Application of Basic Science to Anesthesia Case File

Application of Basic Science to Anesthesia Case File

Lydia Conlay, MD, PhD, MBA, Julia Pollock, MD, Mary Ann Vann, MD, Sheela Pai, MD, Eugene C. Toy, MD

Case 5

A 42-year-old woman is undergoing surgery for a bilateral tubal ligation. She has undergone endotracheal intubation. The medical student, who received a degree in physics in college, notices that the anesthesiologist is working with the Ambu bag to ventilate the patient. The student speculates about decreasing the work required by shortening the endotracheal tube (ETT).

➤ If the ETT is shortened by 25%, how would that affect the work of breathing?

ANSWER TO CASE 5:

Application of Basic Science to Anesthesia

Summary: The patient has undergone endotracheal intubation.

➤ Physiologic change: Shortening the endotracheal tube by 25% would decrease the pressure required, and hence the work of breathing, by about one-third. ANALYSIS

Objectives

1. Review principles of physics.

2. Understand how the above principles are applied to the practice of anesthesiology.

Considerations

Shortening the endotracheal tube would, indeed, theoretically reduce the work of breathing. However, during laparoscopy, the patient is paralyzed, and the work of breathing is assumed by the ventilator. Thus, from a practical perspective, it is rarely necessary to shorten the endotracheal tube.

APPROACH TO

Basic Science in Anesthesia

Anesthesia practice involves application of basic science principles on a daily basis. These principles include fluid mechanics, physical properties of gases, combustion and fires, and electrical safety.

CLINICAL APPROACH

Fluid Mechanics

An understanding of basic fluid mechanics is important for the understanding of several processes managed by anesthesiologists in the operating room, such as gas flow and circulation. Most of the discussion that follows is derived from analysis of noncompressible newtonian fluids. But even though air and blood do not fall into this category, the concepts still apply.

The word “laminar” comes from the same root as the familiar “lamina” meaning “layers,” and signifies that in this type of flow the layers do not mix. Laminar flow can be envisioned as flow down a straight, calm river. The water 

Figure 5–1. Types of flow are illustrated: axisymmetric laminar (top), asymmetric laminar (middle), and tubulent flow (bottom).

in the middle is flowing fastest and very little water is flowing at the sides; in fact, it can be described as a parabola. Turbulent flow, however, is more chaotic, and can be envisioned as the flow of the water as it flows over rocks or around a bend. The “lamina” of the water—and therefore the energy required to move them—are no longer all moving in the same direction (Figure 5–1).

What determines whether a flow is laminar or turbulent? The first factor to consider is the properties of the fluid, specifically the kinematic viscosity (ν) which is the ratio of the viscosity (μ) of the fluid to its density (ρ). Next to be considered are the diameter of the conduit (d) and the linear velocity of the fluid (v). The ratio of inertia force divided by the viscous force of the fluid is known as the Reynolds number. A dimensionless quantity, the Reynolds number is defined as:

Reynolds number = vd/v

Flow changes from laminar to turbulent at a Reynolds number of approximately 2300. It is apparent that for any given conduit and fluid, there will be a defined velocity at which the flow changes from laminar to turbulent. Turbulence will also occur wherever there is a sharp turn in the conduit, because the instantaneous velocity at that point increases. 

Why does it matter to an anesthesiologist whether the flow is laminar or turbulent? The Hagen-Poiseuille equation describes laminar flow:

ΔP = 8μvavgL/r2

where ΔP is the pressure drop across a conduit, vavg represents the average linear velocity, r represents the radius of the conduit and L represents the length of the conduit. Since vavg is the flow (Q) divided by the cross-sectional area, for a circular conduit (pipe or tube) this means that

Q = ΔPπr4/8μL

or in other words, flow is proportional to the fourth power of the radius for a given pressure drop and inversely proportional to the length of the tube. Thus, the larger an i.v., the faster blood can be administered. Similarly the longer the catheter, the more resistance there is to the flow of fluids through it.

Turbulent flow, however, is described by a complex equation which considers the frictional properties of the material through which the fluid is flowing. The equation tells us that turbulent flow is proportional to the square root of the pressure drop, and the fifth power of the radius. Turbulent flow is also inversely proportional to the length of the pipe and the density (not the viscosity) of the fluid.

Clinically, this means that the pressure required to breathe through a 6 mm ID (inner diameter) endotracheal tube will be approximately three times the pressure required to breathe through an 8 mm ID tube assuming laminar flow. For turbulent flow, the pressure required for the same breath will be approximately nine times as much. (In practice, such flow would typically be turbulent.) Shortening the endotracheal tube by 25% would decrease the pressure required, and hence the work of breathing, by about one-third. Similar comparisons can be made for the (usually laminar) flow through intravenous catheters and the (usually turbulent) flow through blood vessels.

Physical Properties of Gases

In addition to the fluid properties of a gas, static properties are also important. Although the gases we use in clinical practice are not “ideal gases,” the qualitative properties of the ideal gas equation can still be applied:

PV = nRT

where P represents pressure, V represents volume, n represents number of moles, T represents absolute temperature, and R represents the ideal gas constant.

For example, for any amount of gas at a constant temperature, the product of pressure and volume will be a constant, so as pressure increases the volume decreases. Thus Boyle law can be represented:

PV = k or P1V1 = P2V2

Similarly, at a given pressure, a rise in temperature will cause a gas to expand (Charles law.)

The concepts regarding pressure and partial pressure are also key to understanding many aspects of anesthetic gases. The pressure of a gas mixture (Ptotal) is the same as the atmospheric pressure to which the mixture is exposed in mm Hg (1 atm = 760 mm Hg). Moreover, the partial pressure of a gas in a mixture is the same as its proportion of molecules in the mixture (Dalton law).

Ptotal = P1 + P2 +... Pn

For example, in a mixture of 21% oxygen in nitrogen at 760 mm Hg barometric pressure (1 atm of pressure), the partial pressure of oxygen is 160 mm Hg and the partial pressure of nitrogen is 600 mm Hg. The same mixture of air in a hyperbaric chamber at 1520 mm Hg (2 atm) would have a partial pressure of oxygen of 320 mm Hg. 

At equilibrium, every liquid also has its own characteristic vapor pressure, which is exclusively a function of temperature. For example, the vapor pressure of isoflurane at 25°C is 295 mm Hg. So at room temperature (approximately 22°C), isoflurane exists primarily as a liquid, it must be heated slightly to enter the gaseous phase. And from the gas laws discussed earlier, it is easy to understand that the temperature must be constant in order to ensure the output of a specific, known quantity of isoflurane from the vaporizer.

At 1 atm, a saturated solution of isoflurane in air (such as found inside a vaporizer) would consist of 295 mm Hg partial pressure of isoflurane, 98 mm Hg partial pressure of oxygen, and 367 mm Hg partial pressure of nitrogen, or 38.8% isoflurane. In the same hyperbaric chamber at 2 atm, the mixture would consist of 295 mm Hg partial pressure of isoflurane, 257 mm Hg partial pressure of oxygen, and 968 mm Hg of nitrogen, or 19.4% isoflurane. Thus using the gas laws, the effect of varying atmospheric pressure on the output of a vaporizer calibrated at sea level can be understood. This has a clinical applicability when anesthetizing patients at high altitudes (even as in some parts of Colorado) or in a hyperbaric chamber.

Fires and Explosions

Despite the fact that highly flammable anesthetics are no longer used in the United States, fires and explosions in the operating room still occur. A fire requires three components: an oxidizer, a fuel, and a source of ignition.

Oxygen is not, in and of itself, flammable. But it is a potent, primary source of oxidation in an operating room. Nitrous oxide also supports combustion. In fact, several of the halogenated anesthetic agents are more flammable in nitrous oxide than in oxygen. Yet none approach the flammability of the older anesthetics, such as ether and cyclopropane.

Fuels abound in the operating room, especially on the operative field. Everything from tape to gauze to drapes will burn under the right conditions. Flammable gases present in the operating room include hydrogen and methane from the intestines (fires have been reported when electrocautery is used to open the bowel), as well as vapors from some skin-disinfection solutions. Alcohol-based disinfectants, which have pooled unnoticed around the surgical field, are especially flammable. (An explosion rather than a fire will occur if the flammable gas and the oxidizer are present in stoichiometric proportions.) The patient’s tissues do not act as a fuel because of their high moisture content, but of course are at risk of thermal injury from adjacent flames.

Any heat source may act as a source of ignition if it generates enough energy. The most common ignition sources are the electrocautery and the laser. It should be noted that gases do not absorb laser energy, and therefore will not burn until the laser generates heat by contacting a solid such as tissue or any other object in the field. The energy of laser cautery is sufficient to ignite a fire either from the generation of heat or from the generation of a spark. Fires may occur when the laser beam contacts a surgical drape under which anesthetic gases are pooled (eg, patients receiving monitored anesthesia care with supplemental oxygen or a mask general anesthetic).

Head and neck surgery poses a special risk. Endotracheal tubes themselves are flammable. For surgery within the airway (eg, laser excision of a vocal cord lesion) specialized metallic tubes exist which will not burn. Alternatively, a regular endotracheal tube may be carefully wrapped with metallic tape, although the liability should an injury occur generally discourages this practice. The cuff of either of these tubes is still flammable. Many practitioners will therefore inflate the cuff with saline instead of air with the intent of immediately extinguishing any fire that may occur.

If an endotracheal tube is ignited, the most important goal is to minimize thermal injury. Before removing the burning tube from the patient, the oxygen source (anesthesia circuit) must be disconnected to prevent the tube from becoming a blowtorch injuring airway tissues on the way out. At the same time, if the fire is in the surgical field (eg, tracheostomy surgery), sterile saline should be poured on the fire to extinguish the flame, cool the surrounding tissues thereby minimizing thermal injury. Finally, the airway should be immediately re-intubated and not extubated until the full extent of airway injury and resultant edema can be assessed.

Electrical Safety

The risks of electricity in the operating room include macroshock, microshock, and electrical burns.

All electricity requires a “closed circuit” to flow. If the circuit is interrupted, the electricity flows to the ground (which acts as a huge sink for electrons). It flows through any pathway it can find, including an accidentally grounded patient or anesthesiologist. This is called a macroshock, which occurs when a grounded person makes contact with a live electrical wire.

Macroshock is prevented by the isolation of any equipment that will come in contact with the patient from the main electrical supply. Electrical isolation uses a transformer to convert electricity through a coil to a magnetic field, and then from the magnetic field to electricity again through a second coil, which has no connection to ground. (The metal cases of these pieces of equipment are grounded to prevent macroshock to personnel who may contact them.) Any short circuit between either side of the isolation transformer and ground will not result in the flow of current; however, the system would then be equivalent to a non-isolated, traditionally grounded one. Conversion of an isolated piece of equipment to a grounded piece of equipment is detected by the line isolation monitor in operating rooms. This monitor will alarm if any piece of equipment is inadvertently grounded and therefore no longer isolated.

Even tiny currents of electricity can be dangerous if they contact the myocardium, which can occur by the transmission of currents through pacemaker wires or saline-filled monitoring catheters. Again, since electricity takes the path of least resistance to either complete its circuit or flow to ground, the best way to avoid microshock, in addition to isolating the patient from the main power source, is to provide the current a path that takes it away from the heart. This is the purpose of the dispersive electrode of the electrocautery system—to complete the circuit of electricity back to the electrosurgical unit. (The electrode is often erroneously referred to as the “grounding pad” but its function is exactly the opposite of “grounding” the patient.) To minimize the current passing through or near the heart, the dispersive electrode should be placed as close as possible to the site of the surgery so that the current will travel minimally through the body. Ideally, the electrosurgical unit should have an alarm that will sound if the return current is interrupted for any reason.

The dispersive electrode has a relatively large surface area through which the electrical current can pass on its way back to the electrosurgical unit. (Remember that this is the same amount of electricity that is efficiently burning the tissue as it passes through the small tip of the cautery.) If the return to the unit passes through a smaller surface area, for example, if the dispersive electrode partially loses contact with the patient’s skin, the skin under the electrode is at risk for a burn. In the same manner, if the patient were to be inadvertently grounded, say through his ECG electrodes, the current could preferentially pass through those very small electrodes on its way to ground and cause burns to the skin.

Comprehension Questions

5.1. A 63-year-old patient undergoing an open reduction internal fixation of a hip fracture requires a blood transfusion. After the fluid warmer is introduced into the i.v. circuit, the blood drips much more slowly than it previously had. Which of the following answers best accounts for this phenomenon?

    A. The i.v. has infiltrated.

    B. The diameter of the tubing in the blood warmer is smaller than the diameter of the intravenous tubing set.

    C. The fluid warmer effectively adds length to the intravenous tubing set.

    D. Blood is thicker than water.

5.2. The material used for a vaporizer should have which of the following qualities?

    A. Low specific heat, low thermal conductivity

    B. Low specific heat, high thermal conductivity

    C. High specific heat, low thermal conductivity

    D. High specific heat, high thermal conductivity

ANSWERS

5.1. C. The fluid warmer effectively adds length to the intravenous tubing set. While it is also possible that the i.v. has become infiltrated, the temporal association with the introduction of the blood warmer into the circuit suggests that the warmer is somehow related to the slowing of the infusion. Even if the diameter of the tubing in the blood warmer was smaller than the diameter of the i.v. set, the smallest diameter—and thus the “bottleneck” with respect to diameter is likely to be the i.v. catheter itself. Although blood is indeed more viscous than water, the blood ran faster prior to the induction of the fluid warmer.

5.2. D. High specific heat of the material will act as a heat source to replace the heat lost during vaporization, and high thermal conductivity will facilitate transfer of heat from the surroundings to replace the lost heat of vaporization as well, both helping to maintain the liquid at constant temperature and therefore maintain a constant vapor pressure. This is the reason that early vaporizers were constructed of copper (“copper kettle”) or brass (Vernitrol vaporizer.)

Clinical Pearls

➤ Flow is proportional to the fourth power of the radius (r 4), and inversely proportional to the length of a tube.

➤ Even tiny currents of electricity can be dangerous if they contact the myocardium via pacemaker wires or saline-filled monitoring catheters.

➤ In case of fire, the goal is to minimize thermal injury to the patient. In the case of airway fire, this requires immediate disconnection of the patient from the oxygen source (before removal of the endotracheal tube.)

References

Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena. 2nd ed. New York, NY: John Wiley and Sons; 2007. 

Davis PD, Kenny GNC. Basic Physics and Measurement in Anesthesia. 5th ed. Edinburgh, UK: Elsevier; 2003. 

Lobato EB, Gravenstein N, Kirby RR, eds. Complications in Anesthesiology. 3rd ed. Philadelphia, PA: Lippincott, Williams & Wilkins; 2008. 

Welty J, Wicks CE, Rorrer GL, Wilson RE. Fundamentals of Momentum, Heat and Mass Transfer. 5th ed. New York, NY: John Wiley and Sons; 2008.

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