When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often dicult to derive spatiotemporally directed predictions regarding experimentally induced e↵ects. A paradigm of 'non-directed' hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called 'statistical parametric mapping' (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be e↵ective for analyzing 3D scalar fields, the current results are the first to demonstrate its e↵ectiveness for 1D vector field analysis. It was concluded that SPM o↵ers a generalized, statistically comprehensive solution to scalar extraction's oversimplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems.

Statistical parametric mapping (SPM) is a topological methodology for detecting field changes in smooth n-dimensional continua. Many classes of biomechanical data are smooth and contained within discrete bounds and as such are well suited to SPM analyses. The current paper accompanies release of 'SPM1D', a free and open-source Python package for conducting SPM analyses on a set of registered 1D curves. Three example applications are presented: (i) kinematics, (ii) ground reaction forces and (iii) contact pressure distribution in probabilistic finite element modelling. In addition to offering a high-level interface to a variety of common statistical tests like t tests, regression and ANOVA, SPM1D also emphasises fundamental concepts of SPM theory through stand-alone example scripts. Source code and documentation are available at: www.tpataky. net/spm1d/.

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The masticatory musculature of rodents has evolved to enable both gnawing at the incisors and chewing at the molars. In particular, the masseter muscle is highly specialised, having extended anteriorly to originate from the rostrum. All living rodents have achieved this masseteric expansion in one of three ways, known as the sciuromorph, hystricomorph and myomorph conditions. Here, we used finite element analysis (FEA) to investigate the biomechanical implications of these three morphologies, in a squirrel, guinea pig and rat. In particular, we wished to determine whether each of the three morphologies is better adapted for either gnawing or chewing. Results show that squirrels are more efficient at muscle-bite force transmission during incisor gnawing than guinea pigs, and that guinea pigs are more efficient at molar chewing than squirrels. This matches the known diet of nuts and seeds that squirrels gnaw, and of grasses that guinea pigs grind down with their molars. Surprisingly, results also indicate that rats are more efficient as well as more versatile feeders than both the squirrel and guinea pig. There seems to be no compromise in biting efficiency to accommodate the wider range of foodstuffs and the more general feeding behaviour adopted by rats. Our results show that the morphology of the skull and masticatory muscles have allowed squirrels to specialise as gnawers and guinea pigs as chewers, but that rats are high-performance generalists, which helps explain their overwhelming success as a group.

Biomechanical processes are often manifested as one-dimensional (1D) trajectories. It has been shown that 1D confidence intervals (CIs) are biased when based on 0D statistical procedures, and the nonparametric 1D bootstrap CI has emerged in the Biomechanics literature as a viable solution. The primary purpose of this paper was to clarify that, for 1D biomechanics datasets, the distinction between 0D and 1D methods is much more important than the distinction between parametric and non-parametric procedures. A secondary purpose was to demonstrate that a parametric equivalent to the 1D bootstrap exists in the form of a random field theory (RFT) correction for multiple comparisons. To emphasize these points we analyzed six datasets consisting of force and kinematic trajectories in one-sample, paired, two-sample and regression designs. Results showed, first, that the 1D bootstrap and other 1D nonparametric CIs were qualitatively identical to RFT CIs, and all were very di↵erent from 0D CIs. Second, 1D parametric and 1D non-parametric hypothesis testing results were qualitatively identical for all six datasets. Last, we highlight the limitations of 1D CIs by demonstrating that they are complex, designdependent, and thus non-generalizable. These results suggest that (i) analyses of 1D data based on 0D models of randomness are generally biased unless one has explicitly specified an a priori 0D variable, and (ii) parametric and non-parametric 1D hypothesis testing provide an unambiguous framework for analysis when one's hypothesis explicitly or implicitly pertains to whole 1D trajectories.