Essay: The Mantis Shrimp

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Though neither the biggest nor the fastest animal on earth, the mantis shrimp is one of Mother Nature’s most exquisite creations, a perfect specimen of the harmonisation between physics and nature. It is amongst the smaller marine creatures in the marine ecosystem, no longer than 30 cm in length, but its abilities demonstrate several interesting physics phenomena and have inspired numerous technologies as well. To this end, two features of the mantis shrimp merit special attention: its rapid punch and its extraordinary vision.

Not a Shrimp?

Mantis shrimps are marine crustaceans of order Stomatopoda. Ironically, mantis shrimps are not actually shrimps but are named as such due to their similarity in appearance to shrimps and the land-dwelling praying mantis. Mantis shrimps inhabit the shores of shallow tropical or subtropical waters and usually live in uninhibited burrows, coral reefs or rock crevices. They spend the majority of their lives in their burrows, and only come out to hunt for food, which includes clams, fish and other small invertebrates [1].

There are two kinds of mantis shrimps: “spearers” and “smashers”. “Spearer” mantis shrimps use spiny barbed claws to stab their prey while “smasher” mantis shrimps have distinct modified claws, known as raptorial appendages that they use to break the shells of other crustaceans for food [2].

Figure 1: The peacock mantis shrimp Odontodactylus scyllarus, is an example of a “smasher” mantis shrimp. [2]

Animalia Brus Lee

One such “smasher” is the peacock mantis shrimp Odontodactylus scyllarus, shown in figure 1. Researchers have studied them extensively and have found out that they can deliver strikes of up to 1500 N that last only a few milliseconds. Such punches can reach speeds of over 20 m s-1 and astonishing accelerations of over 105 m s-2, equivalent to that of a .22 calibre bullet [2]. This makes it the bearer of the world’s fastest punch, and also warrants the moniker “Bruce Lee of the animal kingdom”.

Figure 2: Two force peaks observed for a single punch exerted by the mantis shrimp. [2]

Researchers also found that, surprisingly, a single strike generates two significant short, high-amplitude force peaks, typically 390-480 μs apart [2], as shown in figure 2. While the first peak is certainly due to the impact of the punch, some unapparent occurrence gives rise to the second peak.

Spooky Bubbles

With the aid of high-speed cameras, researchers discovered that tiny bubbles are formed when a mantis shrimp delivers a blow, as seen in figure 3. These bubbles, known as cavitation bubbles, arise due to the rapid acceleration of the mantis shrimp’s appendage, which leaves behind a region of low pressure between the appendage and the surface it strikes.

Figure 3 [2]: Pictures of the mantis shrimp’s punch captured using a high-speed camera. Cavitation bubbles are observed between its club and the surface it is striking.

The formation of the bubble can be explained using the Clausius-Clapeyron relation [3],

dP/dT=L/TΔv , (1)

where dP/dT is the rate of change of pressure P with respect to temperature T, L is the specific latent heat and Δv is the change in specific volume. The Clausius-Clapeyron relation implies that the boiling point of a substance is dependent on pressure.

For water, dP/dT=0.036 atm K-1, meaning a decrease in pressure of 0.036 atm lowers the boiling point by 1 K [3]. As such, in the region of extremely low pressure left behind by the rapidly retracting appendage, water will boil at the ambient temperature, forming a bubble [4].

When the Bubble Bursts…

The bubble will not grow in size indefinitely and will eventually collapse. It turns out that this collapse is extremely violent, which gives rise to the second force peak we saw earlier. Such a collapse occurs when the bubble reaches its maximum radius RM, and the partial pressure of gas PGM will be very small, about 10-3 atm [4].

The dynamics of bubbles in a liquid can be described by the Rayleigh-Plesset equation [4]:

(P_B (t)-P_∞ (t))/ρ_L =R (d^2 R)/(dt^2 )+3/2 (dR/dt)^2+(4ν_L)/R dR/dt+2S/(ρ_L R) , (2)

where P_B (t) is the pressure within the bubble, P_∞ (t) is the pressure of the liquid, ρ_L is the density of the liquid, R(t) is the radius of the bubble, ν_L is the kinematic viscosity of the liquid and S is the surface tension of the bubble.

Figure 4 [4]: Schematic of a bubble used to derive the Rayleigh-Plesset Equation.

The Rayleigh-Plesset equation can be used to show that the pressure pulse radiated into the liquid has a peak pressure amplitude P_p roughly given as

P_p≈100R_M P_∞/r , (3)

where r is the radial position within the liquid from the centre of the bubble [4]. Inserting some numbers, if P_∞≈1 atm, a considerable pulse of 100 atm will be felt at a distance R_M away. These results have been verified experimentally in laboratories and are considered accurate.

Thus, a mantis shrimp’s punch not only exerts a powerful blow on impact, the collapse of the cavitation bubble it creates on impact with a surface generates another forceful pulse. As such, even if the claw misses its prey, the resulting shock wave is powerful enough to stun or even kill the prey [5].

Interestingly, mantis shrimps in aquariums have been known to break double-paned aquarium glass with a single blow [5], which is probably why we have never seen them in aquariums before.

As Hot as the Sun

Besides the pulse that the cavitation bubble generates upon collapse, another shocking event occurs simultaneously. During the final stages of the collapse of the bubble, the air in the bubble is greatly compressed due to the inertia of the inrushing liquid. Since this occurs in an extremely short span of time, in the order of microseconds, it can be assumed that the compression is adiabatic [4]. The first law of thermodynamics thus predicts that the temperature inside the bubble will increase.

Earlier versions of calculations with initial conditions similar to the depths and temperatures of where mantis shrimps can be found suggested that temperatures as high as 8800 K could occur within the bubble [4]. However, after including factors such as heat transfer between the liquid and gas which cannot be ignored due to the steep temperature gradients and short length scales involved, the maximum temperature at the centre of the bubble was determined to be 6700 K [6]. Although lower than the initial suggested temperature, these temperatures are still absolutely mind-blowing and are in fact hotter than the bottom of the Sun’s photosphere, which has a temperature of 6600 K [7]. However, it should be noted that these temperatures are short-lived, lasting only 2-3 μs before it cools rapidly [6].

Let there be Light

Using high-speed cameras, researchers also observed that faint, short-lived pulses of light, typically lasting only 100-200 ps, were emitted when the cavitation bubble collapsed, as shown in figure 5. This phenomenon, in which faint light is produced due to the high temperatures and pressures inside the collapsing bubble, is known as sonoluminescence.

Figure 5 [2]: Sonoluminescence, the emission of light in a cavitation bubble, observed when the mantis shrimp delivers a punch.

As sonoluminescence is still not a well-understood phenomenon, the
re are many models seeking to explain why it occurs. Some of these models include the hot-spot model, radiative recombination and chemical reactions.

The hot-spot model asserts that the light is emitted from plasma created due to the immense temperature and pressure inside the bubble. Light is emitted in a process known as bremsstrahlung radiation, in which charged particles emit light as they are accelerated due to the electric field of other atoms. In the collapsing bubble, electrons in the plasma interact with neutral atoms and ions, leading to bremsstrahlung radiation [8].

Another possible explanation for why light is produced involves the process of radiative recombination, in which energetic electrons in the plasma recombine with ions, and while doing so, releasing the extra energy as a photon [9].

An alternative model suggests that chemical reactions that take place in the bubble are responsible for the emission of light. In this model, the high temperatures in the bubble causes water to dissociate into its ions H2O → H+ + OH-, which then recombine again to give off light [9].

Mantis Mechanics

These interesting phenomena beg the question: how are mantis shrimps able to deliver such a fast punch? As stated earlier, the mantis shrimp has the world’s fastest punch, with an acceleration of 105 m s-2. To be able to move so fast in water, a large amount of energy must be released very quickly.

Mantis shrimps enhance their power output through the use of a click mechanism, whereby latches inhibit appendage movements until muscle contraction is the greatest [10]. When the latch is released, the accumulated energy is released over a much shorter period than the original muscle contraction. However, the muscles of the mantis shrimp are only capable of storing a small fraction of the energy compared to what is observed in an average strike, implying that they need a specialised spring-like click mechanism [10].

One model suggests that the elastic energy is stored in a “compressive, saddle-shaped spring, a stiff exoskeletal structure located dorsally on the merus (the enlarged proximal segment)” of all mantis shrimps [10]. Figure 6 shows a schematic of this saddle-shaped spring. Hyperbolic-paraboloid (saddle-shaped) surfaces are common in everyday engineering and architecture, as their opposite and transverse curvatures are able to endure massive forces by distributing stresses across the entire three-dimensional surface. Similarly, the saddle-shaped spring of the mantis shrimp reduces the chances of local buckling while compressing and extending when it strikes [10].

Figure 6 [10]: Left: Compressed (top) and released (bottom) saddle-shaped structure in the mantis shrimp’s raptorial appendage. Right: Saddle-shaped structure modelled as a spring being compressed (top) and released (bottom). This saddle-shaped structure allows the mantis shrimp to release large amount of stored energy rapidly, and also reduces the chances of damage to itself.

Plywood and Herringbone

Besides being able to punch so fast, the fact that mantis shrimps’ raptorial appendages are able to withstand such large forces inspired researchers to analyse the structure of their clubs. In some groundbreaking research, researchers have discovered that a distinctive herringbone structure, that has yet to be found in other animals, exists in the fibres of the mantis shrimp’s claws. This unique and sturdy herringbone structure protects the club from damage during impact and also enables it to exert large amounts of force on its prey [11].

To appreciate how this helps strengthen the club, it is useful to understand how varying fibre orientations help strengthen materials. For example, plywood, as seen in figure 7, is strengthened by stacking many layers of wood in with the fibres of successive layers orientated perpendicularly to each other [12].

Figure 7 [13]: Structure of plywood. Successive layers have fibres arranged perpendicular to each other to increase structural integrity.

Similarly, the alpha-chitin fibres in the mantis shrimp’s claws are orientated in varying directions. Instead of just being perpendicular to each other, each layer is orientated with a slight angular offset to the other, leading to a helicoidal structure. On top of that, the fibres in the same plane are sinusoidally arranged, leading to the herringbone structure shown below in figure 8 [11]. This special structure helps improve resilience by increasing the path length for crack growth, allowing for more energy to be dissipated [11].

Figure 8 [11]: The helicoidal (left) and herringbone (right) structure of alpha-chitin fibres in the mantis shrimp’s claws.

The mantis shrimp’s clubs were also placed in a synchrotron, and bombarded with x-rays to study the material composition of its club. It was found that the claw was not only made of a single material, but instead consisted of different composites with different Young’s moduli- a measure of the resistance of the material to elastic deformation, or how stiff a material is [14].

Cross-sectional analysis of the club revealed that there were 3 distinct domains- the impact region, the periodic region and the striated region, as seen in figure 9, each region with consecutively decreasing Young’s moduli [15]. Researchers speculate that the propagation of cracks is hampered by the changing Young’s moduli, which enhance the damage tolerance and impact resistance. The degree to which such cracks propagate will depend on the direction of the crack relative to the orientation of the chitin fibre [15].

Figure 9 [15]: 3 distinct dimains of the mantis shrimp’s club, each region with different composition and Young’s moduli.

Scientists are applying these insights to develop next-generation aeroplanes, body armour and football helmets [16], which will be capable of withstanding far greater stresses than they are presently able to.

EYE EXTRAVAGANZA

Besides punches that give rise to amazing physics, the mantis shrimp’s vision is also a pertinent example of the embodiment of physics within nature.

Colours We Cannot See

Humans are able to perceive colours as we have three types of photoreceptors, known as cones, in our eyes. Each cone has peak spectral responsivities spaced through the visible spectrum. The three types of cones are the L, M, and S cones, referring to their ability to detect long- (peaking at about 560 nm), middle- (peaking at about 530 nm) and short- (peaking at about 420 nm) wavelength light respectively [17]. A graph of the spectral responsivities of cones in human eyes is shown in figure 10. The range of wavelengths that the cones in human eyes can detect fall within the visible spectrum of 400 nm to 700 nm, allowing us to see all the colours in the visible spectrum.

Figure 10 [17]: Spectral responsivities of the S, M and L cones in human eyes. The S, M and L cones have spectral peaks at 420 nm, 530 nm and 560 nm respectively.

For some perspective, a comparison with dogs can be made. Dogs only have two cones in their eyes, with spectral peaks of about 429 nm to 555 nm [18], corresponding to blue and green light respectively. This results in dogs only being able to perceive blue, green and shades of yellow.

In comparison, the mantis shrimp has not two, not three, but twelve cones in their eyes [19]! This allows them to see all the colours of the visible spectrum, and on top of that, ultraviolet light, which humans are not able to see. Mantis shrimps are able to see ultraviolet light as they have four cones with spectral peaks at 315 nm, 330 nm, 340 nm and 380 nm [20], which all fall within 10 nm to 400 nm, the range of ultraviolet light. The graphs o
f the spectral responsivities of the cones in the mantis shrimp’s eyes is shown below in figure 11.

Figure 11 [19]: Spectral responsivities of cones in the mantis shrimp’s eyes. Mantis shrimps have cones with spectral peaks in the ultraviolet spectrum, allowing them to see ultraviolet light.

That’s not just it…

The mantis shrimp’s amazing vision does not just stop there. Besides being able to see ultraviolet light, the mantis shrimp is also able to see circularly and linearly polarised light.

To appreciate how this happens, we first recognise that light is a transverse electromagnetic (EM) wave. A EM wave travelling in the z direction at time t can be described by its electric field E,

E=(■(E_(0,x)@E_(0,y) )) cos⁡〖(kz-ωt)〗 , (4)

where E_(0,x) and E_(0,y) are the initial x and y components of the wave and ω is the angular frequency of the wave. In unpolarised light, the plane of vibration of the electric field vector changes with time. Light is linearly polarised when the plane of vibration of the electric field is restricted to a single plane [21], as shown in figure 12.

Figure 12: Linear polarisation. Unpolarised light passed through a polariser is restricted only to the plane of polarisation of the polariser.

Circular polarisation arises when E_(0,x)=E_(0,y)=E_0 are of equal amplitude but are offset by a certain phase difference δ= -π/2+2mπ where m=0, ±1, ±2,…The consequent wave is thus

E=E_0 (■(cos⁡(kz-ωt)@sin⁡(kz-ωt) )) . (5)

In this case, the direction of E is not restricted to a single plane. Although its amplitude is constant, its direction is constantly changing with time. The resultant electric field vector is rotating clockwise with angular frequency ω, and is known as a right-circularly polarised wave, depicted in figure 13. A phase difference of δ= π/2+2mπ will result in E rotating clockwise, leading to left-circularly polarised waves [21].

Figure 13 [21]: Right-circularly polarised light.

Odontodactylus Ophthalmology

Unlike the mantis shrimp which is able to distinguish linearly and circularly polarised light, humans are not able to do so. Mantis shrimps are able to detect circularly polarised light due to the difference in structure of their compound eyes.

A mantis shrimp’s compound eye is made of hundreds of visual units, the ommatidia. Each ommatidium comprises a cornea covering a lens, behind which lie eight photoreceptors, known as retinular cells, bundled around a light guide, the rhabdom [22]. Mantis shrimps are able to detect polarised light as their photoreceptors are preferentially sensitive to a specific electric field vector direction, which require specific configurations of microvilli, the basic building blocks that construct the photoreceptive rhabdom [23]. The structure of the mantis shrimp’s ommatidia is shown in figure 14.

Figure 14 [24]: Structure of the mantis shrimp’s ommatidia, the visual unit in its compound eyes. Mantis shrimps are able to detect polarised light as microvilli in their rhabdom are orientated in a specific sense.

Being adapted to see polarised skylight better enables the mantis shrimp in navigation, orientation, detecting prey, avoiding predators and intra-species signalling [22].

Cameras with Mantis Shrimp Vision

Inspired by the mantis shrimp’s superior eyesight, researchers are developing cameras that are capable of detecting circularly polarised light. The cameras, which can be used during endoscopies, are able to detect polarisation patterns in human tissue. At the cellular level, cancer cells are disorganised when compared with healthy cells. Using current colonoscopy techniques, doctors use black and white images to look for abnormal shapes, that may be signs of developing cancer cells. However, cancerous tissue may be flat, making it indistinguishable from healthy tissue. Using cameras that can detect circularly polarised light can help identify these cells as cancerous and healthy tissue react differently to circularly polarised light, as seen below in figure 15 [25].

Figure 15 [25]: Colonoscopy using a black and white camera (left) and using a camera that can detect circularly polarised light (right). Cancer cells are indistinguishable from healthy cells in the black and white image but appear as light green patches when using a camera capable of detecting circularly polarised light.

Mother Nature’s Secrets

With its powerful punch and vivid vision, the mantis shrimp truly is the epitome of scientific wonders that Mother Nature has to offer. However, there are still, without a doubt, many animals with similarly remarkable adaptations that we have not discovered. There still remains an abundance of knowledge from Mother Nature which we have yet to unravel.

References:

[Cover Page Photo] Schlanger, Zoë. “Mantis Shrimp Have Perfected the Eye Roll to See Things We Can’t Imagine.” Newsweek, 19 July 2016, www.newsweek.com/mantis-shrimp-have-perfected-eye-roll-better-see-things-we-cant-even-imagine-480162

[1] “Mantis Shrimp.” Lamar.edu, www.lamar.edu/arts-sciences/biology/marine-critters/marine-critters-2/mantis-shrimp.html.

[2] Patek, S. N. “Extreme Impact and Cavitation Forces of a Biological Hammer: Strike Forces of the Peacock Mantis Shrimp Odontodactylus Scyllarus.” Journal of Experimental Biology, vol. 208, no. 19, Jan. 2005, pp. 3655–3664., doi:10.1242/jeb.01831.

[3] Tymms, Vijay. “17. The Clausius-Clapeyron Relation .” Thermodynamics, 2017.

[4] Brennen, Christopher E. “Cavitation Bubble Collapse.” Cavitation and Bubble Dynamics, Oxford University Press, 1995, pp. 79–107.

[5] Holley, Dennis. “Phylum Arthropoda: Sovereigns of the Teran Empire.” General Zoology: Investigating the Animal World, 2015, pp. 387–388.

[6] Fujikawa, Shigeo, and Teruaki Akamatsu. “Effects of the Non-Equilibrium Condensation of Vapour on the Pressure Wave Produced by the Collapse of a Bubble in a Liquid.” Journal of Fluid Mechanics, vol. 97, no. 03, 1980, p. 481., doi:10.1017/s0022112080002662.

[7] Williams, David R. “Sun Fact Sheet.” NASA, NASA, 16 Dec. 2016, nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html.

[8] Yasui, Kyuichi, et al. “Sonoluminescence.” Applied Spectroscopy Reviews, vol. 39, no. 3, 2004, pp. 399–436., doi:10.1081/asr-200030202.

[9] Brenner, Michael P., et al. “Single-Bubble Sonoluminescence.” Reviews of Modern Physics, vol. 74, no. 2, 2002, pp. 425–484., doi:10.1103/revmodphys.74.425.

[10] Patek, S. N., et al. “Deadly Strike Mechanism of a Mantis Shrimp.” Nature, vol. 428, no. 6985, 2004, pp. 819–820., doi:10.1038/428819a.

[11] Yaraghi, Nicholas A., et al. “A Sinusoidally Architected Helicoidal Biocomposite.” Advanced Materials, vol. 28, no. 32, 2016, pp. 6835–6844., doi:10.1002/adma.201600786.

[12] Sandlin, Destin, director. MANTIS MURDER SHRIMP (Slow Motion) – Smarter Every Day 121. YouTube, 1 Sept. 2014, www.youtube.com/watch?v=LXrxCT0NpHo&t=194s.

[13] Carll, Kenneth. “The Many Types and Grades of Plywood.” Plywood, www.carllswoodproducts.com/plywood.html.

[14] Ashby, M. F., and David R. H. Jones. “The Elastic Moduli.” Engineering Materials 1: an Introduction to Properties, Applications and Design, Butterworth-Heinemann, 2014, pp. 29–54.

[15] Weaver, J. C., et al. “The Stomatopod Dactyl Club: A Formidable Damage-Tolerant Biological Hamm
er.” Science, vol. 336, no. 6086, July 2012, pp. 1275–1280., doi:10.1126/science.1218764.

[16] Nightingale, Sarah. “Mantis Shrimp Inspires next Generation of Ultra-Strong Materials.”Phys.org – News and Articles on Science and Technology, 31 May 2016, phys.org/news/2016-05-mantis-shrimp-ultra-strong-materials.html.

[17] Fairchild, Mark D. Color Appearance Models. Wiley, 2006.

[18] Neitz, Jay, et al. “Color Vision in the Dog.” Visual Neuroscience, vol. 3, no. 02, 1989, pp. 119–125., doi:10.1017/s0952523800004430.

[19] Zaidi, Qasim, et al. “Evolution of Neural Computations: Mantis Shrimp and Human Color Decoding.” i-Perception, vol. 5, no. 6, 2014, pp. 492–496., doi:10.1068/i0662sas.

[20] Marshall, Justin, and Johannes Oberwinkler. “The Colourful World of the Mantis Shrimp.”Nature, vol. 401, no. 6756, 1999, pp. 873–874., doi:10.1038/44751.

[21] Hecht, Eugene. “Polarization .” Optics, Pearson, 2017.

[22] Kleinlogel, Sonja, and Andrew G. White. “The Secret World of Shrimps: Polarisation Vision at Its Best.” PLoS ONE, vol. 3, no. 5, 2008, doi:10.1371/journal.pone.0002190.

[23] Chiou, Tsyr-Huei, et al. “Circular Polarization Vision in a Stomatopod Crustacean.” Current Biology, vol. 18, no. 6, 2008, pp. 429–434., doi:10.1016/j.cub.2008.02.066.

[24] Campbell, Neil, and Jane Reece. “Sensory and Motor Mechanisms.” LinkedIn SlideShare, 16 Sept. 2010, www.slideshare.net/jayswan/ohhs-ap-biology-chapter-50-presentation.

[25] Boyle, Elliott Kennerson and Carrie. “The Snail-Smashing, Fish-Spearing, Eye-Popping Mantis Shrimp.” KQED Science, 15 Nov. 2016, ww2.kqed.org/science/2016/11/15/the-snail-smashing-fish-spearing-eye-popping-mantis-shrimp/.

Introduction:

Brief ecological facts about the mantis shrimp: species, size, where they can be found, what they eat and more.

Introduction to the article: focus on mantis shrimp’s vision, punch and technologies inspired by studying it.

Physics of its vision and inspired technologies:

Context (dogs, humans, butterflies…) and facts about its vision (trinocular vision, 12 color cone receptors and ability to perceive circularly polarised light)

Basic optics: what colors are, the visible spectrum and what is polarisation.

How humans perceive EM radiation out of the visible spectrum and polarised light.

What trinocular vision is and how human vision differs.

Technologies inspired by the mantis shrimp:

DVD players with clearer resolution

Early stage cancer detecting cameras

Physics of its punch and inspired technologies:

Facts about its punch (speed, force, 2 main phenomena: super cavitation and sonoluminescence)

Physics of cavitation and why it occurs when the mantis shrimp punches

Physics of sonoluminescence: Possible theories explaining this phenomenon as it is still not a well understood phenomenon.

Technologies inspired by the mantis shrimp:

Ultra-strong materials through studying the composition of its claws. (Varying composition and orientation of layers in its claws allow it to withstand such extreme forces, draw parallel other “strengthened” materials that usually only have varying orientations.)

Conclusion

Reader will learn all of the above and should take away the fact that mantis shrimps are amazing animals.

Reader will not learn a lot about:

The biology of the mantis shrimp, such as why it has all these adaptations.

The behavior of the mantis shrimp

This article also mainly focuses on one smashing of the mantis shrimp. Readers will not learn much about other species, the spearer mantis shrimp.

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