In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in ...In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane.展开更多
Background: Studies have shown a strong correlation between the growth of E2 in serum and estrone-3-glucuronide (E1-3G) in urine during ovarian stimulation. Thus, we developed theoretical models for using urinary E1-3...Background: Studies have shown a strong correlation between the growth of E2 in serum and estrone-3-glucuronide (E1-3G) in urine during ovarian stimulation. Thus, we developed theoretical models for using urinary E1-3G in ovarian stimulation and focused on their experimental verification and analysis. Methods: A prospective, observational pilot study was conducted involving 54 patients who underwent 54 cycles of ovarian stimulation. The goal was to establish the growth rate of urinary E1-3G during the course of stimulation and to determine the daily upper and lower limits of growth rates at which stimulation is appropriate and safe. Controlled ovarian stimulation was performed using two different stimulation protocols—an antagonist protocol in 25 cases and a progestin-primed ovarian stimulation protocol (PPOS) in 29 cases, with fixed doses of gonadotropins. From the second day of stimulation, patients self-measured their daily urine E1-3G levels at home using a portable analyzer. In parallel, a standard ultrasound follow-up protocol accompanied by a determination of E2, LH, and P levels was applied to optimally control stimulation. Results: The average daily growth rates in both groups were about 50%. The daily increase in E1-3G for the antagonist protocol ranged from 14% to 79%, while they were 28% to 79% for the PPOS protocol. Conclusion: This is the first study to analyze the dynamics of E1-3G in two different protocols and to estimate the limits of its increase during the entire course of the stimulation. The results confirm our theoretical model for the viability of using urinary E1-3G for monitoring ovarian stimulation.展开更多
文摘In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane.
文摘Background: Studies have shown a strong correlation between the growth of E2 in serum and estrone-3-glucuronide (E1-3G) in urine during ovarian stimulation. Thus, we developed theoretical models for using urinary E1-3G in ovarian stimulation and focused on their experimental verification and analysis. Methods: A prospective, observational pilot study was conducted involving 54 patients who underwent 54 cycles of ovarian stimulation. The goal was to establish the growth rate of urinary E1-3G during the course of stimulation and to determine the daily upper and lower limits of growth rates at which stimulation is appropriate and safe. Controlled ovarian stimulation was performed using two different stimulation protocols—an antagonist protocol in 25 cases and a progestin-primed ovarian stimulation protocol (PPOS) in 29 cases, with fixed doses of gonadotropins. From the second day of stimulation, patients self-measured their daily urine E1-3G levels at home using a portable analyzer. In parallel, a standard ultrasound follow-up protocol accompanied by a determination of E2, LH, and P levels was applied to optimally control stimulation. Results: The average daily growth rates in both groups were about 50%. The daily increase in E1-3G for the antagonist protocol ranged from 14% to 79%, while they were 28% to 79% for the PPOS protocol. Conclusion: This is the first study to analyze the dynamics of E1-3G in two different protocols and to estimate the limits of its increase during the entire course of the stimulation. The results confirm our theoretical model for the viability of using urinary E1-3G for monitoring ovarian stimulation.
