The number of biomedical applications of hydrogels is increasing rapidly on account of their unique physical, structural, and mechanical properties. The utility of hydrogels as drug delivery systems or tissue engineering scaffolds critically depends on the control of diffusion of solutes through the hydrogel matrix. Predicting or even modeling this diffusion is challenging due to the complex structure of hydrogels. Currently, the diffusivity of solutes in hydrogels is typically modeled by one of three main theories proceeding from distinct diffusion mechanisms: (i) hydrodynamic, (ii) free volume, and (iii) obstruction theory. Yet, a comprehensive predictive model is lacking. Thus, time and capital-intensive trial-and-error procedures are used to test the viability of hydrogel applications. In this work, we have developed a model for the diffusivity of solutes in hydrogels combining the three main theoretical frameworks, which we call the multiscale diffusion model (MSDM). We verified the MSDM by analyzing the diffusivity of dextran of different sizes in a series of poly(ethylene glycol) (PEG) hydrogels with distinct mesh sizes. We measured the subnanoscopic free volume by positron annihilation lifetime spectroscopy (PALS) to characterize the physical hierarchy of these materials. In addition, we performed a meta-analysis of literature data from previous studies on the diffusion of solutes in hydrogels. The model presented outperforms traditional models in predicting solute diffusivity in hydrogels and provides a practical approach to predicting the transport properties of solutes such as drugs through hydrogels used in many biomedical applications.

Positron annihilation lifetime spectroscopy (PALS) provides a direct measurement of the free volume void sizes in polymers and biological systems. This free volume is critical in explaining and understanding physical and mechanical properties of polymers. Moreover, PALS has been recently proposed as a potential tool in detecting cancer at early stages, probing the differences in the subnanometer scale free volume voids between cancerous/healthy skin samples of the same patient. Despite several investigations on free volume in complex cancerous tissues, no positron annihilation studies of living cancer cell cultures have been reported. We demonstrate that PALS can be applied to the study in human living 3D cell cultures. The technique is also capable to detect atomic scale changes in the size of the free volume voids due to the biological responses to TGF-β. PALS may be developed to characterize the effect of different culture conditions in the free volume voids of cells grown in vitro.

Positron annihilation lifetime spectroscopy (PALS) can measure changes in local free volume voids in lipid bilayers. PALS has been applied, together with differential scanning calorimetry (DSC) and molecular dynamics (MD) simulations, to study free volume voids in DPPC and DPPC:ceramide (85:15 mol:mol) model membranes in the 20-60 ºC range. The free volume void average size clearly increases with the gel-fluid phase transition of the lipid, or lipid mixture. Ceramide increases void size at all temperatures, particularly in the range causing the gel-fluid transition of the mixture. A parallel study of PALS and calorimetric data indicates that, for the complex thermotropic transition of the DPPC:ceramide mixture, PALS is detecting the transition of the DPPC component, while calorimetry changes indicate mainly the melting of the ceramide-enriched domains. Molecular dynamics calculations provide a clear distinction between ceramide-rich and -poor domains, and show that the voids are predominantly located near the membrane nodal plane. The ceramide-induced increase in void volume size occurs as well at temperatures when both phospholipid and ceramide are in the fluid state, indicating that the effect is not the result of phospholipid-ceramide domain coexistence. The above observations may be related to hitherto unexplained properties of ceramide, such as the increase in membrane permeability, and the induction of transmembrane (flip-flop) lipid motion.

Free volume voids in lipid bilayers can be measured by positron annihilation lifetime spectroscopy (PALS). This technique has been applied, together with differential scanning calorimetry and molecular dynamics (MD) simulations, to study the effects of cholesterol (Chol) and ceramide (Cer) on free volume voids in sphingomyelin (SM) or dipalmitoylphosphatidylcholine (DPPC) bilayers. Binary lipid samples with Chol were studied (DPPC:Chol 60:40, SM:Chol 60:40 mol ratio), and no phase transition was detected in the 20–60 °C range, in agreement with calorimetric data. Chol-driven liquid-ordered phase showed an intermediate free volume void size as compared to gel and fluid phases. For SM and SM:Cer (85:15 mol:mol) model membranes measured in the 20–60 °C range the gel-to-fluid phase transition could be observed with a related increase in free volume, which was more pronounced for the SM:Cer sample. MD simulations suggest a hitherto unsuspected lipid tilting in SM:Cer bilayers but not in pure SM. Ternary samples of DPPC:Cer:Chol (54:23:23) and SM:Cer:Chol (54:23:23) were measured, and a clear pattern of free volume increase was observed in the 20–60 °C because of the gel-to-fluid transition. Interestingly, MD simulations showed a tendency of Cer to change its distribution along the membrane to make room for Chol in ternary mixtures. The results suggest that the gel phase formed in these ternary mixtures is stabilized by Chol–Cer interactions.

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