BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Lecture 7: Hydrogel Biomaterials: Structure and Physical Chemistry Last Day: programmed/regulated/multifactor controlled release for drug delivery and tissue engineering Today: Applications of hydrogels in bioengineering Covalent hydrogels structure and chemistry of biomedical gels Thermodynamics of hydrogel swelling Reading: N.A. Peppas et al., ‘Physicochemical foundations and structural design of hydrogels in medicine and biology,’ Annu. Rev. Biomed. Eng., 2, 9-29 (2000). Supplementary Reading: P.J. Flory, ‘Principles of Polymer Chemistry,’ Cornell University Press, Ithaca, pp. 464- 469, pp. 576-581 (Statistical thermodynamics of networks and network swelling) Applications of hydrogels in bioengineering ? Hydrogels: insoluble network of polymer chains that swell in aqueous solutions ? Gels can be classified by the type of crosslinker: 1 ? Covalent - covalent junctions ? Physical - non-covalent junctions Lecture 7 – Hydrogels 1 1 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Physical gels: example- Hydrophobic water interactions in physical gels Physical gels are formed by noncovalent Example blocks: cross-links Poly(ethylene glycol) (PEG) Hydrophilic B blocks Hydrophobic A blocks Poly(propylene oxide) (PPO) Poly(butylene oxide) (PBO) ? Key properties of gels for bioengineering applications: 1. in situ formability 2. degradability 3. responsive swelling 4. tissue-like structure/properties ? In situ formability null Gelation of liquid solutions by: ? Irradiation with light ? Temperature change (e.g. 4°C to 37°C) ? Cross-linking enzymes ? Presence of divalent salts ON BOARD: In situ formation ￥h ν ￥Heat ￥Crosslinking by enzymes ￥Introduction of divalent cations (e.g. Ca ++ , Mg ++ ) Lecture 7 – Hydrogels 1 2 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Key properties of hydrogels for bioengineering applications: example: ?printable?gels ?T Chilled/heated (Landers et al. 2002) printing heads provide 4-70°C dispensing Temperature-controlled stage (Irvine lab) ? Degradability ON BOARD: Degradability ￥Hydrolysis ￥Enzymatic attack Gel with degradable cross- Eliminible/metabolizable links or network chains Water-soluble fragments ? Responsive swelling null Temperature-, pH-, and molecule-responsive swelling null Basis of sensors and ‘smart’ materials null (to be covered later) Lecture 7 – Hydrogels 1 3 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Lecture 7 – Hydrogels 1 4 of 15 ON BOARD: Responsive swelling ￥ ?pH ￥ ?T ￥ ?c (change in concentration of a molecule ? Tissue-like structure/properties null Form swollen networks similar to collagen, elastin, proteoglycans ? General areas of application in bioengineering: ? Controlled release ON BOARD: Controlled release ? Tissue barriers (Hubbell 2,3 ) null Prevent thrombosis (vessel blocked by coagulating platelets) and restenosis (re-narrowing of blood vessel after operation) in vessels after vascular injury/angioplasty/etc. null Prevent tissue-tissue adhesion after an operation Tissue barriers and conformal coatings (An and Hubbell 2000) Adsorbed layer of photoinitiatorBlood vessel Photoinitiator solution PEG-diacrylate solution Green laser 3) 2) 1) Two layers of hydrogel formed in situ vessel BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 ? TE scaffolds/cell encapsulation/immunoisolation 4,5 Poly(methyl methacrylate) microspheres Perfect connectivity for cell migration Improved nutrient transport No ? dead volume? O.D. Velev and A.M. Lenhoff, Curr. Opin. Coll. Interf. Sci. 5, 56 (2000) Advantages: 1. 2. 3. Hydrogel precursor polymerize Dissolve microspheres Ordered porous structure Hydrogel ?inverse opals? Optical micrograph/20 μm pores 60 μm Fluorescence micrograph/60 μm pores ? Biosensors (to be covered later) ? Contact lenses Lecture 7 – Hydrogels 1 5 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Structure of covalent hydrogel biomaterials Chemical and physical structure Structure and swelling of hydrogel materials ?ineffective network = = = x x = x x x x x chain? ? effective network chain? = x = = = x = polymerization solution hydrogel dilution swelling ? Networks formed by stitching together monomers in aqueous solutions via cross-linkers that are multifunctional units o Draw an example of a crosslinker: bisacrylamide ? networks from hydrophilic vinyl monomers ? hydroxyethyl methacrylate ? poly(ethylene glycol) methacrylate ? acrylic acid ? acrylamide, N-isopropylacrylamide ? Common crosslinkers: null PEGDMA, EGDMA null bis-acrylamide ? Hydrogels undergo swelling in analogy to dilution of free polymer chains in solution o Difference lies in limit to ‘dilution’ when chains are cross-linked together (ENTROPIC) ? Poly(2-hydroxyethyl methacrylate) hydrogels 6 ? One of the first biomedical hydrogels; applied to contact lenses in late 1950s Lecture 7 – Hydrogels 1 6 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 PEGDMA-co-PHEMA CH 3 CH 3 CH 3 CH 3 -CH 2 -CH-CH 2 -C-CH 2 -CH-CH 2 -CH- C=O O CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 OH CH 2 CH 2 O C=O -CH 2 -CH-CH 2 -C-CH 2 -CH-CH 2 -CH- C=O C=O O O CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 OH OH (Chielline et al. 7 ) Interpenetrating networks ? Useful for obtaining gels with properties in between two different materials o E.g. mix a swelling polymer with a temperature- or pH-responsive polymer to obtain networks that have a defined amount of swelling in response to changes in temperature or pH Interpenetrating networks x x x x x o Sem-interpenetrating networks: second component is entangled with first network but not cross-linked Biological recognition of hydrogels ? Inclusion of peptide-functionalized co-monomers allows hydrogels to have tailored biological recognition properties similar to solid degradable polymers o Promoting cell adhesion: Incorporating biological recognition: peptides photopolymerization = PEG -WGRGDSP adhesion sequence NR6 fibroblast adhesion on PEG-RGD hydrogel (no cell adhesion on ligand-free hydrogels) C=O C=O C=O O O O OH OH O C=O O OH Lecture 7 – Hydrogels 1 7 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Promoting remodeling/cell migration through synthetic networks: PEG photopolymerization = = PEG peptides -GWGLGPAGK- -CH 2 CH 2 O- collagenase sequence collagenase B.K. Mann, A.S. Gobin, A.T. Tsai, R.H. Schmedlen, J.L. West, Biomaterials 22, 3045 (2001) Example synthesis strategy: photoencapsulation of live cells 5 ? Photoencapsulation: expose solution of cells, prepolymer/cross-linker/monomer, and photoinitiator to light to initiate free radical polymerization = = = = = = = = = = = = = = = = In sterile culture media: hν Cyclohexyl phenyl ketone: UV hν ? Provides very rapid polymerization (2-20 seconds typical), at neutral pH and room temp. – 37°C ? ‘soft’ UV photoinitiators are common and non-toxic (illuminate at 365 nm) Lecture 7 – Hydrogels 1 8 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 ? Cells can be entrapped with high viability 4,8 : UV lamp liquid gel Example Biomedical Hydrogel Materials 6 Formed from hydrophilic biocompatible polymers, often polymers that can be safely eliminated by the body if the gel breaks down. CH 3 CH=C C=O O R General methacrylates Lecture 7 – Hydrogels 1 9 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Chemical structure of biodegradable hydrogels Mechanism I: (non-degradable water-soluble polymers with degradable cross-links) ? Degradable cross-links o e.g. dextran hydrogels 9 ? bacterial exo-polysaccharide ? branched polymer composed of α-1,6-linked D-glucopyranose residues with a low % of α-1,2 and 1,3 side chainsDextran with polylactide crosslinks: hydrolyzable crosslinks 9 ? dextran can be functionalized with methacrylate and then crosslinked in the presence of a small amount of vinyl monomer: d degradable gels show first swelling then dissolution as cross-links are hydrolyzed: Lecture 7 – Hydrogels 1 10 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Mechanism III: ? Co-encapsulation of degradation catalyst o e.g. dextran hydrogels 9 encapsulating dextranase enzyme ? polymerization is carried out in the presence of protein to be delivered and a bacterial dextranase: dextranase breaks down the dextran chains over time, releasing protein ? degradation/protein release rate depends on amount of enzyme encapsulated Thermodynamics of hydrogel swelling Derivation of the free energy of polymer chains cross-linked in the presence of solvent ? Theory originally developed by Flory and Rehner for solid rubber networks exposed to solvent 10,11 ? Adapted to describe hydrogels in biomedical applications by Bray and Merrill 12 Description of the model Polymer and solvent (water) are modeled as segments of equal volume- polymer chains are composed of connected segments Energy of contacts: ?ω 12 (Flory 13 ) Model parameters μ 1 bath chemical potential of water in external bath ( = μ 1 0 ) μ 1 chemical potential of water in the hydrogel μ 1 0 chemical potential of pure water in standard state ?w 12 pair contact interaction energy for polymer with water z model lattice coordination number x number of segments per polymer molecule Lecture 7 – Hydrogels 1 11 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 M Molecular weight of polymer chains before cross-linking M c Molecular weight of cross-linked subchains n 1 number of water molecules in swollen gel χ polymer-solvent interaction parameter k B Boltzman constant T absolute temperature (Kelvin) v m , 1 molar volume of solvent (water) v m,2 molar volume of polymer v sp , 1 specific volume of solvent (water) v sp,2 specific volume of polymer V 2 total volume of polymer V s total volume of swollen hydrogel V r total volume of relaxed hydrogel ν number of subchains in network ν e number of ‘effective’ subchains in network φ 1 volume fraction of water in swollen gel φ 2,s volume fraction of polymer in swollen gel φ 2,r volume fraction of polymer in relaxed gel ? Subchains, M c , and ‘effective’ chains Assume cross-links are randomly placed; on average, all are equidistant ν = number of subchains in cross-linked network ν e = number of ? A effective?subchains: tethered at both ends M = MW of original chains M c = MW of subchains = MW between cross-links Example: assume polymer chains have a molecular weight M = 4A and each ?subchain?has molecular weight A: ν = 24 ν e = 12 Two useful relationships: ν= V 2 /v sp,2 M c ν e = ν(1 - 2(M c /M)) Lecture 7 – Hydrogels 1 12 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 ? Physical picture of the equilibrium described: o Polymer chains are cross-linked in water o Relaxed network is moved to a large bath of water and swells to a new equilibrium Cross-linking V r (relaxed) Expansion factor: α α x α y α z = α 3 = V s /Vr = (V 2 + n 1 v m,1 )/V r swelling V s φ 2,s = V 2 /(V 2 + n 1 v m,1 ) volume fraction of polymer in swollen gel φ 2,r = V 2 /V r volume fraction of polymer in relaxed gel Derivation of the equilibrium properties ? We want to calculate the change in free energy as the network is cross-linked and first exposed to a surrounding solvent bath that can trigger solvent to enters/leave the hydrogel ? The free energy of the system can be written as a contribution from mixing and an elastic retracting energy: ?G total = ?G mix + ?G el At equilibrium, the chemical potentials of solvent inside and outside the gel are equal: Eqn 1 μ 1 bath = μ 1 0 Eqn 2 μ 1 =μ 1 chemical potential of bath is water’s standard state Eqn 3 0 =?(μ 1 ) mix +?(μ 1 ) total = ? ? ? ?(?G total ) ? ? ? =?(μ 1 ) el dn 1 T ,P ? ?(μ 1 ) mix and ?(μ 1 ) el will depend on the degree of swelling and thus allow us to calculate the swelling if we know the physicochemical parameters of the system… ? Determining the contribution from mixing: o Based on Flory’s original lattice liquid model Lecture 7 – Hydrogels 1 13 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Eqn 4 ?G mix = ?H mix – T?S mix ? Free energy can be decreased by entropy gain on mixing (more configurations, ?S mix > 0) and favorable solvent- polymer interactions (?H mix < 0) O CH 2 CH C O O H CH 2 H o …drives SWELLING of hydrophilic networks in water ? Enthalpy of mixing: count contacts and provide ?ω 12 energy per contact: o ?ω 12 accounts for energy of moving a molecule of solvent from pure water into pure polymer o # contacts between 1 and 2 = (total number of polymer segments in system)(# contacts with solvent) = (n 2 x)[(number neighbors per segment)(probability that neighbor is solvent)] = (n 2 v 2 )(z)(φ 1 ) = zn 1 φ 2 Eqn 5 ?H mix = z?ω 12 x 1 n 1 φ 2 ? Define the polymer-solvent interaction parameter: Eqn 6 χ = z?ω 12 x 1 /k B T (unitless) Eqn 7 therefore ?H mix = k B Tn 1 φ 2 ? Now derive ?S mix : we won’t derive it here: o Based on fundamental equation: Eqn 8 S = k B ln ? ? Where ? is the number of configurations possible in the system. ? Lower configurational entropy if chains of network are stretched ?G el > 0 ? Resists chain stretching, competes against ?G mix and ?G ion , driving network collapse ? Flory derived an expression for the # ways free polymer chains could be arranged on the lattice: Eqn 9 ?S mix = k B ln(? solution /? separate ) = -k B [n 1 ln φ 1 + n 2 ln φ 2 ] ? For a gel, the number of ‘free’ polymer chains n2 = 0, so: Eqn 10 ?G mix = k B T[n 1 ln φ 1 + χn 1 φ 2 ] ? The chemical potential change can be obtained by differentiating Eqn 10: Eqn 11 Lecture 7 – Hydrogels 1 14 of 15 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 References 1. Nguyen, K. T. & West, J. L. Photopolymerizable hydrogels for tissue engineering applications. Biomaterials 23, 4307-14 (2002). 2. An, Y. & Hubbell, J. A. Intraarterial protein delivery via intimally-adherent bilayer hydrogels. J Control Release 64, 205-15 (2000). 3. Hubbell, J. A. Hydrogel systems for barriers and local drug delivery in the control of wound healing. Journal of Controlled Release 39, 305-313 (1996). 4. Elisseeff, J. et al. Photoencapsulation of chondrocytes in poly(ethylene oxide)-based semi-interpenetrating networks. Journal of Biomedical Materials Research 51, 164-171 (2000). 5. Jen, A. C., Wake, M. C. & Mikos, A. G. Review: Hydrogels for cell immobilization. Biotechnology and Bioengineering 50, 357-364 (1996). 6. Peppas, N. A., Huang, Y., Torres-Lugo, M., Ward, J. H. & Zhang, J. Physicochemical foundations and structural design of hydrogels in medicine and biology. Annu Rev Biomed Eng 2, 9-29 (2000). 7. Chiellini, F., Petrucci, F., Ranucci, E. & Solaro, R. in Biomedical Polymers and Polymer Therapeutics (eds. Chiellini, E., Sunamoto, J., Migliaresi, C., Ottenbrite, R. M. & Cohn, D.) 63-74 (Kluwer, New York, 1999). 8. Anseth, K. S. & Burdick, J. A. New directions in photopolymerizable biomaterials. Mrs Bulletin 27, 130-136 (2002). 9. Hennink, W. E. et al. in Biomedical Polymers and Polymer Therapeutics (eds. Chiellini, E., Sunamoto, J., Migliaresi, C., Ottenbrite, R. M. & Cohn, D.) 3-18 (Kluwer, New York, 2001). 10. Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. II. Swelling. J. Chem. Phys. 11, 521-526 (1943). 11. Flory, P. J. & Rehner Jr., J. Statistical mechanics of cross-linked polymer networks. I. Rubberlike elasticity. J. Chem. Phys. 11, 512-520 (1943). 12. Peppas, N. A. & Merrill, E. W. Polyvinyl-Alcohol) Hydrogels - Reinforcement of Radiation-Crosslinked Networks by Crystallization. Journal of Polymer Science Part a-Polymer Chemistry 14, 441-457 (1976). 13. Flory, P. J. Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953). Lecture 7 – Hydrogels 1 15 of 15