Global Existence and Weak-Strong Uniqueness for Chemotaxis Compressible Navier-Stokes Equations Modeling Vascular Network Formation.

A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier-Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, which triggers the migration of the endothelial cells and the blood vessel formation. The coupling of the equations is realized by the chemotaxis force in the momentum balance equation. The global existence of finite energy weak solutions is shown for adiabatic pressure coefficients γ>8/5. The solutions satisfy a relative energy inequality, which allows for the proof of the weak-strong uniqueness property.

Doppler Ultrasound Evaluation of the Efficacy of High Intensity Focused Ultrasound in Treatment of Cesarean Section Scar Pregnancy.

OBJECTIVE: To investigate the value of Doppler ultrasound in evaluating the efficacy of high intensity focused ultrasound (HIFU) in treatment of cesarean section scar pregnancy. STUDY DESIGN: Observational study. PLACE AND DURATION OF STUDY: Department of Ultrasonography, The Second people's Hospital of Liaocheng City Affiliated to Shandong First Medical University, China, from January 2015 to December 2017. METHODOLOGY: Forty-six patients with cesarean section scar pregnancy treated with HIFU were enrolled. Doppler ultrasound images, blood flow resistance index (RI) and ß-human chorionic gonadotropin (ß-hCG) levels were analyzed. RESULTS: Among 46 patients, 31 cases (68.89%) were embryo sac type while 15 cases (32.61%) were mass-type. After 4 weeks of HIFU treatment, among 31 cases of embryo sac type of cesarean scar pregnancy, slightly increased echogenicity and thickened walls of yolk sac were observed in 15 cases (48.39%), heart beat disappeared in 12 cases (38.71%) and fetal heart rate as still regular in four cases (12.90%). Among 15 cases of mass-type treated with 4 weeks of HIFU, echogenicity was slightly elevated at first, then echogenicity of center zone decreased, resulting in mixed echoes, finally the volumes of mass decreased to varying degrees and blood flow reduced significantly, leading to slight strong mull echoes. Compared with before treatment of HIFU, RI levels were higher after 4 weeks treatment of HIFU (p<0.001), while the blood ß-hCG levels were lower (p<0.001). CONCLUSION: Doppler ultrasound can provide accurate qualitative diagnosis of cesarean section scar pregnancy, and possess higher clinical value in evaluating the treatment efficacy of cesarean section scar pregnancy with HIFU.