Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Mathematical investigation of normal and abnormal wound healing dynamics: local and non-local models

The movement of cells during (normal and abnormal) wound healing is the result of biomechanical interactions that combine cell responses with growth factors as well as cell-cell and cell-matrix interactions (adhesion and remodelling). It is known that cells can communicate and interact locally and non-locally with other cells inside the tissues through mechanical forces that act locally and at a distance, as well as through long non-conventional cell protrusions. In this study, we consider a non-local partial differential equation model for the interactions between fibroblasts, macrophages and the extracellular matrix (ECM) via a growth factor (TGF-$ \beta $) in the context of wound healing. For the non-local interactions, we consider two types of kernels (i.e., a Gaussian kernel and a cone-shaped kernel), two types of cell-ECM adhesion functions (i.e., adhesion only to higher-density ECM vs. adhesion to higher-/lower-density ECM) and two types of cell proliferation terms (i.e., with and without decay due to overcrowding). We investigate numerically the dynamics of this non-local model, as well as the dynamics of the localised versions of this model (i.e., those obtained when the cell perception radius decreases to 0). The results suggest the following: (ⅰ) local models explain normal wound healing and non-local models could also explain abnormal wound healing (although the results are parameter-dependent); (ⅱ) the models can explain two types of wound healing, i.e., by primary intention, when the wound margins come together from the side, and by secondary intention when the wound heals from the bottom up.

Which experimental models and explorations to use in regenerative endodontics? A comprehensive review on standard practices

Since the discovery of dental pulp stem cells, a lot of teams have expressed an interest in dental pulp regeneration. Many approaches, experimental models and biological explorations have been developed, each including the use of stem cells and scaffolds with the final goal being clinical application in humans. In this review, the authors' objective was to compare the experimental models and strategies used for the development of biomaterials for tissue engineering of dental pulp with stem cells. Electronic queries were conducted on PubMed using the following terms: pulp regeneration, scaffold, stem cells, tissue engineering and biomaterial. The extracted data included the following information: the strategy envisaged, the type of stem cells, the experimental models, the exploration or analysis methods, the cytotoxicity or viability or proliferation cellular tests, the tests of scaffold antibacterial properties and take into account the vascularization of the regenerated dental pulp. From the 71 selected articles, 59% focused on the "cell-transplantation" strategy, 82% used in vitro experimentation, 58% in vivo animal models and only one described an in vivo in situ human clinical study. 87% used dental pulp stem cells. A majority of the studies reported histology (75%) and immunohistochemistry explorations (66%). 73% mentioned the use of cytotoxicity, proliferation or viability tests. 48% took vascularization into account but only 6% studied the antibacterial properties of the scaffolds. This article gives an overview of the methods used to regenerate dental pulp from stem cells and should help researchers create the best development strategies for research in this field.

Odontoblastic differentiation of dental pulp stem cells from healthy and carious teeth on an original PCL-based 3D scaffold

AIMS

To isolate and characterize dental pulp stem cells (DPSCs) obtained from carious and healthy mature teeth extracted when conservative treatment was not possible or for orthodontic reasons; to evaluate the ability of DPSCs to colonize, proliferate and differentiate into functional odontoblast-like cells when cultured onto a polycaprolactone cone made by jet-spraying and prototyped into a design similar to a gutta-percha cone.

METHODOLOGY

DPSCs were obtained from nine carious and 12 healthy mature teeth. Then cells were characterized by flow cytometry and submitted to multidifferentiation to confirm their multipotency. These DPSCs were then cultured on a polycaprolactone cone in an odontoblastic differentiation medium. Cell proliferation, colonization of the biomaterial and functional differentiation of cells were histologically assessed. For the characterization, a t-Student test was used to compare the two groups.

RESULTS

In all cell cultures, characterization highlighted a mesenchymal stem cell phenotype (CD105+, CD90+, CD73+, CD11b-, CD34-, CD45-, HLA-DR-). No significant differences were found between cultures obtained from carious and healthy mature teeth. DPSCs from both origins were able to differentiate into osteocytes, adipocytes and chondrocytes. Cell colonization was observed both on the surface and in the thickness of polycaprolactone cones as well as a mineralized pericellular matrix deposit composed of type I collagen, alkaline phosphatase, osteocalcin and dentin sialophosphoprotein.

CONCLUSIONS

DPSCs were isolated from both carious and healthy mature teeth. They were able to colonize and proliferate within a polycaprolactone cone and could be differentiated into functional odontoblast-like cells.