A 3D Mathematical Model of Coupled Stem Cell-Nutrient Dynamics in Myocardial Regeneration Therapy

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering

BACKGROUND

Advances in cartilage tissue engineering have demonstrated noteworthy potential for developing cartilage for implantation onto sites impacted by joint degeneration and injury. To supplement resource-intensive in vivo and in vitro studies required for cartilage tissue engineering, computational models and simulations can assist in enhancing experimental design.

METHODS

Research articles pertinent to cartilage tissue engineering and computer modeling were identified, reviewed, and summarized. Various applications of computer modeling for cartilage tissue engineering are highlighted, limitations of in silico modeling are addressed, and suggestions for future work are enumerated.

RESULTS

Computational modeling can help better characterize shear stresses generated by bioreactor fluid flow, refine scaffold geometry, customize the mechanical properties of engineered cartilage tissue, and model rates of cell growth and dynamics. Thus, results from in silico studies can help resourcefully enhance in vitro and in vivo studies; however, the limitations of these studies, such as the underlying assumptions and simplifications applied in each model, should always be addressed and justified where applicable. In silico models should also seek validation and verification when possible.

CONCLUSION

Future studies may adopt similar approaches to supplement in vitro trials and further investigate effects of mechanical stimulation on chondrocyte and stem cell dynamics. Additionally, as precision medicine, machine learning, and powerful open-source software become more popular and accessible, applications of multi-scale and multiphysics computational models in cartilage tissue engineering are expected to increase.

Different angiogenesis modes and endothelial responses in implanted porous biomaterials

An in vivo experimental model based on implanting porous biomaterials to study angiogenesis was proposed. In the implanted porous polyvinyl alcohol, three major modes of angiogenesis, sprouting, intussusception and splitting, were found. By electron microscopy and three-dimensional simulation of the angiogenic vessels, we investigated the morphological characteristics of the three modes and paid special attention to the initial morphological difference between intussusception and splitting, and it was confirmed that the endothelial abluminal invagination and intraluminal protrusion are pre-representations of intussusception and splitting, respectively. Based on immunohistochemical analysis of HIF-1α, VEGF and Flt-1 expressions, it was demonstrated that the dominant mode of angiogenesis is related to the local hypoxic condition, and that there is difference in the response of endothelial cells to hypoxia-induced VEGF between sprouting and splitting. Specifically, in the biomaterials implanted for 3 days, the higher expression and gradient of VEGF induced by severe hypoxia in the avascular area caused sprouting of the peripheral capillaries, and in the biomaterial implanted for 9 days, with moderate hypoxia, splitting became a dominant mode. Whether on day 3 or day 9, Flt-1 expression in sprouting endothelia was significantly higher than that in splitting endothelia, which indicates that sprouting is caused by the strong response of endothelial cells to VEGF, while splitting is associated with their weaker response. As a typical experimental example, these results show the effectiveness of the porous biomaterial implantation model for studying angiogenesis, which is expected to become a new general model.