## 1 Introduction  
Biodegradable magnesium (Mg) alloys are becoming key materials for biomedical orthopedic applications because of their light weight and high strength md [1]. Mg alloys' density of 1.7 g/cm\({}^{3}\) to 2.0 g/cm\({}^{3}\) is close to the natural bone density which ranges from 1.8 to 2.1 g/cm\({}^{3}\)[2]. The stiffness modulus of pure magnesium is 45 GPa, which is in the range of human bone modulus of elasticity (40 to 57 GPa) [3; 4]. The similarity in mechanical properties of magnesium with natural bone makes it an excellent candidate for biomedical applications for developing biodegradable orthopedic medical devices [1]. However, the high corrosion rate of Mg alloys limits its orthopedic applications. Zinc (Zn) has been used to alloy Mg (Mg-Zn alloy) to improve the corrosion resistance [5]. Zn also was alloyed with Mg to Zn-Mg alloy showing homogenous microstructure, slowly uniform degradation, improved mechanical properties, and good biocompatibility [6]. Zn-Mg alloy was believed to be an excellent candidate material for the application of load-bearing biodegradable implant [6]. Biodegradable alloys have been studied in various physiological environments to understand the corrosion behavior of these biomaterials [1; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. Corrosion rate is one of the most studied properties of biodegradable alloys due to the importance of describing the corrosion behavior quantitatively in wide-ranging application environments.  
Volume loss, mass loss, and hydrogen evolution have been used to determine corrosion rate of biodegradable alloys in in vitro tests; though these methods often give different rates [19]. There are discrepancies between degradation rate of magnesium in vitro tests, weight loss, and evolution of hydrogen gas, as compared to in vivo studies in orthopedics applications [20; 21]. Corrosion rate of Mg-Gd-Zn alloys calculated by mass loss was lower than that calculated by hydrogen evolution from a eudiometer [22]. The corrosion rates obtained from the mass loss measurements were presumably because it is difficult to remove the corrosion products completely after these samples corroded severely in the long immersion test [22]. Corrosion rates of magnesium and its alloys in vitro is studied extensively to find a relationship on the weight loss to evolution of hydrogen gas after immersion testing [7; 18; 23]. However, accumulation of non-soluble products on the samples during immersion time makes weight loss not viable to accurately determine degradation [24]. The tendency of the corrosion rates obtained from in vitro corrosion tests calculated by mass loss were in the opposite direction as those obtained from the in vivo study measured by volume loss [25]. Methodology to evaluate the corrosion rates in vitro and in vivo has been reviewed, in which mass loss was used in an in vitro immersion test [26; 27] and strictly speaking not an in vivo method [28]. Volume loss to calculate corrosion rate has been used in studies in vivo [26; 29] as well as ex vivo and in vitro [30; 31].  
In this study, mass loss, volume loss, and hydrogen evolution were used to calculate corrosion rate of four Mg-based alloys, pure Mg and Zn. The approach of this research effort used eudiometric set ups to immerse biodegradable samples, and then conducted measurement of volume of hydrogen gas evolution every 48 h up to 14 days. The weight loss by a scale and volume loss by Micro-computed tomography (micro-CT) measurements were collected after 30 days' immersion in the eudiometer chambers. Corrosion rates of tested biodegradable samples calculated by hydrogen evolution, mass loss, and volume loss were compared statistically.