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

Abstract

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.

Figure 1

Dynamic puncture. (a) The operating speeds of common biological puncture systems (from left to right: jumping cholla (Opuntia fulgida; photo credit: San Bernardino National Forest, source: flickr.com), stinging nettle (photo credit: vatra voda, source: unsplash.com), hornet (photo credit: the United States Geological Survey, source: unsplash.com), viper (Crotalus adamanteus; photo credit: The New York Public Library, source: unsplash.com), pileated woodpecker (photo by Jasper Garratt, source: unsplash.com), jellyfish (photo credit: Ganapathy Kumar, Monterey Bay Aquarium, source: unsplash.com), trap-jaw ant (Formicidae, Odontomachus clarus; adapted from photo by Jen Schlauch, source: flickr.com) and an artificial puncture tool (medical needle) span six orders of magnitude. They can be categorized into quasi-static and dynamic regimes. (b) A schematic illustration (top view) of the setups of the dynamic puncture experiment. (c) A still-frame high-speed image of the puncturing projectile captured at the onset of impact with the material sample. The velocity (v) and half cusp angle ($\theta$) of the projectile are determined using image processing. Inset left: microscopic image of the tip of the projectile, where the tip radius (r) is measured; inset right: representative microscopic image of an undeformed puncture fracture surface produced by a projectile with $2\theta ={30}^{\circ }$ at $v\approx 50$ m/s. White dashed lines are included to outline the fracture surface. Scale bars: 10 mm (orange); 200 μm (white); 4 mm (yellow).

Figure 2

Rate-dependent angular sensitivity: the dependence of the normalized depth of puncture ($d_{\text{norm}}$) on cusp angle ($2\theta$) variations at different puncture speeds (v). As v increases from a quasi-static condition (10 mm/min) to $v\approx 50$ m/s, the sensitivity of $d_{\text{norm}}$ to changes of $\theta$ diminishes. The slope of the fitting curve approaches that of the estimated upper bound, i.e., (5). Note puncture is not possible for $2\theta ={60}^{\circ }$ at the three lowest puncture speeds (crosses). The dashed lines indicate extrapolations of the fitting curves. The coefficients of determination of the curve fits: $R^2\ge 0.99$. Controlled tip radius: $r\approx 110\pm 12$ μm.