarcolemma of adjacent fibers together, allowing transmission of the force of contraction and producing the mechanical syncytium. 3 Gap junctions are found in the longitudinal segments of the disk. The gap junctions contain channels for the free diffusion of ions between cells and have low electrical impedance, which together result in the electrical syncytium of the myocardium. Gap junctions are sparse and small in sinoatrial (SA) and AV nodal cells, where conduction is slow, whereas gap junctions are plentiful and elongated in Purkinje cells, where conduction is rapid.