PHYSTCOCHEMICAL PROPERTIES AFFECTING THE PERCUTANEOUS ABSORPTION OF NIFEDIPINE

The effect of nifedipine saturation solubility in several cosolvent systems on nifedipine permeation through hairless mouse skin is evaluated. The effects of patch components is measured by (1) identifying those factors which significantly affect the permeation of nifedipine and (2) selecting settings for these factors which optimize flux and lag times. Of particular interest is the application of solubility theory toward the estimation of theoretical partition coefficients which were, it turn, useful in predicting the effect of donor composition on nifedipine permeation. A stoichiometric approach was taken to examine the influence of permeation enhancers on skin permeability of this calcium channel blocker. Inherent in this approach is that a change in one component requires collateral change in the next; a deficiency best handled by an experimental design of the mixture type. The ultimate objective was to apply regression techniques to interpret, on a molar basis, the data obtained from in vitro permeation experiments. The model obtained was employed to: (I) identify both the magnitude and significance of synergism between formulation components and (2) optimize the desired response. Data from these inquiries have contributed toward the rational selection of components in a viable transdermal dosage form.


ACKNOWLEDGEMENTS
In preparing this work, I find myself indebted first and foremost to my major professor. I thank him for his many words and deeds on my behalf, particularly the brainstorming sessions that provided the wellspring of thoughts and ideas expressed in this thesis. The generosity of Lohmann Therapie Systeme, our German benefactors, is gratefully acknowledged. While at LTS I was the recipient of the boundless hospitality and insight of Dr. Walter Muller to whom I am especially grateful.
I acknowledge the patience and willingness of my committee and members of our department who have dealt with the unusual demands of this project, most notably the periods of sleep deprivation induced by the intense sampling schemes. Kudos go to Dr. Zia for first suggesting the use of dimethylisosorbide which helped permit the achievement of useful permeation rates. Charlene Yang is the Academic Computer Center's greatest natural resource. Pardeep Sethi imparted expertise on our initial skin permeation experiments and George Sienkevitch was helpful in the search for an appropriate experimental design to fulfill the special requirements of our approach.
Their comments and criticisms were well received and much appreciated.
Finally, for those whose predilection has placed them on the path of graduate study, I close with some words of inspiration attributed to St. form. Since the scope of the project was is unusually broad , we divide the main body of the dissertation into a general introduction followed by three chapters that address the issues of solubility, penetration enhancement and optimization.
The dissertation is best envisioned as proceeding chronologically through three distinct phases. Section I serves to introduce the interrelationship of several physical and chemical properties, particularly solubility phenomenon, on the permeation of a    pharmaceutical products have demonstrated the merits of delivering therapeutic agents through the skin. 2 Optimally designed transdermal dosage forms release drug in vivo according to pharmacokinetically rational rates so that concentrations are maintained within therapeutically desirable ranges. Drugs poorly available by the oral route may achieve therapeutic concentrations since drugs absorbed percutaneously are not subject to hepatic first pass metabolism. The transdermal route of administration may increase compliance by minimizing the inconvenience of remedication . This is a decided advantage in conditions e.g. hypertension where the effect of the disease is often sublime. The net result is a sustained, reliable, extended duration of drug action similar to an intravenous infusion without the many disincentives associated with the intravenous route of administration.
As the concepts underlying drug delivery system design becomes clearer 3 • 4 • 5 " 6 the potential of skin as a site of administration for systemically active drugs is being realized . Unfortunately , the transdermal route of adminjstration cannot be employed ( for a large number of drugs and the problems that limit drug suitability have been outlined and discussed. 7 " 8 Briefly, the s]<jn is an efficient barrier to the ingress of foreign materials so that few drugs penetrate the s]<jn at rates sufficient to permit clinically useful transdermal application. Transdermal delivery of drugs for systemic effects is currently limited to nonirritating , lipophilic drugs of small molecular weight (less than 1000 daltons) and high potency (less than 21 mg per day) that enter the s]<jn by passive diffusion. Of the several layers of epidermis, the stratum comeum is generally recognized as the primary barrier to transdermal diffusion. The contribution of the stratum comeum to overall diffusional resistance tends to be larger for molecules of low molecular weight and lipophilicity. 9 Formulations and methodologies which permit more than a few milligrams of drug to be delivered across this barrier would expand the range of candidate drugs that might be successfully marketed as a TDS. In the case of hydrophobic drugs it remains unclear how to determine a priori the optimal physicochemical properties required in a transdermal delivery system to best overcome the barrier function of the s]<jn. Thus, research efforts targeted toward maximizing penetration have unquestionably high clinical and financial implications.
Choice of Penneant -With the exception of a recent publication by Diez et al' 0 ,no comparative percutaneous absorption studies have been done to evaluate the dihydropyridine calcium channel antagonists as suitable TDS candidates.
Nifedipine,(dimethyl l ,4-dihydro-2 ,6-dimethyl -4,(nitrophenyl)-3 ,5-pyridine dicarboxylate) is an ideal model permeant for this 2 research. Nifedipine is an active calcium-channel antagonist that exerts its pharmacological action by blocking postexcitation of ca++ ions into cardiac and vascular smooth muscle. Since its discovery in 1968, nifedipine has become accepted as a first line treatment of angina and hypertension. 11 12 Nifedipine is poorly water soluble and its bioavailability is low when administered orally in the solid crystalline form. Previous pharmacokinetic studies have shown extraordinary interindividual variability of the plasma levels of the drug following oral administration.'3 The variability in peak plasma levels (as much as 10 fold) is presumably due to the wide differences in oral bioavailability and first pass metabolism. The development of an alternative to the oral route that would bypass these significant, highly variable effects would offer significant advantages. Also, since transdermal administration minimizes pulse entry into the systemic circulation, undesirable side effects associated with unnecessarily high plasma levels of drug may be avoided.
The average steady state plasma concentration of nifedipine, following an average oral daily dose of 30mg per day , is 47 (± 20) ng/ml. 14 Clinical studies have shown that the hypotensive effect as well as the untoward side effects are correlated with the plasma nifedipine concentration." When the plasma concentration of nifedipine increases rapidly, there is a marked increase in heart rate and little effect on blood pressure. Conversely, this undesirable situation is reversed when administered by slow intravenous infusion or sustained release tablet. 16 Transient, high plasma levels observed following oral administration of conventional capsules may vary by tenfold and increase the likelihood of undesirable high hemodynamic 3 effects. 17 An important feature of transdermal delivery systems is that they permit sustained, constant drug levels over a day or more. The transdermal route is also appealing since it can provide a zero-order rate of drug delivery, reduce problems associated with the aforementioned side effects and thereby improve patient compliance. The success of the Estraderm TM patch is evidence for the real need for the controlled delivery of drugs that undergo significant first pass effect. Transdermal estradiol relieves postmenopausal symptoms with one-tenth the amount of an oral dose of estrogen because the hormone enters the bloodstream directly, thus avoiding first-pass liver metabolism." Excessive estrogen levels (and side effects) are reduced when the drug is administered by a TDS. Nitroglycerin, the mainstay of anginal therapy, has enjoyed wide acceptance in patch form since once-a-day application contributes significantly towards patient compliance and avoids the large fluctuations in plasma levels following the oral administration. Finally, an important argument in favor of nifedipine is that the constant delivery of nifedipine is not thought to lead to the estabEshment of tolerance as seen with nitroglycerin. 19 Following oral administration as a soft elastic gelatin capsule, nifedipine is completely absorbed with an absorption half life of 4 hours . Following intravenous administration, the drug is rapidly cleared from the plasma. When administered orally, nifedipine undergoes significant, variable first pass metabolism resulting in cmax values between 40-200 ng/ml and an absolute bioavailability of 45% to 68%. 20 Binding of nifedipine to plasma protein is concentration dependent and ranges from 92-98%. The drug appears to distribute in a volume slightly larger than total body 4 water. The elimination half life of 2 to 3 hours necessitates administration at intervals of every four to six hours.
Convenient once a day dosage regimens are highly desirable in general, and especially for the treatment of asymptomatic diseases such as hypertension.
Shortcomings associated with its rapid elimination following oral administration prompted the development of innovative drug delivery systems capable of zero-order drug delivery that prolong pharmacologic activity over a 24 hour period. 21  Nifedipine, like estradiol, has a relatively high melting point. All three drugs are classified as "extremely lipophilic", as demon strated by their n-octanol:water partition coefficient. Of the drugs li sted, the steroids bear the best overall similarity and strategies used to enhance their penetration theoretically should apply equally well to nifedipine.
Nifedipine is compatible with many pharmaceutically useful solvents, thermostable, and nonhygroscopic. Owing to the extreme low basicity of the dihydropyridine nitrogen it is not possible to obtain stable salts with acids. There is no influence of pH (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and ionic strength on stability. It is extremely sensitive to light below 450 nm. The major metabolite, a nitropyridine, formed by enzymatic oxidation is identical to that formed by photodegradation under visible light. High Pressure Liquid Chromatography (HPLC) provided a straightforward, validated, stability-indicating analytical method of quantitatively measuring nifedipine and its primary breakdown products in vitro 40 and in vivo . 41 42 In summary, having considered the physical characteristics of the drug and proposed TDS, it appears that the physical, chemical and pharmacokinetic attributes of nifedipine conform with those required of a drug candidate for transdermal delivery system development.
Solubility theory -The solubi lity of a drug in one or more components of a pharmaceutical dosage form is valuable information which can be used to characterize its behavior. This is especially true of topical dosage forms where the solubility of drug can be related to dissolution rate, thermodynamic activity, vehicle release rate, and apparent permeation rates . Transdermal delivery is a diffusion process driven by the establishment of a thermodynamic activity gradient of diffusant within the skin.
When a drug is applied topically, it diffuses passively out of its carrier vehicle into the surface tissue of the skin. The movement continues through the stratum corneum 8 and into the viable epidermis and dermis with the gradient terminating at the upper reaches of the microcirculation of the skin in the dermal layer. The fundamental equation describing diffusion in membranes such as skin is Fick's First Law. For the steady state case, the amount M of material flowing through a unit cross section, S, of a barrier in unit time, t, is known as the flux , J, The flux in tum is proportional to the concentration gradient, dC/dx: (2) in which D is the diffusion coefficient of a penetrant, C is its concentration, and x is the distance of movement perpendicular to the barrier. When donor and receptor compartments are separated by a semipermeable membrane of cross-sectional area S and thickness h, and the concentrations of the diffusant in the membrane in the donor and receptor sides are C, and C 2 , respectively, then equation (I) may be rewritten The values of C 1 and C 2 within the membrane are difficult to determine (3) experimentally but can be approximated by the partition coefficient, K, multiplied by the concentration c. on the donor side or C, on the receiver side of the membrane dM C[C, (4) for which, under sink conditions, C, "" 0. Thus, for a fixed surface area, the diffusion of permeant from donor to receptor is proportional to a gradient in thermodynamic activity. If the vehicle in no way changes the properties of the membrane (i.e., D and K remain constant) nor does the vehicle codiffuse with the drug then P=DK/h is a constant and equation (4) implies that an increase in the thermodynamic activity of a species in solution should be accompanied by an increase in permeability. While the activity of the permeant will vary according to the composition of solvent(s) used in the donor medium , it may be held constant for the duration of an experiment for a given donor by using a saturated solution in the presence of excess solid drug .
Many have recognized that intrinsic solvent effects significantly affect drug transport across the stratum corneum and underlying epidermal membranes 43 and that variation in vehicle composition often has a marked effect on the release of drug from the dosage form. 44 However, for those cases in which P=DK/h is a constant, enhancement of tran sdermal delivery by maximizing thermodynamic potential has been achieved with volatile and nonvolatile mixtures to enhance "the escaping tendency" of drug from a formulation by creating supersaturated conditions. 45  Consequently, our efforts have been directed towards using the solubility parameter to predict percutaneous flux of nifedipine.
We employ the Hildebrand approach 50 to obtain the logarithm of the ideal mole V2<l>~{o1 -li2)2

2.3RT
13 (5) (6) where X 2 is the mole fraction solubility of nifedipine at temperature T, ,.H, is the heat of fusion of the solute at its melting point T"' , and 'Yi is the activity coefficient of the drug in the vehjcle. The first part of the right-hand side of equation (5) gives the ideal solubility, whereas the second part, log 1'2> gives the contribution of the solutesolvent interactions to the deviations of the measured solubility, X,, from the ideal solubility. Regular solution theory describes the activity coefficient of the drug in the vehicle, given by equation (6), where 0, is the solubility parameter of N, o 1 is the solubility parameter of the vehicle, V 2 is the molar volume of N, R is the gas constant and Tis absolute temperature. The volume fraction of the solvent, 4' 1 , is calculated from 51 (7) The main limitation has been that the solubility parameter concept is strictly applicable only to nonpolar systems where dispersion forces predominate. Other forces exerted by intermolecular interactions in liquids with similar solubility parameter may result in very different solubility profiles. This is due, in part, to differences in the three intermolecular forces commonly referred to as the London, Keesom and Hydrogen bonding attractions. Hanson and Beerblower 52 partitioned the cohesive energies into three terms: od is the dispersion forces observed in nonpolar, hydrocarbon mixtures, 0 0 reflects dipole-dipole interactions or 'orientation' forces between molecules e.g. , acetone, and o. describes the acid-base character associated with all varieties of strong donor-acceptor interaction between solute and solvent.
14 This third term is not restricted to hydrogen bonding. The total cohesive energy density, AE/V, for a species may be partitioned into contributions from dispersion forces , dipolar interactions, and hydrogen bonding: AEv is the energy of vaporization of a liquid , AH" its enthalpy of vaporization, R the gas constant, T is the absolute temperature, and V is the liquid molar volume. The quantity o is the total solubility parameter and o 2 is the cohesive energy density for a solvent or solute allowing equation (8) to be rewritten as (10) The dispersion parameter, o,, is obtained from data for the compound's homomorph, defined as a saturated hydrocarbon having essentially the same chemical structure, size, and shape as those of the polar compound. The polar parameter, o., was calculated using a modified equation from Bottcher: The hydrogen bond parameter for a hydroxyl compound is obtained from (11) (2) the method requires only a knowledge of the structural formula of the compound.
The distribution of a drug between two phases, represented by the term K introduced in equation (4), is given in equation (13) Y2 log K = logy skin (13) Since each activity coefficient in equation (13) can be calculated from equation (6) , a theoretical partition coefficient can be calculated by substituting the values for the calculated activity coefficients into equation (13). Use of the difference between the solubility parameter of drug and membrane to explain differences in biological activity of drugs was first introduced by Mullins." Sloan used the expanded form of equation (13) as a means of calculating theoretical solubilities of theophylline in hairless mouse skin so that theoretical vehicle-membrane partition coefficients between skin and various polar and non polar vehicles could be estimated. 59 In a separate study, salicylic acid was used as a model compound to study the relationship between the solubility parameter of drug and membrane on transport through lipoidal membranes. 60 In both cases, a good fit between the theoretical partition coefficients and the experimentally determined permeability coefficients were obtained. The influence of solute solubility on flux in vivo has also been noted for estradiol. 61 We propose to examine the properties that seem to limit drug suitability so that the rational formulation of a new generation of transdermal systems can occur.
Penetration enhancers -Of the various layers of the skin, the stratum comeum is believed to pose the greatest diffusional resistance. Since diffusion through the stratum corneum is usually the rate limiting step, enhancement of permeability is usually directed toward reversibly altering the properties of the stratum corneum.
The term "penetration enhancer" is applied to agents which reduce the diffusional resistance of the stratum corneum, by reversibly damaging it, or by altering its physicochemical nature. The previous discussion considers only the simple situation in which diffusion occurs in a single homogenous medium. However, skin is a heterogeneous multilayer tissue. The concentration gradient developed over several strata is analogous to an electrical circuit, either in series or in parallel, where each strata contributes a unique diffusional resistance. While the total resistance of the composite is essentially a function of the high resistance of the stratum corneum, it is incorrect to attribute the properties of one single layer to the individual properties of the composite layers. Modeling the skin in this superficial manner may give rise to false assumptions on how these properties may be altered. That the permeation process is more complex than the simple case of diffusion through the stratum comeum suggests and that the subdivisions of the skin should be considered individually.
The partition coefficient is crucially important in promoting a high initial concentration of the agent within the upper strata of the epidermis. Nonpolar molecules are expected to diffuse passively though the lipid domains of the stratum comeum intercellular space. If the intercellular transepidermal pathway transport mechanisms control drug passage through skin , one would expect the partioning behavior of the drug to influence its permeation and a correlation should exist between partition and permeability that, in tum, relates structure to permeant flux. In practice, partition coefficients based on various reference systems are often unreliable predictors of relative permeabilities but at least constitute a frame of reference from which to envision drug movement through the skin . Given the high octanol-water partition coefficient of nifedipine (10,000: 1) and that the solubility parameters of porcine skin and nifedipine are nearly identical leads to the supposition that: (I) nifedipine should have high affinity for and readily penetrate stratum corneum lipids and (2) significant resistance to nifedipine diffusion should reside in the deeper dermal layers. Scheuplein had calculated that a tissue-water partition coefficient of > 400 was required before a 200 micron layer of dermis had a diffusional resistance comparable to that of stratum corneum 10 microns thick. 62 Indeed, our experiments on stripped skin have confirmed that a significant barrier to diffusion still exists even when the stratum corneum has been removed . Therefore, the ideal patch design would encompass the following functions: (1) initial high activity of drug in the patch creates a severe gradient forcing the drug from the patch into the epidermis; (2) release of enhancer(s) to alter the diffusion coefficient of the drug; and (3) release of cosolvent at a prescribed rate so as to modify nifedipine solubility in the lower epidermal and dermal layers.

19
Chemical enhancers can be grouped into two general categories: amphoteric molecules (such as Azone and oleic acid) and cosolvent molecules (such as dimethylsulfoxide, propylene glycol, and ethanol). 63 Amphoterics are thought to enhance permeation by increasing the diffusivity of the permeant through the stratum comeum, while cosolvents are used to promote the partitioning of drug in the skin layers. It is often difficult to distinguish from the array of possible mechanisms by which an ingredient may influence permeant diffusion . For example, surfactants can alter the kinetics of drug permeation through the skin by a direct effect on the skin barrier, through complexation or solubilization of the drug, by improving wetting of the membrane or through alteration of the permeability of skin to water. 64 65 66 Generally, a penetration enhancer is selected based on the physicochemical properties of the permeant. Since lipophilic drugs are believed to penetrate the stratum comeum by passive diffusion though the intercellular lipids, materials (e.g. , oleic acid or Azone) that are known to increase the diffusivity of permeants in the 'lipoidal' pathway should be better suited than enhancers that affect the proposed 'polar' pathway. Alternatively, the polar pathway, proposed to account for the anomalous permeation of small or ionizable molecules, would seem unsuited for nifedipine, which is a molecule of moderate molecular weight, insignificant pKa, and poor water solubility. A preliminary saturation solubility profile compiled from the literature shows nifedipine to have affinity for solvents of moderate dipole moment with minimal hydrogen bonding interactions. Nifedipine appears to lie midway in the lipophilic-hydrophilic continuum, prohibiting generalizations regarding passage via a lipoidal or polar route and, of course, the subsequent choice of enhancer. For permeants with poor solubility profiles, the cosolvent-type permeation enhancers have been successfully employed either alone or in combination. Generally, these enhancers exert their influence rapidly, but this influence diminishes relatively soon after the delivery system has been removed from the skjn. Because they penetrate the skjn, there may be questions regarding toxicity and irritation during chronic application.
Utiljzation of enhancers to optimize transdermal delivery introduces potential adverse interactions between drug, enhancer, system components, and skjn. 67 Unfortunately, it remains unclear how to best choose ideal enhancer combinations.
An interesting approach to enhancer selection is based on the use of quantitative structure-activity relationships to predict the pharmacological properties of organic compounds. This is accomplished by the assignment of organic and inorganic values for a given compound depending on structural components. 68 Hori obtained conceptional diagrams on which classical enhancers and newer enhancers were located in quite different regions. What emerged was a clear relationship between pharmacological actions and the physicochemical properties of organic compounds.
These studies provided an impetus for our search for appropriate enhancers, based on physicochemical properties, that interact in a positive synergistic manner to enhance nifedipine delivery. A review of material s considered in the present work now follows. Ethanol is presumed to exert its influence by swelling and softening the stratum corneum, thereby reducing its effectiveness as a permeation barrier.

Alcohols
A reservoir-type therapeutic transdermal system using pure ethanol or ethyl acetate to provide constant release of estradiol are well tolerated. n The effects of ethanol on the adhesive strength of a variety of control membrane laminates have been examined. 73 Alza controls a patent on ethanol as an absorption enhancer and it is incorporated in their Estraderm and Duragesic products. Estradiol alone cannot permeate the skin to produce adequate plasma levels, hence the Estraderm patch uses ethanol to promote the partitioning of the drug into the stratum corneum and so reduce this barrier's resistance to drug transport. The transport rate from a saturated ethanol/water donor suspension is approximately 20 times that found for aqueous suspensions. In the Duragesic patch, alcohol (O. lml/!Ocm2) is used to increase the permeability of the skin to fentanyl and to enhance the rate of drug flow through the rate-limiting membrane. Only a small amount of alcohol ( < 0.1 ml per 10 cm 2 ) is actually released from the system during a 72-hour application period. A linear dependence of ethanol on drug penetration has been observed in nitroglycerin 74 and for the ethanol-ethyl-acetate cosolvent in levonorgestrel. 75 Twist and Zatz have shown that the relative flux from a series of alcohols is 22 correlated with the amount of alcohol imbibed by polydimethylsiloxane membranes. 76 Good et al 77  Propylene Glycol (PG) -PG has been shown to significantly increase the solubility of drugs in the stratum comeum and therefore enhance the permeability of the skin. 79 Cited as a penetration enhancer, PG also alters the release rate of steroids by its effect on permeant thermodynamic activity. This may be partially explained by the ability of PG to permeate the skin in substantial amounts. 80 • 81 PG may both increase and decrease permeation of substances and appears to aid penetration best when combined with surface active agents. 82 Nomura et al. 83 observed that PG was readily absorbed through rat skin and that PG percutaneous absorption profiles were similar to those of indomethacin, suggesting that PG and indomethacin penetrate together through the skin. Sheth et al 84  circulating, non-esterified fatty acids. 86 Long-chain fatty acids have been shown to li.:: effective penetration enhancers for several lipophilic molecules through hairless mouse skin in the presence of cosolvents. 87 Work performed in a multicenter collaboration established that the cis-isomer of oleic acid disrupts the "lipid fluidity" of the stratum corneum; the trans isomer did not demonstrate this effect. 88 This increased chain mobility is the hypothetical 'fluidization' of lipid bilayers thought to be responsible for the penetration enhancement of agents that act on the lipoidal pathway such as oleic acid. 89 In light of the considerable attention with regard to their effect on membrane permeability, the effect of long chain fatty acids and alcohols on nifedipine permeation was investigated.

Objectives of the Present Study
I. Screening studies targeted toward the identification of formulation components that enable the model permeant, nifedipine, to be delivered in measurable quantities across a semipermeable membrane. Percutaneous penetration is considered primarily a passive diffusion process that is driven by the difference between the thermodynamic activities of drug in the vehicle and the slcin . 11 If the permeation is Fickian it may be described by equation (1) and the driving force is the concentration differential between donor and receptor.
Equation (1) suggests that one scheme for optimizing flux is to ensure that the (1) medicament is at its maximum thermodynamic activity within the vehicle. It has been shown that thermodynamic activity and chemical potential are simply a measure of 'escaping tendency' of a drug from a vehicle and that the higher this property, the greater the amount of drug should partition from the vehicle into the epidermis.' 2 Assuming all terms in the model remain constant, maximal flux should occur when the penetrant has achieved maximal thermodynamic activity. By definition, maximal activity occurs when solid drug is in equilibrium with drug dissolved in the vehicle.
Under ideal circumstances diffusion is neither rate limited by the intrinsic dissolution rate or affected by the partitioning characteristics of the drug; and all vehicles that contain drug as a finely ground suspension also exist as a saturated solution which sustain constant escaping tendency for the duration of the experiment. and centrifuged at 3000 RPM for ten minutes. The aqueous supernatent is aspirated, the organic phase evaporated to dryness and reconstituted with I ml of mobile phase.

Materials
Mass balance was performed by washing the donor compartments with 10 ml of methanol each, taking care to remove any solid nifedipine particles and to keep the time of contact of methanol to a minimum (less than 3 minutes total). The methanol washes were combined, diluted and measured by HPLC. The receptor phase was changed and the skin kept in contact for 23 hours with fresh receptor fluid to allow any residual drug to leach out. At the end of 23 hours, the receptor phase was removed and analyzed. After another I hours of contact between the skin and the fresh receptor phase, the receptor phase was analyzed to assure that no more nifedipine had leached from the skin. Recoveries of approximately 90% of the original applied dose were achieved. To confirm that donor did not significantly alter barrier properties, donor was reapplied at the 48 hour mark and sampling continued until 72 hours.
We have adopted the protocol described by Sloan'" to observe the effect of permeant solubility upon in vitro diffusion experiments in hairless mouse skin over 72 hour periods. Application of regular solution theory to predict the partitioning process requires three essential features in the experimental design: (!) saturated solutions are applied to the skin, (2) after each initial application period, a 24 hour washout period is used to determine the degree of accumulation in the skin, and (3) after the washout period, a second application of saturated drug solution is applied to determine the degree of damage to the skin .
Calculations -We assume that the properties of interest are functionally related to the the donor composition and that by changing the proportions of ingredients, x., the properties of the donor will change also. We assume the properties of the mixture to be a simple linear combination of its component cosolvents, of which the solubility parameter, o, for n solvents is (2) The solubility parameters were obtained from the literature" or, if unavailable, estimated using the method proposed by Fedors 12 demonstrated for nifedipine in ( after 24 hours. The 24 hour nifedipine receptor concentrations, C,, 4 • were averaged and the amount permeated at 24 hours normalized for the surface area of skin in the 25mm diameter cell, Q 24 ., was calculated according to equation (5): v, 5) and the mean Q 24 .-values were used to compare penetration from different solutions.

RESULTS AND DISCUSSION
The ultraviolet (UV) spectra of nifedipine in methanolic solution obeys Beer's law between 0.22 and 80 µg/ml with a sharp absorption maxima at 238 and a broad band between 325 to 370 nm. The nitrosopyridine and nitropyridine structures in Figure 2 have maxima at 280-310 and 277 nm, respectively, which is in agreement with literature values. 17 18 The intersection of these spectra, the isosbestic point, was used as the detection wavelength for quantification by UV spectroscopy. The broad absorption band from 325 to 370 nm is relatively immune to solvent-induced chromic shifts and was used when other uv-absorbers interfered at the isosbestic point. While the metabolic and photodecomposition products of nifedipine are resolved under the HPLC conditions employed , they were not detected in the receptor fluid at the assay minimum level of detection (0.04 µg/ml). Although the metabolic fate of nifedipine in skin in vivo is unknown , we assume that metabolic breakdown products are not produced to measurable degree in the excised skin.

47
The limited solubility of nifedipine may violate the assumption that diffusion is the rate limiting step in the permeation process. Consequently, it was important to determine the influence of equilibration time on the equi librium saturation solubility, C,. The C, of nifedipine as a function of various equilibration times presented in Table II show no significant dependency of dissolution on equilibration period. The saturation solubility of nifedipine in water is only 0.006 mg/ml and in PEG 400 it is 99 mg/ml. The saturation solubility of nifedipine in the 25% and 40% binary mixtures of PEG in normal saline are reduced to 0.240 and 0.462 mg/ml, respectively . The influence of even moderate amounts of water results in a sharp decrease in nifedipine solubility in ternary mixtures of PEG:DMI:water or PG:DMI:water. As drug diffuses from the nonpolar environment of the epidermis into the hydrated layers below, the poor water solubility of nifedipine may impede its diffusion at the dermal:epidermal interface.
The ideal and experimentally observed mole fraction solubilities of nifedipine in binary cosolvents are compared in Figure 5, Figure 6 and the quaternary systems in Figure 7 . Ideal mole fraction solubilities, calculated from Equation (4) consistently underestimate the solubilities determined experimentally which infer the existence of strong intermolecular attractive forces between nifedipine and cosolvent molecules.
This nonideality, resulting from the second term of equation (4)    100 coefficient, and a total solubility parameter matching that of the skin, appears at first glance to posses the prerequisite qualities of a 'good' candidate for transdermal therapy because of its 'lipophilic' nature. However, our solubility results clearly show that nifedipine appears to interact strongly with solvents primarily via Keesom forces which accounts for a poor solubility in lipids (hydrocarbons, fixed oils, etc.) and a low hexane:buffer partition coefficient. In addition, recovery studies show that only small amounts ( < 10 %) of the total dose applied partition into and are retained by the excised skin. Furthermore, our results of differential scanning calorimetry shown in Figure 8 reveals a melting point and enthalpy of fusion of nifedipine that is uncharacteristically high for those compounds in Table I on page 7 generally classified as lipophilic. Jn view of the many contradictions that can be ascribed to attempting a lipophilic-hydrophilic designation for nifedipine, a relationship between . .     (3). Likewise, in a study of the permeation of estradiol from varied concentrations of PEG 400, Valia and Chien 22 found that drug permeation rates decreased as the PEG level increased (i.e. , estradiol solubility in donor increases). The solubility of nifedipine is approximately constant in the PEG:DMI binary systems. The modest permeation rates from PEG:DMI systems did not differ significantly (p=0.05) due to the high variability in the data.
The trend for PG:DMI binary cosolvent mixtures of low solubility (high %PG) to display higher fluxes is also consistent with equation (3). The corollary between the works cited and our results suggests that drug solubility in the donor is itself a poor indicator of permeation. Apparently , an optimal point for penetration, corresponding to the product of Cv and PC,_., exists after which drug is less easily released from donor vehicles displaying high nifedipine solubilities. Khalil and Martin 23 showed that the rate of transfer of salicylic acid from one phase to a second phase was directly dependent on the differences between the solubility parameter of the solute and the two phases . Furthermore, the closer the solubility paran1eter of salicylic acid was to that of the membrane, the faster was the rate of transfer of acid. The solubility parameters of DMI, nifedipine, porcine stratum corneum, and propylene glycol are 18.4,20.5,20.5,and 28.6 MPa 112 , respectively. If large differences in the solubility parameter between permeant and donor accelerate diffusion, better fluxes are predicted from binary mixtures high in PG and low DMI. The results presented in Figure   is not available at this time.

63
In summary, the transdermal permeation of nifedipine was examined in terms of its solubility profile. Although thermodynamic diffusant activity was a poor predictor of nifedipine permeability, it was possible to predict in a relative manner permeation response based on the initial donor solubility parameter. These results support the hypothesis that a linkage between nifedipine and vehicle codiffusion may exist and further studies to establish the nature of this dependency are underway.  The present gap in knowledge dictates a systematic inquiry of those physicochemical properties of both drug and vehicle that limit drug suitability so that the rational formulation of new generations of transdermal delivery systems can occur.
Of the several layers of epidermis, the stratum corneum (SC) is recognized to be the primary barrier to transdermal diffusion . Although only IO to 15 % of the total SC mass is composed of lipids, these lipids largely dictate the overall skin permeability properties. However, the skin is a heterogenous laminate which, due to its composition, may offer differential influence on overall skin permeability. Methods -A series of experiments was set up using vehicles consisting of dimethylisosorbide' (DM) mixed with equimolar amounts of even-numbered alkanols• and alkanoic acids' (8-18 C

RESULTS
A selection of the physical and laboratory data from the solubility and permeation studies performed on pure alcohols (Table VI) and from donor suspensions of binary cosolvent systems (Table V) where P = permeability, dQ/dt = the slope of the straight portion of the penetration curve, A = the surface area (4.9 cm 2 ) and C, = the equilibrium saturation concentration of drug in the donor phase.
In Table VII the values of the component proportions, x;, were set equal to each other so that the relative effects of the components could be assessed. In many   solubility in skin and those that affect drug diffusivity were shown to affect nifedipine diffusion to improve permeation rates and lag times . In many cases, lag times of formulations without hydroxyl moieties were unacceptably long; lag times were found to respond favorably to addition of alcohols. Positive synergistic relationships between combinations of enhancers that modify drug solubility in skin and those that affect drug diffu si vity were shown to affect nifedipine diffusion to achieve desired permeation rates and lag times.  Due to the positive effects of cis-oleic acid on the percutaneous adsorption of 78 nifedipine noted in Figure 11, this acid was studied more extensively. Figure 12 shows

DISCUSSION
To gain an understanding of the mechanism of skin permeation, the effect of alkyl chain length of alkanols, alkanoic acids, and isopropyl esters on nifedipine skin permeation was investigated . Table VI shows that as the chain length increased, the transdermal permeation rate decreased initially and then increased as the number of methylene groups in the alkyl chain exceeded ten . This effect was also observed for to Figure 13 shows clearly that the intensity of enhancer effect is highly dependent upon the choice of vehicle.
Azone at levels of 1-3 %, has been shown to enhance the penetration of a related dihydropyridine, nicardipine, through excised abdominal skin of the hairless rat using pHEMA as a rate-controlli ng membrane.9 Previous work has shown that the optimum concentration of Azone varies with both drug and the formulation being examined with 2-10% enhancing while excessive amounts having deleterious effects on permeation. 10 Sezaki et al 11 observed that as the oil:water partition coefficient increases, there is a tendency for penetration to decrease in skin not pretreated with Arone and Azone-like enhancers and noted that a time element may be involved. The response of nifedipine permeation to Arone is shown in Figure 14. The permeation of nifedipine under the influence of oleic acid and Azone are quite different, suggesting that there are distinct loci in the stratum comeum upon which they exert their effect. Neither Arone 12 or PEG 13 is systemically absorbed to appreciable degree. Although both materials are very good solvents for nifedipine, azone, like PEG, had little effect on skin permeability as seen in Figure 14. When DMl or PG are substituted for PEG as the base solvent in the binary mixtures, permeation rate is magnified several fold. Since DMI and PEG share similar solubilities for nifedipine, the enhancement cannot be attributed to enhancement of thermodynamic activity.
Both DMI and PG are readily absorbed when applied topically, suggesting that higher flux values may be linked to the ability of the solvent to penetrate and modify the dynamics of drug:skin partitioning.
Experiments on stripped skin have shown that a significant barrier to diffusion still exists even when the stratum comeum has been removed. Figure 15 is particularly interesting in that stripped skin offered slightly less resistance to

24
changes resulting from replacement of water by the vehicle. 15 Lipophilic solutes which permeate readily through the stratum comeum may be rate-limited by the epidermal or dermal layers. In the case of nifedipine, removal of the stratum comeum lipids probably accelerates the movement of the PG, ET and DM components which results in more rapid depletion of these key components from the donor phase. In this way, the results of the skin stripping experiment lend further credence to cosolvent control.
The data obtained suggest strongly that enhanced transport is dependent on several factors. and PEG possess comparable C, values, the former readily permeates the skjn while the latter does not. Since the donor was applied as a suspension (an infinite dose design), the asymptotic behavior of the profiles in Figure 13 are unexpected while similar experiments, using PEG as the base solvent displayed in Figure 12, do not.
The rapid depletion of the OM component from the donor would explain why Q versus t profiles for systems containing small amounts of OM display asymptotes well before supply of nifedipine in the donor system is exhausted and constitute strong evidence for a possible linkage of solvent:drug in the permeation process.
For a very lipid-soluble drug, clearance from the viable tissue may replace diffusion through the stratum corneum as the rate limiting step in the overall process of percutaneous absorption. Conventional models portray the skjn beneath the patch as a sink for the permeating molecule. If this assumption does not hold , passage through the stratum corneum may no longer be the rate limiting step to permeation and it would be incorrect to target the stratum corneum as the barrier to diffusion. In such cases, patches that incorporate penetration enhancers whose actions are restricted to altering the barrier properties of the stratum comeum would be inferior to those that incorporate agents that would promote partitioning from the epidermal to the dermal la ye rs.
The partition coefficient is crucially important in promoting a high initial concentration of the agent within the upper strata of the epidermis. Based on the solubility parameter of 10 (cal/cm 3 ) 1 n for porcine skin, one would expect nifedipine to have a high affinity for the stratum comeum. Scheuplein has calculated that a tissue-water partition coefficient of > 400 was required before a 200 micron layer of dermis had a diffusional resistance comparable to that of stratum comeum 10 microns thick. 16 With an octanol-water partition coefficient of 10,000: 1, a significant 85 resistance to nifedipine may well reside in the deeper dermal layers.
Notice in Table V that  Furthermore, although Table V and Table VII show poor results with saturated acids and alcohols with molecular weight near that of myristic acid, the second and third highest J values derive from formulations containing the isopropyl ester of myristic acid. IPM, like PG, did not solubilize nifedipine as well as DMI or PG, yet higher fluxes were achieved from these systems. This is probably due to the fact that nifedipine, being more soluble in the DM:OA cosolvent, prefers to remain in the donor compartment.
Another plausible explanation is that PG, being much more polar than OM, enhances the movement of OA out of the donor, effectively "pushing" the OA into the skin where its effect can be exerted. This push effect is augmented by the effect of Essentially, donors that cannot interact and sequester water molecules (higher alcohols and acids) should and do display a larger "push" effect.
The asymptotic behavior of the Q versus t curves at 12-24h for some cosolvent blends deserves comment. All factors being equal, the maximal rate of transdermal transport should occur from systems of higher thermodynamic activity, that is from suspensions versus solutions. In Table IX the results obtained from a system 87 containing drug at 50% below and 10% above its experimentally determined saturation solubility show suspension and solution gave comparable permeation rates. If saturated and subsaturated mixtures represent different levels of activity, these results show that thermodynamic activity is not a critical factor in these systems. If Extraction of hairless mouse skin following permeation experiments in vitro recover very small quantities ( < 10%) of the administered dose. Two inferences emerge from this observation: either the skin as a whole has poor affinity for nifedipine (i.e., the solubility parameter is not 10 Hil) or that the deposition of nifedipine in the SC is minimal ( i.e., the skin does indeed have a high binding potential for nifedipine, but that it constitutes such a small percentage of the skin that the quantity of nifedipine that it contains is exceedingly small) . Alternatively, the solvent may dissolve the stratum corneum , leaving skin with very different qualities.
This latter alternative is unlikely, since J values obtained post 24 hours following repeat application of donor were similar to those obtained from the steady-state portion of the 0-24 hours Q versus t profiles.
The data in Table VII  Our interpretation of these results is as follows. Given that 0 0 ,r "" .S", binary mixtures whose solubility parameter approaches that of the stratum corneum have higher C, values and J values should decrease. Conversely mixtures having solubility parameters greater than 10 have lower nifedipine solubilities, a condition which favors drug movement from donor into skin. This trend is observed in Table VI and   Table VII,  Conclusions -Unsaturated, long-chain acids had pronounced effects which appear to be selective for cis-unsaturated fatty acids as they were not observed for their saturated ( myristic, and nonadecanoic) or trans-unsaturated acids (elaidic) counterparts. It was found that the permeability of nifedipine through hairless mouse skin is controlled by both the solubility of the drug in the donor and the ability of donor to both disturb and pass through the epidermal skin layers. The shape of Q vs t plots displayed a strong dependency on the quantity of cosolvent applied . These results imply that a linkage between nifedipine and vehicle codiffusion may exist and further studies to establish the nature of this dependency are presently underway.

ABSTRACT
The effects of transdermal device components on nifedipine permeation were evaluated by (l) identifying those factors which significantly affect the permeation of nifedipine and (2) selecting levels for these factors which optimize flux and lag times.
Of primary interest was the role of solubility and its influence on the permeation enhancers chosen to increase the skin permeability of this hydrophobic calcium channel blocker. A McLean Anderson mixture design was employed to obtain a stoichiometric interpretation of the permeation process. In addition to demonstrating solvent-induced permeation enhancement, the mechanisms by which solvents enhance permeation are discussed. The ultimate objective was to apply regression techniques to interpret, on a molar basis, the data obtained from in vitro permeation experiments.
The model obtained was used to identify both the magnitude and significance of the synergism between formulation components and to optimize the desired response.
Data from these inquiries have contributed toward the rational selection of components in a viable transdermal dosage form that permit transdermal delivery of nifedipine at rates in excess of the 31 µg/h•cm 2 required for potential therapeutic response.

Introduction
The design points comprise the vertices and centroids of a convex polyhedron suitable for fitting first-degree and quadratic models in the constrained mixture space. The resulting factor space and the design point designations are presented in Figure 16.
Insight gained from this design permitted tighter constraints on the experimental space such that the mole fraction of OA and ET was fixed at the 10% level and the levels of the other two components were allowed to vary. This second experiment is referred to as Design II. Experimental design, analysis and optimization were performed using the ADX™ menu system of SAS/QC and SAS/STAT software, Version 6.0 (SAS Institute, Inc. Carey, NC) .

Results and Discussion
Of the many factors that will influence the effectiveness of penetration The results which appear in Table X and Table XI offer   To test this theory, Design 11 was augmented with additional formulations such that the ratio of OA to ET was held constant and the proportion of PG to DM allowed to vary. These results, reported in Table XII,    that leveled out at around 18 hours . While each factor-level combination receives the same number of solvent molecules, all donor formulations consist of suspensions of 10% excess nifedipine so that the amount of nifedipine actually applied to the skin does vary as a function of nifedipine solubility in the formulation . Only rarely did the total amount of nifedipine permeated approach the amount initially applied and these formulation were biphasic rather than asymptotic. Since this asymptotic behavior is restricted to donor formulations at low levels of DM, it was initially believed to result from depletion of DM in the donor. To test this theory, a formulation consisting of PG:OA:ET:DM (50: 10: 10:30) were applied in doses of 6 and 18 µmo! of cosolvent per cell. In Figure 18, Q versus T profiles of the lower dose asymptotes; cells receiving the higher dose did not display an asymptote. Upon termination of the experiment, the amount of nifedipine remaining in the donor compartment of those cells showing asymptotes revealed that for the 6 µmol dose, the amount of nifedipine permeated is approximately 16% of the amount initially applied.
The amount of nifedipine recovered in the skin was comparatively small ( ,.,33 of amount permeated). Crystals of nifedipine were visible in all donor compartments and it is assumed that a sufficient excess of drug ( ""80%) remained to maintain the concentration gradient. In terms of nifedipine solubility, donors high in PG and low in DM possess a lower saturation solubility. Also, as DM diffuses into the skin, the donor simultaneously acquires transpired moisture from the skin, the net effect of which is to lower nifedipine solubility and create a diffusional force favoring partition of nifedipine out of the donor and into the skin. Furthermore, it has been proposed that solvents alter the dermal environment by alteration of hydrogen bonding of dermal water or by its ability to solubilize drug. This combination of events alters drug solubility during the experimental period in a manner that favors nifedipine permeation and is consistent with the observation of asymptotic or biphasic behavior.
The expression of formulation constituents as mole fraction permits a unique opportunity to model the diffusion process from a stoichiometric perspective.
Adoption of this reference system permits the experimental data to be modeled in a meaningful way that illuminates the relative importance of the individual components  Table XIII and the significance of the regression is shown in Table XlV . The magnitude of the parameter estimates in Table XIII reveal that all four main effects were not significant. Of the six possible two-way interactions, the synergistic blending of OA appears to be real since all fJ;; for i =j =2 terms are greater than zero. Synergism among the other components may not be real, since ( The elucidation of the synergistic interactions among vehicle components responsible for the superior performance of these quaternary systems is a conclusion difficult to identify in four factor space and emphasizes the importance of treating the data to this type of analysis. Gross observation of the Q versus t profiles would have led to the (incorrect) conclusion that DMI had a deleterious effect on permeation.
However, the model predicts that it is not so much the main effects, but rather the interaction between OA and the other three components which explains enhanced permeation.
Since all four factors affect the response, it is not possible to identify a region The predicted response surface for flux ( Figure 19) and lag time ( Figure 20) correspond exclusively to systems in which the level of both oleic acid and ethanol is held at the mole fraction level of 10%. Unfortunately, since all four two-way interactions with OA and the remaining factors affect the response, such plots cannot be readily used to identify a region of maximum (or minimum) response for the present n +4 factor space. One solution is to set constraints on lag time and optimize flux subject to this constraint. As an alternative, a ridge analysis is used to locate the range of 'optimum' response within the design space. As a second alternative, the predicted response surface for flux within the constraints of three factors may be examined at discrete levels of the fourth factor in a manner analogous to a radiological CAT scan. Such conceptualizations, produced under the SAS ADX system, offer an advantage over the three-dimensional plot in Figure 19 in that they Ill Table XV. Ridge analysis of data in Table XI. -----Type of ridge = MINIMUM ----- x, X2 x, x. permit visualization of three rather than two factors ( Figure 21 through Figure 24). The eigenvalues and eigenvectors obtained from regression analysis predict elliptical response surfaces for both lag time and flux that are most sensitive to changes in the levels of OA and DM, while the level of PG relative to these key components should not influence the slope of either response surface as significantly.
This behavior is readily apparent in Figure 21 through Figure  indicate that the flux response is least sensitive to this component. Regions having narrow contour intervals, such as those parallel to the base of Figure 21, predict that the flux response will change rapidly with changes corresponding to horizontal movement from regions of low to high oleic acid. Clearly, movement in this direction results in rapid achievement of optimal fluxes followed by equally rapid decline in predicted permeation rates. An additional feature of the system is that it also provides a measure of confidence in the response estimates via plotting of the standard error as shown in Figure 25. These results suggest that a relatively high level of PG and low levels of OA, ET and DM will give maximum flux and minimum Jag times.
From a stoichiometric perspective, the diffusion process to be envisioned as one in which OA and DM are the rate limjting factors, while ET and PG have less activity and are present in excess. Based on these results of the regression, optimal performance should be realized from a formulation high in PG relative to the other components. A compromise is accepted in formulation 9 in Table XII ( Figure 26. The results of these permeation experiments conform to predictions based on eigenvalues obtained from the model obtained from the data in Table X The minimum and maximum predicted flux response values expected from various formulation combinations are shown in Table XV. The maximum flux predicted by the model was expected from a mole fraction ratio of 70: 12: 13:5, the permeation results which are presented in Figure 15. Note that this ridge maximum is outside the constraints of the polyhedron withjn Figure 16. and the amount of error Hkely to be incurred generally rises on the periphery of the experimental space. Figure 25 shows that all approximation are expected to be particularly imprecise near the edges of the experimental region determined by the design space. This optimized formulation (designated P42. l) yielded a flux of 60 ± 6 µg/h•cm 2 and a lag time of only 2 hours which is twice that required to deliver an equivalent oral druly dose.
In summary, regression analysis have been successfully applied to data for handling large, complex data sets that can be applied to many fields of research.

126
The source code for SIMPLEX SAS Al is also supplied as it shows the means by which the various properties of the formulation studied were calculated.
In our laboratory, a Waters Baseline 810 chromatography workstation has been programmed to acquire data under its Summary option to allow storage of data on floppy disk to be uploaded to the mainframe via a modem telecommunications link.
A novel method for coding the individual data points was developed. This scheme was successfully utilized by six researchers sharing the apparatus to manage thousands of data points without mishap. In addition, it provides a functionally useful format to be read by subsequent data processing steps in the SAS system . The specifics of this program are discussed in detail in the section titled "CELLS3 SAS Al" .

CELLS3 SAS A I
A particularly useful format for maintaining integrity of the data sets that also provides for efficient identification and retrieval has been to code the data points in the following hierarchal structure: assay, notebook page, formulation reference, replicate number (i.e., variables VI thorough V4) followed by the drive unit position, sample interval, and the time the sample was taken. This is accomplished by first allocating space in a hard disk subdirectory and then assigning each chromatogram a unique 8 digit filename and sample name in the "LOAD QUE" option. Following data acquisition and storage as an ASCII file on floppy disk , the sample names (which are comprised of the four identifiers VI thorough V4 assigned in the "LOAD QUE" 127 step) are quickly expanded, using the "SEARCH/REPLACE" feature of any wordprocessor, to the format utilized by the INPUT statement in the data step DATA ASCON in program CELLS3 SAS AL CELLS3 SAS Al was written in modular fashion using the SAS macro facilities which allow for a great deal of versatility.
"Method" refers to the Baseline 810 program containing the instructions used to inject, acquire, and process chromatograms and calculate the amount of nifedipine using peak areas by the external standard method.
It is essential that the user of the SAS ADX'M menu (SAS Institute Inc. Carey, NC) be aware that the device driver of the present version of SAS (6.01) at this installation must be modified in order to obtain hardcopy of graphics produced. Prior to invoking the SAS ADX system at URI, the user must insure that the following essential steps have been properly executed: (1) the Q2200PS driver has been modified from REPLACE to APPEND.
(2) the following statements : ADX is configured to display color graphics upon any graphics terminal by specifying "DEVICE=TEK4107" when prompted by the system. Direction of graphics output from the SAS ADX system to the University laser printer requires that the user exit the ADX system and at the CMS READY prompt type FILEL, tab down to the 'filename filetype filemode' (i.e. , the repository of the graphic stream provided to the system in the statement above) and typing the following command RPRINT I LP 1 PS upon which the graphic image may be recovered at the Dispatch Office in Tyler Hall.

INTRODUCTION
This appendix discusses the rationale behind the attainment of the following objectives: (1) identify the key independent variables which influence the problem and principle responses to be measured; (2) the fitting of some proposed model for the purpose of describing the shape of the response surface over the simplex factor space; and (3) determining the roles played by the individual components. Identification of the right blend of solvents which would allow adequate solubility, stability, permeability with minimal irritancy and lag time at a reasonable cost posed a challenge best solved by the use of appropriate statistical and mathematical tools.
These objectives have been achieved through the use of mixture designs. A mixture design is performed by mixing together several ingredients. 6 Much of the introductory principles of mixture designs, models and the analysis of mixture data may be found primarily in the EXPERIMENTS WITH MIXTURES: Designs, Models, and the Analysis of Mixture Data 7 from which this appendix draws heavily.
In factorial experiments, the response varies depending on the actual amounts of each of the independent variables (i.e., "factors"). However, unlike factorial experiments, the distinguishing feature of a mixture design is that the independent, controllable factors represent proportionate amounts of the mixture rather than unrestrained amounts, the proportions of which must be nonnegative and sum to unity. These restrictions limit the manner in which an investigator may: (1) Since our primary interest is to explain the permeation process from a molecular perspective, the proportionate amounts of mixture component is expressed in mole fraction terms rather than by volume or by weight. The two measured responses of interest (i .e., flux and lag time) are derived from the profiles obtained by plotting the steady state nifedipine permeation as a function of time. The flux is quantified from the slope and the lag time from the point of intersection with the abscissa of the back extrapolated portion of these curves. Due to practical considerations such as cost, irritancy and stability in order to form valid mixtures from which an acceptable formulation could be made, component i must be present in some minimum amount a; and maximum amount c,. In other words, the proportion X; of component i must be bounded below by a; > O and above by c,< 1.0. The quantity a, is known as the 'lower bound ', c, the 'upper bound ', and in addition to usual constraints , x, ~ 0 , x, +x 2 + . .. +x.= 1, a second limitation for the constrained simplex is O< a;Sx;SC; S l , i=l,2, ... ,q To be effective the donor must contain relative proportions of the components restricted to the following upper, C;. and lower, a;, bounds:
The experimental region or factor space of mixture experiments is different than that of factorial experiments. Mixture designs are referred to as a simplex designs because the experimental region of interest, defined by the values ascribed to X;. take on the shape of a simplex (i.e., "a regular figure of n + 1 vertices in n space"). In contrast, for a 2• factorial experiment, where x; take on the values of ± 1, the factor space is a cuboidal, q·dimensional space. Thus, for a 2 4 factorial, this space is a tetrahedron while for a 2 4 mixture it is a pyramid. The experimental design space constitutes a polyhedron whose eight vertices (points l ·8) are based on the component restrictions mentioned above. The simplex coordinate system for q=3 can be plotted on triangular graph paper; graphical representation of q > 3 is less groups of three of more vertices where each vertex has the same value x; for one of the components. The overall centroid, which is defined as the average of the eight vertices, is listed as point (9). Taken together, the design points comprise the vertices and centroids of the faces, sides and edges of a convex polyhedron compatible with the requirements outlined by Snee" for fitting first-degree and quadratic models. The resulting factor space and the design point designations are presented in Figure 16.
The dimensions of a {q,m} simplex-lattice must conform to the number of components (q) and the order (m) of the fitted model. The number of design points, n, is n = (q+m-1)1 ml(q-l)l Therefore, a quadratic model fitted to the data obtained from the four-component formulations is designated a {4,2} simplex and requires at least ten well chosen (3) points, a cubic model a minimum of 20 points, and a quartic model 35 points. The number of terms in the canonical polynomials for these four component formulations would be 4, 10, 14, and 20 for a linear, quadratic, special cubic, and full cubic, respectively. These requirements are enumerated here to illustrate how rapidly such designs can escalate. Obviously, a compromise must be struck between accurate modeling of nifedipine permeation and restricting the study to manageable proportions. This investigation utilized a {4,2} design to delimit the study, so that useful results could be obtained with the time and funds available. which is the special simplex-centroid model of equation (6) when q =4. In trying to decide on the particular form of the Scheffe's-type canonical polynomial model to be fitted to data collected at the points of a q =4 simplex-centroid design, it is noted that the special cubic model or simplex-centroid model of equation (6) is chosen over the lower-degree models because the terms in the special cubic model not only provide a measure of each pure blend, but provide measures of the binary and ternary blends.
Rather than sequentially build the model by starting with the first-degree polynomial and work towards the special cubic model, we began with the complete special cubic model fitted to the data and work backward by testing the usefulness of the cubic term, the quadratic term, the crossproduct terms and finally the similarity of the linear terms in the model. The test statistics are those discussed by  Consequently, the following questions are posed: I. Is the flux and lag time response surfaces likely to be planar over the experimental space or are combinations of cosolvents likely to cause departures from linearity in the surface shape? If the blending of multiple-components is not additive, which pairs are likely to have synergistic or antagonistic effects? Are complete (quaternary) blends likely to have more desirable responses than ternary , binary or even pure blends? Also, if we assume the relationship between components is linear, should the permeation results be collected at vertices of the pyramid only, or should we use complete mixtures that are very close to the vertices? Furthermore, even if the relationship is linear, should midledge or interior points be collected to check the assumption of linearity?
2. If the simplex arrangement chosen for the distinct possibility that the surface is not planar, should additional observations be collected at interior points of the polyhedron for the purpose of checking the fit inside the triangle? If so, is the centroid of the triangle the location at which to sample the interior? general polynomials are used because the x;'s are constrained to sum to one and standard computer regression programs cannot be used for fitting the models when the x;'s sum to unity without creating problems in the calculations.
Terms of higher degree must be added to account for curvature in one or more directions. Quadratic and cubic models with interaction terms was employed. As

RESULTS
The functional form of equation (6) of the relationship between the responses (flux and lag time) and the factors are given in Table XIII on page 110. The results of a ridge analysis are used to locate the optimum response within the design space (Table XV). This technique computes the estimated ridge of optimum responses for increasing radii from the center of the original design. The optimum values start at the center point and follow the path of steepest descent of ascent, respectively until within the region of experimentation the expected maximum and minimum are found.
These results suggest that a relatively high level of PG and low levels of OA, ET and DM will give maximum flux and minimum lag times. Note, however, that the standard error increases as the optimum response ridge moves away from the center point of the design and toward the boundary of the design space, indicating that predictions near the edge are inherently less reliable.
The ridge analysis output is only a list of numbers; to better understand it, consider a plot of the ridge values superimposed on the factor-response profile plot for each factor. Each profile plot is simply a scatter plot of one factor's values against response predictions made over the entire region of experimentation. A profile plot thus shows the relationship of the factor to the response, as well as giving an indication of interactions with other factors. Superimposing the ridge analysis gives an indication of the movement and flow of the optimal response ridge over the multidimensional response surface. When sorted, it becomes obvious that the two objectives, maximizing flux while minimizing flux, conflict with one another. One solution is to set constraints on lag time that it lie below and to optimize flux subject to this constraint. Algorithms are available that permit several responses to be simultaneously analyzed to identify mixtures that strike compromises between maximization of some response (e.g. flux) and minimization of another (e.g. lag time) . 12 This useful feature is also incorporated into the SAS ADX menu system.
It is not possible to picture response surfaces of a cubic model because they are hyperplanes in four-dimensional space. The eigenvalues provide additional information about the sensitivity of the stationary point to deviations from the optimum. The relative magnitude of the eigenvalues indicate the relative rate of change for each of the canonical direction w;. Those with the largest magnitude change quickest and it is these directions that are the most sensitive to deviation from the actual stationary point. The smaller eigenvalues indicate direction of lesser sensitivity. Unequal eigenvalues suggests that the behavior of the response function results in contours that are elliptical . The major axis belongs to the least sensitive direction (given by an eigenvector) and the minor axis is that of the greater eigenvalue. This ridge analysis provides further knowledge about which directions must be estimated most precisely and which are less important.
The crossproduct coefficient estimates (the {Jijs) measure curvilinear departure from a hypothetically planar response surface. The synergistic blending of OA appears to be real since all fJ ;; for i =j =2 terms are greater than zero. Synergism among the other components may not be real, since {J" is not significantly greater than zero based on the comparison of each coefficient estimate to the value of its standard error in the form of an approximate Student's I-statistic and then comparing each computed value oft to the tabled value t 15 , 0 _ 25 The sign of the {J's and the 152 corresponding value of the t-statistic lead us to infer that the individual terms are antagonistic toward one another in overall formulation performance while combinations of factor 2 (i.e., oleic acid) strongly interacts with all three factors .
Furthermore, the magnitude of the interaction terms are large and probably represents the driving force for enhanced permeability in these systems. Frequently, the fabrication of PSA's require heat to assist crosslinking and to drive off residual solvent. 4 The deleterious effect of high temperatures required by solvent-based and hot-melt coating processes pose Hmitations on the selection of enhancers such that avoidance of a heating step would be useful. Low temperature curing of silicone rubber to prepare a monolithic TDS would be particularly useful when enhancers of low vapor pressure are incorporated into the formulation . This study evaluates silicone elastomer matrices containing drug and penetration enhancer fabricated by polymerizing silicone precursors at room temperature. Alternatively, steps that require processing at elevated temperatures may be executed prior to the addition of heat-sensitive components. This was accomplished by the formation of PSA films and their subsequent lamination , at room temperature, to a layer incorporating the drug and enhancers. Matrix and reservoir-type devices thus formed are evaluated to deliver drug and enhancer to the skin. to form a patch with a reservoir between the Celgard and backing layer (see Figure 27). The patch reservoir was loaded by inserting a hypodermic syringe into the orifice leading into the reservoir chamber, expressing 0.3 ml of the stock drug:cosolvent mixtures containing 10% excess nifedipine into the chamber and heat sealing the orifice. Patches were stored for one week prior to testing to allow the reservoir components to equiJjbrate with the PSA.

EXPERIMENTAL
Partioning studies -An equilibrium method 5 was used to determine the membrane-vehicle partition coefficient. Medical grade silicone adhesive was cast into membranes, ground into small pieces, weighed and placed into screw top test tubes. the density of the dimethylsiloxane was assumed to be unity, which is a reasonable approximation. 6 The partition coefficient was calculated by dividing the membrane solubility by the saturation solubility in the solvent system under consideration. Total amount recoverable was determined by placing membranes in 30 ml scintillation vials and agitated at 30 oscillations per minute at 37°C. The fluid in the vials was replaced until no more nifedipine was detected.
Kinetic studies -Screening of PSA films were carried out by measurement of penetration rates through freshly excised hairless mouse skins mounted in Franz cells to measure their usefulness as delivery devices. The laminates were placed on the excised skin, a 200 gram weight placed atop for 2 minutes, and then mounted in the Franz cell.
RFSULTS -The physical properties of the films studied and permeation of nifedipine through the materials tested in this initial screening are shown in Table XVI. No decomposition of nifedipine could be detected by HPLC, suggesting that the patch components were resistant to oxidation and did not need stabilizing additives often necessary in many organic-based PSAs. In addition to the numerous advantages reported for silicone-based devices, 7 ·s.t. 9 the silicone PSA tested appears to retain a suitable degree of tack for initial bonding, conformance to skin contours and accommodation of skin movement needed to hold the TDS in place for several days, sufficient cohesive strength is observed leaving no residue when removed .
Physical compatibility when measured by the 180 degree peel test showed the adhesive strength of the 200µ films were affected in the following order: SISPSA < SPSA < PPSA < HMPSA. The results in Table XVI show good physical stability in silicone PSA. To our knowledge, there is but one report evaluating nifedipine:PSA Silicone elastomer high medium X7-4301 compatibility and this was performed at a I% loading level. 10 Best performance was obtained from a TDS design composed of four basic components: an impermeable backing, an adhesive, a drug reservoir, and microporous membrane to contain the drug suspended in vehicle. The amount of nifedipine permeated as a function of time for the silicone reservoir device is shown in Figure 28. These results demonstrate that, in terms of nifedipine permeation rates and physical properties, silicone is the best choice of the PSA's examined. The range of drugs that may be formulated as TDS's, particularly drugs whose permeation profiles are linked to the codiffusion of vehicle, may be extended by the adoption of reservoir-type designs.
In summary, the in-vitro skin permeation profiles of nifedipine (N) under the influence of selected penetration enhancers from adhesive matrix devices was . . 25 evaluated using excised hairless mouse skin . Prototype devices containing permeation enhancers were prepared from silicone adhesives, silicone elastomer, pressure sensitive acrylic, and PIB pressure sensitive adhesives (PSA). Release from thin fLlms of these materials applied directly to the skin was poor. Fluxes were substantially higher when the drug:cosolvent mixture was fabricated as a reservoir system.

APPENDIX D CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
The ultimate goal of this type of research is not restricted to merely overcoming the formidable barrier posed by the skin but rather is an attempt to avoid the empirical approach in favor of quantitative, scientific tactics. We have achieved the former and made significant progress with the latter. Admittedly, extrapolation of the results of our inquiries to other systems is a dangerous exercise. More often than not, conclusions are merely assumptions to be tentatively entertained . Yet the decision process behind the choice of the enhancer-solvent combinations for other hydrophobic penetrants having different physicochemical properties is a topic worthy of further consideration. If our hypotheses regarding the crucial effect of solubilization within the epidermal layers is correct and if our observations were mirrored by other permeants, inferences made early in the development process regarding TDS design could be justified.
Foremost in our minds at this time is the disposition of non-drug components that constitute the donor. The data presented constitutes a strong case for a hypothetical linkage of solvent permeation with drug permeation and their measurement holds the key to the interpretation of the information we have gathered.
Furthermore, measurements should be conducted to determine skin uptake of enhancers e.g., oleic acid because it may be that enhancer skin uptake, hence penetration enhancement, is dependent on thermodynamic activity of the oleic acid in vehicle rather than that of the drug . Sheets of epidermis, including the horny layer, may be separated from the underlying dermis and mounted in diffusion cells so that the diffusion and preferential uptake of compounds may be followed. Future work might utilize these techniques in the hope of correlating flux through intact skin to flux through the perturbed membrane, thus identifying the site of control.
The techniques used in this thesis were subject to constraints imposed by equipment; alternative strategies could have been employed to examine the effect of cosolvent composition on permeation. Although we employed an infinite dose design with regard to drug, the results clearly display a dependence of permeation on the molar amount of cosolvent applied and future work might take this into consideration.
Radiolabeled drug and cosolvent would permit direct quantitation. Unfortunately, radiolabeled nifedipine and dimethylisosorbide were unavailable for use in these experiments; methods that permit direct quantitative measurements of drug and enhancer in the skin compartment should be considered. The potential of microdialysis, a new bioanalytical sampling technique that permits dermal flux of topically applied compounds to be monitored directly, has proved to be a powerful technique in the characterization of dermal transport of  Finally, a need exists to develop methods to predict the in vivo performance of TDSs. Such methods would be invaluable in engineering new systems. As we increase our understanding of how dosage form components interact with the skin we likewise increase our proximity to this elusive goal .