Plantar Force Spectra Across Midsole Densities and Treadmill Speeds: A Spatially Resolved Analysis in Relation to Material Properties

Running shoe midsoles are designed to attenuate impact forces while maintaining or improving performance. However, the literature is equivocal, likely due to measurement systems, whereas in vitro testing is conclusively favourable. This study investigated three densities of ATPU foam, comparing in vitro mechanical properties with in vivo plantar force spectral characteristics derived from individualised pressure distributions during treadmill running at varied speeds. In vitro results of slab foam and shoes showed strong positive relationships between impact variables normalised to total impact energy and foam density (r2 > 0.90), and strong negative relationships for time-domain variables normalised to deformation (mm) as density increased (r2 > 0.89). During running, lower midsole density increased ground contact time across speeds (p = 0.041), while spatially resolved high-frequency PSD and peak impact force both decreased (p = 0.043; p = 0.030). However, there were no differences between total vertical force and midsole density (p = 0.232). Relationships between in vitro Peak G and high-frequency PSD were strong across all speeds (r2 = 0.63–0.91). Conversely, reducing midsole density increased active peak force across speeds (p = 0.003), which was strongly related to in vitro energy return (r2 > 0.89). Therefore, plantar force spectra and spatially resolved analyses demonstrate how foam density properties translate from in vitro to in vivo treadmill running, with lower-density foam improving impact attenuation but elevating propulsive forces. Future work needs to verify this in an outdoor setting.