A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres)

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.

Three-dimensional scaffold-free microtissues engineered for cardiac repair

Cardiovascular diseases, including myocardial infarction (MI), persist as the leading cause of mortality and morbidity worldwide. The limited regenerative capacity of the myocardium presents significant challenges specifically for the treatment of MI and, subsequently, heart failure (HF). Traditional therapeutic approaches mainly rely on limiting the induced damage or the stress on the remaining viable myocardium through pharmacological regulation of remodeling mechanisms, rather than replacement or regeneration of the injured tissue. The emerging alternative regenerative medicine-based approaches have focused on restoring the damaged myocardial tissue with newly engineered functional and bioinspired tissue units. Cardiac regenerative medicine approaches can be broadly categorized into three groups: cell-based therapies, scaffold-based cardiac tissue engineering, and scaffold-free cardiac tissue engineering. Despite significant advancements, however, the clinical translation of these approaches has been critically hindered by two key obstacles for successful structural and functional replacement of the damaged myocardium, namely: poor engraftment of engineered tissue into the damaged cardiac muscle and weak electromechanical coupling of transplanted cells with the native tissue. To that end, the integration of micro- and nanoscale technologies along with recent advancements in stem cell technologies have opened new avenues for engineering of structurally mature and highly functional scaffold-based (SB-CMTs) and scaffold-free cardiac microtissues (SF-CMTs) with enhanced cellular organization and electromechanical coupling for the treatment of MI and HF. In this review article, we will present the state-of-the-art approaches and recent advancements in the engineering of SF-CMTs for myocardial repair.

Are Tumor Cell Lineages Solely Shaped by Mechanical Forces?

This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.

A Macroscopic Mathematical Model for Cell Migration Assays Using a Real-Time Cell Analysis

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells during the course of time and provide a Cell Index which is proportional to cellular morphology, spreading, ruffling and adhesion quality as well as cell number. In this paper we propose a macroscopic mathematical model, based on advection-reaction-diffusion partial differential equations, describing the cell migration assay using the real-time technology. We carried out numerical simulations to compare simulated model dynamics with data of observed biological experiments on three different cell lines and in two experimental settings: absence of chemotactic signals (basal migration) and presence of a chemoattractant. Overall we conclude that our minimal mathematical model is able to describe the phenomenon in the real time scale and numerical results show a good agreement with the experimental evidences.