A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection-reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.

A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the wellseparated length scales of the material: the pores are small compared to the macroscale, with a spatially periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and vice versa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils.

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Understanding the uptake of a drug by diseased tissue, and the drug's subsequent spatiotemporal distribution, are central factors in the development of effective targeted therapies. However, the interaction between the pathophysiology of diseased tissue and individual therapeutic agents can be complex, and can vary across tissue types and across subjects. Here, we show that the combination of mathematical modelling, of high-resolution optical imaging of intact and optically cleared tumour tissue from animal models, and of in vivo imaging of vascular perfusion predicts the heterogeneous uptake, by large tissue samples, of specific therapeutic agents, as well as their spatiotemporal distribution. In particular, by using murine models of colorectal cancer and glioma, we report and validate predictions of steady-state blood flow and intravascular and interstitial fluid pressure in tumours, of the spatially heterogeneous uptake of chelated gadolinium by tumours, and of the effect of a vascular disrupting agent on tumour vasculature.

Blinking is vital to maintain the integrity of the ocular surface and its characteristics such as blink duration and speed can vary significantly, depending on the health of the eyes. The blink is so rapid that special techniques are required to characterize it. In this study, a high-speed camera was used to record and characterize voluntary blinking. The blinking motion of 25 healthy volunteers was recorded at 600 frames per second. Master curves for the palpebral aperture and blinking speed were constructed using palpebral aperture versus time data taken from the high-speed camera recordings, which show that one blink can be divided into four phases; closing, closed, early opening and late opening. Analysis of data from the high-speed camera images was used to calculate the palpebral aperture, peak blinking speed, average blinking speed and duration of voluntary blinking and compare it with data generated by other methods previously used to evaluate voluntary blinking. The advantages of the high-speed camera method over the others are discussed, thereby supporting the high potential usefulness of the method in clinical research.