麻省理工大学：《生物材料的分子结构》教学讲义（英文版）Problem set 3

Problem set 3 BE462J3.962 Day 6 Spring 2003 Due: (20 pts total A recent study of controlled release of a model small-molecule drug from poly (lactide-co-glycolide) microspheres prepared by the single-emulsion method found that the diffusion constant of the drug through the polymer was best related to the polymer's molecular weight according to D(O=Do+ In this equation, and Do are constants, and M(t) is the molecular weight of the matrix polymer. From data obtained on PLGA microspheres the constants were determined to be φ=21x10cm2(kgmo|e)s Do =4.9x10cm/s We can use this expression for D(t) in the charlier controlled release model to obtain modified expressions for h(t) and Q(t)(we'll call this model B, and the expression derived in class model A Assume that the molecular weight M(t)=Moe, where Mo is the initial molecular weight and k is the degradation rate constant for PLGA hydrolysis. A reasonable estimate for k is Degradation rate constant for PLGa hydrolysis: k=9.8E-03 hr (5 pts)Quantitatively, will the diffusion constant in model B given above differ significantly from that obtained from model a derived in class over experimentally-relevant timescales? pts) Using the model B formula above for the diffusion constant, derive a new expression for he thickness of the diffusion field h(t) in the Charlier model. Assume M(t) has an exponential cay with time as derived in class 3.(10 pts)Using the data above and that given below, determine how long release experiments that measure Q(t)(total amount of drug released at time t) would need to be carried out to distinguish which of the two models for the diffusion constant (D= Doe as derived in class, or the expression given above) best represents release of HGH from a PLGa matrix in the framework of the Charlier model (Hint: plot Q(t) for each of the two models; solve for Q(t) in model B by numerically ntegrating an expression dQ=(.)dt. Solubility of HGH in PLGA matrix cs=6.12E04g/cm3 Concentration of HGH encapsulated in the matrix: Co=0.02 g/cm Surface area of release matrix A=1.67cm Initial molecular weight of the matrix M=78,000g/moe BE.462 PS 3 1 of 1

Problem Set 3 BE.462J/3.962J Issued: Day 6 Spring 2003 Due: Day 8 (20 pts total) A recent study of controlled release of a model small-molecule drug from poly(lactide-co-glycolide) microspheres prepared by the single-emulsion method found that the diffusion constant of the drug through the polymer was best related to the polymer’s molecular weight according to: φ D(t) = D0 + M(t) In this equation, φ and D0 are constants, and M(t) is the molecular weight of the matrix polymer. From data obtained on PLGA microspheres, the constants were determined to be: φ = 2.1x10-11 cm2 (kg/mole)/s D0 = 4.9x10-12 cm2 /s We can use this expression for D(t) in the Charlier controlled release model to obtain modified expressions for h(t) and Q(t) (we’ll call this model B, and the expression derived in class model A). Assume that the molecular weight M(t) = M0e-kt, where M0 is the initial molecular weight and k is the degradation rate constant for PLGA hydrolysis. A reasonable estimate for k is: Degradation rate constant for PLGA hydrolysis: k = 9.8E-03 hr-1 1. (5 pts) Quantitatively, will the diffusion constant in model B given above differ significantly from that obtained from model A derived in class over experimentally-relevant timescales? 2. (5 pts) Using the model B formula above for the diffusion constant, derive a new expression for the thickness of the diffusion field h(t) in the Charlier model. Assume M(t) has an exponential decay with time as derived in class. 3. (10 pts) Using the data above and that given below, determine how long release experiments that measure Q(t) (total amount of drug released at time t) would need to be carried out to distinguish which of the two models for the diffusion constant (D = D0ekt as derived in class, or the expression given above) best represents release of HGH from a PLGA matrix in the framework of the Charlier model. (Hint: plot Q(t) for each of the two models; solve for Q(t) in model B by numerically integrating an expression dQ = (…)dt.) Solubility of HGH in PLGA matrix: Cs = 6.12E-04 g/cm3 Concentration of HGH encapsulated in the matrix: C0 = 0.02 g/cm3 Surface area of release matrix: A = 1.67 cm2 Initial molecular weight of the matrix: M0 = 78,000 g/mole BE.462 PS 3 1 of 1