The potential and limits of Thin-Plate Spline retrodeformation on asymmetrical objects:simulation of taphonomic deformations andapplication on a fossil sample of limb long bones

Abstract

In this study, we suggest a method adapted to the retrodeformation of asymmetrical objects – such as limb bones – by quantitatively estimating the effectiveness of the Thin-Plate Splines (TPS) interpolation function as a retrodeformation tool. To do so, taphonomic deformations were first simulated on a single horse femur. The original bone was then used as a reference in order to drive the retrodeformation using anatomical landmarks. This approach, based on a single bone, enabled us to evaluate the performance of the retrodeformation procedure. Then, the same approach was performed on a sample of rhino femora but using a different specimen (from the same species) as the reference in order to account for morphological variation. We also added sliding semi-landmarks on anatomical curves. Finally, retrodeformation was applied on a sample of sauropodomorph dinosaur femora by building a mean shape based on several well-preserved fossil specimens. Results show that entirely flattened and stretched bones are more efficiently retrodeformed than bent and twisted bones. Introduction of morphological variation increased the efficiency of retrodeformation for bent and locally stretched bones. The application to the sample of fossils produced similar results but also highlighted the difficulty of retrodeforming bones with a combination of different deformations. TPS interpolation is an efficient tool of retrodeformation for asymmetrical objects, especially for bones with only one affine deformation such as flattening or stretching. Finding a threshold of landmark number to use for this process would be the next step because it would allow us to ensure the quality of retrodeformation while keeping available a reasonable number of landmarks in order to perform shape analysis on retrodeformed bones. Twisted and bent fossils are frequently discovered and we suggest that these kinds of deformations should be studied with caution, especially when combined with other types of taphonomic distortions.

Femoral specializations to locomotor habits in early archosauriforms

“…Taphonomical alterations impact the original shape of a fossil and consequently alter its biological information (Eifremov, 1940; Webster & Hughes, 1999). Accounting for taphonomy is even more relevant when performing geometric morphometric and statistical analyses, such as here on limb bones (Hedrick et al, 2018; Lefebvre et al, 2020; Pintore et al, 2021 in press , Wynd et al, 2021). Thus, only complete femora without clear, visible distortion of the anteroposterior curvature of the diaphysis and of the proximodistal angle between the two epiphyses were considered.…”

“…independently of locomotor habit (Figure 3a-e; "Typ, Par, Rev, Rio, Pla, Mus," Figure 4a). Such morphological convergence between heavy terrestrial and semi-aquatic quadrupeds is intriguing because it evolved to serve opposite functions in relation to environmental factors (e.g., buoyancy in a low gravity environment vs. improved resistance to gravitational forces on land) and has already been studied among some massive animals through a microanatomical approach (Houssaye et al, 2016(Houssaye et al, , 2021. We suggest that this convergence should be investigated further in archosauriforms using a similar approach coupled with biomechanical analyses in order to decipher specializations between these two functional constraints which seemed to drive the appearance of convergent femoral morphologies.…”

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

“…Similarly, methods to quantify deformation and characterize local and global deformation [ 42 ] improve the accuracy of retrodeformation by better understanding how specimens have been altered, as can explorations of the range and modes of taphonomic variation within species represented by frequent fossil specimens [ 43 ]. Figuring the extent of retrodeformation as tension maps of mesh distortions [ 5 ] or maps coloured by relative mesh distance between pre- and postretrodeformed conditions [ 44 ] present options for method documentation.…”

“…9: 220519 fossil specimens [43]. Figuring the extent of retrodeformation as tension maps of mesh distortions [5] or maps coloured by relative mesh distance between pre-and postretrodeformed conditions [44] present options for method documentation.…”

Topology-Based Three-Dimensional Reconstruction of Delicate Skeletal Fossil Remains and the Quantification of Their Taphonomic Deformation

“…(1) The method generally assumes bilateral symmetry in the initial object, although it can in theory be applied to generally asymmetrical objects (e.g., long bones), if at least two of them are preserved; however, results for such objects may be less reliable than for symmetrical objects (see Hedrick et al, 2019;Pintore et al, 2022). Small individual shape variation and fluctuating asymmetry cannot be taken into account directly.…”