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International Journal of
eISSN: 2574-9862

Avian & Wildlife Biology

Short Communication Volume 4 Issue 3

Insect heart resonance appearance simulation of Colorado potato beetle (leptinotarsa, doryphora, decemlineata say)

Galyna I Sokol, Tatyana L Savchuk, Denis V Larichev, TA Ribalka, ES Mironenko

Oles Honchar Dnipro National University, Ukraine

Correspondence: Galyna I Sokol, Oles Honchar Dnipro National University, Ukraine

Received: April 23, 2019 | Published: May 27, 2019

Citation: Sokol GI, Savchuk TL, Larichev DV, et al. Insect heart resonance appearance simulation of Colorado potato beetle (leptinotarsa, doryphora, decemlineata say). Int J Avian & Wildlife Biol. 2019;4(3):76-78 DOI: 10.15406/ijawb.2019.04.00155

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Abstract

Aims: The aim of this work was to simulate a multi-chamber system of insect heart, to determine the rigidity of its multi-chamber system and the resonant frequency.

Results: Currently, it is important to solve the problem of the destruction of plant pests, namely the Colorado beetles. A method was developed for mechanical system resonant frequencies determining, which thereby make a scheme for a complex multi-chamber system of insect heart of Colorado potato beetle based on the electro-acoustic analogies method. The resonance properties simulation of insect heart was conducted by electromechanical analogies approach. Resonant frequency of the multi-chamber acoustic system of the Colorado potato beetles was calculated. Estimated that it is 1179 [Hz].

Keywords: body mechanical properties, insect heart, resonant frequency, hardness

Introduction

Insect’s class is the most numerous, comprising more than 1 million species. Insects have inhabited a variety of terrestrial habitats, soil, fresh water, coastal seas. A large variety of habitats in the terrestrial environment contributed to the speciation and the wide distribution of this large group of arthropods. Most insects benefit as plants pollinators, some of them produce substances (honey, wax, varnish, silk), which are used as food products and raw materials for industry. Through the large biomass and diversity of trophic relations, insects take part in the biosphere circulation of substances, in soil formation processes. Among the insects that do not benefit, there are pests of forest and agricultural crops, carriers of plant, animal and human diseases. For example, potato or Colorado potato beetle (Leptinotarsa, Doryphora, decemlineata Say). It belongs to the tongs family (Crysomelidae), up to 1 sm in length and up to 7 mm in width. Their body is reddish-yellow, elytra light yellow with 5 black longitudinal stripes; there are several black dots on their chest shield, sometimes merging into spots; the apex of thickening antennae and the posterior margin of the head are also black. The potato beetle was discovered and described in 1823 in the Rocky Mountains, where it inhabited and ate at the expense of wild-growing members of the nightshade family (Solaneae); later it switched to the colonists potato plantations. The first devastations produced by it were noticed in 1859 in the state of Colorado - hence the name of the beetle.1–6 The Colorado potato beetle causes great damage to the potato crop. Destruction is an important issue. The Colorado potato beetle has a multi-chamber heart. We believe that this is the most vulnerable part of his body. The heartbreak leads to the death of the Colorado potato beetle. This determines the relevance of the chosen topic. The aim of this work was to simulate a multi-chamber system of insect heart, to determine the rigidity of its multi-chamber system and the resonant frequency.

Main part

The heart of the insect has the following form. It is shown in Figure 1.7

Figure 1 The heart of the insect.

Physical model of insect heart

For Colorado potato beetle heart resonant frequency determining, is necessary to calculate heart mass and its rigidity like a multi-chamber system. For such systems analyzing, it is reasonable to develop a unified theory based on the Lagrangian formalism, in which three systems-mechanical, electrical, and acoustic-are treated in the same way. This method names "electroacoustic analogies". The system of electroacoustic analogies contain following correspondences: pressure-electrical voltage, volumetric velocity-electrical current, electrical resistance-acoustic resistance, electrical capacitance-total compressibility of the volume, inductance-mass.

Therefore, in work based on electroacoustic analogies methodology was developed a methodology for determining mechanical system resonant frequencies which replaces insect heart. Multi-chamber acoustic system scheme is shown in Figure 2. It based on the data from source.2 Because insect heart is not a continuous thin rod, but interconnected chambers filled with blood; let us represent the heart system as a form of successively connected chambers resembling a kind of filter. There are some holes, spines in the connections of the individual chambers.

Figure 2 Insect heart multi-chamber acoustic system model.

Mathematical model

Studying design scheme of the oscillating system is depicted as discrete masses interconnected by elastic connections. When solving the problem of calculating the frequency characteristics of an oscillating system, it is replaced by an equivalent one. It is necessary to determine mechanical system mass and stiffness which is analogous to the insect heart. Based on these quantities knowledge’s, heart resonant frequency is determined.

Body or a separate organ resonant frequency of a live insect from the expression (1)

f= 1 2π C m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=zgaca WF9aWaaSaaaeaacaWFXaaabaGaa8Nmaiaa=b8aaaWaaOaaaeaadaWc aaqaaiaa=neaaeaacaWFTbaaaaWcbeaaaaa@3E71@ , (1)

where C - system stiffness; f - resonant frequency; m - body tissue mass.

It is known that the reduced stiffness of an equivalent mechanical system with a series connection of elements is equal to [2].

1 C 1 + 1 C 2 +......+ 1 C n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaamaalaaabaacbi Gaa8xmaaqaaiaa=neadaWgaaWcbaGaa8xmaaqabaaaaOGaa83kamaa laaabaGaa8xmaaqaaiaa=neadaWgaaWcbaGaa8NmaaqabaaaaOGaa8 3kaiaa=5cacaWFUaGaa8Nlaiaa=5cacaWFUaGaa8Nlaiaa=TcadaWc aaqaaiaa=fdaaeaacaWFdbWaaSbaaSqaaiaa=5gaaeqaaaaaaaa@45D2@ , (2)

Where С1, С2, ……, Сn - stiffness in some areas.

While simulation, the dimensions of the heart, presented,3 were taken into account. The approximate length of the abdomen is about 8 mm. Heart passes through the abdomen in the long tube shape, one end of which is usually closed. Let us suppose the length of the entire cardiac system L, equal to 8 mm. The abdominal region has 9-10 segments. The heart is swollen in each segment and divided into chambers. For the most part, the cameras are only in the abdomen, but in the first abdominal segment there is often no isolated camera. Thus, provided that the abdominal section of the Colorado potato beetle has 9 segments, the number of chambers in it equal 8 and they are filled with blood. The length of the spine is lo = 10-4 [m], the length of one of the heart system chambers is lk = 10-3 [m].

Results of the resonant frequency multi-chamber acoustic system calculation

For resonant frequency determining of the Colorado potato beetle heart, it is necessary to calculate its heart mass m and its rigidity C as a multi-chamber resonance system.

Spine cross-sectional area calculation denoted S2. Adopt:

S2= S1/3,

Where S1 - chambers cross-sectional area; d1-chamber diameter.

Provided that beetle body diameter is ≈3.5 mm, and the stem diameter is 1/7 of total insect body diameter, we obtain insect body diameter d1, which is d 1 =5* 10 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=rgada WgaaWcbaGaaGymaaqabaGccqGH9aqpcaaI1aGaaiOkaiaaigdacaaI WaWaaWbaaSqabeaacqGHsislcaaI0aaaaaaa@3FCC@ [m].

Calculation the cross-sectional area of the camera S1.

S 1 = π* d 1 2 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=nfada WgaaWcbaGaa8xmaaqabaGccaWF9aWaaSaaaeaacaWFapGaa8Nkaiaa =rgadaqhaaWcbaGaa8xmaaqaaiaa=jdaaaaakeaacaWF0aaaaaaa@3FE5@ [m2].

Then the cross-sectional area of ostia S2 will be 6.53 × 10-8 [m2].

Blood density is taken ρ = 103 [kg / m3].

Calculate the mass m0 of one spine [kg]. The value of m0 is numerically equal to 6.53 * 10-9 [kg].

The mass of one camera mk is determined from the expression

m k =ρ* l k * S 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=1gada WgaaWcbaGaa83AaaqabaGccaWF9aGaa8xWdiaa=PcacaWFSbWaaSba aSqaaiaa=TgaaeqaaOGaa8Nkaiaa=nfadaWgaaWcbaGaa8xmaaqaba aaaa@4160@

The calculated mass magnitude mk is numerically equal to 19.625* 10-8 [kg].

The total mass of the seven osti and eight chambers will be

m ok =8* m k +7* m o MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=1gada WgaaWcbaGaa83Baiaa=TgaaeqaaOGaa8xpaiaa=HdacaWFQaGaa8xB amaaBaaaleaacaWGRbaabeaakiabgUcaRiaaiEdacaGGQaGaamyBam aaBaaaleaacaWGVbaabeaaaaa@43CF@ ,

mok is equal to 161.58 * 10-8 [kg].

Total mass of the insect entire heart mΣ equals three total masses of the awns and chambers,

m Σ =3* m ok =484,74+ 10 8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaiaad2gadaWgaa WcbaGaeu4Odmfabeaakiabg2da9iaaiodacaGGQaGaamyBamaaBaaa leaacaWGVbGaam4AaaqabaGccqGH9aqpcaaI0aGaaGioaiaaisdaca GGSaGaaG4naiaaisdacqGHRaWkcaaIXaGaaGimamaaCaaaleqabaGa eyOeI0IaaGioaaaaaaa@49FA@ [kg].

The fluid flexibility in the cavity of one of the chambers Km, if the heart chamber is modeled by a Helmholtz resonator (see [2]), determines from the expression

K M = V γ* p ac * S 2 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=Teada WgaaWcbaGaa8xtaaqabaGccaWF9aWaaSaaaeaacaWFwbaabaGaa83S diaa=PcacaWFWbWaaSbaaSqaaiaa=fgacaWFJbaabeaakiaa=Pcaca WFtbWaa0baaSqaaiaa=jdaaeaacaWFYaaaaaaaaaa@438C@ ,

Where V - is the volume of the chamber; γ - is the specific weight of blood; pac - acoustic pressure of blood in the system.

We assume that the acoustic pressure inside of the blood chamber is pac = 20 [N/m2], and the specific weight is γ = 9810 [N /m3]. The calculated value of flexibility was Km = 0.2337 [m/N].

The rigidity of the camera is equal to Ck = 1/Km = 4.279 [N/m].

Total rigidity of eight chambers and seven ostia system was defined as

1 C Σ = 8 C k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaamaalaaabaGaaG ymaaqaaiaadoeadaWgaaWcbaGaeu4OdmfabeaaaaGccqGH9aqpdaWc aaqaaiaaiIdaaeaacaWGdbWaaSbaaSqaaiaadUgaaeqaaaaaaaa@3F34@ ,

Consequently

C Σ = C k 8 =0,5349 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaiaadoeadaWgaa WcbaGaeu4Odmfabeaakiabg2da9maalaaabaGaam4qamaaBaaaleaa caWGRbaabeaaaOqaaiaaiIdaaaGaeyypa0JaaGimaiaacYcacaaI1a GaaG4maiaaisdacaaI5aaaaa@43E0@ [N/m].

As a calculated result, it was obtained that the resonant frequency of Colorado potato beetle heart is equal to

f pe3 = 1 2π C Σ m Σ =1179 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=wjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqadeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa=zgada WgaaWcbaGaa8hCaiaa=vgacaWFZaaabeaakiaa=1dadaWcaaqaaiaa =fdaaeaacaWFYaGaa8hWdaaadaGcaaqaamaalaaabaGaa83qamaaBa aaleaacaWFJoaabeaaaOqaaiaa=1gadaWgaaWcbaGaa83Odaqabaaa aaqabaGccaWF9aGaa8xmaiaa=fdacaWF3aGaa8xoaaaa@4775@ [Hz].

The discussion of the results

The impact of vibrations on the heart of the Colorado potato beetle with a given frequency will lead to its rupture. This would entail the death of the Colorado potato beetle. The effects of the disastrous effect of vibrations on living organisms are described in Sokol.1 The resonance frequency and stiffness of insets harmful for plants (Colorado beetle) are defined. In the laboratory conditions death of the beetle under the influence of acoustics waves was stated. Experimental studies in which the value of the destructive frequency for the Colorado potato beetle is obtained on a vibrating stand is described in Sapozhkov.2 It was obtained that biological death was registered for a beetle with a mass of 100 mg after exposure to him at a frequency of 1500 Hz, 4 hours after exposure to vibrations.

Conclusion

  1. A method was developed for mechanical system resonant frequencies determining, which thereby make a scheme for a complex multi-chamber system of insect heart based on the electro-acoustic analogies method.
  2. Resonant frequency of the multi-chamber acoustic system of the Colorado potato beetles was calculated. Estimated that it is 1179 [Hz].

Acknowledgements

None.

Conflict of interest

Author declares that there are no conflicts of interest.

References

  1. Sokol GI. Features of infrasonic processes in the infrasonic frequency range. Dnepropetrovsk: Promin; 2000. 136 p.
  2. Sapozhkov MA. Electroacoustics. Moscow: Communication; 1978. 272 p.
  3. A unique experiment conducted on the ISS. Russia. 2014.
  4. NASA has sent ants into space. National Geographic. 2014.
  5. Sokol GI. OM Duplischeva. Vibration technologies in rigidity and resonant frequency determination of insect bodies. Technologies and Technologies. 2007;1(46):20–24.
  6. SN Romanov. Biological effect of vibration and sound. L Nauka. 1991; 210 p.
  7. Encyclopedic dictionary Brockhaus and Efron.
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