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SIDE BY SIDE CELL. spectrophotometer. s urge chamber. computer. pump. Thermostatic unit. Thermostatic unit. Teflon adapter. Donor. Receiver. membrane. jacket. jacket. solid drug. stirrer. Magnetic engine. Magnetic engine. 2 - DRUG DIFFUSION MEASUREMENT. TEFLON ADAPTER. - PowerPoint PPT Presentation
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SIDE BY SIDE CELL
Magnetic engine
Magnetic engine
Donor Receiver
Teflon adapter
solid drug
membrane
stirrer
Thermostatic unit Thermostatic unit
jack
et
jac ke t
pump
surge chamber
spectrophotometer
computer
2 - DRUG DIFFUSION MEASUREMENT
MAGNETIC STIRRERS
TEFLON ADAPTERDONOR CHAMBER RECEIVER CHAMBER
THERMOSTATICJACKET
DONOR RECEIVER
STIRRER
jack
etjacket
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
R 30
Particles initial surface area
330
0
43
43
p RM
RMN
30
0
43
p RMN
SOLID DRUG
M N M N R p p p34
3
R RMM
00
3
XCD
ttC 1
w1
XCD
ttC m
mm
XCD
ttC 2
w2
1st stagnant layer
membrane
2nd stagnant layer
FICK LAW
BOUNDARY CONDITIONS
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
0
1w
dd d
d
XXCSD
tM
tCV dDPdd
d CCSKVtM
sP
BOUNDARY CONDITIONS
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
11
m1
whX
m
hX XCD
XCD
2121
2w
mm
hhXhhX XCD
XCD
p1
m KCC
p2
m KCC
BOUNDARY CONDITIONS
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
321
2w
rr
hhhXXCSD
tCV
0
0.2
0.4
0.6
0.8
1
1.2
0 1000 2000 3000 4000 5000 6000 7000t+
Cd+ , C
r+
H = 1H = 0.5H = 0.25H = 0.01
Cd+
Cr+
SIMULATION: NO DISSOLUTION
Vr = Vd
2m
m
hDtt
d0
d
CCCd
d0
r
CCCr
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
hDtt
d0
d
CCCd
d0
r
CCCr
D1 = 8.8*10-6 cm2/sDm = 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 200000t+
Cd+ , C
r+ Cd+
Cr+
Kd = 10-6cm/s
A = 5000 g/cm2
Cs = 12495 g/cm3
S = 10 cm2
SIMULATION: STEADY STATE APPROXIMATION
tDhn
n
n
enV
KChhthD
VSKC
Cm
2
m
122
r
pd0mm
m
m
r
pd0r
126
Cd = Cd0 (constant drug concentration in the donor)Cr = 0 (sink conditions in the receiver)
FICK eq. solution (only membrane) is:
For t ∞
LttVPSCC r
d0r m
p
hDK
P
m
2m
6DhtL
Membrane Permeability
For a trilaminate system the solution is:
LttVPSCC r
d0r
For t ∞
p2p1213p3p1312p3p2321
p3p2p1321
KKDDhKKDDhKKDDhKKKDDD
P
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( 21321d
eBeBBC rr tttt mm)t( 21321r
11 21210 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
VSK
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(
cm/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
dd
d CKNRtCV
tM
PARTICLES SURFACE
SDP2p
3pp 4
34
dd
dd
CKRR
ttM
Md =drug amount in the donor (soluble)
Mp = solid particle mass
tCKRtCKR
tCKC SDP2p0
22SDP
p033SDP2d 3
tCKRR
SDPp0p
d
P4VN
34 3p0
P0P
RMN
2p0P0 4 RNA
34 3p0
P0P
RMN
A
R 3p0
A = Particles initial surface areaMp0 = initial particles mass
Theophylline m.(powder; water 37°C)
020406080
100120140160
0 5 10 15 20
t(s)
C(
g/cm
3 )
Modelexp
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∞
900p .
VCCCVKg
5 THICKNESS OF STAGNANT LAYERS SANDWICHING THE MEMBRANE
Donor Receiver
MEMBRANE
stirrer
jack
etjac ke t
stirrer
STAGNANT LAYER
STAGNANT LAYER
Donor
DRUGja
cket
stirrer
0
50
100
150
200
250
300
0 100 200 300 400 500 600t(s)
C(
g/m
l)
mediamodello
t
VhSD
sseCC R
W
1S
hss = 60.7 m
STAGNANT LAYER
0
10
20
30
40
50
60
70
80
0 500 1000 1500 2000 2500t (s)
Cr(
g/cm
3 )4 - RESULTS
- Model- Linear approximation
Experimental data
Vr = 100 cm3 Dm = (5.1± 0.64)*10-6 cm2/sVd = 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
