A mechanical model of blastocyst hatching. (January 2021) - Tvergaard, Viggo; Needleman, Daniel; Needleman, Alan
Abstract: We develop a continuum mechanics model of blastocyst hatching. The blastocyst and the zona pellucida are modeled as concentric thick-walled initially spherical shells embedded in a viscous medium. Each shell is characterized by a nonlinear elastic–viscous–constitutive relation. The stiffer outer shell (the zona pellucida) contains an opening. The softer inner shell (the blastocyst) is subject to a continually increasing pressure, which can eventually drive the escape of the inner shell from the outer shell ("hatching"). The focus is on the continuum mechanics modeling framework and illustrating the sort of quantitative predictions that can be made. Numerical examples are presented for the predicted dependence of the evolution of the escape process on values of parameters characterizing the constitutive response of the shells, on the viscosity of the external medium and on the size of the opening in the zona pellucida.