A Mathematical Model for the Mechanics of a Mosquito Bite with Applications to Microneedle Design
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Date
2007-08-08
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Abstract
How does the female mosquito push its fascicle, a flexible tube the size of a single human hair, through human skin so that she may suck blood? This process is not very well understood, and this paper attempts to take a mathematical approach, approximating the fascicle as a long Euler column to explain its mechanics. It is believed that the mosquito is using a combination of conservative and non-conservative forces during its attempt to pierce the skin, which leads to some forms of instability before it succeeds. The mosquitos fascicle is also covered in a sheath called the labium, whose purpose was not know to any certainty, and is seen in this paper as a support mechanism providing the fascicle with lateral support while it tries to pierce the skin. The hypotheses presented are based upon high-speed video of the mosquito during feeding and Scanning Electron Microscopy pictures of its anatomy, so they are believed to be reasonably accurate.
A new equation is derived based on classical column theory, with both Beck and Euler forces present, and a foundation stiffness factor is added to represent the effects of the labium. This equation is verified to be accurate; solved numerically for different values of foundation stiffness to determine its relative importance to the critical load of failure, compared to increases in non-conservative forces. The results indicate that by increasing foundation stiffness it is theoretically possible to raise the critical buckling load of such a structure by a factor two times or more compared to the buckling load when only conservative and nonconservative forces are present.
Microneedles taking advantage of such added stiffness could possibly be much smaller in size than microneedles without this support.
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Keywords
bite, mosquito, mechanics, model, microneedle, micro
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Degree
MS
Discipline
Mechanical Engineering
