SIDE BY SIDE

CELL

Magnetic engine

Magnetic engine

Donor Receiver

Teflon adapter

solid drug

membrane

stirrer

Thermostatic unit Thermostatic unit

jack

et

jacket

pump

surge chamber

spectrophotometer

computer

2 - DRUG DIFFUSION MEASUREMENT

MAGNETIC STIRRERS

TEFLON ADAPTERDONOR CHAMBER RECEIVER CHAMBER

THERMOSTATICJACKET

DONOR RECEIVER

STIRRER

jac

ke

t jack

et

POWDER DISSOLUTION

DRUG PERMEATION

DRUG CONCENTRATION INCREASE

2 - MODELING

dissolution

(K t)

solid drug (M )

donor 1st

layer 2nd

layermembrane receiver

X = 0

concentration profile

h 1 h 2 h 3

X = h 1 X = h 1+ h 2 X = h 1+ h 2+h 3

MATHEMATICALL MODELING

SOLID SURFACE VARIATION: MONODISPERSED PARTICLES SYSTEM

20P0 4 RNA

A

R3

0

Particles initial surface area

330

0

4

3

4

3p R

M

R

MN

30

0

4

3p R

MN

SOLID DRUG

M N M N R p p p34

3

R RM

M 0

0

3

X

CD

tt

C 1w

1

X

CD

tt

C mm

m

X

CD

tt

C 2w

2

1st stagnant layer

membrane

2nd stagnant layer

FICK LAW

BOUNDARY CONDITIONS

dissolution

(K t)

solid drug (M )

donor 1st layer 2

nd

layermembrane receiver

X = 0

concentration profile

h 1 h 2 h 3

X = h 1 X = h 1+ h 2 X = h 1+ h 2+h 3

0

1w

dd d

d

XX

CSD

t

M

t

CV dDPdd

dCCSKV

t

MsP

BOUNDARY CONDITIONS

dissolution

(K t)

solid drug (M )

donor 1st layer 2

nd

layermembrane receiver

X = 0

concentration profile

h 1 h 2 h 3

X = h 1 X = h 1+ h 2 X = h 1+ h 2+h 3

11

m1

whX

m

hX X

CD

X

CD

2121

2w

mm

hhXhhX X

CD

X

CD

p1

m KC

C p

2

m KC

C

BOUNDARY CONDITIONS

dissolution

(K t)

solid drug (M )

donor 1st layer 2

nd

layermembrane receiver

X = 0

concentration profile

h 1 h 2 h 3

X = h 1 X = h 1+ h 2 X = h 1+ h 2+h 3

321

2w

rr

hhhXX

CSD

t

CV

0

0.2

0.4

0.6

0.8

1

1.2

0 1000 2000 3000 4000 5000 6000 7000

t+

Cd+ , C

r+

H = 1

H = 0.5

H = 0.25

H = 0.01

Cd+

Cr+

SIMULATION: NO DISSOLUTION

Vr = Vd

2m

m

h

Dtt

d0

d

C

CCd

d0

r

C

CCr

D1 = 8.8*10-6 cm2/s

Dm = 5.3*10-6 cm2/s

D1 = D2

Kp = 0.8

*hm

H = Stagnant layer thickness

*hm

*hm

*hm

hm = 100 m

S = 10 cm2

SIMULATION: PROFILE CONCENTRATION

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4X+=X/hm

Cm+

membrane

1st layer 2nd layer

t+ = 0

t+ = 533

t+ = 5333

donor

receiver

t+ = 0.266

Vr = Vd

D1 = 8.8*10-6 cm2/s

Dm = 5.3*10-6 cm2/s

D1 = D2

Kp = 0.8

h1 = h2 = 0.5*hm

hm = 100 m

S = 10 cm2

SIMULATION: DISSOLUTION

Vr = 800 cm3

2m

m

h

Dtt

d0

d

C

CCd

d0

r

C

CCr

D1 = 8.8*10-6 cm2/s

Dm = 5.3*10-6 cm2/s

D1 = D2

Kp = 0.8

Vd = 100 cm3

h1 = h2 = hm=100m

0

0.2

0.4

0.6

0.8

1

1.2

0 50000 100000 150000 200000

t+

Cd+ , C

r+ Cd+

Cr+

Kd = 10-6cm/s

A = 5000 g/cm2

Cs = 12495 g/cm3

S = 10 cm2

SIMULATION: STEADY STATE APPROXIMATION

tDh

n

n

n

enV

KChht

h

D

V

SKCC

m

2

m

122

r

pd0mm

m

m

r

pd0r

12

6

Cd = Cd0 (constant drug concentration in the donor)Cr = 0 (sink conditions in the receiver)

FICK eq. solution (only membrane) is:

For t ∞

LttV

PSCC

r

d0r m

p

h

DKP

m

2m

6D

htL

Membrane Permeability

For a trilaminate system the solution is:

LttV

PSCC

r

d0r

For t ∞

p2p1213p3p1312p3p2321

p3p2p1321

KKDDhKKDDhKKDDh

KKKDDDP

L

12

1

1 1

2

2 2

3

3 3

22

2

1

1 1

2

2

3

3 3

32

3

1

1 1

2

2 2

3

3 3

1 2 3

1 3 1 3

1

1 1

2

2 2

36 2 2 2 6

2 2 6

t

h

D

h

D K

h

D K

h

D K

h

D

h

D K

h

D K

h

D K

h

D

h

D K

h

D K

h

D K

K h h h

D D K K

h

D K

h

D K

1 2 2

2

h

D K3 3

SIMULATION: LINEAR PROFILES (THIN MEMBRANES)

d 1 2 1 2C t A A e A em mt t( ) 3

r 1 2 1 3 2C t B B e B em mt t( )

M t M E e E em mt t( ) 0 1 1 2 2 11

SIMULATION: LINEAR PROFILES (THIN MEMBRANES)

EMPIRICAL APPROACH

eAeAAC rr tttt mm)t(

21

321d

eBeBBC rr tttt mm)t(

21

321r

11 21

210

eEeEMtM rr tttt mm

3 - DRUG DIFFUSION COEFFICIENT MEASUREMENT

REQUIRES THE DETERMINATION OF:

1 DRUG SOLUBILITY CS IN THE RELEASE ENVIRONMEMT

2 DRUG DIFFUSION COEFFICIENT DW IN THE RELEASE ENVIRONMEMT

3 DRUG POWDER DISSOLUTION CONSTANT KDP

4 DRUG PARTITION COEFFICIENT Kp (MEMBRANE/RELEASE ENVIRONMENT)

5 THICKNESS OF STAGNANT LAYERS SANDWICHING THE MEMBRANE

CASE STUDY: THEOPHYLLINE AND ALGINATES

THEOPHYLLINE MONOHYDRATED- Carlo Erba , Milano- (C7H8N4O2*H2O); MW 198, WHITE CRYSTALLINE POWDER

- DENSITY 1.49 ± 01 g/ cm3 (Helium picnometer)- SURFACE AREA = 2941 cm2/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++)

OO O

OH

OH

OHOH

OH

O

O OH

O

OCa 2+Ca++

Ca++ Ca++Ca++ Ca++ Ca++Ca++

EGG BOX CONFIGURATION

1 DRUG SOLUBILITY CS IN THE RELEASE ENVIRONMEMT

Cs = 12945 ± 104 g/cm3 (DISTILLED WATER 37°C)

2 DRUG DIFFUSION COEFFICIENT DW IN THE RELEASE ENVIRONMEMT

t

V

SK

eCC Rd

S 1

Kd = 0.62*DW2/3 1/2 *-1/6

0

0.0005

0.001

0.0015

0.002

0.0025

0 1 2 3 4 5

0.5

Kd(c

m/s

)

DW = (8.2 ± 0.6)*10-6 cm2/s (DISTILLED WATER 37°C)

IDRIDR

3 DRUG POWDER DISSOLUTION CONSTANT KDP

Magnetic engine

Donor

solid drug

jack

et

SEALING TAPE

- SINK CONDITIONS- Np MONOSIZED SPHERICAL PARTICLES (Rp0 INITIAL RADIUS)

t = 0

Rp0

t > 0

Rp

DISSOLUTION

SDPp2p

dd

d 4d

d

d

dCKNR

t

CV

t

M

PARTICLES SURFACE

SDP2p

3pp 4

3

4

d

d

d

dCKR

R

tt

M

Md =drug amount in the donor (soluble)

Mp = solid particle mass

tCKRtCKR

tCKC SDP2p0

22SDP

p033SDP2d 3

tCK

RR

SDPp0p

d

P4

V

N

34 3p0

P0P

R

MN

2p0P0 4 RNA

34 3p0

P0P

R

MN

A

R3

p0

A = Particles initial surface areaMp0 = initial particles mass

Theophylline m.(powder; water 37°C)

0

20

40

60

80

100

120

140

160

0 5 10 15 20

t(s)

C(

g/c

m3 )

Model

exp

KDP = 1.2*10-3 cm/s

4 DRUG PARTITION COEFFICIENT Kp (MEMBRANE/RELEASE ENVIRONMENT)

Cylindrical gel

(DISTILLED WATER 37°C)IDR

C0 = 20 g/cm3

V

Vg

24 hC∞

M0 = V*C∞+Vg* Cg∞

Kp = Cg∞ /C∞

900

p .VC

CCVK

g

5 THICKNESS OF STAGNANT LAYERS SANDWICHING THE MEMBRANE

Donor Receiver

MEMBRANE

stirrer

jack

etjack

et

stirrer

STAGNANT LAYER

STAGNANT LAYER

Donor

DRUGja

ck

et

stirrer

0

50

100

150

200

250

300

0 100 200 300 400 500 600t(s)

C(

g/m

l)

media

modello

t

Vh

SD

sseCC R

W

1S

hss = 60.7 m

STAGNANT LAYER

0

10

20

30

40

50

60

70

80

0 500 1000 1500 2000 2500

t (s)

Cr( g

/cm

3 )

4 - RESULTS

- Model- Linear approximation

Experimental data

Vr = 100 cm3 Dm = (5.1± 0.64)*10-6 cm2/s

Vd = 100 cm3

S = 10 cm2

%P = 4

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500

t(s)

Cr( g

/cm

3 )T = 25°C

1%

2%

4%

T = 37°C

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500

t(s)

Cr( g

/cm

3 )

1%

2%

4%

MEMBRANES CHARACTERISTICS

DIFFUSION COEFFICIENTS