side by side cell magnetic engine donorreceiver teflon adapter solid drug membrane stirrer...

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