To understand the action of anesthetic drugs, I needed to understand the process by which the drugs enter the body and are transported to the brain and other tissues. These are basic principles of physics (eg, flow and diffusion), chemistry (eg, solubility), and physiology (eg, metabolism). In my days on the third floor of the Fort Leavenworth hospital, I expressed these concepts in equations. My differential equations provided precise, testable descriptions of the processes of anesthetic uptake and distribution.

John was not particularly interested in my studies of uptake and distribution when I became his fellow. However, he saw that this was important to me and accepted my initiatives. To pursue my mathematical models required resources beyond clinical laboratories. Fortunately, the University of California at San Francisco was a world-class medical school with all the trimmings. I took a course in Fortran and worked with the teacher to express my equations in that language. One cool spring night we converted our Fortran code into punch cards and read those into Berkeley’s massive IBM computer. Who could not be impressed by a computer with so many vacuum tubes that it required an air-conditioned building just to keep from melting. We pressed the GO button and awaited the result. Streams of neatly folded pages, each with hundreds of lines of results flowed out of the printer. Within a few minutes on that cool spring Berkeley night my equations produced a year’s worth of Ft. Leavenworth work. I now had predictions that I could experimentally test.

In John’s lab, I’d learned to use the infrared analyzer to measure CO₂. John had other infrared analyzers that measured nearly all inhaled anesthetics, and I learned to use those, too. We pushed these analyzers to their limit to determine anesthetic solubilities in blood, tissues, and the materials in the anesthetic circuits used to deliver anesthetics to patients.¹ However, as our research progressed, we needed ever greater sensitivity in our assays. We learned about something called a gas chromatograph, a device that increased our reach a million-fold. We purchased one, and then two.

In 1961, a wonderful event brought John back to uptake and distribution. In that year, Emanuel Papper, the chairman of the Department of Anesthesiology at Columbia University, invited John to participate in a 1962 Conference on Anesthetic Uptake and Distribution (the first conference on the topic). As a good mentor, John saw to it that I was also invited to participate. All my efforts, equations, predictions, and ideas would have a forum!

In 1960, Henry Price used principles of blood flow and tissue solubility to explain the distribution of thiopental after intravenous injection.² This work led John,³ Thomas MacKrell,⁴ and William Mapleson⁵ to predict the uptake and distribution of inhaled anesthetics using the same concepts. I also incorporated Price’s work into my equations. However, John, Thomas, and William used mathematical approximations (rather than my exact iterative approach) to predict the uptake and distribution of inhaled anesthetics. They applied their equations to the rates of increase of the alveolar (F_A) to inspired (F_I) anesthetic concentrations (the F_A/F_I ratio), which they presented at the conference. However, I knew that their approximations were incorrect because they did not predict the effect of the inspired concentration, the concentration effect.

At the meeting John and Tom MacKrell spoke first, presenting the predictions of uptake and distribution from their work with simulation models based on resisters and capacitors. I went next, presenting the results of my differential equations solved computationally at Berkeley. I showed that the approximate equations used by John and Tom could not correctly incorporate dynamic aspects such as the nonlinear influence of inspired concentration of a gas on its own rate of uptake. William Mapleson presented his results last. This wry Welshman started by saying his “…talk was in shambles.” He thought he offered novel solutions, but Severinghaus and MacKrell had already presented nearly identical work. Even worse, I showed that their work was incomplete, as it could not predict either the concentration or the second gas effects.

As is so often the case, their work was not “wrong,” per se, but simply incomplete. Science advances from initial approximations of the truth to better approximations. My differential equations were a better mathematical model than their simulations based on resisters and capacitors. As expected, yet better models came along. For example, none of us had paid attention to the work of William Perl, who rightly pointed out in 1960 that uptake might be influenced by the movement of gas from one tissue to an adjacent tissue, eg, intertissue diffusion.⁶ He repeated this possibility at the conference.⁷ Of course, he was right, and our models evolved to accommodate more data.

The proceedings of the 1962 New York conference were published the following year. For the anesthesia community, this led to a seminal transformation by quantifying the movement of anesthetics into and throughout the body. It was a major contribution to the evolution of anesthesia from a clinical art into a quantitative science. It was the culmination of my thoughts that began with my 1958 conversation with John after his lecture to Iowa residents. I had filled my days at Fort Leavenworth with differential equations that yielded their predictions only through laborious calculation. These calculations predicted the effect of differential blood flow and solubility on anesthetic distribution, and underlay the fortuitous discovery of the concentration effect.⁸ The conference participants shared the conclusions that differential tissue blood flow as well as solubility determined the effect site concentrations of anesthetics.

My work prompted Dr. Cullen to invite me to apply for an NIH Research Career Development Award, something that would provide financial support for full-time research. John would mentor me for five more years. “Yes!” I said, addicted to what I was doing and might do with John. And so my 1- or 2-year sojourn in California extended to forever. What follows is more of a scientific odyssey than a personal autobiography, a journey that largely took place starting in the 1960s and continuing through the 1970s, and beyond.

My earliest work, the construction of the differential equations describing the travel of anesthetics into and throughout the body, relied on solubility values determined by other investigators. But now, invested in the chase and possessing the means for making my own determinations, I contributed my share of basic biological findings. What a wonderful adventure, erecting this dusty, dull, dreary, and absolutely indispensable underpinning to inhaled anesthetic pharmacokinetics. From 1961 to 1970, we published 16 reports that incorporated the measurement of solubility. This decreased to two or three reports per decade in subsequent years, most of these in concert with reports on new anesthetics.

The early approaches to describing the partial pressure of anesthetic in the brain (or wherever the anesthetic acted) were predicated on the assumption of a constant inspired anesthetic concentration. The answer typically took the form of a curve showing the ratio of F_A (the fraction of anesthetic in the alveoli) to F_I (the fraction of anesthetic in the inspired gas) over time. But that isn’t how anesthesia is given. Experienced anesthesiologists know how to administer an
anesthetic with high concentrations initially, to achieve a nearly immediate effect. After that, the inspired concentration is quickly reduced, as the anesthesiologist precisely titrates the amount of anesthetic required for the suppression of the response to the surgical stimulus. A sustained constant alveolar (end-tidal) anesthetic concentration provides a closer approximation to the clinical delivery of inhaled anesthetics than delivery of a constant inspired anesthetic concentration. In 1963, Neri Guadagni and I reported on this approach with halothane.⁹

Holding the alveolar concentration constant got closer to a constant anesthetic state than did the application of a constant inspired concentration. However, to be useful, the alveolar concentration had to be reflected in the effect site in the central nervous system, wherever that unknown site might be. This required allowing sufficient time to transfer anesthetic from lungs to site. We could get closer to a constant anesthetic state if we could impose a sustained anesthetizing concentration at the effect site. We didn’t know how to do that, in part because we didn’t know where that site was (it turned out that for some anesthetics, it wasn’t even the brain).¹⁰,¹¹ And, besides, how would we sample the anesthetic at that site? Brain samples were certainly not going to be approved in patients (or anyone else).

It had been known for decades that inhaled anesthetics affected the electroencephalogram.¹²,¹³ Based on this work, Albert Faulconer suggested that we use EEG waveforms as surrogate measures of anesthetic concentration at the effect site. We demonstrated this for ether in the 1960s.¹⁴ Years later, Chris Hull,¹⁵ a British anesthesiologist, and Lewis Sheiner,¹⁶ a clinical pharmacologist at UCSF, worked out the mathematics of characterizing plasma—effect site equilibration rates for muscle relaxants. The effect site is one of the fundamental concepts in anesthetic pharmacology. Decades later, the EEG became a standard clinical monitor of the effect of inhaled and intravenous anesthetics and sedatives on the brain.¹⁷

We quantified the effects of changes in ventilation and cardiac output on the rate of rise in the alveolar anesthetic concentration.¹⁸,¹⁹ It is obvious that an increase in alveolar ventilation delivers more anesthetic to the lungs and thereby accelerates the rise. However, as I discovered in 1956 after hearing John Severinghaus explain it, it is less obvious that increased solubility decreases the rate of rise. It is also less obvious why alterations in ventilation minimally affect the acceleration of poorly soluble anesthetics such as nitrous oxide but greatly affect the acceleration of highly soluble anesthetics such as ether.

Why does solubility play such a profound role? F_A/F_I rapidly increases with poorly soluble anesthetics since little of what is delivered to the lungs is removed. As an extreme case, consider inhaling a substance with no solubility in body tissues at all. After a few breaths to wash in the inspired substance, F_A equals F_I. Even if the patient stops breathing after these first few breaths, F_A continues to equal F_I. This is why, for poorly soluble anesthetics, F_A quickly rises toward and only slowly falls from F_I, even if ventilation is depressed. An increase in ventilation cannot have much effect since F_A quickly rises toward F_I under any circumstances. Conversely, blood absorbs most of a highly soluble anesthetic delivered to the lungs and would do so even if normal ventilation were doubled. Alveolar concentration is proportional to the concentration in blood. With a very soluble anesthetic, doubling ventilation approximately doubles the rise in alveolar concentration until equilibrium is approached.

In contrast to the effect of increasing ventilation, increasing cardiac output hinders the rise in alveolar concentration. As with the effect of changes in ventilation, a change in cardiac output has little effect on the alveolar concentration for poorly soluble anesthetics and a larger, even proportional effect for highly soluble anesthetics. Mathematically, the capacity for anesthetic transport is the product of cardiac output and solubility. That is why they are interchangeable. If you understand one, you understand both.

Anesthetics may depress ventilation, circulation, or both.²⁰,²¹,²² There is some safety when anesthetics depress ventilation and the patient is spontaneously breathing. As breathing slows, the rate of rise in anesthetic concentration also slows, particularly for the more soluble anesthetics as explained above. Anesthetic-induced depression of ventilation creates negative feedback limiting the rise in anesthetic concentration. Thus, spontaneous ventilation increases the safety of inhaled anesthetics.²³ Adding further to the safety of spontaneous ventilation, anesthetic-induced depression of ventilation increases PaCO₂, which in turn increases cardiac output.²⁴,²⁵

As explained above, the increase in cardiac output decreases the rate of rise of alveolar anesthetic concentration, limiting cardiovascular depression. Conversely, using mechanical ventilation to sustain a normal PaCO₂ bypasses this potentially important safety feedback loop, leading to concentration-related depression of cardiac output.²¹,²⁶ Anesthetic depression of circulation decreases uptake, hastening the rise of F_A/F_I. The increased F_A further depresses cardiac output, further increasing F_A/F_I. This positive feedback loop can lead to cardiovascular collapse and death.²³ Changes in cardiac output also affect the distribution of anesthetics into peripheral tissues,¹⁸ a complex pharmacokinetic feedback system that is necessarily described by differential equations.

The interactions of solubility, ventilation, cardiac output, anesthetic concentration, and its uptake are more complex than these introductory comments imply. For example, consider a subject inspiring a low concentration of a highly soluble anesthetic. Ignoring the effects on CO₂, doubling ventilation in this subject will double alveolar and (thus) arterial concentrations. Now let’s consider the same subject breathing an intermediate concentration of the same highly soluble anesthetic. Again, ignoring the effects on CO₂, if ventilation is doubled then the alveolar concentration more than doubles. The reason is that the uptake of anesthetic will draw more air and anesthetic into the lungs. Almost paradoxically, ventilation more than doubles. Add to these thoughts the effect of the fresh gas inflow rate. A lower fresh gas inflow rate limits the effects of increased ventilation since more gas is rebreathed and uptake has depleted the anesthetic from the rebreathed gases, limiting the capacity of anesthetic uptake to enhance ventilation.

Further complicating matters, surgical stimulation increases both ventilation (in the spontaneously breathing patient) and cardiac output. This antagonizes the ventilatory and circulatory depression caused by inhaled anesthetics.²⁷,²⁸ In the study by France and colleagues,²⁸ surgical stimulation increased both alveolar ventilation and production of carbon dioxide, without materially changing PaCO₂ at a given target MAC value (1.0, 1.5, or 2.0 MAC). This indicates that surgical stimulation increased metabolism, ventilation, and cardiac output concurrently and to approximately the same extent. As noted in the succeeding paragraph, such concurrent increases can increase F_A/F_I: proportional increases in both cardiac output and ventilation have opposing effects that might exactly oppose each other were it not for the effect of increased cardiac output on tissue time constants.

To explain this, I need to introduce the three concepts: tissue volume, tissue flow, and the time constant. Tissue volume is the capacity of a tissue to hold anesthetic, calculated as anesthetic solubility in the tissue times tissue mass. Tissue flow is total blood flow to the tissue. The time constant is the tissue volume divided by flow. Volume and flow can be expressed for the total tissue, as just described, or per unit of tissue mass. It does not matter; the time constant is the same.

The time constant is the time it takes for a 63% change in tissue concentration following a step change in blood concentration. If cardiac output increases the flow of anesthetic to tissues, then the time constants (volume/flow) for the tissues will decrease. This decrease in the tissue time constant increases the rate at which tissues come into equilibrium with the arterial concentration. This accelerates the rate of rise in F_A/F_I.

This seems paradoxical! Didn’t I explain a few paragraphs ago that an increase in cardiac output slows the rate of rise in F_A/F_I? Yes, but, as they say, it’s complex. The net effect of increased cardiac output is slower rise in F_A/F_I. However, the
effect of increasing uptake from the lungs with increasing cardiac output is slightly offset by the more rapid rise to steady state in peripheral tissues based on the smaller (shorter) time constants.

Stimulation did not change F_A in the study by France and colleagues²⁸ because the F_A was controlled at targeted levels by altering the delivered concentration of anesthetic.

Most of the previous discussion considered the effect of changes in ventilation or changes in circulation independent of each other. But these often occur concurrently. In perhaps the simplest case, assume that ventilation and cardiac output increase in proportion to each other; if ventilation doubles or triples, so does cardiac output. Further, assume that the increases in blood flow occur proportionately in all tissues: if blood flow to the heart doubles, so does blood flow to all other tissues. What then happens to the rise in F_A/F_I? It would be easy to be misled into thinking that the answer is “nothing.” That is not correct. Consider the extreme case in which ventilation and cardiac output are both infinitely fast. In that case, F_A/F_I rises instantly from 0 to 1 the moment the anesthetic delivery starts. As a physiologically plausible example, consider a doubling of ventilation and cardiac output. A doubling of ventilation initially doubles delivery of anesthetic to the lungs. If cardiac output doubles, that doubles the blood passing the lungs that removes anesthetic. However, while the doubling of cardiac output initially offsets the doubling of ventilation, it hastens delivery of anesthetic to tissues (exactly as increasing ventilation hastens delivery of anesthesia to the lungs). A doubling of blood flow to a tissue approximately halves the time for equilibration of anesthetic with the tissue, thereby returning increasingly greater concentrations of anesthetic to the lungs. The greater blood flow cannot compensate for the greater delivery of anesthetic by ventilation and the rate of rise in F_A/F_I must increase.²⁹ This simplest case may explain what happens to F_A/F_I when metabolism increases in febrile patients or perhaps hyperthyroid patients. Metabolism, CO₂ production in all tissues, ventilation, and blood flow increase in rough proportion (ignoring differential blood flows needed to manage temperature regulation).

Nature provides a satisfying experiment testing the above hypothesis. Proportionate increases in ventilation, cardiac output, and the distribution of blood flow per kg of tissue occur with decreasing size of animals. The rat has a greater ventilation and cardiac output per kg than a human. Thus, the rate of increase in F_A/F_I should be more rapid in a rat than a human, and more rapid in a human than a whale. Wahrenbrock and others showed that this was the case.³⁰

Under some conditions, the proportional changes in blood flow assumed in previous paragraphs are not found. Ventilation and cardiac output may both double, but the increased cardiac output may not be proportionately increased to all tissues, being more than doubled for some and less for others. This can variously affect the rate of increase in F_A/F_I. In the extreme case of hypovolemic shock, cerebral blood flow is preserved at the expense of blood flow to everything else. In this reduced heart-brain circuit, F_A/F_I rises extremely fast, raising considerable risk of cardiovascular collapse and death.

In the very young patient, the vessel rich group (VRG) of tissues (which include the brain, heart, splanchnic bed, kidney, and endocrine glands) constitutes a greater fraction of body mass, has a greater metabolic rate, and receives a greater blood flow than in the older patient.²⁹ Although ventilation and cardiac output may be proportionately greater per kg of tissue in the young patient (ie, both ventilation and cardiac output might be 30% greater in the young), two factors lead to a faster rise in F_A/F_I in the younger patient. First, as when the increased blood flow is distributed proportionately to all tissues, the greater blood flow in the young patient accelerates the equilibrium of tissue and blood anesthetic partial pressures (shortens the time constant for tissue equilibration) and thus uptake slows more rapidly in the young, increasing the rate of rise of F_A/F_I. Second, the increase in cardiac output is not proportionately distributed. The brain and other VRG tissues are bigger relative to other tissues in the young. They receive a greater fraction of the cardiac output. The brain and other VRG tissues normally equilibrate quickly with time constants of 3 or 4 minutes in adults and even shorter time constants in the young. Because these tissues receive a greater fraction of the cardiac output in children, their rapid equilibration results in a more rapid rise in blood concentration, which hastens the rise of F_A/F_I.

The above argument indicates a more rapid induction of anesthesia in the young. And the smaller functional residual capacity in the younger patient would accelerate the equilibration of the gases in the lung, adding further to the speed of induction. The increased fraction of cardiac output delivered to the brain decreases the time constant for blood-brain equilibration, further speeding induction of anesthesia. If the inspired concentration is not increased, the higher MAC values in young patients³¹,³² might slightly offset the faster equilibration kinetics. Even if the same inspired concentration is used in young and older patients, induction is usually more rapid in the young patient.

In the above example, children have a proportionate increase in regional blood flow to rapidly equilibrating tissues, which increases the rate of increase in F_A/F_I and thus the rate of anesthetic induction. The opposite situation will
occur if, instead, there is an increase in regional blood flow to muscle or (especially) fat, which have huge capacity to store anesthetic. These tissues equilibrate very slowly. Even though these tissues will equilibrate more quickly if they receive a greater fraction of cardiac output, that will not compensate for the slower equilibration in brain and other rapidly equilibrating tissues because of fractionally reduced blood flow. The net effect of a proportional increase in blood flow to muscle and fat will be to slow the rise of F_A/F_I and the onset of anesthesia.

Consider the case of an increase in cardiac output matched by a proportional increase in ventilation, but with a redistribution of cardiac output to muscle (eg, exercise). The net effect might be a slower increase in F_A/F_I because a significant fraction of the drug taken up from the lungs is dumped into a muscle sink.³³ For a time, uptake is increased, and thereby the rate of rise of F_A/F_I slows. Excitation on induction of anesthesia might supply circumstances leading to an increased blood flow to muscle… and a delay in induction of anesthesia. Similarly, weight reduction or injection of a beta-agonist can increase blood flow to fat.³⁴ The increased blood flow to fat would be expected to slow the rise of F_A/F_I during induction of anesthesia.

In my clinical practice in the 1960s, I would occasionally anesthetize children. I remember seeing these principles play out when I anesthetized them with ether. I would tell them stories and pretends. “There’s a rabbit in the mask that you are going to breathe from and this funny rabbit smells of onions because he eats onions. See if you can smell the rabbit.” And the patient and I would see if we could smell the rabbit. I adjusted the gaseous river of highly soluble ether flowing into child’s lungs as I maintained the happy deception of the rabbit with halitosis. By and by the child went to sleep. When the child woke he would ask where the rabbit had gone. I don’t think I ever explained that the rabbit had vanished into thin (and expired) air.

A decrease in body temperature influences both pharmacokinetics and pharmacodynamics of inhaled anesthetics, increasingly delaying induction of anesthesia as anesthetic solubility increases.³⁵ Consider the changes in pharmacodynamics. MAC rectilinearly decreases for potent clinical anesthetics as temperature decreases.³⁶,³⁷ One might think that if the patient is cold, then the decrease in MAC with colder temperature would result in a more rapid onset of anesthetic effect. However, as is so often the case, it is more complicated.

Pharmacokinetics also change with decreasing temperature. For starters, decreasing body temperature increases the solubility of anesthetics in the brain and other tissues.³⁸ As we know, increased solubility slows the onset of anesthesia. Decreasing temperatures also decrease metabolism, which decreases both ventilation and cardiac output. A decrease in ventilation slows the delivery of anesthetic to the lungs, and a decrease in perfusion slows the delivery of anesthetic to the brain and other tissues, but it may increase the rate of rise of F_A/F_I because uptake from the alveoli decreases.

However, it gets more complex still. Not only does solubility increase in the brain, it increases in the blood. This slows the rate of rise of the anesthetic partial pressure in blood. However, the blood has more capacity to deliver anesthetic to the brain. The significantly reduced cerebral oxygen requirements with hypothermia will reduce cerebral blood flow, overall decreasing anesthetic delivery.

The net result is that induction of anesthesia slows as body temperature decreases. If the cold patient is given the same inspired concentration as a normothermic patient, the eventual anesthetic state will be more profound in the cold patient. However, the slowing of induction differs among anesthetics as a function of solubility. A more soluble anesthetic will have greater delay in induction consequent to a decrease in temperature than a less soluble anesthetic.³⁵ Fortunately, this is mostly an intellectual exercise because our patients typically come to us at 37°.

The usefulness of the F_A/F_I ratio depends on the partial pressure fraction in arterial blood, F_a, closely following the partial pressure fraction in the alveoli, F_A. Unfortunately, F_A-F_a differences do appear in normal subjects, particularly early in anesthesia.³⁹ For nitrous oxide, the differences become minimal within a half hour of breathing a constant F_I.³⁹

F_A-F_a differences become clinically important in the presence of ventilation/perfusion (V/Q) mismatch. V/Q mismatch may occur with diseases such as emphysema, atelectasis, pneumonia, and pneumothorax, as well as with congenital anomalies. Anesthetics also cause V/Q mismatch through bronchodilation, evidenced by the increase in the gradient for arterial to end-tidal gas for CO₂ (the a-A gradient) seen with induction of anesthesia. Common interventions such as muscle paralysis and mechanical ventilation cause some V/Q mismatch.

A more extreme case is endobronchial intubation (placement of the tracheal tube into a main bronchus), which results in ventilation confined to the left
or right lung. The ventilated lung gets twice the normal ventilation, while the other lung isn’t ventilated at all. The nonventilated lung is still perfused. Since no anesthetic is delivered, no anesthetic is taken up by the blood perfusing that lung. F_A, as measured using end-tidal concentrations, and F_a, the arterial concentration, will diverge.⁴⁰

Not surprisingly, the divergence of alveolar and arterial concentration with endobronchial intubation (or V/Q mismatch generally) is a function of solubility. Consider a poorly soluble gas, such as nitrous oxide or cyclopropane. For such drugs, the rate of rise of F_A/F_I is primarily determined by the rate of equilibration with the inspired gas, not by systemic uptake from the lungs. (Consider the extreme case of an insoluble gas. The rate of rise of F_A/F_I would be entirely determined by the rate of washin from the breathing circuit.) As a result, for a poorly soluble gas, following endobronchial intubation end-tidal increase in partial pressure would not deviate greatly from normal. F_A, measured in the ventilated lung, is primarily determined by washin from the circuit. Increasing ventilation cannot increase F_A to more than F_I. As a result, increasing ventilation to one lung cannot compensate for not ventilating the other lung at all for a poorly soluble anesthetic. The result is that for a poorly soluble anesthetic the arterial partial pressure initially would be approximately half normal.⁴⁰