Dissociation Constant or pKa

The dissociation constant or pKa, also known as the ionization constant, is related to the amino terminus. As noted above the N‐terminus has two forms, cationic (BH⁺) and free base (B), that are in equilibrium, although the proportion of one and the other depends on the following two factors (Covino 1972).

1. The dissociation constant or pKa specific to each anesthetic is defined as the pH at which 50% of the molecules in the local anesthetic adopt the BH⁺ form and the other 50% the B form (Table 5.2).
2. The pH of the tissues because this modifies the proportion of the dissociated forms in keeping with the Henderson–Hasselbalch equation (Henderson 1908; Hasselbalch 1917):
   

   whereby

   

Although the physiological pH is 7.4, the pH in tissues may drop to 6 or lower in the presence of inflammation or pus (Schade et al. 1921; De Jong and Cullen 1963). The proportion of the B form, which diffuses across cell membranes, consequently declines, rendering the anesthetic less effective since a smaller amount reaches the axon interior.

The pKa value effects two properties of local anesthetics: the onset of action and anesthetic potency.

1. Onset of local anesthetic action. The lower the pKa, the greater the proportion of free base (B) in the anesthetic in tissues at physiological pH (7.4) and the speedier its diffusion inside the axon after crossing the cell membrane. In the axon interior (axoplasm) it reaches a new B ↔ BH⁺ equilibrium, enabling the cationic form (BH⁺) to act on the protein receptor (Ritchie et al. 1965a, b), blocking the sodium channels and with them the nerve impulse. This is the property that pKa affects most significantly.
2. Anesthetic potency. The lower the pKa, the higher the potency of the local anesthetic, as more anesthetic penetrates the membrane more quickly, leaving less outside to be captured by the bloodstream (Courtney 1980; Wildsmith et al. 1987). The effect of pKa is minor here, acting merely as a coadjutant. As discussed below, other factors such as lipid solubility have a heavier impact on the potency of local anesthetics.

Partition Coefficient or Lipid Solubility

The partition coefficient or lipid solubility, also known as the diffusion coefficient, a measure of the relative penetration of drugs in biological membranes, is closely related to drug–cell membrane component binding. While the partition coefficient is actually a measure of lipid solubility, in practice the two terms are used indistinctly (Tucker et al. 1970). The two best‐known methods for determining lipid solubility yield very different values, although as the data in Table 5.3 shows, they exhibit a consistent pattern.

Lipid solubility affects a number of properties of local anesthetics, as discussed below.

1. Relative anesthetic potency. The higher the lipid solubility, the higher the anesthetic potency. Although it is the single most important factor in anesthetic potency (Courtney 1980; Wildsmith et al. 1987), others act as coadjutants: (i) as noted earlier, pKa impacts potency, which is greater at lower pKa values; (ii) binding to blood plasma proteins also plays a role, for the more strongly the anesthetic binds, the higher is it potency (Truant and Takman 1959; Tucker et al. 1970); and (iii) the larger the size of the drug molecule, the higher the potency (Courtney 1980; Butterworth and Strichartz 1990). The reference for anesthetic potency, procaine, is assigned a value of 1 and all other anesthetics are measured against that standard.
2. Relative toxicity. Lipid solubility is closely related to toxicity (Covino 1987; Garfield and Grugino 1987), such that the higher the former the higher the latter (Covino 1972; Gangorosa 1981). Procaine, which is also the reference for toxicity, is assigned a value of 1 and all other anesthetics are measured against that standard.
3. Topical anesthetic effectiveness (Gangorosa 1981). Although topical anesthesia depends on both the lipid solubility and anesthetic concentration, a certain level of lipid solubility can be defined that ensures good topical anesthetic action with no need to increase the concentration to intolerably high proportions (Table 5.3).

Protein Binding

The ability of local anesthetics to bind to plasma proteins has been studied primarily for α₁‐acid glycoprotein (Routledge et al. 1980; Meunier et al. 2001) and to a lesser extent, albumin (Mather et al. 1971; Meunier et al. 2001). An equilibrium between the fraction of anesthetic bound to proteins and the free portion is reached in a matter of microseconds (Widman 1975), the latter being the pharmacologically active fraction (Tucker et al. 1970; Tucker and Mather 1975).

Anesthetic binding to proteins conditions the duration of their effect: the more strongly they bind, the longer the duration (Covino 1981; Milam and Giovannitti Jr. 1984). That is because the transmembrane receptors for local anesthetics are also proteins (Covino 1981). These considerations are summarized in Table 5.4.

Vasodilation

Nearly all local anesthetics generate vasodilation in two ways: (i) they cause the smooth muscle cells lining the vessels to relax (Aps and Reynolds 1976; Covino and Giddon 1981) and (ii) they block sympathetic type B nerve fibers that control vasoconstriction. However, exceptions exist.

• Cocaine has an indirect vasoconstrictive effect because it blocks mono‐amine‐oxidase (MAO), an enzyme, preventing the recapture of nerve ending norepinephrine, which is a vasoconstrictor (Muscholl 1961; Covino and Giddon 1981).
• Mepivacaine is slightly vasoconstrictive (Du Mesnil de Rochemont and Hensel 1960; Lindorf et al. 1974; Lindorf 1979; Vongsavan et al. 2000), as is ropivacaine (Iida et al. 2001; Timponi et al. 2006), although the effect is less widely acknowledged in the latter (De Oliveira et al. 2014).

Vasodilation increases blood flow and with it, anesthetic transport, which in turn lowers anesthetic potency and duration (Widman 1975; Aps and Reynolds 1976). One curious effect is that the higher the concentration of the drug, the greater is its vasodilatory effect, partially offsetting the increase in potency afforded by higher concentrations (Aps and Reynolds 1976; Reynolds et al. 1976). The clinical conclusion is that the greater the vasodilatory effect of an anesthetic, the greater the benefit to be administered with a vasoconstrictor, which enhances anesthetic potency and duration, hindering vascular absorption of the local anesthetic and thereby lowering the risk of systemic toxicity. Further to the data listed in Table 5.5, in amide‐type anesthetics, the vasodilatory effect rises with anesthetic potency (Covino and Giddon 1981).

Assessment of Local Anesthesia in Dentistry

Such methods are insufficient in dentistry, as the dental pulp is an organ not present in any other part of the body and which is very difficult to anesthetize. Unlike readily anesthetized soft tissues where the effect is long‐lasting, the duration of pulpal anesthesia is much shorter (Björn 1946; Björn and Huldt 1947) (Figure 5.3).

An effective assessment method was developed in 1946 by Hilding Björn (1907–1995), who used an electric pulp tester (EPT) to study the efficacy of anesthetic solutions. The device may be applied repeatedly to assess the duration of pulpal anesthesia, the criteria for which is if the tooth fails to respond to the maximum stimulus of the EPT. The reasoning behind this is that if the patient feels discomfort at less than the maximum stimulus, then there is a risk that the patient may respond to stimuli during the dental procedure (Björn 1946; Björn and Huldt 1947; Certosimo and Archer 1996). Moreover, successive electrical testing over a given time has been shown to induce no harm in the dental pulp (McDaniel et al. 1973). Recent research has found that the myelinated Aδ fibers in the pulp are stimulated by the EPT, whereas the unmyelinated polymodal C fibers are not (Lin and Chandler 2008; Sampaio et al. 2012).

Björn standardized the procedure by selecting the maxillary lateral incisor (LI) as the target, as this tooth exhibits scant anatomical variations and can be anesthetized with buccal infiltration, a simple technique which also limits individual variation. By injecting 1 ml of solution, Björn ensured that the experimental conditions were standardized and reproducible in all the series studied (Björn 1947; Björn and Huldt 1947). Such standardization is lacking in other methods (i.e. restorations, scaling, root canals, extractions) and uniform pain stimulus is difficult to attain and assess, and such methods furnish no information on the anesthetic effect in the pulp.

Mandibular block studies are useful for obtaining clinical information on that anesthetic technique and its limitations, but are of scant utility in assessing the effectiveness of local anesthetic solutions for a number of reasons.

1. Technique sensitivity: As the technique is more difficult, failures due to technical errors are common. High interindividual variability, in turn, renders it more difficult to standardize.
2. Accessory innervations: Despite a successful block indicated by an anesthetized lower lip, the patient may still have sensation in the pulp due to the high frequency of accessory innervation in the lower arch such as the buccal nerve and mylohyoid nerve (see Chapter 19).
3. Anatomic variation: Anatomic variation in the mandible such as double mandibular foramen, accessory canals, high lingula, and variable gonial angle may result in anesthetic failure despite the use of correctly implemented standardized techniques to fail (see Chapter 19).

All the above‐mentioned variables are difficult to control and standardize, and thus reduce the utility of using mandibular block injections to assess local anesthetic solution efficacy.

Anesthetic Parameter

Certain variables, listed below, may be used as surrogate indicators of the clinical efficacy of anesthetic solutions, and these indicators may vary depending on the specific local anesthetic and vasoconstrictor, and their respective concentrations.

• Of the four variables selected here (Annexes 21 and 27), three are related to buccal infiltration of the maxillary lateral incisor (LI) with 1 ml of the local anesthetic solution (Annex 21):
  1. The percentage of LI pulpal anesthesia, i.e. the % of times the tooth is successfully anesthetized: 95%, for example.
  2. The mean duration in minutes of pulpal anesthesia in the LI: 45 minutes (written as 45′), for example.
  3. The mean duration in minutes of soft tissue anesthesia (upper lip anesthesia): 190 minutes (190′), for example.
• The fourth is related to mandibular block with 1.8 ml (equivalent to one cartridge) of the solution using the direct or conventional technique (Annex 27):
  4. The mean duration in minutes of lower lip anesthesia (soft tissue anesthesia): 200 minutes (200′), for example.

These four variables were used to build the anesthetic parameter, as follows: 95%‐45′/190′‐200′. This is the parameter for the standard solution, 2% lidocaine with 1:100 000 epinephrine (10 μg/ml) (L‐100) or 1:80 000 epinephrine (12.5 μg/ml) (L‐80). It means that injection of 1 ml of this solution in the maxillary lateral incisor ensures pulpal anesthesia in 95% of individuals that lasts on average for 45 minutes. In addition, soft tissue anesthesia lasts 190 minutes in the upper lip and 200 minutes in the lower, in the latter case after mandibular block with 1.8 ml of anesthetic solution. The first two values (% of anesthesia and duration in minutes of pulpal anesthesia) assess the potency and efficacy of the local anesthetic solution and the other two (duration of upper and lower lip anesthesia) provide information that can be conveyed to patients about the approximate post‐procedure duration of the perceivable effects (Figure 5.3).

The main advantage to this approach is that different solutions can be compared in a standard format, helping to choose the anesthetic solution best suited to the circumstances and to predict the expected results.

Concentration and Volume

Medical practice often calls for anesthetizing large areas of (readily anesthetized) soft tissue, which in turn requires large volumes of anesthetic solution (20–30 ml for caudal or epidural block and up to 60 ml for intercostal or brachial plexus block). More diluted solutions are used under such conditions, with a lower concentration of anesthetic (Moore et al. 1972, 1977) and a standard epinephrine concentration of 1:200 000 (5 μg/ml) (Bonica 1959; Moore et al. 1972).

In dentistry, by contrast, the area involved is small and the target tissue is the dental pulp, which is very difficult to anesthetize. As a result, small volumes of more highly concentrated anesthetic solutions and vasoconstrictors are used (note: doses of over 5–7 ml per session, equivalent to three to four 1.8 ml cartridges, are rare) (Table 5.6). In dentistry, the standard epinephrine concentration is 1:100 000 (10 μg/ml), double the standard value applied in other areas of medical practice.

Concentration and Anesthetic Potency

Anesthetic potency has long been known to rise with concentration in animals (Gasser and Erlanger 1929; Campbell and Adriani 1958). In clinical dental studies 5% lidocaine was observed to yield better results than the 2% solution (Eldridge and Rood 1977; Rood and Sowray 1980; Lambrianidis et al. 1980). Clinical trials using the Björn EPT also proved that more highly concentrated solutions anesthetized dental pulp more effectively (Table 5.8).