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1. A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth

   https://doi.org/10.1038/s41540-023-00278-5  

   Ramezani, Alireza; Britton, Samuel; Zandi, Roya; Alber, Mark; Nematbakhsh, Ali; Chen, Weitao (May 2023, npj Systems Biology and Applications)

   Abstract The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate. 

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2. Diffeomorphic shape evolution coupled with a reaction-diffusion PDE on a growth potential

   https://doi.org/10.1090/qam/1600  

   Hsieh, Dai-Ni; Arguillère, Sylvain; Charon, Nicolas; Younes, Laurent (March 2022, Quarterly of Applied Mathematics)

   This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D. 

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3. Domain fluctuations in ferroelectric low-strain BaTiO3 thin film

   Li, Jianheng; Zhong, Louie; Jangid, Rahul; Meera, Fnu; Rippy, Geoffery; Ainslie, Kenneth; Kohne, Chris; Everhardt, Arnoud; Noheda, Beatriz; Zhang, Yugang; et al (November 2020, Physical review materials)

   null (Ed.)

   A ferroelectric BaTiO3 thin film grown on a NdScO3 substrate was studied using x-ray photon correlation spectroscopy (XPCS) to characterize thermal fluctuations near the a/b to a/c domain structure transformation present in this low-strain material, which is absent in the bulk. XPCS studies provide a direct comparison of the role of domain fluctuations in first- and second-order phase transformations. The a/b to a/c domain trans- formation is accompanied by a decrease in fluctuation timescales, and an increase in intensity and correlation length. Surprisingly, domain fluctuations are observed up to 25 °C above the transformation, concomitant with the growth of a/c domains and coexistence of both domain types. After a small window of stability, as the Curie temperature is approached, a/c domain fluctuations are observed, albeit slower, potentially due to the structural transformation associated with the ferroelectric to paraelectric transformation. The observed time evolution and reconfiguration of domain patterns highlight the role played by phase coexistence and elastic boundary conditions in altering fluctuation timescales in ferroelectric thin film 

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4. Uncertainty quantification of TMS simulations considering MRI segmentation errors

   https://doi.org/10.1088/1741-2552/ac5586  

   Zhang, Hao; Gomez, Luis J; Guilleminot, Johann (March 2022, Journal of Neural Engineering)

   Abstract Objective. Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy. Approach. The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field. Main results. Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter (WM), compartments. In contrast, E-field predictions are highly sensitive to possible cerebrospinal fluid (CSF) segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and WM interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates. Significance. The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors. 

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5. Local equilibrium of particle density in planar Lorentz processes

   https://doi.org/10.1088/1361-6544/ac1163  

   Nándori, Péter; Teolis, Trevor (August 2021, Nonlinearity)

   Abstract Particles are injected into a large planar domain through the boundary and perform a random or sufficiently chaotic deterministic motion inside the domain. Our main example is the Sinai billiard, which periodically extended to our large planar domain, is referred to as the Lorentz process. Assuming that the particles move independently from one another and the boundary is also absorbing, we prove the emergence of local equilibrium of the particle density in the diffusive scaling limit in two scenarios. One scenario is an arbitrary domain with piece-wise smooth boundary and a carefully chosen injection rule; the other scenario is a rectangular domain and a much more general injection mechanism. We study the latter scenario in an abstract framework that includes Lorentz processes and random walks and hopefully allows for more applications in the future. 

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