predicting elastic modulus of calcium phosphate-containing 3d composite bone scaffolds using machine-learning approaches

In this work, we implemented machine learning (ml) regression tools to predict the elastic moduli of 3d composite scaffolds based on calcium phosphates (such as hydroxyapatite, tricalcium phosphate, biphasic calcium phosphate, etc.) and polymers (such as alginate, chitosan, polycaprolactone, etc.) for bone tissue engineering applications. the study aimed to evaluate the performance of multiple linear regression (lr), ridge regression (rg), random forest (rf), and decision tree regression (dtr) models in predicting the modulus of 3d bone scaffolds. this investigation used a dataset of 3d composite scaffolds with varying compositions of calcium phosphates and polymers. the data for this work was extracted from over 100 case study papers on 10 types of calcium phosphates and 50 types of polymers. calcium phosphates were represented to ml models based on the presence of elements and compounds in their composition. on the other hand, polymers were coded using smiles chemical notation and converted into chemical fingerprints by the rdkit library in python. two fingerprinting approaches were implemented: maccskeys and morgan. maccskeys converts any smiles string into an array of 166 zeros and ones based on the presence of atoms and bonds, while the morgan method fragments the chemical structure and makes a more unique fingerprint. in contrast to maccskeys, the output size of the morgan fingerprint array can be tuned to reach an optimum result. different sizes of morgan fingerprints ranging from 50 to 1000 arrays were examined, and the best prediction results were achieved with an array size of 500. other features that were extracted from the literature included the calcium phosphate content, porosity of the scaffold, and the average pore size. the dataset was split into training sets (70%) and testing sets (30%), and the models were trained on the former and evaluated on the latter. the study found that the random forest model showed the best results in predicting the moduli of the composite scaffolds. the random forest model had the highest r-squared value (0.94) among all the models tested (0.57 for lr, 0.59 for rg, and 0.87 for dtr). k-fold cross-validation has also been performed and the rf showed the highest value of 0.69 compared to that of rg and dtr regression (0.61 and 0.62, respectively). the findings indicated that the multiple linear regression and ridge models performed poorly in predicting the moduli of the 3d composite scaffolds. these evaluations were repeated with datasets with maccskeys fingerprints and without fingerprints. the results showed that using fingerprints significantly enhances the prediction capability of the trained models and morgan is a more accurate fingerprinting methodology compared to maccskeys. the random forest model showed the lowest mean squared error (mse) and mean absolute error (mae). the calculation of r-squared value alongside mse and mae for both the training set and the test set exhibited underfitting for multiple linear regression which indicates that this model cannot accurately capture relationships between the dataset's features and the target variable. in conclusion, the study found that the random forest model showed the best results in predicting the moduli of 3d scaffolds based on calcium phosphates and polymers. this research highlights the importance of selecting the appropriate machine-learning regression tool for predicting the moduli of 3d scaffolds. it provides a valuable contribution to the field of biomaterials, where the prediction of the moduli of 3d scaffolds is crucial for the development of new biomaterials and tissue engineering applications.