Machine Learning Model for Predicting the Material Properties and Bone Formation Rate and Direct Inverse Analysis of the Model for New Synthesis Conditions of Bioceramics

Abstract

Bioceramics, such as hydroxyapatite and β-tricalcium phosphate, are widely used in orthopedics and oral surgery because they are free in shape and size and are not harvested from patients or donors. General development of bioceramics requires a great deal of effort, a long time, and many animal experiments. Because an animal experiment takes several months and is currently regarded as an ethical problem, the number of experiments should be reduced. In this study, machine learning was applied to construct mathematical models to predict the material properties, including the porosity, compressive strength, Ca2+ dissolution rate, and bone formation rate, from the synthesis conditions and to design synthesis conditions of bioceramics with desired bone formation rates. We propose two types of models: model 1 to predict the material properties, crystallite sizes, and second selected Fourier transform infrared wavenumbers of the resulting bioceramics from the synthesis conditions, such as the starting powder conditions, and model 2 to predict the bone formation rate from the material properties, crystallite sizes, second selected Fourier transform infrared wavenumbers, and animal experimental conditions of bioceramics. Both models were constructed using Gaussian mixture regression, enabling direct inverse analysis of the models. Furthermore, by visualization of the models, the relationships among the bone formation rate, material properties, and animal experimental conditions can be understood to establish guidelines for designing the synthesis conditions. We succeeded in designing artificial bone synthesis conditions with bone formation rate exceeding existing bone formation rates.

Material Design of Porous Hydroxyapatite Ceramics via Inverse Analysis of an Estimation Model for Bone-Forming Ability Based on Machine Learning and Experimental Validation of Biological Hard Tissue Responses

“…Models 1 and Model 2 were constructed using Gaussian mixture regression (GMR) [25,26]. GMR is a regression analysis method with Gaussian mixture model (GMM) [27], a machine learning model that represents the relationship between y and the explanatory variables x as a superposition of multiple gaussian distributions.…”

“…To evaluate the accuracy of Model 1 and Model 2, we used double cross-validation (DCV) [25,28], a method that allows accuracy verification with a small number of samples. DCV is a nested cross-validation (CV) method used to evaluate the predictability of a model.…”

“…Although there have been studies using machine learning to predict biomaterial structure and properties [22,23] and predict bone formation in animal experiments with materials [24], it has been impossible to predict the in vivo responses in animal experiments from bioceramic material synthesis conditions using machine learning. Although we have previously constructed a model that predicts bone-formation rates using the results of animal experiments on developed bioceramics and proposed material fabrication conditions based on desired bone-formation rates [25], we have not performed experiments based on the proposed experimental conditions or validated the validity and practicality of the models.…”

Prediction of bone formation rate of bioceramics using machine learning and image analysis

“…6,7 In our previous study, to reduce the duration, cost, and the number of animal experiments, the bone formation rate was first predicted using a machine learning model. 8,9 Synthesis conditions, material properties, implantation conditions, FT-IR, and XRD were used as explanatory variables X, the bone formation rate was used as the objective variable Y, and then a machine learning model Y = f (X) was constructed. By inputting X values into the model, the bone formation rate could be predicted without the need for animal experiments.…”