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1. Biocompatible micro tweezers for 3D hydrogel organoid array mechanical characterization

   https://doi.org/10.1371/journal.pone.0262950  

   Alhudaithy, Soliman ; Hoshino, Kazunori ( January 2022 , PLOS ONE)

   Jabbari, Esmaiel (Ed.)

   This study presents novel biocompatible Polydimethylsiloxane (PDMS)-based micromechanical tweezers (μTweezers) capable of the stiffness characterization and manipulation of hydrogel-based organoids. The system showed great potential for complementing established mechanical characterization methods such as Atomic Force Microscopy (AFM), parallel plate compression (PPC), and nanoindentation, while significantly reducing the volume of valuable hydrogels used for testing. We achieved a volume reduction of ~0.22 μl/sample using the μTweezers vs. ~157 μl/sample using the PPC, while targeting high-throughput measurement of widely adopted micro-mesoscale (a few hundred μm-1500 μm) 3D cell cultures. The μTweezers applied and measured nano-millinewton forces through cantilever’ deflection with high linearity and tunability for different applications; the assembly is compatible with typical inverted optical microscopes and fit on standard tissue culture Petri dishes, allowing mechanical compression characterization of arrayed 3D hydrogel-based organoids in a high throughput manner. The average achievable output per group was 40 tests per hour, where 20 organoids and 20 reference images in one 35 mm petri dish were tested, illustrating efficient productivity to match the increasing demand on 3D organoids’ applications. The changes in stiffness of collagen I hydrogel organoids in four conditions were measured, with ovarian cancer cells (SKOV3) or without (control). The Young’s modulus of the control group (Control—day 0, E = 407± 146, n = 4) measured by PPC was used as a reference modulus, where the relative elastic compressive modulus of the other groups based on the stiffness measurements was also calculated (control-day 0, E = 407 Pa), (SKOV3-day 0, E = 318 Pa), (control-day 5, E = 528 Pa), and (SKOV3-day 5, E = 376 Pa). The SKOV3-embedded hydrogel-based organoids had more shrinkage and lowered moduli on day 0 and day 5 than controls, consistently, while SKOV3 embedded organoids increased in stiffness in a similar trend to the collagen I control from day 0 to day 5. The proposed method can contribute to the biomedical, biochemical, and regenerative engineering fields, where bulk mechanical characterization is of interest. The μTweezers will also provide attractive design and application concepts to soft membrane-micro 3D robotics, sensors, and actuators. 

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2. Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

   https://doi.org/10.3390/fluids6010016  

   Mou, Changhong ; Wang, Zhu ; Wells, David R. ; Xie, Xuping ; Iliescu, Traian ( January 2021 , Fluids)

   null (Ed.)

   Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows. 

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3. Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems

   https://doi.org/10.3390/applmech1030011  

   Son, Jeongeun ; Du, Dongping ; Du, Yuncheng ( September 2020 , Applied Mechanics)

   null (Ed.)

   Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive because it often involves high-dimensional integrals. To address this, a generalized dimension reduction method (gDRM) is coupled with quadrature rules to convert a high-dimensional integral in the SG into a few lower dimensional ones that can be rapidly solved. The performance of the algorithm is validated with two examples describing the dynamic behavior of cells. Compared to other UQ techniques (e.g., nonintrusive PCE), the results show the potential of the algorithm to tackle UQ in more complicated biological systems. 

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4. A Graph Theoretic Approach for Near Real-Time Prediction of Part-Level Thermal History in Metal Additive Manufacturing Processes

   https://doi.org/10.1115/MSEC2019-2875  

   Yavari, Reza ; Cole, Kevin D. ; Rao, Prahalad ( June 2019 , ASME Manufacturing Science and Engineering Conference)

   The goal of this work is to predict the effect of part geometry and process parameters on the instantaneous spatial distribution of heat, called the heat flux or thermal history, in metal parts as they are being built layer-by-layer using additive manufacturing (AM) processes. In pursuit of this goal, the objective of this work is to develop and verify a graph theory-based approach for predicting the heat flux in metal AM parts. This objective is consequential to overcome the current poor process consistency and part quality in AM. One of the main reasons for poor part quality in metal AM processes is ascribed to the heat flux in the part. For instance, constrained heat flux because of ill-considered part design leads to defects, such as warping and thermal stress-induced cracking. Existing non-proprietary approaches to predict the heat flux in AM at the part-level predominantly use mesh-based finite element analyses that are computationally tortuous — the simulation of a few layers typically requires several hours, if not days. Hence, to alleviate these challenges in metal AM processes, there is a need for efficient computational thermal models to predict the heat flux, and thereby guide part design and selection of process parameters instead of expensive empirical testing. Compared to finite element analysis techniques, the proposed mesh-free graph theory-based approach facilitates layer-by-layer simulation of the heat flux within a few minutes on a desktop computer. To explore these assertions we conducted the following two studies: (1) comparing the heat diffusion trends predicted using the graph theory approach, with finite element analysis and analytical heat transfer calculations based on Green’s functions for an elementary cuboid geometry which is subjected to an impulse heat input in a certain part of its volume, and (2) simulating the layer-by-layer deposition of three part geometries in a laser powder bed fusion metal AM process with: (a) Goldak’s moving heat source finite element method, (b) the proposed graph theory approach, and (c) further comparing the heat flux predictions from the last two approaches with a commercial solution. From the first study we report that the heat flux trend approximated by the graph theory approach is found to be accurate within 5% of the Green’s functions-based analytical solution (in terms of the symmetric mean absolute percentage error). Results from the second study show that the heat flux trends predicted for the AM parts using graph theory approach agrees with finite element analysis with error less than 15%. More pertinently, the computational time for predicting the heat flux was significantly reduced with graph theory, for instance, in one of the AM case studies the time taken to predict the heat flux in a part was less than 3 minutes using the graph theory approach compared to over 3 hours with finite element analysis. While this paper is restricted to theoretical development and verification of the graph theory approach for heat flux prediction, our forthcoming research will focus on experimental validation through in-process sensor-based heat flux measurements.

    

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5. Thermal Modeling in Metal Additive Manufacturing Using Graph Theory

   https://doi.org/10.1115/1.4043648  

   Yavari, M. Reza ; Cole, Kevin D. ; Rao, Prahalada ( July 2019 , Journal of Manufacturing Science and Engineering)

   The goal of this work is to predict the effect of part geometry and process parameters on the instantaneous spatiotemporal distribution of temperature, also called the thermal field or temperature history, in metal parts as they are being built layer-by-layer using additive manufacturing (AM) processes. In pursuit of this goal, the objective of this work is to develop and verify a graph theory-based approach for predicting the temperature distribution in metal AM parts. This objective is consequential to overcome the current poor process consistency and part quality in AM. One of the main reasons for poor part quality in metal AM processes is ascribed to the nature of temperature distribution in the part. For instance, steep thermal gradients created in the part during printing leads to defects, such as warping and thermal stress-induced cracking. Existing nonproprietary approaches to predict the temperature distribution in AM parts predominantly use mesh-based finite element analyses that are computationally tortuous—the simulation of a few layers typically requires several hours, if not days. Hence, to alleviate these challenges in metal AM processes, there is a need for efficient computational models to predict the temperature distribution, and thereby guide part design and selection of process parameters instead of expensive empirical testing. Compared with finite element analyses techniques, the proposed mesh-free graph theory-based approach facilitates prediction of the temperature distribution within a few minutes on a desktop computer. To explore these assertions, we conducted the following two studies: (1) comparing the heat diffusion trends predicted using the graph theory approach with finite element analysis, and analytical heat transfer calculations based on Green’s functions for an elementary cuboid geometry which is subjected to an impulse heat input in a certain part of its volume and (2) simulating the laser powder bed fusion metal AM of three-part geometries with (a) Goldak’s moving heat source finite element method, (b) the proposed graph theory approach, and (c) further comparing the thermal trends predicted from the last two approaches with a commercial solution. From the first study, we report that the thermal trends approximated by the graph theory approach are found to be accurate within 5% of the Green’s functions-based analytical solution (in terms of the symmetric mean absolute percentage error). Results from the second study show that the thermal trends predicted for the AM parts using graph theory approach agree with finite element analyses, and the computational time for predicting the temperature distribution was significantly reduced with graph theory. For instance, for one of the AM part geometries studied, the temperature trends were predicted in less than 18 min within 10% error using the graph theory approach compared with over 180 min with finite element analyses. Although this paper is restricted to theoretical development and verification of the graph theory approach, our forthcoming research will focus on experimental validation through in-process thermal measurements. 

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