Physically-based simulation of elastic-plastic fusion of 3D bioprinted spheroids

Spheroids are microtissues containing cells organized in a spherical shape whose diameter is usually less than a millimetre. Depending on the properties of the environment they are placed in, some nearby spheroids spontaneously fuse and generate a tissue. Given their potential to mimic features typical of body parts and their ability to assemble by fusing in permissive hydrogels, they have been used as building blocks to 3D bioprint human tissue parts. Parameters controlling the shape and size of a bioprinted tissue using fusing spheroid cultures include cell composition, hydrogel properties, and their relative initial position. Hence, simulating, anticipating, and then controlling the spheroid fusion process is essential to control the shape and size of the bioprinted tissue. This study presents the first physically-based framework to simulate the fusion process of bioprinted spheroids. The simulation is based on elastic-plastic solid and fluid continuum mechanics models. Both models use the 'smoothed particle hydrodynamics' method, which is based on discretizing the continuous medium into a finite number of particles and solving the differential equations related to the physical properties (e.g. Navier-Stokes equation) using a smoothing kernel function. To further investigate the effects of such parameters on spheroid shape and geometry, we performed sensitivity and morphological analysis to validate our simulations within-vitrospheroids. Through ourin-silicosimulations by changing the aforementioned parameters, we show that the proposed models appropriately simulate the range of the elastic-plastic behaviours ofin-vitrofusing spheroids to generate tissues of desired shapes and sizes. Altogether, this study presented a physically-based simulation that can provide a framework for monitoring and controlling the geometrical shape of spheroids, directly impacting future research using spheroids for tissue bioprinting.

A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

Morphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work.

Simulation-based joint estimation of body deformation and elasticity parameters for medical image analysis

Estimation of tissue stiffness is an important means of noninvasive cancer detection. Existing elasticity reconstruction methods usually depend on a dense displacement field (inferred from ultrasound orMR images) and known external forces.Many imaging modalities, however, cannot provide details within an organ and therefore cannot provide such a displacement field. Furthermore, force exertion and measurement can be difficult for some internal organs, making boundary forces another missing parameter. We propose a general method for estimating elasticity and boundary forces automatically using an iterative optimization framework, given the desired (target) output surface. During the optimization, the input model is deformed by the simulator, and an objective function based on the distance between the deformed surface and the target surface is minimized numerically. The optimization framework does not depend on a particular simulation method and is therefore suitable for different physical models. We show a positive correlation between clinical prostate cancer stage (a clinical measure of severity) and the recovered elasticity of the organ. Since the surface correspondence is established, our method also provides a non-rigid image registration, where the quality of the deformation fields is guaranteed, as they are computed using a physics-based simulation.