Computational mechano-chemo-biology: a tool for the design of tissue scaffolds

Multiscale modeling of bone tissue mechanobiology

Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.

Exploring cardiac form and function: A length-scale computational biology approach

The ability to adequately pump blood throughout the body is the result of tightly regulated feedback mechanisms that exist across many spatial scales in the heart. Diseases which impede the function at any one of the spatial scales can cause detrimental cardiac remodeling and eventual heart failure. An overarching goal of cardiac research is to use engineered heart tissue in vitro to study the physiology of diseased heart tissue, develop cell replacement therapies, and explore drug testing applications. A commonality within the field is to manipulate the flow of mechanical signals across the various spatial scales to direct self-organization and build functional tissue. Doing so requires an understanding of how chemical, electrical, and mechanical cues can be used to alter the cellular microenvironment. We discuss how mathematical models have been used in conjunction with experimental techniques to explore various structure-function relations that exist across numerous spatial scales. We highlight how a systems biology approach can be employed to recapitulate in vivo characteristics in vitro at the tissue, cell, and subcellular scales. Specific focus is placed on the interplay between experimental and theoretical approaches. Various modeling methods are showcased to demonstrate the breadth and power afforded to the systems biology approach. An overview of modeling methodologies exemplifies how the strengths of different scientific disciplines can be used to supplement and/or inspire new avenues of experimental exploration. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Experimental characterization and computational modeling of hydrogel cross-linking for bioprinting applications

Alginate-based hydrogels are extensively used to create bioinks for bioprinting, due to their biocompatibility, low toxicity, low costs, and slight gelling. Modeling of bioprinting process can boost experimental design reducing trial-and-error tests. To this aim, the cross-linking kinetics for the chemical gelation of sodium alginate hydrogels via calcium chloride diffusion is analyzed. Experimental measurements on the absorbed volume of calcium chloride in the hydrogel are obtained at different times. Moreover, a reaction-diffusion model is developed, accounting for the dependence of diffusive properties on the gelation degree. The coupled chemical system is solved using finite element discretizations which include the inhomogeneous evolution of hydrogel state in time and space. Experimental results are fitted within the proposed modeling framework, which is thereby calibrated and validated. Moreover, the importance of accounting for cross-linking-dependent diffusive properties is highlighted, showing that, if a constant diffusivity property is employed, the model does not properly capture the experimental evidence. Since the analyzed mechanisms highly affect the evolution of the front of the solidified gel in the final bioprinted structure, the present study is a step towards the development of reliable computational tools for the in silico optimization of protocols and post-printing treatments for bioprinting applications.

Combined experimental and computational characterization of crosslinked collagen-based hydrogels

Collagen hydrogels are widely used for in-vitro experiments and tissue engineering applications. Their use has been extended due to their biocompatibility with cells and their capacity to mimic biological tissues; nevertheless their mechanical properties are not always optimal for these purposes. Hydrogels are formed by a network of polymer filaments embedded on an aqueous substrate and their mechanical properties are mainly defined by the filament network architecture and the individual filament properties. To increase properties of native collagen, such as stiffness or strain-stiffening, these networks can be modified by adding crosslinking agents that alter the network architecture, increasing the unions between filaments. In this work, we have investigated the effect of one crosslinking agent, transglutaminase, in collagen hydrogels with varying collagen concentration. We have observed a linear dependency of the gel rigidity on the collagen concentration. Moreover, the addition of transglutaminase has induced an earlier strain-stiffening of the collagen gels. In addition, to better understand the mechanical implications of collagen concentration and crosslinkers inclusion, we have adapted an existing computational model, based on the worm-like chain model (WLC), to reproduce the mechanical behavior of the collagen gels. With this model we can estimate the parameters of the biopolymer networks without more sophisticated techniques, such as image processing or network reconstruction, or, inversely, predict the mechanical properties of a defined collagen network.

Computationally designed lattices with tuned properties for tissue engineering using 3D printing

Tissue scaffolds provide structural support while facilitating tissue growth, but are challenging to design due to diverse property trade-offs. Here, a computational approach was developed for modeling scaffolds with lattice structures of eight different topologies and assessing properties relevant to bone tissue engineering applications. Evaluated properties include porosity, pore size, surface-volume ratio, elastic modulus, shear modulus, and permeability. Lattice topologies were generated by patterning beam-based unit cells, with design parameters for beam diameter and unit cell length. Finite element simulations were conducted for each topology and quantified how elastic modulus and shear modulus scale with porosity, and how permeability scales with porosity cubed over surface-volume ratio squared. Lattices were compared with controlled properties related to porosity and pore size. Relative comparisons suggest that lattice topology leads to specializations in achievable properties. For instance, Cube topologies tend to have high elastic and low shear moduli while Octet topologies have high shear moduli and surface-volume ratios but low permeability. The developed method was utilized to analyze property trade-offs as beam diameter was altered for a given topology, and used to prototype a 3D printed lattice embedded in an interbody cage for spinal fusion treatments. Findings provide a basis for modeling and understanding relative differences among beam-based lattices designed to facilitate bone tissue growth.