SIDE BY SIDE CELL Magnetic engine DonorReceiver Teflon adapter solid drug membrane stirrer Thermostatic unit jacket pump surge chamber spectrophotometer computer

2 - DRUG DIFFUSION MEASUREMENT MAGNETIC STIRRERS TEFLON ADAPTER DONOR CHAMBER RECEIVER CHAMBER THERMOSTATIC JACKET

DONOR RECEIVER STIRRER jacket POWDER DISSOLUTION DRUG PERMEATION DRUG CONCENTRATION INCREASE 2 - MODELING

MATHEMATICALL MODELING

SOLID SURFACE VARIATION: MONODISPERSED PARTICLES SYSTEM Particles initial surface area SOLID DRUG

1 st stagnant layer membrane 2 nd stagnant layer FICK LAW

BOUNDARY CONDITIONS

SIMULATION: NO DISSOLUTION V r = V d D 1 = 8.8*10 -6 cm 2 /s D m = 5.3*10 -6 cm 2 /s D 1 = D 2 K p = 0.8 *h m H = Stagnant layer thickness *h m h m = 100  m S = 10 cm 2

SIMULATION: PROFILE CONCENTRATION V r = V d D 1 = 8.8*10 -6 cm 2 /s D m = 5.3*10 -6 cm 2 /s D 1 = D 2 K p = 0.8 h 1 = h 2 = 0.5*h m h m = 100  m S = 10 cm 2

SIMULATION: DISSOLUTION V r = 800 cm 3 D 1 = 8.8*10 -6 cm 2 /s D m = 5.3*10 -6 cm 2 /s D 1 = D 2 K p = 0.8 V d = 100 cm 3 h 1 = h 2 = h m =100  m K d = cm/s A = 5000 g/cm 2 C s =  g/cm 3 S = 10 cm 2

SIMULATION: STEADY STATE APPROXIMATION C d = C d0 (constant drug concentration in the donor) C r = 0 (sink conditions in the receiver) FICK eq. solution (only membrane) is: For t∞ Membrane Permeability

For a trilaminate system the solution is: For t∞

SIMULATION: LINEAR PROFILES (THIN MEMBRANES)

EMPIRICAL APPROACH

3 - DRUG DIFFUSION COEFFICIENT MEASUREMENT REQUIRES THE DETERMINATION OF: 1 DRUG SOLUBILITY C S IN THE RELEASE ENVIRONMEMT 2 DRUG DIFFUSION COEFFICIENT D W IN THE RELEASE ENVIRONMEMT 3 DRUG POWDER DISSOLUTION CONSTANT K DP 4 DRUG PARTITION COEFFICIENT K p (MEMBRANE/RELEASE ENVIRONMENT) 5 THICKNESS OF STAGNANT LAYERS SANDWICHING THE MEMBRANE

CASE STUDY: THEOPHYLLINE AND ALGINATES THEOPHYLLINE MONOHYDRATED - Carlo Erba, Milano - (C 7 H 8 N 4 O 2 *H 2 O); MW 198, WHITE CRYSTALLINE POWDER - DENSITY 1.49 ± 01 g/ cm 3 (Helium picnometer) - SURFACE AREA = 2941 cm 2 /g (mercury porosimeter) - U.V. PEAK ABSORBANCE 271 nm ALGINATE: - Protanal LF 20/ 60, Pronova Biopolymer, Drammen, Norway) - THEY ARE EXTRACTED FROM BROWN SEAWEED - SEQUENCE OF GULURONATE AND MANNURONATE (LF 20/60: 70% GULURONATE) - THEY FORM STRONG PHYSICAL GELS IN PRESENCE OF DIVALENT IONS (TYPICALLY Ca ++ )

Ca ++ EGG BOX CONFIGURATION

1 DRUG SOLUBILITY C S IN THE RELEASE ENVIRONMEMT C s = ± 104  g/cm 3 ( DISTILLED WATER 37°C) 2 DRUG DIFFUSION COEFFICIENT D W IN THE RELEASE ENVIRONMEMT K d = 0.62*D W 2/3  1/2 * -1/6 D W = (8.2 ± 0.6)*10 -6 cm 2 /s ( DISTILLED WATER 37°C) IDR

3 DRUG POWDER DISSOLUTION CONSTANT K DP Magnetic engine Donor solid drug jacket SEALING TAPE

- SINK CONDITIONS - N p MONOSIZED SPHERICAL PARTICLES (R p0 INITIAL RADIUS) t = 0 R p0 t > 0 RpRp DISSOLUTION PARTICLES SURFACE M d = drug amount in the donor (soluble) M p = solid particle mass

A = Particles initial surface area M p0 = initial particles mass

K DP = 1.2*10 -3 cm/s

4 DRUG PARTITION COEFFICIENT K p (MEMBRANE/RELEASE ENVIRONMENT) Cylindrical gel ( DISTILLED WATER 37°C) IDR C 0 = 20  g/cm 3 V VgVg 24 hC∞C∞ M 0 = V*C ∞ +V g * C g∞ K p = C g∞ /C ∞

5 THICKNESS OF STAGNANT LAYERS SANDWICHING THE MEMBRANE DonorReceiver MEMBRANE stirrer jacket stirrer STAGNANT LAYER

Donor DRUG jacket stirrer h ss = 60.7  m STAGNANT LAYER

4 - RESULTS - Model - Linear approximation Experimental data V r = 100 cm 3 D m = (5.1± 0.64)*10 -6 cm 2 /s V d = 100 cm 3 S = 10 cm 2 %P = 4

T = 25°C 1% 2% 4%

T = 37°C 1% 2% 4%

MEMBRANES CHARACTERISTICS

DIFFUSION COEFFICIENTS