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A biplanar X-ray method for three-dimensional analysis of track formation

Richard G. Ellis and Stephen M. Gatesy

Plain Language Abstract

We describe a method for studying the motion of sediment in three dimensions using two X-ray machines to record videos of footprint formation. By combining movement of sedimentary particles with movement of the foot, we can study the origin of tracks in living animals and models to better interpret tracks made by dinosaurs and other extinct forms.

Resumen en Español

Un método mediante rayos X biplanares para el análisis tridimensional de la formación de rastros de pisadas

Los rastros surgen de una compleja interacción entre el animal y el sustrato. El estudio de este proceso dinámico resulta complicado dado que las interacciones pie-sedimento y sedimento-sedimento son rápidas y quedan ocultas a la vista. En este trabajo describimos un nuevo método para visualizar y cuantificar movimientos en tres dimensiones tanto de un penetrador con una morfología apropiada como del sedimento durante la formación de rastros. Nuestro método consiste en la adquisición de imágenes mediante rayos X biplanares y un flujo de trabajo basado en la animación para reconstruir las trayectorias de las cuentas metálicas diseminadas en el sedimento. Los rayos X permiten analizar a 30 imágenes por segundo y con una resolución submilimétrica los desplazamientos subsuperficiales, normalmente ocultos por el pie y la matriz opaca. Los resultados de dos estudios de rastros de tridáctilos en barro semilíquido proporcionan ejemplos novedosos, con visualizaciones animadas, de datos de conjunto y de partículas específicas, así como medidas de precisión y exactitud. Esta metodología tiene potencial para ligar mecánicamente morfologías específicas de rastros con movimientos del pie, esclarecer la formación de calcos, validar modelos computacionales y establecer un nuevo estándar para la reconstrucción de la locomoción a partir de huellas de pisadas fósiles basado en evidencias.

Palabras clave: formación de rastros; análisis 3-D de movimiento; métodos experimentales; cinemática del pie

Traducción: Miguel Company

Résumé en Français

Une méthode à rayons-X biplan pour l'analyse de la formation des empreintes

Les empreintes naissent de l'interaction complexe entre l'animal et le substrat. L'étude de ce processus dynamique est un défi du fait que les interactions pied-sédiment et sédiment-sédiment sont rapides et non visibles. Ici, nous décrivons une nouvelle méthode pour visualiser et quantifier les mouvements en 3D, utilisant à la fois la morphologie précise du marquer d'empreinte et un sédiment ressemblant durant la formation de l'empreinte. Notre méthode utilise une imagerie à rayons-X biplan et une progression basée sur une animation afin de reconstruire les trajectoires de billes métalliques semées au travers d'un volume de sédiment. Les rayons-X permettent une analyse à 30 images par seconds et une résolution submillimétrique du mouvement de la sous-surface qui est normalement cachée par le pied et l'opacité de la matrice. Les résultats originaux provenant de deux cas d'études d'empreintes tridactyles dans une boue semi-liquide fournissent une visualisation animée, des exemples de l'ensemble et des données spécifiques des particules, de même que des mesures de précision et d'exactitude. Cette méthode a le potentiel de lier mécaniquement les morphologies spécifiques des empreintes au mouvement du pied, de clarifier la formation de la sous-empreinte, de valider les modèles virtuels, et d'établir un nouveau standard de reconstruction des empreintes fossiles reposant sur des données expérimentales concrètes.

Mots clés : formation des empreintes, analyse de mouvement 3D ; méthode expérimentale, rayons-X ; cinématique du pied

Translator: Olivier Maridet

Deutsche Zusammenfassung

Eine biplanare Röntgenmethode zur dreidimensionalen Untersuchung von Spurenentstehung

Spuren entstehen durch ein komplexes Zusammenspiel von Tier und Substrat. Es ist eine Herausforderung diesen dynamischen Prozess zu untersuchen, da die meisten Fuß-Sediment und Sediment-Sediment Interaktionen schnell und im Verborgenen ablaufen. Hier beschreiben wir eine neue Methode um 3-D Bewegungen sichtbar zu machen und zu quantifizieren. Dabei ist während der Spurenentstehung sowohl der Körper morphologisch akkurat als auch das Sediment realistisch. Unsere Methode benutzt eine biplanare Röntgenaufnahme und einen Animations-basierten Arbeitsablauf um den Verlauf von Metallperlen, die über das gesamte Sediment verteilt sind, zu rekonstruieren. Röntgenstrahlen erlauben es die Untergrund-Bewegung, die normalerweise durch den Fuß oder eine opake Matrix verborgen wäre mit Submillimeter-Auflösung bei 30 Bildern pro Sekunde zu analysieren. Ergebnisse aus zwei Fallstudien mit tridactylen Spuren in halbflüssigem Schlamm haben neue und animierte Visualisierungen, Beispiele von Gesamt – und partikelspezifischen Daten und Maße von Genauigkeit und Präzision ergeben. Diese Methode hat das Potential um mechanistisch spezifische Spurenmorphologien mit der Fußbewegung in Einklang zu bringen, Untergrundspuren zu klären, Rechenmodelle zu validieren und einen neuen Maßstab für evidenzbasierte Rekonstruktion von Bewegung anhand von fossilen Fußspuren zu setzen.

SCHLÜSSELWÖRTER: Spurenentstehung; 3-D Bewegungsanalyse; experimentelle Methoden; Röntgen; Fuß-Kinematik

Translators: Eva Gebauer

Arabic

324 arab

Translator: Ashraf M.T. Elewa

 

 

 

FIGURE 1. Hardware setup for biplanar X-ray analysis of footprint formation and its virtual counterpart. 1.1, experimental configuration for the repeated plunge trials. X-rays emitted from each source are captured by the image intensifier and recorded by video camera. The second image intensifier is largely hidden by the scissor lift. The rig has been simplified to show the cast foot model more clearly. 1.2, 3-D scene of key elements in Maya software (click here to view ANIMATION for 1.2). Each X-ray source is represented by a calibrated virtual camera, which views undistorted video from the correct perspective. Digital models are registered to reconstruct 3-D indenter and sediment marker motion within the volume of X-ray intersection.

fig 1

FIGURE 2. External and internal imaging of indenter and sediment motion. 2.1, a repeatable plunge sequence showing the cast foot model entering the soft substrate (click here to view VIDEO for 2.1). Several 2 mm lead beads are visible on the surface. 2.2, undistorted X-ray image as viewed through camera 2 (click here to view VIDEO for 2.2). Lead beads appear as black dots. 2.3, rotoscoped models foot cast (green), surface (red), sub-surface (aqua), and sub-tray (magenta) beads (click here to view ANIMATION for 2.3). Only a small fraction of the analyzed beads is visible externally in 1.1. Digit III is ~9 cm in length.

fig 2

FIGURE 3. Estimate of precision based on the variability in six measured distances between the four beads embedded in the cast foot model. 3.1, within each trial, the standard deviation in inter-bead distance was less than 0.2 mm (mean 0.11 mm). 3.2, absolute deviation of average inter-bead distance from each trial was within 0.12 mm of the group mean.

fig 3

FIGURE 4. Position of 810 beads and the foot cast model compiled from 14 repeatable plunge trials (click here to view ANIMATION for 4). Axes are 1 cm in length.

fig 4

FIGURE 5. Summary of 810 bead paths compiled from 14 repeatable plunge trials. 5.1, perspective view (click here to view ANIMATION for 5.1). 5.2, dorsal view. 5.3, lateral view. 5.4, posterior view. Starting above the substrate (opaque model), the foot cast penetrated down and forward at 39° before stopping (transparent model) 4.5 cm below the original surface. Bead displacements dropped off rapidly with distance from the indenter. The foot drove nearby beads downward and forward, frequently along curving paths. Beads in front of the foot moved forward, outward, and upward. Axes are 1 cm in length.

fig 5

FIGURE 6. Bead motion during descent of the three main toes from the surface (opaque model) through the top 1 cm of sediment (transparent model) in lateral view. 6.1, a bead path visualization showing a dramatic dropoff in movement with starting depth. Axes are 1 cm in length. 6.2, plot of vertical bead displacement relative to starting depth. The foot model penetrated 1 cm (arrow); only a few beads near the surface descended as far. The indenter's influence decayed rapidly with starting depth. 6.3, beads in their starting position colored by 2 mm increments of downward displacement. Beads with a net upward motion are not shown.

fig 6

FIGURE 7. Detailed trajectories of seven beads affected by digit III. In world space, the descending toe drives the sediment markers down. 7.1, anterior view (click here to view ANIMATION for 7.1). 7.2, perspective view (click here to view ANIMATION for 7.2). All but the deepest bead diverge around the toe and then converge into a collapsed slit above. In the model's reference frame, sediment markers flow up toward, around, and over the stationary digit. 7.3, anterior view (click here to view ANIMATION for 7.3). 7.4, perspective view (click here to view ANIMATION for 7.4). Axes are 5 mm in length.

fig 7

FIGURE 8. A full motion sequence of the turkey foot simulating penetration (8a-8b), mid-stance (8b-8c), withdrawal (8c-8d), and collapse (8d-8e) to create a deep track (click here to view VIDEO for 8). Digit III is ~9 cm in length.

fig 8

FIGURE 9. Rotoscoped beads of a full motion trial as seen through camera 1 (click here to view ANIMATION for 9). Green beads are embedded in the foot, whereas red beads are in and on the substrate. The path of one bead is traced in red.

fig 9

FIGURE 10. Reconstructed foot motion and bead paths from a full motion trial in lateral view (click here to view ANIMATION for 10). Beads embedded in the turkey foot are linked by rigid segments to represent the four digits (I-IV), tarsometatarsus (t), and spur (s). The path of one bead (red) is highlighted. Axes are 2 cm in length.

fig 10

FIGURE 11. Motion of the bead highlighted in Figure 9 and Figure 10. 11.1, lateral view of the bead's trajectory (one point per frame) relative to the undisturbed sediment surface. Major events and the penetration, mid-stance, withdrawal, and collapse phases are designated. Axes are 1 cm in length. 11.2, cumulative displacement versus time graph. Phases of the tracking event are distinguished by changes in velocity (slope).

fig 11

 

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This email address is being protected from spambots. You need JavaScript enabled to view it.
author1Department of Ecology and Evolutionary Biology
Brown University
Providence, Rhode Island
USA
and
Structure and Motion Lab
The Royal Veterinary College
Hawkshead Lane
North Mymms, Hatfield
Hertfordshire, AL9 7TA
United Kingdom

Rich Ellis is currently a Whitaker Fellow at the Royal Veterinary College in London, UK. He received is ScB from Brown University studying geology-biology and his MS in physiology from the University of Colorado Boulder. He currently works studying the sit-to-stand transition in mammals and birds. He is interested in questions of whole-body biomechanics. Why do dissimilar animals with varied task requirements use of only a few different gaits? What factors constrain mammalian movement?

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This email address is being protected from spambots. You need JavaScript enabled to view it. (correspondence author)
author2Department of Ecology and Evolutionary Biology
Brown University
Providence, Rhode Island
USA

Stephen Gatesy is Professor of Biology at Brown University. He received his degrees from Colgate University (BA) and Harvard University (AM, PhD), and was a postdoctoral fellow at Emory University, the University of Montana, and Harvard University. His research is directed at understanding the evolution of the vertebrate locomotor system, particularly focusing on theropod bipedalism and the origin of bird flight. Gatesy and his students combine data from structural, functional, historical, and computer modeling approaches. Over the last decade, he has been at the forefront of integrating x-ray imaging and animation-based motion analyses.

 

TABLE 1. Evaluation of X-ray bead tracking accuracy using the four foot cast beads. Inter-bead distances measured 10 times by electronic calipers (mean ± standard deviation) are compared to mean inter-bead distances from each of our 14 repeatable trials. P-values were calculated using a two-tailed Students t-test assuming unequal variance. The difference was less than 0.3 mm in all cases.

Inter-bead Distance

Calipers (mm)

X-ray (mm)

Difference

p-value

tarsometatarsus-II

34.9 ± 0.35

35.2 ± 0.07

0.303

0.026

tarsometatarsus-III

90.5 ± 0.40

90.7 ± 0.06

0.191

0.184

tarsometatarsus-IV

71.6 ± 0.29

71.8 ±0.05

0.200

0.077

II-III

71.8 ± 0.15

71.6 ± 0.05

0.179

0.008

II-IV

71.5 ± 0.27

71.4 ± 0.06

0.088

0.373

III-IV

53.8 ± 0.27

54.0 ± 0.05

0.189

0.053