Determination of the polymer-solvent interaction parameter for PEG hydrogels in water: Application of a self learning algorithm

Abstract

Concentrating on the case of poly(ethylene glycol) hydrogels, this paper introduces a methodology that enables a natural integration between the development of a so-called mechanistic model and experimental data relating material’s processing to response. In a nutshell, we develop a data-driven modeling component that is able to learn and indirectly infer its own parameters and structure by observing experimental data. Using this method, we investigate the relationship between processing conditions, microstructure and chemistry (cross-link density and polymer-solvent interactions) and response (swelling and elasticity) of non-degradable and degradable PEG hydrogels. We show that the method not only enables the determination of the polymer-solvent interaction parameter, but also it predicts that this parameter, among others, varies with processing conditions and degradation. The proposed methodology therefore offers a new approach that accounts for subtle changes in the hydrogel processing.

Enhanced mechanical properties of photo-clickable thiol–ene PEG hydrogels through repeated photopolymerization of in-swollen macromer

“…We estimated crosslink density, ρ x and the polymer-solvent interaction parameter, χ 12 using a self-learning model described by Akalp et al 29 This model uses the experimentally determined parameters of polymer volume fraction ( i.e .,ϕ) and the modulus of the fully swollen as inputs and solves for ρ x and χ 12 by combining Flory-Rehner theory with theories of mixture and poroelasticity. 30–33 The model assumes isotropic swelling and uses a modified version of Flory-Rehner theory that neglects the contribution of chain ends.…”

Tuning Reaction and Diffusion Mediated Degradation of Enzyme‐Sensitive Hydrogels

“…We employed a multi-phasic mixture model that we have previously developed and applied to poly(ethylene glycol) (PEG) hydrogels. [6,7] We investigated a hydrogel platform based on a thiol-norbornene PEG hydrogel system with peptide crosslinks comprised of the collagenase-sensitive peptide VPLS-LYSG (Scheme 1B). [8] The enzyme that was used in this study was a commercially available collagenase blend.…”

“…Initial values for hydrogel, based on experimentally determined equilibrium swelling ratio and compressive modulus, were used as inputs to the model to estimate the initial crosslink density in a non-solvent using Flory-Rehner and Rubber elasticity theory [10] and a recently developed self-learning algorithm to estimate the polymer-solvent interaction parameter. [7] The computational model was able to capture the experimental front velocity using an average enzyme radius of 8.5 nm and values for the Michaelis-Menten kinetic constants, k cat with a value of 2 s −1 and K m with a value of 120 μM, which were used for all hydrogel crosslink cases. The value for network connectivity ( β ) was varied independently for each hydrogel case (Figure 1C i – iii ) and assumed to be higher than the ideal value of β (Figure 1A i – iii ) due to crosslinking imperfections (e.g., cyclization and dangling ends).…”

Tuning tissue growth with scaffold degradation in enzyme-sensitive hydrogels: a mathematical model

“…To compare the stiffness of the gel to that of the linked ECM, we define a new dimensionless parameter E * = E ECM /E gel where $E_{gel}=\rho RT(1.05J_0^{-1∕3}-{\left(2.1J_0\right)}^{-1})$ is the secant modulus for 5% strain (31) and E ECM = μ (3 λ + 2 μ )/( λ + μ ). The evolution of the construct's properties is now affected by the three non-dimensional parameters $r_e^{\ast }$, ${\kappa }_e^{\ast }$, ${\kappa }_m^{\ast }$ and the ECM properties μ * and λ *.…”

“…1). The hydrogel's elastic modulus can be adjusted by changing the molecular weight of the monomers or formulation (31), while its degradation kinetics can be controlled by changing the amino acids in the peptide (32). As shown in Fig.…”