Blood flow measurements in skin and underlying tissues by microsphere method: Application to dermal pharmacokinetics of polar nonelectrolytes

RESEARCH ARTICLES

Blood Flow Measurements in Skin and Underlying Tissues by Microsphere Method: Application to Dermal Pharmacokinetics of Polar Nonelectrolytes

PARMINDER SINGH* AND MICHAEL s. ROBERTS**‘ Received Au ust 21, 1992, from the *Department of Pharmacy, The University of Queensland, Queensland, Australia 4072, and the *Depattment of Medicine, $he Univemity of Queensland, Princess Alexandra Hospital, Brisbane, Queensland, Australia 4 102. January 12, 1993.

Accepted for publication

Abstract 0 Blood flow rates to skin and underlying tissues in rats were determined by the radioactive microsphere technique. The dermal and local tissue clearance of two polar solutes, tritiated water and ‘‘C-iabeled sucrose, was assessed in anesthetized and sacrificed rats. The dermal clearance of tritiated water in the presence of viable dermal blood supply (6.1 7 f 1.41 mUminIlO0 g) was similar in magnitude but more variable than the blood flow to skin estimated by the microsphere technique (5.18 2 0.25 mUrnin/l00 9). The dermal clearance of sucrose (1.66 2 0.32 mUminll00 g) was approximately one quarter the dermal clearance for water, the difference corresponding to the free diffusion coefficients of the two solutes. The permeability coefficients of tritiated water in various tissues were estimated by both a pseudo-steady-state mass balance approach and numerical integration of differential equations (for dermis only) with a “series compartmental” model, from the tissue concentrations obtained in sacrificed rats. The estimates from numerical integration were comparable to those obtained by mass balance, confirming the general structure of the model. The obsenred tissue concentrations of tritiated water and sucrose in the anesthetized animal compared well with values predicted from the model.

Drugs may be applied topically to the skin either for a local effect in the skin or for a systemic effect.l.2 Although pharmacokinetic models have been proposed for modeling trans- dermal drug delivery,- little is known.about dermal pharmacokinetics,e.7 and limited information is available for a species penetrating locally as a function of depth into the skin and underlying tissues.8 The blood flow values to skin9 and underlying tissues should be known in order to understand dermal pharmacokinetics and local tissue distribution of topically applied drugs. The microsphere method of HalesloJl was employed to quantitate blood flow to skin and underlying tissues [i.e., subcutaneous tissue, fascia, superficial muscle or muscle lining, muscle, fat pad, and deep muscle (below the fat pad)] in rats. This method assumes that microspheres are trapped in arterioles in the first pass through circulation, are distributed in proportion to the cardiac output, and have no effects on the hemodynamics.

The approach of using clearance of freely diffusible indica- tors from a local injection site to measure local blood flow is alreadyestablished.1zAn inert gas like ‘“Xe is injected in the region of local tissue or organ, and its clearance is monitored by a scintillation counter. The disappearance rate is a function of local blood flow and thus measures blood flow in the particular organ or tissue.13 The dermal clearance of tritiated water was examined based on the above hypothesis and compared with the blood flow to skin observed with the microsphere method. The placement of the drug solution on the exposed dermis in vivo avoids the stratum corneum barrier and simulates perfect delivery to the dermis. Delivery

of solute to underlying tissues then occurs by the processes of diffusion and tissue perfusion. The relative contribution of direct diffusion to tissue perfusion will be determined by variables such as the physicochemical properties of the solute, local blood flow in the tissues, tissue plasma partitioning, and changes in the systemic clearance of the solute. Lipophilic solutes, such as lidocaine, can penetrate deep into the underlying tissues, whereas ionized solutes such as salicylate, are effectively removed by the dermal blood supply.14

In this study, the blood flows to individual tissues below a dermal application site were quantified with microspheres. The disappearance of tritiated water and sucrose from solutions applied to the exposed dermis was then monitored in anesthetized and sacrificed animals. A pharmacokinetic model for local tissue penetration and distribution into the systemic blood was developed, and the predictions of tissue concentrations based on blood flows and apparent tissue- tissue clearances were validated with experimentally obtained tissue concentrations.

Theoretical Section Model Development-The pharmacokinetic model pro-

posed to describe local tissue penetration of a polar neutral compound after its dermal application is presented in Figure 1. Each tissue can be described as a compartments-in-series, each joined in parallel to a central plasma compartment. According to this model, solute diffuses to the ith tissue compartment from the tissue compartment overlying it (i + 1) and into the tissue compartment underlying it (i - 1). Distribution into the plasma compartment is defined by the blood supply to individual tissues. The differential mass balance equations were then written for each compartment to describe the inflow, outflow, and disappearance of the drug assuming: (1) a pseudo equilibrium exists between a given tissue and the blood perfusing that tissue, (2) lateral spread of a solute from below the applied site is negligible, and (3) the apparent partition coefficient between tissues is unity.

The rate of change in the amount of solute in the cell compartment (Figure 1) at any time is defined by eq 1:

In eq 1, ks4 is the transfer rate constant between cell solution and dermis (h-’), Ad is the amount of solute in dermis, A, is the amount of solute in solution, and kd is the dermialwater partition coefficient.

Given that a monoexponential decline was observed for the concentrations in solutions applied to the dermis of anesthe-

OO22-3549/93/0soO-O873$02.50/0 0 1993, American Pharmaceutical Association

Journal of Pharmaceutical Sciences I 873 Vol. 82, No. 9, September 1993

1 Figure 1-A pharmacokinetic model for local tissue penetration of dermally applied nonelectrolytes. Refer to text for meaning of various terms.

tized rats, the backward flux from dermis to cell was ne- glected. The integrated form of eq 1 with an assumed negligible backflux is shown in eq 2:

A, = A,exp(-k,,dt) (2)

In eq 2, A, is the amount of solute in the cell solution at time zero. Equation 2 may also be expressed in terms of the concentration of solute in solution at any time, C,, and the original concentration, C,, by noting that A, = V,Cs and A, = V,C,, where V, is the volume of the solution.

The rate of change in the amount of solute in the dermal compartment is given by eq 3:

subcutaneous tissue. It is convenient to express eq 3 in physiological pharmacokinetic notation by defining the clearance of solute between dermal absorption cell and dermis as cL,,d (mL/h) and the clearance of solute between dermis and subcutaneous tissue as CLd,, (mL/h). It should be noted that the following equalities also exist: ksud V, = cL,,d, kdu, vd

where C, is the concentration in subcutaneous tissue, and vd and V, are the apparent volumes (mL) of dermis and subcutaneous tissue. Equation 3 can now be re-expressed in the following form:

= CLdu,, kd-, v, = CLd-,, & = c d vd, and A, = CSC v,,

The rate of change of concentration in all deeper underlying tissue compartments with time for the model in Figure 1 can be described by eq 5:

In eq 5, VT,i is the apparent volume of ith tissue (mL), CL,,,,,, is the clearance between i + 1 tissue and ith tissue (mL/h), CLT.i-i-1 is the clearance between ith tissue and i - 1 tissue (mL/h), CT,i is the concentration in the ith tissue (fraction of initial concentration), C,,, is the concentration in the i + 1 tissue (fraction of initial concentration), CT.i-1 is the concentration in the i - 1 tissue (fraction of initial concentration), and QT,i is the blood flow to the ith tissue (mL/h/g).

In the absence of blood flow (i.e., sacrifid animal), each solute moves between tissues solely by diffusion. The solute concentration in the solution adjacent to the dermis in the sacrificed animal shows a systematic deviation from a single exponential decline (Figure ZA). The negligible dermal backflux assumption used for anesthetized rat was therefore not appropriate in this modeling. The mass balance equations in the absence of viable blood supply, for the solution in the dermal absorption cell and the ith tissue, are then given by eqs 6 and 7:

(3) Convergence of the nonlinear regression modeling of eq 7 was not achieved in the deep tissues of the sacrificed animal

tion), Cd is the concentration of solute in dermis (fraction of initial concentration), and A, is the amount of solute in cLT. i+l - i (cT. i+ l - c T , i ) = CLT.i-i-l(CT.i - cT. i -1) (8)

874 I Joumal of Pharmaceutical Sciences Vol. 82, No. 9, September 1993

- P

1 C

t

CID 0 a

1.6 ‘ I , I

0 4 0 8 0 1 2 0

45-8 period while a reference blood sample was withdrawn from the femoral artery at a constant rate of 0.68 mWmin (Harvard infusion- withdrawal pump). The pressure was monitored before and after the infusion to ensure that the infusion and blood withdrawal did not affect the arterial pressure. The animal was then sacrificed with an overdose of anesthetic ether, and tissues of interest were subse- quently removed.

Blood flow to different tissues and the cardiac output were determined as follows:10

Tissue blood flow (mWmin/lOO g) =

withdrawal rate of blood x tissue cpm

cpm in withdrawn blood (9)

2.02 c B

1.00 0 4 0 8 0 1 2 0

Time (mln.)

Figure 2-(A) Disappearance versus time profile of tritiated water from a solution applied to rat dermis. (B) Disappearance versus time profile of sucrose from a solution applied to rat dermis. Key: (0) sacrificed animal; (0) anesthetized animal. Values are reported as mean f SD (n = 4).

Experimental Section Chemicals and Instruments-[14C]Sucrose (632 mCi/mmol), tri-

tiated water (1 mCi/g), and the microspheres, 15 * 3 (mean fi SD) pm diameter, labeled with either [llsSnl or [“Sc] were purchased from New England Nuclear, Wilmington, DE. Sucrose was from Sigma Chemical Company, St. Louis, MO. Liquid scintillation cocktails BCS (biodegradable counting scintillant) and OCS (organic counting scintillant) and tissue solubilizer (NCS) were purchased from Amer- sham International, England. All other reagents used were of analytical grade.

Zimmer’s electrodermatome (model 901, USA) was used for removing rat epidermis. A liquid scintillation counter (Tri-carb 4000 series, United Technologies Packard, La Grange, IL) and a gamma spec- trometer (model 5325, Packard, La Grange, IL) were used to deter- mine radioactivity in the samples.

Animals-Male Wistar rats (300450 g) were used in the studies. The animals were housed under standard laboratory conditions of 20.0 f 0.5 “C and 55-75% relative humidity and were supplied with normal pellet diet and water ad libitum. All experiments had previously been approved by the Animal Experimentation Commit- tee of the University and Princess Alexandra Hospital.

Blood Flow Measurements-The animal was anesthetized with pentobarbitone (35 mgkg) and placed on its side; the body temperature was maintained at 37 “C with a heating pad. For injection of microspheres, a polyethylene catheter (i.d., 0.58 mm; o.d., 0.97 mm) was passed into the left cardiac ventricle via the right common carotid artery. The characteristic pattern of pulse pressure was used as an index of location of the tip, and a catheter was placed in left common carotid artery for recording the blood pressure. A femoral artery was catheterized for withdrawing “microsphere reference” sample.11 Ra- diolabeled microspheres were injected into the left ventricle over a

Cardiac output (mL/min/100 g) =

dose (cpm) x withdrawal rate of blood cpm in withdrawn blood

(10)

The total amount of radioactivity (cpm) injected was determined by subtracting residues in the syringe from the original dose. The radioactivity in blood (cpm) was determined by adding the amount of radioactivity in the blood sample and in the syringe used to collect the blood sample.

In Vivo Dermal Penetration and Local Tissue Uptake Studies (Anesthetized Animals)-The rats were lightly anesthetized with pentobarbitone (35 m a ) , and their body temperature was maintained at 37 “C by placing them on a heating pad. The hair from the 4-cma dorsum area was removed with electric clippers, and the epidermis was removed by means of an electrodermatome set at a thickness of 80 pm.14 A glass cell (i.d., 1.8 cm) was then adhered to the exposed dermis and warmed to 37 “C with an external heating device.2-14 A solution of tritiated water or sucrose previously warmed to837 “C was introduced into the dermal glass cell, and the solution was stirred by a glass stirrer driven by an external motor.

Samples were removed from the dermal cell at predetermined times and placed in preweighed scintillation vials. The glass cell containing drug solution was removed from the rat dermis at 2 h post application, and the application area was wiped dry with blotting paper. A blood sample was then taken from the tail vein, and the animal was sacrificed with an overdose of anesthetic ether. Immediately there- after, the tissues below the treated site (i.e., dermis, subcutaneous tissue, fascia, muecle lining or superficial muscle, muscle, fat pad, and deep muscle) were dissected and placed in preweighed scintillatibn vials.14 The dissecting scissors and forceps were thoroughly cleaned after each tiseue separation to prevent any cross contamination between diferent tiseue layers. Similar tissues from the contralateral side were also removed. Tissue and plasma samples were stored at -20 “C prior to analysis.

In V i o Dermal Penetration and Local Tissue Uptake Studies (Sacrificed Animals)-The rats were initially anesthetized with an intraperitoneal injection of pentobarbitone (35 m e ) and, after removing epidermis as described above, were d c e d by an overdose of anesthetic ether. Dermal perfusion studies were then con- ducted in post mortem rats.

Clearance (CL) of either water or sucrose into the dermis was estimated from the plot of percent solute remaining in the dermal cell versus time using eq 11:

CL = kV (11)

In eq 11, k is the disappearance rate constant, and Vis volume (mL) of the solution applied to the dermis.2.14 The contribution of the clearance due to blood supply was estimated by subtracting dermal clearance obtained in Bacrificed animals (clearance due to diffusion) from that obtained in anesthetized animals.

Zero time samples from the cell were used to represent the initial solution concentration and tritium and carbon-14 activity in the tissues and plasma converted to fraction of initial solution concentration (concentration fraction) .I4


In Vitro Dermal Absorption Studies-Human skin was obtained from the midabdominal region of cadavers. The epidermis was separated from the dermis by the heat method.15 Isolated human dermis was mounted in side-by-side glass diffusion cells and sub- merged in water bath at 37 "C. Isotonic phosphate buffer (pH 7.4) was added to the receptor compartment, and the solution of the solute in isotonic phosphate buffer (pH 7.4) was added to the donor compartment. Samples were removed from the receptor side at predetermined times and analyzed for either tritiated water or sucroe.

The cumulative amount of tritiated water or sucrose appearing in the receptor side was plotted against time. The slope of the linear portion of the plot gave the steady-state flux that, when divided by initial concentration, gave the permeability coefficient.16

Analysis of Radioactivity-Aqueous samples removed from the glass cells in in vivo dermal and in vitro dermal penetration studies were directly mixed with 5 mL of liquid scintillation cocktail BCS and counted on liquid scintillation counter. The tissue samples were solubilized with 50 pL of water and 1 mL of tissue solubilizer NCS at 50 "C for 6-8 h. After cooling the digested eamples to room temperature, 0.03% of glacial acetic acid was added to each tissue sample followed by 10 mL of organic scintillant OCS.14 The plasma samples were solubilized with tissue solubilizer (five parts for one part of plasma) at room temperature and treated with glacial acetic acid. Tissues, blood samples, injection syringes, cannula, etc. in the microsphere method were assayed with a well-type gamma spectrom- eter for 10 min each. Each observation is a mean f SD of three to four determinations.

Data Analysis-The apparent tissue clearances were estimated by a pseudosteady-state mass balance approach, according to eq 8, from the tissue concentrations obtained in sacrificed rats. Apparent clearance for dermis was also deduced from the model by numerical integration of eqs 6 and 7, by fitting tritiated water data obtained in sacrificed rats, using the MINIM computer program.17 The MINIM computer program17 was also used to numerically integrate eqs 2,4, and 5, assuming experimentally obtained blood flow rates and apparent tissu+tissue clearances from sacrificed animals as con- stants. To estimate the muscle concentrations, eq 5 was numerically integrated for subcutaneous tissue, fascia, superficial muscle, and muscle with polynomial input function representation of the predicted solute concentrations in the dermis-time profile. The estimates for solute concentrations in the tissues were compared with the experimentally determined values. The final model fitting was deemed acceptable based on the regression goodness of fit criteria that included the Akaike information criteria (AIC),18 a lack of systemic deviations in the residuals, and a high regression coefficient (1.2 > 0.9).

Results and Discussion The blood flow values to skin and underlying tissues

obtained in rats with microspheres are given in Table I. The arterial blood pressure was unafFected by left ventricle cath- eterization and by infusion of microspheres and withdrawal of reference samples. The mean blood pressure was 92 k 13 mmHg. The flows to the left and right kidneys were not significantly different and provide verification of an adequate distribution of microspheres. The mean cardiac output was 35.8 k 3.4 mL/min/100 g. The observed blood flow values agree well with the previously reported values in skin (5-7

Table I-Blood Flow In Skin and Underlylng Tlssues In Anesthetlzed Rats Estimated with Microspheres

Tissue

Skin Subcutaneous tissue Fascia S. muscle Muscle Fat pad Deep muscle Heart Kidnev

Blood Flow, mUminIlO0 ga

5.18 2 0.25 3.59 & 0.24 3.10 f 1 .OO 6.92 2 0.45 7.13 f 1.36 0.59 f 0.20 5.42 f 1.04 482 2 102 256 f 40

Depth from Skin Surface, mm

2.5 4.0 5.0 6.0 8.0

12.0 15.0

b - -

a Mean 2 SD. -, Not determined.

mWmin/lOO gig), muscle (6-8 m4mid100 g19, kidney (255- 264 mumin per 100 PO), and heart (420620 mL/min/100 g20-22).

Figures 2A and 2B show the percent tritiated water or sucrose remaining in dermal absorption cell with time in anesthetized and dead rats. The dermal clearances for sucrose and water were 99 times higher in anesthetized rat than in the dead rat (Table 111, confirming the importance of dermal blood flow in clearing topically applied compounds.2~23~2~ Clearance of tritiated water or sucrose applied to the dermis of sacrificed rat occurs mainly by diffusion, whereas in anesthetized rat, clearance is due to both diffusion to deeper tissues and removal by blood supply. The difference in dermal clearances between sacrificed and anesthetized animal should therefore represent the clearance due to the viable blood supply.23,24 The dermal clearances for tritiated water and sucrose in anesthetized and sacrificed animals are given in Table 11. The dermal clearances of tritiated water due to removal by blood flow was 6.17 mL/min/100 g. This value agreed closely with the observed blood flow to dermis (5.18 mL/min/100 g) determined by the microsphere method. Hence, dermal clearance of tritiated water in the presence of viable blood supply closely reflects blood flow to the skin.

The dermal clearance of sucrose in the presence of viable blood flow was 1.66 mL/min/l00 g, which is approximately one-fourth of that for water. The difference between the dermal clearances for tritiated water and sucrose can be interpreted in terms of difference in the molecular size of the two solutes. The dermis is essentially aqueous in nature,26,26 and the mobility of water through dermis has been reported to be comparable to that through a layer of stagnant water.27 For a sphere of radius r diffusing in a continuous fluid, the diffusion coefficient D is given by the Stokes-Einstein equation:

In eq 12, K is the Boltzmann constant, T is the absolute temperature, and 7 is the coefficient of viscosity of the medium.28 The Stokes-Einstein molecular radii for sucroae and water have been reported to be 4.81 x lo-' and 1.17 x lo-' cm, respectively, and corresponding free diffusion coefficients in water at 37 "C are 0.675 x cm2/s for sucrose and 2.78 x cm2/s for water.29 The diffusion coefficient for water is thus four times that for sucrose, whereas the molecular radius is four times smaller than sucrose.

The permeability coefficient across rat dermis in vivo (k,) is defined by the clearance (CL,) divided by the area of application (A) and is related to diffusion coefficient by eq 13:

(13)

In eq 13, K, is the partition coefficient of the solute between the membrane and solvent, D , is the diffusion constant of the solute in the membrane, and h is the thickness of membrane.27 Given that the partition coefficients for a series of

Table Il-Clearance Into the Rat Dermls ( C W

CL, (anesthetized), CL, (sacrificed), CL, (blood flow), mUminll00 g mUh mUh Solute

Water 1.10 f 0.24 0.36 f 0.02 6.1 7 f 1.41 Sucrose 0.32 f 0.02 0.12 f 0.04 1.66 f 0.32

eMean -c SD.

876 I Journal of Pharmaceutical Sciences Vol. 82, No. 9, September 1993

nonelectrolytes across isolated dermis have been reported to be constant,26 the permeability coefficient of a compound (or dermal clearance) across a given thickness of rat dermis in vivo should depend on the diffusion coefficient of the applied solute within the membrane. A difference in the dermal clearance (or permeability coefficient) value of approximately four between water and sucrose (Table IT) corresponds to the fourfold difference in the diffusion coefficient (or molecular radius) for the two solutes. A similar size dependency has been reported for drug absorption for both muscle and subcutaneous tissue.30.31 Variations in the water and sucrose dermal clearances (Table 11) probably reflect variations in the thickness of dermis between individual rats or variability introduced during manual removal of epidermis by the electrodermatome. Such variability was not present for water and sucrose in isolated human dermis from the same specimen (thus uniform thickness), the permeability coefficients of tritiated water and sucrose being 0.058 f 0.006 and 0.014 2 .003 cm/h, respectively, representing a fourfold difference that is consistent with earlier observation.

Figures 3A and 3B show the local tissue distribution of tritiated water and sucrose as a function of tissue depth following dermal application in anesthetized and sacrificed rats. The high concentrations of water and sucrose in the

Tr A

.1 1 1 I 1 I I I I

0 2 4 6 8 1 0 1 2

= .01 - g .w1 - e

.oO01 -

B

1

.ooOol' I I 1 I

0 2 4 6 8 1 0 1 2

TISSUE DEPTH (mm)

Figure *(A) Tissue distribution of tritiated water after application to rat dermis. (B) Tissue distribution of sucrose after application to rat dermis. Key: (B) underlying tissues in Sacrificed animal; (0) underlying tissues in anesthetized animal; (0) contralateral tissues in anesthetized animal. Values are reported as mean f SD (n = 4).

underlying tissues for sacrificed animal relative to anesthetized animal reflect the absence of the blood supply and the diffusion of the solutes to regions below the application site. The levels of sucrose in underlying tissues were less than those for water in both anesthetized and sacrificed rats, which is consistent with the difference in their molecular sizes. The concentrations of tritiated water and sucrose in underlying tissues were an order higher than similar tissues on the contralateral side, suggesting direct transport of the two solutes immediately beneath the application site. The observed fractions for tritiated water and sucrose in plasma were 0.0059 f 0.0015 and 0.0017 5 0.00012, respectively (i.e., a waterlsucrose ratio of -3.5). It is therefore evident that the uptake of both solutes into the blood is predominantly limited by diffusion.

The permeability coefficient of water in the dermis can be estimated by either nonlinear least square regression analysis or by a pseudo-steady-state approximation, in which dCJdt in eq 6 is assumed to be zero to yield

Comparable values are obtained for the two methods (Table 1111, justifying a pseudo-steady-state approach when regreasion estimates could not be obtained. Establishment of pseudo-steady state was further validated at 4 h time, when the concentration fractions obtained in underlying tissues (0.34-0.04) were comparable with those at 2 h (0.39-0.05). The calculated values of the apparent clearance, permeability coefficient, and diffusion coefficient of water for various tissues are given in Table III. The W o n coefficients were estimated with eq 13, with the approx- imate thickness of each tissue as given in Table I and assuming a dermis-water partition coefficient for tritiated water of 0.62s and unity for other tissues. The water permeability and diffusion coefficients for dermis agree closely with the reported values of 1.66 x and 6.9 x lop6 cm2/s, respectively.26 The water permeability coefficient of m w l e is similar in order to the reported value of 28 x lo-' cm/s32 for the muscle capillary membranes. Given that the permeability coefficient of sucrose in muscle capillary membranes is -4.9 x cm/s,s the water- sucrose permeability coefficient is estimated to be 4.68 for muscle, which is similar ta the free difFusion coefficients ratio.

The permeability coefficients derived by the pseudo-steady- state method in the sacrificed rat and blood flow values obtained with microspheres in anesthetized rats were then used as parameters in the "series compartmental" model, and the concentrations of tritiated water in the underlying tissues of anesthetized rats were predicted. The predicted concentrations compared well with the experimentally determined values (Figure 41, validating both the blood flow values and estimated permeability coefficients.

When the permeability coefficients for sucrose in each tissue are assumed to be one quarter that for water (in accordance with the difference in their free diffusion coefficients), the predicted concentrations of sucrose in the underlying tissues of the anesthetized rat 2 h post dermal application also compare well with the observed values (Figure 51, providing further validation of the approach.

The relative contributions of tissue diffusion and perfusion in removing a dermally applied solute can be estimated from the estimated clearance due to diffusion (CLdiff,,) and the blood flow to individual tissue (QT.i, eq 15) and are shown in Table Iv:

Percent contribution of tissue diffusion

CLdiff~.i

cL&ffT.i i- QT.i - -


Table Ill-Apparent Clearance, Permeablllty Coefflclent, and Dlffuslon Coefflclent of Water for Dlfferent Tlssues in the Rat.

% Thickness, Apparent Apparent Permeability ApparentDMm Apparent Permeabil mmb Clearance, mUhc coefficient, cm/s (x l md Coefficient, cm2/s (x 1 @)e Coefficient, cmls (x 10 )' Tissue

Dermis 2 0.36 2 0.02 3.94 f 0.22 1.31 f 0.07 5.44 2 2.54 f 0.81 27.78 f 8.86 5.56 -+ 1.77 9 Subcutaneous 1 0.73 f 0.19 7.98 f 2.08 0.80 f 0.21 - Fascia 1 0.61 f 0.16 6.67 f 1.75 0.67 k 0.18 - S. muscle 2 2.10 2 0.60 22.97 f 6.56 4.59 f 1.31 - Muscle

Fat pad 4 0.33 f 0.10 3.61 ? 1.09 1.44 f 0.43

* Mean ? SD. From ref 14. Estimated by pseudo-steady-state approach with eq 8 and the data from sacriiced rats (Figure 3a). Estimated with eq 13. Estimated with eq 13 assuming a partition coefficient of 0.6 for dermis2' and unity for other tissues. Estimated by nonlinear regression analysis of data in Figure 3a for sacrificed animal. g-, Not determined.

-

0.01

0

0.M

Table IV-Relative Contrlbutlons of Dlfhralon and Pertuslon In Tlssue Penetratlon of Water and Sucrosea

Water Sucrose Diffusion, % Perfusion, % Dision, % Perfusion, %

Tissue ~~~~ ~ ~

Dermis 37 63 16 84 Subcutaneous 54 46 22 78 Fascia 28 72 .9 91 S. muscle 16 84 5 95 Muscle 33 67 11 89 Fat Dad 42 58 15 85

DERMIS SUBCUT FASCIA MUSCLE

TISSUE

Flgure Moncentration fraction of tritiated water in underlying tissues after application to anesthetized rat dermis in vivo. Key: (0) observed; (B) predicted from the model.

IT L

0.02 - 0 t; E 4

DERMIS SUBCUT FASCIA MUSCLE

TISSUE

Flgure 5-Concentration fraction of sucrose in underlying tissues after application to anesthetized rat dermis in vivo. Key: (0) observed; (B) predicted from the model.

According to Table IV, the dermal diffusion accounts for -37% and 17% ofthe dermal clearance for tritiated water and sucrose, respectively. A similar contribution was observed when dermal clearance of either tritiated water or sucrose in the sacrificed animal (clearance due to diffusion) was divided by its respective clearance in the anesthetized animal (clearance due to both diffusion and blood perfusion; Table 111, which also indirectly validates the blood flow values.

In comparison with the excised skin studies, the experimental technique used in this work involves a viable micro- circulation and dermis, thus providing a more realistic in- sight into the processes of absorption and disposition of topically applied solutes. The value of viable skin microcir- culatory and metabolic systems (as compared with excised

a Estimated with eq 15.

skin slab) in studying the disposition of topically applied solutes has also been recognized by other workers.2,23,2**3a6 The experimental and pharmacokinetic model described in the present work is an initial attempt at understanding and predicting the local disposition (as a function of tissue depth) of topically applied polar nonelectrolytes. Future work should be directed towards extending and applying the present approach to other solutes like anesthetics, steroids, and nonsteroidal anti-inflammatory drugs.

Conclusion-Blood flows to skin and underlying tissues have been determined with radiolabeled microspheres. The results indicate that dermal clearance of tritiated water in the presence of viable blood flow reflects the observed blood flow to skin, and therefore validates the microsphere method of blood flow measurement. The clearance of tritiated water can be used to assess blood flow to local tissues such as skin and subcutaneous or muscle, though it is not truly noninvasive. The permeability coefficients of polar noneledrolytes in tissues appear to be related to their free diffusion coefficients. The concentrations of polar nonelectrolytes in deeper underlying tissues after their dermal application can be predicted by a pharmacokinetic model in which the blood flows and permeability coefficient values of water for individual tissues are known parameters.

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193-203. 3. Chandrasekaran, S. K.; Bayne, W.; Shaw, J. E. J. Phunn. Sci.

1978,67,1370-1374. 4. Guy, R. H.; Hadgraft, J.; Maibach, H. I. Znt. J . Phann. 1982,11,

119-129. 5. Kubota, K.; Ishizaki, T. J. Phurmacokinet. Bwphann. 1986,14,

40-39. 6. Barry, B.W. In Dru Delivery Systems: Fundamentals and

Techniques; Johnson, #.; Lloyd-Jones, J. G., Eds.; Ellis Horwood: England, 1987; pp 200-223.

7. Carver, M. P.; Williams, P. L.; Riviere, J. E. ToxkoZ. Appl. Pharmacol. 1989,97,324-337.

8. Guy, R. H.; Maibach, H. I. J. Phann. Sci. 1983, 72,13761380. 9. Riviere, J. E.; Williams, P. L. J. Phann. Sci. 1992,81,601-602.

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Acknowledgments This work was sup rted by the National Health & Medical

Research Council of A",stralia. MSR acknowledges the generous sup rt of Queensland and Northern New South Wales Lions Kidney an&edical Research Foundation. We are grateful to J. R. S. Hales and A.A. Fawcett for assistance with the microsphere measurements.

Journal of Pharmaceutical Sciences 1 879 Vol. 82, No. 9. SeDtember 1993

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