The superficial dorsal horn is a major site of termination of nociceptive primary afferents. Fast excitatory synaptic transmission in this region is mediated mainly by release of glutamate onto postsynaptic AMPA and NMDA receptors. NMDA receptors are known to be Ca2+-permeable and to provide synaptically localized Ca2+ signals that mediate short-term and long-term changes in synaptic strength. Less well known is a subpopulation of AMPA receptors that is Ca2+-permeable and has been shown to be synaptically localized on dorsal horn neurons in culture (Gu et al., 1996) and expressed by dorsal horn neurons in situ (Nagy et al., 1994; Engelman et al., 1997). We used kainate-induced cobalt uptake as a functional marker of neurons expressing Ca2+-permeable AMPA receptors and combined this with markers of nociceptive primary afferents in the postnatal rat dorsal horn. We have shown that cobalt-positive neurons are located in lamina I and outer lamina II, a region strongly innervated by nociceptors. These cobalt-positive neurons colocalize with afferents labeled by LD2, and with the most dorsal region of capsaicin-sensitive and IB4- and LA4-positive afferents. In contrast, inner lamina II has a sparser distribution of cobalt-positive neurons. Some lamina I neurons expressing the NK1 receptor, the receptor for substance P, are also cobalt positive. These neurons are likely to be projection neurons in the nociceptive pathway. On the basis of all of these observations, we propose that Ca2+-permeable AMPA receptors are localized to mediate transmission of nociceptive information.

Poisson's ratio (ν) is the negative ratio of the lateral-to-axial strain of a material under compression or tension and ranges between À1 and þ0.5 for 3D isotropic materials, according to elasticity theory, [1] and À1 and þ1 for 2D isotropic materials. [2] Auxetic materials (and structures) have a negative Poisson's ratio (NPR) as they expand laterally when stretched and contract laterally when compressed. [3] Auxetics can have enhanced properties including increased resistance to indentation and increased energy absorption under compression. [4,5] They also exhibit synclastic curvature, [3,6] which could improve the conformability of clothing to the body. Such properties make auxetics ideal candidates for enhancing personal protective equipment (PPE) in sport, [7] such as those used in rugby, [8] American football, [9] or snow sports. [10] Head injuries, for example, still frequently occur in sport despite developments in helmet technology and increased user uptake. [11,12] Shear thickening materials are often used in sporting PPE products, such as snowboard back protectors, but their ability to limit impact forces can change with temperature. [13] Approximately 4.5 million people are treated in EU hospitals for sports-related injuries annually, [14] at a cost of €2.4 billion (%£2 billion), [15] which could be reduced with more effective protection and better regulation. Better fitting, more comfortable, and higher-performing auxetic PPE has the potential to increase participation in sport and improve general well-being, both physically and mentally. [16] In addition, a more active population could reduce healthcare costs, particularly as National Health Service providers spent %£900 million on addressing health issues related to physical inactivity in the UK in 2009/2010. [17] There are also social health benefits of practicing a sport with others. [18] Bailly et al. found that snow-sport participants with an injury that was not to the head were less likely to be wearing a helmet than those without an injury, [19] challenging the concerns of Wilson that sporting participants who wear PPE take more risks. [20] Although auxetic systems can be found in nature, [21] research into these materials has typically focused on manmade products like open-cell foam, which was first manufactured by Lakes using thermomechanical techniques that combined compression and heating. [3] Auxetic foam fabrication has also been investigated by Chan and Evans. [4,22] Scarpa et al. were the first to report the dynamic response of auxetic open-cell foam, highlighting its potential in crashworthiness applications. [23] More recently, this potential was demonstrated further; open-cell auxetic foam reduced the peak acceleration of drop tower impacts (energies up to 5.6 J) by two to three times, compared with its conventional

Tennis racket properties are of interest to sports engineers and designers as it allows them to evaluate performance, review trends and compare designs. This study explored mathematical models that correlated to the mass moments of inertia of a tennis racket, both about an axis through the butt and about the longitudinal axis, using its dimensions, mass and centre of mass location. The models were tested on 416 rackets, dating from 1874 to 2017. Results showed that moments of inertia about the butt and longitudinal axis can be estimated to within − 4 to 5% and − 11 to 12% of measured values, respectively, using the proposed models on original rackets. When rackets were customised, with 30 g of additional mass, moment of inertia about the butt could be estimated within 6%, but the model for moment of inertia about the longitudinal axis was less accurate (largest error at 25%). A Stepwise Linear Regression model indicated that racket mass and then centre of mass location had the largest effect on moment of inertia about the handle, with head width having the largest effect on moment of inertia about the longitudinal axis.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Auxetic (negative Poisson’s ratio) and gradient open cell foams have shown promise for their conformability and high impact energy absorption—useful in applications like protective equipment, footwear and prosthetics. Recent methods fabricated auxetic closed cell foam by steaming conventional closed cell foam. Methods developed herein control the cell structure of auxetic closed cell foam, to produce novel intentionally anisotropic and gradient auxetic closed cell foam. Pins passed through the foam constrained or stretched regions during steaming to further modify cell structure, and impart gradients in cell structure, Young’s modulus and Poisson’s ratios. Fabricated foams had Poisson’s ratios between 1 and −1. Imparted Young’s moduli of 1–12 MPa were similar to foams used in footwear, prosthesis, helmets and other impact protection. The effect of changes to cell structure on Young’s moduli and Poisson’s ratio are explained by combining analytical models of auxetic open cell and conventional closed cell foam.

There are currently no restrictions on the coefficient of friction of tennis courts or strings. The aim of this paper was to determine the effect of friction on tennis ball impacts. Finite element models were used to determine the effect of friction for oblique spinning impacts both between a tennis ball and a rigid surface and between a tennis ball and the string bed of a freely suspended racket. The results showed that during an oblique impact a tennis ball can behave in any of the following ways: first, it can slide, second, it can slide and then 'overspin', or, third, it can slide, overspin, and then converge towards rolling. The ball will slide throughout the majority of impacts on the court during play. Therefore, the rebound topspin of the ball will increase with increasing court friction and the horizontal rebound velocity will decrease. The ball will roll off the string bed for the majority of groundstrokes, and the rebound properties will effectively be independent of string bed friction.