Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales.

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Wall Shear Stress Analysis and Optimization in Tissue Engineering TPMS Scaffolds.

When designing scaffolds for bone tissue engineering (BTE), the wall shear stress (WSS), due to the fluid flow inside the scaffold, is an important factor to consider as it influences the cellular process involved in new tissue formation. The present work analyzed the average WSS in Schwartz diamond (SD) and gyroid (SG) scaffolds with different surface topologies and mesh elements using computational fluid dynamics (CFD) analysis. It was found that scaffold meshes with a smooth surface topology with tetrahedral elements had WSS levels 35% higher than the equivalent scaffold with a non-smooth surface topology with hexahedral elements. The present work also investigated the possibility of implementing the optimization algorithm simulated annealing to aid in the design of BTE scaffolds with a specific average WSS, with the outputs showing that the algorithm was able to reach WSS levels in the vicinity of 5 mPa (physiological range) within the established limit of 100 iterations. This proved the efficacy of combining CFD and optimization methods in the design of BTE scaffolds.

3D Modeling of the Crystalline Lens Complex under Pseudoexfoliation.

Pseudoexfoliation, one of the most frequent crystalline lens complex disorders, is prevalent in up to 30% of individuals older than 60 years old. This disease can lead to severe conditions, such as subluxation or dislocation of the lens, due to the weakening of the zonules. The goal for the present study was to understand the relevant biomechanical features that can lead to the worsening of an individual's visual capacity under pseudoexfoliation. To this end, finite element models based on a 62-year-old lens complex were developed, composed by the capsular bag, cortex, nucleus, anterior, equatorial, and posterior zonular fibers. Healthy and pseudoexfoliative conditions were simulated, varying the location of the zonulopathy (inferior/superior) and the degenerated layer. The accommodative capacity of the models with inferior dialysis of the zonular fibers was, on average, 4.7% greater than for the cases with superior dialysis. If the three sets of zonules were disrupted, this discrepancy increased to 14.9%. The present work provides relevant data to be further analyzed in clinical scenarios, as these models (and their future extension to a wider age range) can help in identifying the most influential regions for the reduction of the visual capacity of the lens.

Challenges in computational fluid dynamics applications for bone tissue engineering.

Bone injuries or defects that require invasive surgical treatment are a serious clinical issue, particularly when it comes to treatment success and effectiveness. Accordingly, bone tissue engineering (BTE) has been researching the use of computational fluid dynamics (CFD) analysis tools to assist in designing optimal scaffolds that better promote bone growth and repair. This paper aims to offer a comprehensive review of recent studies that use CFD analysis in BTE. The mechanical and fluidic properties of a given scaffold are coupled to each other via the scaffold architecture, meaning an optimization of one may negatively affect the other. For example, designs that improve scaffold permeability normally result in a decreased average wall shear stress. Linked with these findings, it appears there are very few studies in this area that state a specific application for their scaffolds and those that do are focused on in vitro bioreactor environments. Finally, this review also demonstrates a scarcity of studies that combine CFD with optimization methods to improve scaffold design. This highlights an important direction of research for the development of the next generation of BTE scaffolds.

Computational Challenges in Tissue Engineering for the Spine.

This paper deals with a brief review of the recent developments in computational modelling applied to innovative treatments of spine diseases. Additionally, it provides a perspective on the research directions expected for the forthcoming years. The spine is composed of distinct and complex tissues that require specific modelling approaches. With the advent of additive manufacturing and increasing computational power, patient-specific treatments have moved from being a research trend to a reality in clinical practice, but there are many issues to be addressed before such approaches become universal. Here, it is identified that the major setback resides in validation of these computational techniques prior to approval by regulatory agencies. Nevertheless, there are very promising indicators in terms of optimised scaffold modelling for both disc arthroplasty and vertebroplasty, powered by a decisive contribution from imaging methods.

Numerical-experimental analysis of the permeability-porosity relationship in triply periodic minimal surfaces scaffolds.

Bone Tissue Engineering has been focusing on improving the current methods for bone repair, being the use of scaffolds presented as an upgrade to traditional surgery techniques. Scaffolds are artificially porous matrices, meant to promote cell seeding and proliferation, being these properties influenced by the permeability of the structure. This work employed experimental pressure drop tests and Computational Fluid Dynamics models to assess permeability (and fluid streamlines) within different triply periodic minimal surfaces scaffold geometries (Schwarz D, Gyroid and Schwarz P). The pressure outputs from the computational analysis presented a good correlation with the experimental results, with R2 equal to 0.903; they have also shown that a lower porosity may not mean a lower permeability if the geometry is altered, such as the difference between 60% porous Gyroid scaffolds (8.1*10-9 mm2) and 70% porous Schwarz D scaffolds (7.1*10-9 mm2). Fluid streamlines revealed how the Gyroid geometries are the most appropriate design for most bone tissue engineering applications, due to their consistent fluid permeation, followed by Schwarz D. The Schwarz P geometries have shown flat streamlines and significant variation of the permeability with the porosity (an increase of 10% in their porosity lead to an increase in the permeability from 5.1*10-9 mm2 to 11.7*10-9 mm2), which would imply a poor environment for cell seeding and proliferation.

On the permeability of TPMS scaffolds.

This study presents an experimental evaluation of permeability of triply periodic minimal surfaces (TPMS). Permeability is widely used to characterize scaffolds for Tissue Engineering (TE) applications as it gives information about the structure porosity, pore size, tortuosity and pore interconnectivity which have an important impact in cell seeding and proliferation. Three different TPMS structures were used: Schwartz Diamond (SD), Gyroid (SG) and Schwartz Primitive (SP), in four different porosity levels (50, 60, 70 and 80%). Overall, the SG scaffold type was determined to be the most permeable one while the SD was the least permeable. Furthermore, the presence of microscopic inertial pressure losses was verified and the Forchheimer's law proved to be a good mathematical tool as a Darcy's law expansion for the calculation of the structure's permeability while the weak-inertia regime was hard to detect or quantify.

Poroelastic Modeling of Highly Hydrated Collagen Hydrogels: Experimental Results vs. Numerical Simulation With Custom and Commercial Finite Element Solvers.

This study presents a comparison between the performances of two Finite Element (FE) solvers for the modeling of the poroelastic behavior of highly hydrated collagen hydrogels. Characterization of collagen hydrogels has been a widespread challenge since this is one of the most used natural biomaterials for Tissue Engineering (TE) applications. V-Biomech® is a free custom FE solver oriented to soft tissue modeling, while Abaqus® is a general-purpose commercial FE package which is widely used for biomechanics computational modeling. Poroelastic simulations with both solvers were compared to two experimental protocols performed by Busby et al. (2013) and Chandran and Barocas (2004), also using different implementations of the frequently used Neo-Hookean hyperelastic model. The average differences between solvers outputs were under 5% throughout the different tests and hydrogel properties. Thus, differences were small enough to be considered negligible and within the variability found experimentally from one sample to another. This work demonstrates that constitutive modeling of soft tissues, such as collagen hydrogels can be achieved with either V-Biomech or Abaqus standard options (without user-subroutine), which is important for the biomechanics and biomaterials research community. V-Biomech has shown its potential for the validation of biomechanical characterization of soft tissues, while Abaqus' versatility is useful for the modeling and analysis of TE applications where other complex phenomena may also need to be captured.