Application Note | ElastoSens™ Bio
AI-based prediction of hydrogel gelation kinetics and their mechanical properties
by Gloria Pinilla, M.Sc.
Application Specialist, Rheolution Inc.
SUMMARY
- Hydrogel design is a complex and multidimensional process.
- The development of hydrogels has been hampered by the traditional experimental iterative approach. Advanced predictive tools such as AI have the potential to change the paradigm from data-based experimental science to data-driven predictive science.
- An AI model for the prediction of the gelation kinetics and viscoelastic properties of PEGDA hydrogels was developed.
- ElastoSens™ Bio was used to generate the database used for the training and the validation of the AI model.
- The AI model was successfully validated given its high predictive accuracy (3% Mean error; R2≥0.97).
INTRODUCTION
Hydrogels are biomaterials that are widely studied in the biomedical field. They are used, for example, to produce contact lenses and wound dressings, for drug release systems, or as scaffolds for tissue engineering. The design of such hydrogels is often multidimensional since multiple parameters related to their chemical composition and physical properties affect how they are going to behave in vivo. Currently, hydrogel development follows a traditional ‘trial-and-error’ approach, in which one parameter is iteratively varied (input) to analyze the effect on another parameter (output). For example, the mechanical properties (input) were altered to see the effect on the cell adhesion (output) [1]. However, scientists struggle to understand how multiple parameters influence each other and how this relates to the behavior and the performance of hydrogels [2]. This limitation hampers the process of hydrogel formulation, which has a major impact on the development of new applications and on the commercialization of new products.
Imagine being able to predict how a hydrogel behaves and performs just by knowing its composition. In this application note, we propose an Artificial Intelligence (AI) model that predicts the time evolution of the shear storage modulus (G’) of PEGDA hydrogels by only knowing their composition. The ElastoSens™ Bio was used to generate the datasets that served for the training and the validation of the model.
MATERIALS AND METHODS
AI refers to a field of computer science dedicated to the creation of systems able to perform tasks that usually require human intelligence, such as learning or problem solving. It includes approaches that allow computers to learn from data without being explicitly programmed. For example, it has been extensively used for the prediction of economics and market evolution, for face recognition, for GPS and navigation predictive systems, or for medical imaging diagnosis. In biomaterials, some interesting applications have been explored, such as the screening of peptide interaction for the intelligent design of self-assembly hydrogels [3] or to predict cell adhesion and protein adsorption on polymeric surfaces based on their surface topology [4]. However, to the best of our knowledge, few studies have used AI to predict how hydrogels evolve with time (kinetics) and behave mechanically based on their multifactorial composition. In this work, we use a supervised AI-learning approach which aims to develop a model that can predict output values (or labels) from a set of input data (or features). Specifically, this AI model was based on Random Forest algorithm as a learning method.
Figure 1 illustrates the AI workflow of this work. Briefly, data generated from lab experiences using the ElastoSens™ Bio was used to build a database. This database was split into two datasets that were used for the training or for the validation of the AI model. First, the training dataset passed through the AI algorithm. The learning algorithm found patterns in the training data such that the input parameters corresponded to a specific output value (target). The output of the training process was the AI trained model. Finally, the validation dataset was used to provide new input values to the trained model in order to predict gelation kinetics (output) and compare them to the experimentally measured ones. The prediction of the gelation kinetics may serve to direct future experiences or to obtain trustful data without the need of performing wet experiences.
Figure 1. AI approach used in this work.
DATABASE GENERATION
PEGDA was used in this study to train and validate the AI predictive model. Polyethylene (glycol) Diacrylate (PEGDA) is a PEG-derived monomer that crosslinks in presence of the photoinitiator lithium phenyl-2,4,6-trimethylbenzoylphosphinate (LAP), which absorbs blue light (405 nm) and creates free-radicals that induce the polymerization of the acrylate groups of PEGDA [5].
Three parameters were used to create different combinations for the generation of the database: PEGDA concentration, light intensity and time.
- The PEGDA concentration was varied from 5-12% w/w (15 conditions). To prepare the PEGDA solutions, a 3% w/w LAP solution (pw, Belwezda, Sigma Aldrich) was dissolved in distilled water (30 min at 40 °C), to obtain a final concentration of 0.5% w/w LAP. Then, liquid PEGDA (Sigma Aldrich) was added to the LAP-water solution and the mix PEGDA-LAP-water was further stirred for 4 h at 40 °C. Solutions were stored at 4 °C protected from light. The time evolution of the shear storage modulus (G’) was measured on the ElastoSens™ Bio at 25 °C.
- The light intensity was varied from 2-20 mW/cm2 (8 conditions) in the ElastoSens™ Bio.
- The measurement time varied between 0 and 500 s with a time step of 3 s. This includes a 2 min sequence without light (to ensure that all samples were set at the same temperature) plus a 6 min light exposure sequence.
AI TRAINING AND VALIDATION
The training dataset was composed of 90 experimental kinetics (i.e. time evolution of the shear storage modulus G’), for the different combinations of PEGDA concentration and light intensity (Figure 2).
The validation phase can be further divided in two steps (Figure 2B). First, we provide to the model different combinations of PEGDA, light intensity and time that were different from the ones provided in the training phase (validation inputs). The AI trained model predicted the output, which in this case is the time evolution of the shear storage modulus (predicted output). Then, using the ElastoSens™ Bio, we experimentally measured the gelation kinetics of samples formulated with exactly the same validation input parameters that we used to generate the predicted gelation kinetics.
Figure 2. Schematic representation of the AI training and validation phases.
To validate the accuracy of the predicted output, we calculated the mean error for each curve using the following equation:
RESULTS
Figure 3 shows the kinetics of the complete database obtained with the ElastoSens™ Bio. The shear storage modulus G’ increased with the PEGDA concentration (light intensity was kept constant at 16 mW/cm2 – Figure 3A), showing that a more rigid hydrogel was obtained with higher amounts of monomer. This can be explained by a higher polymer content in the hydrogel, which translates in a higher crosslinking density. The rate of crosslinking (exhibited by the slope of the curves) also increased with the PEGDA concentration. The light intensity accelerated the polymerization by increasing both the rate of crosslinking and the gelation time (Figure 3B), since the solutions started gelifying earlier when higher light intensities were applied.
Figure 3. Effect of PEGDA concentration (A) and light intensity (B) on the gelation kinetics of PEGDA hydrogels. This database was obtained with the use of ElastoSens™ Bio.
Figure 4 shows the gelation curves for three measured (orange dashed lines) and predicted (dark black lines) kinetics corresponding to three different combinations of PEGDA and light intensity (12% PEGDA, 8 mW/cm2; 9.5% PEGDA, 4 mW/cm2; 6.5% PEGDA, 2 mW/cm2). The shear storage modulus (G’) and the crosslinking rate increased with the PEGDA concentration. The predicted kinetics curves greatly fitted the experimentally measured ones (3% average Mean error), demonstrating the success of the AI model to predict the gelation kinetics and the mechanical properties of the PEGDA gels.
Figure 4. Predicted (dark blue lines) vs. Measured (orange dashed lines) gelation kinetics of PEGDA hydrogels.
The AI trained model determined the importance of each input (feature) for building the predictive model (Table 1). The model is mostly dependent on the PEGDA concentration and on time, since the importance of these features are 57% and 42%, respectively. The light intensity had a slight influence on the model, demonstrated by a feature importance of 1%.
Table 1. Feature importance on the AI predictive model.
In addition to the whole kinetics, we also compared the predicted and measured values of the following descriptors of the gelation curves (Figure 5):
Figure 5. The descriptors of the gelation kinetics.
- The gelation time (Gel. time, s) is the time when the PEGDA solution starts to form a gel (liquid-sol transition), which is defined by the time when tan(𝛿) is maximum.
- The rate of crosslinking (Rate, Pa/s) is the first derivative of the shear storage modulus G’ (slope of the curve, dG’/dt). The maximum rate of crosslinking describes the maximum speed of the polymerization reaction.
- The shear storage modulus at 400s (G’ (400s), Pa) describes the shear elastic modulus of the hydrogel after the gelation process (plateau of the curve).
Figure 6 depicts the correlation between the experimental and the predicted values for each descriptor. All three correlations show a linear distribution, with slopes of approximately 1 and with coefficient of determination R2≥0.97, which consistently demonstrates the high level of accuracy achieved by the AI-based prediction. One can observe that the distribution of the gelation time points is a bit more dispersed. This may be due to the low contrast in gelation time between the different conditions (approximately 25 seconds) and the fact that the time step between measurements was 3 seconds. However, the good correlation is demonstrated by a R2 coefficient of 0.969 (Figure 6A).
Figure 6. The correlation between the predicted and measured values for each descriptor are represented in this figure.
CONCLUSIONS AND PERSPECTIVES
In this study, an AI model was developed for the prediction of the gelation kinetics and viscoelastic properties of PEGDA hydrogels. ElastoSens™ Bio was used to generate good quality databases for the training and the validation of the AI predictive model. The AI model was successfully validated with a good accuracy: 3% average Mean error for the prediction of kinetics and R2≥0.97 for the prediction of curve descriptors.
Understanding how complex hydrogels behave when multiple parameters of their formulation change has the potential to widespread their use and to accelerate the development of new applications and products for regenerative medicine and drug delivery.
REFERENCES
[1] Blacklock, J., Vetter, A., Lankenau, A., Oupický, D., & Möhwald, H. (2010). Tuning the mechanical properties of bioreducible multilayer films for improved cell adhesion and transfection activity. Biomaterials, 31(27), 7167-7174.
[2] Suwardi, A., Wang, F., Xue, K., Han, M. Y., Teo, P., Wang, P., … & Loh, X. J. (2022). Machine Learning‐Driven Biomaterials Evolution. Advanced Materials, 34(1), 2102703.
[3] Li, F., Han, J., Cao, T., Lam, W., Fan, B., Tang, W., … & Li, L. (2019). Design of self-assembly dipeptide hydrogels and machine learning via their chemical features. Proceedings of the National Academy of Sciences, 116(23), 11259-11264.
[4] Yang, J., Mei, Y., Hook, A. L., Taylor, M., Urquhart, A. J., Bogatyrev, S. R., … & Alexander, M. R. (2010). Polymer surface functionalities that control human embryoid body cell adhesion revealed by high throughput surface characterization of combinatorial material microarrays. Biomaterials, 31(34), 8827-8838.
[5] Fairbanks, B. D., Schwartz, M. P., Bowman, C. N., & Anseth, K. S. (2009). Photoinitiated polymerization of PEG-diacrylate with lithium phenyl-2, 4, 6-trimethylbenzoylphosphinate: polymerization rate and cytocompatibility. Biomaterials, 30(35), 6702-6707.
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