Polymeric Drug Delivery

Polymeric Drug Delivery

Drug Concentration

Overdose

Therapeutic

Underdose

Time

•

Sustained release – Complexation, slowly dissolving coatings, use of derivatives with reduced solubility – Sensitive to environmental conditions to which they are exposed

•

• • • • • • • • • • • • • • •

Controlled release – Release rate is determined by the device itself – More accurate, predictable administration rate Incorporate drug into a polymeric matrix Release drug at a known rate over a prolonged duration Release drug directly to the site of action Constant release - often the goal - difficult to achieve Deliver drug such that concentration in tissue is in appropriate range Protection of the drug from enzymatic degradation - particularly applicable to peptide and protein drugs Matrix systems - monolithic devices Rate controlling membranes - reservoir devices Degradable polymers Variety of configurations Release rates generally determined by solution of Fick’s Laws with appropriate boundary conditions Most important class is nonporous, homogeneous polymeric films Transport occurs by dissolution of permeating species in the polymer at one interface and diffusion down a gradient in thermodynamic activity Measurably permeable to drugs with MW less than 400 Transport governed by Fick’s Law J = −D

dC m dx

Assuming that the permeant on either side of the membrane is in equilibrium with the respective surface layerConcentration just inside the membrane can be related to the concentration in the adjacent solution

Cm ( o ) = KC ( o ) at x = 0 Cm ( l ) = KC (l ) at x = l

•

Assuming that D and K are constant (good assumption since drugs have low solubility in polymers) ∆Cm l DK ∆C = l

J =D

•

Release rates attainable from solution diffusion membrane controlled devices constrained by physical limitations – Device thickness – Molecular weight of drug is greater than 500, must expect a substantial decrease in the achievable release rate – Release rates between 1 and 200 mg/cm2 h expected

Dissolved Drug • Consider a matrix system containing drug • This system is placed in a solution containing no drug and the drug diffuses from the system to the solution • What does the release profile (amount of drug released from the system per unit time) look like? • Solution of Fick’s Law for a semi-infinite case • Express desorption of dissolved drug from the slab by either of the series:

[

∞ Mt 8 exp − D( 2n + 1) π 2t / l 2 =1− ∑ M∞ ( 2n + 1) 2 π 2 n =0 2

]

0.5

∞ Mt nl   Dt   1 = 4 2   + 2∑ (−1) n ierfc  M∞ 2 Dl  l   π n =1

• •

Simplifications can be made which apply over different ranges of the desorption curve - accurate to 1% Derived from 2), for the early portion of the desorption curve  Dt Mt = 4 2 M∞  πl

   

0≤

Mt ≤ 0 .6 M∞

Derived from 1), for the late portion  − π 2 Dt Mt 8 = 1 − 2 exp  2 M∞ π  l

 M  0.4 ≤ t ≤ 1.0 M∞ 

• • •

The drug release rate at any time is also of interest Obtained from differentiation of approximation equations to give: dM t D = 2M ∞ dt πl 2t

 π 2 Dt dM t 8 DM ∞  − 2 = exp dt l2 l 

•

Early time

  

Late time

Time to release half of the drug (half life of the device) t0.5 = 0.0492

l2 D

Release rate at half time: 16 DM ∞  dM t    = πl 2  dt 0.5

Theory versus Experimental • Early time approximation for cylinder Mt Dt Dt =4 2 − 2 M∞ r π r dM t / M ∞ D D =2 2 − 2 dt r πt r

< 0.4

Late time approximation for cylinder  − 2.405 2 Dt  Mt 4   =1 − exp   M∞ 2.405 2 r2   2  − 2.405 Dt  dM t / M ∞ 4 D  = 2 exp    dt r r2  

Dispersed Drug • Release rate and mass of drug released at any time are given by:

• • • •

Drug dispersed as a solid in the membrane phase instead of being dissolved release kinetics altered Total concentration of drug Co (dissolved + dispersed) larger than the solubility of the drug in the membrane, Cs Higuchi, J Pharm Sci 50 874 (1961) Release rate and mass of drug released at any time are given by: M t = A[ DtCs ( 2Co − C s ) ] ≅ A( 2 DtCs Co )

0. 5

0.5

Co > > C s

dMt A  DCs ( 2Co − Cs )  =  dt 2 t  A  2 DCs Co  ≅  2  t  t∞ =

l 2 Co 8DCs

0.5

0. 5

Co > > C s