An analytical equation for predicting corrosion rates of biodegradable Zn–0.45Mn–0.2Mg alloy via symbolic regression

Abstract

Corrosion rates of biodegradable Zn alloys are directly related to their post-implantation safety and effectiveness. However, highly accurate and interpretable “white-box” machine learning models for predicting their corrosion rates remain largely unexplored. This study proposes a data-driven method coupled with accelerated corrosion testing for predicting the corrosion rates of biodegradable Zn–0.45Mn–0.2Mg (wt%) alloy. A symbolic regression (SR) machine-learning model was established based on an analytical expression of the corrosion rate and four corrosion parameters. Outperforming five other machine-learning models, the SR model achieved a determination coefficient of 0.97 and prediction errors in the verification experiments of less than 10%. This study contributes to a paradigm shift from qualitative to quantitative analysis for corrosion research on biodegradable metals.

1. Introduction

In recent years, biodegradable metal implants (Mg-based, Fe-based, and Zn-based alloys) have become a research hotspot in the field of medical biomaterials owing to their biodegradability, low rates of surgical complications, and elimination of secondary surgical removal risks [1–2]. However, Mg-based alloys have limitations such as high degradation rates, significant hydrogen evolution, and premature failure, while the application prospects of Fe-based alloys are limited by their low degradation rates, long-term retention of corrosion products in vivo, and chronic inflammatory reactions [3]. By contrast, Zn-based alloys offer moderate degradation rates because the standard electrode potential of Zn (−0.76 V) are between those of Mg (−2.37 V) and Fe (−0.44 V). Additionally, Zn-based alloys do not produce hydrogen during degradation, generate nontoxic and fully absorbable corrosion products, and possess favorable antibacterial properties. These characteristics make Zn-based alloys promising biodegradable alternatives to Mg- and Fe-based alloys [4]. Zn-based alloys have shown wide application potential in medical devices such as vascular stents, orthopedic implants, tissue staplers, and marker clips [5].

An ideal biodegradable implant for orthopedic and vascular applications should maintain mechanical integrity for 3–6 months post-implantation and undergo complete degradation within 1–2 years [6–9]. Therefore, corrosion rate is a critical metric for the selection of suitable Zn alloys. In vitro immersion testing of biodegradable Zn alloys has become the most common method for corrosion rate measurements owing to its simple operation and low cost [10–14]. Generally, test duration of more than one year is required to obtain the corrosion rate when the material is completely degraded; therefore, short-term accelerated corrosion is used to predict long-term corrosion rates. Accelerated corrosion methods have been extensively applied to predict the corrosion rates and service lives of materials such as steels [15–16], concrete [17–19], and polymers [20–22]; however, these methods have scarcely been extended to biodegradable metals. In addition, the use of accelerated corrosion methods to predict corrosion rates still depends primarily on expressions of traditional empirical models [18,23], and explicit prediction expressions derived using machine learning (ML) methods have rarely been reported in the available literature.

In the field of corrosion, research has been usually limited to either qualitative or quantitative analyses focusing on only one or two parameters governing the corrosion rate [24–28]. However, the corrosion rate is in fact governed by a complex interplay of multiple parameters, including the corrosion medium, temperature, time, and electrical current. Traditional theories and empirical models have faced difficulties in revealing quantitative relationships between multiple (>3) corrosion parameters and the corrosion rate. Thus, establishing explicit analytical expressions to quantitatively investigate the influence of complex corrosion parameters on the corrosion rate represents a highly promising direction for future research.

For biodegradable Zn alloys, the current data-driven research is still in the initial stages of employing “black-box” ML models. Chen et al. [29] introduced a prediction model for the corrosion rate of Zn–Mn alloys based on the support vector regression (SVR) algorithm, achieving a prediction error of 16.5%. Davletshin et al. [30] employed the extreme-gradient boosting (XGBoost