Analysis of two layered peristaltic-ciliary transport of Jeffrey fluid and in vitro preimplantation embryo development

The analysis of peristaltic-ciliary transport in the human female fallopian tube, specifically in relation to the growing embryo, is a matter of considerable physiological importance. This paper proposes a biomechanical model that incorporates a finite permeable tube consisting of two layers, where the Jeffrey fluid model characterizes the viscoelastic properties of the growing embryo and continuously secreting fluid. Jeffrey fluid entering with some negative pressure gradient forms the core fluid layer while continuously secreting Jeffrey fluid forms the peripheral fluid layer. The resulting partial differential equations are solved for closed-form solutions after employing the assumption of long wavelength. The analysis delineated that increasing the constant secretion velocity, Darcy number, and Reynolds number leads to a decrease in the appropriate residue time of the core fluid layer and a reduction in the size of the secreting fluid bolus in the peripheral fluid layer. Eventually, the boluses completely disappear when the constant secretion velocity exceeds 3.0 Progesterone ( \(P_4\) $P_4$ ) and estradiol ( \(E_2\) $E_2$ ) directly regulate the transportation of the growing embryo, while luteinizing hormone (LH) and follicle-stimulating hormone (FSH), prolactin, anti-mullerian hormone (AMH), and thyroid-stimulating hormone (TSH) have an indirect effects. Based on the number and size of blastomeres, the percentage of fragmentation, and the presence of multinucleated blastomeres two groups were formed in an in vitro experiment. Out of 50 patients, 26 (76.5%) were pregnant in a group of the good quality embryos, and only 8 (23.5%) were in a group of the bad quality embryos. The transport of growing embryo in the human fallopian tube and preimplantation development of human embryos in in vitro are constraint by baseline hormones FSH, LH, prolactin, \(E_{2}\) $E_2$ , AMH, and TSH.