Computational modelling of local calcium ions release from calcium phosphate-based scaffolds

A multiparametric advection-diffusion reduced-order model for molecular transport in scaffolds for osteoinduction

Scaffolds are microporous biocompatible structures that serve as material support for cells to proliferate, differentiate and form functional tissue. In particular, in the field of bone regeneration, insertion of scaffolds in a proper physiological environment is known to favour bone formation by releasing calcium ions, among others, triggering differentiation of mesenchymal cells into osteoblasts. Computational simulation of molecular distributions through scaffolds is a potential tool to study the scaffolds’ performance or optimal designs, to analyse their impact on cell differentiation, and also to move towards reduction in animal experimentation. Unfortunately, the required numerical models are often highly complex and computationally too costly to develop parametric studies. In this context, we propose a computational parametric reduced-order model to obtain the distribution of calcium ions in the interstitial fluid flowing through scaffolds, depending on several physical parameters. We use the well-known Proper Orthogonal Decomposition (POD) with two different variations: local POD and POD with quadratic approximations. Computations are performed using two realistic geometries based on a foamed and a 3D-printed scaffolds. The location of regions with high concentration of calcium in the numerical simulations is in fair agreement with regions of bone formation shown in experimental observations reported in the literature. Besides, reduced-order solutions accurately approximate the reference finite element solutions, with a significant decrease in the number of degrees of freedom, thus avoiding computationally expensive simulations, especially when performing a parametric analysis. The proposed reduced-order model is a competitive tool to assist the design of scaffolds in osteoinduction research.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Cytocompatibility and Bioactive Ion Release Profiles of Phosphoserine Bone Adhesive: Bridge from In Vitro to In Vivo

One major challenge when developing new biomaterials is translating in vitro testing to in vivo models. We have recently shown that a single formulation of a bone tissue adhesive, phosphoserine modified cement (PMC), is safe and resorbable in vivo. Herein, we screened many new adhesive formulations, for cytocompatibility and bioactive ion release, with three cell lines: MDPC23 odontoblasts, MC3T3 preosteoblasts, and L929 fibroblasts. Most formulations were cytocompatible by indirect contact testing (ISO 10993-12). Formulations with larger amounts of phosphoserine (>50%) had delayed setting times, greater ion release, and cytotoxicity in vitro. The trends in ion release from the adhesive that were cured for 24 h (standard for in vitro) were similar to release from the adhesives cured only for 5−10 min (standard for in vivo), suggesting that we may be able to predict the material behavior in vivo, using in vitro methods. Adhesives containing calcium phosphate and silicate were both cytocompatible for seven days in direct contact with cell monolayers, and ion release increased the alkaline phosphatase (ALP) activity in odontoblasts, but not pre-osteoblasts. This is the first study evaluating how PMC formulation affects osteogenic cell differentiation (ALP), cytocompatibility, and ion release, using in situ curing conditions similar to conditions in vivo.

A 3D printed in vitro bone model for the assessment of molecular and cellular cues in metastatic neuroblastoma

Metastasis is a complex and multifactorial process highly dependent on the interaction between disseminated tumor cells and the pre-metastatic niche. The metastatic sites detected in the bone of patients affected by neuroblastoma (NB), a malignancy of the developing sympathetic nervous system, are particularly aggressive. To improve our current knowledge of metastatic tumor cell biology and improve treatment success, appropriate in vitro and in vivo models that more closely resemble the native metastatic niche are needed. In this study, the impact of the geometry of synthetic β-tricalcium-phosphate (β-TCP) structures on the interaction of NB tumor cells with the stromal component has been examined. The tumor microenvironment is dynamically shaped by the stroma, which sustains the growth of NB cells inside the metastatic niche. The 3D growth conditions are a determining factor for the cell proliferation rate in β-TCP. With respect to planar counterparts, channeled 3D β-TCP structures stimulate more interleukin-6 and Fibronectin production and define Connexin 43 distribution inside the cells. Together, these results highlight how the biomechanical properties of the 3D microenvironment enable tumor cells to form spheroid-shaped arrangements. This, in turn, facilitates their pro-migratory and pro-invasive patterns and mimics the in vivo situation by translating realistic mechanobiological cues to the metastatic NB.

High-Throughput Methods in the Discovery and Study of Biomaterials and Materiobiology

The complex interaction of cells with biomaterials (i.e., materiobiology) plays an increasingly pivotal role in the development of novel implants, biomedical devices, and tissue engineering scaffolds to treat diseases, aid in the restoration of bodily functions, construct healthy tissues, or regenerate diseased ones. However, the conventional approaches are incapable of screening the huge amount of potential material parameter combinations to identify the optimal cell responses and involve a combination of serendipity and many series of trial-and-error experiments. For advanced tissue engineering and regenerative medicine, highly efficient and complex bioanalysis platforms are expected to explore the complex interaction of cells with biomaterials using combinatorial approaches that offer desired complex microenvironments during healing, development, and homeostasis. In this review, we first introduce materiobiology and its high-throughput screening (HTS). Then we present an in-depth of the recent progress of 2D/3D HTS platforms (i.e., gradient and microarray) in the principle, preparation, screening for materiobiology, and combination with other advanced technologies. The Compendium for Biomaterial Transcriptomics and high content imaging, computational simulations, and their translation toward commercial and clinical uses are highlighted. In the final section, current challenges and future perspectives are discussed. High-throughput experimentation within the field of materiobiology enables the elucidation of the relationships between biomaterial properties and biological behavior and thereby serves as a potential tool for accelerating the development of high-performance biomaterials.

Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs

Amending the neglect of finite dissolution in traditional release models, this study proposed a more generalized drug release model considering the simultaneous dissolution and diffusion procedure from a drug-loaded spherical matrix. How the shape factor (n = 0, 1/2, and 2/3 for the planar, cylindrical, and spherical geometry, respectively) of dispersed drug particles affected the release from the matrix was examined for the first time. Numerical solutions of this generalized model were validated by consensus with a short-time analytical solution for planar drugs and by the approach of the diffusion-controlled limits with Higuchi’s model. The drug release rate increases with the ratio of dissolution/diffusion rate (G) and the ratio of solubility/drug loading (K) but decreases with the shape factor of drug particles. A zero-order release profile is identified for planar drugs before starting the surface depletion layer, and also found for cylindrical and spherical dispersed drugs when K and G are small, i.e. the loaded drug is mainly un-dissolved and the drug release rate is dissolution-controlled. It is also shown that for the case of a small G value, the variation of drug release profile, due to the drug particle geometry, becomes prominent. Detailed comparison with the results of the traditional Higuchi’s model indicates that Higuchi’s model can be applied only when G is large because of the assumption of an instantaneous dissolution. For K = 1/101–1/2, the present analysis suggests an error of 33–85% for drug release predicted by Higuchi’s model for G = 10⁰, 14–44% error for G = 10¹, while a less than 5% error for G ≧ 10³.

Continuum Modeling and Simulation in Bone Tissue Engineering

Bone tissue engineering is currently a mature methodology from a research perspective. Moreover, modeling and simulation of involved processes and phenomena in BTE have been proved in a number of papers to be an excellent assessment tool in the stages of design and proof of concept through in-vivo or in-vitro experimentation. In this paper, a review of the most relevant contributions in modeling and simulation, in silico, in BTE applications is conducted. The most popular in silico simulations in BTE are classified into: (i) Mechanics modeling and scaffold design, (ii) transport and flow modeling, and (iii) modeling of physical phenomena. The paper is restricted to the review of the numerical implementation and simulation of continuum theories applied to different processes in BTE, such that molecular dynamics or discrete approaches are out of the scope of the paper. Two main conclusions are drawn at the end of the paper: First, the great potential and advantages that in silico simulation offers in BTE, and second, the need for interdisciplinary collaboration to further validate numerical models developed in BTE.

Deciphering the combined effect of bone morphogenetic protein 6 and calcium phosphate on bone formation capacity of periosteum derived cells-based tissue engineering constructs

Cell based combination products with growth factors on optimal carriers represent a promising tissue engineering strategy to treat large bone defects. In this concept, bone morphogenetic protein (BMP) and calcium phosphate (CaP)-based scaffolds can act as potent components of the constructs to steer stem cell specification, differentiation and initiate subsequent in vivo bone formation. However, limited insight into BMP dosage and the cross-talk between BMP and CaP materials, hampers the optimization of in vivo bone formation and subsequent clinical translation. Herein, we combined human periosteum derived progenitor cells with different doses of BMP6 and with three types of clinical grade CaP-scaffolds (ChronOs®, ReproBone™, & CopiOs®). Comprehensive cellular and molecular analysis was performed based on in vitro cell metabolic activity and signaling pathway activation, as well as in vivo ectopic bone forming capacity after 2 weeks and 5 weeks in nude mice. Our data showed that cells seeded on CaP scaffolds with an intermediate Ca²⁺ release rate combined with low or medium dosage of BMP6 demonstrated a robust new bone formation after 5 weeks, which was contributed by both donor and host cells. This phenomenon might be due to the delicate balance between Ca²⁺ and BMP pathways, allowing an appropriate activation of the canonical BMP signaling pathway that is required for in vivo bone formation. For high BMP6 dosage, we found that the BMP6 dosage overrides the effect of the Ca²⁺ release rate and this appeared to be a dominant factor for ectopic bone formation. Taken together, this study illustrates the importance of matching BMP dosage and CaP properties to allow an appropriate activation of canonical BMP signaling that is crucial for in vivo bone formation. It also provides insightful knowledge with regard to clinical translation of cell-based constructs for bone regeneration. STATEMENT OF SIGNIFICANCE: The combination of bone morphogenetic proteins (BMP) and calcium phosphate (CaP)-based biomaterials with mesenchymal stromal cells represents a promising therapeutic strategy to treat large bone defects, an unmet medical need. However, there is limited insight into the optimization of these combination products, which hampers subsequent successful clinical translation. Our data reveal a delicate balance between Ca²⁺ and BMP pathways, allowing an appropriate activation of canonical BMP signaling required for in vivo bone formation. Our findings illustrate the importance of matching BMP dosage and CaP properties in the development of cell-based constructs for bone regeneration.

Model of dissolution in the framework of tissue engineering and drug delivery

Dissolution phenomena are ubiquitously present in biomaterials in many different fields. Despite the advantages of simulation-based design of biomaterials in medical applications, additional efforts are needed to derive reliable models which describe the process of dissolution. A phenomenologically based model, available for simulation of dissolution in biomaterials, is introduced in this paper. The model turns into a set of reaction-diffusion equations implemented in a finite element numerical framework. First, a parametric analysis is conducted in order to explore the role of model parameters on the overall dissolution process. Then, the model is calibrated and validated versus a straightforward but rigorous experimental setup. Results show that the mathematical model macroscopically reproduces the main physicochemical phenomena that take place in the tests, corroborating its usefulness for design of biomaterials in the tissue engineering and drug delivery research areas.

How Not To Drown in Data: A Guide for Biomaterial Engineers

High-throughput assays that produce hundreds of measurements per sample are powerful tools for quantifying cell-material interactions. With advances in automation and miniaturization in material fabrication, hundreds of biomaterial samples can be rapidly produced, which can then be characterized using these assays. However, the resulting deluge of data can be overwhelming. To the rescue are computational methods that are well suited to these problems. Machine learning techniques provide a vast array of tools to make predictions about cell-material interactions and to find patterns in cellular responses. Computational simulations allow researchers to pose and test hypotheses and perform experiments in silico. This review describes approaches from these two domains that can be brought to bear on the problem of analyzing biomaterial screening data.