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