9: Pharmacokinetic and Toxicokinetic Principles

Pharmacokinetics is the study of the absorption, distribution, metabolism, and excretion of xenobiotics. Xenobiotics are substances that are foreign to the body and include natural or synthetic chemicals, drugs, pesticides, environmental agents, and industrial agents.⁴⁹ Mathematical models and equations are used to describe and to predict these phenomena. Pharmacodynamics is the term used to describe an investigation of the relationship of xenobiotic concentration to clinical effects. Toxicokinetics, which is analogous to pharmacokinetics, is the study of the absorption, distribution, metabolism, and excretion of a xenobiotic under circumstances that produce toxicity. Toxicodynamics, which is analogous to pharmacodynamics, is the study of the relationship of toxic concentrations of xenobiotics to clinical effects.

Overdoses provide many challenges to the mathematical precision of toxicokinetics and toxicodynamics because many of the variables, such as dose, time of ingestion, and presence of vomiting, that affect the result are often unknown. In contrast to the therapeutic setting, atypical solubility characteristics are noted, and saturation of enzymatic processes occurs. Intestinal or hepatic enzymatic saturation or alterations in transporters may lead to enhanced absorption through a decrease in first-pass effect. Metabolism before the xenobiotic reaches the blood is referred to as the first-pass effect.^2,76 Saturation of plasma protein binding results in more free xenobiotic available in the plasma. Saturation of hepatic enzymes or active renal tubular secretion leads to prolonged elimination. In addition, age, obesity, gender, pharmacogenetics and pharmacogenomics, chronopharmacokinetics (diurnal variations), and the effects of illness and compromised organ perfusion all further inhibit attempts to achieve precise analyses.^{3,17,40,45,68,72} Furthermore, various treatments may alter one or more pharmacokinetic and toxicokinetic parameters. There are numerous approaches to recognizing these variables, such as obtaining historical information from the patient’s family and friends, performing pill counts, procuring sequential serum concentrations during the phases of toxicity, and occasionally repeating a pharmacokinetic evaluation during therapeutic dosing of that same xenobiotic to obtain comparative data.

Although different, plasma concentration and serum concentration are terms often used interchangeably. When a reference or calculation is made with regard to a concentration in the body, it is actually a plasma concentration. When concentrations are measured in the laboratory, a serum concentration (clotted and centrifuged blood) is often determined. In reality, the laboratory measurements of most xenobiotics in serum or plasma are nearly equivalent. Frequently, this is not the case for whole-blood determination if the xenobiotic distributes into the erythrocyte, such as lead and most other heavy metals.

Despite all of the confounding and individual variability, toxicokinetic principles may nonetheless be applied to facilitate our understanding and to make certain predictions. These principles may be used to help evaluate whether a certain antidote or extracorporeal removal method is appropriate for use, when the serum concentration might be expected to decrease into the therapeutic range (if one exists), what ingested dose might be considered potentially toxic, what the onset and duration of toxicity might be, and what the importance is of a serum concentration. While considering all of these factors, the clinical status of the patient is paramount, and mathematical formulas and equations can never substitute for a sound clinical assessment. This chapter explains the principles and presents the mathematics in a user-friendly fashion.⁷⁹

Absorption is the process by which a xenobiotic enters the body. A xenobiotic must reach the bloodstream and then be distributed to the site or sites of action to cause a systemic effect. Both the rate (k_a) and extent of absorption (F) are measurable and important determinants of toxicity. The rate of absorption often predicts the onset of action and relies on dosage form, and the extent of absorption (bioavailability) often predicts the intensity of the effect and depends in part on first-pass effects.^36,37 Figure 9–1 depicts how changes in the rate of absorption may affect toxicity when the bioavailability is held constant versus how toxicity may be affected by changes in bioavailability when the rate of absorption is held constant.

The route by which the xenobiotic enters the body significantly affects both the rate and extent of absorption. As an approximation, the rate of absorption proceeds in the following order from fastest to slowest: intravenous (IV), inhalation > sublingual > intramuscular, subcutaneous, intranasal, oral > cutaneous, rectal. After the oral intake of 200 mg (0.59 mmole) of cocaine hydrochloride, the onset of action is 20 minutes, with an average peak concentration of 200 ng/mL.⁷¹ In marked contrast, smoking 200 mg (0.66 mmole) of cocaine freebase results in an onset of action of 8 seconds and a peak concentration of 640 ng/mL. When administered IV as 200 mg cocaine hydrochloride, it then has an onset of action of 30 seconds and a peak concentration of 1000 ng/mL.⁷¹

A xenobiotic must diffuse through a number of membranes before it can reach its site of action. Figure 9–2 shows the number of membranes through which a xenobiotic typically diffuses. Membranes are predominantly composed of phospholipids and cholesterol in addition to other lipid compounds.⁵⁴ A phospholipid is composed of a polar head and a fatty acid tail, which are arranged in membranes so that the fatty acid tails are inside and the polar heads face outward in a mirror image.⁵⁸ ­Proteins are found on both sides of the membranes and may traverse the ­membrane.⁵⁴ These proteins may function as receptors and channels. Pores are found throughout the membranes. The principles relating to diffusion apply to absorption, distribution, certain aspects of elimination, and each mechanism that permits a xenobiotic to be transported through a membrane.

Transport through membranes occurs via (1) passive diffusion; (2) filtration or bulk flow, which is most important in renal and biliary secretion as the mechanism of transport associated with the movement of molecules with a molecular weight less than 100 Da, with water directly through aquapores; (3) carrier-mediated active or facilitated transport, which is saturable; and (4) rarely, endocytosis (Fig. 9–2). Most xenobiotics traverse membranes via simple passive diffusion. The rate of diffusion is determined by the Fick’s law of diffusion (Equation 9–1):

Where:

• D = diffusion coefficient

• A = surface area of the membrane

• h = membrane thickness

• K = partition coefficient

• C₁ − C₂ = difference in concentrations of the xenobiotic on each side of the membrane

The driving force for passive diffusion is the difference between the concentrations of the xenobiotic on the opposing sides of the membrane. D is a constant for each xenobiotic and is derived when the difference in concentrations between the two sides of the membrane is one. The larger the surface area A, the higher the rate of diffusion. Most ingested xenobiotics are absorbed more rapidly in the small intestine than in the stomach because of the tremendous increase in surface area created by the ­presence of microvilli. The partition constant or ratio (previously called the ­coefficient) K_ow represents the lipid-to-water partitioning of the nonionized xenobiotic with pH adjustment to favor nonionized xenobiotic. To a substantial degree, the more lipid soluble a xenobiotic is, the more easily it crosses membranes. The logarithm of the K_ow is known as the log P. The distribution constant or ratio represents the lipid-to-water partitioning of the sum of the nonionized plus ionized in the octanol and water phase and is pH dependent. The logarithm of the distribution constant is called log D and is most useful when measured at physiologic pH. Membrane thickness (h) is inversely proportional to the rate at which a xenobiotic diffuses through the membrane. Xenobiotics that are uncharged, nonpolar, of low molecular weight, and of the appropriate lipid solubility have the highest rates of passive diffusion.

The extent of ionization of weak electrolytes (weak acids and weak bases) affects their rate of passive diffusion. Nonpolar and uncharged molecules penetrate faster. The Henderson-Hasselbalch relationship is used to determine the degree of ionization. An acid (HA), by definition, gives up a proton, and a base (B) accepts a proton. Acids and bases can be nonionized (uncharged, molecular, free), positively charged (cationic), or negatively charged (anionic). Aspirin and phenobarbital are uncharged acids (RCOOH), and pseudoephedrine HCl is a cationic acid. Morphine, amphetamine, and amitriptyline are nonionized bases (RNH₂), and sodium valproate is an anionic base. The equilibrium dissociation constants K_a and K_b can then be described. K_a × K_b = K_w, and K_w is the dissociation constant of water. Because these numbers are difficult to work with, they are transformed using logarithms. By Equations 9–2A and 9–2B:

B + H2O → BH⁺ + OH^-

To work with these numbers in a more comfortable fashion, the negative log of both sides is determined. The results are given in Equations 9–3A and 9–3B.

By definition, the negative log of [H⁺] is expressed as pH, and the negative log of K_a is pK_a. Rearranging the equations gives the familiar forms of the ­Henderson-Hasselbalch equations, as shown in Equations 9–4A, 9–4B, and 9–4C:

Because uncharged molecules traverse membranes more rapidly, it is understood that weak acids cross membranes more rapidly in an acidic environment, and weak bases move more rapidly in a basic environment. When the pH equals the pK_a, half of the xenobiotic is charged, and half is uncharged. An acid with a low pK_a is a strong acid, and a base with a low pK_a is a weak base. For an acid, a pH less than the pK_a favors the protonated or uncharged species facilitating membrane diffusion, and for a base, a pH greater than the pK_a achieves the same result. Table 9–1 lists the pH of selected body fluids, and Fig. 9–3 illustrates the extent of charged versus uncharged xenobiotic at different pH and pK_a and pK_b values.

Lipid solubility and ionization each have a distinct influence on absorption. Figure 9–4 demonstrates these characteristics for three ­different xenobiotics. Although the three xenobiotics have similar pK_a and pK_b values, their different partition constants result in different degrees of absorption from the stomach.

Specialized transport mechanisms are either adenosine triphosphate (ATP) dependent to transport xenobiotics against a concentration gradient (ie, active transport) or ATP independent and lack the ability to transport against a concentration gradient (ie, facilitated transport). These transport mechanisms are of importance in numerous parts of the body, including the intestines, liver, lungs, kidneys, and biliary system. These same principles apply to a small number of lipid-insoluble molecules that resemble essential endogenous molecules.^28,64 For example, 5-fluorouracil resembles pyrimidine and is transported by the same system, and thallium and lead are actively absorbed by the endogenous transport mechanisms that absorb and transport potassium and calcium, respectively. Filtration is generally considered to be of limited importance in the absorption of most xenobiotics but is substantially more important with regard to renal and biliary elimination. Endocytosis, which describes the encircling of a xenobiotic by a cellular membrane, is responsible for the absorption of large macromolecules such as the oral Sabin polio vaccine.⁶⁴

Gastrointestinal (GI) absorption is affected by xenobiotic-related characteristics such as dosage form, degree of ionization, partition constant, and patient factors (eg, GI blood flow; GI motility; and the presence or absence of food, ethanol, or other interfering substances such as calcium) (Fig. 9–5).

The formulation of a xenobiotic is extremely important in predicting GI absorption. Disintegration and dissolution must precede absorption.­ Disintegration is usually much more rapid than dissolution except for modified-release products. Modified release is a broad term that encompasses products that are delayed-release and extended-release formulations. These modified-release formulations are designed to release the xenobiotic over a prolonged period of time to simulate the blood concentrations achieved with the use of a constant IV infusion. By definition, extended-release formulations decrease the frequency of drug administration by at least 50% compared with immediate-release formulations, and they include controlled-release, sustained-release, and prolonged-release formulations. These formulations minimize blood concentration fluctuations, reduce peak-related side effects, reduce dosing frequency, and improve patient compliance. A variety of products use different pharmaceutical strategies, including dissolution control (encapsulation or matrix; Feosol), diffusion control (membrane or matrix; Plendil ER), erosion (Sinemet CR), osmotic pump systems (Procardia XL, Glucotrol XL), and ion exchange resins (MS Contin suspension). Overdoses with modified-release formulations often result in a prolonged absorption phase, a delay to peak concentrations, and a prolonged duration of effect.⁷ Some delayed-release preparations are enteric coated and specifically designed to bypass the stomach and to release drug in the small intestine. Other delayed-release formulations (eg, Verelan PM) are designed to release the drug later but not specifically designed to bypass release in the stomach. Enteric-coated (acetylsalicylic acid {ASA}, divalproex sodium) formulations resist disintegration and delay the time to onset of effect.⁶ Dissolution is affected by ionization, solubility, and the partition coefficient. In the overdose setting, the formation of poorly soluble or adherent masses such as concretions of foreign material termed bezoars significantly delay the time to onset of toxicity (Table 9–2).^{4,11,29,30,60}

Most ingested xenobiotics are primarily absorbed in the small intestine as a result of the large surface area and extensive blood flow of the small intestines.⁵⁹ Critically ill patients who are hypotensive, have a reduced cardiac output, or are receiving vasopressors such as norepinephrine have a decreased perfusion of vital organs, including the GI tract, kidneys, and liver.³ Not only is absorption delayed, but elimination is also diminished.⁵⁷ Total GI transit time can be from 0.4 to 5 days, and small intestinal transit time is usually 3 to 4 hours. Extremely short GI transit times reduce absorption. This change in transit time is the unproven rationale for use of whole-bowel irrigation (WBI). Delays in emptying of the stomach impair absorption as a result of the delay in delivery to the small intestine. Delays in gastric emptying occur as a result of the presence of food, especially fatty meals; agents with anticholinergic, opioid, or antiserotonergic properties; ethanol; and any xenobiotic that results in pylorospasm (salicylates, iron).

Bioavailability is a measure of the amount of xenobiotic that reaches the systemic circulation unchanged (Equation 9–5).³⁸ The fractional absorption (F) of a xenobiotic is defined by the area under the plasma drug concentration versus time curve (AUC) of the designated route of absorption compared with the AUC of the IV route. The AUC for each route represents the amount absorbed.

Gastric emptying and activated charcoal are used to decrease the bioavailability of ingested xenobiotics. The oral administration of certain chelators (deferoxamine, d-penicillamine) actually enhances the bioavailability of the complexed xenobiotic. The net effect of some chelators, such as succimer, is a reduction in body burden via enhanced urinary elimination even though absorption is enhanced.³¹

Presystemic metabolism may decrease or increase the bioavailability of a xenobiotic or a metabolite.⁵³ The GI tract contains microbial organisms that can metabolize or degrade xenobiotics such as digoxin and oral contraceptives and enzymes, such as peptidases, that metabolize insulin.⁵⁴ However, in rare cases, GI hydrolysis can convert a xenobiotic into a toxic metabolite, as occurs when amygdalin is enzymatically hydrolyzed to produce cyanide, a metabolic step that does not occur when amygdalin is administered intravenously.²⁷ Xenobiotic metabolizing enzymes and influx and efflux transporters such as organic anion transporting polypeptides (OATP) and P-glycoprotein (P-gp), respectively, may also affect bioavailability. Xenobiotic-metabolizing enzymes are found in the lumen of the small intestine and can substantially decrease the absorption of a xenobiotic.^44,73 Some of the xenobiotic that enters the cell can then be removed by the P-gp transporter from the cell and returned to the GI lumen and reexposed to the metabolizing enzymes.^44,73 Venous drainage from the stomach and intestines delivers orally (and intraperitoneally) administered xenobiotics to the liver via the portal vein and avoids direct delivery to the systemic circulation. This venous drainage allows hepatic metabolism to occur before the xenobiotic reaches the blood, and as previously mentioned, is referred to as the first-pass effect.^2,76 The hepatic extraction ratio is the percentage of xenobiotic metabolized in one pass of blood through the liver.⁴⁷ Xenobiotics that undergo significant first-pass metabolism (eg, propranolol, verapamil) are used at much lower IV doses than oral doses. Some drugs, such as lidocaine and nitroglycerin, are not administered by the oral route because of significant first-pass effect.⁴ Instead, sublingual, transcutaneous (topical), and rectal administration of drugs are used to bypass the portal circulation and avoid first-pass metabolism.

In the overdose setting, presystemic metabolism may be saturated, leading to an increased bioavailability of xenobiotics such as cyclic antidepressants, phenothiazines, opioids, and many β-adrenergic antagonists.⁵⁶ Hepatic metabolism usually transforms the xenobiotic into a less active metabolite but occasionally results in the formation of a more toxic xenobiotic such as occurs with the transformation of parathion to paraoxon.⁵¹ Biliary excretion into the small intestine usually occurs for these transformed xenobiotics of molecular weights greater than 350 Da and may result in a xenobiotic appearing in the feces even though it had not been administered orally.^34,54,67 Hepatic conjugated metabolites such as glucuronides may be hydrolyzed in the intestines to the parent form or to another active metabolite that can be reabsorbed by the enterohepatic circulation.^41,49,52,54 The enterohepatic circulation may be responsible for what is termed a double-peak phenomenon after the administration of certain xenobiotics.⁶⁴ The double-peak phenomenon is characterized as a serum concentration that decreases and then increases again as xenobiotic is reabsorbed from the GI tract. Other causes include variability in stomach emptying, presence of food, or failure of a tablet dosage form.⁶⁴

After the xenobiotic reaches the systemic circulation, it is available for transport to peripheral tissue compartments and to the liver and kidney for elimination. Both the rate and extent of distribution depend on many of the same principles discussed with regard to diffusion. Additional factors include affinity of the xenobiotic for plasma (plasma protein binding) and tissue proteins, acid–base status of the patient (which affects ionization), drug transporters, and physiologic barriers to distribution (blood–brain barrier, placental transfer, blood–testis barrier).^23,35,58 Blood flow, the percentage of free xenobiotic in the plasma, the activity of transporters account for the initial phase of distribution, and xenobiotic affinities determine the final distribution pattern. Whereas the adrenal glands, kidneys, liver, heart, and brain receive from 55 to 550 mL/min/100 g of tissue of blood flow, the skin, muscle, connective tissue, and fat receive 1 to 5 mL/min/100 g of tissue of blood flow.⁶² Hypoperfusion of the various organs in the critically ill and injured affects absorption, distribution, and elimination.⁷⁴

ATP-binding cassette (ABC) transporters are active ATP-dependent transmembrane protein carriers of which P-gp was the initial example ­discovered.⁹ Approximately 50 ABC transporters exist, and they are divided into subfamilies based on their similarities. Several members of the ABC superfamily, including P-gp, are under extensive investigation because of their role in controlling xenobiotic entry into, distribution in, and elimination from the body as well as their contributions to xenobiotic interactions.^21,32,73 The discovery of P-gp resulted from an investigation into why certain tumors exhibit multidrug resistance to many antineoplastics. P-gp (ABCB1) as well as ABCC and ABCG2 are known to be efflux transporters located in the intestines, renal proximal tubules, hepatic bile canaliculi, placenta, and blood–brain barrier and are responsible for the intra- to extracellular transport of various xenobiotics.¹⁶ First-generation transport inhibitors such as amiodarone, ketoconazole, quinidine, and verapamil are responsible for increasing body concentrations of P-gp substrates such as digoxin, the protease inhibitors, vinca alkaloids, and paclitaxel. St. John’s wort is a transport inducer, and it lowers serum concentrations of these same xenobiotics. Second- and third-generation xenobiotics that will affect transport with a higher affinity and specificity are in development.^18,65 Many of the same xenobiotics that affect cytochrome P450 CYP3A4 also affect P-gp (Appendix Chap. 13: Cytochrome P450 Substrates Inhibitors and Inducers).

The organic anion transporting polypeptides (OATPs) are another group of transporters found in the liver, kidneys, intestines, brain, and placenta that affect the absorption, distribution, and elimination of many xenobiotics and contribute to xenobiotic interactions. They include the organic anion transporters (OATs) and the organic cation transporters (OCTs).¹⁸ For example, probenecid increases the serum concentrations of penicillin by inhibiting the OAT responsible for the active secretion of penicillin by the renal tubular cells, and cimetidine inhibits the OCT responsible for the renal elimination of procainamide and metformin. A variety of OAT inhibitors are being investigated to decrease the hepatic uptake of amatoxins¹⁸ (Chap. 120).

Volume of distribution (Vd) is the proportionality term used to relate the dose of the xenobiotic that the individual receives with the resultant plasma concentration. Vd is an apparent or theoretical volume into which a xenobiotic distributes. It is a measure of how much xenobiotic is located inside versus outside of the plasma compartment after administration of a xenobiotic. Because only the plasma compartment is routinely assayed, the amount that remains in the plasma can be used to calculate the movement out of the blood. In a 70-kg man, the total body water (TBW) is 60% of total body weight, or 42 L, with two-thirds (28 L) of the fluid accounted for by intracellular fluid. Of the 14 L of extracellular fluid, 8 L is considered interstitial or between the cells; 3 L, or 0.04 L/kg, is plasma; and 6 L, or 0.08 L/kg, is blood. If 42 g of a xenobiotic is administered and remains in the plasma compartment (Vd = 0.04 L/kg), the concentration would be 15 g/L. If the distribution of the 42 g of xenobiotic approximated TBW (methanol; 0.6 L/kg), the concentration would be 1 g/L (usually reported as 100 mg/dL). These calculations can be performed by using Equation 9–6, where S equals the percent pure drug if a salt form is used.

Experimental determination of Vd involves administering an IV dose of the xenobiotic and extrapolating the plasma concentration time curve back to time zero (C0). If the determination takes place after steady state has been achieved, the volume of distribution is then referred to as the Vdss. For many xenobiotics, the Vd is known and readily available in the literature (Table 9–3). When the Vd and the dose ingested are known, a maximum predicted plasma concentration can be calculated after assuming all of the xenobiotic is absorbed and no elimination occurred. This assumption usually overestimates the plasma concentration. Distribution is complex, and differential affinities for various storage sites in the body, such as plasma proteins, liver, kidney, fat, and bone, determine where a xenobiotic ultimately resides.

For the purposes of determining the utility of extracorporeal removal of a xenobiotic, a low Vd is often considered to be less than 1 L/kg. For some xenobiotics, such as digoxin (Vd = 7 L/kg) and the cyclic antidepressants (Vd = 10–15 L/kg), the Vd is much larger than the actual volume of the body. A large Vd indicates that the xenobiotic resides outside of the plasma compartment, but again, it does not describe the site of distribution.

The site of accumulation of a xenobiotic may or may not be a site of action or toxicity. If the site of accumulation is not a site of toxicity, then the storage depot may be relatively inactive, and the accumulation at that site may be theoretically protective to the animal or person.⁵⁸ Selective accumulation of xenobiotics occurs in certain areas of the body because of affinity for certain tissue-binding proteins. For example, the kidney contains metallothionein, which has a high affinity for metals such as cadmium, lead, and mercury.²³ The retina contains the pigment melanin, which binds and accumulates chlorpromazine, thioridazine, and chloroquine.²³ Other examples of xenobiotics accumulating at primary sites of toxicity are carbon monoxide binding to hemoglobin and myoglobin and paraquat distributing to type II alveolar cells in the lungs.⁵⁵ Dichlorodiphenyltrichloroethane (DDT), chlordane, and polychlorinated biphenyls are stored in fat and can be mobilized if malnutrition develops.⁷⁷ Lead sequestered in bone³³ is not immediately toxic, but mobilization of bone through an increase in osteoclast activity⁵⁸ (hyperparathyroidism, pregnancy, immobilization) may free lead for distribution to sites of toxicity in the central nervous system (CNS) or blood.

Several plasma proteins bind xenobiotics and act as carriers and storage depots. The percentage of protein binding varies among xenobiotics, as do their affinities and potential for reversibility. After it is bound to plasma protein, a xenobiotic with high binding affinity will remain largely confined to the plasma until elimination occurs. However, dissociation and reassociation may occur if another carrier is available with a higher binding affinity. Most plasma measurements of xenobiotic concentrations reflect total xenobiotic (bound plus unbound). Only the unbound xenobiotic is free to diffuse through membranes for distribution or for elimination. Albumin binds primarily to weakly acidic, poorly water-soluble xenobiotics, which include salicylates, phenytoin, and warfarin, as well as endogenous substances, including free fatty acids, cortisone, aldosterone, thyroxine, and unconjugated bilirubin.⁶² α₁-Acid glyco-protein usually binds basic xenobiotics, including lidocaine, imipramine, and propranolol.⁶² Transferrin, a β₁-globulin, transports iron, and ceruloplasmin carries copper.

Phenytoin is an example of a xenobiotic whose effects are significantly influenced by changes in concentration of plasma albumin because only free phenytoin is active. When albumin concentrations are in the normal range, approximately 90% of phenytoin is bound to albumin. As the albumin concentration decreases, more phenytoin is free for distribution, and a greater clinical response to the same serum phenytoin concentration is often observed. The free plasma phenytoin concentration can be calculated based on the albumin concentration. This achieves an appropriate interpretation (adjusted) of total phenytoin within the conventional therapeutic range of 10 to 20 mg/L of free plus bound phenytoin (Equation 9–7).

The clinical implications are that a malnourished patient with an albumin of 2 g/dL receiving phenytoin can manifest toxicity with a plasma phenytoin concentration of 14 mg/L. This measurement is total phenytoin (bound + unbound). Because the patient has a reduced albumin concentration, this actually represents a substantially higher proportion and absolute amount of active unbound phenytoin. Substitution into the above equation of 14 mg/L for actual plasma phenytoin concentration and 2 g/dL for albumin gives an adjusted plasma phenytoin concentration of 23.3 mg/L (therapeutic range, 10–20 mg/L).

Although drug interactions are often attributed to the displacement of xenobiotics from plasma protein binding, concurrent metabolic interactions are usually more consequential. Displacement transiently increases the amount of unbound, active drug. This may result in an immediate increase in drug effect. This is followed by enhanced distribution and elimination of unbound drug. Gradually, the unbound plasma concentration returns to predisplacement concentrations.⁵⁹

Saturation of plasma proteins may occur in the therapeutic range for a drug such as valproic acid. Acute saturation of plasma protein binding after an overdose often leads to consequential adverse effects. Saturation of plasma protein binding with salicylates and iron after overdose increase distribution to the CNS (salicylates) or to the liver, heart, and other tissues (iron), increasing toxicity.

Specific therapeutic maneuvers in the overdose setting are designed to alter xenobiotic distribution by inactivating or enhancing elimination to limit toxicity. These therapeutic maneuvers include manipulation of serum or urine pH (salicylates), the use of chelators (lead), and the use of antibodies or antibody fragments (digoxin).

The Vd permits predictions about plasma concentrations and assists in defining whether an extracorporeal method of removal is beneficial for a particular toxin. If the Vd is large (>1 L/kg), it is unlikely that hemodialysis, hemoperfusion, or exchange transfusion would be effective because most of the xenobiotic is outside of the plasma compartment. Plasma ­protein binding also influences this decision. If the xenobiotic is more tightly bound to plasma proteins than to activated charcoal, then hemoperfusion is unlikely to be beneficial even if the Vd of the xenobiotic is small. In addition, high plasma protein binding limits the effectiveness of hemodialysis because only unbound xenobiotic will freely cross the dialysis membrane. Exchange transfusion can be effective for a xenobiotic with a small Vd and substantial plasma protein binding because both bound and free xenobiotic are removed simultaneously.

Removal of a parent xenobiotic from the body (elimination) begins as soon as the xenobiotic is delivered to clearance organs such as the liver, kidneys, and lungs. Elimination includes biotransformation and excretion. Elimination begins immediately but may not be the predominant kinetic process until absorption and distribution are substantially completed. The functional integrity of the cardiovascular, pulmonary, renal, and hepatic ­systems are major determinants of the efficiency of xenobiotic removal and of therapeutically administered antidotes. The xenobiotics themselves may cause kidney or liver (eg, APAP) failure, subsequently compromising their own elimination. Other factors that influence elimination include older age (enzyme maturation), competition or inhibition of elimination processes by interacting xenobiotics, saturation of enzymatic processes, gender, pharmacogenetics and pharmacogenomics, obesity, and the physicochemical properties of the xenobiotic.⁴⁶

Elimination can be accomplished by biotransformation to one or more metabolites or by excretion from the body of unchanged xenobiotic. Excretion may occur via the kidneys, lungs, GI tract, and body secretions (sweat, tears, milk). Because of their water solubility, hydrophilic (polar) or charged xenobiotics and their metabolites are generally excreted via the kidney. The majority of xenobiotic metabolism occurs in the liver, but it also occurs in the blood, skin, GI tract, placenta, or kidneys. Lipophilic (uncharged or nonpolar) xenobiotics are usually metabolized in the liver to hydrophilic metabolites, which are then excreted by the kidneys.^24,51 These metabolites are generally inactive, but if active, they may contribute to toxicity. Examples of active metabolites include nortriptyline (derived from amitriptyline), N-acetylprocainamide (derived from procainamide) and normeperidine (derived from meperidine).

Metabolic reactions catalyzed by enzymes, categorized as either phase I or phase II, may result in pharmacologically active metabolites; frequently, the latter have different toxicities than the parent compounds. Phase I (asynthetic), or preparative metabolism, which may or may not precede phase II, is responsible for introducing polar groups onto nonpolar xenobiotics by oxidation (hydroxylation, dealkylation, deamination), reduction (alcohol dehydrogenase, azo reduction), and hydrolysis (ester hydrolysis).^22,49 Phase II, or synthetic, reactions conjugate the polar group with a glucuronide, sulfate, acetate, methyl or glutathione or amino acids such as glycine, ­taurine, and glutamic acid, creating more polar metabolites.^14,22,49

Comparatively, phase II reactions produce a much larger increase in hydrophilicity than phase I reactions. The enzymes involved in these reactions have low substrate specificity, and those in the liver are usually localized to either the endoplasmic reticulum (microsomes) or the soluble fraction of the cytoplasm (cytosol).⁴⁹ The location of the enzymes becomes important if they form reactive metabolites, which then concentrate at the site of metabolism and cause toxicity. For example, APAP causes centrilobular necrosis because the CYP2E1 enzymes, which form N-acetyl-p-benzoquinoneimine (NAPQI), the toxic metabolite, are located in their highest concentration in that zone of the liver.

The enzymes that metabolize the largest variety of xenobiotics are heme-containing proteins referred to as CYP monooxygenase enzymes.^28,49 This group of enzymes, formerly called the mixed function oxidase system, is found in abundance in the microsomal endoplasmic reticulum of the liver. These cytochrome P450 metabolizing enzymes (CYPs) primarily catalyze the oxidation of xenobiotics. Cytochrome P450 in a reduced state (Fe²⁺) binds carbon monoxide. Its discovery and initial name resulted from spectral identification of the colored CO-bound cytochrome P450, which absorbs light maximally at 450 nm. The cytochrome P450 system is composed of many enzymes grouped according to their respective gene families and subfamilies, of which approximately 57 of these functional human genes have been sequenced. Members of a gene family have more than 40% similarity of their amino acid sequencing, and subfamilies have more than 55% similarity. For example, the CYP2D6*1a gene encodes wild-type ­protein (enzyme) CYP2D6, where 2 represents the family, D the subfamily and 6 the individual gene, and *1a the mutant allele; CYP2D6.1 represents the most common or wild-type allele.

Toxicity may result from induction or inhibition of CYP enzymes by another xenobiotic, resulting in a consequential drug interaction (Chap. 13). Many of these interactions are predictable based on the known xenobiotic affinities and their capability to induce or inhibit the P450 system.^{12,42,49,50,66} However, polymorphism (individual genetic expression of enzymes),¹ stereoisomer variability⁷⁵ (enantiomers with different potencies and isoenzyme affinities), and the capability to metabolize a xenobiotic by alternate pathways contribute to unexpected metabolic outcomes. The pharmaceutical industry is now exploiting the concept of chiral switching (marketing a single enantiomer instead of the racemic mixture) to alter efficacy or side effect profiles. Enantiomers are named either according to the direction in which they rotate polarized light (l or – for levorotatory, and d or + for ­dextrorotatory) or according to the absolute spatial orientation of the groups at the chiral center (S or R). Chiral means “hand” in Greek, and the latter designations refer to either sinister (left-handed) or rectus (right-handed). There is no direct correlation between levorotatory or dextrorotatory and S and R, which indicates the direction polarized light is rotated by a solution of the xenobiotic.⁷⁰

The liver reduces the oral bioavailability of xenobiotics with high extraction ratios. The bioavailabilities of xenobiotics with high extraction ratios are greatly affected by enzyme induction and enzyme inhibition; the reverse is true for xenobiotics with a low extraction ratio. After the xenobiotic is in the blood, the hepatic elimination is affected by blood flow to the liver, the intrinsic hepatic metabolism, and plasma protein binding. If the hepatic metabolism of a xenobiotic is very high, then the only limit to hepatic clearance is blood flow to the liver, and not protein binding. However, if the intrinsic hepatic metabolism for a xenobiotic is low, then blood flow to the liver is not consequential. Plasma protein binding becomes important because only unbound xenobiotics can be cleared by the liver. Because enzyme inhibition and induction greatly affect intrinsic hepatic metabolism, these factors are also important.

Excretion is primarily accomplished by the kidneys, with biliary, pulmonary, and body fluid secretions contributing to lesser degrees. Urinary excretion occurs through glomerular filtration, tubular secretion, and passive tubular reabsorption. The glomerulus filters unbound xenobiotics of a particular size and shape in a manner that is not saturable (but is subject to renal blood flow and perfusion). Passive tubular reabsorption accounts for the reabsorption of uncharged, lipid-soluble xenobiotics and is therefore influenced by the pH of the urine and the pK_a or pK_b of the xenobiotic. The principles of diffusion discussed earlier permit, for example, the ion trapping of salicylate (pK_a = 3.5) in the urine through urinary alkalinization. Tubular secretion is an active process carried out by drug transporters (OATs, OCTs) and subject to saturation and drug interactions (Table 9–4).

The effects of obesity on elimination are being studied. Obesity is the accumulation of adipose tissue far in excess of that which is considered normal for a person’s age and gender. The National Institutes of Health defines obesity as a body mass index (BMI) greater than 30 and overweight as a BMI between 25 and 29.9. The BMI is calculated by dividing a person’s weight in kilograms by the individual’s height in meters squared (m²). By this criterion, about one-third of the adult US population is obese. Obesity poses problems in determining the correct loading dose and maintenance dose for therapeutic xenobiotics and for the estimation of serum concentrations and elimination times in the overdose setting.^10,26,39,48 A number of formulas have been proposed to classify body size in addition to BMI, but none has been tested adequately in the obese population. Obese patients have not only an increase in adipose tissue but also an increase in lean body mass of 20% to 55%, which results in the alteration of the distribution of both lipophilic and hydrophilic xenobiotics. In general, the absorption of xenobiotics in obese patients does not appear to be affected, but distribution is affected. The effect of obesity on hepatic metabolism requires additional study, although some studies suggest a nonlinear increase in clearance. The glomerular filtration rate increases in obesity. For example, although aminoglycosides are hydrophilic, because of an increase in fat free mass in obese patients, a dosing weight correction of 40% is used to calculate both the loading dose and the maintenance dose (Dosing body weight = 0.4 × {Actual body weight − Ideal body weight} + Ideal body weight). Preliminary studies with propofol, a very lipophilic drug, suggest that induction and maintenance doses correlate better with actual body weight. These equations are found in Table 9–5. One recent evaluation suggests using 40% of actual body weight instead of ideal body weight in the Cockcroft-Gault formula to estimate kidney function in the obese.

Models exist to study and describe the movement of xenobiotics in the body with mathematical equations. Traditional compartmental models (one or two compartments) are data based and assume that changes in plasma concentrations represent proportional changes in tissue concentrations (Fig. 9–6).⁴⁷ Advances in computer technology facilitate the use of the classic concepts developed in the late 1930s.⁶⁹ Physiologic models consider the unique movement characteristics of xenobiotics based on known or theoretical biologic processes. This allows the prediction of tissue concentrations while incorporating the effects of changing physiologic parameters and affording better extrapolation from laboratory animals.⁷⁹ Unfortunately, physiologic modeling is still in its infancy, and the mathematical modeling it entails is often very complex.¹⁹ The commonest mathematical equations used are based on traditional compartmental modeling.

The one-compartment model is the simplest approach for analytic purposes and is applied to xenobiotics that enter and rapidly distribute throughout the body. This model assumes that changes in plasma concentrations will result in and reflect proportional changes in tissue concentrations. Many xenobiotics, such as digoxin, lithium, and lidocaine, do not instantaneously equilibrate with the tissues and are better described by a two-compartment model. In the two-compartment or more than two-compartment model, a xenobiotic is distributed instantaneously to highly perfused tissues (central compartment) and then is secondarily, and more slowly, distributed to a peripheral compartment. Elimination is assumed to take place from the central compartment.

If the rate of a reaction is directly proportional to the concentration of xenobiotic, it is termed first order or linear. Processes that are capacity limited or saturable are termed nonlinear (not proportional to the concentration of xenobiotic) and are described by the Michaelis-Menten equation, which is derived from enzyme kinetics. Calculus is used to derive the first-order equation.⁷⁹ Rate is directly proportional to concentration of xenobiotic, as in Equation 9–8.

An infinitesimal change in concentration of a xenobiotic (dC) with respect to an infinitesimal change in time (dt) is directly proportional to the concentration (C) of the xenobiotic as in Equation 9–9:

The proportionality constant k is added to the right side of the expression to mathematically allow the introduction of an equality sign. The constant k represents all of the bodily factors, such as metabolism and excretion, which contribute to the determination of concentration (Equation 9–10).

Introducing a negative sign to the left-hand side of the equation describes the “decay” or decreasing xenobiotic concentration (Equation 9–11).

This equation is impractical because of the difficulty of measuring infinitesimal changes in C or t. Therefore, the use of calculus allows the integration or summing of all of the changes from one concentration to another beginning at time zero and terminating at time t. This relationship is mathematically represented by the integration sign (∫). The sign ∫ means to integrate the term from concentration at time zero (C₀) to concentration at a given time t (C_t). ∫ means the same with respect to time, where t₀ = zero. Before this application, the previous equation is first rearranged (Equation 9–12).

The integration of dC divided by C is the natural logarithm of C (ln C), and the integration of dt is t (Equation 9–13).

The vertical straight lines proscribe the evaluation of the terms between those two limits. The following series of manipulations is then performed (Equation 9–14A, 14B, 14C, a and 14D).

Equation 9–14D can be recognized as taking the form of an equation of a straight line (Equation 9–15), where the slope is equal to the negative rate constant k and the intercept is C₀.

Instead of working with natural logarithms, an exponential form (the antilog) of Equation 9–14D may be used (Equation 9–16).

Graphing the ln (natural logarithm) of the concentration of the xenobiotic at various times for a first-order reaction is a straight line. Equation 9–16 describes the events when only one first-order process occurs. This is appropriate for a one-compartment model (Fig. 9–7).

In this model, regardless of the concentration of the xenobiotic, the rate (percentage) of decline is constant. The absolute amount of xenobiotic eliminated changes continuously while the percent eliminated remains constant. k is reported in h⁻¹. A k_e of 0.10 h⁻¹ means that the xenobiotic is being processed (eliminated) at a rate of 10% per hour. k is often designated as k_e and referred to as the elimination rate constant. The time necessary for the xenobiotic concentration to be reduced by 50% is called the half-life. The half-life is determined by a rearrangement of Equation 9–14D whereby C2 becomes C at time t2 and C1 becomes C at t1 and by rearrangement giving Equation 9–17:

Substitution of 2 for C₁ and 1 for C₂ or 100 for C₁ and 50 for C₂ gives Equations 9–18A and 9–18B:

The use of semilog paper facilitates graphing the first-order equation. If natural logs are used to calculate slope, then k_e = –slope, and if common logs are used to calculate slope, then k_e = –2.303 × slope (Fig. 9–7).

The mathematical modeling becomes more complex when more than one first-order process contributes to the overall elimination process. The equation that incorporates two first-order rates is used for a two-compartment model and is Equation 9–19.

Figure 9–8 demonstrates a two-compartment model where α often represents the distribution phase and β is the elimination phase.

The rate of reaction of a saturable process is not linear (ie, not proportional to the concentration of xenobiotic) when saturation occurs (Fig. 9–9). This model is best described by the Michaelis-Menten equation used in enzyme kinetics (Equation 9–20) in which v is the velocity or rate of the enzymatic reaction, C is the concentration of the xenobiotic, V_max is the maximum velocity of the reaction between the enzyme and the xenobiotic at high xenobiotic concentrations, and K_m is the substrate concentration at which the reaction rate is half of the V_max.⁷⁹

Application of this equation to toxicokinetics requires v to become the infinitesimal change in concentration of a xenobiotic (dC) with respect to an infinitesimal change in time (dt) as previously discussed (Equation 9–10). V_max and K_m both reflect the influences of diverse biologic processes. The Michaelis-Menten equation then becomes Equation 9–21, in which the negative sign again represents decay:

When the concentration of the xenobiotic is very low (C <<< K_m), it can be dropped from the bottom right of the equation because its contribution becomes negligible, and the resultant equation is described as a first-order process (Equation 9–22A and 9–22B). Conceptually, this is understandable because at a very low xenobiotic concentration, the process is not saturated.

Because V_max divided by K_m is a constant, k, then:

However, when the concentrations of the xenobiotic are extremely high and exceed the capacity of the system (C >>> K_m), the rate becomes fixed at a constant maximal rate regardless of the exact concentration of the xenobiotic, termed a zero-order reaction. Tables 9–6A and 9–6B compare a first-order reaction with a zero-order reaction. In this particular example, zero order is faster, but if the fraction of xenobiotic eliminated in the first-order example were 0.4, then the amount of xenobiotic in the body would decrease below 100 before the xenobiotic in the zero-order example. It is inappropriate to perform half-life calculations on a xenobiotic displaying zero-order behavior because the metabolic rates are continuously changing. Sometimes the term apparent half-life is used if it is unclear if the xenobiotic is exhibiting zero-order or first-order pharmacokinetics. After an overdose, enzyme saturation is a common occurrence because the capacity of enzyme systems is overwhelmed.

Clearance (Cl) is the relationship between the rate of transfer or elimination of a xenobiotic from a reference fluid (usually plasma) to the plasma concentration (Cp) of the xenobiotic and is expressed in units of volume per unit time mL/min (Equation 9–23).^25,47,61

The determination of creatinine clearance is a well-known example of the concept of clearance. Creatinine clearance (Cl_CR) is determined by Equation 9–24:

in which U is the concentration of creatinine in urine (mg/mL), V is the volume flow of urine (mL/min), Cp is the plasma concentration of creatinine (mg/mL), and the units for clearance are milliliters per minute. A creatinine clearance of 100 mL/min means that 100 mL of plasma is completely cleared of creatinine every minute. Clearance for a particular eliminating organ or for extracorporeal elimination is calculated with Equation 9–25:

Cl = clearance for the eliminating organ or extracorporeal device

Q_b = blood flow to the organ or device

ER = extraction ratio

C_in = xenobiotic concentration in fluid (blood or serum) entering the organ or device

C_out = xenobiotic concentration in fluid (blood or serum) leaving the organ or device

Clearance can be applied to any elimination process independent of the precise mechanisms (ie, first order, Michaelis-Menten) and represents the sum total of all of the rate constants for xenobiotic elimination. Total body clearance (Cl_{total body}) is the sum of the clearances of each of the individual eliminating processes, as seen in Equation 9–26:

For a first-order process (one-compartment model), clearance is given by Equation 9–27:

Experimentally, the clearance can be derived by examining the IV dose of xenobiotic in relation to the AUC from time zero to time t (Equation 9–28). The AUC is calculated using the trapezoidal rule or through integral calculus (units, eg, {mg × hour}/mL) (Figs. 9–10 and 9–11).

When exposure to a xenobiotic occurs at a fixed rate, the plasma concentration of the xenobiotic gradually achieves a plateau concentration at which the rate of absorption equals the rate of elimination and is termed steady state. The time to achieve 95% of steady-state concentration for a first-order process depends on the half-life and usually necessitates 5 half-lives. The concentration achieved at steady state depends on the Vd, the rate of exposure, and the half-life.

Iatrogenic toxicity may occur in the therapeutic setting when dosing decisions are based on serum concentrations determined before achieving a steady state. This adverse event is particularly common when using xenobiotics with long half-lives such as digoxin⁷⁸ and phenytoin.

Peak plasma concentrations (C_max) of a xenobiotic occur at the time of peak absorption. At this point in time, the absorption rate is at least equal to the elimination rate. Thereafter, the elimination rate predominates, and plasma concentrations begin to decline. Whereas the C_max depends on the dose, the rate of absorption (k_a), the rate of elimination (k_e), and the time to peak (t_max) are independent of dose and only depend on the k_a and k_e. For the same dose of xenobiotic, if the k_e remains constant and the rate of absorption decreases, then the t_max will occur later, and the C_max will be slightly lower (Table 9–7). Controlled-release dosage forms and xenobiotics that form concretions and have a decreased rate of absorption may not achieve peak concentrations until many hours after an immediate-release preparation with rapid absorption. The AUC will remain the same. However, if the k_a remains constant and the k_e is increased, then the t_max occurs sooner, the C_max decreases, and the AUC decreases (Table 9–7).⁵² Values are based on a single oral dose (100 mg) that is 100% bioavailable (F = 1) and has an apparent Vd of 10 L. The drug follows a one-compartment open model. The AUC is calculated by the trapezoidal rule from 0 to 24 hours.

In the overdose setting, gastric emptying, single-dose activated charcoal, and WBI decrease k_a. Multiple-dose activated charcoal, manipulation of pH to promote ion trapping to facilitate elimination, and certain chelators (ie, succimer, deferoxamine) increase k_e and are likely to decrease C_max, t_max, and AUC.

For serum concentrations to have significance, there must be an established relationship between effect and serum concentration. Many medications, such as valproic acid, digoxin, carbamazepine, lithium, and cyclosporine, have established therapeutic ranges. However, there are also many drugs (eg, diazepam, propranolol, verapamil) for which there is no established therapeutic range. Some xenobiotics (eg, physostigmine) exhibit hysteresis in which the effect increases as the serum concentration decreases. For many xenobiotics, very little information on toxicodynamics is available. Sequential serum concentrations often are collected for retrospective analysis in an attempt to correlate serum concentrations and toxicity. Tolerance to drugs, such as ethanol, also influences the interpretation of serum concentrations. Tolerance is an example of a pharmacodynamic or toxicodynamic effect as a result of cellular adaptation, and it occurs when larger doses of a xenobiotic are necessary to achieve the same clinical or pharmacologic result.

Other factors that influence the interpretation of serum concentrations include chronicity of dosing (a single dose vs. multiple doses); whether absorption is still ongoing and therefore concentrations are still increasing; whether distribution is still ongoing and therefore concentrations are uninterpretable (Fig. 9–12); or whether the value is a peak, trough, or steady-state concentration. Collection of accurate data for analysis requires at least 4 data points during at least 1 elimination half-life. Clinical examples in which interpretation is dependent on the dosing pattern of a single dose versus multiple doses include digoxin, lithium, vancomycin, and APAP. Controlled-release preparations and xenobiotics that delay gastric emptying or form concretions are expected to have prolonged absorptive phases and require serial serum concentrations to obtain a meaningful analysis of serum concentrations (Chap. 6). A combination of trough, peak, and minimum inhibitory concentrations is often consequential for monitoring antibiotics such as gentamicin.^8,43

Pitfalls in interpretation arise when the units for a particular serum concentration are not obtained or are unfamiliar (eg, mmol/L) to the ­clinician. The type of analysis generally applied clinically may not be appropriate to massive overdoses, and the laboratory may make errors in dilution, or errors can be inherent in the assay (Chap. 6). In these cases, the director of the laboratory should be consulted for advice with regard to the availability of a reference laboratory. The type of collection tube (eg, plasma or serum instead of whole blood for certain metals), the receptacle, or the conditions during delivery of the sample result in inaccurate or inadequate information. When in doubt, the laboratory toxicologist or chemist should be called before sample collection. The laboratory usually measures total xenobiotic (free plus bound), and for xenobiotics that are highly plasma protein bound, reductions in albumin increase free concentrations and alter the interpretation of the reported concentration (Equation 9–7). Active metabolites may contribute to toxicity and may not be measured.³⁷ During extracorporeal methods of elimination, ideal criteria for determining the amount removed require assay of the dialysate or activated charcoal cartridge or multiple simultaneous serum concentrations going into and out of the device rather than random serum concentrations (Chap. 10). Clearance calculations for drugs such as lithium that partition significantly into the red blood cells are more accurate when measurements are taken on whole blood.^13,20 The patient’s weight and height and, when indicated, hemoglobin, creatinine, albumin, and other parameters to assess elimination pathways may be helpful.

• Pharmacokinetics and toxicokinetics are the study of the absorption, distribution, metabolism, and excretion of drugs in the therapeutic and overdose settings, respectively.

• Phamacokinetics and toxicokinetics can help predict the onset and duration of toxicity when serum concentrations are related to therapeutic and toxic effects.

• Interpretation of serum concentrations relies on many factors dependent on the drugs (eg, dosage form, single versus multiple doses) and the patient (tolerance, genetic profile).

References