A Mathematical Model of Liver Cell Aggregation In Vitro

Abstract

"Authors may self-archive the author's accepted manuscript of their articles on their own websites. Authors may also deposit this version of the article in any repository, provided it is only made publicly available 12 months after official publication or later. He/ she may not use the publisher's version (the final article), which is posted on SpringerLink and other Springer websites, for the purpose of self-archiving or deposit. Furthermore, the author may only post his/her version provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com"". th March, 2014A mathematical model of liver cell aggregation in vitroThe behaviour of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques.We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that, provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work.

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

“…We observe that for this control simulation the cells aggregate, forming two roughly circular clusters, centred on the regions with higher initial cell density. The formation of compact cell clusters, of approximately uniform density with clearly defined edges is similar to the behaviour seen in a one-dimensional multiphase model of cell aggregation (Green et al, 2009). The collagen density evolves to a similar complementary pattern; with regions of high cell density coinciding with regions of low collagen density.…”

“…We note that if no collagen (φ c ≡ 0) is present, and the viscosity of the medium is negligible then only cells and medium are present and our model reduces to that of (Green et al, 2009). In this case non-trivial steady states are possible for which regions containing cells at density φ n = Φ alternate with regions in which φ n = 0 (we note that for such cell distributions, the function φ n Σ n ≡ 0 and, hence, the pressure gradients vanish).…”

Non-local models for the formation of hepatocyte–stellate cell aggregates

“…As a result, increasing research effort is being focused on the in vitro engineering of liver tissue for such devices, as well as for drug testing and, potentially, for transplantation (Green et al, 2009). Approximately 80% of a healthy liver is composed of hepatocytes (Mitaka, 1998), cells which perform most of its biological functions (Selden et al, 1999).…”

Cancer as Multifaceted Disease

“…Here a Gompretzian exponential growth was introduced in [10] which describes the tumor growth prior to treatment by radiation; the model incorporates biological cancer markers; more progress could be made by using models of liver cell aggregation [42] [43].…”