Influential factors in dosage form design

Influential factors in dosage form design

Each drug substance has intrinsic chemical and physical characteristics that must be considered before the development of its pharmaceutical formulation. Among these characteristics are the particle size, surface area, the drug’s solubility, pH, partition coefficient, dissolution rate, physical form, and stability. All these factors are discussed below, except the particle size and dissolution rate, which will be discussed in the next chapter.

Molecular size and volume

Molecular size and volume have important implications for drug absorp-tion. Tight junctions can block the passage of even relatively small molecules, whereas gap junctions are looser. Molecules up to 1,200 Da can pass freely between cells; however, larger molecules cannot pass through gap junctions. Drug diffusion in simple liquid is expressed by Stokes–Einstein equation:

D = RT/6πηr

where:

D is the diffusion of drugs

R is the gas constant = 8.313 JK⁻¹mol⁻¹

T is the temperature (Kelvin)

η is the solvent viscosity

r is the solvated radius of diffusing solute

Since volume (V) = (4/3) πr3, the above equation suggests that drug diffu-sivity is inversely proportional to the molecular volume. Molecular volume is dependent on molecular weight, conformation, and heteroatom content. Molecules with a compact conformation will have a lower molecular vol-ume and thus a higher diffusivity. As shown in Figure 3.1, the diffusion and permeability of the endothelial monolayer to molecules decreased with increasing molecular weight.

A drug must diffuse through a variety of biological membranes after administration into the body. In addition, drugs in many controlled-release

Figure 3.1 Diffusion (a) and permeability (b) of compounds with different molecular weight across an endothelial monolayer at 37°C.

systems must diffuse through a rate-controlling membrane or matrix. The ability of a drug to diffuse through membranes is a function of its molecu-lar size and volume. For drugs with a molecular weight greater than 500, diffusion in many polymeric matrices is very small. Lipinski devised the so-called Rule of 5, which refers to drug-like properties of molecules. It states that poor oral absorption is more likely when the drug molecule has:

·           More than five hydrogen-bond donors (–OH groups or –NH groups).

·           A molecular weight greater than 800.

·           A log P > 5.

·           More than 10H-bond acceptors.

However, this rule is not applicable to the compounds that are substrates for transporters.

Drug solubility and pH

Pharmacological activity is dependent on solubilization of a drug sub-stance in physiological fluids. Therefore, a drug substance must pos-sess some aqueous solubility for systemic absorption and therapeutic response. Enhanced aqueous solubility may be achieved by forming salts or esters, by chemical complexation, by reducing the drug’s particle size (i.e., micronization), or by creating an amorphous solid. One of the most important factors in the formulation process is pH, as it affects solubility and stability of weakly acidic or basic compounds. Changes in pH can lead to ionization or salt formation. Adjustment in pH is often used to increase the solubility of ionizable drugs, because the ionized molecular species have higher water solubility than their neutral species. According to Equations 3.1 and 3.2, the total solubility, S_T, is the function of intrin-sic solubility, S₀, and the difference between the molecule’s pK _a and the solution pH. The intrinsic solubility is the solubility of the neutral spe-cies. Weak acids can be solubilized at pHs below their acidic pK_a, whereas weak bases can be solubilized at pHs above their basic pK_a. For every pH unit away from the pK_a, the weak acid–base solubility increases 10-fold. Thus, solubility can be achieved as long as the formulation pH is at least 3 units away from the pK_a. Adjusting solution pH is the simplest and most common method to increase water solubility in injectable products.

For a weak acid S_T = S₀(1 + 10^{pH−p K}a ) (3.1)

For a weak base S_T = S₀(1 + 10^{p K}a ^−pH) (3.2)

Unlike a weak acid or base, the solubility of a strong acid or base is less affected by pH. The drugs without ionizable groups are often solubilized by the combination of an aqueous solution and water-soluble organic solvent/ surfactant. Frequently, a solute is more soluble in a mixture of solvents than in one solvent alone. This phenomenon is known as cosolvency, and the solvents that in combination increase the solubility of the solute are called cosolvents. The addition of a cosolvent can increase the solubility of hydro-phobic molecules by reducing the dielectric constant, which is a measure of the influence by a medium on the energy needed to separate two oppositely charged bodies. Some of the cosolvents commonly being used in pharmaceu-tical formulations include ethyl alcohol, glycerin, sorbitol, propylene glycol, and polyethylene glycols (PEGs). Polyethylene glycol 300 or 400, propyl-ene glycol, glycerin, dimethylacetamide (DMA), N-methyl 2-pyrrolidone (NMP), dimethyl sulfoxide (DMSO), Cremophor, and polysorbate 80 are often used for solubilization of drugs that have no ionizable groups. As shown in Figure 3.2, the solubility of phenobarbital is, for example, signifi-cantly increased in a mixture of water, alcohol, and glycerin compared with one of these solvents alone. 

Figure 3.2 Effect of cosolvents on the solubility of phenobarbital in a mixture of water, alcohol, and glycerin at 25°C. (Reproduced from Krause, G.M. and Gross, J.M., J. Am. Pharm. Assoc. Ed., 40, 137, 1951. With permission.)

However, the use of cosolvents often leads to the precipitation of the drug on dilution during the administration of the drug solution into the body, resulting in pain or tissue damage.

Excipients that solubilize a molecule via specific interactions, such as complexation with a drug molecule in a noncovalent manner, lower the chemical potential of the molecules in solution. These noncovalent solubility-enhancing interactions are the basis of the phenomenon that like dissolves like and include van der Waals forces, hydrogen bonding, dipole–dipole, ion–dipole interactions, and, in certain cases, favorable electromagnetic interactions. Solutes dissolve better in solvents of similar polarity. Therefore, to dissolve a highly polar or ionic compound, one should use a solvent that is highly polar or has a high dielectric constant. On the contrary, to dissolve a drug that is nonpolar, one should use a solvent that is relatively nonpolar or has a low dielectric constant.

Table 3.2 Water solubility of different substituent

Drug solubility can also be enhanced by altering its structure; this is one basis for the use of prodrugs. A prodrug is a drug that is therapeutically inactive when administered but becomes activated in the body by chemical or enzymatic processing. The addition of polar groups, such as carboxylic acids, ketones, and amines, can increase aqueous solubility by increasing the hydrogen bonding and the dipole–dipole interaction between the drug molecule and the water molecules. Table 3.2 lists different substituents that will have significant influence on the water solubility of drugs. Substituents can be classified as either hydrophobic or hydrophilic, depending on their polarity. The position of the substituents on the molecule can also influence its effect.

Lipophilicity and partition coefficient

Partitioning is the ability of a compound to distribute in two immiscible liquids. When a weak acid or base drug is added to two immiscible liq-uids, some drug goes to the nonpolar phase and some drug goes to the aqueous layer. Because like dissolves like, the nonpolar species migrates (partitions) to the nonpolar layer and the polar species migrate to the polar aqueous layer.

To produce a pharmacologic response, a drug molecule must first cross a bio-logic membrane, which acts as a lipophilic barrier to many drugs. Since passive diffusion is the predominant mechanism by which many drugs are transported, the lipophilic nature of the molecules is important. A drug’s partition coeffi-cient is a measure of its distribution in a lipophilic–hydrophilic phase system, and it indicates the drug’s ability to penetrate biologic multiphase systems. The octanol–water partition coefficient is commonly used in formulation develop-ment and is defined as:

P = Concentration of drug in octanol or nonpolar phase / Concentration of drug in water or polar phase

For an ionizable drug, the following equation is applicable:

P = Concentration of drug in octanol or nonpolar phase / (1 − α)(Concentration of drug in water of polar phase)

In this equation, α is equal to the degree of ionization. The concentration in aqueous phase is estimated by an analytical assay, and concentration in octanol or other organic phases is deduced by subtracting the aque-ous amount from the total amount placed in the solvents. Partition coef-ficient can be used for drug extraction from plants or biologic fluids, drug absorption from dosage forms, and recovery of antibiotics from fermenta-tion broth.

The logarithm of partition coefficient (P) is known as log P. Log P is a measure of lipophilicity and is used widely, since many pharmaceutical and biological events depend on lipophilic characteristics. Often, the log P of a compound is quoted. Table 3.3 lists the log P values of some representative compounds. For a given drug:

If log P = 0, there is equal drug distribution in both phases.

If log P > 0, the drug is lipid soluble.

If log P < 0, the drug is water soluble.

In general, the higher the log P, the higher the affinity for lipid membranes and thus the more rapidly the drug passes through the membrane via pas-sive diffusion. However, there is a parabolic relationship between log P and drug activity when percentage of drug absorption is plotted against log P values (Figure 3.3). The parabolic nature of bioactivity and log P values is due to the fact that drugs with high log P values, protein bind-ing, low solubility, and binding to extraneous sites cause them to have a

Table 3.3 Log P values of representative drugs

Drug : Log P

Acetylsalicylic acid 1.19

Amiodarone 6.7

Benzocaine 1.89

Bromocriptine 6.6

Bupivacaine 3.4

Caffeine 0.01

Chlorpromazine 5.3

Cortisone 1.47

Desipramine 4.0

Glutethimide 1.9

Haloperidol 1.53

Hydrocortisone 4.3

Indomethacin 3.1

Lidocaine 2.26

Methadone 3.9

Misoprostol 2.9

Ondansetron 3.2

Pergolide 3.8

Phenytoin 2.5

Physostigmine 2.2

Prednisone 1.46

Sulfadimethoxine 1.56

Sulfadiazine 0.12

Sulfathiazole 0.35

Tetracaine 3.56

Thiopentone 2.8

Xamoterol 0.5

Zimeldine 2.7

lower bioactivity. Decrease in activity is due to the limitation in solubility beyond a certain log P value. If a drug is too lipophilic, it will remain in the lipid membrane and not partition out again into the underlying aque-ous environment. On the other hand, very polar compounds with very high log P values are not sufficiently lipophilic to be able to pass through lipid membrane barriers.

Figure 3.3 Relationship between drug absorption and log P. Decrease in the drug absorp-tion beyond a certain log P value is probably due to its binding to plasma proteins, reduction in free drug levels, or its binding to extraneous sites.

Polymorphism

The capacity of a substance to exist in more than one solid state forms is known as polymorphism, and the different crystalline forms are called polymorphs. If the change from one polymorph to another is reversible, the process is enantiotropic. However, if the transition from a metasta-ble to a stable polymorph is unidirectional, the system is monotropic. Polymorphic forms may exhibit detectable differences in some or all of the following properties: melting point, dissolution rate, solubility, and stabil-ity. Drug substances can be amorphous (i.e., without regular molecular lattice arrangements), crystalline (which are more oriented or aligned), polymorphic, anhydrous, or solvated. An important form in the formula-tion is the crystal or amorphous form of the drug substance. Many drug substances can exist in more than one crystalline form, with different lat-tice arrangements. This property is termed polymorphism. Drugs may undergo a change from one metastable polymorphic form to a more stable polymorphic form. Various drugs are known to exist in different polymor-phic forms (e.g., cortisone and prednisolone). Polymorphic forms usually exhibit different physicochemical properties, including melting point and solubility, which can affect the dissolution rate and thus the extent of their absorption. The amorphous form of a compound is always more soluble than the corresponding crystal form. Changes in crystal characteristics can influence bioavailability and stability and thus can have important impli-cations for dosage form design. For example, insulin exhibits a differing degree of activity, depending on its state. The amorphous form of insulin is rapidly absorbed and has short duration of action, whereas the large crys-talline product is more slowly absorbed and has a longer duration of action.

Stability

The chemical and physical stability of a drug substance alone and when combined with formulation components is critical to preparing a successful pharmaceutical product. Drugs containing one of the following functional groups are liable to undergo hydrolytic degradation: ester, amide, lactose, lactam, imide, or carbamate. Drugs that contain ester linkages include acetylsalicylic acid, physostigmine, methyldopa, tetracaine, and procaine. For example, the hydrolysis of acetylsalicylic acid (commercially known as aspirin) is represented in Figure 3.4. Aspirin is hydrolyzed to salicylic acid and acetic acid.

Nitrazepam, chlordiazepoxide, penicillins, and cephalosporins are also susceptible to hydrolysis. Several methods are available to stabilize drug solutions that are susceptible to hydrolysis. For example, protection against moisture in formulation, processing, and packaging may prevent decompo-sition. Suspending drugs in nonaqueous solvents such as alcohol, glycerin, or propylene glycol may also reduce hydrolysis.

After hydrolysis, oxidation is the next most common pathway for drug degradation. Drugs that undergo oxidative degradation include morphine, dopamine, adrenaline, steroids, antibiotics, and vitamins. Oxidation can be minimized by storage under anaerobic conditions. Since it is very dif-ficult to remove all of the oxygen from a container, antioxidants are often added to formulations to prevent oxidation.

Excipients used to prepare a solid dosage can also affect the drug’s stability, possibly by increasing the moisture content of the preparation. Excipients, such as starch and povidone, have very high water contents.

Figure 3.4 Hydrolysis of aspirin. Acetylsalicylic acid (aspirin) is hydrolyzed to salicylic acid and acetic acid.

Povidone contains about 28% equilibrium moisture at 75% relative humid-ity. However, the effect of this high moisture content on the stability of a drug will depend on how strongly it is bound and whether the moisture can come in contact with the drug. Effects of tablet excipients on drug decom-positions are widely reported in the literature. For an example, magnesium trisilicate is known to cause increased hydrolysis of aspirin in the tablet because of its high moisture content.

pK_a/Dissociation constants

Many drug substances are either weak acids or weak bases and thus undergo a phenomenon known as dissociation when dissolved in liquid medium. If this dissociation involves a separation of charges, then there is a change in the electrical charge distribution on the species and a separation into two or more charged particles, or ionization. The extent of ionization of a drug has an important effect on the formulation and pharmacokinetic profiles of the drug. The extent of dissociation or ionization is dependent on the pH of the medium containing the drug. Table 3.4 lists the normal pHs of some organs and body fluids, which are used in the prediction of the percentage ionization of drugs in vivo. In a formulation, often, the vehicle is adjusted to a certain pH to obtain a certain level of ionization of the drug for solubility and stability. The extent of ionization of a drug has a strong effect on its extent of absorption, distribution, and elimination.

Acids tend to donate protons to a system at pH greater than 7, and bases tend to accept protons when added to acidic system (i.e., at pH < 7). Many drugs are weak acids or bases and therefore exist in both unionized and ionized forms; the ratio of these two forms vary with pH. 

Table 3.4 Nominal pH values of some body fluids and sites

The fraction of a drug that is ionized in solution is given by the dissociation constant (K_a) of the drug. Such dissociation constants are conveniently expressed in terms of pK_a values for both acidic and basic drugs. For a weak acidic drug, HA (e.g., aspirin and phenylbutazone), the equilibrium is presented by:

HA ↔ H⁺+A⁻

The symbol (↔) indicates that equilibrium exists between the free acid and its conjugate base. According to the Bronsted–Lowry theory of acids and bases, an acid is a substance that will donate a proton and a base is a sub-stance that will accept a proton. Based on this theory, the conjugate base A⁻ may accept a proton and revert to the free acid. Therefore, the dissocia-tion constant for this reaction is:

K₁[HA] ↔ K₂[H⁺][A⁻]

Taking logarithms of both sides:

log K_a = log[H⁺ ] + log[A⁻ ] − log[HA]

The signs in this equation may be reversed to give the following equation:

-log K_a = − log[H⁺ ] − log[A⁻ ] + log [HA]

This is a general equation applicable for any weakly acidic drugs.

Similarly, for a weak basic drug (e.g., chlorpromazine) →B + H⁺ = BH⁺

∴ pK_a = pH + log[BH ⁺ ] / [ B] for a weakly basic drug.

These equations are known as Henderson–Hasselbalch equations. This equation describes the derivation of pH as a measure of acidity (using pK_a) in biologic and chemical systems. The equation is also useful for estimat-ing the pH of a buffer solution and finding the equilibrium pH in acid– base reactions. Bracketed quantities such as [Base] and [Acid] denote the molar concentration of the quantity enclosed. Based on these equations, it is apparent that the pK_a is equal to the pH when the concentration of the ionized and nonionized species is equal (i.e., log1 = 0). It is therefore impor-tant to realize that a compound is only 50% ionized when the pK_a is equal to the pH. Ionization constants are usually expressed in terms of pK_a values for both acidic and basic drugs. The strength of acid is inversely related to the magnitude of its pK_a. The lower is the pK_a, the stronger is the acid. Conversely, the strength of a base is directly related to the magnitude of its pK_a. The pK _a of a strong base is high. The pK_a values of a series of drugs are listed in Table 3.5. Acidic drugs are completely unionized at pHs up to 2 units below their pK_a and are completely ionized at pHs greater than 2 units above their pK_a. Conversely, basic drugs are completely ionized at pH up to 2 units below their pK_a and are completely unionized when the pH is greater than 2 units above their pK_a. Both types of drugs are exactly 50% ionized at their pK _a values. Some drugs can donate or accept more than one proton, and so, they may have several pK_a values.

For either weak acid or base, the ionized species, BH⁺ and A⁻, have very low solubility and are virtually unable to permeate membrane, except where specific transport mechanisms exist. The lipid solubility of the uncharged drugs will depend on the physicochemical properties of the drug.

Proteins and peptides contain both acidic (−COOH) and basic (−NH₂) groups. The pK_a values of ionizable groups in proteins and peptides can be significantly different from those of the corresponding groups when they are isolated in solution. 

Table 3.5 pK_a values of typical acidic and basic drugs

Therefore, these compounds are often referred to as amphoteric in nature. The pH of a solution determines the net charge on the molecule and ultimately the solubility. Since water is a polar solvent and ionic species are more water soluble than the nonionic ones, a conjugate acid (BH⁺) and a conjugate base (A−) are generally more water soluble than the corresponding free base (B) or free acid (HA).

Example 3.1

The pK_a value of aspirin, which is a weak acid, is about 3.5. What are the ratios of unionized and ionized forms of this drug in the stomach (pH 2) and in the plasma (pH 7.4)? Why does aspirin often cause gas-tric bleeding?

Answer:

According to the Henderson–Hasselbalch equation,

where C_u is the concentration of unionized drug and C_i is the concen-tration of ionized drug.

∴ C_u/ Ci = antilog1.5 = 31.62:1

In the plasma,

log C_u/ C_i = pK_a − pH = 3.5 − 7 .4 = −3 .9

∴ C_u/C_i  = antilog( − 3.9) = 1.259 ×10⁻⁴ : 1

Therefore, most of the administered aspirin remains unionized in the stomach, and thus, it is rapidly taken up by the stomach, leading to gastric bleeding.

Degree of ionization and pH-partition theory

For a drug to cross a membrane barrier, it must normally be lipid solu-ble to get into the biological membranes. The ionized forms of acidic and basic drugs have low lipid:water partition coefficients compared with the coefficients of the corresponding unionized molecules. Lipid membranes are preferentially permeable to the latter species. Thus, an increase in the fraction of a drug that is unionized will increase the rate of drug trans-port across the lipid membrane. This phenomenon can be explained by the pH-partition theory, which states that drugs are absorbed from biological membranes by passive diffusion, depending on the fraction of the union-ized form of the drug at the pH of that biological membrane. Based on the Henderson–Hasselbalch equation, the degree of ionization of a drug will depend on both its pK_a value and the solution’s pH.

The gastrointestinal (GI) tract acts as a lipophilic barrier, and thus, ionized drugs, which will be more hydrophilic, will have minimal membrane trans-port compared with the unionized form of the drug. The solution pH will affect the overall partition coefficient of an ionizable substance. The pI of the molecule is the pH at which there is a 50:50 mixture of conjugate acid–base forms. The conjugate acid form will predominate at a pH lower than the pK_a, and the conjugate base form will be present at a pH higher than the pK_a.

Limitations of pH-partition theory

Although the pH-partition theory is useful, it often does not hold true. For example, most weak acids are well absorbed from the small intes-tine, which is contrary to the prediction of the pH-partition hypothesis. Similarly, quaternary ammonium compounds are ionized at all pHs but are readily absorbed from the GI tract. These discrepancies arise because pH-partition theory does not take into account the following:

·           The small intestine has a large epithelial surface area for drug absorp-tion to take place. This large epithelial area results from mucosa, villi, and microvilli (Figure 3.5). The large mucosal surface area compen-sates for ionization effects.

·           Drugs have a relatively long residence time in the small intestine, which also compensates for ionization effects.

Figure 3.5 Drug absorption across small intestine. The small intestine has a large epi-thelial surface area due to mucosa, villi, and microvilli. This large surface area compensates the effect of drug ionization on its absorption across the small intestine and invalidates pH-partition theory of drug absorption.

·           Charged drugs, such as quaternary ammonium compounds and tetra-cyclines, may interact with oppositely charged organic ions, resulting in a neutral species, which is absorbable.

·           Some drugs are absorbed via active pathways.

·           Many more.