The seeding density of therapeutic cells in engineered tissue impacts both cell survival and vascularization. Excessively high seeded cell densities can result in increased death and thus waste of valuable cells, whereas lower seeded cell densities may not provide sufficient support for the tissue in vivo , reducing efficacy. Additionally, the production of growth factors by therapeutic cells in low oxygen environments offers a way of generating growth factor gradients, which are important for vascularization, but hypoxia can also induce unwanted levels of cell death. This is a complex problem that lends itself to a combination of computational modelling and experimentation. Here, we present a spatio-temporal mathematical model parametrized using in vitro data capable of simulating the interactions between a therapeutic cell population, oxygen concentrations and vascular endothelial growth factor (VEGF) concentrations in engineered tissues. Simulations of collagen nerve repair constructs suggest that specific seeded cell densities and non-uniform spatial distributions of seeded cells could enhance cell survival and the generation of VEGF gradients. These predictions can now be tested using targeted experiments.

Cross-linked filament bundles, such as in cilia and flagella, are ubiquitous in biology. They are considered in textbooks as simple filaments with larger stiffness. Recent observations of flagellar counterbend, however, show that induction of curvature in one section of a passive flagellum instigates a compensatory counter-curvature elsewhere, exposing the intricate role of the diminutive cross-linking proteins at large-scales. We show that this effect, a material property of the cross-linking mechanics, modifies the bundle dynamics non-trivially, and induces a bimodal L 2 − L 3 length-dependent material response that departs from the Euler-Bernoulli theory. Hence, the use of simpler theories to analyse experiments can result in paradoxical interpretations. Remarkably, the counterbend dynamics instigates counter-waves in opposition to driven oscillations in distant parts of the bundle, with potential impact on the regulation of flagellar bending waves. These results have a range of physical and biological applications, including the empirical disentanglement of material quantities via counterbend dynamics.

We present a validation study comparing results from a patient-specific lattice-Boltzmann simulation to transcranial Doppler (TCD) velocity measurements in four different planes of the middle cerebral artery (MCA). As part of the study, we compared simulations using a Newtonian and a Carreau-Yasuda rheology model. We also investigated the viability of using downscaled velocities to reduce the required resolution. Simulations with unscaled velocities predict the maximum flow velocity with an error of less than 9%, independent of the rheology model chosen. The accuracy of the simulation predictions worsens considerably when simulations are run at reduced velocity, as is for example the case when inflow velocities from healthy individuals are used on a vascular model of a stroke patient. Our results demonstrate the importance of using directly measured and patient-specific inflow velocities when simulating blood flow in MCAs. We conclude that localized TCD measurements together with predictive simulations can be used to obtain flow estimates with high fidelity over a larger region, and reduce the need for more invasive flow measurement procedures.

Implantable devices utilizing bioengineered tissue are increasingly showing promise as viable clinical solutions. The design of bioengineered constructs is currently directed according to the results of experiments that are used to test a wide range of different combinations and spatial arrangements of biomaterials, cells and chemical factors. There is an outstanding need to accelerate the design process and reduce financial costs, whilst minimizing the required number of animal‐based experiments. These aims could be achieved through the incorporation of mathematical modelling as a preliminary design tool. Here we focus on tissue‐engineered constructs for peripheral nerve repair, which are designed to aid nerve and blood vessel growth and repair after peripheral nerve injury. We offer insight into the role that mathematical modelling can play within tissue engineering, and motivate the use of modelling as a tool capable of improving and accelerating the design of nerve repair constructs in particular. Specific case studies are presented in order to illustrate the potential of mathematical modelling to direct construct design. Copyright © 2016 The Authors Journal of Tissue Engineering and Regenerative Medicine Published by John Wiley & Sons Ltd.

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