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Abstract
Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell communication to replicate common spatial arrangements like checkerboard and engulfing patterns. In this model, the cell-cell communication has been implemented as a signal that disperses throughout the tissue. On the other hand, machine learning models have been developed for pattern recognition and pattern reconstruction tasks. We combined synthetic data generated by the mathematical model with spatial summary statistics and deep learning algorithms to recognize and reconstruct cell fate patterns in organoids of mouse embryonic stem cells. Application of Moran’s index and pair correlation functions for in vitro and synthetic data from the model showed local clustering and radial segregation. To assess the patterns as a whole, a graph neural network was developed and trained on synthetic data from the model. Application to in vitro data predicted a low signal dispersion value. To test this result, we implemented a multilayer perceptron for the prediction of a given cell fate based on the fates of the neighboring cells. The results show a 70% accuracy of cell fate imputation based on the nine nearest neighbors of a cell. Overall, our approach combines deep learning with mathematical modeling to link cell fate patterns with potential underlying mechanisms.
Author summary
Mammalian embryo development relies on organized differentiation of stem cells into different lineages. Particularly at the early stages of embryogenesis, cells of different fates form three-dimensional spatial patterns that are difficult to identify by eye. Pattern quantification and mathematical modeling have produced first insights into potential mechanisms for the cell fate arrangements. However, these approaches have relied on classifications of the patterns such as inside-out or random, or used summary statistics such as pair correlation functions or cluster radii. Deep neural networks allow characterizing patterns directly. Since the tissue context can be readily reproduced by a graph, we implemented a graph neural network to characterize the patterns of embryonic stem cell organoids as a whole. In addition, we implemented a multilayer perceptron model to reconstruct the fate of a given cell based on its neighbors. To train and test the models, we used synthetic data generated by our mathematical model for cell-cell communication. This interplay of deep learning and mathematical modeling in combination with summary statistics allowed us to identify a potential mechanism for cell fate determination in mouse embryonic stem cells. Our results agree with a mechanism with a dispersion of the intercellular signal that links a cell’s fate to those of the local neighborhood.
Objective: This study aims to critically evaluate the effectiveness and accuracy of a time safing and cost-efficient open-source algorithm for in-house planning of mandibular reconstructions using the free osteocutaneous fibula graft. The evaluation focuses on quantifying anatomical accuracy and assessing the impact on ischemia time.
Methods: A pilot study was conducted, including patients who underwent in-house planned computer-aided design and manufacturing (CAD/CAM) of free fibula flaps between 2021 and 2023. Out of all patient cases, we included all with postoperative 3D imaging in the study. The study utilized open-source software tools for the planning step, and three-dimensional (3D) printing techniques. The Hausdorff distance and Dice coefficient metrics were used to evaluate the accuracy of the planning procedure.
Results: The study assessed eight patients (five males and three females, mean age 61.75 ± 3.69 years) with different diagnoses such as osteoradionecrosis and oral squamous cell carcinoma. The average ischemia time was 68.38 ± 27.95 min. For the evaluation of preoperative planning vs. the postoperative outcome, the mean Hausdorff Distance was 1.22 ± 0.40. The Dice Coefficients yielded a mean of 0.77 ± 0.07, suggesting a satisfactory concordance between the planned and postoperative states. Dice Coefficient and Hausdorff Distance revealed significant correlations with ischemia time (Spearman's rho = −0.810, p = 0.015 and Spearman's rho = 0.762, p = 0.028, respectively). Linear regression models adjusting for disease type further substantiated these findings.
Conclusions: The in-house planning algorithm not only achieved high anatomical accuracy, as reflected by the Dice Coefficients and Hausdorff Distance metrics, but this accuracy also exhibited a significant correlation with reduced ischemia time. This underlines the critical role of meticulous planning in surgical outcomes. Additionally, the algorithm's open-source nature renders it cost-efficient, easy to learn, and broadly applicable, offering promising avenues for enhancing both healthcare affordability and accessibility.