Abstract
To reduce breast motion with a bra, we need to understand what drives the motion of the breasts, and what variables change as support increases. Quantifying breast-torso coordination and movement complexity across the gait cycle may offer deeper insights than previously reported discrete time lag. We aimed to compare breast-torso coordination and mutual influence across breast support conditions during running. Twelve female participants ran on a treadmill at 10 km h -1 with an encapsulation and compression sports bra, and in no bra. Nipple and torso position was recorded. Vector coding, granger causality and transfer entropy were calculated within gait cycles. In both bra conditions, a greater percentage of gait cycles was spent with the breast and torso in-phase (> 90%) compared to no bra running (~ 66%, p < 0.001), with most time spent in-phase in the encapsulation versus compression bra (p = 0.006). There was a main effect of breast support condition on Granger causality (p < 0.001), both from breast to torso and torso to breast. Transfer of information was highest from torso to breast, compared to breast to torso in all conditions. Overall, these results provide novel insight into the mutual and complex interaction between the breast and the torso while running in different bra conditions. The approaches presented allow for a greater understanding of bra support conditions than existing discrete measures, which may relate to comfort and performance. Therefore, measures of coupling, predictability and transfer of complexity should be employed in future work examining these features. angles can be divided into four coordination patterns, or frequency bins of 45° (Fig. 4 ) 8 . The four frequency bins represent coordination patterns: in-phase; anti-phase; proximal phase dominancy (proximal segment leading) and distal phase dominancy (distal segment leading) 8, 9, 15, 18 . Based on evidence from work by Risius et al. 4 , we would expect that reduced time lag with increased bra support conditions implies more in-phase coupling between the breast and torso. Examining the coordination between the breast and torso through the entire running gait cycle using vector coding will offer insights into the fundamentals of breast movement and the support requirements and/or performance of sports bras, particularly as the timing of peak breast skin strain in each region of the breast varies across the gait cycle 1 . Coordination in movement patterns provides one view on coupling between the breast and torso. Since the breast and the torso are mechanically linked, they have an effect on each other. In understanding coupling through this mutual influence we took two approaches. Firstly, Granger causality 19 is a technique that measures the mutual influence, testing how the knowledge of one signal can help improve the prediction of another, specifically, if the history of signal X contains information to predict signal Y beyond the information contained in the history of signal Y alone, then there is a predictive relationship. External support of a sports bra constrains the movement of the breast relative to the torso. For example, compression bras limit breast movement by compressing and flattening the breasts onto the torso 20 , whereas encapsulation sports bras have moulded cups that support each breast separately 20, 21 . Compression and encapsulation bras have demonstrated 51% and 59% reductions in breast displacement in running, respectively, relative to no bra 22 . On the other hand, no significant difference in torso kinematics was reported with increased breast support during running 4 , while torso movement variability has been shown to increase 3 . Therefore, based on previous work, it is likely that prediction of the breast motion during dynamic activity will be improved with knowledge of the torso motion in more supportive bra conditions compared to no bra or less supportive conditions. Quantifying this effect could inform modelling studies that have previously modelled the torso as the suprasternal notch providing the driving force to the breast 23 , as well as informing performance aspects of bra design. Secondly, complexity of movement has been related to health status 24 and may also be an important factor in comfort in breast motion as breast movement has been described as more "erratic" In water, in which movement was more comfortable, compared to land 25 . Transfer entropy is based on Shannon's information theory and the complexity of information contained in the signal, and is used to quantify to what degree complexity contained in the torso signal is transferred to the breast signal and vice versa. Thus, the complexity of the torso motion that is transferred to the breast may be an aspect of coupling related to comfort. Quantifying the transfer entropy between the torso and breast provides information that transcends the current mechanical understanding of breast motion, by establishing the extent to which signal complexity is transferred between the two systems. The aim of this study was to quantify and compare breast-torso coordination and mutual influence as a function of sports bra type during running. Although breast displacement in running is multi-planar, for simplicity, only vertical displacement was analysed. Nonetheless, previous work has shown that at speeds of 10 km/h and above the vertical component accounts for around 50% of total displacement 22 . Based on previous literature which shows that vertical breast displacement reduces from no bra running to running in a compression sports bra and finally to running in an encapsulation sports bra; it was hypothesised that (1) based on vector coding, the mean phase angle between the breast and torso would be more in-phase with increased breast support across the running cycle; (2) based on Granger causality, in more supportive bra conditions, knowledge of torso motion will improve prediction of breast motion more than in less supportive bra conditions, and (3) based on transfer entropy, the level of breast support will affect the transference of signal characteristics from one system (torso or breast) to the other system, and that this transference will increase as breast support increases.
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