Hemodynamics workshop self-study week 3

Question 1

________ is the study of the physical phenomena that determine the flow and mechanical charateristics of the circulation.

Answer 1

Hemodynamics

Question 2

True or false: The rship btwn hydrostatic pressure and flow defines the resistance to flow that is present in a system. Resistance to flow is a propery of the system through which flow is occurring. Pressure and flow do not change resistance. The resistance does not change unless the character of the system does, for example through vasoconstriction.

Answer 2

True.

Question 3

Physiologically, what is the most important determinant of resistance to flow? Describe Poiseuille’s law.

Answer 3

1. radius
2. Poiseuille’s law defines the relationship btwn the variables that determine resistance to flow in a single tube.

R =η x l x 8/(π x r⁴)

Note that the radius of the vessel, r, is the most powerful determinant of resistance bc of the 4th power exponent (small changesin r produce much larger changes in R). The radius, r, is the variable that is controlled physiologically by arterioles. Resistance goes up when arterioles constrict (r goes down). Resistance goes down when arterioles dilate (r goes up). This is by far the most important physiological mechanism by which resistance is modified. The viscosity of blood, η, generally changes only when pathology is present. The length of the vessel, l, changes only during growth.

Question 4

How is pressure generated/produced in the cardiovascular system? How is pressure calculated? What is the importance of pressure as it relates to flow?

Answer 4

Pressure is generally produced by a pump (the heart). Pressure is also produced by vertical columns of fluid for which gravity provides the force. Pressure generated by the vertical column of fluid (P) must be overcome before blood flow will occur:

P = ρ x g x h

ρ=density, g is gravitational constant, and h is height. A pressure gradient is a pressure difference btwn two hydraulically connected locations in the system (P1 - P2 = ΔP). A pressure gradient must be present if flow is to occur. If blood flows from one point to another, a pressure gradient is present even if it appears that pressure at those two points are the same.

Question 5

What is flow? How is it calculated (Ohm’s Law)?

Answer 5

Flow is the volume of fluid moved per unit time. Flow is determined by the pressure gradient that is present (ΔP) and the resistance to flow (R). This relationship is expressed as Ohm’s Law:

Q=ΔP/R

Question 6

How is resistance in a system calculated? What is the difference btwn the values of the total resistance in the 2 types of systems?

Answer 6

The total resistance to flow posed by a number of individual resistances depends on the geometry of the system.

Resistances in series are in sequence in the path of flow and all flow goes through the resistances one after another. The total resistance is calculated:

Rtotal = R1 + R2 + R3

For resistance in series, the total resistance is always greater than that of any single resistance.

Parallel resistance exists when flow is divided btwn resistances (total flow=flow through 1+ flow through 2…) Total resistance in this case is calculated:

1/Rtotal = 1/R1 + 1/R2 + 1/R3

For resistances in parallel, the total resistance is always less than that of any single resistance. Generally speaking, resistances in the body which control flow to the organ systems are in parallel. However, there are notable exceptions to this rule. For example, the two beds in the renal system are in series with one another.

Question 7

How is velocity of flow (distance per unit time) determined? How is this related to turbulence?

Answer 7

Velocity of flow of a fluid (v) in a system in inversely proportional to the total cross-sectional area available for that flow:

Q=v x A or v=Q/A

If the flow (ml/min) remains constant, the narrower the vessel (or orifice), the higher flow velocity will be. If flow velocity becomes too high, turbulence will result and audible sounds can be generated (remember that murmurs are due to turbulent flow through a valve)

Question 8

How does flow velocity determine whether or not flow is laminar? What is critical velocity and how is it calculated? How is turbulent flow heard upon ausculation and what is this sound due to?

Answer 8

Flow is propotional to the pressure gradient (Ohm’s Law) until a critical velocity is reached and turbulent flow results. Because energy is dissipated by turbulence, flow does not increase as much for a given increase in pressure gradient once this critical velocity is reached. The critical velocity is defined by the Reynold’s number for the system. The Reynold’s number is a function of mean flow velocity (v_m), diameter of the vessel (D), density (ρ), and viscosity (η) of the fluid.

Re = D x v_m x ρ/η

Above a critical value for Reynold’s number, flow is non-laminar (turbulent). The chances that you will get turbulence (i.e. when you calculate a high Reynold’s number) go up with increasing vessel diameter, fluid density, and mean flow velocity and with decreasing viscosity. The concept of increasing vessel diameter increasing Reynold’s number can be confusing bc we know that with decreasing diameter of a tube, velocity increases and we would therefore think that turbulence should be more likely in a small vessel. This is wrong! Note that the velocity at which fluid travels is faster in smaller vessels when flow (ml/s) is the same. The Reynold’s equation states that turbulence is more likely to happen in vessels with large diameter when fluid is traveling at the same velocity.

Non-laminar turbulent flow in the circulation can often be heard with a stethoscpe and such sounds are generically referred to as murmurs. Murmurs occur because flow velocity is higher than normal. For instance the velocity of flow is increased as the heart attempts to pump the same volume of blood at the same flow rate through a narrow stenotic valve. Similarly, an insufficient or “leaky” valve allows a relatively large volume of blood to flow back through the small opeing btwn flaps of a valve which do not completely close.

Question 9

What is compliance? How is it calculated?

Answer 9

Compliance i.e. the pressure-volume rship is used as a measure of the “stretchiness” of a structure.

C = ΔV/ΔP

A change in the volume contained in a compartment will cause a change in pressure and similarly, a change in pressure in a compartment will cause a change in the volume of the compartment. the magnitude of these changes is determined by the compliance of the compartment.

Compliance is a property of the material structure being described and does not change unless the properties of the structure changes. The compliance is more or less constant in the physiological range. Note that compliance of blood vessels is decreased when the smooth muscle in the walls of the vessels contracts. This is because the walls “harden” much like skeletal muscle in the arm when they are flexed.

Question 10

What is the Law of LaPlace? How is it related to aneurysms? How is it related to rate of oxygen consumption in the heart? (think of case study pt)

Answer 10

The Law of LaPlace describes the tension in the wall of a vessel:

T = P_t r/µ

µ=wall thickness, P_t=distending pressure, r=radius of the vessel, and T= wall tension (force per unit length tangential to vessel wall). The tension in a wall is effectively P_t x r if the wall is very thin (as in a capillary) but wall thickness must be accounted for if it is significant. At any given distending pressure (P_t) small vessels (small r) have lower wall tension (T) and can be thinner without rupturing. A vessel which must have thin walls (i.e. a capillary) therefore must be small. The larger the vessel (or container such as the heart) the greater the tension in the wall at any pressure. The tension in the wall of a structure must never exceed tehhe mechanical strength of the structure or it will burst. The tension in the wall of a vessel increases as the radius (size of a vessel) increases. A bulge in the wall of a vessel is known as an aneurysm and the tension in that section of the vessel will increase and perhaps to a level that causes the vessel to rupture.

The tension in the wall of the heart (the work it is doing and the size of the ventricles) is a major determinant of its rate of oxygen consumption. In our case study pt, the LV, LA, and RV are all very enlarged with little or no thickening of the walls of the ventricle. Given the law of LaPlace, the increased ventricular and atrial diameters mean that wall stress is extremely high in this pt. Increased wall stress causes increased oxygen consumption in the cardiac tissue. The increased oxygen demand takes place as the perfusion pressure (MAP) is down in the pt. Reduced perfusion and higher oxygen demand: not a good combo