Image 1: Art by Alondra Moreno Santana
The act of walking is so routine that many of us take it for granted, yet it requires complex coordination, muscle engagement, and joint dynamics to be possible. Joints—points in the body where two or more bones meet and interact—are intricate structures. They work with a variety of other anatomical structures, including muscles, cartilage, and ligaments, to facilitate movement. Studying joints in living organisms is relatively straightforward: researchers can observe them in real-time during motion and analyze the results afterward. Understanding joint dynamics in animals that have been extinct for millions of years, such as dinosaurs, is far more complicated. At best, all that is left of these extinct species is their bones; joint models must rely solely on bone-bone interactions, without any of the soft tissue that once filled the gaps.
For years, paleontologists have relied on intuition to infer what the joints of extinct species looked like and how they moved. They would examine how intersecting bones fit together and then present assumptions about the joint structures of extinct species based on what seemed plausible. However, this method was subjective, based solely on ‘looking right’. As a result, joint reconstructions of extinct species relied largely on expert opinion regarding the perceived correctness of fit.
A new study led by Armita Manafzadeh, a postdoctoral associate at the Yale Institute for Biospheric Studies, offers a new approach to exploring how joints fit together in extinct species based on bone-bone interactions. With the help of animation, we may now have a method to calculate the fit of different bones at a given joint and quantitatively determine the bone configurations the joint likely had.
Animating Motion
For her research, Manafzadeh visualized joints and their potential range of movement using a 3D animation software called Autodesk Maya. This software could translate mathematical calculations into movement. “Instead of creating videos that ‘look right,’ we’re instead able to create simulations of dinosaur locomotion that harness the quantitative data we’ve collected,” said Stephen Gatesy, a professor of biology and medical science at Brown University and co-author of the study.
The actual paleontology of the research isn’t too complicated—it’s the math, the modeling, and the precise animating where the complexities of the research emerge. In collaboration with Gatesy, her PhD advisor, and Bhart-Anjan Bhullar, an associate professor of earth and planetary sciences at Yale and Manafzadeh’s post-doctoral advisor, Manafzadeh devised a formula that assigns a specific numerical score to each possible configuration of bones within a joint. Termed an “articulation score,” this value takes into account three main factors of the bone interaction: the overlap, symmetry, and congruence of the joint.
In Autodesk, users can construct 3D representations of articular surfaces, which are the surfaces of bones that come into contact with each other at a joint. The researchers were essentially modeling interactions between bones to see what fit and what didn’t. Rays, which are lines extending infinitely from a set point, are cast perpendicularly from vertices of the 3D representation of one of these articular surfaces. These rays will then either intersect with the complementary articular surface, or they will miss entirely.
For the first factor, the three-dimensional overlap of the joint, the team was interested in how much contact two bones could have at a joint. The researchers quantified how aligned the curves of two bones at a joint were. If they were sufficiently aligned, the surfaces of the joint could exhibit meaningful biomechanical interaction for motion to occur. This value was quantified as the proportion of the rays cast from the first articular surface that intersected the complementary articular surface.
The second component of the score is the symmetry of the joint. Manafzadeh was looking at ankle and toe joints, which are biarticular, meaning that there are four articular surfaces—forming two joints—between two bones. If the joint is symmetrical, this would mean that the alignment and structure of the bones on both sides of the joint are balanced, allowing for a more even distribution of weight and greater stability during activities such as walking and running. If the joint is asymmetrical, that would mean that there are differences in the alignment or shape of the bones on either side of the joint, which can affect the stability and range of motion of the joint.
The final factor in evaluating the articulation score is the congruence of the joint, which is a measure of how well the bones fit together. This value is generated based on the average angle at which the emitted rays hit the complementary articular surface. Rays that hit the complementary surface tangentially, or at an angle close to zero degrees, receive a low score. This indicates poor alignment of the bones at the joint and limited joint functionality. Conversely, rays that hit the complementary surface at or close to a ninety-degree angle receive a high score to indicate a snug joint fit.
Each of these three factors is weighted to calculate the overall articulation score, which serves as a measure of the viability of a given joint arrangement.
Turning Theory into Data
Manafzadeh was interested in testing her formula using two birds, the guineafowl and the emu, which are considered ‘extant dinosaurs,’ meaning that they are modern descendants of ancient dinosaur species, based on evolutionary paleontology. These birds presumably share certain methods of movement and joint structure with their ancient dinosaur ancestors.
Using her formula, Manafzadeh calculated articulation scores for the various ankle and toe joint positions in these living birds by visualizing their skeletal elements with X-rays. If the birds’ joint poses yielded reasonable articulation scores that corresponded with experimental movement data, it would validate the efficacy of her formula in predicting the suitability of specific joint poses for movement. And that’s just what she found: the joint poses most used by the emu and guineafowl received very high articulation scores, indicating a correlation between a high articulation score and the likelihood of that joint pose being used by the animal. This result didn’t come as a surprise to her: it made sense that animals use joint poses that fit well when moving. Nevertheless, she had now created a method to quantify this intuition. “The hardest part of this project was trying to transform the intuition for why a joint ‘looks right’ or ‘looks wrong’ into a quantitative metric,” Manafzadeh said. “There was a lot of trial and error involved, as well as reading a lot of scientific literature from the past two centuries and trying to infer what researchers were thinking.”
Now that she knew the formula worked in extant dinosaurs, it was time to test it in extinct dinosaurs.
Yale’s Deinonychus
The Deinonychus is an extremely well-preserved, extinct dinosaur whose fossils were discovered by Yale paleontologist John Ostrom in the 1960s. The discovery of its fossil supported the theory that birds are related to dinosaurs and sparked widespread public fascination with dinosaurs—it’s the iconic “raptor” from Jurassic Park, recognized for its distinctive large sickle claw on its second toe. Manafzadeh wanted to figure out exactly how Deinonychus walked.
Using guineafowl movement data as a foundation and applying joint constraints based on Deinonychus foot structure, Manafzadeh reconstructed a stride cycle showing how Deinonychus walked. This reconstruction was consistent with evidence from the interaction of its bone surfaces.
She then used her formula to identify the toe joint poses with the highest articulation scores in the Deinonychus and developed a new theory regarding the function of its distinctive raptor claw. She observed that the joint positions associated with stabbing and pinning had higher articulation scores compared to those associated with slashing and digging, and her previous experimental data indicated that a high articulation score suggests a higher likelihood of the toe joints being in that configuration. Therefore, she concluded that Deinonychus likely utilized its clawed digits more for stabbing or pinning rather than for slashing or digging.
Because the Deinonychus is such a well-known and thoroughly studied extinct dinosaur, when Manafzadeh shared her findings, the paleontological community was understandably excited. Furthermore, when comparing Manafzadeh’s joint positions with the highest articulation scores and the joint models that expert paleontologists created, minimal differences were observed. Thus, in some cases, this new research reinforces intuition rather than dismissing it while also introducing a key quantitative method to support other paleontologists’ conclusions.
The research has implications far beyond the joint poses of specific species. By using this formula to analyze more species, both extinct and extant, we can expand our understanding of vertebrate motion and the features that have been preserved or developed through evolution. “Ultimately, the more animals we do this kind of analysis for, the better we’ll be able to piece together the history of vertebrate evolution and understand how behaviors like feeding, running, and flying have evolved over deep time,” Manafzadeh said.