Airway Resistance

Reynolds number (Re) gives a measure of the ratio of inertial forces to viscous forces. Describes the relation between density of the fluid, diameter of the tube, velocity of flow and viscosity of fluid. The higher the value of Re greater the probability of turbulence. When Re is less than 2000 flow is usually not turbulent. When Re is more than 3000 flow is always turbulent.

Small airway have low reynold number, large cross sectional area, large diameter and air flows at a very low velocity.

Ref: Physiology of respiration By Michael P. Hlastala, Albert J. Berger, Page 52; Review of Medical Physiology by William ganong, 22nd edn/page 583

A, B, C i.e. Forced expiration, Dense air, Low lung volume

C i.e. Dynamic compression of airways

Forced Expiration, Equal Pressure Point & Dynamic Airway Compression

– Alveolar pressure (P_A) is the sum of leural pressure (Pm) and elastic recoil pressure (Pei).  • and this is the driving pressure for expiratory gas flow. Because alveolar pressure exceeds atmospheric pressure (during expiration), gas begins to flow from alveolus to mouth, through open glottis. As gas flows out of alveoli the transmural pressure across the air way (Pia) decreases. In otherwords, there is a gradual decrease in airway pressure (P_aw) from distal (alveoli) to proximal (trachea) respiratory tract. This gradual pressure dissipation is caused by

1. Expiratory airflow resistance (frictional pressure loss); the major site of resistance along bronchial tree is large bronchi (Berne & Levy) / medium sized bronchi (John West).

ii.As the overall cross sectional area of the airways decreases towards the trachea, gas velocity increases. This acceleration of gas flow decreases the pressure (Paw) and can make flow turbulent (increasing resistance).

iii.As air moves out of lung, the lung volume decreases; which inturn decreases the driving pressure (alveolar pressure – intrapleural pressure) and the airways become narrower (increasing resistance).

– The positive transpulmonary (P_L) and transairwa ressure (P_t.)  hold the alveoli and airway open. Because PL = PA – PP and  P_ia = P_a, – PPI I; it also means that alveolar pressure (PA) or

Just beyond the (proximal to) equal pressure point the transairway pressure (Pta) becomes negative. Because P_ta = Pressure in the airway expanding it (P_aw) – Pressure around

the airway compressing it (i.e. pleural pressure Po)

That is why no amount of expiratory effort will increase the flow further because the higher pleural pressure (which rises with increased expiratory effort) also tends to collapse the airway at the equal pressure point (EPP), just as it tends to increase the gradient for expiratory gas flow (by increasing the pressure gradient b/w alveoli and atmosphere).

– That is how dynamic airway compression limits air flow in normal subjects during a forced expiration and the airflow is independent of total driving pressure. In other words during dynamic compression, flow is determined by transpulmonary pressure (PL = PA — Pri) or alveolar pressure minus pleural pressure (not mouth pressure). Hence the expiratory flow is effort independent, flow limited and has greater airway resistance (than during inspiration).

– Equal pressure point is dynamic (not static). In normal lungs (without disease), the EPP occurs in airways that contain cartilage and thus they resist collapse. As expiration progresses (i.e. lung volume and elastic recoil pressure decreases), the EPP moves distally, deeper into the lung, closer to the alveoli. This occurs because the resistance of airways rises (d/t decrease in radius) as the lung volume falls, and therefore the pressure within airways fall more rapidly with distance from the alveoli. This resistive drop in airway pressure is greater in diseased lung (with airway obstruction secondary to mucus accumulation and inflammation). As a result EPP occurs in small airways that are devoid of cartilage causing them to collapse (premature airway closure). The major site of increased resistance in patients with COPD is in airways 2mm dia.

– Dynamic airway compression may occur in diseased lung at relatively low expiratory flow rates, thus reducing exercise ability. DCA is exaggerated in emphysema because of reduced lung elastic recoil and loss of radial traction on airways.

Examples

For example at the start of expiration, pressure inside alveolus (PA) is 0 (i.e. no air flow) and pleural pressure (Po) is – 30 cm H₂0. So transpulmonary pressure (P_L) of + 30 cm (P_i. = P_A – P_Pi = 0 – (-30) = + 30) of water is holding the alveoli open. Because there is no flow , the pressure inside airways (Paw) is also 0 and similarly + 30 cm F120 of transairway pressure holds the airway open (P_t. = Paw – Ppi).

With the contraction of expratory muscles both pleural and alveolar pressure rises + 90 cm each and becomes + 60 cm H₂0 and + 90 cm 1-1₂0 respectively. So the P_i. remains same but because of higher alveolar pressure (in comparison to atmosphere) airflow begins.

Because of gradual decrease in lung volume (decreasing driving pressure) and expiratory airflow resistance, there is gradual dissipation of airway pressure (Paw). And at equal pressure point (i.e. the point at which the pressure inside the airways equals the pressure outside the airways) the airways become compressed (dynamic airway compression).

Airway Resistance

Highest airway resistance is in medium sized/large bronchi. The smallest airways contribute very little to overall total resistance because in smaller airways

1. With increase in effective cross sectional area the airflow velocity decreases substantially and flow becomes laminar and
2. The airway exist in parallel rather than in series. The resistance of

D i.e. Effective velocity in small vessels is less

D i.e. Increase in diameter of blood vessels

Probability of turbulence increases with Reynolds number > 3000, increase in velocity (above critical level), density of blood and diameter of vessel or with decrease in viscosity.

Average velocity of flow is inversely proportional to the total cross sectional area of the vessel. Therefore the average velocity of flow is high in aorta declines steadily in smaller vessels and is lowest in capillaries. So the cause of laminar flow in small vessels mainly is large area of cross section and less effective velocityQ.

Laminar (Streamline) Flow

– A streamline flow is also K/ a laminar flow because it moves in layers (or lamina). So a dye carefully introduced into a given lamina (layer) remain in that lamina as the fluid moves longitudinally along the tube.

In laminar flow the layer touching the wall of tube adheres to it and hardly moves b/o friction, while the concentric layer or lamina next to it shear/slide against this motionless layer with less friction. In this way the inner lamina moves faster than laminae on their outside with the result that the portion of fluid at the center moves fastest. This is why the shape of progressing front is parabola.

The velocity at the center of stream (in stream line flow) is maximal and equal to twice the mean velocity of flow across the entire cross section of the tube. Flow of blood in vessels is normally laminar (stream line), which means the layer in the center of stream has highest velocity & peripheral layer (near blood vessel wall) has lowest. Streamline flow is silent. Therefore no sounds are heard with stethoscope in normal arteries.

– Average velocity of flow is inversely proportional to the total cross section area of that vessel. Therefore the average velocity of blood is high (33 cm/s) in aorta (CS 2.5 cm²), declines steadily in smaller vessels and is lowest in the capillaries (0.3 mm/s), which have 1000 times the total cross sectional area of aorta (i.e. 2500 cm2).

The average velocity of blood flow increases again in veins and is relatively high in venacava, although not so high as in the aorta. So the cause of laminar flow in small vessels is large area of cross section and less average velocityQ.

Turbulence

–  Turbulent flow is a chaotic flow with irregular motions and flows in all directions; it forms eddies or whirlpools and fluid elements do not remain confined to definite lamina, but rapid, radial mixing occurs.

–  Turbulent flow offers more resistance than laminar flow; so greater pressure is required to force a given flow of fluid through the same tube when the flow is turbulent than when it is laminar. In turbulent flow, pressure drop is approximately proportional to the square of flow rate whereas in laminar flow, the pressure drop is proportional to the square of flow rate whereas in laminar flow, the pressure drop is proportional to the first power of the flow rate. So to produce same flow a pump like heart must do considerably more work if turbulence develops.

– Laminar flow occurs at velocities upto critical velocity, at or above which the flow becomes turbulent, and creates sound. Turbulent flow accounts for development of heart sounds, murmurs a/w valvular heart disease, Korotkov sounds heard during the measurement of arterial blood pressure, bruits heard over arteries constricted by atherosclerotic phaque and functional cardiac murmurs heard in patients with hyper dynamic circulation (as thyrotoxicosis & severe chronic anemia).

Turbulence is more common in anemia because of reduced viscosity and high flow velocities a/w high cardiac output.

– Turbulence is usually accompanied by audible vibrations. Blood clots and thrombi are more likely to develop in turbulent flow than in laminarflow.

Ans. is ‘d’ i.e., Blood flow decreases sixteen-fold

If everything else remains constant, blood flow is direactly poroportional to 4^th power of radius.

Thus, if the diameter (or radius) is reduced to half, blood flow will decrease sixteen-fold.

Blood flow is directly proportioned to 4th power of radius.

POISEUILLE’S LAW:

• Also referred as “Hagen-Poiseille’s Law”.
• Poiseuille’s equation states, 
  • Q = P1 – P2 * { (Π r4) / (8 η L)}
  • Q – Flow rate
  • (P1 – P2) – Pressure difference across vessel (provided P1 > P2).
  • η – Blood viscosity.
  • r – Radius.
  • L – Tube length.
• If parameter values remains constant, 
  • Blood flow is directly proportional to 4th power of radius.

• Resistance of vessel to blood flow can be calculated by combining Ohm’s law with Poiseuille’s equation.
  • By substituting values of Q from Poiseuille’s law in Ohm’s law.

• Implying, resistance is mainly affected by,
  • Blood vessel radius,
  • Vasodilatation/vasoconstriction.