The importance of muscle architecture in biomechanical reconstructions of extinct animals: a case study using Tyrannosaurus rex

Abstract

Functional reconstructions of extinct animals represent a crucial step towards understanding palaeocological interactions, selective pressures and macroevolutionary patterns in the fossil record. In recent years, computational approaches have revolutionised the field of 'evolutionary biomechanics' and have, in general, resulted in convergence of quantitative estimates of performance on increasingly narrow ranges for well studied taxa. Studies of body mass and locomotor performance of Tyrannosaurus rex - arguably the most intensively studied extinct animal - typify this pattern, with numerous independent studies predicting similar body masses and maximum locomotor speeds for this animal. In stark contrast to this trend, recent estimates of maximum bite force in T. rex vary considerably (> 50%) despite use of similar quantitative methodologies. Herein we demonstrate that the mechanistic causes of these disparate predictions are indicative of important and underappreciated limiting factors in biomechanical reconstructions of extinct organisms. Detailed comparison of previous models of T. rex bite force reveals that estimations of muscle fibre lengths and architecture are the principal source of disagreement between studies, and therefore that these parameters represents the greatest source of uncertainty in these reconstructions, and potentially therefore extinct animals generally. To address the issue of fibre length and architecture estimation in extinct animals we present data tabulated from the literature of muscle architecture from over 1100 muscles measured in extant terrestrial animals. Application of this dataset in a reanalysis of T. rex bite force emphasises the need for more data on jaw musculature from living carnivorous animals, alongside increased sophistication of modelling approaches. In the latter respect we predict that implementing limits on skeletal loading into musculoskeletal models will narrow predictions for T. rex bite force by excluding higher-end estimates.

Keywords: Tyrannosaurus; biomechanics; bite performance; evolution; modelling.

Figure 1

(a) The palaeontological pyramid of inference (modified from Witmer, 1995). Witmer (1995) conceptualised this scientific process as a hierarchy of sequential steps in the form of an ‘inverted pyramid of inference’, in which progression from actual fossilised hard tissues to ‘higher level’ ecological and macroevoluationary conclusions requires extrapolation and inference in the form of soft tissue and functional reconstructions. (b) Conceptualisation of biomechanical predictions for an extensively studied ‘exemplar’ taxon over time. In this scenario, continued research effort and methodological refinements lead predictions of biomechanical performance to converge on an increasingly narrower range, which hopefully lies close to the actual functional capabilities of that organism, signified by the dashed horizontal line.

Figure 2

Example of the generic workflow used to construct biomechanical models of T. rex to estimate bite force (modified from Bates & Falkingham, 2012). (a) Computer‐aided design approaches are used to estimate muscle volumes, before (b) muscle lines of actions relative to the jaw joints and biting positions (i.e. teeth) are mathematically reconstructed. (c) This basic workflow was used to derive highly disparate estimates of static or sustained bite force for the same specimen of T. rex by Bates & Falkingham (2012) and Gignac & Erickson (2017).

Figure 3

Comparison of muscle properties reconstructed for the same specimen of T. rex by Bates & Falkingham (2012, 2018) and Gignac & Erickson (2017). In each graph, white bars are values from Bates & Falkingham (2012, 2018), where error bars correspond to ranges predicted from their anatomical reconstructions and tested in their sensitivity analysis. Black bars are values from Gignac & Erickson (2017). These graphs show that the range of (a) muscle volumes, (b) muscle moment arms and (c) the value for maximum isometric stress used by Bates & Falkingham (2012) are lower than those of Gignac & Erickson (2017), indicating that these parameters cannot be responsible for the higher bite forces predicted by the former study. For example, (c) standardising the value maximum isometric stress across these studies actually increases, rather than decreases, the disparity in muscle and bite force predictions. However, despite (a) reconstructing smaller muscle volumes, Bates & Falkingham (2012) derived (d) much larger muscle physiological cross‐sectional areas for jaw‐closing muscles due to their use of a fibre length to muscle length (FL : ML) ratio of 0.25, vs. the higher ratio of 1 used by Gignac & Erickson (2017). This explains the larger muscle and bite forces predicted by Bates & Falkingham (2012). Recalculating the physiological cross‐sectional areas of muscle volumes reconstructed by Bates & Falkingham (2012) using FL : ML = 1 results in values lower than those of Gignac & Erickson (2017).

Figure 4

Analysis of the ratio of fibre length to (a) muscle belly length and (b) muscle‐tendon unit length in 1130 measurements of muscle architecture in extant vertebrates (see Appendix S2 for data). Best fit lines were calculated using reduced major axis (RMA) regression.

Figure 5

Reanalysis of the biomechanical models of Bates & Falkingham (2012) and Gignac & Erickson (2017) based on our analysis of relative muscle fibre length and architecture in Fig. 4 and previous data on ranges for soft tissue input values used in studies of extinct animals (Bates et al. 2010; Bates & Falkingham, 2012). Error bars have been calculated for the model of Gignac & Erickson based on error estimates for individual parameters used in Bates & Falkingham (2012) and Bates et al. (2010).