Chapter 14

Chemistry and Physics of Anesthesia

The dynamics of much of anesthesia practice lie within the framework of chemical and physical science. Chemistry, the study of matter composition, properties, and behavior at the atomic and molecular level, and physics, the study of motion, matter, and energy interaction, are two foundations for nurse anesthetist practice. Chemistry and physics explain such actions as pressure, flow, diffusion, expansion, contraction, and other processes that are intimately intertwined with the delivery of anesthetics. From the ancient philosophical beginnings of atomic theory and the proverbial falling apple of Newtonian physics (Sir Isaac Newton, 1642-1727) to current advances in quantum mechanics, discoveries have led to advances and application for anesthesiology. To understand these laws and theories is to understand the how and why of our practice, give us rationale for clinical interventions, and allow us the ability to manipulate dynamic processes to our patients’ favor.

The dynamics of anesthesia herein are explained primarily by the atomic and kinetic molecular theories, Newtonian physics, thermodynamics, and the quantum mechanics of electromagnetic radiation. This chapter provides a short, concise resource that focuses on the chemistry and physics of anesthesia.

General Chemistry: Matter and Energy

The universe is composed of two main constituents, matter and energy. Energy is explored more thoroughly in the section on physics. Matter is the tangible composition of the universe that may be solid, liquid, gas, or plasma. Solids are defined as material that resists changes in shape and volume. Liquids are fluids that exhibit minimal to no compressibility and may change volume with changes in pressure and temperature. Gases are also fluids but are compressible and easily change volume with changes in pressure and temperature. Plasma is a mixture of ionized gas and free-floating electrons. It has been postulated that more than 99% of the universe’s matter is plasma.

International System of Measurement

When studying and interacting with matter and energy, it is necessary to have a system of standardized units of measurement. The Systéme International (SI) is a set of standardized units of measure based on the metric scale. The SI uses 7 base quantities for measurement (Table 14-1) and 12 standard prefixes for naming units of measure to denote quantity (Table 14-2). Other units or combinations of units may be used in addition to those shown. Additionally, temperature and pressure affect the behavior of matter, and a standardized reference has been established for both. The standard temperature and pressure (STP) is 100.00 kilopascals at 273 kelvin.

TABLE 14-1

Systéme International Seven Base Quantities for Measurement

SI Unit	Symbol	Quantity
meter	m	Length
kilogram	kg	Mass
second	s	Time
ampere	A	Electric current
kelvin	K	Temperature
candela	cd	Luminous intensity
mole	mol	Amount substance

TABLE 14-2

Systéme International Prefixes

Name	Symbol	Factor
tera-	T	10¹²
giga-	G	10⁹
mega-	M	10⁶
kilo-	k	10³
hecto-	h	10²
deca-	da	10¹
deci-	d	10⁻¹
centi-	c	10⁻²
milli-	m	10⁻³
micro-	µ	10⁻⁶
nano-	n	10⁻⁹
pico-	p	10⁻¹²

Elements

Elements are matter that possess similar atoms containing the same protons. The periodic chart of the elements lists these elements according to their chemical characteristics. Vertical columns known as groups list elements with similar properties. Horizontal rows are known as periods. Atomic size progresses up across rows from left to right. Atomic weights are listed with each element on the chart (Figure 14-1).

FIGURE 14-1 The Periodic Table. (From Patton KT, Thibodeau GA. Anatomy & Physiology. 8th ed. St Louis: Mosby; 2013.)

Atomic Structure

Atomic theory has its origins in the philosophical musings of the ancient Greek philosopher Democritus, who described indivisible building blocks of matter referred to as “atomos.”¹ The orbital theory of atomic structure was later put forth by Ernesto Rutherford (1871-1937) and improved upon by Neils Bohr (1885-1962), who described electron orbits in terms of energy levels and ability to emit quantized energy by stimulated emission. The atomic theory describes atoms as having a central core, the nucleus, with orbiting particles called electrons (Figure 14-2). Electrons are negatively charged. The nucleus contains protons and neutrons. Protons have a positive charge and are larger than electrons. Neutrons lack a charge and are similar in size to protons. The number of protons in an atom constitutes its atomic number. Electrons, much smaller than protons and neutrons, orbit around the nucleus and are negatively charged.

FIGURE 14-2 Atomic structure showing nucleus containing protons and neutrons with orbiting electrons.

Molecular Bond Types

Molecules are composed of two or more bonded atoms. Electrons in the outermost shell are called valence electrons and are involved in molecular bonding. Molecular bonding may occur by direct sharing of electrons or by thermodynamic interaction due to distribution of electron charge. Atoms with unpaired valence electrons are reactive and tend to form bonds that will fill their outer shell. Covalent and electrostatic are two general types of bonds. Atoms may bond to atoms of the same element (e.g., oxygen) or to different element atoms (e.g., water). Compounds are bonded atoms of differing elements.

Covalent Bonds

The physical sharing of electrons between atoms constitutes a covalent bond. The sharing of one pair of electrons is called a single bond, sharing two pairs of electrons is a double bond, and sharing three pairs of electrons is a triple bond. Often covalent bonds are stronger than electrostatic bonds. Covalent bonding may be between same or different atoms that share similar electronegativity.

Electrostatic Bonds

Electrostatic bonds are made by attraction of electrons between atoms. Electrostatic bonding may be ion-to-ion interaction, ion-to-dipole interaction, or dipole-to-dipole interaction and follow the general rule of “opposites attract,” with negative charges attracting positive charges.

Ion-Ion Bonding

Ion-to-ion bonds are the strongest of the electrostatic bonds. These bonds are not directional and occur anywhere along the outer electron shell of an atom. Molecules with ionic bonds have high melting and boiling points. Sodium chloride (table salt) is an example of ion-to-ion bonding (Figure 14-3).

FIGURE 14-3 Ion-to-ion bond representation between sodium and chloride ions.

Ion-Dipole Bonding

Ion-to-dipole bonds are weaker than ion-ion bonds, with only partial charges involved. Some molecules have structural arrangements that produce an uneven distribution of electrons. This uneven distribution of charges creates a dipole in which there is a more positive or more negative side to the molecule, although the molecule does not have a formal charge. An example of a molecule with an uneven charge distribution is water. The spatial arrangement of water’s hydrogens toward one side of an oxygen atom causes that side to have a more positive character and the opposite side to have a more negative character. This dipole of water may bond to an ion of opposite charge. The ions of sodium and chlorine bond to water by ion-to-dipole interaction (Figure 14-4).

FIGURE 14-4 Ion-to-dipole bond representation between a water molecule and sodium ion.

Water is an example of dipole-to-dipole molecular bonding. The spatial arrangement of water’s hydrogens at a 105-degree angle to each other causes this molecule to be dipolar (Figure 14-5). The dipolar nature of water molecules allows them to form weak bonds with one another (Figure 14-6). The polar sides of water molecules also enable them to bond to ions and other polar molecules. For this reason, water is a convenient solvent for many substances such as drugs. Surface tension of water is a physical characteristic that is caused by water’s dipole-to-dipole intermolecular attractions.

FIGURE 14-5 Hydrogen atoms’ bond angle in a water molecule.

FIGURE 14-6 Dipole-to-dipole bond representation between two water molecules.

Some molecules may have induced dipoles caused by momentary uneven spatial distribution of electrons. Induced dipoles are not permanent. These temporary dipoles may lead to weak bonding between nonpolar molecules. Oils represent nonpolar molecules that display induced dipole bonding, often called London dispersion forces. London dispersion forces are the weakest of all molecular bonds. Despite this weakness, London dispersion forces at very low temperatures allow oxygen and nitrogen to become liquids.

Molecular Bonding Representations

There are several ways to denote bonding and electron distribution. The Lewis structure (electron dot structure) shows the valence electrons as they bond among atoms. Lewis structures may show dots or lines to represent electrons. Again, only outer shell valence electrons are represented and not lower, fully filled shells. Skeletal diagrams are another frequently used method to represent molecular bonding. In organic chemistry, skeletal diagrams use lines to show atom bonding often omitting the letter C for carbon (Figure 14-7).

FIGURE 14-7 Skeletal diagram of diisopropyl phenol molecule.

The Valence Shell Electron Pair Repulsion diagrams (VSEPR) are more descriptive Lewis structures based on the theory of the same name. These diagrams represent electron repulsions, and the resultant approximation of the geometric distribution of atoms in covalently bonded molecules (Figure 14-8).

FIGURE 14-8 Valence Shell Electron Pair Repulsion (VSEPR) diagram of a tetrahedral-shaped molecule.

Molecular Modeling

Molecular models are detailed representations of molecules. Electrons are in constant “orbit” in an atom, and attempts have been made to graphically represent their space-occupying possible locations (Figure 14-9). Space-filling models reflect the “electron cloud” of specific atoms in a molecule. These models can appear as spherical, ball and stick, or ribbon-like representations of atoms and molecules that are affixed to one another. Molecular modeling is expanding our understanding not only of molecular geometries but also molecular behavior.²

FIGURE 14-9 Molecular model of sugammadex encapsulating a rocuronium molecule. (From Zhang M-Q, et al. Angew Chem Int Ed. 2002;41(2):265. © Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

Isomers

Isomers are molecules that have the same chemical formula but different structural formulas. The number and type of atoms and bonds are the same in isomers, but the arrangement of the atoms is different. Isomers may be structural or stereoisomers. Structural isomers have the same molecular formula, but their atoms are located in different places. Enflurane and isoflurane are examples of structural isomers. Structural isomers are truly different molecules with differing physical and chemical properties. Stereoisomers are molecules that have a similar geometric arrangement of atoms but differ in their spatial position. Stereoisomers may be enantiomers or diastereomers. Enantiomers are mirror images of one another, cannot be superimposed, and possess similar chemical and physical properties. Enantiomers are optically active and can rotate polarized light in a clockwise fashion (prefix + or dextro) or counterclockwise fashion (prefix − or levo). Racemic chemical compositions contain 50% of the levo form isomer and 50% of the dextro form isomer. Diastereomers are not mirror images and may have differing physical and chemical properties.

Bond Breaking

Bond energy is the amount of energy needed to make or break a bond. Energy is released when a bond is formed, and energy is consumed with breaking a bond. The energy released when a bond is formed is the same amount of energy needed to break that same chemical bond. Short bonds, such as covalent bonds, tend to possess greater bond energies than longer, electrostatic bonds. When molecular bonds are broken, new molecular bonds are often formed and energy is released. An example of this is adenosine triphosphate (ATP) conversion to adenosine diphosphate (ADP). Energy is actually consumed in the process of breaking an ATP bond. A greater amount of energy is released when the free phosphate forms new bonds with hydrogen.³ Bond energies are measured as an enthalpy change.

Enthalpy

Enthalpy is the total amount of energy possessed by a system. A system can be on the atomic scale or the macroscopic scale. The enthalpy of a system is the total of all kinetic and potential energy. The stored, or potential, energy includes its height in relation to the force of gravity and the energy stored in the bonds of molecules and atoms and even subatomic particles. All movement, as well as stored energy, must be accounted for and summated to know the enthalpy of a system. Thus the total amount of energy contained within a system is increasingly difficult to quantify, especially with increasing complexity of a system. The difficulty in measuring all the energy in a particular system requires a simpler method to evaluate energy involved in chemical reactions. Therefore, change of energy (ΔH) rather than total energy (enthalpy) of a system is measured.

Organic Compounds

Organic chemistry is the study of carbon-containing molecules. Biological life on earth is based on carbon-containing compounds. Carbon is a unique atom that combines with many atoms in multiple arrangements, owing to its four valence electrons available for bonding. Carbon may make single, double, or triple covalent bonds with other atoms or molecules.

Hydrocarbons

Hydrocarbons are molecules composed entirely of carbon atoms with hydrogen atoms attached. These molecules are often found in straight chains, with or without branches. Saturated hydrocarbons are single-bonded carbon chains with all available carbon bonds attached to hydrogen. Hydrocarbons containing only single-bonded carbon atoms are called alkanes. The six-carbon hydrocarbon shown in Figure 14-10 is called a hexane. The hex– prefix denotes six carbons and the –ane suffix denotes an alkane with all single bonds.

FIGURE 14-10 Hexane.

Unsaturated hydrocarbons have one or more double or triple bonds between carbon atoms. Hydrocarbons containing double-bonded carbons are called alkenes and triple-bonded carbons are called alkynes. The six-carbon hydrocarbon containing a double bond is called hexene (Figure 14-11).

FIGURE 14-11 Hexene.

Cyclic hydrocarbons are carbon chains in a ring structure. They may contain multiple carbon atoms and may have single, double, or triple bonds. The cyclic hydrocarbons hexane and benzene (1,3,5 cyclohexatriene) are shown in Figure 14-12.

FIGURE 14-12 Hexane and benzene.

Saturated and unsaturated hydrocarbons that have hydrogens omitted are known as alkyls, are very reactive, and bond to functional groups. Cyclic hydrocarbons omitting a hydrogen on any carbon atom are called aryls, are reactive, and also bind with functional groups.

Functional Groups

Functional groups impart unique characteristics to molecules. There are many functional groups in organic chemistry, and several have importance in anesthesia.

Amines are derivatives of ammonia (NH₃) and have the general formula NR₃. Only one or two of the R groups may be hydrogen. All amines have a lone pair of electrons on the nitrogen.

Alcohols have the general formula ROH, where R represents any alkyl group. The hydroxyl group (OH) of alcohols is highly polar and easily forms hydrogen bonds with other polar molecules. The polarity of the hydroxyl group allows alcohols to dissolve many other polar molecules.

FIGURE 14-13 Phenol and disopropyl phenol molecules.

Ethers have the general formula ROR′, where R and R′ are alkyl groups attached by oxygen. Ethers are inert and do not react with oxidizing or reducing agents but are highly flammable. The outdated anesthetic agent diethyl ether clearly shows both alkyl groups bonded to oxygen (Figure 14-14). Halogen substitution on ethers alters anesthetic characteristics, such as blood solubility and potency, while lowering flammability.

FIGURE 14-14 Diethyl ether.

Several functional groups contain a structural arrangement of carbon double bonded to oxygen. This is known as a carbonyl group and structurally identified as C=O. The carbonyl group is polar, with the oxygen being more electrically negative. This polar characteristic is imparted to functional groups that contain a carbonyl group. The carbonyl group, though not a functional group by itself, is a key component of the following functional groups: aldehydes, ketones, carboxylic acids, esters, and amides.

• Aldehydes have the general formula RCHO.

• Ketones have the general formula RCOR′.

• Carboxylic acids have the general formula RCOOH.

• Esters have the general formula RCOOR.

• Amides have the general formulas RCONH₂, RCONHR, or RCONR₂.

SolubilIty

Solubility is the maximum amount of one substance (solute) that is able to dissolve into another (solvent). The factors that may affect solubility of solutes in solvents are the intermolecular interactions between the substances, temperature, and pressure.

Solids and Liquids

Solubility is enhanced by intermolecular interactions between substances that have similar electron configurations. “Like dissolves like” is often used to describe solubility. Salt (NaCl) in water is an example. The similar polarity of water and salt’s constituent parts promote dissolving. Temperature also affects solubility. Energy is required to break the bonds of substances that are dissolving. Most often this is an endothermic reaction, which means it requires more energy than it produces. It consumes heat rather than produces heat. With endothermic reactions, solubility is increased with increased temperature; the additional energy (heat) drives greater dissolving. Most reactions of solids dissolving in liquids are endothermic. Occasionally the process may be exothermic, meaning energy is released in excess of the energy required to break the bonds of the solute. In this unique scenario, increases in temperature will decrease solubility. Pressure exerts little to no influence on solubility of solids and liquids.

Gases

Gas solubility in liquids is inversely related to temperature. As temperature increases, less gas is able to dissolve into a liquid. An increased temperature represents greater kinetic energy. Greater kinetic energy allows dissolved gas molecules to escape and prevents further dissolving. Lower temperature slows the kinetic energy of gas molecules, allowing them to dissolve into liquids. A clinical example of temperature affecting solubility is seen with the slower emergence of hypothermic patients receiving volatile-agent general anesthetics. The hypothermic patient retains anesthetic gases in the blood because of increased solubility related to temperature.⁴ Gas solubility in a liquid is directly proportional to pressure and is described by Henry’s law.⁵

Henry’s Law

Henry’s law (William Henry, 1775-1836) states “at constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas at equilibrium above the gas-liquid interface.” The formula is:

where p is the partial pressure of the solute above the solution, k is Henry’s constant, and c is the concentration of the solute in solution. Increasing the partial pressure of a gas above a liquid will increase the amount of gas that dissolves in the liquid. Increased delivery of oxygen (Fio₂) to patients to improve arterial oxygenation (Pao₂) and overpressurizing (high concentration) anesthetics reflect the direct relationship of pressure and solubility described by Henry’s law. “Overpressurizing” is the process of significantly increasing a volatile anesthetic concentration (partial pressure) delivered to a patient to increase the alveolar concentration, and therefore the amount dissolved in the blood, to speed uptake.

Diffusion

Diffusion is the process of net movement of one type of molecule through space as a result of random motion intended to minimize a concentration gradient (Figure 14-15). This basic process occurs by Brownian (Robert Brown, 1773-1858) motion, which is driven by the inherent kinetic energy of the molecules.⁶ Temperature is directly proportional to kinetic energy. Kinetic energy allows molecules to move freely in a fluid, and therefore mixtures of fluids tend to evenly distribute. The velocity at which a molecule may distribute is determined by its molecular weight. Every molecule at a given temperature will have the same kinetic energy, independent of its size, but its velocity may differ. From the formula for kinetic energy, KE = (½) mv², we can determine that if the mass of a molecule is changed, there must be an opposite change in velocity. Greater velocity correlates with faster diffusion. Thus, molecules with smaller mass will diffuse faster.

FIGURE 14-15 Diffusion of water and NaCl.

Graham’s Law

Thomas Graham (1805-1869) determined that the rate of effusion (gas diffusion through an orifice) of a gas is inversely proportional to the square root of its molecular weight. The formula is:

where r is the rate of diffusion, and mw is the molecular weight. Graham’s law determines the faster diffusion of smaller molecules compared to larger molecules. Graham’s law is helpful in understanding the effect of molecular weight on diffusion but is limited in fully describing all the factors influencing diffusion.

Diffusion Through Permeable and Semipermeable Membranes

Diffusion may occur through open space or through permeable membranes (tissues). If a fluid (gas or liquid) is permeable through a membrane, then the diffusion that occurs is dependent on five factors. These factors include concentration gradient, tissue area, and fluid tissue solubility, which are all directly proportional to diffusion. Membrane thickness and molecular weight are factors that are inversely proportional to diffusion.

Osmosis

Osmosis is the movement of water across a semipermeable membrane to equilibrate a concentration gradient (Figure 14-16). Semipermeable membranes are permeable to water only and not to solute. Osmotic pressure is the force needed to stop osmosis from occurring. Oncotic pressure is the osmotic pressure by plasma proteins and electrolytes in capillaries. Oncotic pressure balances the hydrostatic pressure tendency to push water out of capillaries. Normal oncotic pressure is approximately 28 mmHg. Our vascular system is a semipermeable membrane that responds to intravascular delivery of colloids by sequestering fluid.^7,8

FIGURE 14-16 Osmosis of water through a semipermeable membrane.

Diffusion in Anesthesia

Diffusion is a passive process driven by entropy (see Entropy in this chapter). The diffusion of oxygen and nitrous oxide represents both positive and negative consequences of this process. Nitrous oxide diffuses into air-filled cavities; therefore, delivery of nitrous oxide is contraindicated in patients with pneumothorax or where air-filled cavity expansion is undesirable.⁹ Nitrous oxide expansion of endotracheal cuffs may cause tracheal mucosal damage.^10,11 Distention of bowel during nitrous oxide delivery also has been documented.^12,13 Apneic oxygenation is well known and exemplifies the beneficial process of diffusion.¹⁴ An intubated patient who has previously been ventilated with 100% oxygen and remains connected to the ventilation circuit with 100% oxygen flow will maintain an acceptable Pao₂ if ventilation is ceased. The continual diffusion of oxygen into the blood is driven by a concentration gradient that continually diffuses oxygen into the alveoli via the ventilator circuit. The diffusion of gases across biological tissues is expressed by Fick’s law.

Fick’s Law

Fick’s law for diffusion of a gas across a tissue plane is an encompassing law that accounts for molecular weight, concentration gradient, solubility, and membrane interactions. Fick’s law states that diffusion of a gas across a semipermeable membrane is directly proportional to the partial pressure gradient, the membrane solubility of the gas, and the membrane area and is inversely proportional to the membrane thickness and molecular weight of the gas. Specific application of the Fick equation for diffusion of respiratory gases is as follows:

where J is diffusion flux, α is the solubility constant for oxygen, D is diffusivity, Δx is the membrane thickness, and (Pao₂ − Pcapo₂) is the alveolar-capillary oxygen partial pressure difference. Fick’s equation allows determination of pulmonary gas exchange.15,16 The diffusion hypoxia that occurs after the delivery of nitrous oxide is discontinued, and low inspired oxygen is administered as explained by Fick’s equation.¹⁷

Newtonian Physics

Gravity

All life on earth is well aware of gravity. From our first steps to our last, gravity affects every facet of our daily lives. It is a unidirectional force pulling objects down toward earth’s center. Gravity appears to pull on heavy objects with greater force than lighter objects, but this is not necessarily true. Aristotle saw gravity this way and felt it was due to an object’s desire to return to its natural position at rest on the earth. It took 2000 years to change that perspective. Gravity pulls on all objects with a force of 9.81 m/sec/sec (32 ft/sec/sec). Sir Isaac Newton’s law of gravity derived that, “Each particle of matter attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” The formula for gravity is:

where G is the gravitational constant (6.67 × 10⁻¹¹Nm²/kg²⁾, m1 and m2 are the masses of the two objects for which you are calculating the force, and d is the distance between the centers of gravity of the two masses. Remember that mass and weight are not the same. Mass is the total of all matter in an object—the sum of all the electrons’, protons’, and neutrons’ equal mass. Weight is the total effect of gravity pulling on all these electrons, protons, and neutrons of an object. An example often cited is that you may weigh 70 kilograms on earth due to the gravitational pull on all your atoms, but you would weigh less on the moon, which has less gravitational pull. Your mass or total amount of matter remains the same on earth or the moon.

The earth attracts all other objects around it with a force of 9.81 m/sec/sec, and those objects in turn attract the earth in relation to their mass and distance from the planet. The formula for gravitational acceleration is:

where g is gravitational acceleration, G is the gravitational constant, M_e is the mass of earth, and r²_e is the mean radius of earth. Earth’s attraction for objects is proportional to mass for all objects at the same distance. One might want to say that larger-mass objects would accelerate or be pulled faster to earth, but objects also resist movement proportional to their mass (third law of motion). Gravity pulls on one atom of carbon with 9.81 m/sec/sec force, and the carbon atom resists this pull with a force of x. Gravity pulls on two carbon atoms with a force of 9.81 m/sec/sec on each atom for a total gravitational force of 9.81 m/sec/sec × 2, or 19.62 m/sec/sec. Two carbon atoms resist movement twice (2×) as much as one carbon atom, thus the net gravitational effect (falling) is the same. This is how greater-mass objects are pulled by gravity with the same force and fall at the same acceleration as lesser-mass objects.

This equal attraction on objects is often hidden in everyday life, owing to the effect of air molecules interacting with falling objects. Assuredly, all objects fall due to gravity at the same speed in a vacuum that is devoid of other molecules. Air molecules possess energy, move about, and interact with other matter. This causes friction. Greater friction equals greater force against the pull of gravity and slowing of a fall, but in a vacuum all objects fall equally at equal velocities.

Newton’s Laws of Motion

• Newton’s first law (law of inertia): A body in motion tends to stay in motion unless acted upon by another force.

• Newton’s second law (law of acceleration): Acceleration of a body is in the direction of and proportional to the force (F), and that acceleration (a) is inverse to the mass (m) of the body, F = ma. If multiple forces exist, the direction and acceleration are proportional to the sum of all the forces. These are called vectors.

• Newton’s third law (law of reciprocal action): For every action, there is an equal and opposite reaction. It states that objects exert equal but opposite forces on one another.¹⁸ Example: An apple on a desk pulls down with a gravitational force equal to the force that the table resists.

Force

Force is the amount of energy required to move an object. From the understanding that the force of gravity pulls equally on all objects proportional to mass, a standardization of force became possible. Because we know that gravity pulls (accelerates) all objects with a force of 9.81 m/sec/sec, this force would also be 9.81 m/sec/sec if applied to any given weight. The force of gravity applied to 1 kg weight creates a standard by which other forces may be compared, quantified, and measured. Thus the force required to accelerate a 1 kg weight 1 meter per second became known as the newton.

The newton is the standard measure of force derived from the force of gravity.

One newton is equivalent to 1/9.81 kg weight or 102 g weight. Force is mass multiplied by acceleration. The formula for force is:

where F is force, m is mass, and a is acceleration. Often in settings of small measures of force, the newton is too large. A dyne is 1000th of a newton. A dyne is the force required to move a 1-g weight 1 cm per second. Dynes are used in calculating systemic and pulmonary vascular resistance.19,20

Pulmonary vascular resistance (PVR) is the measure of the pulmonary vascular system’s resistance to flow from the right ventricle. Normal PVR is 100 to 200 dyne sec/cm⁵. Systemic vascular resistance (SVR) is the measure of the peripheral vascular system’s resistance to flow that must be overcome for flow to occur. The left ventricle must therefore pump blood with a force greater than the resistance of the vascular system. The formula for calculating SVR is 80 × (MAP − CVP)/CO = SVR. Normal SVR is 900 to 1200 dyne sec/cm⁵.

Another application of force measurement in anesthesia is the technology of accelerometry used to measure the degree of neuromuscular blockade.21,22 Accelerometry uses a piezoelectric disk to generate an electric current in proportion to acceleration (see Piezoelectric Effect in this chapter). An accelerometer measures the acceleration caused by the contraction of the adductor pollicis muscle after ulnar nerve stimulation. A comparison of baseline stimulated muscle twitches (forces) to twitches suppressed by neuromuscular blocking agents allows the quantification of the degree of neuromuscular blockade.²³ Accelerometers provide objective twitch data referenced to the patient’s baseline twitch response.²⁴ Visual or tactile assessment of twitch heights is subjective and less reliable than accelerometry.^24,25

Force is a basic phenomenon of physics that permeates the universe. Because all matter possesses mass, and all mass has some degree of acceleration, force exists everywhere. All forces possess direction. The study of force direction is explored with vectors.

Vectors

Two basic types of values describe our physical world: scalar and vector. Scalar values are fully described by magnitude alone, they possess no motion, and they include mass, energy, and work. Vector values are fully described by magnitude and direction. Vectors express motion and are described by the mathematics of force, speed, velocity, acceleration, distance, and displacement. Vector diagrams are scaled representations of vectors, with an arrow starting at a given magnitude and pointing in the direction of the force summation.

An electrocardiogram (ECG) is an example of a type of vector diagram that allows us to calculate the predominant direction of electrical force in the myocardium. An ECG records electrical flow as an upward or downward deflection on graph paper. When the flow is toward the positive electrode, an upward deflection will record. When the flow is away from the positive electrode, a downward deflection will record. Twelve-lead ECGs are scaled graphs with multiple points of reference used to measure the force direction of the electrical conductance. As multiple points of reference are recorded, direction of electrical flow predominance may be determined (vector summation). This is the principle behind determining axis deviation of the heart.

Axis deviation estimates the summation of forces that shift from the normal direction of electrical flow in the heart. Electrocardiogram vector diagrams are scaled clockwise from 0 degrees in the east position. The normal axis of electrical flow summation in the heart is between −30 degrees and +90 degrees. The axis determination steps that follow are based on identifying the positive (upward) deflections of the 12-lead electrocardiogram, which represents electrical flow toward the positive electrode. Because the normal axis of electrical flow is between −30 and +90 degrees, positive deflections in leads I and II would represent electrical flow in the normal direction. Negative deflections in lead I or lead II would reflect a deviation of normal axis and requires determination of the electrical flow vector. Vector deviations are described as left, right, or right superior. Several methods are available for quick determination of myocardial electrical axis deviation. Figure 14-17, Table 14-3, and Table 14-4 offer help in determining axis deviation.

TABLE 14-3

Axis Deviation Determination Methods

Vector Method	Inspection Method	Grant Method
I+, aVF+ = Normal axis	I+, III+ = Normal axis	I+, II+ = Normal axis
I−, aVF− = Superior right	I− = Right axis	I+, II− = Left axis
I−, aVF+ = Right axis	III−, II− = Left axis	I−, II+ = Right axis
I+, aVF− see lead II (if II+ = Normal; if II− = Left axis)		I−, II− = Superior right

TABLE 14-4

Axis Deviations from Normal

Normal Axis	−30 to +90 degrees
Left axis deviation	−30 to −90 degrees
Right axis deviation	+90 to ±180 degrees
Superior right axis deviation	−90 to ±180 degrees

FIGURE 14-17 Electrocardiogram lead placement with vector direction and location of normal and abnormal axes.

Pressure

Pressure is defined as force over area, where P is pressure, f is force, and a is area.

Increasing the area in which a given force is applied will result in a lower pressure. The smaller the area to which the set force is applied, the greater the pressure. The standard unit of measurement for pressure is the pascal (Pa). A pascal is the force of 1 newton (N) over 1 square meter.

A pascal equals 102 g weight acting over an area of 1 square meter. Remember, a newton equals 102 g weight. This is a very small unit of pressure. As the newton was fractionalized to the dyne for the purpose of establishing a more convenient unit of force measurement, the pascal was increased a thousand times to create the kilopascal (kPa) unit. A kilopascal is more convenient to use for measuring pressures. A kilopascal equals 1000 N or 102 kg acting over an area of 1 m².

Syringes represent an example of the pressure generated by a force over a given area. Equal force (20 N) applied to the plungers of different syringes generates different pressures, depending on the area over which the force was applied. The force applied will cause greater pressure on injection with a tuberculin (TB) syringe (plunger area = 8.55 × 10⁻⁶ m²) than with a larger 10-mL syringe (plunger area 3.42 × 10⁻⁵ m²). As you increase the area to which a fixed force (20 N) is applied, the product of the equation, pressure (in atmospheres), becomes smaller.

These calculations show the extremely high pressures that can be generated by exerting a force over a small area. The tuberculin syringe generates more than 20 atmospheres of pressure and can rupture catheters if used to flush or dislodge blockages. Larger syringes are recommended for flushing or unclogging enteral feeding tubes because of the potential for generating high pressures with smaller syringes.26–28

Atmospheric Pressure

As previously discussed, gravity pulls on all objects, including the atoms and molecules of the atmosphere. Because these atoms and molecules have low mass, they have low gravitational pull but nonetheless are pulled toward Earth. The cumulative effect of gravity on atmospheric gases gives rise to atmospheric pressure. Atmospheric gases are less concentrated at altitude and more concentrated at sea level. Atmospheric pressure is the column of gravitational force on gases over a given area. This can be measured and is equivalent at sea level to 100 kPa (or 14.7 lb per square inch, 1020 cm of H₂O, or 760 mmHg—all equivalent to one another). Standard pressure in the SI is 100 kPa. Other units of pressure measurement include the following with their equivalents. It is best to memorize these:

1 torr = 1 mmHg

1 kPa = 10.2 cm H₂O = 7.5 mmHg

1 atm = 760 mmHg = 760 torr = 1 bar = 100 kPa = 1020 cm H₂O = 14.7 lb/inch₂

Pressure Measurement

The simplest method for determining pressure is the manometer. A manometer is a liquid-filled tube that is open to atmospheric pressure on one end and exposed to a pressure for measurement on the other end (Figure 14-18). A pressure greater than atmospheric pressure (760 mmHg) will displace the column of liquid proportional to the pressure difference (Δh). Calibrating the column of liquid allows for quantification of the pressure.

FIGURE 14-18 Manometer showing change in liquid column height (Δh) related to pressure applied.

A sphygmomanometer uses an inflatable cuff connected to a mercury-filled manometer to measure blood pressure. As the inflated cuff is slowly deflated, the arterial flow resumes, causing a pressure wave that is transmitted to a mercury column. The mercury column is calibrated to show the measured pressure in millimeters of mercury. A more recent advancement in blood pressure measurement is oscillometry. Oscillometry automates noninvasive blood pressure measurements by recording the oscillations in pressure caused by arterial pulsation.²⁹ As an inflated cuff is deflated, multiple measurements are made of these oscillations. Oscillations increase at systolic pressure and are maximal at the mean arterial pressure. Algorithmic computation of systolic and diastolic pressures is derived from the mean arterial pressure. Often these noninvasive automated blood pressure monitors use the piezoelectric principle to record the pressure oscillations and a microprocessor to derive the systolic and diastolic measurements.³⁰ Invasive blood pressure monitors use a piezoelectric transducer that converts pressure waves into electrical signals. Blood pressure measurements are gauge pressures that are zeroed to atmospheric pressure.

Gauge and Absolute Pressure

Different pressure measurements may use different zero reference points. The zero reference point may be a complete vacuum devoid of all molecules and molecular collisions that impart pressure. This is true zero pressure and is the reference point used when measuring absolute pressure. Absolute pressure is atmospheric pressure plus gauge pressure. Gauge pressure is zero referenced at atmospheric pressure and reads zero at 760 mmHg at sea level. Gauge pressure is absolute pressure minus atmospheric pressure.

Bourdon gauges are often used in anesthesia to measure high pressures, such as in gas cylinders, and are zero referenced to atmospheric pressure (Figure 14-19). Bourdon gauges contain a coiled tube that expands as pressure is applied. A linkage connects the coil to a rotating arm that records the pressure. The American Society for Testing Materials International mandates that the zero reading of Bourdon gauges lie between the 6 o’clock and 9 o’clock positions. Other methods of pressure measurement in anesthesia include manometers.

FIGURE 14-19 Bourdon gauge showing gauge pressure (inside pressures) referenced to absolute pressure (outside pressures).

Thermodynamics

The three laws of thermodynamics explain the relationship between heat and energy and their exchange during work processes:

1. Law of conservation of energy. Energy cannot be created or destroyed. The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to the system minus the work done by the system on the surroundings.

2. Energy moves toward greater entropy or randomness. The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

3. Absolute zero (0° K or −273.15° C) is void of all energy. Absolute zero is theoretical, because it has been impossible to achieve. As a system approaches absolute zero of temperature, all processes cease, and the entropy of a system approaches a minimum value.

Energy

Energy can be defined as the exertion of force (kinetic) or the capacity (potential) to do work. Energy can be expressed as mechanical work, chemical reactions, or heat. The unit of measurement for energy is the joule. A joule is the force of 1 newton that moves its point of application 1 meter in the direction of that force. Two types of energy are potential and kinetic. Potential energy is energy waiting to be used. It is energy that is stored and available to be converted into power. Potential energy is defined as mass (m) times gravity (g) times height (h).

Kinetic energy is energy of movement. Kinetic means movement. Kinetic energy is defined as one half the product of mass times the velocity squared.

Entropy

Entropy is the universe’s trend to equilibrate all things. It is the process that allows everything from ice melting to gas expansion. Sleep and the induction of general anesthesia have been proposed to be entropic processes.31–34 All of these processes involve the equilibration of energy. Even matter is a form of energy. Entropy is unidirectional; it is the movement of energy from high concentration to lower concentration. It moves because of a gradient. The difference in the gradient influences the speed of the flow. Greater difference usually equals greater flow, and always from higher concentration to lower concentration. All energy and matter tend to follow this rule. An example of this unidirectional action is ice added to lemonade. Ice does not make lemonade colder, lemonade makes ice warmer. Diffusion, which will be covered later, is also a process driven by entropy. Entropy ends when all energy is equally distributed. Entropy is the underlying process promoting spontaneous and elicited movement in our everyday lives and the universe in general. Essentially, entropy drives the universe. This process should be kept in mind when learning or reviewing any dynamic concepts of anesthesia.³⁵

Temperature

Matter may change form with the addition of greater heat energy. An example we see every day is the melting of an ice cube into liquid water, and liquid water into vapor with the addition of greater heat energy. Liquid water, with the addition of heat energy, expands. This is due to the water molecules moving apart with greater kinetic energy that ultimately allows them to escape individually as a vapor. Another liquid, mercury, also expands with the addition of heat energy. When placed in the bottom of a closed glass cylinder, the expansion is limited to one direction in relation to the energy applied. This is a simple application of heat energy (kinetic energy) interacting with matter to allow analysis of the thermal state: a thermometer.

Temperature is the measurement of the thermal state of an object. Heat is thermal energy; temperature is the quantitative measurement of that energy. Several temperature scales exist: Fahrenheit, Celsius, and Kelvin (Figure 14-20). Gabriel Daniel Fahrenheit (1686-1736) is credited with inventing the mercury thermometer (1714) and devising the Fahrenheit temperature scale. The Celsius (Anders Celsius, 1701-1744) or centigrade scale is the primary scale used for everyday temperature measurements. The Kelvin scale (William Thompson Lord Kelvin, 1824-1907) was developed to better reflect mathematically the temperature/pressure relationship of gases and is used when calculating their behaviors. Water freezes at 273.15° K and boils at 373.15° K. Conversion among temperature scales is as follows: