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Journal of the Royal Society Interface logoLink to Journal of the Royal Society Interface
. 2018 Aug 29;15(145):20180312. doi: 10.1098/rsif.2018.0312

A simple, high-resolution, non-destructive method for determining the spatial gradient of the elastic modulus of insect cuticle

S h Eshghi 1,†, M Jafarpour 2,†, A Darvizeh 2, S N Gorb 3, H Rajabi 3,✉
PMCID: PMC6127184  PMID: 30158184

Abstract

Nature has evolved structures with high load-carrying capacity and long-term durability. The principles underlying the functionality of such structures, if studied systematically, can inspire the design of more efficient engineering systems. An important step in this process is to characterize the material properties of the structure under investigation. However, direct mechanical measurements on small complex-shaped biological samples involve numerous technical challenges. To overcome these challenges, we developed a method for estimation of the elastic modulus of insect cuticle, the second most abundant biological composite in nature, through simple light microscopy. In brief, we established a quantitative link between the autofluorescence of different constituent materials of insect cuticle, and the resulting mechanical properties. This approach was verified using data on cuticular structures of three different insect species. The method presented in this study allows three-dimensional visualisation of the elastic modulus, which is impossible with any other available technique. This is especially important for precise finite-element modelling of cuticle, which is known to have spatially graded properties. Considering the simplicity, ease of implementation and high-resolution of the results, our method is a crucial step towards a better understanding of material–function relationships in insect cuticle, and can potentially be adapted for other graded biological materials.

Keywords: biological composite, graded properties, stiffness, autofluorescence, modelling

1. Introduction

Biological materials, such as wood [1], bone [2], tooth enamel [3], mollusc shell [4,5], bird eggshell [6,7], etc., are known for their complex architecture. They consist of spatially arranged lamellae, structured at different levels of hierarchy. These characteristics enable them to fine-tune their mechanical properties, including stiffness, tensile/compressive strength, fracture toughness and fatigue resistance, in response to specific functional needs [8].

The composite structure often results in dramatic spatial gradients in the mechanical properties of biological materials [9]. Such graded properties may significantly vary over the volume of an individual structure. An excellent example of this can be found in cuticle of insects and other arthropods [10]. Cuticle, known to be the second most abundant biological composite in nature, forms the exoskeleton of all arthropod species. Insect cuticle basically consists of chitin nanofibres embedded in a matrix of protein [11]. However, the stiffness of the cuticle in different insect body parts may range over seven orders of magnitude [12].

Previous studies have suggested that the observed gradients in material properties, especially in the elastic modulus, can strongly influence the functionality of a biological structure [13–15]. Therefore, detailed investigations of the graded properties of biological systems can lead to a better understanding of their structure–material–function relationships. This is, indeed, reflected in several recent attempts to quantify the heterogeneity of properties in biological materials [10,13,14,16–18]. Such studies are made possible by using modern small-scale testing techniques. These techniques, such as micro- and nano-indentation, allow the measurement of material properties at small scales, compared with the macroscopic bulk properties obtained by conventional mechanical tests.

Owing to several factors involved, micro- and nanometre scale measurements on biological systems are extremely challenging in practice [19]. The major challenges associated with such measurements are: (i) surface preparation, especially when dealing with samples with high surface roughness [20]; (ii) desiccation of natively hydrated specimens, because it can significantly influence their material properties [21]; (iii) time-dependent behaviour of most biological materials, which makes it difficult to choose a right material model [22]; (iv) anisotropic properties of natural materials, in which directionality of testing influences measurements [23]; (v) the small volume of many biological specimens, which may lead to the influence of underlying substrates on the measured properties [20] and finally (vi) the relatively large range of the elastic modulus found in biological samples, especially when compared with metals and traditional engineering materials [24]. The latter usually causes additional technical challenges when trying to adapt the standard indentation techniques to cover the full range of elastic moduli of such materials. These problems could be even more pronounced when dealing with small-size irregular-shaped cuticles of insects [25].

Recently, our team developed a method for three-dimensional visualization of the material composition of insect cuticle [26]. In this method, a confocal laser scanning microscope (CLSM) is used to analyse the distribution of different materials in the cuticle based on their specific autofluorescence when excited by the laser light. The use of different emission filters transmitting light at certain wavelengths allows the detection of blue, green and red autofluorescence emitted by resilin, less sclerotized and highly sclerotized cuticle, respectively. The method has already been used to study the material composition of cuticle from different body parts of several insect species, such as adhesive tarsal setae of ladybird beetles [17], attachment devices of louse flies [27], wings of dragonflies and damselflies [28], mouthparts of damselfly larvae [29], tibiae of stick insects [30], elongated intromittent organs of cassidine beetles [31], etc. Is there a link between the specific autofluorescence and the material properties of the cuticle?

There is a clear dependency between the material composition of a composite and its mechanical properties. Hence, it is reasonable to hypothesize that the determination of the material distribution of insect cuticle based on the autofluorescence of the constituent materials can help quantify its graded properties. Here, we aim to quantify the relationship between the material composition and the elastic modulus in insect cuticle. If successful, we will be able to use only a fluorescence image instead of expensive and time-consuming mechanical tests to estimate the modulus of this complex biological composite. For this purpose, we first use a CLSM image of an adhesive seta of the ladybird beetle Coccinella septempunctata [17] to analyse the distribution of different materials within the structure. A combination of image processing (IP) and genetic algorithm (GA) is employed to find Young's modulus of each constituent material in the seta, which results in the ‘best’ match with experimentally obtained moduli at a set of measurement points. The finite-element (FE) method is then used to test whether a model of the seta just using data obtained from the CLSM image is able to simulate its real behaviour under loading. We test the validity of the obtained moduli for two other insect cuticles having completely different geometries and material gradients: the male flagellum of the beetle Cassida rubiginosa and the hindleg tibia of the stick insect Carausius morosus. These examples were selected because experimental data on their mechanical behaviour under loading are available in the literature [30,31].

2. Methods

2.1. Confocal laser scanning microscopy

CLSM has been suggested to be a useful technique for detailed three-dimensional visualization of the distribution of materials within insect cuticle [26]. This method takes advantage of the autofluorescence properties of the materials of which cuticle is made. In this method, a confocal laser scanning microscope is used to demonstrate the presence of resilin-dominated, less sclerotized and highly sclerotized cuticle based on their blue, green and red autofluorescence, respectively.

In this study, we used CLSM images of the tarsal seta of the ladybird beetle Coccinella septempunctata ([17]; figure 1a), the male flagellum of the beetle Cassida rubiginosa ([31]; figure 3a) and the hindleg tibia of the stick insect Carausius morosus ([30]; figure 4a). The employed CLSM images were taken according to the protocol recommended by Michels & Gorb [26]. They were all obtained using a Zeiss LSM 700 confocal laser scanning microscope (Carl Zeiss Microscopy, Jena, Germany) equipped with four stable solid-state lasers with wavelengths of 405, 488, 555 and 639 nm. The following four emission filters were used to transmit the emitted light by specimens to detector: BP420–480, LP490, LP560 and LP640 nm.

Figure 1.

Figure 1.

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Gradient of properties along the length of a single adhesive tarsal seta of the ladybird beetle Coccinella septempunctata. (a) CLSM image of the seta [17]. The upward- and leftward-pointing arrows shown in the top right corner of the figure indicate the anterior side and distal end of the seta. (b) Red, (c) green and (d) blue components of the CLSM image. The brighter a pixel is, the higher the intensity of the component in that pixel. (e) Changes of Young's modulus along 38 µm of the length of the seta from the tip. Box plots represent the experimental data measured by AFM nanoindentations [17]. The borders of the boxes indicate the 25th and 75th percentiles, a line within them marks the median, and the whiskers (error bars) define the 10th and 90th percentiles. Upward-pointing red triangles show Young's moduli estimated by our method. (f) The error of the GA in prediction of Young's modulus in comparison to the measurements. The solid line indicates the median. The upper and lower dash lines define the range of the experimental data. Scale bar, 10 µm.

Figure 3.

Figure 3.

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Evaluation of the validity of the method for the example of the flagellum of the beetle Cassida rubiginosa. (a) CLSM image of the proximal part of the flagellum [31]. (b) Distribution of Young's modulus in the same region of the flagellum obtained by the method presented in this study. (c) Schematic diagram of the experimental set-up used by Matsumura et al. [31]. The proximal part of the flagellum with a length of approximately 340 µm was fixed on two sides. A glass sphere connected to a glass capillary was utilized to bend the flagellum with a force of 2.56 µN applied to the middle of the test specimen. (d) Comparison of the deflection of the flagellum obtained from the experiments (black circles) and the numerical simulation (upward-pointing red triangles). (e) The difference between the deflections obtained from the two methods. The average difference is lower than 0.24 mm. Scale bar, 10 µm.

Figure 4.

Figure 4.

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Evaluation of the validity of the method for the example of the hindleg tibia of the stick insect Carausius morosus [30]. (a) CLSM image of a cross section from the middle part of the tibia [30]. The area surrounded by dash-lines indicates a region of the image analysed by our method. (b) Distribution of Young's modulus in the cross section of the flagellum obtained by the method presented in this study. (c) Schematic diagram of the experiment conducted by Schmitt et al. [30]. The tibia was fixed at the distal (lower) part and an axial compressive load was applied to its proximal (upper) part. The loading continued until the tibia failed by buckling. (d) Comparison of the experimentally measured buckling loads (white circles) with the numerically predicted one (upward-pointing red triangle). The difference between the loads is about 3.9 mN. Scale bar, 100 µm.

2.2. Image processing and genetic algorithm

A GA was developed to quantify the relationship between the distribution of materials in the tarsal seta of the ladybird beetle Coccinella septempunctata and its graded properties, in particular Young's modulus. To this end, we used the colours appearing in the CLSM image of the seta (figure 1a) as a measure of its material composition. Taking into account that any colour in an RGB image is composed of three primaries (i.e. red, green and blue), the first aim was to find Young's modulus corresponding to each of them (ER, EG and EB for red, green and blue primary, respectively). According to the literature, Young's modulus of insect cuticle varies from 1 KPa [12] to 20 GPa [32], in extensible intersegmental membrane and tibial flexor apodeme of the locust, respectively. Therefore, we let the GA randomly choose any number in this range.

Young's modulus of a pixel with any other colour, except the primary colours, was calculated using one of the following two ways: (i) by taking the sum of the product of the value of each primary in that pixel and its corresponding Young's modulus or (ii) by multiplying the value of the dominant primary in the pixel by its corresponding Young's modulus. This was made possible by the use of the two equations below:

2.2. 2.1

and

2.2. 2.2

where Epixel is the Young's modulus of any pixel in the CLSM image. vR, vG and vB are intensities of the red, green and blue primary components of the pixel, respectively, as a number between 0 and 1. The higher the number, the more of that colour is included in the pixel. ER, EG and EB are Young's moduli corresponding to the red, green and blue primary colours, respectively. The GA is allowed to use any of these two equations which lead to more accurate results.

The results of the GA were compared with those of AFM nanoindentations (see §2.4.1) at 38 measurement sites. The objective was to minimize the difference between these two at each indentation site. To this end, Young's modulus at any indentation site, EGA, was assumed to be equal to the average of the moduli of a certain number, N, of pixels underneath that site:

2.2. 2.3

Similar to ER, EG, EB and Epixel, N was also regarded as a variable in our GA analysis.

The simulation started with an initial population size of 100 with randomly generated genetic information. This size of population was chosen to allow high interchange among the genomes and avoid convergence to a local optimum. Seventy per cent of the population were subjected to crossover. The probability of mutation was set on 0.3. The individuals were chosen for crossover and mutation using a uniform selection method. A maximum number of iterations of 300 was used as a stopping criterion.

2.3. Graphical user interface

To easily implement the method, we developed a MATLAB graphical user interface (GUI). The input of the GUI is a CLSM image of the desired structure, which should preferably be in PNG or JPG formats. The developed GUI employs Young's moduli of the primary colours obtained from the GA (ER, EG and EB) to calculate the corresponding modulus of any pixel in the imported image (Epixel). The generated data are used to illustrate the distribution of Young's modulus over the image of the structure under investigation. These data are also saved as an excel file which includes the coordinates of the analysed pixels and Young's modulus corresponding to each of them. To be readily applied to an FE model, a user has the option to reduce the amount of data in the excel file. Using this option, the user can save data obtained from less number of sections along the width of the used image and less number of pixels in each section. The developed GUI is available as a supplementary data (see electronic supplementary material, data S1).

2.4. Numerical analysis

To test the validity of our method, we performed three sets of numerical analyses. The FE software package ABAQUS/Standard (v6.14) was used to develop geometric models of the tarsal seta of the ladybird beetle Coccinella septempunctata, the male flagellum of the beetle Cassida rubiginosa and the hindleg tibia of the stick insect Carausius morosus. After determining the distribution of Young's modulus of the mentioned structures based on their CLSM images, the obtained properties were assigned to the developed models. To test the accuracy of the assigned properties, the FE models were then used to reproduce the results from mechanical tests.

2.4.1. AFM nanoindentations on the adhesive seta

To simulate the mechanical behaviour of the tarsal seta of the ladybird beetle Coccinella septempunctata under indentation, we developed a two-dimensional FE model. The general purpose 8-node plane stress elements with reduced integration (CPS8R) were employed for this purpose. Two types of stiffness gradients were assigned to this geometric model. The first one was made based on the data of the atomic force microscopy (AFM) nanoindentations performed by Peisker et al. [17]. In this gradient of stiffness, Young's modulus is constant across each section of the model and equal to that measured experimentally at that section. The modulus between these sections was determined by a linear interpolation. This gradient of stiffness was developed for the median, 10th, 25th, 75th and 90th percentiles. The gradient developed according to the median values is shown in figure 2a.

Figure 2.

Figure 2.

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Evaluation of the validity of the method for the example of the seta of the ladybird beetle Coccinella septempunctata. Distribution of Young's modulus in the seta obtained by (a) the AFM nanoindentations [17] and (b) the method presented in this study. The gradient of the modulus obtained by AFM nanoindentations is shown for median values. (c) The forces required for 50 nm indentation at seven indentation sites are presented for the stiffness gradient obtained by the method explained in this study (upward-pointing red triangles). Comparisons are made between these forces and those required for the same indentation depth in a model having stiffness gradients according to the experimental data (bar plots). (d) The error of our method in determining the force at each indentation site. The average error is about 0.06. Scale bar, 10 µm. (Online version in colour.)

The second type of stiffness gradient was made based on the data obtained from our method. In this gradient, each point in the FE model has a Young's modulus according to its colour in the CLSM image of the seta. To define the values of the modulus directly at the integration points of elements, we used a USDFLD subroutine. This stiffness gradient is presented in figure 2b.

The seta model was subjected to indentation with a sharp tip similar to that used in the experiments conducted by Peisker et al. [17]. A surface to surface contact pair was employed to constrain the indentation of the tip into the model. The other side of the model, adhered to a substrate during the indentations, was assumed to be fixed in all directions. For all developed stiffness gradients, we calculated forces required for 50 nm displacement at seven randomly selected indentation sites with equal distances, as shown in figure 2a.

In all simulations, a mesh convergence analysis was conducted to find results that were not dependent on the mesh size.

2.4.2. Bending of the flagellum

In order to measure the stiffness of the male flagellum of the beetle Cassida rubiginosa, Matsumura et al. [31] conducted three-point bending tests (figure 3c). In their experiments, the proximal part of the flagellum with a length of 300–340 µm was placed between two insect pins. A bending force of 2.56 µN was applied to the middle of the flagellum by means of a glass sphere adhered to a glass capillary.

We estimated the gradient of Young's modulus within the flagellum based on the CLSM image given in figure 3a. The obtained data were used to simulate the deflection of the flagellum under the same loading condition as described above. To this end, a three-dimensional geometric model of the flagellum was developed using the general purpose linear brick elements with reduced integration (C3D8R). The model had an external diameter of 5.7 µm and a thickness of 1 µm. Using a USDFLD subroutine, we assigned the estimated Young's moduli directly to the integration points of the model. After constraining displacements at fixation sites, we applied a 2.56 µN bending force to the middle of the model by a rigidly modelled sphere. The deflection of the model was measured and compared with the experimental results. A mesh convergence analysis was performed to find the mesh size required for obtaining accurate results.

2.4.3. Buckling of the tibia

In a recent study, we investigated the failure of the hindleg tibia of the stick insect Carausius morosus [30]. We found that the tibiae of adult individuals under uniaxial compression fail by buckling. To test the accuracy of our method in prediction of Young's modulus of the tibia, here we aimed to reproduce the previous buckling experiments.

The hindleg tibia was measured to have a length of 12.3 mm, an average external diameter of 450 µm and an average thickness of 78 µm. In comparison to its other sizes, the thickness of the tibia is almost negligible. Hence, we used the general purpose linear four-sided shell elements with reduced integration (S4R) to develop a geometric model of the tibia. To better represent the real geometry, the model was designed to have a varying thickness along its length. To this end, we measured the thickness of the tibia in eight cross sections and used a linear interpolation between them.

Taking into account the presence of a material gradient across the thickness of the tibia (figure 4a), we determined the distribution of Young's modulus using the method presented in this study (figure 4b). To assign the graded stiffness to the model, we first introduced a temperature field. Young's modulus was defined as a function of temperature. An initial gradient of temperature that matches the graded properties was then applied to the model.

A linear perturbation analysis was conducted to estimate the critical force required to buckle the model of the tibia under uniaxial compression. After performing a mesh convergence analysis, the buckling force was computationally measured and compared with those obtained from the experiments.

3. Results

Figure 1a shows a CLSM image of a single adhesive tarsal seta of the ladybird beetle Coccinella septempunctata [17]. This RGB image is converted into three greyscale images showing the intensity of each primary colour (figure 1b–d). As can be seen here, the proximal part of the seta is dominated by red colour (figure 1a,b), which indicates a high level of sclerotization of cuticle in this area. In the distal part, in contrast, the seta exhibits high blue autofluorescence (figure 1a,d), suggesting the presence of a high proportion of resilin. At the interface of these two regions, in the middle, the seta shows lower levels of sclerotization (figure 1a,c), resulting in the presence of yellow and green colours.

Peisker et al. [17] conducted AFM nanoindentations at 38 measurement sites along the seta starting from the tip. The distance between the measurement sites was set to be 1 µm. Figure 1e presents Young's moduli of the seta obtained from the AFM nanoindentations at these sites (bar plots). The results show the presence of a stiffness gradient along the length of the seta. Young's modulus of the seta cuticle significantly increases from the tip to the base. This is in accordance with the observation of a resilin-dominated tip and a sclerotized base in the CLSM image shown in figure 1a.

Figure 1e shows the best match obtained between the experimental data and those from the GA (upward-pointing red triangles). The minimum error was found when Young's moduli of the blue, green and red primaries in the CLSM image were set on 1.95 MPa, 1.5 GPa and 6.8 GPa, respectively. The optimal solution was obtained when considering only the effect of the dominant primary on Young's modulus of each pixel, rather than the effect of all of them together (see equation (2.2)). The GA further suggested consideration of about 30% of the pixels underneath the indentation sites to obtain the most accurate results.

The error of the GA in prediction of Young's modulus in comparison to those measured by AFM nanoindentations is shown in figure 1f for all indentation sites. The error at each site was defined as the difference between the result of the GA and the median Young's modulus divided by the range of the experimental data. As seen here, the estimated Young's moduli are fairly close to the median values of the experimentally measured ones. The average of the error is about 0.06, 0.15 and 0.02 for the resilin-dominated (1–15 µm), less sclerotized (16–26 µm) and highly sclerotized cuticle (27–38 µm), respectively.

In order to test the validity of our findings, we performed a numerical analysis. We developed a geometric model of the seta and assigned two different types of stiffness gradients to it. The first type is a gradient of stiffness similar to that obtained in AFM nanoindentations, in which Young's modulus is constant across each section of the model and equal to that measured experimentally (figure 2a). The second type is a stiffness gradient developed based on the data obtained from the CLSM, in which each element of the model has a Young's modulus in accordance to its specific colour in the CLSM image (figure 2b). Figure 2c represents the force required for 50 nm displacement of a sharp indenter at seven randomly selected indentation sites on the model (figure 2a), and compares it for each stiffness gradient. As seen here, the forces predicted by the stiffness gradient achieved by our method (upward-pointing red triangles) always lie within the range of those estimated by the experimentally obtained gradient of stiffness (bar plots). Using the same method as described before, we measured the error of our method (figure 2d). The average error of 0.06 indicates the precision of the estimations.

As the second case study, we chose the male flagellum of the beetle Cassida rubiginosa. The flagellum in this species is an elongated thin-walled tube [31]. A recent study showed that this part of the intromittent organ is not homogeneous, but has a material gradient [33]. Figure 3a shows this gradient in the proximal region of the flagellum obtained by the CLSM. We used the CLSM image in figure 3a to quantify the distribution of Young's modulus within of the flagellum. Young's moduli corresponding to the primary colours obtained from the example of the adhesive seta were employed here to calculate the modulus of each pixel with a certain colour using the same approach as described before. The acquired moduli were then assigned to a geometric model of the flagellum (figure 3b). The model was used to test whether the obtained Young's moduli could be used to reproduce the behaviour of the flagellum under loading. We simulated the three-point bending tests conducted by Matsumura et al. [31] (figure 3c). Figure 3d presents the displacement of our model and that of the biological flagellum under the same loading condition. The difference between these two is given in figure 3e. Considering the maximum displacement of the specimen, 10.83 mm, the average difference of 0.24 mm between the results indicates the high precision of the method.

In a recent work, we showed the presence of a material gradient along the thickness of the hindleg tibia of the stick insect Carausius morosus [30]. Figure 4a shows this gradient in a CLSM image of a cross section of the tibia. As a third case study, we used our method to estimate Young's modulus of the tibia cuticle based on this CLSM image. Figure 4b presents the distribution of Young's modulus within the same section. We assigned the acquired gradient of Young's modulus to a geometric model of the tibia. The model was then used to simulate the behaviour of the tibia when subject to uniaxial compression. According to previous observations, under compression, the hindleg tibia fails by elastic buckling [30]. This type of failure is known to be strongly dependent on the stiffness of the material of which the structure is made [34]. The computational results showed that our model is well able to simulate this failure mode. Figure 4d presents the critical buckling load versus slenderness obtained from the measurements [30] and the simulation. The difference between the buckling load of the model and test specimens was found to be smaller than 3.9 mN (experimental buckling loads vary between 115.6 N and 141.9 N).

For ease of use, we developed a software application, which is controlled via a MATLAB GUI (see the electronic supplementary material, data S1). By using a CLSM image as input, the software application displays the distribution of Young's modulus over the image of the desired structure. The generated data could also be saved as an Excel file containing the coordinates of the pixels in the CLSM image and Young's modulus corresponding to each pixel.

4. Discussion

4.1. Validity of the method

Taking into account the detailed available biomechanical data [17], we used the example of the adhesive tarsal seta as our primary case study. After evaluating the performance of our method using this example, we demonstrated its robustness by applying it to two other cuticular structures, having different geometries and material distributions. For all given examples, the calculated errors were sufficiently small. Therefore, we could conclude that the method presented in this study is capable of estimating Young's modulus of insect cuticle based on its specific autofluorescence properties.

The largest errors were associated with the predicted Young's moduli of regions dominated by green autofluorescence (less sclerotized cuticle). These regions are usually located in the interval between highly sclerotized and resilin-dominated cuticle. Looking at Young's moduli of the less sclerotized cuticle in figure 1e, from 16 to 26 µm, one can also find a large variance in the experimentally measured values. The large scattering of the data in this region makes it difficult to find a single value to represent Young's modulus of regions composed of cuticle with a low degree of sclerotization.

In order to find an optimum match between Young's moduli obtained from our method and those from mechanical tests of the seta, the GA suggested the use of 30% of the total number of pixels of the CLSM image underneath the indentation sites. This is interesting because the distance represented by this number of pixels is about 10 times the indentation depth used in AFM nanoindentations (50 nm, [17]), in which the generated stress can influence results of the experiments.

4.2. Advantages of the method

A confocal laser scanning microscope captures multiple two-dimensional images at different depths of a sample [35]. The two-dimensional images taken at different focal planes are employed for three-dimensional reconstructions. Although any of the two-dimensional images can be used to estimate Young's modulus over single sections of the sample, when using a three-dimensional image, our method allows us to capture the spatial distribution of Young's modulus over its volume. This is especially important for detailed FE analysis of biological materials having spatially graded properties. FE models are increasingly used to study the performance of biological materials, but often require many simplifying assumptions. One of these is that of a more or less uniform distribution of material properties [36], because it is currently impossible to obtain high-resolution three-dimensional data on the material properties of small, complex biological materials. The resolution of the method, of course, depends on the total number of pixels in the used CLSM image. However, even in low image pixel resolutions, its resolution is still much higher than that of any micro- or nano-mechanical test.

In addition to high-resolution results, our method offers distinct advantages over time-consuming and challenging mechanical testing techniques, and for complex structures will be possibly the only method to estimate local mechanical properties. The method requires only minimal sample preparation. After embedding a sample into glycerine and scanning it using a confocal laser scanning microscope, the obtained CLSM image can be directly fed into the provided MATLAB routines. The developed GUI makes the method easy to implement, and eliminates the need to know a programming language. Taking into account the importance of the material properties in the functioning of insect cuticle, and other biological materials, our method can provide a significant step towards better understanding of material–function relationships in such natural composites. The method can potentially be adapted for other biological materials exhibiting autofluorescence, such as plants, skin and living cells [37]. For biological materials having no autofluorescence, fluorescence dyes could be used to visualize components of interest.

4.3. Limitations, challenges and future directions

This study enabled us to find a correlation between the material composition of insect cuticle (based on the autofluorescence of the constituent materials) and its Young's modulus. Although the obtained results were very promising, one should still take into account some potential limitations. A major limitation arises from the complexities of the cuticle, as a biological composite. In such a complex material, the mechanical properties may be influenced by other factors than the material composition only. Some previous studies have addressed the effect of microstructure and desiccation, as two other influential factors, on the properties of insect cuticle and similar laminated composites [15,21,38]. However, the effect of these factors relative to each other remains still unknown.

When calculating Young's modulus at an indentation site, we assumed all points underneath that site to have the same impact. Although it is a reasonable approximation to significantly reduce the computational time, the points closer to the AFM probe may have more influence on the results. Therefore, a future study could consider the relative influence of these points on the estimated Young's modulus at each indentation site.

In order to calculate Young's modulus of a pixel with a certain colour, the GA developed in this study was allowed to use two different approaches: first, by considering the influence of all the primary colours of the pixel and, second, by considering only the effect of the dominant primary. Although the first approach was expected to give more reasonable results compared to the latter, it led to no optimal solution. An alternative approach, however, could be to consider the influence of all primary colours in a pixel not only according to their relative intensity, as done in the first method, but also by assigning a ‘weight’ factor to the modulus corresponding to each primary. This weight factor should determine the influence of the modulus of the dominant primary colour in comparison to the other primaries in a pixel. The reason is that the intensity of a primary colour in a pixel, which indicates a higher portion of the material causing that autofluorescence, may not be linearly proportional to the influence of that material on the overall stiffness of the cuticle in that point. Future research, therefore, is planned to use genetic programming (GP) to test whether this approach leads to more accurate estimations. The ultimate aim is to develop a ‘modulus map’ corresponding to a colour map (palette) that contains Young's moduli for all approximately 16 million possible colours that could appear in a CLSM image.

The method presented in this study interprets the intensity of the primary colours in a CLSM image of a structure as a measure of its material composition. Therefore, an inappropriate manipulation, enhancement or adjustment of the input image or a part of it could influence the results of the method. That is why it is recommended to always use an image in its original form.

It is also important to note that, when scanning a specimen, oversaturation should be avoided by adjusting the intensities of laser lines and the exposure times. Special care should also be taken to interpret the CLSM results of specimens that are not excited under regular intensities of the excitation light source. In such cases, an unusual increase in the intensity of the light source could result in unrealistic autofluorescence of specimens.

In this study, we analysed the CLSM images in the three-dimensional colour space RGB. From a technical point of view, this is a reasonable choice as all colour cameras have three classes of sensors (mimicking human colour vision). This is again a logical choice, because our aim was to differentiate between the three different emission wavelengths of the resilin, less-sclerotized cuticle and highly sclerotized cuticle. From a purely theoretical standpoint, however, one could use any type of colour space (two-dimensional or more). The choice of a proper type of colour space could be an important task when adjusting our method to other biological composites that have less or more constituent materials.

Supplementary Material

Supplementary Data 1
rsif20180312supp1.txt (218B, txt)

Acknowledgements

The authors are extremely grateful to Dr David Labonte (University of Cambridge) for his valuable comments and suggestions. We thank Dr Yoko Matsumura (Kiel University) for sharing the CLSM images of the flagellum of the beetle Cassida rubiginosa and data of the bending tests. We thank Vahid Nooraeefar (Ahrar Institute of Technology & Higher Education), Halvor T. Tramsen (Kiel University) and Saeed Nezamivand Chegini (Ahrar Institute of Technology & Higher Education) for their helpful comments. We appreciate the technical support of Dr Jan Michels (Kiel University) regarding the CLSM. The kind support of Amirhossein Asgharnia (University of Guilan) and Mohammad Aryaei (University of Guilan) in the beginning of this study is also greatly appreciated. S.N.G. acknowledges support of CARBTRIB Project of The Leverhulme Trust (UK).

Data accessibility

All supporting data are made available either in the article or the electronic supplementary material. The FE models can be made available on request: please contact H.R. at hrajabi@zoologie.uni-kiel.de; harajabi@hotmail.com.

Authors' contributions

Sh.E., M.J. and H.R. designed the study, conducted the research and analysed the data; A.D., S.N.G. and H.R. coordinated the study; H.R. wrote the manuscript; Sh.E., M.J., H.R. and S.N.G. reviewed the manuscript and contributed to revision; Sh.E., M.J., A.D., S.N.G. and H.R. discussed the results and gave the final approval for publication.

Competing interests

We declare we have no competing interests.

Funding

This study was financially supported by ‘Federal State Funding at Kiel University’ to H.R.

References

  • 1.Dinwoodie JM. 1989. Wood: nature's cellular, polymeric, fibre-composite. London, UK: The Institute of Metals. [Google Scholar]
  • 2.Rho JY, Kuhn-Spearing L, Zioupos P. 1998. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 20, 92–102. ( 10.1016/S1350-4533(98)00007-1) [DOI] [PubMed] [Google Scholar]
  • 3.Habelitz S, Marshall SJ, Marshall GW, Balooch M. 2001. Mechanical properties of human dental enamel on the nanometre scale. Arch. Oral Biol. 46, 173–183. ( 10.1016/S0003-9969(00)00089-3) [DOI] [PubMed] [Google Scholar]
  • 4.Rajabi H, Darvizeh A, Shafiei A, Eshghi Sh, Khaheshi A. 2014. Experimental and numerical investigations of Otala lactea’s shell—I. Quasi-static analysis. J. Mech. Behav. Biomed. Mater. 32, 8–16. ( 10.1016/j.jmbbm.2013.12.008) [DOI] [PubMed] [Google Scholar]
  • 5.Shojaei MF, Mohammadi V, Rajabi H, Darvizeh A. 2012. Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume. J. Mech. Behav. Biomed. Mater. 16, 38–54. ( 10.1016/j.jmbbm.2012.08.006) [DOI] [PubMed] [Google Scholar]
  • 6.Tullet SG. 1987. Egg shell formation and quality. In Egg quality—current problems and recent advances (eds Wells RG, Belyavin CG). London, UK: Butterworths. [Google Scholar]
  • 7.Darvizeh A, Rajabi H, Fatahtooei Nejad S, Khaheshi A, Haghdoust P. 2013. Biomechanical properties of hen's eggshell: experimental study and numerical modeling. World Acad. Sci. Eng. Technol. 7, 456–459. [Google Scholar]
  • 8.Dunlop JW, Fratzl P. 2010. Biological composites. Annu. Rev. Mater. Res. 40, 1–24. ( 10.1146/annurev-matsci-070909-104421) [DOI] [Google Scholar]
  • 9.Bar-On B, Wagner HD. 2013. New insights into the Young's modulus of staggered biological composites. Mater. Sci. Eng. C 33, 603–607. ( 10.1016/j.msec.2012.10.003) [DOI] [PubMed] [Google Scholar]
  • 10.Rajabi H, Jafarpour M, Darvizeh A, Dirks JH, Gorb SN. 2017. Stiffness distribution in insect cuticle: a continuous or a discontinuous profile? J. R. Soc. Interface 14, 20170310 ( 10.1098/rsif.2017.0310) [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 11.Rudall KM. 1963. The chitin/protein complexes of insect cuticles. Adv. Insect Physiol. 1, 257–313. ( 10.1016/S0065-2806(08)60177-0) [DOI] [Google Scholar]
  • 12.Vincent JF, Wegst UG. 2004. Design and mechanical properties of insect cuticle. Arthropod. Struct. Dev. 33, 187–199. ( 10.1016/j.asd.2004.05.006) [DOI] [PubMed] [Google Scholar]
  • 13.Graupner N, Labonte D, Müssig J. 2017. Rhubarb petioles inspire biodegradable cellulose fibre-reinforced PLA composites with increased impact strength. Compos. Part A: Appl. Sci. Manuf. 98, 218–226. ( 10.1016/j.compositesa.2017.03.021) [DOI] [Google Scholar]
  • 14.Graupner N, Labonte D, Humburg H, Buzkan T, Dörgens A, Kelterer W, Müssig J. 2017. Functional gradients in the pericarp of the green coconut inspire asymmetric fibre-composites with improved impact strength, and preserved flexural and tensile properties. Bioinspir. Biomim. 12, 026009 ( 10.1088/1748-3190/aa5262) [DOI] [PubMed] [Google Scholar]
  • 15.Suresh S. 2001. Graded materials for resistance to contact deformation and damage. Science 292, 2447–2451. ( 10.1126/science.1059716) [DOI] [PubMed] [Google Scholar]
  • 16.Barbakadze N, Enders S, Gorb S, Arzt E. 2006. Local mechanical properties of the head articulation cuticle in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae). J. Exp. Biol. 209, 722–730. ( 10.1242/jeb.02065) [DOI] [PubMed] [Google Scholar]
  • 17.Peisker H, Michels J, Gorb SN. 2013. Evidence for a material gradient in the adhesive tarsal setae of the ladybird beetle Coccinella septempunctata. Nat. Commun. 4, 1661 ( 10.1038/ncomms2576) [DOI] [PubMed] [Google Scholar]
  • 18.Sun JY, Tong J, Zhou J. 2006. Application of nano-indenter for investigation of the properties of the elytra cuticle of the dung beetle (Copris ochus Motschulsky). IEE Proc. Nanobiotechnol. 153, 129–133. ( 10.1049/ip-nbt:20050050) [DOI] [PubMed] [Google Scholar]
  • 19.Oyen ML. 2013. Nanoindentation of biological and biomimetic materials. Exp. Tech. 37, 73–87. ( 10.1111/j.1747-1567.2011.00716.x) [DOI] [Google Scholar]
  • 20.Ebenstein DM. 2011. Nanoindentation of soft tissues and other biological materials. In Handbook of nanoindentation with biological applications (ed. Oyen ML.), pp. 279–324. Singapore: Pan Stanford Publishing Pte. Ltd. [Google Scholar]
  • 21.Klocke D, Schmitz H. 2011. Water as a major modulator of the mechanical properties of insect cuticle. Acta Biomater. 7, 2935–2942. ( 10.1016/j.actbio.2011.04.004) [DOI] [PubMed] [Google Scholar]
  • 22.Bustamante J, Panzarino JF, Rupert TJ, Loudon C. 2017. Forces to pierce cuticle of tarsi and material properties determined by nanoindentation: the Achilles' heel of bed bugs. Biol. Open 6, 1541–1551. ( 10.1242/bio.028381) [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 23.Ferguson VL, Olesiak SE. 2010. Nanoindentation of bone. In Handbook of nanoindentation with biological applications (ed. Oyen ML.), pp. 185–240. Singapore: Pan Stanford Publishing Pte. Ltd. [Google Scholar]
  • 24.Van Vliet KJ. 2011. Instrumentation and experimentation. In Handbook of nanoindentation with biological applications (ed. Oyen ML.), pp. 39–76. Singapore: Pan Stanford Publishing Pte. Ltd. [Google Scholar]
  • 25.Enders S, Barbakadse N, Gorb SN, Arzt E. 2004. Exploring biological surfaces by nanoindentation. J. Mater. Res. 19, 880–887. ( 10.1557/jmr.2004.19.3.880) [DOI] [Google Scholar]
  • 26.Michels J, Gorb SN. 2012. Detailed three-dimensional visualization of resilin in the exoskeleton of arthropods using confocal laser scanning microscopy. J. Microsc. 245, 1–16. ( 10.1111/j.1365-2818.2011.03523.x) [DOI] [PubMed] [Google Scholar]
  • 27.Petersen DS, Kreuter N, Heepe L, Büsse S, Wellbrock AH, Witte K, Gorb SN. 2018. Holding tight on feathers—structural specializations and attachment properties of the avian ectoparasite Crataerina pallida (Diptera, Hippoboscidae). J. Exp. Biol. 221, 179242 ( 10.1242/jeb.179242) [DOI] [PubMed] [Google Scholar]
  • 28.Rajabi H, Ghoroubi N, Stamm K, Appel E, Gorb SN. 2017. Dragonfly wing nodus: a one-way hinge contributing to the asymmetric wing deformation. Acta Biomater. 60, 330–338. ( 10.1016/j.actbio.2017.07.034) [DOI] [PubMed] [Google Scholar]
  • 29.Büsse S, Gorb SN. 2018. Material composition of the mouthpart cuticle in a damselfly larva (Insecta: Odonata) and its biomechanical significance. R. Soc. open sci. 5, 172117 ( 10.1098/rsos.172117) [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 30.Schmitt M, Büscher TH, Gorb SN, Rajabi H. 2017. How does a slender tibia resist buckling? The effect of material, structural and geometric characteristics on the buckling behaviour of the hindleg tibia in the postembryonic development of the stick insect Carausius morosus. J. Exp. Biol. 221, 173047 ( 10.1242/jeb.173047) [DOI] [PubMed] [Google Scholar]
  • 31.Matsumura Y, Kovalev AE, Gorb SN. 2017. Penetration mechanics of a beetle intromittent organ with bending stiffness gradient and a soft tip. Sci. Adv. 3, eaao5469 ( 10.1126/sciadv.aao5469) [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 32.Ker RF. 1977. Some structural and mechanical properties of locust and beetle cuticle. PhD thesis, Oxford University Press, Oxford, UK. [Google Scholar]
  • 33.Filippov AE, Matsumura Y, Kovalev AE, Gorb SN. 2016. Stiffness gradient of the beetle penis facilitates propulsion in the spiraled female spermathecal duct. Sci. Rep. 6, 27608 ( 10.1038/srep27608) [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Cedolin L. 2010. Stability of structures: elastic, inelastic, fracture and damage theories. Singapore: World Scientific. [Google Scholar]
  • 35.Pawley JB. 2006. Handbook of biological confocal microscopy, 3rd edn Berlin, Germany: Springer. [Google Scholar]
  • 36.Rajabi H, Moghadami M, Darvizeh A. 2011. Investigation of microstructure, natural frequencies and vibration modes of dragonfly wing. J. Bionic Eng. 8, 165–173. ( 10.1016/S1672-6529(11)60014-0) [DOI] [Google Scholar]
  • 37.Amos WB, White JG. 2003. How the confocal laser scanning microscope entered biological research. Biol. Cell 95, 335–342. ( 10.1016/S0248-4900(03)00078-9) [DOI] [PubMed] [Google Scholar]
  • 38.Dirks JH, Taylor D. 2012. Fracture toughness of locust cuticle. J. Exp. Biol. 215, 1502–1508. ( 10.1242/jeb.068221) [DOI] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Data 1
rsif20180312supp1.txt (218B, txt)

Data Availability Statement

All supporting data are made available either in the article or the electronic supplementary material. The FE models can be made available on request: please contact H.R. at hrajabi@zoologie.uni-kiel.de; harajabi@hotmail.com.

Articles from Journal of the Royal Society Interface are provided here courtesy of The Royal Society

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