A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor

Citation: Kaul H, Cui Z, Ventikos Y ( A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor Himanshu Kaul 0 Zhanfeng Cui 0 Yiannis Ventikos 0 Roeland M.H. Merks, Centrum Wiskunde & Informatica (CWI) & Netherlands Institute for Systems Biology, Netherlands 0 Institute of Biomedical Engineering and Department of Engineering Science, University of Oxford , Oxford , United Kingdom Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications. - The diseases of cellular deficiency [1] can be only treated if the lost cell population is either regenerated or compensated using autologous substitutes [2,3]. Given that certain adult human tissues lose their capacity to regenerate [4], they rely exclusively, in case of a critical injury, on functionally similar substitutes [47]. The principles of tissue engineering can be used to develop such biological substitutes, with remarkably similar properties as those of the host tissues, in vitro [4,69]. This requires recapitulation of certain key developmental events ex vivo thereby necessitating tight control over the artificial growth environment [3,7,10]. Bioreactors, which have evolved significantly in both their complexity and functionality over the last two decades, are devices that have been successfully utilized towards this end [2,3,10]. Apart from their primary design objective (which is to regulate the cellular microenvironment to support cell viability, promote their 3D organization and provide the cells with spatiotemporally controlled signals) they also offer the user the possibility to seed cells dynamically within 3D matrices, overcome the constraints inherent to static cultures and stimulate the developing constructs physically [3,10]. Despite the technological advances that have been made in the sector of regenerative medicine and bioreactor technology, there is still a pressing need for safe and clinically efficacious autologous substitutes [3]. Translating regenerative medicine from bench to bed-side would not only require a good product but also robust, controllable and cost-effective manufacturing bioprocesses that are compliant with the evolving regulatory frameworks [3,11]. Bioreactors serve ideally towards this end as they are the key element for the development of automated, standardized, traceable, cost-effective and safe manufacturing processes for engineered tissues for clinical applications [3]. However, utilized primarily as black boxes, where trial and error eventually leads to the desirable cellular outcome [3,12], bioreactors have an enormous ground to cover for that eventuality to be realized. Currently, the yields are qualitatively poor and the process of cell growth is often not reproducible. The problem stems from the fact that little is known about the impact of specific bioreactor mass transport characteristics and features on the expansion and growth of cells within the device. Investigators in recent years have begun applying computational tools [12,13] to study mass transport inside the bioreactor and how that may influence cell dynamics, but this extremely complex interplay has thus far proven elusive. Analyses based on tackling directly the differential equations governing transport have not only been successful in quantifying mass transport and hydrodynamics inside the bioreactors; their use has been extended to, given certain assumptions, studying cellular dynamics as well [12,14]. Such models usually either assume absence of neo-tissue within the interconnected pore space in a scaffold or cell attachment only along the surfaces of the scaffold [12]. The differential approach models the cell population, the surrounding extra-cellular framework and nutrients as distributed continua [14]. The matrix in which the cells grow can be treated as a porous medium [14] and one can utilize a wide variety of available computational methods to quantify the distribution of any number of substances being transported and diffusing inside it. Whereas the continuum approach captures the transport phenomena quite accurately, the fact that it investigates biological phenomena at cell population level, disregarding entirely the cellular heterogeneity central to biological function [14,15] and the low-level system details [16], hinders detailed analysis of cellular dynamics [11,17,18]. In order to understand the impact of cell level behavior on the overall cell population discrete models can be employed [14 16,18]. The cellular automata approach has been used extensively to trace the microscopic details of cellular dynamics more directly and accurately by attributing a set of evolution/transition rules to the computational grids that can represent biological entities such as the cell or the physical microenvironment [14,19]. The models that have been tried using this approach usually assume a constant supply of nutrients, which is not fully reflective of the actual conditions even under carefully designed experiments [15,20]. Furthermore, the discrete models available in the literature, despite capturing processes such as contact inhibition, persis (...truncated)