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Previous studies in our laboratory have demonstrated that skin electrical resistance can be controlled by an alternating current (AC) electric field. By maintaining constant skin resistance, AC iontophoresis has been shown to reduce the iontophoretic flux variability of neutral permeants. Recently, it was found that symmetric square-wave AC could enhance iontophoretic transport of both neutral and ionic permeants by means of electrophoresis and/or electroosmosis in a synthetic membrane system, and a model was presented to describe the experimental results. The objective of the present study was to assess the effects of AC voltage and frequency and direct current (DC) offset on the flux of neutral and ionic model permeants with human epidermal membrane (HEM). Experiments were conducted under two different conditions: constant AC voltage iontophoresis and iontophoresis using constant HEM resistance with DC offset voltage. The following are the main findings in these experiments. In the constant AC voltage study, when the permeability data were compared at the same HEM electrical resistance, it was demonstrated that AC even at high frequency (approximately 1 kHz) could enhance the transport of the ionic permeant (tetraethylammonium ion) across HEM, but no enhancement was observed for the neutral permeant (arabinose). For the ionic permeant flux enhancement, the higher the applied AC voltage, the greater the flux enhancement. There was little or no AC frequency dependence of the flux enhancement in the frequency range of 50-1000 Hz. In the constant HEM resistance study of AC with DC offset, approximately linear relationships were observed between flux enhancement and the DC offset voltage for both the neutral and ionic permeants, and these results were found to be consistent with predictions of the modified Nernst-Planck model for conventional constant voltage DC iontophoresis. When the DC offset voltage was increased, the AC component of the flux enhancement for the ionic permeant decreased, eventually appearing to contribute negligibly to the total flux enhancement at high DC offset voltages.

One of the primary safety and tolerability limitations of direct current iontophoresis is the potential for electrochemical burns associated with the necessary current densities and/or application times required for effective treatment. Alternating current (AC) transdermal iontophoresis has the potential to eliminate electrochemical burns that are frequently observed during direct current transdermal iontophoresis. Although it has been demonstrated that the intrinsic permeability of skin can be increased by applying low-to-moderate AC voltages, transdermal transport phenomena and enhancement under AC conditions have not been systematically studied and are not well understood. The aim of the present work was to study the fundamental transport mechanisms of square-wave AC iontophoresis using a synthetic membrane system. The model synthetic membrane used was a composite Nuclepore membrane. AC frequencies ranging from 20 to 1000 Hz and AC fields ranging from 0.25 to 0.5 V/membrane were investigated. A charged permeant, tetraethyl ammonium, and a neutral permeant, arabinose, were used. The transport studies showed that flux was enhanced by increasing the AC voltage and decreasing AC frequency. Two theoretical transport models were developed: one is a homogeneous membrane model; the other is a heterogeneous membrane model. Experimental transport data were compared with computer simulations based on these models. Excellent agreement between model predictions and experimental data was observed when the data were compared with the simulations from the heterogeneous membrane model.

The present study aimed to investigate new pore induction as a flux-enhancing mechanism in human epidermal membrane (HEM) with low to moderate voltage electric fields. The extent of pore induction and the effective pore sizes of these induced pores were to be assessed using a low frequency (12.5 Hz) low to moderate voltage (2.0 to 4.0 V) square-wave alternating current (ac) “passive” permeation method (ac iontophoresis). This ac approach was to allow for inducing and sustaining a state of pore induction in HEM while permitting no significant transport enhancement via electroosmosis; thus, transport enhancement entirely due to new pore induction (enhanced passive permeation) was to be assessed without any contributions from electroosmosis. Good proportionality between the increase in HEM permeability and its electrical conductance was found with the “passive” transport data obtained during square-wave ac iontophoresis using urea as the model permeant. Typically, at 3.0 to 4.0 V, HEM conductance increases (and permeability increases) ranged from around 3- to 30-fold. These results appear to be the first direct evidence that new pore induction in HEM is a significant flux enhancing mechanism under moderate voltage conditions. The extents of pore induction in HEM under low frequency moderate voltage (2.0 to 3.0 V) ac, pulsed direct current (dc), and continuous dc were also compared. The extents of pore induction from square-wave ac and pulsed dc were generally of the same order of magnitude but somewhat less than that observed during continuous dc iontophoresis at the same applied voltage and duration, suggesting less extent of pore induction with reversing polarity or when a brief delay is provided between pulses to allow for membrane depolarization. The average effective pore sizes calculated for the induced pores from the experimental data with urea and mannitol as probe permeants and the hindered transport theory were 12 ± 2 A, which are of the same order of magnitude as those of preexisting pores determined from conventional passive diffusion experiments.

This study aimed to gain mechanistic insights into the nature of the pore pathway of fully hydrated human stratum corneum from lag time data obtained using a model polar permeant, urea. Lag times were deduced from transport experiments with human epidermal membranes and with human epidermal membranes after ethanol or chloroform–methanol treatment. A tortuous pore pathway transport model and a `bottleneck' transport model were employed for data analysis, and their appropriateness for the observed data was examined. Important outcomes from the present study with intact and with delipidized stratum corneum were as follows. Long lag times (around 60–800 min) for the transport of urea in human epidermal membranes were generally observed. These results were consistent with an extremely tortuous pore pathway as would be expected if it is associated with the polar/aqueous region of the stratum corneum intercellular lipids (i.e. the bilayers in the intercellular region). The permeability of the stratum corneum increased after ethanol treatment, and, at the same time, the tortuosity decreased but remained relatively high. Chloroform–methanol treatment further increased the permeability and further decreased the tortuosity. Since delipidization by ethanol and chloroform–methanol treatments decreased the tortuosity of the pore pathway, these results suggest that the effectively highly tortuous pathway for polar permeants in stratum corneum may be associated with the polar regions of the intercellular lipids. Untreated skin samples that had high electrical resistance were observed to have longer lag times than those with low resistance; this is consistent with the hypothesis that skin samples of high resistance have less appendage routes or less damage and transport polar permeants predominantly via the tortuous pathways involving the intercellular lipid regions of the stratum corneum. Neither the tortuous pathway transport model alone nor the `bottleneck' transport model alone seems to perfectly represent the experimental data, and a modified model (a hybrid of the two models) has been proposed to be more consistent with the lag time data and the morphology of fully hydrated stratum corneum. The present study has demonstrated the usefulness of lag times obtained with a polar permeant in better understanding the transport mechanisms involved with the pore pathway.

The effects of permeant charge (z) on iontophoretic-enhanced transport were investigated with synthetic Nucleopore membranes and with human epidermal membranes using a four-electrode potentiostat with side-by-side diffusion cells. The modified Nernst-Planck model (Nernst-Planck theory with an additional transport term to correct for the effect of the convective solvent flow due to electroosmosis) was first examined in a Nuclepore membrane system with model permeants calcein (z = -4), salicylate (z = -1), and a series of polystyrene sulfonates (from monomer to molecular weight of approximately 8000 with a z range of -1 to approximately -40). The flux enhancement (E) for each permeant was determined at 470 mV. Mannitol (a neutral molecule) was used as a probe to determine a correction for convective solvent flow under the same applied voltage conditions. Good agreement between the experimental results and the predictions from the modified Nernst-Planck model was found for calcein, salicylate, and polystyrene sulfonates up to molecular weight of approximately 1800 (z approximately -8). The flux enhancements for the higher molecular weight polystyrene sulfonates with greater z values were more than a factor of three lower than theoretical predictions; the electrophoretic effect and counterion binding to the permeants are proposed as possible explanations for these discrepancies between experiment and the modified Nernst-Planck theory. In the studies with human epidermal membranes, iontophoretic flux enhancements for calcein, salicylate, and taurocholate were determined at 250 and/or 470 mV. The flux enhancements were generally consistent with the results calculated from the modified Nernst-Planck model.

The temperature dependence of in vitro permeation through human epidermal membrane (HEM) was determined for urea, mannitol, tetraethylammonium ion (TEA), and corticosterone. The effect of temperature upon HEM electrical resistance was also measured. The majority of the experiments involved measuring the permeability coefficients of a specific permeant at 27 degrees C and 39 degrees C for a given HEM sample, the electrical resistance was also measured at each temperature. Similar experiments were also conducted with a model synthetic porous membrane. The effect of temperature was quantitated as the ratio of the permeability at 39 degrees C to the permeability at 27 degrees C for each permeant. These ratios observed for HEM with urea, mannitol, and TEA as the permeants were 1.66 +/- 0.05, 1.76 +/- 0.14, and 1.71 +/- 0.11, respectively. The change in temperature was shown to have a similar effect upon the electrical conductance of the HEM samples. The observed ratio for corticosterone permeation was 4.5 +/- 0.4. The experimental ratios observed for the three polar/ionic permeants were shown to approach those obtained from the model porous membrane and differed greatly from the ratio observed for the more lipophilic corticosterone, indicating differences in the effective transport mechanism/pathway for these classes of permeants. The permeability of urea was also observed to be inversely proportional to the electrical resistance of the HEM samples; this relationship was shown to be independent of temperature over the temperature range studied. The temperature dependence data and the observed relationship between urea permeability and electrical resistance strongly support the existence of a porous permeation pathway through the HEM as an operative diffusional route for polar-ionic permeants.

The influences of 1‐ethyl‐, 1‐butyl‐, 1‐hexyl‐, and 1‐octyl‐2‐pyrrolidone in their saline solutions on the transport of β ‐estradiol, corticosterone, and hydrocortisone across hairless mouse skin under in vitro conditions have been investigated by the physical model approach. The experimental data were interpreted with a physical model that treats the stratum coneum as a diffusional barrier with a lipoidal pathway and a pore pathway. Enhancement factors ( E values) for the lipoidal pathway were calculated from the permeability coefficients and solubility data as a function of the 1‐alkyl‐2‐pyrrolione concentration for all three permeants. A pattern of increasing E values with increasing 1‐alkyl‐2‐pyrrolidone chain length was found, and the results were essentially the same for all three steroidal permeants. A nearly semilogarithmic linear relationship was also obtained between the enhancement potency and the carbon number of the alkyl chain; there was about an ∼ 3.5‐fold increase in the enhancement potency per 1‐alkyl‐2‐pyrrolidone methylene group. An important outcome of this research is that the enhancement potencies of the 1‐alkyl‐2‐pyrrolidones were essentially the same as those for the previously studied n ‐alkanols when compared at the same carbon numbers of the alkyl groups. This result is somewhat surprising as it suggests that the enhancer action resides (in its entirely) in the alkyl group, and the nature of the polar head group may not be intrinsically important in transdermal enhancement of the lipoidal pathway within a class of permeation enhancers.

Copolymers of polylactic acid (PLA) and polyglycolic acid (PGA) spontaneously form solid depots when a solution of the copolymer in a pharmaceutically acceptable solvent is injected into water. Key formulation variables which affect the performance of these systems were evaluated in the present study. The solubilities of various co-polymer ratios of PLGA were investigated as a function of the solvent solubility parameter, and it was found that the ideal range was 9–11 (cal/cm 3 ) 1/2 . The in vitro release into phosphate buffered saline of fluorescein-labeled bovine serum albumin was evaluated from systems dissolved in either dimethyl sulfoxide (DMSO) or N-methyl-2-pyrrolidone (NMP). For high molecular weight PLGA in NMP, the initial burst (which was found to be inversely proportional to polymer percent) is followed by zero-order release for up to 2 weeks. A significantly different release pattern is observed with DMSO. With low molecular weight PLGA in DMSO or NMP, it was possible to totally eliminate the initial burst, and have zero-order delivery for at least 1 week.

The in vitro passive transport of urea, mannitol, sucrose and raffinose across intact and ethanol treated human epidermal membrane was investigated. The intent of this study was to characterize the barrier properties and permeation pathways of these membranes for polar permeants under passive conditions. Based upon the relative permeabilities of these four solutes and hindered diffusion theory, the experimental data was adequately modeled for both membrane systems according to permeation through a porous membrane. Effective pore radii estimates for intact human epidermal membrane fell between 15 A to 25 A while similar estimates fell compactly between 15 A to 20 A for ethanol treated human epidermal membrane. Similarities between the relative permeabilities of human epidermal membrane for the four permeants studied and the relative permeabilities of these same permeants through ethanol pretreated human epidermal membrane indicate that significant similarities exist between the permeation pathways for both membrane systems. The results of this study have important implications for transdermal drug delivery in general and more specifically for strategies of designing effective chemical permeation enhancement systems.

In many cases it is instructive to use a single human epidermal membrane (HEM) sample to perform successive in vitro permeability experiments under varied experimental conditions. This study focused upon the feasibility of such successive permeability experiments in side-by-side, two-chamber diffusion cells. It was shown that for permeability experimental protocols which involved performing one permeability experiment per day and extensive washing between permeability experiments, the barrier properties of HEM samples were altered significantly within the first 72 h of the protocol. However, if the HEM is supported in the diffusion cell with a porous synthetic membrane, a single HEM sample remains essentially unaltered with respect to mannitol permeability and electrical resistance for up to 5 days. This suggests that protecting the HEM from physical stress is an essential element in performing successive permeability experiments.

Passive transport studies with net negatively charged model, porous membranes have shown that cationic solutes preferentially partition into the membrane relative to anionic solutes. In addition to direct electric field effects, iontophoretic transport studies with similar membranes have shown that convective solvent flow may increase the cationic solute flux, while impeding the anionic solute flux across the membrane. These observations show the importance of the electric potential within the membrane pores. The radial electric potential is a function of the surface charge density of the pore "wall" and the ionic strength of the electrolyte. The Poisson-Boltzmann equation may be used to describe the relationship between surface charge density and the electrical potential profile. In the present study, the transport pathways for charged and uncharged solutes were modeled as right cylindrical pores. Assuming a particular value for the surface charge density, the numerical solution to the Poisson-Boltzmann equation (in cylindrical coordinates) was solved to obtain the radial potential profile. This profile was then used to predict the electroosmotic velocity (at 0.1, 0.01, and 0.001 M ionic strengths) from the equations of fluid motion. Through comparison with experimental velocity data, a best estimate of the surface charge density was established and then used to predict the partition coefficients at each ionic strength. The surface charge density was found to be essentially independent of ionic strength with a mean value of 0.0068 C/m2. The predicted partition coefficients were in good agreement with the experimentally determined values which indicated that the surface charge density determined from the velocity calculations was a reasonable estimate.

Previous studies in our laboratory have shown that enhanced, constant permeant fluxes across human skin can be achieved by applying an alternating current (AC) to maintain skin electrical conductance at a constant level. Relative to conventional direct current (DC) iontophoresis, for which current is maintained at a constant level, this newly developed constant conductance alternating current (CCAC) method achieves constant fluxes with less inter- and intra-sample variability. The present study focused upon further investigating the permeability properties of human skin during CCAC iontophoresis at a variety of target resistance/conductance values. A three-stage experimental protocol was used with flux measurements determined on 3 consecutive days. Stage I was an AC only protocol (symmetrical AC square-wave signal), stage II was an AC plus DC protocol (AC square-wave with DC offset voltage), and stage III was a repeat of stage I. During this three-stage protocol, the skin electrical resistance was maintained at a constant target value by manually adjusting the applied AC voltage. Radiolabeled mannitol and urea were model permeants in all experiments. Their fluxes were determined and used to characterize the permeability properties of human skin. The results from the present study established that: (i) the CCAC protocol made it possible to reduce HEM electrical resistance to different target levels as low as 0.8 kΩ cm 2 and maintain the specific resistance level throughout the flux experiment, (ii) permeant fluxes are proportional to skin electrical conductance, (iii) under the studied CCAC passive conditions, membrane pore size tends to increase as skin resistance decreases, and (iv) as the membrane breaks down, its pore sizes become larger.

The purpose of the present study was to compare conventional constant direct current (DC) transdermal iontophoresis with a new constant conductance alternating current (AC) iontophoresis method. The new method was developed with the intent of reducing flux drift during iontophoresis and minimizing skin-to-skin variability. The constant conductance AC iontophoresis studies involved three electrical components: (1) an initial applied potential used to decrease the human epidermal membrane (HEM) electrical resistance to a target level of either 1.5 or 3.0 kΩ cm 2 , (2) an applied 50 Hz square-wave AC with a variable potential adjusted to maintain the HEM conductance at the target level during the transport study, and (3) a low voltage DC offset of 0 (passive), 0.25, or 0.40 V applied simultaneously with the AC to assist permeant transport. Current densities of 0.13 and 0.26 mA/cm 2 were chosen for the conventional constant current DC iontophoresis studies. Mannitol was used as the probe permeant for all studies. The constant current DC studies showed significant increases in mannitol flux with time during a given experiment and large skin-to-skin variability. Compared to the constant current DC experiments, the mannitol flux remained more constant during the constant conductance AC iontophoresis and skin-to-skin variability was significantly reduced. On a mechanistic level, changes in the transport properties during constant current DC iontophoresis indicate changes in the membrane parameters such as porosity, effective pore size, and/or pore surface charge density during the conventional method of iontophoresis. The results from the constant conductance AC iontophoresis transport studies imply that this method effectively maintains the membrane parameters that affect transport at a constant state this providing for a relatively constant permanent flux.

An experimental protocol, using an initial 1 min direct current (DC) applied potential of 4 V followed by alternating current (AC), was established to: (a) increase conductance and permeability and decrease lag time for human epidermal membrane (HEM) relative to unaltered HEM and; (b) maintain constant conductance and permeability during flux studies. The protocol allowed specific permeation parameters of the membrane to be characterized under electrically enhanced, constant flux conditions. The permeability, lag time, and effective membrane thickness were determined using a nonionic polar permeant, urea, while the enhanced conductance was maintained at a constant level with AC. A tortuous pore pathway model was employed to analyze the data. The AC protocol increased membrane permeability, and decreased lag time and effective membrane thickness relative to similar parameters obtained in previous studies from unaltered HEM. Lag times ranged from 32.0 to 105.5 min, and permeability coefficients calculated from steady state fluxes ranged from 1.68 to 6.03x10(-7) cm/s for HEM samples with electrical resistance values during transport of 2.3-8.0 kOmega x cm2. Effective membrane thicknesses were calculated to range from 0.34 to 0.61 cm during AC iontophoresis. Significant additional results were obtained when the protocol was applied for two consecutive runs using the same HEM sample, with time for the HEM sample to recover between runs. During the second run, the applied potential was adjusted to reproduce the conductance obtained on the first run. Under these conditions, the consecutive runs yielded essentially the same lag time, permeability and effective membrane thickness values. These results suggest that constant fluxes can be achieved by keeping HEM electrical conductance constant during AC iontophoresis.

It has been shown that significant pore induction (electroporation) occurs in human epidermal membrane (HEM) during iontophoresis even at moderate applied voltages (1–10 V). Recent efforts in our laboratory have been aimed at quantifying HEM electroporation by examining the proportionality between flux enhancement due to electroporation and electrical conductance changes during iontophoresis. The specific purpose of the present study was to test the hypothesis that by matching the background electrolyte ion sizes with the permeant ion sizes, the flux enhancement due to electroporation can be quantified by the change in HEM electrical conductance. In this study, radiolabeled tetraethylammonium (TEA+), methylammonium (MA+), and mannitol were the permeants. Potassium chloride (KCl), tetraethylammonium bromide (TEAB), tetraethylammonium pivalate (TEAP), and sodium fluoride (NaF) were the background electrolytes. Iontophoresis experiments were carried out over an applied voltage range of 1 to 3 V. The experimental flux enhancement results were compared with the theoretical predictions from the Nernst–Planck model after corrections were made: (a) for HEM pore induction during iontophoresis based on electrical conductance changes and (b) for electroosmosis employing mannitol as the neutral probe permeant. In experiments where the ion sizes of the background electrolyte and permeant were closely matched (e.g., TEA+ as the permeant and TEAP as the background electrolyte), there was excellent agreement between experimental results and theoretical predictions of the modified Nernst–Planck model, with only modest data scatter. When the electrolyte and permeant sizes were quite different (e.g., TEA+/KCl and MA+/TEAP), the experimental flux data were inconsistent with model predictions and there were large variations in the experimental results. The results of the present study illustrate that permeant flux enhancement can be predicted by the modified Nernst-Planck model even during moderate voltage iontophoresis when electroporation is operative. © 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:932–942, 2001

This study focused upon the enhancement effects of ionic surfactants upon passive and electroosmotic transdermal flux. The first phase of the study involved validating theories relating surface properties of a membrane to electroosmotic solvent flow under appropriate experimental conditions using a synthetic model membrane (stack of 50 Nuclepore membranes). Numerical solutions to the Poisson-Boltzmann equation and the equations of fluid motion served as the theoretical basis for the experimental studies. Important outcomes of the model membrane studies were that electroosmotic solvent flow velocity was enhanced by the addition of an anionic surfactant, sodium dodecyl sulfate, and reversed by the addition of a cationic surfactant, dodecyltrimethylammonium bromide. The effective membrane pore wall surface charge densities were determined under a variety of experimental conditions. Adsorption of dodecyl sulfate to the pore wall increased the net negative charge on the pore wall. A reversal of the net pore wall surface charge density resulted from the adsorption of dodecyltrimethylammonium. The interrelationship between electroosmosis, surfactant adsorption, and ionic strength was also evaluated. The second phase of the study was an investigation of the effects of sodium dodecyl sulfate upon the transport of neutral polar permeants through human epidermal membrane (HEM). Fluxes of [14C]urea and [3H]sucrose were simultaneously measured across HEM samples under passive and 250 mV conditions; flux measurements were made before, during, and after HEM exposure to sodium dodecyl sulfate. A systematic analysis of the experimental data made it possible to elucidate the specific contributions of sodium dodecyl sulfate and the applied electric potential to the overall flux enhancement. Sodium dodecyl sulfate enhanced the intrinsic passive permeability of the HEM, and it also enhanced the contribution of electroosmosis to the flux during iontophoresis.

□ This report describes the results of iontophoresis experiments involving the transport of polar nonelectrolytes across human epidermal membrane (HEM) at a moderate applied voltage of 2.0 V and where the data are interpreted via a convective transport model and hindered transport theory. A principal finding is that although HEM iontophoresis at 2.0 V resulted in a large increase in HEM porosity, the pore radii of the newly induced pores in HEM as calculated from the iontophoresis data using the hindered transport theory were found to be in the range of 6–12 A. This supports the view that electroporation at these modest applied voltages results in pores with sizes the same order of magnitude but somewhat smaller than those estimated for the preexisting pores in HEM prior to electroporation. This outcome is also important from a practical standpoint, as flux enhancement for large molecules (such as oligonucleotides and polypeptides) arising from electroporation under these conditions would be expected to be significantly less than if the resulting pore sizes were much greater. Providing a “prepulse” of 4.0, 8.0, and 15 V prior to the 2.0 V iontophoresis generally gave greater increases in HEM conductance (and, therefore, in porosity) but did not significantly change the deduced effective pore radii (around 5–9 A). The alteration during and the recovery of HEM after iontophoresis was also investigated. The recovery behavior was found to be dependent upon both the duration of the applied voltage and the magnitude of its effects: the recovery for a HEM sample that experienced a large increase in electrical conductance during iontophoresis was generally poorer than that for a sample that was more resistant to the electric field. Incomplete recovery was generally observed in experiments with long iontophoresis duration (50 min) and with the higher voltages (4.0, 8.0 V, and 15 V). In these cases, the barrier properties of HEM were more greatly altered as indicated by larger increases in the electrical conductance and passive permeability of HEM after iontophoresis.

This study focused upon quantitatively determining the influence of permeant molecular size upon flux enhancement which results from electroosmosis. The first phase of the study involved validation of a fundamental model describing the molecular size dependence of flux enhancement which results from convective solvent flow. This was accomplished using a model synthetic membrane (stack of 50 Nuclepore membranes) and four model permeants with a molecular weight range of 60–504 (urea, mannitol, sucrose, and raffinose). The steady-state flux of each permeant was determined under passive conditions and applied voltages of 125, 250, 500, and 1000 mV using side-by-side diffusion cells and a four-electrode potentiostat system. On the basis of the permeability enhancement for each permeant at each applied voltage (relative to the passive permeability) it was possible to calculate the effective solvent flow velocity from each permeant at each field strength. An important finding was that the flux enhancement due to electroosmosis was strongly molecular weight dependent (i.e., the flux enhancement ratio was around 4 times greater for raffinose than for urea, with mannitol and sucrose yielding intermediate values), while the calculated effective flow velocity at each voltage was independent of the molecular weight of the permeant. This coupled with a linear correlation between flow velocity and applied voltage served to establish the validity of the method and model. The second phase of the study was an extension of the model to human epidermal membrane (HEM). These experiments involved simultaneously measuring the fluxes of [14C]urea and [3H]sucrose across HEM samples under passive, 250 mV, and 500 mV conditions. Similar to the Nuclepore system, the observed flux enhancement ratios with HEM were approximately 3 times greater for sucrose than for urea. A detailed analysis of the HEM data showed semiquantitative agreement between predictions of the model and experimental results.