In vitro ovine articular chondrocyte proliferation: experiments and modelling

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

Numerical rate function determination in partial differential equations modeling cell population dynamics

This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.

A novel quantitative model of cell cycle progression based on cyclin-dependent kinases activity and population balances

Cell cycle regulates proliferative cell capacity under normal or pathologic conditions, and in general it governs all in vivo/in vitro cell growth and proliferation processes. Mathematical simulation by means of reliable and predictive models represents an important tool to interpret experiment results, to facilitate the definition of the optimal operating conditions for in vitro cultivation, or to predict the effect of a specific drug in normal/pathologic mammalian cells. Along these lines, a novel model of cell cycle progression is proposed in this work. Specifically, it is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases experienced by each cell of the entire population during its own life. The transition between two consecutive cell cycle phases is simulated by taking advantage of the biochemical kinetic model developed by Gérard and Goldbeter (2009) which involves cyclin-dependent kinases (CDKs) whose regulation is achieved through a variety of mechanisms that include association with cyclins and protein inhibitors, phosphorylation-dephosphorylation, and cyclin synthesis or degradation. This biochemical model properly describes the entire cell cycle of mammalian cells by maintaining a sufficient level of detail useful to identify check point for transition and to estimate phase duration required by PB. Specific examples are discussed to illustrate the ability of the proposed model to simulate the effect of drugs for in vitro trials of interest in oncology, regenerative medicine and tissue engineering.

Enhanced migration of human bone marrow stromal cells in modified collagen hydrogels

PURPOSE

Collagen I hydrogels are widely used as scaffolds for regeneration of articular cartilage defects. We hypothesised that ingrowth might be improved by removing the superficial layer of a compressed hydrogel. The control group consisted of the original unmodified product.

METHODS

The migration of human bone marrow stromal cells (hBMSCs) into the hydrogel was evaluated by confocal microscopy. We quantified the DNA concentration of the hydrogel for each group and time point and evaluated the chondrogenic differentiation of cells.

RESULTS

After one week, the detectable amount of cells at the depth of 26-50 μm was significantly higher in the modified matrix (MM) than in the non-modified matrix (NM) (p = 0.011). The maximum depth of penetration was 75 μm (NM) and 200 μm (MM). After three weeks, the maximum depth of penetration was 175 μm (NM) and 200 μm (MM). Likewise, at a depth of 0-25 μm the amount of detectable cells was significantly higher in the MM group (p = 0.003). After 14 days, the concentration of DNA was significantly higher in the samples of the MM than in the control group (p = 0.000). Staining of histological sections and labelling with collagen II antibodies showed that a chondrogenic differentiation of cells in the scaffold can occur during in vitro cultivation.

CONCLUSIONS

Removing the superficial layer is essential to ensuring proper ingrowth of cells within the compressed hydrogel. Compressed hydrogels contribute better to cartilage regeneration after surface modification.