Introduction

The basic principle of closed-circuit anesthesia is maintenance of a constant anesthetic state by adding gases and vapors to the breathing circuit at the same rate that the patient’s body removes those same substances. Often, the desired anesthetic state is first established using a high fresh gas flow (FGF) composed of gases, such as oxygen and nitrous oxide or air, and vapors (e.g., isoflurane, sevoflurane, desflurane). Once a steady state is attained, inspired and end-expired gas concentrations or tensions are noted, and FGF is reduced. Throughout this chapter, the words tension and partial pressure are used interchangeably. For gases, they have the same value as concentration. This is discussed under the section Partial Pressure. The circuit and patient gas tensions are maintained constant by adding oxygen, nitrous oxide, and agent vapor to the breathing circuit. In one common approach to closed-circuit maintenance, the amount of gas and vapor administered is determined empirically by titration. Several different titration endpoints can be used. Choices include maintenance of inspired tension, expired tension, and/or estimated anesthetic depth. When titrating against a defined endpoint, drugs can be added in a measured or quantified manner, or they can be added empirically without regard to the total amount administered. In closed-circuit anesthesia techniques, carbon dioxide is removed from exhaled gas, and the remaining exhaled gases and vapors are added to the FGF to produce inhaled gas. One advantage of this technique is that all gases exhaled are already warmed and humidified by the patient and are therefore well suited for rebreathing. Another advantage is that oxygen consumption is monitored by titration. A final advantage is that cost is reduced dramatically.

In closed-circuit and low-flow anesthesia, inhaled gas is formed from two sources, and exhaled gas forms most of what the patient will breathe. In addition to exhaled gas, fresh gas is added in the correct quantity and composition to achieve the inspired gas tensions desired. The same inspired and expired gas tensions are established with a closed circuit as with a semiclosed or open (nonrebreathing) circuit. In this chapter the terms open circuit and nonrebreathing circuit are used interchangeably.

Closed-Circuit Anesthesia

Closed-circuit anesthesia can be viewed in several different ways. From one perspective, it is an anesthetic technique unlike all others. The classical closed-circuit literature describes theory and practice different from other techniques. In the classic closed-circuit approach, once a stable level of anesthesia is established with high-flow oxygen, nitrous oxide, and volatile agent, FGF is reduced to the patient’s predicted oxygen consumption (243 mL/min for a 70-kg adult), predicted nitrous oxide uptake rate (approximately 100 mL/min after the first 30 min), and predicted inhaled agent uptake. Nitrous oxide and agent uptake rates are calculated according to a mathematical formula based on body weight.

The traditional closed-circuit anesthesia literature uses anesthetic liquid injection or infusion rather than a vaporizer. Liquid agent is administered to the breathing circuit according to a prescribed time regimen. Specifically, the drug administration rate is inversely proportional to the square root of time (t):

This empiric relationship was first noted by Severinghaus for nitrous oxide in 1954 and was popularized by Lowe beginning in 1972. Severinghaus’s original data demonstrated that nitrous oxide uptake followed this power/function relationship fairly closely in the subjects he studied. Connor and Philip recently revalidated this mathematical relationship numerically and analytically.

A scientific explanation exists for this curious and unexpected relationship. It has long been known that body tissues perfused with blood of a constant drug concentration or vapor tension have an uptake rate that decreases with time. Specifically, theory and research have demonstrated that uptake into each tissue takes the form of an exponential:

and

where <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='t12′>t12t12
t 1 2
equals the time required to achieve half the final value in response to a step input.

Total body uptake is the sum of the individual uptakes by each tissue. In this case, uptake is the sum of a group of exponentials of different amplitudes (K _tissue ) and time constants (τ _tissue ). The sum of these exponentials is approximately equal to the power function, <SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='K×t−0.5′>K×t−0.5K×t−0.5
K × t − 0.5
. It must be emphasized that the exponential relationship for a single tissue is derived theoretically and can be demonstrated empirically. But the power/function relationship is an empiric one that approximates the multiple exponential functions that describe the uptake into diverse tissues.

Partial Pressure, Tension, and Concentration

Throughout this chapter, the words tension and partial pressure are used interchangeably. This physical variable represents the effective pressure exerted by a gas, whether it is in the gas phase alone, in combination with another gas, or dissolved in blood or tissue.

Partial pressure is expressed in percent of 1 atmosphere (1 atm = 760 mm Hg). Expressing partial pressure this way serves several purposes. When partial pressure is expressed as percent of 1 atm, partial pressure and concentration have the same numeric value for gases. For example, 1 vol% isoflurane has an isoflurane tension of 1% of 1 atm, an expression often shortened to 1%. For blood and tissues, partial pressure is also expressed as a percent. By this definition, a tissue anesthetic measure of 1% does not represent 1% concentration; rather, it represents a partial pressure of 1% of 1 atm or 1% times 760 mm Hg, or 7.6 mm Hg in terms of absolute pressure.

Next, when partial pressure is expressed as a percent of one standard atmosphere (i.e., 760 mm Hg), the numbers and concepts work equally well at any atmospheric pressure. This is because the physiologic effects of inhaled anesthetics are the result of partial pressure and not concentration. Thus, anesthetic tensions in the apparatus and patient are the variables that best explain kinetics in an understandable way.

When anesthetics are present in liquid or tissue, their concentrations are equal to their partial pressure × tissue/gas solubility × atmospheric pressure, according to Henry’s law. According to Dalton’s law, for multiple gases, this applies to each as if it were alone.

It is believed that the blood leaving each tissue compartment is in equilibrium with the tissues in that compartment, therefore the partial pressure in venous blood is equal to that in the tissues, as Graham’s law states. The blood entering each compartment has the same partial pressure of all gases as the arterial blood has everywhere. In the absence of lung shunt, arterial partial pressure equals alveolar partial pressure. Clinicians measure end-tidal (ET) gas concentrations or partial pressures. End-tidal partial pressure equals alveolar partial pressure when there is no physiologic dead space. After an infinite amount of time, the partial pressure of anesthetic inspired gas, alveolar gas, arterial blood, all tissues, and all venous blood, including mixed venous blood, is equal. At this time, there is no blood uptake of anesthetic at all. Thus the inspired and expired partial pressures are equal as well. Thus, after an infinite amount of time, the partial pressure of anesthetic throughout the system, from vaporizer to all tissues, is the same.

The above paragraph is a simplification that serves well in most situations. Exploring this further, in the presence of lung shunt, arterial tension is closer to mixed venous tension than it would be otherwise. When physiologic dead space is present, some of the gas leaving the lungs is inspired gas, rather than alveolar gas. This makes end-tidal partial pressure closer to inspired partial pressure than it would otherwise be. These are temporary limitations. After an infinite amount of time, these effects disappear as well, and anesthetic tension is equal everywhere. Because the alive body continues to consume oxygen and produce carbon dioxide, this equalization does not occur with these gases.

Lowe Technique

In the classic Lowe technique for closed-circuit anesthesia, a loading dose of anesthetic vapor is administered to the breathing circuit to bring circuit tension to that desired in the patient’s alveoli. This level is somewhat higher than in the inspired gas. A unit dose for maintenance is then selected according to the patient’s body weight and is proportional to body mass to the three-quarter power (kg ^3/4 ), a relationship first shown by Kleiber that has been further described by Brody. Kleiber’s law goes on to state that many parameters of metabolic and circulatory processes—oxygen consumption, carbon dioxide production, cardiac output, and daily liquid requirement—are proportional to body mass raised to the three-quarter power.

In Lowe’s classic closed-circuit anesthesia, unit doses are administered at specific times with intervals between administrations increasing with time. These intervals, in minutes, are the sequence of odd integers {1, 3, 5, 7, 9, …} This results in injections being made at 0, 1, 4, 9, 16, and 25 minutes. This is referred to as the square root of time model, in that these injection times are the series of numbers whose square roots are sequential integers. This strange number manipulation may seem farfetched; however, Connor and Philip demonstrated that this relationship approximated the uptake of nitrous oxide shown by Severinghaus with remarkable accuracy.

Even closed-circuit enthusiasts advise care and careful observation of the patient, as always. Lowe recommended that after 25 minutes, the square root of time method should be modified, and that the intervals between injections should not be lengthened as much (Lowe, personal communication, 1979). This is because after 25 minutes of anesthetic at constant depth, the rate of uptake becomes almost constant. By this time, fast (vessel-rich) tissues have equilibrated with arterial blood. Meanwhile, uptake into muscle and fat are diminishing slowly, more slowly than the square root of time, because of their long time constants.

It must be noted that the original 1972 theory and “cookbook” for closed-circuit anesthesia was written during the era of more primitive measurement and analysis (in 1972, the digital pocket calculator had not yet replaced the analog slide rule). Anesthetic agent analysis was uncommon, and the only clinically available device was the Dräger Narkotest (Dräger Medical, Telford, PA), which consisted of a slowly responding silicone rubber band in a box connected to a mechanical indicator. The “rubber band in a box” stretched in proportion to the potency of the single or combined inhalation anesthetic tensions administered.

With each administration technique—open circuit, semiclosed circuit with high flow, semiclosed circuit with low flow, closed circuit with vaporizer, and closed circuit with liquid injection—each patient’s inspired, end-expired, and alveolar anesthetic tensions are the same and are independent of administration technique. Thus from the patient’s viewpoint, all inhalation anesthetic administration techniques are equivalent. The only difference is in the way the drugs are administered and the resulting waste or lack thereof.

Although the conventional closed-circuit literature used models created by fitting experimental data to particular mathematical formulations, this chapter does not rely on these. Rather it assumes that an anesthetic agent monitor is available and in use, measuring inspired and expired anesthetic concentrations. The dosage administration scheme is adjusted on the basis of a patient’s measured and needed levels of inspired and expired vapor and nitrous oxide. Delivered oxygen flow is adjusted similarly. In the absence of a multigas monitor, closed-circuit anesthesia may still be employed, but greater vigilance and understanding of anesthetic depth and uptake of anesthetic and oxygen are required.