SIDE BY SIDE CELL
description
Transcript of SIDE BY SIDE CELL
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