Maths in Medicine: How to Survive a Science Fair

When talking to secondary school students, first impressions are crucial. Accidentally say something that sounds boring and you'll lose them in seconds. A physical demonstration can be an eye-catching way to begin an activity or spark off a conversation about mathematics. This is especially true in the context of an event like a science fair where there are hundreds of other exhibitors and stands, possibly involving loud music and/or dancing robots! In this article we describe three devices that were built to illustrate specific physical phenomena that occur in the human body. Each device corresponds to a simple mathematical model which contains both elements that are accessible to pupils in the early years of secondary education and more challenging mathematical concepts that might appeal to A-level students. Two of the devices relate to the Windkessel effect, a physical phenomenon that regulates blood flow, and the third demonstrates the elastic properties of ligaments and tendons

A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils

A new strain energy function for the hyperelastic modelling of ligaments and tendons whose fascicles have a helical arrangement of fibrils is derived. The stress-strain response of a single fascicle whose fibrils exhibit varying levels of crimp throughout its radius is calculated and used to determine the form of the strain energy function. The new constitutive law is used to model uniaxial extension test data for human patellar tendon and is shown to provide an excellent fit, with the average relative error being 9.8%. It is then used to model shear and predicts that the stresses required to shear a tendon are much smaller than those required to uniaxially stretch it to the same strain level. Finally, the strain energy function is used to model ligaments and tendons whose fascicles are helical, and the relative effects of the fibril helix angle, the fascicle helix angle and the fibril crimp variable are compared. It is shown that they all have a significant effect; the fibril crimp variable governs the non-linearity of the stress-strain curve, whereas the helix angles primarily affect its stiffness. Smaller values of the helix angles lead to stiffer tendons; therefore, the model predicts that one would expect to see fewer helical sub-structures in stiff positional tendons, and more in those that are required to be more flexible

Re-defining upstream fish passage

In efforts to re-establish populations of migratory fish in areas previously blocked by man-made barriers, upstream migration of adults needs to be facilitated past those barriers. Passage solutions need to meet the standards of being safe, timely, efficient and effective. While traditional upstream adult passage solutions may meet these agency standards, the upfront planning and implementation costs associated with these solutions severely impacts the timing and financial viability of these programs. In an environment of increasing pressures on fish populations caused by climate change and habitat degradation, solutions that are cheaper and quicker to deploy are needed. In this talk we describe a pilot adult volitional passage system that took less than 3 months to install in 2017 at a high head dam in Washington State, USA, and the results from that system. This pilot was made possible by collaboration of private industry, tribal interests and the federal government. We will look at the technology used and additional testing that has been performed to make sure that the solution meets the acceptable standards. Biologists and engineers may be able to use this project as an example to accelerate other passage implementations with industry and government participation

Advances in machine vision scanning

Observation of migrating fish provides critical data required for recovery and management actions. Considerable resource is expended to count, speciate and sort migrating fish at purpose-built viewing facilities within dams and other man-made barriers. Manual operators observe and record the data in real time or post analyze video recordings. However, the data gathered, and decisions made are inherently prone to human error, operator fatigue and fish directional behavior. Turbidity can also exacerbate accuracy - the main reason that prior automation attempts have been largely unproductive. Recent development of machine vision technology used in manufacturing and fruit harvesting operations provides the potential for dramatically improving and simplifying fisheries data collection. In this session we describe an adaptation of the current state of the art to fisheries management. Using a simple false weir configuration, the fish are dewatered, singulated and descend a short, wetted slide. Controlled lighting and high-speed imagery from radially arranged cameras provide multiple photographs of consistent quality for real time processing. Using combinations of machine learning, image recognition and triangulation, the control system computers are able to simultaneously synthesize the needed data and provide signals for sorting actions in less than 2 seconds, with an extremely high degree of accuracy. Fish counts, and individual fork length and girth measurements can already be reliably captured. Currently under development are algorithms that include fin clip detection (for separation of wild and hatchery fish), and some speciation applications – primarily focused on exclusion of invasive species. The automated nature of the system facilitates 24-hour operation with real-time decisions and remote access to image data. Volitional fish passage is not interrupted, fish are not physically handled, spend minimal time de-watered and are efficiently classified allowing for selective passage

Employing pre-stress to generate finite cloaks for antiplane elastic waves

It is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. This appears to provide a mechanism for broadband cloaking since dispersive effects due to metamaterial microstructure will not arise.Comment: 4 pages, 2 figure

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $\mu(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with $I$-dependent rheology. When the $I$-dependence comes from a specific friction coefficient $\mu(I)$, our results show that, with compressibility, the equations are well-posed for all deformation rates provided that $\mu(I)$ satisfies certain minimal, physically natural, inequalities

The relative compliance of energy-storing tendons may be due to the helical fibril arrangement of their fascicles

T.S. acknowledges funding for this work from the EPSRC through grant no. EP/L017997/1

Evaluation of a Terrain Attribute Model for Locating Areas Suitable for Grassed Waterways in Agricultural Settings

Grassed waterways placed in high water flow zones substantially reduce erosion in agricultural fields. A recent study proposed a statistical model for waterway planning for a farm in the Outer Bluegrass physiographic region of Kentucky. The logistic regression model identified where channel erosion was likely to occur based on elevation-derived terrain attributes. The objective of this study was to test their model in fields located in the Western Coal Fields physiographic region where soils differ substantially. Model predictions corresponded well with known areas of concentrated flow (i.e., maps of existing waterways, surface drains, and observations of erosion). The geographic inference space of the waterway planning model was large. Overall, the results indicated that the geographic inference space of the waterway planning model was larger than expected. This analysis suggested that the proposed modeling procedure was robust and has the potential to be an effective tool to help conservationists identify areas where waterways should be located on some Kentucky landscapes

MyRun: balancing design for reflection, recounting and openness in a museum-based participatory platform

Cultural organisations are increasingly looking towards using digital technologies to supplement, augment and extend visitors' experiences of exhibits and museums. In this paper, we describe the design and evaluation of MyRun, a 'participatory platform' for a museum. Our goal with MyRun was to use experience-centered design principles of reflecting, recounting and openness as a basis for engaging visitors in sharing stories about experiences related to a nationally significant cultural event. We undertook a qualitative evaluation of the system based upon observations of its use, the contributions visitors made to the platform, and interviews with 10 visitors. We discuss how visitors approached MyRun, contributed and browsed stories, and the challenges associated with the expectations visitors and curators placed on cultural exhibits. We close by identifying a series of design opportunities for future participatory platforms in museum settings