A mechanobiological model for tumor spheroid evolution with application to glioblastoma: A continuum multiphysics approach.

BACKGROUND: Spheroids are in vitro quasi-spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. The main objective of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics. METHOD: We propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroid evolution under in vitro suspension, namely, nutrient diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines. RESULTS: Our model is able to explain in a novel way quite different setups, such as spheroid growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution. CONCLUSIONS: Glioblastoma tumor spheroid evolution is driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease.

Time-Dependent Collagen Fibered Structure in the Early Distraction Callus: Imaging Characterization and Mathematical Modeling.

Collagen is a ubiquitous protein present in regenerating bone tissues that experiences multiple biological phenomena during distraction osteogenesis until the deposition of phosphate crystals. This work combines fluorescence techniques and mathematical modeling to shed light on the mechano-structural processes behind the maturation and accommodation-to-mineralization of the callus tissue. Ovine metatarsal bone calluses were analyzed through confocal images at different stages of the early distraction osteogenesis process, quantifying the fiber orientation distribution and mean intensity as fiber density measure. Likewise, a mathematical model based on the experimental data was defined to micromechanically characterize the apparent stiffening of the tissue within the distracted callus. A reorganization of the fibers around the distraction axis and increased fiber density were found as the bone fragments were gradually separated. Given the degree of significance between the mathematical model and previous in vivo data, reorganization, densification, and bundle maturation phenomena seem to explain the apparent mechanical maturation observed in the tissue theoretically.

Understanding glioblastoma invasion using physically-guided neural networks with internal variables.

Microfluidic capacities for both recreating and monitoring cell cultures have opened the door to the use of Data Science and Machine Learning tools for understanding and simulating tumor evolution under controlled conditions. In this work, we show how these techniques could be applied to study Glioblastoma, the deadliest and most frequent primary brain tumor. In particular, we study Glioblastoma invasion using the recent concept of Physically-Guided Neural Networks with Internal Variables (PGNNIV), able to combine data obtained from microfluidic devices and some physical knowledge governing the tumor evolution. The physics is introduced in the network structure by means of a nonlinear advection-diffusion-reaction partial differential equation that models the Glioblastoma evolution. On the other hand, multilayer perceptrons combined with a nodal deconvolution technique are used for learning the go or grow metabolic behavior which characterises the Glioblastoma invasion. The PGNNIV is here trained using synthetic data obtained from in silico tests created under different oxygenation conditions, using a previously validated model. The unravelling capacity of PGNNIV enables discovering complex metabolic processes in a non-parametric way, thus giving explanatory capacity to the networks, and, as a consequence, surpassing the predictive power of any parametric approach and for any kind of stimulus. Besides, the possibility of working, for a particular tumor, with different boundary and initial conditions, permits the use of PGNNIV for defining virtual therapies and for drug design, thus making the first steps towards in silico personalised medicine.

Computational Multiscale Solvers for Continuum Approaches.

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.

In vivo measurement of skin surface strain and sub-surface layer deformation induced by natural tissue stretching.

Stratum corneum and epidermal layers change in terms of thickness and roughness with gender, age and anatomical site. Knowledge of the mechanical and tribological properties of skin associated with these structural changes are needed to aid in the design of exoskeletons, prostheses, orthotics, body mounted sensors used for kinematics measurements and in optimum use of wearable on-body devices. In this case study, optical coherence tomography (OCT) and digital image correlation (DIC) were combined to determine skin surface strain and sub-surface deformation behaviour of the volar forearm due to natural tissue stretching. The thickness of the epidermis together with geometry changes of the dermal-epidermal junction boundary were calculated during change in the arm angle, from flexion (90°) to full extension (180°). This posture change caused an increase in skin surface Lagrange strain, typically by 25% which induced considerable morphological changes in the upper skin layers evidenced by reduction of epidermal layer thickness (20%), flattening of the dermal-epidermal junction undulation (45-50% reduction of flatness being expressed as Ra and Rz roughness profile height change) and reduction of skin surface roughness Ra and Rz (40-50%). The newly developed method, DIC combined with OCT imaging, is a powerful, fast and non-invasive methodology to study structural skin changes in real time and the tissue response provoked by mechanical loading or stretching.

Cell-biomaterial mechanical interaction in the framework of tissue engineering: insights, computational modeling and perspectives.

Tissue engineering is an emerging field of research which combines the use of cell-seeded biomaterials both in vitro and/or in vivo with the aim of promoting new tissue formation or regeneration. In this context, how cells colonize and interact with the biomaterial is critical in order to get a functional tissue engineering product. Cell-biomaterial interaction is referred to here as the phenomenon involved in adherent cells attachment to the biomaterial surface, and their related cell functions such as growth, differentiation, migration or apoptosis. This process is inherently complex in nature involving many physico-chemical events which take place at different scales ranging from molecular to cell body (organelle) levels. Moreover, it has been demonstrated that the mechanical environment at the cell-biomaterial location may play an important role in the subsequent cell function, which remains to be elucidated. In this paper, the state-of-the-art research in the physics and mechanics of cell-biomaterial interaction is reviewed with an emphasis on focal adhesions. The paper is focused on the different models developed at different scales available to simulate certain features of cell-biomaterial interaction. A proper understanding of cell-biomaterial interaction, as well as the development of predictive models in this sense, may add some light in tissue engineering and regenerative medicine fields.

The pro-angiogenic properties of multi-functional bioactive glass composite scaffolds.

The angiogenic properties of micron-sized (m-BG) and nano-sized (n-BG) bioactive glass (BG) filled poly(D,L lactide) (PDLLA) composites were investigated. On the basis of cell culture work investigating the secretion of vascular endothelial growth factor (VEGF) by human fibroblasts in contact with composite films (0, 5, 10, 20 wt %), porous 3D composite scaffolds, optimised with respect to the BG filler content capable of inducing angiogenic response, were produced. The in vivo vascularisation of the scaffolds was studied in a rat animal model and quantified using stereological analyses. The prepared scaffolds had high porosities (81-93%), permeability (k = 5.4-8.6 x 10⁻9 m²) and compressive strength values (0.4-1.6 MPa) all in the range of trabecular bone. On composite films containing 20 wt % m-BG or n-BG, human fibroblasts produced 5 times higher VEGF than on pure PDLLA films. After 8 weeks of implantation, m-BG and n-BG containing scaffolds were well-infiltrated with newly formed tissue and demonstrated higher vascularisation and percentage blood vessel to tissue (11.6-15.1%) than PDLLA scaffolds (8.5%). This work thus shows potential for the regeneration of hard-soft tissue defects and increased bone formation arising from enhanced vascularisation of the construct.

A rotating bed system bioreactor enables cultivation of primary osteoblasts on well-characterized Sponceram regarding structural and flow properties.

The development of bone tissue engineering depends on the availability of suitable biomaterials, a well-defined and controlled bioreactor system, and on the use of adequate cells. The biomaterial must fulfill chemical, biological, and mechanical requirements. Besides biocompatibility, the structural and flow characteristics of the biomaterial are of utmost importance for a successful dynamic cultivation of osteoblasts, since fluid percolation within the microstructure must be assured to supply to cells nutrients and waste removal. Therefore, the biomaterial must consist of a three-dimensional structure, exhibit high porosity and present an interconnected porous network. Sponceram, a ZrO(2) based porous ceramic, is characterized in the presented work with regard to its microstructural design. Intrinsic permeability is obtained through a standard Darcy's experiment, while Young's modulus is derived from a two plates stress-strain test in the linear range. Furthermore, the material is applied for the dynamic cultivation of primary osteoblasts in a newly developed rotating bed bioreactor.

On the effect of substrate curvature on cell mechanics.

Cell movement on a substrate or within the extracellular matrix is the phenomenological response to a biochemical signals' cascade transcripted into biophysical processes and viceversa. The process is complex in nature, including different length scales from the whole cell to organelle and protein levels, where substrate/ECM curvature has been shown to play an important role on cell's behavior. From a macroscopic perspective, the cytoskeleton may be modeled as a continuum body unbalanced by internal protein motors. In this work, we propose a cell constitutive model to simulate cell attachment on curved substrates, activated by contractile forces. We first analyze a single fiber bundle composed by microtubules, actin filaments and myosin machinery. Then, the model is macroscopically extended to the cytoskeletal level using homogenization. Substrate curvature has two implications in our model: (i) it forces fibers to work in a curved (bent) position and (ii) it eventually creates a pre-deformation state in the cytoskeleton. Interestingly, the model shows higher contractile force inhibition as curvature increases when implemented over different substrate morphologies, being this consistent with experimental results. The presented model may result useful in many new regenerative medicine techniques, miniaturized experimental tests, or to analyze cell behavior on manufactured nanoscaffolds for tissue engineering.

Permeability evaluation of 45S5 Bioglass-based scaffolds for bone tissue engineering.

Permeability is a key parameter for microstructural design of scaffolds, since it is related to their capability for waste removal and nutrients/oxygen supply. In this framework, Darcy's experiments were carried out in order to determine the relationship between the pressure drop gradient and the fluid flow velocity in Bioglass-based scaffolds to obtain the scaffold's permeability. Using deionised water as working fluid, the measured average permeability value on scaffolds of 90-95% porosity was 1.96 x 10(-9) m(2). This value lies in the published range of permeability values for trabecular bone.

Mechanical and flow characterization of Sponceram carriers: Evaluation by homogenization theory and experimental validation.

The experimental evidence of the dependence of cell proliferation and differentiation in vitro on the mechanical environment aims to the need of characterization of porous scaffolds in terms of mechanical and flow properties. In this sense, the Young's modulus and intrinsic permeability for three types of Sponceram(R) cell carriers developed for in-vitro applications are here analyzed. Young's modulus and ultimate compression stress were obtained by performing a two-plates compression test carried out in a universal microtester machine Instron(R) for several representative samples of each specimen. A permeability test was also implemented to correlate flow rate and pressure gradient in the linear range. Furthermore, porosity and specific surface were obtained through micro-CTs of the scaffold microstructure. These experimental data were compared with those obtained numerically by homogenization for several representative volume elements (RVEs) of the scaffolds microstructure. The good agreement found between numerical and experimental results let us consider that the use of numerical techniques is an attractive tool for the analysis of complex scaffold microstructures. Moreover, Sponceram(R) carriers are shown to have very appropriate properties as bone bioscaffolds which let us recommending further clinical and numerical research on these specific materials.