IMPROVING 9-INTERSECTION MODEL BY REPLACING THE COMPLEMENT WITH VORONOI REGION

9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (?A), interior (A 0) and (A ?) withB’s boundary (?B), interior (B 0) and exterior (B ?). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (?A∩B ?,A 0∩?B ?,A ?∩?B,A ?∩B 0 andA ?∩B ?)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.

Endometrial membrane organoids from human embryonic stem cell combined with the 3D Matrigel for endometrium regeneration in asherman syndrome

Asherman’s syndrome(AS),a leading cause of uterine infertility worldwide,is characterized by scarring of the uterine surfaces lacking endometrial epithelial cells,which prevents endometrial regeneration.Current research on cell therapy for AS focuses on mesenchymal and adult stem cells from the endometrium.However,insufficient number,lack of purity,and rapid senescence of endometrial epithelial progenitor cells(EEPCs)during experimental processes restrict their use in cell therapies.In this study,we induced human embryonic stem cells-9(H9-ESC)into EEPCs by optimizing the induction factors from the definitive endoderm.EEPCs,which act as endometrial epithelial cells,accompanied by human endometrial stromal cells provide a niche environment for the development of endometrial membrane organoids(EMOs)in an in vitro 3D culture model.To investigate the function of EMOs,we transplanted tissue-engineered constructs with EMOs into an in vivo rat AS model.The implantation of EMOs into the damaged endometrium facilitates endometrial regeneration and angiogenesis.Implanting EMOs developed from human embryonic stem cells into the endometrium might prove useful for“endometrial re-engineering”in the treatment of Asherman’s syndrome.