Research into cellular engineered bone grafts offers a promising solution to problems associated with the currently used auto- and allografts. Bioreactor systems can facilitate the development of functional cellular bone grafts by augmenting mass transport through media convection and shear flow-induced mechanical stimulation. Developing successful and reproducible protocols for growing bone tissue in vitro is dependent on tuning the bioreactor operating conditions to the specific cell type and graft design. This process, largely reliant on a trial-and-error approach, is challenging, time-consuming and expensive. Modelling can streamline the process by providing further insight into the effect of the bioreactor environment on the cell culture, and by identifying a beneficial range of operational settings to stimulate tissue production. Models can explore the impact of changing flow speeds, scaffold properties, and nutrient and growth factor concentrations. Aiming to act as an introductory reference for bone tissue engineers looking to direct their experimental work, this article presents a comprehensive framework of mathematical models on various aspects of bioreactor bone cultures and overviews modelling case studies from literature.

Tissue engineering has the potential to augment bone grafting. Employing microcarriers as cell-expansion vehicles is a promising bottom-up bone tissue engineering strategy. Here we propose a collaborative approach between experimental work and mathematical modelling to develop protocols for growing microcarrier-based engineered constructs of clinically relevant size. Experiments in 96-well plates characterise cell growth with the model human cell line MG-63 using four phosphate glass microcarrier materials. Three of the materials are doped with 5 mol% TiO2 and contain 0%, 2% or 5% CoO, and the fourth material is doped only with 7% TiO2 (0% CoO). A mathematical model of cell growth is parameterised by finding material-specific growth coefficients through data-fitting against these experiments. The parameterised mathematical model offers more insight into the material performance by comparing culture outcome against clinically relevant criteria: maximising final cell number starting with the lowest cell number in the shortest time frame. Based on this analysis, material 7% TiO2 is identified as the most promising.

Tissue engineering is a promising approach for bone regeneration; yet challenges remain that limit successful translation to patients. It is necessary to understand how real-world manufacturing processes will affect the constituent cells and biomaterials that are needed to create engineered bone. Bioactive phosphate glasses processed into microspheres are an attractive platform for expanding bone-forming cells and also for driving their osteogenic differentiation and maturation. The aim of this study was to assess whether Ti-doped phosphate glass microspheres could support osteoblastic cell responses in dynamic cell culture environments. Dynamic culture conditions were achieved using microwell studies under orbital agitation. Dimensionless parameters such as the Froude number were used to inform the choice of agitation speeds, and the impact on cell proliferation and microunit formation was quantified. We found that phosphate glass microspheres doped with titanium dioxide at both 5 and 7 mol% provided a suitable biomaterial platform for effective culture of MG63 osteoblastic cells and was not cytotoxic. Dynamic culture conditions supported expansion of MG63 cells and both 150 and 300 rpm orbital shake resulted in higher cell yield than static cultures at the end of the culture (day 13). The Froude number analysis provided insight into how the microunit size could be manipulated to enable an appropriate agitation speed to be used, while ensuring buoyancy of the microunits. These small-scale experiments and analyses provide understanding of the impact of fluid flow on cell expansion that will have increasing importance when scaling up to process technologies that can deliver clinical quantities of cell-microsphere units. Such knowledge will enable future engineering of living bone-like material using processing systems such as bioreactors that use mixing and agitation for nutrient transfer, therefore introducing cells to dynamic culture conditions.

This paper discusses the design of engineering mathematics assessment that encourages learning beyond algorithmic recall. Our approach is based on the MATH (mathematical assessment task hierarchy) taxonomy. We propose using mathematics as a tool to analyse relatable problems and produce clear engineering deliverables to ensure that academic knowledge is translated to real-life situations. Creating engineering scenarios was instrumental in fostering active engagement, enquiry, creativity and reducing opportunities for academic misconduct in our first-year engineering mathematics assessments. An example of an exam question covering the topics of calculus, linear algebra, and dimensional analysis is given to illustrate the concepts discussed. Qualitative feedback from 203 students on an assessment paper containing the question shown herein is also included. Our data shows that most students had little to no previous exposure to real-world questions and that most of their time engaging with the assessment was spent critically analysing the problems. In addition, student feedback showed that contextual assessment is perceived as more challenging and exciting than pure mathematics problems and that students believe contextual assessment adds value to their education.

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