Therefore, a comparison of the geometric effects reflected by the generalizations of the Berry phase of purified states or thermal vacua is expected to be achievable in future experiments on quantum computers or quantum simulators. For example, one may consider two identical composite quantum systems of Example V.1 of the generalized Berry phase and then apply a partial transposition to one of the composite systems. As a consequence, the composite system with a partial transposition corresponds to a purified state while the one without partial transposition may be viewed as a thermal vacuum. By applying parallel transport that involves the ancilla to both composite systems and extract their generalized Berry phase after a cycle, a π-phase difference is expected between the two composite systems. Given the large phase difference between them after a cycle, the result is robust against small perturbations or noise from the hardware and offers another demonstration of geometrical protection of information. We have presented two generalizations of the Berry phase, the thermal Berry phase and generalized Berry phase, for distinguishing the two state-vector representations of mixed states via the purified state and thermal vacuum. From the geometrical and physical points of view, pots with drainage holes the generalized Berry phase has more desirable properties since the thermal Berry phase is generated by a temperature-dependent thermal Hamiltonian and may carry non-geometrical information.
We caution that while the transformations can be on the system, ancilla, or both in the construction of the generalized Berry phase, an operation on the ancilla is necessary if we want to differentiate the purified state and thermal vacuum.The two state-vector representations of mixed states via purified states or thermal vacua have been developed in different branches of physics, but both have been realized on quantum computers [32, 33]. We have pointed out that their difference lies in a partial transposition of the ancilla, which has its origin in the Hilbert-Schmidt product. Available physical quantities, including previously studied geometric phases, cannot differentiate the two representations. By analogue of the adiabatic process of pure states, the thermal Berry phase has been constructed and shown to differentiate a purified state froma thermal vacuum. However, the thermal Berry phase may include non-geometrical information. The generalized Berry phase is then constructed by generalizing the parallel-transport condition to properly include the system and ancilla, and only geometrical contributions are included. Depending on the protocol and setup, the generalized Berry phase may also differentiate the purified state and thermal vacuum. Future demonstrations of the interplay between geometric effects and partial transposition of state-vector representations of mixed states on quantum computers or simulators will advance our understanding of quantum systems at finite temperatures.Magnesium has great potentials to serve as next-generation bio-resorbable implants for medical applications due to their excellent mechanical properties, biodegradability, and bio-compatibility . Biodegradability of Mg-based implants and interactions with relevant cells have been studied in vitro for orthopedic and urological applications. Most of the in vitro studies on the degradation of Mg-based implants were performed by immersion in physiologically relevant fluids at the body temperature of 37°C to represent the chemical and thermal environment in vivo.
It is desirable to include physiological loading as one of the key contributing factors when studying in vitro degradation of Mgbased metals for medical implant applications, because mechanical stress could increase the corrosion rates of Mg-based alloys and composites. For example, cyclic loading significantly increased the corrosion rates of high purity magnesium , binary Mg-1Ca, and ternary Mg–2Zn–0.2Ca alloys in simulated body fluid. Li et al. reported that the degradation of Mg/Poly wires was accelerated under a dynamic compressive stress of 0.9 MPa at a frequency of 2.5 Hz. Mg-based alloys are known to be susceptible to stress corrosion cracking ; and Mg-based implants may degrade faster and experience sudden fracture under load, especially in a humid environment such as inside the body. Mechanical behaviors of Mg have been investigated using a slow rate test method in modified simulated body fluid, and Mg did show a lower elongation and ultimate tensile strength due to SSC. Thus, it is important to study the degradation behaviors of Mg-based implants under load for a long period of time, preferably weeks to months, to understand the properties of these implants as they degrade. Although in vivo studies in animal models can provide complimentary information about the performance of Mg-based implants under load, the load in small animal models, such as rats, cannot be directly translated to the human study due to the significant differences in musculoskeletal structures between small mammals and human. Before clinical studies, large animal models, such as sheep and dogs, are often recommended for evaluating orthopedic implants because they have similar loading conditions as human. However, long-term studies in large animal models are always costly and involving sacrifice of many animals.
Therefore, the objective of this study was to develop and build a novel loading device to simulate the human-like physiological loading conditions in vitro for studying biodegradable implants in a long period of time from weeks to months. The degradation behaviors of Mg rods under applied loads of 500 N were investigated for up to two weeks using this loading device. Mg rods were cut into 15 mm × 6 mm using a handsaw, and then polished using silicon carbide papers from 600 grit to 1200 grit. The polished samples were degreased and cleaned in acetone for 30 min and in 100% ethanol for 30 min respectively, using an ultrasonic cleaner . Before immersion, all of the Mg samples were weighed using an analytical balance , and the mass of each sample was recorded as the initial mass . The well design of the loading chamber for housing the Mg samples is shown in Figure 3. To prevent the galvanic corrosion between the Mg samples and the piston, the wells and the caps on the pistons were machined out of Teflon to avoid the metal to metal contact. The Mg rod samples were placed into Teflon wells and immersed in 2.5 mL of revised simulated body fluid that has the same ionic composition as human blood plasma. A load of 500 N was applied on each Mg rod at room temperature until the prescribed immersion time point is reached. The Mg rod controls were also placed in the Teflon wells respectively and immersed in 2.5 mL of rSBF but without load. The Mg rod samples were immersed in rSBF for 3 days, 1 week, and 2 weeks. The rSBF was replenished every other day. The immersion degradation experiment was run in triplicate concurrently. After each immersion period, the rSBF was collected from the wells and the Mg rod samples were dried in a vacuum at room temperature. The macroscopic images of the dried Mg rod samples that were tested with or without 500 N of load were taken using a camera . The dried Mg samples were also weighed using an analytical balance to determine the final mass after immersion. The mass change of Mg samples at different time points was then calculated following the equation /Mo, drainage pot where Mf is the final mass and Mo is the initial mass. The pH of the collected rSBF was measured using a pH meter . The Mg2+ ion concentrations were quantified using inductively coupled plasma – optical emission spectrometry . Briefly, the collected solutions from each well were diluted with deionized water by a factor of 1:100 into a total volume of 10 mL. Mg2+ ion concentrations were then quantified based on the calibration curves generated using Mg2+ standards serially diluted to a concentration of 0.5, 1, 2, and 5 mg/L. The characterization process was repeated for each time point.The macroscopic images of the Mg under load and Mg controls without load showed different surface morphologies after 14 days of immersion in rSBF . Generally, all the Mg samples showed deposition of degradation products after 3 days of immersion. The white degradation products increased as the time increased during the immersion. Mg rods under load, however, had a less degradation products on the surface than that of Mg controls, especially at 7 days and 14 days. Figure 4b shows the mass change of the Mg under load and Mg controls after 14 days of immersion in rSBF. Statistically significant difference was found among the Mg-based samples during the 11 days of immersion [F=175.7, p<0.0001]. All the Mg samples had a significant mass decrease after the immersion. At the 3 days of immersion, all the Mg samples had a mass increase due to the deposition of the degradation products. The Mg under load showed a higher mass increase than the Mg controls. Starting at 7 days of immersion, all the Mg samples had a significant mass decrease, where the Mg under load showed a significantly higher mass loss than the Mg controls. At 14 days of immersion, the mass of Mg controls had no significant change in comparison with the previous time point.
The mass of Mg under load, however, showed a mass loss which was significantly lower than the Mg controls.Figure 4c displays the pH of the rSBF for the Mg under load and Mg controls after 14 days of immersion. Statistically significant difference was found among the Mg-based samples during the 11 days of immersion [F=10.86, p=0.004]. Generally, the pH of Mg-based samples showed an increasing trend as time increased during the immersion. When comparing the Mg under load and Mg controls without load, the pH of Mg controls was higher than that of Mg under load at 3 days and 7 days of immersion. The pH of Mg controls at 14 days, however, showed a lower pH than the previous time point, possibly because the continuous deposition of degradation products slowed the degradation of Mg samples. At 14 days of immersion, the pH of Mg controls was significantly lower than that of Mg under load. From Figure 4d, the Mg2+ ion concentration of the rSBF for the Mg rods under load and Mg controls showed a significant increase during the 14 days of immersion. Statistically significant difference was found among the Mg-based samples during the 11 days of immersion F=55.82, p<0.0001]. The Mg2+ ion concentrations of Mg-based samples showed an increasing trend as time increased during the immersion. The Mg under load showed a higher Mg2+ ion concentration in average than that of Mg controls at all-time points during the immersion. Statistical difference was found at 3 days of immersion and 14 days of immersion.Engineering the loading device for studying Mg-based bio-materials in vitro involves three major challenges, that is, automating, powering, and down scaling in size. Although the current version of our loading device meets the critical design criteria and functional requirements for studying Mg degradation under load, further improvements in the following aspects are still recommended to make the device more user friendly and more robust for repeated experiments. First, automating operation of the loading device can greatly improve the repeatability of experimental results and benefits the users especially in the long-term studies that span from weeks to months. The current pneumatic pistons are powered through an air compressor, which needs to be manually adjusted by the user due to natural accruing air leaks in the system. To improve this, the pneumatic powered pistons can be replaced with electrically powered pistons, and a feedback or closed loop control system can be added for autonomous regulation. One piston type of interest would be hydraulic pistons as they are small, and able to output large forces that would be required for testing various medical implant material. Using these electrical powered pistons, a feedback loop can be created through various means, such as using electrical components that read the output force of the electrical powered pistons, and with that data the device could self correct itself to the desired load output without the need of a user. To implement this, a self adjusting controller such as a PID controller, would be able to provide the device with both versatility and higher accuracy. Second, the device should simulate the body conditions more closely during the in vitro experiments in addition to applying a load onto the implant material. Specifically, it is beneficial to conduct the experiments under standard cell culture conditions inside an incubator, i.e., a sterile, 37°C, 5% CO2/95% air, humidified environment, because such environment resembles the conditions inside the body.