Modelling biological puncture: a mathematical framework for determining the energetics and scaling

Curving expectations: The minimal impact of structural curvature in biological puncture mechanics

Living organisms have evolved various biological puncture tools, such as fangs, stingers, and claws, for prey capture, defense, and other critical biological functions. These tools exhibit diverse morphologies, including a wide range of structural curvatures, from straight cactus spines to crescent-shaped talons found in raptors. While the influence of such curvature on the strength of the tool has been explored, its biomechanical role in puncture performance remains untested. Here, we investigate the effect of curvature on puncture mechanics by integrating experiments with finite element simulations. Our findings reveal that within a wide biologically relevant range, structural curvature has a minimal impact on key metrics of damage initiation or the energies required for deep penetration in isotropic and homogeneous target materials. This unexpected result improves our understanding of the biomechanical pressures driving the morphological diversity of curved puncture tools and provides fundamental insights into the crucial roles of curvature in the biomechanical functions of living puncture systems.

Dental Dynamics: A Fast New Tool for Quantifying Tooth and Jaw Biomechanics in 3D Slicer

Teeth reveal how organisms interact with their environment. Biologists have long looked at the diverse form and function of teeth to study the evolution of feeding, fighting, and development. The exponential rise in the quantity and accessibility of computed tomography (CT) data has enabled morphologists to study teeth at finer resolutions and larger macroevolutionary scales. Measuring tooth function is no easy task, in fact, much of our mechanical understanding is derived from dental shape. Categorical descriptors of tooth shape such as morphological homodonty and heterodonty, overlook nuances in function by reducing tooth diversity for comparative analysis. The functional homodonty method quantitatively assesses the functional diversity of whole dentitions from tooth shape. This method uses tooth surface area and position to calculate the transmission of stress and estimates a threshold for functionally homodont teeth through bootstrapping and clustering techniques. However, some vertebrates have hundreds or thousands of teeth and measuring the shape and function of every individual tooth can be a painstaking task. Here, we present Dental Dynamics, a module for 3D Slicer that allows for the fast and precise quantification of dentitions and jaws. The tool automates the calculation of several tooth traits classically used to describe form and function (i.e., aspect ratio, mechanical advantage, force, etc.). To demonstrate the usefulness of our module we used Dental Dynamics to quantify 780 teeth across 20 salamanders that exhibit diverse ecologies. We coupled these data with the functional homodonty method to investigate the hypothesis that arboreal Aneides salamanders have novel tooth functions. Dental Dynamics provides a new and fast way to measure teeth and increases the accessibility of the functional homodonty method. We hope Dental Dynamics will encourage further theoretical and methodological development for quantifying and studying teeth.

The shape of Nature's stingers revealed

Stinger-like structures in living organisms evolved convergently across taxa for both defensive and offensive purposes, with the main goal being penetration and damage. Our observations over a broad range of taxa and sizes, from microscopic radiolarians to narwhals, reveal a self-similar geometry of the stinger extremity: the diameter (d) increases along the distance from the tip (x) following a power law [Formula: see text] , with the tapering exponent varying universally between 2 and 3. We demonstrate, through analytical and experimental mechanics involving three-dimensional (3D) printing, that this geometry optimizes the stinger's performance; it represents a trade-off between the propensity to buckle, for n smaller than 2, and increased penetration force, for n greater than 3. Moreover, we find that this optimal tapering exponent does not depend on stinger size and aspect ratio (base diameter over length). We conclude that for Nature's stingers, composed of biological materials with moduli ranging from hundreds of megapascals to ten gigapascals, the necessity for a power-law contour increases with sharpness to ensure sufficient stability for penetration of skin-like tissues. Our results offer a solution to the puzzle underlying this universal geometric trait of biological stingers and may provide a new strategy to design needle-like structures for engineering or medical applications.

Biomechanics of cutting: sharpness, wear sensitivity and the scaling of cutting forces in leaf-cutter ant mandibles

Herbivores large and small need to mechanically process plant tissue. Their ability to do so is determined by two forces: the maximum force they can generate, and the minimum force required to fracture the plant tissue. The ratio of these forces determines the relative mechanical effort; how this ratio varies with animal size is challenging to predict. We measured the forces required to cut thin polymer sheets with mandibles from leaf-cutter ant workers which vary by more than one order of magnitude in body mass. Cutting forces were independent of mandible size, but differed by a factor of two between pristine and worn mandibles. Mandibular wear is thus likely a more important determinant of cutting force than mandible size. We rationalize this finding with a biomechanical analysis, which suggests that pristine mandibles are ideally 'sharp'-cutting forces are close to a theoretical minimum, which is independent of tool size and shape, and instead solely depends on the geometric and mechanical properties of the cut tissue. The increase of cutting force due to mandibular wear may be particularly problematic for small ants, which generate lower absolute bite forces, and thus require a larger fraction of their maximum bite force to cut the same plant. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

How venom pore placement may influence puncture performance in snake fangs

When designing experimental studies, it is important to understand the biological context of the question being asked. For example, many biological puncture experiments embed the puncture tool to a standardized depth based on a percentage of the total tool length, to compare the performance between tools. However, this may not always be biologically relevant to the question being asked. To understand how definitions of penetration depth may influence comparative results, we performed puncture experiments on a series of venomous snake fangs using the venom pore location as a functionally relevant depth standard. After exploring variation in pore placement across snake phylogeny, we compared the work expended during puncture experiments across a set of snake fangs using various depth standards: puncture initiation, penetration to a series of depths defined by the venom pore and penetration to 15% of fang length. Contrary to our hypothesis, we found almost no pattern in pore placement between clades, dietary groups or venom toxicity. Rank correlation statistics of our experimental energetics results showed no difference in the broad comparison of fangs when different puncture depth standards were used. However, pairwise comparisons between fangs showed major shifts in significance patterns between the different depth standards used. These results imply that the interpretation of experimental puncture data will heavily depend upon which depth standard is used during the experiments. Our results illustrate the importance of understanding the biological context of the question being addressed when designing comparative experiments.

Investigation of the rate-mediated form-function relationship in biological puncture

Puncture is a vital mechanism for survival in a wide range of organisms across phyla, serving biological functions such as prey capture, defense, and reproduction. Understanding how the shape of the puncture tool affects its functional performance is crucial to uncovering the mechanics underlying the diversity and evolution of puncture-based systems. However, such form-function relationships are often complicated by the dynamic nature of living systems. Puncture systems in particular operate over a wide range of speeds to penetrate biological tissues. Current studies on puncture biomechanics lack systematic characterization of the complex, rate-mediated, interaction between tool and material across this dynamic range. To fill this knowledge gap, we establish a highly controlled experimental framework for dynamic puncture to investigate the relationship between the puncture performance (characterized by the depth of puncture) and the tool sharpness (characterized by the cusp angle) across a wide range of bio-relevant puncture speeds (from quasi-static to [Formula: see text] 50 m/s). Our results show that the sensitivity of puncture performance to variations in tool sharpness reduces at higher puncture speeds. This trend is likely due to rate-based viscoelastic and inertial effects arising from how materials respond to dynamic loads. The rate-dependent form-function relationship has important biological implications: While passive/low-speed puncture organisms likely rely heavily on sharp puncture tools to successfully penetrate and maintain functionalities, higher-speed puncture systems may allow for greater variability in puncture tool shape due to the relatively geometric-insensitive puncture performance, allowing for higher adaptability during the evolutionary process to other mechanical factors.