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Mammalian embryonic development is subject to complex biological relationships that need to be understood. However, before the whole structure of development can be put together, the individual building blocks must first be understood in more detail. One of these building blocks is the second cell fate decision and describes the differentiation of cells of the inner cell mass of the embryo into epiblast and primitive endoderm cells. These cells then spatially segregate and form the subsequent bases for the embryo and yolk sac, respectively. In organoids of the inner cell mass, these two types of progenitor cells are also observed to form, and to some extent to spatially separate. This work has been devoted to these phenomena over the past three years. Plenty of studies already provide some insights into the basic mechanics of this cell differentiation, such that the first signs of epiblast and primitive endoderm differentiation, are the expression levels of transcription factors NANOG and GATA6. Here, cells with low expression of GATA6 and high expression of NANOG adopt the epiblast fate. If the expressions are reversed, a primitive endoderm cell is formed. Regarding the spatial segregation of the two cell types, it is not yet clear what mechanism leads to this. A common hypothesis suggests the differential adhesion of cell as the cause for the spatial rearrangement of cells. In this thesis however, the possibility of a global cell-cell communication is investigated. The approach chosen to study these phenomena follows the motto "mathematics is biology's next microscope". Mathematical modeling is used to transform the central gene regulatory network at the heart of this work into a system of equations that allows us to describe the temporal evolution of NANOG and GATA6 under the influence of an external signal. Special attention is paid to the derivation of new models using methods of statistical mechanics, as well as the comparison with existing models. After a detailed stability analysis the advantages of the derived model become clear by the fact that an exact relationship of the model parameters and the formation of heterogeneous mixtures of two cell types was found. Thus, the model can be easily controlled and the proportions of the resulting cell types can be estimated in advance. This mathematical model is also combined with a mechanism for global cell-cell communication, as well as a model for the growth of an organoid. It is shown that the global cell-cell communication is able to unify the formation of checkerboard patterns as well as engulfing patterns based on differently propagating signals. In addition, the influence of cell division and thus organoid growth on pattern formation is studied in detail. It is shown that this is able to contribute to the formation of clusters and, as a consequence, to breathe some randomness into otherwise perfectly sorted patterns.
Integrative, three-dimensional \(in\) \(silico\) modeling of gas exchange in the human alveolus
(2024)
The lung plays a vital role by exchanging respiratory gases. At the core of this gas exchange is a simple yet crucial passive diffusion process occurring within the alveoli. These balloon-like structures, connected to the peripheral airways, are surrounded by a dense network
of small capillaries. Here, inhaled air comes into close proximity with deoxygenated blood coming from the heart, enabling the exchange of oxygen and carbon dioxide across their concentration gradients.
The efficiency of gas exchange can be measured through indicators such as the diffusion capacity of the lung for oxygen and the reaction half-time. A notable discrepancy exists in humans between physiological estimates of diffusion capacity and the theoretical maximum capacity under optimal structural conditions (morphological estimate). This discrepancy is influenced by a range of interrelated factors, including structural elements like the surface area and thickness of the diffusion barrier, as well as physiological factors such as blood flow dynamics. To unravel the different roles of these factors, we investigated how morphological and physiological properties of the human alveolar micro-environment collectively and individually influence the process of gas exchange. To this end, we developed an integrative in silico approach combining 3D morphological modeling and simulation of blood flow and of oxygen transport.
At the core of our approach lies the simulation software Alvin, serving as an interactive platform for the underlying mathematical model of oxygen transport within the alveolus. Developed by integrating and expanding existing mathematical models, our spatio-temporal model produces results in agreement with experimental data. Alvin allows for real-time parameter adjustments and the execution of multiple simultaneous simulation instances and provides detailed quantitative feedback, offering an immersive exploration of the simulated gas exchange process. The morphological and physiological parameters at play were further investigated with a focus on the microvasculature. By compiling a stereological database from the literature and 3D geometric modeling, we created a sheet-flow model as a realistic representation of the morphology of the human alveolar capillary network. Blood flow was simulated using computational fluid dynamics. Our findings were in line with previous estimations and highlighted the crucial role of viscosity models in predicting pressure drop across the microvasculature. Furthermore, we showcased how our approach can be harnessed to explore structural details, such as the connectivity of the alveolar capillary network with the vascular tree, using blood flow indices. It is important to emphasize that
so far we have relied on different data sources and that experimental validation is needed to move forward.
Integration of our findings into Alvin allowed quantification of the simulated gas exchange process through the diffusion capacity for oxygen and reaction half-time. In addition to evaluating the collective influences of the morphological and physiological properties, our interactive software facilitates the assessment of individual parameter value changes. Exploring blood volume and surface area available for gas exchange revealed linear correlations with diffusion capacity. The blood flow velocity had a positive, non-linear effect on diffusion capacity. The reaction half-time confirmed that under normal conditions, the gas exchange process is not diffusion-limited. Collectively, our alveolar model yielded a diffusion capacity value that fell in the middle of previous physiological and morphological estimates, implying that alveolar-level phenomena contribute to 50% of the diffusion capacity limitations that occur in vivo.
In summary, our integrative in silico approach disentangles various structural and functional influences on alveolar gas exchange, complementing traditional investigations in respiratory
research. We further showcase its utility in teaching and the interpretation of published data. To advance our understanding, future work should prioritize obtaining a cohesive experimental data set and identifying an appropriate viscosity model for blood flow simulations.