These generated distinct mechanical profiles to investigate the impact of geometry and stress on early liver progenitor cell fate using a model liver development system. Using a hydrogel-based microwell platform, we produced arrays of 3D, multicellular microtissues in constrained geometries, including toroids and cylinders.
Three dimensional (3D) microenvironments provide a unique opportunity to investigate the impact of intrinsic mechanical signaling on progenitor cell differentiation.
This approach may serve as a platform for further investigation of signaling mechanisms in the liver and other developmental systems. This system, which integrates microfabrication, imaging, mechanical modeling, and quantitative analysis, demonstrates how microtissue geometry can drive patterning of mechanical stresses that regulate cell differentiation trajectories. Finite element models of predicted stress distributions, combined with mechanical measurements, demonstrates that intercellular tension correlates with increased hepatocytic fate, while compression correlates with decreased hepatocytic and increased biliary fate. Biliary markers are distributed throughout the interior regions of micropatterned tissues and are increased in toroidal tissues when compared with those in cylindrical tissues. Image segmentation allows the tracking of individual cell fate and the characterization of distinct patterning of hepatocytic makers to the outer shell of the microtissues, and the exclusion from the inner diameter surface of the toroids. Using a hydrogel-based microwell platform, arrays of 3D, multicellular microtissues in constrained geometries, including toroids and cylinders are produced. Principal Polynomial Analysis classification coding dimensionality reduction manifold learning.3D microenvironments provide a unique opportunity to investigate the impact of intrinsic mechanical signaling on progenitor cell differentiation. The performance of PPA is evaluated in dimensionality and redundancy reduction, in both synthetic and real datasets from the UCI repository. These properties are demonstrated theoretically and illustrated experimentally. And fourth, the analytical Jacobian allows the computation of the metric induced by the data, thus generalizing the Mahalanobis distance. Third, the analytical nature of PPA leads to a clear geometrical interpretation of the manifold: it allows the computation of Frenet-Serret frames (local features) and of generalized curvatures at any point of the space. Volume preservation also allows an easy computation of information theoretic quantities, such as the reduction in multi-information after the transform. Moreover, it allows to evaluate the performance of dimensionality reduction in sensible (input-domain) units. Invertibility is an important advantage over other learning methods, because it permits to understand the identified features in the input domain where the data has physical meaning. Second, such an inverse can be obtained in closed form. First, PPA is a volume-preserving map, which in turn guarantees the existence of the inverse. Moreover, PPA shows a number of interesting analytical properties. Contrarily to previous approaches, PPA reduces to performing simple univariate regressions, which makes it computationally feasible and robust. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves, instead of straight lines. This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data.