i MULTI-LENGTH SCALE MECHANICAL INVESTIGATION OF THE FLYING INSECT THORAX by Cailin Barrett Casey A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering MONTANA STATE UNIVERSITY Bozeman, Montana July 2024 ©COPYRIGHT by Cailin Barrett Casey 2024 All Rights Reserved ii DEDICATION I want to dedicate this thesis to my family and friends. To my family- I couldn’t be here without you encouraging and supporting me as I follow my dreams. To my friends- I am so lucky to have found friends in each stage of my life who are like family to me, even when the physical distance between us is measured in thousands of miles. iii TABLE OF CONTENTS 1. INTRODUCTION .............................................................................................................. 1 1.1 Indirect Actuation.......................................................................................................... 1 1.2 Modeling Indirect Actuation ......................................................................................... 2 1.3 Synchronous vs Asynchronous Musculature ................................................................ 3 1.4 Applications .................................................................................................................. 6 1.5 Thesis Aims ................................................................................................................... 7 2. THE FLYING INSECT THORACIC CUTICLE IS HETEROGENEOUS IN STRUCTURE AND IN THICKNESS-DEPENDENT MODULUS GRADATION ................................................................................................................... 10 Contribution of Authors and Co-Authors ......................................................................... 10 Manuscript Information .....................................................................................................11 Abstract ............................................................................................................................. 12 2.1 Introduction ................................................................................................................. 13 2.2 Experimental Methods ................................................................................................ 15 2.2.1 Insect Care and Selection of Regions of Interest ......................................... 15 2.2.2 Histological Assessment of Cuticle Structure .............................................. 16 2.2.3 Nanoindentation Assessment of Thorax Cuticle Modulus Gradation............................................................................................................... 16 2.2.4 Confocal Laser Scanning Microscopy ......................................................... 19 2.2.5 Finite Element Analysis ............................................................................... 20 2.2.6 Statistics ....................................................................................................... 21 2.3 Results ......................................................................................................................... 22 2.3.1 Histology ...................................................................................................... 22 2.3.2 Nanoindentation and CLSM ........................................................................ 25 2.3.3 Finite Element Analysis ............................................................................... 27 2.4. Discussion .................................................................................................................. 28 2.5. Conclusions ................................................................................................................ 32 2.6. Acknowledgements .................................................................................................... 32 References ......................................................................................................................... 33 3. EXPERIMENTAL STUDIES SUGGEST DIFFERENCES IN THE DISTRIBUTION OF THORAX ELASTICITY BETWEEN INSECTS WITH SYNCHRONOUS AND ASYNCHRONOUS MUSCULATURE ....................... 38 Contribution of Authors and Co-Authors ......................................................................... 38 Manuscript Information .................................................................................................... 39 Abstract ............................................................................................................................. 40 3.1 Introduction ................................................................................................................. 40 3.2 Methods....................................................................................................................... 45 iv TABLE OF CONTENTS CONTINUED 3.2.1 Specimen Collection and Care ..................................................................... 45 3.2.2 Tethered Flight Testing ................................................................................ 45 3.2.3 Tethered Flight Analysis .............................................................................. 49 3.2.4. Quasi-static Thorax Force-Displacement.................................................... 51 3.2.5 Statistics ....................................................................................................... 53 3.4 Results ......................................................................................................................... 54 3.4.1 Tethered Flight ............................................................................................. 54 3.4.2 Quasi-static Thorax Stiffness ....................................................................... 58 3.5 Discussion ................................................................................................................... 61 3.5.1 Relative Thorax Deformation and Forces .................................................... 61 3.5.2 Dorsal Ventral Thorax Stiffness ................................................................... 63 3.5.3. The Effects of Distributed Elasticity ........................................................... 64 Acknowledgements ........................................................................................................... 66 Data Accessibility ............................................................................................................. 66 References ......................................................................................................................... 67 4. MEASURING THE FREQUENCY RESPONSE FUNCTION FOR THE WING HINGE OF INSECTS WITH SYNCHRONOUS AND ASYNCHRONOUS FLIGHT MUSCLES ....................................................................... 71 Contribution of Authors and Co-Authors ......................................................................... 71 Manuscript Information .................................................................................................... 72 Abstract ............................................................................................................................. 73 4.1 Introduction ................................................................................................................. 73 4.2 Methods....................................................................................................................... 77 4.2.1 Specimen Care and Preparation ................................................................... 77 4.2.2 Experimental Setup ...................................................................................... 78 4.2.3 Data Collection ............................................................................................ 79 4.2.4 Data Analysis ............................................................................................... 80 4.2.5 Frequency Response Curve Fitting .............................................................. 82 4.2.6 Frequency Response Modeling .................................................................... 82 4.2.7 Statistics ....................................................................................................... 85 4.3 Results ......................................................................................................................... 87 4.3.1 Experimental Results ................................................................................... 87 4.3.2 Modeling Results ......................................................................................... 89 4.4 Discussion ................................................................................................................... 91 Acknowledgments............................................................................................................. 94 References ......................................................................................................................... 94 5. CONCLUSION ................................................................................................................. 97 5.1 Contribution to the Field ............................................................................................. 97 v TABLE OF CONTENTS CONTINUED 5.2 Future Directions ...................................................................................................... 101 CUMULATIVE REFERENCES CITED .............................................................................. 103 APPENDICES .......................................................................................................................113 CHAPTER 2 SUPPLEMENTAL INFORMATION ........................................................114 CHAPTER 3 SUPPLEMENTAL INFORMATION ....................................................... 120 CHAPTER 4 SUPPLEMENTAL INFORMATION ....................................................... 126 vi LIST OF TABLES Table Page 1. Table 2.1 Cuticle layer composition by region for M. sexta and A. mellifera. Thickness and percentages (with respect to the total thickness) are reported as mean ± standard deviation. ........................................................................................... 23 2. Table 3.1. Descriptive statistics for flight data. All values are mean ± standard deviation. ............................................................................................................ 56 3. Table 4.1. Input parameters for the model calculated from experimental data and anatomical measurements of the forewings. .............................................................. 85 4. Table 4.2. Results averaged across both the left and right wings (mean ± standard deviation). ........................................................................................................... 87 5. Table B1. in vivo flight data. ........................................................................................... 121 6. Table B2. Thorax compression data. ............................................................................... 124 vii LIST OF FIGURES Figure Page 1. Figure 1.1. The insect thorax (left) can be idealized as a two degree-of- freedom mechanical model (right). Within the mechanical model, the elasticity is lumped into two components: a parallel elastic element of stiffness 𝑘𝑝 that represents the flight muscles and the thorax exoskeleton (highlighted in red), and a series elastic element of torsional stiffness 𝑘𝑠 that represents the rotational elasticity of the wing hinge and the thorax exoskeleton immediately surrounding the wing base (highlighted in blue). The parallel element deforms a distance 𝑥 directly under muscle force 𝐹, which causes the wing to rigidly rotate an amount θ. The wing may rotate an additional amount Φ about the wing hinge if the series element deforms under the inertial and aerodynamic loading of the wing. Left image adapted from Lynch et al 2021 and Snodgrass 1935. ....................................................................... 3 2. Figure 1.2. Representation of synchronous (top) and asynchronous (bottom) muscles where the red represents the time trace of a neurological signal being delivered to the indirect flight muscles and the black represents the time trace of the flight muscle deformation. Adapted from Josephson et al 2000..................................................................................................................................... 4 3. Figure 2.1. Approach for thoracic cuticle assessment. (A) Insects were cross-sectioned in the sagittal plane to expose the dorsal-longitudinal muscle attachment sites and facilitate nanoindentation mapping of modulus gradation through the cuticle thickness. (B) The A. mellifera thorax was assigned functional regions B1-B4, where dashed lines show the dorsal- longitudinal muscles. (C) M. sexta was assigned functional regions M1-M3. (D) From nanoindentation data, the thickness-normalized position of each indent was calculated with reference to the cuticle interior (0 = interior, 1 = exterior). ............................................................................................................................ 19 4. Figure 2.2. FEA schematic of a 2D insect cuticle. v(x) denotes a prescribed displacement field changing in the x-direction. We focused our discussion on middle 5% of the cuticle where the highest stress occurred (light blue). The circles at the lower edge represent a “roller” boundary condition, where the bottom edge of the cuticle is constrained so that it cannot displace in the y-direction but can displace in the x-direction. ................................................................. 21 viii LIST OF FIGURES CONTINUED Figure Page 5. Figure 2.3 Thorax structure from H&E-stained sections differs by insect and region. For all images, the cuticle interior is on the bottom. Endocuticle (black arrows) and exocuticle (white arrows) thicknesses vary between thorax regions for A. mellifera and M. sexta. An epicuticle (red arrows) was only observed for M. sexta. A. mellifera and M. sexta cuticle samples were imaged at 60x and 20x, respectively. Scale bars: 20 µm. ................................................. 24 6. Figure 2.4 Modulus gradation through the cuticle thickness where 0 indicates cuticle interior and 1 indicates exterior. Data are those analyzed for A. mellifera and M. sexta. Each color represents all indents from one array per region. A. mellifera modulus gradients were well-represented by linear fits for all regions. Modulus did not show consistent gradation for M. sexta in any region. ........................................................................................................... 26 7. Figure 2.5 Absolute value correlation metrics compared to correlation- based metrics. A) Correlation dissimilarity (1 - |r(Y, Y’)|) plotted for correlations -1 to 1. B) Square root based dissimilarity plotted for correlations -1 to 1. C) Comparison of correlation-based metric without absolute value to A). D) Comparison of square-root of correlation-based dissimilarity without absolute value B). ........................................................................... 28 8. Figure 3.1 The insect thorax (left) can be idealized as a two degree-of- freedom mechanical model (right). Within the mechanical model, the elasticity is lumped into two components: a parallel elastic element of stiffness 𝑘𝑝 that represents the flight muscles and the thorax exoskeleton (highlighted in red), and a series elastic element of torsional stiffness 𝑘𝑠 that represents the rotational elasticity of the wing hinge and the thorax exoskeleton immediately surrounding the wing base (highlighted in blue). The parallel element deforms a distance 𝑥 directly under muscle force 𝐹, which causes the wing to rigidly rotate an amount θ. The wing may rotate an additional amount Φ about the wing hinge if the series element deforms under the inertial and aerodynamic loading of the wing. Left image adapted from [13,16]. ..................................................................................................................... 43 9. Figure 3.2. In vivo tethered flight experimental set up. A laser vibrometer measures the velocity of the dorsal thorax (numerically integrated to find displacement), and a piezoelectric force sensor measures wing-generated forces at the tether location. The rotation stage is used to align the thorax to improve reflectance to the vibrometer. ............................................................................. 49 ix LIST OF FIGURES CONTINUED Figure Page 10. Figure 3.3. Example of data analysis from B. centralis for (A) in vivo flight data and (B) dorsal-ventral thorax stiffness. (A) Data is shown for both the entire flight period (i-iii) and a single segment within the flight period (iv - vi). First, time series data for the entire flight duration (i) was transformed using Fast Fourier Transform to identify the average wingbeat frequency (ii). Wingbeat frequency was used to divide the flight period into smaller segments for more refined analysis while maintaining a frequency resolution of 1.5% wingbeat frequency (iii). Since wingbeat frequency was variable over the flight period, this process was repeated for each segment (iv – vi). Wingbeat frequency (v) was used to divide each segment into individual wingbeats where the peak-peak values for displacement and total forces were measured using a peak finding algorithm. Peak-to-peak distances were averaged for each segment, and again for the entire flight segment and then converted to amplitudes. (B) The thorax was compressed at 2 Hz for at least 10 cycles (i). Linear regression for force versus displacement was used to determine the average dorsal-ventral stiffness (ii). ........................................................................................................................................... 51 11. Figure 3.4. Thorax compression experimental setup. The thorax is compressed sinusoidally at 2 Hz with in vivo amplitudes, and the resulting compressive forces are measured at the dorsal thorax. Dorsal-ventral thorax stiffness is estimated from the resulting force-displacement curves. ‘y’ denotes thorax deformation............................................................................................... 52 12. Figure 3.5. Scatter plots for average displacement (mm) vs thorax diameter (mm) and wing-generated force (N) vs body mass (g) by specimen. Shapes indicate species and black/white indicates asynchronous and synchronous muscle, respectively. ......................................................................................................... 57 13. Figure 3.6. Individual value plots for specimen. Thorax displacement is relative to thorax diameter and wing force is relative to body weight. P- values refer to the effect of muscle type from associated two-factor ANOVA models. .............................................................................................................................. 58 14. Figure 3.7. Absolute thorax stiffness for all species considered (N = 5 for each species). Mean indicated by a white circle. .............................................................. 60 15. Figure 3.8. Thorax stiffness relative to body weight and thorax diameter for each species, N = 5 for each species. Mean indicated by a white circle. .......................... 60 x LIST OF FIGURES CONTINUED Figure Page 16. Figure 4.1. The thorax of insects that use indirect actuation (left) can be modeled as a two degree of freedom mechanical model (right). The thorax elasticity is approximated by a parallel elastic element (kp) and the wing hinge elasticity is represented by a series elastic element (ks). The compression force F on the thorax causes a displacement x which is statically translated into wing rotation θ via the wing hinge. The wing hinge can also dynamically contribute to wing rotation. The resulting wing rotation from the static thorax displacement and dynamic moment at the wing hinge results in a total wing rotation of ϕ. Adapted from Casey et al 2023................................................................................................................................... 76 17. Figure 4.2. Experimental setup and data analysis. (A) Configuration for compressing the thorax using a shaker, where y is the vertical displacement. (B) Overlaid frames from high speed camera at the top and bottom of the wing rotation where ϕ is the wing angle amplitude (1/2 wing stroke). (C) Example frequency response function magnitude for the wing rotation:thorax displacement for the left (dark blue) and right (light blue) wings. ................................................................................................................................ 79 18. Figure 4.3. A qualitative mechanical model that describes the dynamics of an indirectly-actuated flight system where . ............................................................. 83 19. Figure 4.4. Frequency response function magnitude for thorax compression: stroke angle forE. auxiliaris between 10 and 95 Hz and A. mellifera between 50 and 350 Hz. Error bars are standard deviation at each frequency. N=10,11 for E. auxiliaris and A. mellifera, respectively. ................................................................. 88 20. Figure 4.5. Linear regression between ωp and ζ and ϕ at the lowest testing frequency (quasi-static) . There is no significant relationship between ζ and ωp for E. auxiliaris. ........................................................................................................... 89 21. Figure 4.6. Modeling the impact of aerodynamic damping on wing:thorax magnitude response for E. auxiliaris (Left) and A. mellifera (Right). Top: Model values for wing:thorax magnitude responses overlaid with experimental values at different thorax compression values (CD = 3.4). Bottom: At in vivo flapping amplitudes, ωp is lower than the known flapping frequency of E. auxiliaris, (41 ± 4.3 Hz (Dittemore 2022)) and of A. mellifera (230 Hz with a range from 220-245 Hz (Altshuler et al 2005) for different values of CD. ....................................................................................................... 90 xi LIST OF FIGURES CONTINUED Figure Page 22. Figure A1. Nanoindentation load vs displacement curves for representative arrays from M. sexta (red) and A. mellifera (black). Curves show a smooth loading and unloading curve and a smooth elastic to plastic transition. A short hold near the end of unloading is used to assess thermal drift during the test. .............................................................................................................................115 23. Figure A2. Plotted mixed model ANOVA equations with representative heatmaps for each region demonstrating the change in modulus through the thickness of the cuticle. Dashed lines represent standard error for slope from mixed model ANOVA. The black line on heatmaps indicates cuticle interior. While a single gradient represented most regions well, it did not for B4. In this region, half of the arrays had a steep positive gradient and half had a slight negative gradient which resulted in a mean positive slope. ...................................116 24. Figure A3. Modulus gradation through the cuticle thickness where 0 indicates cuticle interior and 1 indicates exterior. All indentation arrays for A. mellifera and M. sexta are included. Each color represents all indents from one array per region. A. mellifera modulus gradients were well- represented by linear fits for all regions, equations and R2 values are included for all fits. Modulus did not show consistent gradation for M. sexta in any region. ...................................................................................................................117 25. Figure A4. CLSM showed autofluorescent resilin distribution varied by thorax region and specimen in A. mellifera. The presence and location of resilin was inconsistent between specimens (top and bottom). B1 did not have discernable resilin (images demonstrate only autofluorescence of muscle), while regions B2-B4 showed resilin for one specimen but not the other. Histological images from similar cross sections provide a reference for cuticle and muscle location. Green arrows indicate cuticle exterior, blue cuticle interior, and red the resilin dense scutellum hinge. CLSM Images were taken at 25x using a 405 nm laser collecting emission from 420-480 nm. Histological images were taken at 10x. Scale bars: 100 µm. ...................................118 xii LIST OF FIGURES CONTINUED Figure Page 26. Figure A5. CLSM showed autofluorescent resilin throughout the thorax cuticle but distribution varied by region for M. sexta. In particular, M2 lacked resilin on the cuticle interior. Histological images from similar cross sections provide a reference for cuticle and muscle location. Green arrows indicate cuticle exterior and blue cuticle interior. CLSM Images were taken at 25x using a 405 nm laser collecting emission from 420-480 nm. Histological images were taken at 10x. Scale bars: 100 µm. ..........................................119 27. Figure C1. Boxplots for the displacement amplitudes (mm) for each specimen. ........................................................................................................................ 127 28. Figure C2. Line plots for the magnitude frequency response functions for the 11 E. auxiliaris specimens tested for the left and right wings. ................................. 127 29. Figure C3. Line plots for the magnitude frequency response functions of the 11 A. mellifera specimens tested for the left and right wings. ........................................ 128 xiii ABSTRACT Flying insects are small, efficient, and agile- all traits that engineers want to incorporate into designs for small flapping wing drones. Therefore, engineers study flying insects’ adaptations to understand what makes them successful flyers. One such adaptation is indirect actuation. During indirect actuation, the flight muscles deform the thorax exoskeletal. Thorax deformations are translated into wing rotation via the wing hinge, where the wings attach to the exoskeleton. Indirect actuation may reduce the energetic cost of flight by allowing energy to be stored in the thorax during one part of the wing cycle and then used later. Researchers can model indirect actuation as a two-degree-of-freedom mechanical model where a parallel spring represents the combined stiffness of the thorax exoskeleton and indirect flight muscles, and a series spring represents the wing hinge stiffness. However, these stiffnesses have not been evaluated experimentally. Evaluating the thorax stiffness will help us better understand insect flight. I hypothesize that thorax stiffness depends on the flight muscle activation type. Insects with synchronous flight muscles convert one action potential into one wing flap, while those with asynchronous flight muscles can convert a single action potential into many wing flaps. In this thesis I compared the thorax stiffness of insects with synchronous and asynchronous muscle on multiple scales. On a microscale, I measured the elastic modulus of the thorax exoskeleton using nanoindentation. I found differences in the modulus gradient through the cuticle thickness and between thorax regions through between insects with synchronous and asynchronous muscle. On a macroscale, I first qualitatively compared the thorax stiffness for insects with synchronous and asynchronous. I found that insects with asynchronous muscle may rely more on their wing hinge for wing rotation. Next, I created a frequency response function to quantify the role of wing hinge resonance in flight. I found that both insects are flapping post-resonance. These studies improve our understanding of insect flight evolution by elucidating the connections between muscle activation, flight control, and flight energetics. With this knowledge, engineers can make informed decisions about which species they should mimic in their designs. 1 INTRODUCTION Flying insects have exceptional abilities including hovering, aerial maneuvers, and sustained flight (Hedrick et al 2015). At their small size (µg to g (Ellington 1999, Setsuda et al 1999)), flight is energetically costly because of increased drag (Lehmann et al 1997). To overcome the high energetic costs of flight, insects have evolved adaptations that birds and bats do not have, and which may be key to their success at small sizes. 1.1 Indirect Actuation Most flying insects (except dragonflies and damselflies) have evolved indirect actuation. During indirect actuation two sets of antagonistic indirect flight muscles (IFM) deform the thin exoskeletal shell surrounding the thorax (Pringle 1949). IFM forces are converted and amplified into wing rotation via the wing hinge, a complex linkage connecting the wings to the thorax exoskeleton (Nachtigall et al 1998, Rheuben and Kammer 1987). Indirect actuation is hypothesized to reduce the energetic cost of flight through energy cycling (Gau et al 2019). Excess kinetic energy produced by the wings can be stored in the thorax during one part of the wing cycle and used during another later to reduce overall energetic costs (Lynch et al 2021 and Dickinson and Lighton 1995). Elastic elements present in the wing hinge and thorax exoskeleton may be responsible for storing and recycling the elastic energy. However, how the elasticity in each of these regions contributes to efficient flight is largely unknown. Mechanical modeling of the indirect flight system provide a framework for understanding thorax elasticity's role in insects using indirect actuation. 2 1.2 Modeling Indirect Actuation Recent modeling efforts have depicted the indirect flight system as a two-degree freedom mechanical model .The model lumps elasticity in two locations. First, a parallel elastic element approximately representative of the elasticity of the IFMs and the thorax exoskeleton where the muscles connect. Second, a series elastic element approximately representative of the wing hinge and the exoskeleton directly surrounding it. While the IFMs are generally believed to be the primary driver of wing rotation, phase lag between the thorax deformation and wing rotation is evidence of a series elastic contribution (Ando and Kanzaki 2016, Deora et al 2021). Despite multiple papers probing this model through mechanical experiments and modeling (Pons and Beatus 2022, Lynch et al 2021), the effective stiffnesses of the elastic elements have not been evaluated experimentally. I hypothesize that muscle activation type- synchronous and asynchronous may correlate with differences in the contribution of the series and parallel elastic element to wing rotation. 3 Figure 1.1. The insect thorax (left) can be idealized as a two degree-of-freedom mechanical model (right). Within the mechanical model, the elasticity is lumped into two components: a parallel elastic element of stiffness 𝑘𝑝 that represents the flight muscles and the thorax exoskeleton (highlighted in red), and a series elastic element of torsional stiffness 𝑘𝑠 that represents the rotational elasticity of the wing hinge and the thorax exoskeleton immediately surrounding the wing base (highlighted in blue). The parallel element deforms a distance 𝑥 directly under muscle force 𝐹, which causes the wing to rigidly rotate an amount θ. The wing may rotate an additional amount Φ about the wing hinge if the series element deforms under the inertial and aerodynamic loading of the wing. Left image adapted from Lynch et al 2021 and Snodgrass 1935. 1.3 Synchronous vs Asynchronous Musculature Some insects that use indirect actuation have evolved distinct methods of flight muscle activation. Insects with synchronous flight muscles (e.g. Lepidoptera, higher Orthoptera (Tiegs 1955)) convert one action potential into one wing flap. On the other hand, insects with asynchronous flight muscles (e.g. Hymenoptera, Diptera, Coleoptera) convert a single action potential into many wing flaps through delayed stretch activation (Pringle 1949) (Figure 1.2). Consequently, insects with asynchronous muscle can dedicate more space to muscle fibers 4 because less space is required for calcium cycling needed to convert action potentials to muscle contractions (Dickinson and Tu 1997) and are generally able to flap at a higher wing beat frequency (>100 Hz) than insects with synchronous muscle (< 100 Hz) (Josephson et al 2000). There are other important differences between insects with synchronous and asynchronous muscle that may contribute to differences in elasticity between insects with synchronous and asynchronous muscle: muscle stiffness (Josephson et al 2000), wing density per area (San ha et al 2013), and the role of resonance in flight (Gau 2022, Jankauski 2020, Pringle 1949). Figure 1.2. Representation of synchronous (top) and asynchronous (bottom) muscles where the red represents the time trace of a neurological signal being delivered to the indirect flight muscles and the black represents the time trace of the flight muscle deformation. Adapted from Josephson et al 2000. 5 The first important difference is muscle stiffness. Insects with synchronous muscle generally had a passive muscle stiffness that increases greatly when the flight muscles are activated, while insects with asynchronous muscle generally have a higher passive muscle stiffness that only increase slightly when the muscle is activated (Josephson et al 2000). Researchers have hypothesized that the high passive stiffness in insects with asynchronous muscle is necessary for delayed stretch activation (Josephson et al 2000). I hypothesize that differences in muscle stiffness could mean that there are also differences in exoskeletal stiffness where the muscles attach, but this has not been measured. Another important difference is wing density per unit area. The wing density is generally higher in insects with asynchronous musculature compared to those with synchronous musculature (San ha et al 2013). As a result, the inertial forces generated by the flapping wings are believed to be higher in insects with asynchronous musculature (Lynch et al 2021). Aerodynamic forces generated by the flapping wings may also vary between asynchronous and synchronous groups, but they are generally on the same order as the weight of the insect to produce sufficient lift for hover (Berman and Wang 2007). This difference in wing inertial forces could mean that the series elastic element plays a larger role in insects with asynchronous musculature. The third important difference is the role that resonance plays in insects with synchronous and asynchronous muscle. Resonance is a vibrations phenomenon that occurs when a system oscillates near its resonant frequency also known as its natural frequency. For insects, flapping at or near the resonant frequency of their flight system may be energetically favorable because the output amplitude increases without an increase in input (Dudley 2002). While flapping at 6 resonance can be energetically advantageous, there is a tradeoff for control. Flapping at or near resonance means that the insect cannot exert control through frequency modulation (Gau 2021). There is conflicting evidence whether insects are flapping at resonance (Gau 2022, Jankauski 2020, Pringle 1949, Wold et al 2024). This is a difficult trait to measure because the system's resonant frequency is dependent on many different things such as muscle contractions, and wing position. External manipulations that are often necessary for experiments such as tethering the thorax or euthanasia will change the resonant frequency. Euthanasia leads to rigor mortis, where the muscles stiffen (Goff 2010), and rigid tethering creates a boundary condition (Jankauski 2020) both of which increase thorax stiffness. Complicating the problem, there are multiple definitions of what resonance the insect may be flapping at (Pons and Beatus 2022). An insect has infinite natural frequencies because it is a continuous system. But based on the two degree of freedom model, there are two natural frequencies, a thorax natural frequency and a wing hinge natural frequency that are important for insect flight. It is possible that insects with synchronous and asynchronous muscle flap near different natural frequencies. Comparing the thorax elastic properties of insects with synchronous and asynchronous muscle will inform how the thorax evolved to support diverse muscle activation methods and insect flight. 1.4 Applications My work is the next step in understanding how thorax elasticity contributes to flight. The results will help biologists understand the evolution of insect flight, and engineers improve mechanical designs inspired by flying insects such as small flapping wing drones. Small flapping wing drones have diverse applications in agriculture, search and rescue, surveillance, and 7 wildlife monitoring. Insect-inspired flapping wing drones can scale smaller than traditional fixed wing drones, but they also have the shortest flight times (Floreano and Wood 2015). The smallest flapping wing drones (< 5 g) can generally only sustain untethered flight for less than 30 seconds (Jafferis et al 2019, Park and Yoon 2008). In these insect-inspired flapping wing drone designs, the usual workflow is to optimize each component of the design separately (wing, gearbox, tail, etc). However, this differs from how evolution has shaped insect flight. By investigating the role of distributed thorax elasticity on flight performance across insect species, I am identifying individual components that contribute to insect flight that may have evolved together- elasticity at the wing hinge, muscle stiffness, wing beat frequency, wing inertia, and more. Defining these relationships can inform future design processes. 1.5 Thesis Aims In this thesis, my goal is to experimentally assess elasticity in the indirect flight system on multiple length scales and compare thorax elasticity between insects with synchronous and asynchronous muscle. I accomplished this goal by using the two degree of freedom model as my basis for understanding thorax elasticity. My first aim, discussed in Chapter Two, is to assess the parallel elastic element on a microscale by measuring the material properties of the thorax exoskeleton. I measured the elastic modulus of thorax exoskeleton using quasistatic nanoindentation, and used imaging techniques including histology and confocal laser microscopy to investigate cuticle layer organization and how it may contribute to differences in cuticle stiffness. I compared distinct anatomical regions of the thorax for insects with asynchronous (honeybee, Apis mellifera, A. mellifera) and 8 synchronous muscles (hawkmoth, Manduca sexta, M. sexta) to understand how anatomy impacts the material properties of the thorax exoskeleton. I found that cuticle properties vary through cuticle thickness, by thorax region, and between species with asynchronous (honeybee; Apis mellifera) and synchronous (hawkmoth; Manduca sexta) muscles but that mean elastic modulus was the same across species. This work is published in Acta Biomaterialia. My second aim, discussed in Chapter Three, is to compare the distribution of elasticity in the thoraxes of insects with synchronous and asynchronous flight muscles. I measured the stiffness of the series elastic element and the parallel elastic element (Figure 1.1). The study was conducted on six species, three with synchronous muscle and three with asynchronous muscle each with a range of body sizes. I found that wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature. This work is published in The Journal of the Royal Society Interface. Finally in Chapter Four I discuss my third aim- experimentally create a frequency response function between thorax deformation and wing rotation for insects with synchronous and asynchronous muscles. I measured the input:output relationship between thorax compression and wing stroke for the army cutworm moth and the honeybee across a range of biologically relevant frequencies to create a frequency response function. I also create a model that is populated with values from the experimental data to probe what happens to the relationship of thorax displacement: wing rotation outside of the wing rotation range that could be achieved experimentally. 9 From this study I found that there was a peak in the wing rotation: thorax compression response and a corresponding phase shift, indicating that the wing hinge is behaving resonantly and contributing to wing rotation. The model showed that this peak frequency decreased when the thorax was compressed at in vivo compression amplitudes. The peak response at in vivo compression amplitude was much lower than the known flapping frequency for both species. This is evidence that at in vivo wing rotations, both insects are flapping post-resonance. 10 CHAPTER TWO THE FLYING INSECT THORACIC CUTICLE IS HETEROGENEOUS IN STRUCTURE AND IN THICKNESS- DEPENDENT MODULUS GRADATION Contribution of Authors and Co-Authors Manuscript(s) in Chapter(s) 1 Author: Cailin B. Casey Contributions: Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing. Co-Author: Claire Yager Contributions: Conceptualization, Writing – review & editing Co-Author: Mark Jankauski Contributions: Conceptualization, Funding acquisition, Writing – original draft, Writing – review & editing. Co-Author: Chelsea Heveran Contributions: Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing. 11 Manuscript Information Cailin Casey, Claire Yager, Mark Jankauski, Chelsea Heveran Acta Biomaterialia Status of Manuscript: ☐ Prepared for submission to a peer-reviewed journal ☐ Officially submitted to a peer-reviewed journal ☐ Accepted by a peer-reviewed journal X Published in a peer-reviewed journal Elsevier Volume 138 https://doi.org/10.1016/j.actbio.2021.10.035 https://doi.org/10.1016/j.actbio.2021.10.035 12 Abstract The thorax is a specialized structure central to insect flight. In the thorax, flight muscles are surrounded by a thin layer of cuticle. The structure, composition, and material properties of this chitinous structure may influence the efficiency of the thorax in flight. However, these properties, as well as their variation throughout the thorax and between insect taxa, are not known. We provide a multi-faceted assessment of thorax cuticle for fliers with asynchronous (honey bee; Apis mellifera) and synchronous (hawkmoth; Manduca sexta) muscles. These muscle types are defined by the relationship between their activation frequency and the insect’s wingbeat frequency. We investigated cuticle structure using histology, resilin distribution through confocal laser scanning microscopy, and modulus gradation with nanoindentation. Our results suggest that thorax cuticle properties are highly dependent on anatomical region and species. Modulus gradation, but not mean modulus, differed between the two types of fliers. In some regions, A. mellifera had a positive linear modulus gradient from cuticle interior to exterior of about 2 GPa. In M. sexta, modulus values through cuticle thickness were not well represented by linear fits. We utilized finite element modeling to assess how measured modulus gradients influenced maximum stress in cuticle. Stress was reduced when cuticle with a linear gradient was compressed from the high modulus side. These results support the protective role of the A. mellifera thorax cuticle. Our multi-faceted assessment advances our understanding of thorax cuticle structural and material heterogeneity and the potential benefits of material gradation to flying insects. 13 2.1 Introduction As the only invertebrates to evolve flight, insects interest researchers across disciplines. As a group, flying insects can hover, travel long distances, and reach speeds of 25 kilometers per hour [1]. Most insects achieve efficiency, especially necessary for hovering, through a mechanism called indirect actuation. In indirect actuation, flight muscles deform the thorax to indirectly flap the wings [2]. The thorax has two main components- flight muscles, and the thin- walled ellipsoidal or box-like exoskeletal cuticle where flight muscles attach [2]. Cuticle is a composite of chitin, water, and proteins which is organized into distinct layers, including endocuticle, exocuticle, and epicuticle [3]. The thorax contains two main flight muscle groups, the dorsal-ventral muscles (DVM) and the dorsal-longitudinal muscles (DLM). Flight muscle forces are translated into flapping via intricate connections at the wing hinges [3,4]. Within the indirect lineage, fliers have either synchronous or asynchronous flight muscles. For this paper, we will distinguish these insects with asynchronous and synchronous flight muscles as asynchronous and synchronous fliers respectively. Synchronous flight requires a neural impulse for each wing beat and is usually associated with flapping rates of <100 Hz [6]. Asynchronous flight has evolved independently several times and lineages include: Hymenoptera, Diptera and Coleoptera. Synchronous fliers include Lepidoptera, and higher Orthoptera [6]. Asynchronous flight produces work in the thorax through delayed stretch activation leading to multiple flaps per impulse [2]. Asynchronous and synchronous muscle types are defined by the ratio of their activation frequency to the insect’s wingbeat frequency, but the musculature has other distinguishing characteristics as well. The stiffnesses of the two muscle groups differ greatly. Synchronous muscle is quite stiff when it is 14 active and much less so when passive. In asynchronous muscle, the passive muscle is much stiffer than synchronous passive muscle but increases only slightly when active. This stiffness may help allow for delayed stretch activation. The stiffness for passive and active asynchronous muscle generally falls between the passive and active stiffnesses of synchronous muscle [7]. Though there are distinct differences in stiffness between the muscle groups, it is presently unknown if there are differences between the stiffness in the cuticle that two the muscle groups attach to [5][2]. While the physiology of flight muscles has been studied extensively, the cuticle has not. In particular, the roles of thorax cuticle geometry, layering, and material gradation in flight are not well understood. Understanding cuticle heterogeneity within the thorax and between species is an essential first step for understanding the cuticle’s role in efficient flight. Prior nanoindentation studies found increasing elastic modulus and hardness from the cuticle interior to exterior in the gula [8–10], infrared sensillum [9], and elytra [11] of various beetles, the grasshopper mandible [12], and the locust sternum [13]. Although many insect cuticle structures have been studied, the flying insect thorax serves a different function. During flight, large cyclical forces are applied to the thorax, and thus the cuticle might have different material constraints. Material gradation in other structures have been shown to provide protection and improve resilience [14,15]. A modulus gradation in the thorax would be expected to confer the same benefits, though to our knowledge, modulus gradations have not been studied in the thorax cuticle of either synchronous or asynchronous fliers. The goal of the present work is to assess the thorax cuticle layer organization and modulus gradation for flying insects. We used histology, nanoindentation, and confocal laser 15 scanning microscopy (CLSM) to investigate cuticle layer organization, composition (i.e., presence of resilin), and modulus gradation between distinct anatomical regions of the thorax for asynchronous (honey bee, Apis mellifera, A. mellifera) and synchronous (hawkmoth, Manduca sexta, M. sexta) fliers. We further utilized finite element analysis (FEA) to evaluate the impact of modulus gradient on thorax stress concentrations. 2.2 Experimental Methods 2.2.1 Insect Care and Selection of Regions of Interest M. sexta larvae were sourced from Josh’s Frogs (Owosso, MI). Larvae were kept in inverted 0.95 liter plastic insect rearing cups (4 larvae per cup) with gutter mesh used as a climbing matrix. Rearing cups were inspected and cleaned daily. The rearing room was maintained at an ambient temperature of 28 ± 2 °C and larvae were subjected to a 24:0 (L:D) photoperiod to prevent pupal diapause [16]. Larvae were fed Repashy Superfoods Superhorn Hornworm Gutload Diet from Repashy Ventures (Oceanside, CA). Once the dorsal aorta appeared (7-14 days), larvae were moved to a pupation chamber, a large plastic bin with a layer of damp organic potting soil and gutter screen to facilitate adult wing unfurling. Adults emerged within 14-30 days and were sacrificed within two days of emergence with ethyl acetate in a kill jar. A. mellifera specimens were collected from a pollinator garden in Bozeman, MT. To determine whether thorax properties are associated with anatomy, specimens were cross-sectioned in the sagittal plane, which was selected to expose the dorsal-longitudinal flight muscles and their cuticular attachment sites (Figure 2.1A). Thorax cuticle was divided into regions to better understand the cuticle variation. The A. mellifera thorax was divided into 4 regions (Figure 2.1B): The scutum (B1), the scutellum (B2), the postscutellum (B3), and the 16 posterior phragma (B4) [17]. The posterior phragma extends internally to provide an attachment site for the dorsal-longitudinal flight muscles. M. sexta was divided into 3 regions (Figure 2.1C): anterior scutum where the dorsal-longitudinal muscles attach (M1), the dorsal scutum where the dorsal-ventral muscles attach (M2), and the posterior phragma, the posterior site for dorsal- longitudinal muscle attachment (M3). 2.2.2 Histological Assessment of Cuticle Structure Histological staining was used to identify variation in thoracic cuticle structure. After euthanization, specimens used in histology which were preserved with 10% neutral buffered formalin overnight. Formalin fixed specimens were then dehydrated in a graded 70-100% ethanol series, embedded in paraffin, sectioned in the sagittal plane in 5 µm sections, and stained with hematoxylin and eosin (H&E)[18]. Sectioned stained cuticles were imaged with a Nikon Eclipse E800 microscope using the infinity 2 color microscope camera. White balance was set to Red = 1.33 Blue = 1.00 and Green = 2.00. To evaluate cuticle composition, five in-focus locations were selected from each region and the thickness of each cuticle layer was measured using ImageJ 1.53a. 2.2.3 Nanoindentation Assessment of Thorax Cuticle Modulus Gradation Separate insects than studied for histology for both species were prepared for nanoindentation analyses. Insects were dehydrated via a graded ethanol series (70-100%; at least 3 days between each step), cleared with acetone, and embedded in polymethyl methacrylate (PMMA) at 35℃ [19]. Performing nanoindentation in cross-sectioned cuticle facilitated mapping modulus gradation through the cuticle thickness while avoiding possible substrate effects that 17 can occur from ‘top down’ indentation of thin structures of layers of different moduli [20,21]. The cut surface was polished with CarbiMet SiC 600 and 1000 grit abrasive paper lubricated with water, and then with progressively finer (9 to 0.05 µm; Ted Pella) water-based alumina polishing suspension to a mirror finish. Samples were sonicated in water between polishing steps. Nanoindentation (KLA-Tencor iMicro, Berkovich tip) was performed in load-control to a maximum load of 2 mN. The load function was 30s ramp, 60s hold, 10s unload. The 60s hold was sufficient to achieve dissipation of viscous energy, as confirmed using time-displacement plots. Non-overlapping nanoindentation arrays spanned the thorax thickness with 5 µm spacing between indents (Figure 2.1D). This spacing was chosen to maximize resolution of modulus gradient throughout the cuticle while maintaining a spacing of approximately 10 times the indentation depth to minimize the impacts of the plastic zone between indents [22]. Most indents were 400-600 µm deep, which corresponds with an appropriate spacing of 8-10x the spacing between indents. About 1% of indents reached a depth of 900-1000 µm. At these depths, the depth:spacing ratio is 5-5.55, which may introduce error on the scale of 5-10%[22]. At least two non-overlapping arrays were placed in each thoracic region. The reduced modulus (𝐸𝑟) was calculated using the Oliver-Pharr method (Equation 2.1) [23]. A second-order polynomial was fitted to the 95th – 20th percentile of the unloading portion of the load-displacement curve. Stiffness, S, was calculated as the slope of the tangent line to the start of the polynomial fit. The tip contact area (𝐴𝑐) was calibrated using fused silica and measured from contact depth. 18 Equation 2.1: 𝐸𝑟 = 𝑆 2 √ 𝜋 𝐴𝑐 All indents were analyzed except for those that (1) were not on thorax (e.g., in plastic or on cuticle/plastic interface, determined through inspection with a 50x microscope), (2) did not demonstrate a smooth elastic-plastic transition, or (3) did not demonstrate a smooth loading- unloading curve (Appendix A1). The position of each indent was calculated from the relative distance of the residual indent from the outer surface (0 = cuticle interior, 1 = cuticle exterior) (Figure 2.1D).  19 Figure 2.1. Approach for thoracic cuticle assessment. (A) Insects were cross-sectioned in the sagittal plane to expose the dorsal-longitudinal muscle attachment sites and facilitate nanoindentation mapping of modulus gradation through the cuticle thickness. (B) The A. mellifera thorax was assigned functional regions B1-B4, where dashed lines show the dorsal- longitudinal muscles. (C) M. sexta was assigned functional regions M1-M3. (D) From nanoindentation data, the thickness-normalized position of each indent was calculated with reference to the cuticle interior (0 = interior, 1 = exterior). 2.2.4 Confocal Laser Scanning Microscopy Resilin is a rubber-like protein sometimes present in cuticle that aids in elastic energy storage. Isolated resilin has a low elastic modulus (~1 MPa) that stiffens when dehydrated [24,25]. We sought to locate resilin in the thorax cuticle to identify potential areas that may have lower modulus in hydrated cuticle. Resilin is autofluorescent, with excitation of ~350-407 nm and emission of ~413-485 nm [26]. Following nanoindentation, samples were imaged for resilin fluorescence with a Leica TCS SP5 (excitation 405 nm, emission 420-480 nm) [27]. Imaging 20 was performed using a 25x long working distance water immersion objective. Images were processed using Imaris 9.3.0.  2.2.5 Finite Element Analysis We developed a simple 2D FEA model (ABAQUS CAE 2019) to evaluate the impact modulus gradients had on stress in deformed cuticle (Figure 2.2). The cuticle was treated as a rectangle of length 1000 µm long and height 30 µm. The height was assigned as 30 µm because this value is between the mean cuticle thickness measurements for A. mellifera (17 µm) and M. sexta (45 µm). The cuticle was discretized into 1660 linear quadrilateral S4R elements, which was sufficient for convergence of maximum stresses in all cases. For simplicity, only half the cuticle structure was modeled, where the centerline was constrained to only allow deformation along the y-axis. The lower edge has a “roller” boundary condition. The cuticle edge could displace only in the x-direction (represented by circles). A small deformation of 5% of the cuticle thickness was prescribed in the negative y-direction at the top edge of the cuticle section. This deformation magnitude was chosen to ensure that the model remained in the geometrically linear regime. The cuticle was deformed 5% at 0 µm and the deformation linearly decreased so that the cuticle end (500 µm) was not deformed. To our knowledge, the thoracic cuticle deformation (which is not identical to bulk thorax deformation) during flight has not been measured in any insect. Stress depends on material properties as well as thorax geometry. By choosing modulus and cuticle thickness values that are representative of experimental values for A. mellifera and M. sexta we gain a qualitative understanding of how modulus gradients affect stress accumulation in insect cuticle. 21              For the material, we assigned a Poisson’s ratio of 0.3 and one of two elastic moduli distributions. The first was a single uniform modulus, and the second was a 2 GPa linear gradient in the y-direction with a mean modulus of 7 GPa. We considered a positive modulus gradient to represent forces that may be applied from the exterior such as during predation or burrowing. We also considered a model with a negative modulus gradient to represent forces that may be acting from the interior such as flight muscles. In all cases the cuticle material was assumed linear- elastic and isotropic. We focused on the area with the largest stress values by zooming in on the 5% of the cuticle with the largest imposed displacement. Results were mirrored to show the effect of deformation in both directions.  Figure 2.2. FEA schematic of a 2D insect cuticle. v(x) denotes a prescribed displacement field changing in the x-direction. We focused our discussion on middle 5% of the cuticle where the highest stress occurred (light blue). The circles at the lower edge represent a “roller” boundary condition, where the bottom edge of the cuticle is constrained so that it cannot displace in the y- direction but can displace in the x-direction. 2.2.6 Statistics For nanoindentation, two specimens for each species were studied. Between 2 and 7 arrays were collected for each region. To avoid oversampling some regions, two arrays were randomly selected from each region for each specimen for analysis. We sought to test the hypotheses that (1) mean modulus and (2) modulus gradation through the cuticle thickness vary by region. To test our first hypothesis, we generated a mixed model ANOVA with the random 22 effects of specimen and array and the fixed effect of region. To test our second hypothesis, we used a linear mixed model with random effects of specimen and array, fixed effect of region, and a covariate of indent relative position. Relative positions were assigned within the thorax thickness, where 0 indicates the cuticle interior and 1 indicates the cuticle exterior. Separate models were generated for each insect species. For histology, three specimens for each species were evaluated. Mixed model ANOVA (random effect of specimen, fixed effect of region) for each insect species tested the effect of region on cuticle thickness and the composition of layers. Modulus was squared or log transformed, when necessary, to satisfy ANOVA assumptions of residual normality and homoscedasticity. All statistical tests were performed using Minitab v. 19 2020 2.0. The threshold for significance was set a priori at p < 0.05 for all tests. 2.3 Results 2.3.1 Histology H&E staining showed that the thorax composition is heterogeneous between regions for A. mellifera and M. sexta (Figure 2.3). All A. mellifera regions had distinct exocuticle and endocuticle (noted by the stark difference in pink color) except for region B1, where these layers were not distinct. M. sexta had distinct endocuticle and exocuticle separation in M1 and M2 but not M3. M. sexta epicuticle is visible as a thin dark line on the cuticle exterior, which is not seen in A. mellifera. The epicuticle may not be visible with the dark staining of the exocuticle. A. mellifera exocuticle showed dark exocuticle staining for all regions. 23 Table 2.1 Cuticle layer composition by region for M. sexta and A. mellifera. Thickness and percentages (with respect to the total thickness) are reported as mean ± standard deviation. Cuticle Layer B1 B2 B3 B4 M1 M2 M3 Total (µm) 15.58 ± 0.40 24.31 ± 0.73 12.77 ± 2.46 18.20 ± 7.83 48.67 ± 2.77 44.69 ± 3.61 29.81 ± 4.29 Epicuticle - - - - 2.78 ± 0.55 µm 6.23 ± 1.32% 4.23 ± 1.90 µm 10.42 ± 5.29% 2.37 ± 0.36 µm 7.94 ± 0.24% Exocuticle - 9.22 ± 0.52 µm 38.72 ± 2.59% 6.28 ± 1.32 µm 49.64 ± 4.44 % 7.27 ± 2.30 µm 41.44 ± 6.74 % 20.51 ± 3.28 µm 42.75 ± 5.22% 19.01 ± 5.04 µm 41.62 ± 8.85% 13.35 ± 3.37 µm 47.57 ± 3.60% Endocuticle - 15.09 ± 0.83 µm 61.28 ± 2.59% 6.49 ± 1.50 µm 50.35 ± 4.44 % 10.93 ± 5.54 µm 58.56 ± 6.74% 25.44 ± 2.18 µm 51.05 ± 6.49% 23.54 ± 2.04 µm 53.42 ± 4.41% 13.51 ± 1.37 µm 54.71 ± 15.26% For each insect, the thorax composition for each region is reported in Table 2.1. For A. mellifera, region did not have a significant effect on total cuticle thickness (p > 0.05) (B1 = 15.58 ± 0.40, B2 = 24.31 ± 0.73, B3 = 12.77 ± 2.46, B4 = 18.20 ± 7.83). Endocuticle (µm) did vary by region (p = 0.038), with B3 (6.49 ± 1.50 µm) being significantly thinner than B2 (15.09 ± 0.83 µm). Relative cuticle composition (%) did not significantly vary by region. We note that cuticle layering was more difficult to measure in B1, where layers were not distinct. Epicuticle was not detected for A. mellifera. For M. sexta, there was a significant effect of region on total cuticle thickness (p < 0.001). For M. sexta, M1 (48.67 ± 2.77 µm) and M2 (44.69 ± 3.61 µm) had similar thicknesses while M3 (29.81 ± 4.29 µm) was significantly thinner than M1 and M2. The endocuticle for M3 was also significantly thinner than in other regions, but the relative 24 composition of cuticle did not vary by region so this difference can be attributed to the difference in absolute thickness. Some measurements in M3 did not show a clear distinction of endocuticle and exocuticle and in these cases only the total and epicuticle thickness were calculated. Figure 2.3 Thorax structure from H&E-stained sections differs by insect and region. For all images, the cuticle interior is on the bottom. Endocuticle (black arrows) and exocuticle (white arrows) thicknesses vary between thorax regions for A. mellifera and M. sexta. An epicuticle (red arrows) was only observed for M. sexta. A. mellifera and M. sexta cuticle samples were imaged at 60x and 20x, respectively. Scale bars: 20 µm. 25 2.3.2 Nanoindentation and CLSM We used nanoindentation to evaluate the dependence of mean cuticle modulus and modulus gradation on thorax region. The mean modulus did not differ between region for either A. mellifera or M. sexta (p > 0.05 for both). When all data were averaged between regions, modulus did not differ between A. mellifera (7.11 ± 1.47 GPa) and M. sexta (6.75 ± 1.92 GPa) (p > 0.05).  Nanoindentation modulus was graded with respect to cuticle position for A. mellifera (Figure 2.4). This gradation was approximately linear, increasing from the cuticle interior (relative position = 0) to the exterior (relative position = 1) (Appendix A2). We used mixed model ANOVA to evaluate whether these gradations differed between regions for A. mellifera. There was a significant (p < 0.001) interaction between region and relative position, indicating that the linear gradient of modulus (i.e., slope) differs between regions. Equation 2 describes the marginal fits for Er (GPa) by region for A. mellifera from mixed model ANOVA. Equation 2.2: B1: Er = 6.728 + 0.797*relative position B2: Er = 5.582 + 3.068*relative position B3: Er = 4.960 + 2.004*relative position B4: Er = 6.037 + 3.124*relative position The slope in B1 was close to 0 and was much less (97-118%) than in B2-B4. While a single estimate of slope represented most of A. mellifera regions well (Figure 2.4), B4 was more variable. Half of the arrays in this region had a steep positive slope and half had a slight negative slope which resulted in a mean positive slope. Modulus gradients for M. sexta were variable in both direction and shape with no single approximation appropriate for the regional representation 26 of the data. The four arrays from each region that were included in the ANOVA and in Figure 2.4 were randomly selected from a larger sample size which showed similar trends (Appendix A3). Figure 2.4 Modulus gradation through the cuticle thickness where 0 indicates cuticle interior and 1 indicates exterior. Data are those analyzed for A. mellifera and M. sexta. Each color represents all indents from one array per region. A. mellifera modulus gradients were well-represented by linear fits for all regions. Modulus did not show consistent gradation for M. sexta in any region. Because dehydrated resilin stiffen the cuticle [24,25], we employed CLSM to identify areas of cuticle that have the potential for low elastic modulus in hydrated cuticle due to resilin. Resilin identified from blue autofluorescence was present in the cuticle of both insects but varied by species and thorax region (Appendix A4 and A5). The presence of resilin was not associated 27 with a particular modulus value (high or low modulus), including regions where resilin was present only on either the cuticle interior or exterior (Figure 2.4, Appendix A4 and A5). 2.3.3 Finite Element Analysis FEA was used to investigate how experimentally-observed modulus gradients influenced stress distributions in the deformed A. mellifera cuticle. M. sexta modulus distribution varied so much within each region that modeling a particular gradation would not be generalizable. A homogenous cuticle was first modeled to provide a baseline calculation of stress distribution. The cuticle was assigned a modulus of 7 GPa from the mean experimental data. A second model considered elastic moduli that varied linearly from 6 to 8 GPa through the cuticle thickness. A slope of 2 GPa increase across the cuticle thickness was chosen based on an average estimate of slope for A. mellifera. The slope was applied in the positive y-direction and, in a separate model, the negative y-direction based on the potential for forces from flight muscles or from external sources to be acting on the cuticle. The linear modulus gradient influenced the maximum stress, but the stress distribution was insensitive to modulus gradient or direction (Figure 2.5). When the deformation was applied to the high modulus edge, the linearly-graded cuticle experienced a maximum stress 15.3% less than the homogenous cuticle. On the other hand, when the deformation was applied to the low modulus edge, the linearly-graded cuticle experienced a maximum stress 13.3% greater than that experienced by the homogeneous cuticle. This complexifies the stress reduction in the thorax cuticle. Based on our simplified FEA model, a linearly distributed modulus cannot optimally reduce stress for both interior deformation due to flight muscles and exterior deformation from external forces.  28 Figure 2.5 Absolute value correlation metrics compared to correlation-based metrics. A) Correlation dissimilarity (1 - |r(Y, Y’)|) plotted for correlations -1 to 1. B) Square root based dissimilarity plotted for correlations -1 to 1. C) Comparison of correlation-based metric without absolute value to A). D) Comparison of square-root of correlation-based dissimilarity without absolute value B). 2.4. Discussion The thorax is essential for insect flight, yet significant questions remain about its mechanical properties. The thorax must be flexible enough to articulate the wing but must also protect against external forces and resist plastic deformation under the high magnitude forces produced by the flight muscles. Furthermore, the thorax stores and releases elastic energy over a large number of oscillations (e.g., 107 oscillations for A. mellifera [28]) without fatigue. Modulus gradients are observed in other biological materials (e.g., enamel, bamboo, elastomeric fibers) where they help maintain a balance of strength, resilience, and toughness and minimize stress concentrations in complex geometrical structures [29–32]. The purposes of this study were to determine whether insect thorax has graded moduli through the cuticle thickness, whether these gradients depend on thorax region and species, and whether the modulus gradients impact thorax 29 stress concentrations. Understanding thorax cuticle variation is the first step in determining its roles in insect flight. We performed nanoindentation on ethanol-dehydrated, plastic-embedded samples of thorax cuticle. The mean moduli for thorax cuticle in both A. mellifera and M. sexta were in good agreement with values reported for different insect structures. Our measurement of ~7 GPa for dehydrated thorax cuticle for A. mellifera and M. sexta is within the 4.8 to 9.9 GPa reported for the beetle gula [8–10], elytra [11,33], and infrared sensillum [9], and the locust sternum [13] and tibia [34]. These are among the first nanoindentation evaluations for the flying insect thorax cuticle, and specifically within the Hymenoptera and Lepidoptera taxa [35,36]. Studies comparing nanoindentation results from dried and fresh cuticle of the beetle gula [8,10], locust sternum [13], and termite mandibles [37] showed modulus increases of 10% to upwards of 500% with dehydration. Our thorax moduli for M. sexta were ~25% greater than for modulus values of the fresh thorax reported for the same species [36]. This level of stiffening from dehydration is on par with that observed in bone embedded in PMMA [19]. We find this to be an acceptable tradeoff for high spatial resolution testing which is difficult to achieve in fresh samples because of higher surface roughness. Modulus varied throughout the thorax thickness, but the direction and steepness of this gradient depended on insect and region. For two of the four regions, A. mellifera had steep, positive, linear, modulus gradients from cuticle interior to exterior. The positive modulus gradient in A. mellifera thorax agrees with gradients found in non-thorax cuticle for some other insects. Previous work demonstrates that the modulus increases from the cuticle interior to exterior for the gula [8–10], infrared sensillum [9], and elytra [11] of various beetles, the 30 grasshopper mandible [12], and the locust sternum [13]. Increased modulus is observed with sclerotization [38,39], including for some of these insect structures [9,34]. Sclerotization is also associated with dark staining in H&E histology [29,30]. For A. mellifera, the dark staining at the thorax exterior from histological sections indicates that higher modulus is also likely to be influenced by sclerotization [40,41]. A similar dark staining is seen for Drosophila melanogaster abdomen cuticle [40]. However, sclerotization cannot be the only contributor to modulus gradation, since dark banding was seen on the exterior of all A. mellifera histological sections but did not always align with the higher modulus seen at the exterior of the same regions. The apparent lack of sclerotization in the cuticle for M. sexta may partially explain the differences in modulus gradation between M. sexta and A. mellifera found in this study. The differences between A. mellifera and M. sexta thorax cuticle may also be adaptations for behaviors separate from or in conjuncture with flight. For example, most cases of increasing modulus gradient, as seen in A. mellifera, are found for cuticle optimized for protection against predation or during burrowing [11,15,43]. Although A. mellifera do not burrow, most Hymenoptera do (e.g., genera Xylocopa, Andrenida [44]). Thus, the protective cuticle may be residual in the Hymenoptera lineage to adapt for burrowing. We used FEA to assess the impact of the modulus gradient found in A. mellifera on cuticle stress concentration. The 2 GPa gradient applied in FEA is unlikely to represent the exact gradient found in living insect cuticle, but assuming the stress is in the linear regime, there is a linear relationship between the modulus slope and the stress concentrations. Lower stress accumulation is essential for avoiding permanent deformations that could impact thorax performance. The cuticle accumulated the least stress when its modulus was distributed linearly 31 through the thickness, and it was compressed from the highest modulus side. For A. mellifera, this type of compression would likely result from external forces, which fits with our hypothesis that the cuticle gradient is optimized for protection. While simplified, these models illustrate that graded moduli distribution can reduce stress accumulation in some loading contexts. However, further work needs to be done to understand how bulk thorax geometry coupled with cuticle material variation influence peak stresses and energy storage during flight. The thorax likely uses several mechanisms to increase energy return during flight. For both synchronous (e.g., M. sexta) and asynchronous (e.g., A. mellifera) fliers, large power requirements, and low muscular efficiency (<10%) necessitate energy storage in the thorax [45]. Passive, asynchronous muscle is stiffer and behaves more spring-like relative to synchronous muscle [7]. This passive stiffness may be one way that asynchronous muscle stores elastic energy. In M. sexta, mechanical coupling of the scutum and the wing hinges is believed to increase energy return by decoupling the area where the most power is lost (wing hinges) and where the most energy is returned (scutum) [46,47]. Our results suggest that cuticle stiffness does not differ between flying insect lineages, but that the material gradient does. Material gradients may also play a role in this elastic energy storage. Modulus gradients can increase energy return in biomaterials and bioinspired polymers by increasing stretching [31,32]. Further research is needed to identify how these properties or others adapt the thorax cuticle for energy storage in different flight lineages. While this study has elucidated the material properties and structure of flight insect thorax cuticle, the main limitation to our approach is the effects of dehydration. Dehydrating the cuticle was necessary to achieve high spatial resolution for nanoindentation. However, 32 dehydration stiffens the cuticle and may not represent the in vivo material gradients. For instance, it is possible that cuticle with high resilin concentration stiffens more than other areas of cuticle with dehydration, in which case the in vivo gradation would not be observed in our dehydrated samples. Prior literature shows that the effects of dehydration on cuticle material property gradation are inconsistent. Modulus gradients have been shown to disappear and sometimes reverse in dehydrated samples [13,49], though other studies have shown hydrated and dehydrated cuticle demonstrate similar modulus gradients in two species of beetle gula [8,10]. Thus, it is not possible to generalize how dehydration changes our observed gradations from the in vivo state. 2.5. Conclusions We demonstrate that the flying insect thorax is heterogeneous with respect to structure, material composition, and modulus gradient. In A. mellifera, a clear linear modulus gradation is observed in two of the four anatomic regions of interest within the thorax. This linear gradient of modulus with thorax thickness may contribute to decreased stress concentration and protection. This work investigating the properties of the thorax cuticle is a crucial first step for determining the relative contributions of cuticle structure, material composition, and modulus gradient to the efficiency of different forms of flight. 2.6. Acknowledgements We would like to thank Dr. Robert KD Peterson and Miles Maxcer for helping raise insects and Ghazal Vahidi for assistance in sample preparation for nanoindentation. 33 References 1. A. Azuma, T. Watanabe, Flight performance of a dragonfly, Journal of Experimental Biology. 137 (1988) 221–252. 2. J.W.S. Pringle, The excitation and contraction of the flight muscles of insects, The Journal of Physiology. 108 (1949). https://doi.org/10.1113/jphysiol.1949.sp004326 3. W. Nachtigall, A. Wisser, D. Eisinger, Flight of the honey bee. VIII. Functional elements and mechanics of the “flight motor” and the wing joint–one of the most complicated gear-mechanisms in the animal kingdom, Journal of Comparative Physiology B. 168 (1998) 323–344. 4. M.B. Rheuben, A.E. Kammer, Structure and innervation of the third axillary muscle of Manduca relative to its role in turning flight, Journal of Experimental Biology. 131 (1987) 373–402. 5. K.D. Roeder, Movements of the thorax and potential changes in the thoracic muscles of insects during flight, The Biological Bulletin. 100 (1951) 95–106. 6. O.W. Tiegs, The flight muscles of insects-their anatomy and histology; with some observations on the structure of striated muscle in general, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 238 (1955) 221–348. 7. R.K. Josephson, J.G. Malamud, D.R. Stokes, Asynchronous muscle: A primer, Journal of Experimental Biology. 203 (2000) 2713–2722. 8. N. Barbakadze, S. Enders, S. Gorb, E. Arzt, Local mechanical properties of the head articulation cuticle in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae), Journal of Experimental Biology. 209 (2006) 722–730. https://doi.org/10.1242/jeb.02065 9. M. Müller, M. Olek, M. Giersig, H. Schmitz, Micromechanical properties of consecutive layers in specialized insect cuticle: The gula of Pachnoda marginata (Coleoptera, Scarabaeidae) and the infrared sensilla of Melanophila acuminata (Coleoptera, Buprestidae), Journal of Experimental Biology. 211 (2008) 2576–2583. https://doi.org/10.1242/jeb.020164 10. S. Enders, N. Barbakadse, S.N. Gorb, E. Arzt, Exploring biological surfaces by nanoindentation, Journal of Materials Research. 19 (2004) 880–887. https://doi.org/10.1557/jmr.2004.19.3.880 https://doi.org/10.1113/jphysiol.1949.sp004326 https://doi.org/10.1242/jeb.02065 https://doi.org/10.1242/jeb.020164 https://doi.org/10.1557/jmr.2004.19.3.880 34 11. J.Y. Sun, J. Tong, J. Zhou, Application of nano-indenter for investigation of the properties of the elytra cuticle of the dung beetle (Copris ochus Motschulsky), IEE Proceedings: Nanobiotechnology. 153 (2006) 129–133. https://doi.org/10.1049/ip- nbt:20050050 12. T. Schöberl, I.L. Jäger, Wet or dry - Hardness, stiffness and wear resistance of biological materials on the micron scale, Advanced Engineering Materials. 8 (2006) 1164–1169. https://doi.org/10.1002/adem.200600143 13. D. Klocke, H. Schmitz, Water as a major modulator of the mechanical properties of insect cuticle, Acta Biomaterialia. 7 (2011) 2935–2942. https://doi.org/10.1016/j.actbio.2011.04.004 14. H. Rajabi, M. Jafarpour, A. Darvizeh, J.H. Dirks, S.N. Gorb, Stiffness distribution in insect cuticle: A continuous or a discontinuous profile?, Journal of the Royal Society Interface. 14 (2017). https://doi.org/10.1098/rsif.2017.0310 15. M. Jafarpour, S. Eshghi, A. Darvizeh, S. Gorb, H. Rajabi, Functional significance of graded properties of insect cuticle supported by an evolutionary analysis: Functional significance of graded properties of insect cuticle supported by an evolutionary analysis, Journal of the Royal Society Interface. 17 (2020). https://doi.org/10.1098/rsif.2020.0378rsif20200378 16. R.A. Bell, C.G. Rasul, F.G. Joachim, Photoperiodic induction of the pupal diapause in the tobacco hornworm, Manduca sexta, Journal of Insect Physiology. 21 (1975) 1471–1480. 17. R.E. Snodgrass, The thorax of the Hymenoptera, US Government Printing Office, 1910. 18. A.J. Clark, J.D. Triblehorn, Mechanical properties of the cuticles of three cockroach species that differ in their wind-evoked escape behavior, PeerJ. 2 (2014) e501. 19. A.J. Bushby, V.L. Ferguson, A. Boyde, Nanoindentation of bone: Comparison of specimens tested in liquid and embedded in polymethylmethacrylate, Journal of Materials Research. 19 (2004) 249–259. 20. X. Chen, J.J. Vlassak, Numerical study on the measurement of thin film mechanical properties by means of nanoindentation, Journal of Materials Research. 16 (2001) 2974– 2982. 21. Y.-G. Jung, B.R. Lawn, M. Martyniuk, H. Huang, X.Z. Hu, Evaluation of elastic modulus and hardness of thin films by nanoindentation, Journal of Materials Research. 19 (2004) 3076–3080. https://doi.org/10.1049/ip-nbt:20050050 https://doi.org/10.1049/ip-nbt:20050050 https://doi.org/10.1002/adem.200600143 https://doi.org/10.1016/j.actbio.2011.04.004 https://doi.org/10.1098/rsif.2017.0310 https://doi.org/10.1098/rsif.2020.0378rsif20200378 35 22. P. Sudharshan Phani, W.C. Oliver, A critical assessment of the effect of indentation spacing on the measurement of hardness and modulus using instrumented indentation testing, Materials and Design. 164 (2019). https://doi.org/10.1016/j.matdes.2018.107563 23. W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, Journal of Materials Research. 7 (1992) 1564–1583. 24. T. Weis-Fogh, Thermodynamic properties of resilin, a rubber-like protein, Journal of Molecular Biology. 3 (1961) 520–531. 25. J.F.V. Vincent, U.G.K. Wegst, Design and mechanical properties of insect cuticle, Arthropod Structure and Development. 33 (2004) 187–199. https://doi.org/10.1016/j.asd.2004.05.006 26. M. Burrows, S.R. Shaw, G.P. Sutton, Resilin and chitinous cuticle form a composite structure for energy storage in jumping by froghopper insects, BMC Biology. 6 (2008) 1– 16. https://doi.org/10.1186/1741-7007-6-41 27. J. Michels, S.N. Gorb, Detailed three-dimensional visualization of resilin in the exoskeleton of arthropods using confocal laser scanning microscopy, Journal of Microscopy. 245 (2012) 1–16. https://doi.org/10.1111/j.1365-2818.2011.03523.x 28. P.K. Visscher, R. Dukas, Survivorship of foraging honey bees Insectes Sociaux, 1997. 29. A.R. Studart, Biological and bioinspired composites with spatially tunable heterogeneous architectures, Advanced Functional Materials. 23 (2013) 4423–4436. 30. S. Amada, Y. Ichikawa, T. Munekata, Y. Nagase, H. Shimizu, Fiber texture and mechanical graded structure of bamboo, Composites Part B: Engineering. 28 (1997) 13– 20. 31. J.H. Waite, E. Vaccaro, C. Sun, J.M. Lucas, Elastomeric gradients: a hedge against stress concentration in marine holdfasts?, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences. 357 (2002) 143–153. 32. Z. Wu, S. Zhang, A. Vorobyev, K. Gamstedt, K. Wu, C. Guo, S.H. Jeong, Seamless modulus gradient structures for highly resilient, stretchable system integration, Materials Today Physics. 4 (2018) 28–35. 33. Z. Dai, Z. Yang, Macro-/Micro-Structures of Elytra, Mechanical Properties of the Biomaterial and the Coupling Strength Between Elytra in Beetles, Journal of Bionic Engineering. 7 (2010) 6–12. https://doi.org/10.1016/S1672-6529(09)60187-6 https://doi.org/10.1016/j.matdes.2018.107563 https://doi.org/10.1016/j.asd.2004.05.006 https://doi.org/10.1186/1741-7007-6-41 https://doi.org/10.1111/j.1365-2818.2011.03523.x https://doi.org/10.1016/S1672-6529(09)60187-6 36 34. C. Li, S.N. Gorb, H. Rajabi, Cuticle sclerotization determines the difference between the elastic moduli of locust tibiae, Acta Biomaterialia. 103 (2020) 189–195. https://doi.org/10.1016/j.actbio.2019.12.013 35. K. Stamm, B.D. Saltin, J.-H. Dirks, Biomechanics of insect cuticle: an interdisciplinary experimental challenge, Applied Physics A. 127 (2021) 1–9. 36. A.C. Hollenbeck, A.N. Palazotto, Mechanical Characterization of Flight Mechanism in the Hawkmoth Manduca Sexta, Experimental Mechanics. 53 (2013) 1189–1199. https://doi.org/10.1007/s11340-013-9726-5 37. B.W. Cribb, A. Stewart, H. Huang, R. Truss, B. Noller, R. Rasch, M.P. Zalucki, Insect mandibles - Comparative mechanical properties and links with metal incorporation, Naturwissenschaften. 95 (2008) 17–23. https://doi.org/10.1007/s00114-007-0288-1 38. S.O. Andersen, Insect cuticular sclerotization: a review, Insect Biochemistry and Molecular Biology. 40 (2010) 166–178. 39. J.F. Vincent, Insect cuticle: a paradigm for natural composites., Symposia of the Society for Experimental Biology. 34 (1980) 183–210. 40. F. Stringfellow, Functional morphology and histochemistry of structural proteins of the genital cone of Cooperia punctata (von Linstow, 1907) Ransom, 1907, a nematode parasite of ruminants, The Journal of Parasitology. (1969) 1191–1200. 41. S.O. Andersen, M.G. Peter, P. Roepstorff, Cuticular sclerotization in insects, Comparative Biochemistry and Physiology Part B: Biochemistry and Molecular Biology. 113 (1996) 689–705. 42. T. Sztal, H. Chung, S. Berger, P.D. Currie, P. Batterham, P.J. Daborn, A cytochrome p450 conserved in insects is involved in cuticle formation, PloS One. 7 (2012) e36544. 43. Y. Xing, J. Yang, Stiffness distribution in natural insect cuticle reveals an impact resistance strategy, Journal of Biomechanics. 109 (2020) 109952. https://doi.org/10.1016/j.jbiomech.2020.109952 44. S.W.T. Batra, Solitary bees, Scientific American. 250 (1984) 120–127. 45. C.P. Ellington, Power and efficiency of insect flight muscle, 1985. 46. J. Gau, N. Gravish, S. Sponberg, Indirect actuation reduces flight power requirements in Manduca sexta via elastic energy exchange, Journal of the Royal Society Interface. 16 (2019) 1–17. https://doi.org/10.1098/rsif.2019.0543 https://doi.org/10.1016/j.actbio.2019.12.013 https://doi.org/10.1007/s11340-013-9726-5 https://doi.org/10.1007/s00114-007-0288-1 https://doi.org/10.1016/j.jbiomech.2020.109952 https://doi.org/10.1098/rsif.2019.0543 37 47. N. Ando, R. Kanzaki, Flexibility and control of thorax deformation during hawkmoth flight, Biology Letters. 12 (2016). https://doi.org/10.1098/rsbl.2015.0733 48. H. Peisker, J. Michels, S.N. Gorb, Evidence for a material gradient in the adhesive tarsal setae of the ladybird beetle Coccinella septempunctata, Nature Communications. 4 (2013) 1–7. https://doi.org/10.1038/ncomms2576 https://doi.org/10.1098/rsbl.2015.0733 https://doi.org/10.1038/ncomms2576 38 CHAPTER THREE EXPERIMENTAL STUDIES SUGGEST DIFFERENCES IN THE DISTRIBUTION OF THORAX ELASTICITY BETWEEN INSECTS WITH SYNCHRONOUS AND ASYNCHRONOUS MUSCULATURE Contribution of Authors and Co-Authors Manuscript(s) in Chapter(s) 1 Author: Cailin B. Casey Contributions: investigation, methodology, visualization, writing—original draft and writing— review and editing. Co-Author: Chelsea Heveran Contributions: supervision, visualization and writing—review and editing. Co-Author: Mark Jankauski Contributions: conceptualization, methodology, supervision, writing—original draft and writing—review and editing. 39 Manuscript Information Cailin Casey, Chelsea Heveran, Mark Jankauski Journal of the Royal Society Interface Status of Manuscript: ☐ Prepared for submission to a peer-reviewed journal ☐ Officially submitted to a peer-reviewed journal ☐ Accepted by a peer-reviewed journal X Published in a peer-reviewed journal The Royal Society Publishing Volume 20 Issue 201 https://doi.org/10.1098/rsif.2023.0029 https://doi.org/10.1098/rsif.2023.0029 40 Abstract Insects have developed diverse flight actuation mechanisms, including synchronous and asynchronous musculature. Indirect actuation, used by insects with both synchronous and asynchronous musculature, transforms thorax exoskeletal deformation into wing rotation. Though thorax deformation is often attributed exclusively to muscle tension, the inertial and aerodynamic forces generated by the flapping wings may also contribute. In this study, a tethered flight experiment was used to simultaneously measure thorax deformation and the inertial/aerodynamic forces acting on the thorax generated by the flapping wing. Compared to insects with synchronous musculature, insects with asynchronous muscle deformed their thorax 60% less relative to their thorax diameter and their wings generated 2.8 times greater forces relative to their body weight. In a second experiment, dorsal-ventral thorax stiffness was measured across species. Accounting for weight and size, the asynchronous thorax was on average 3.8 times stiffer than the synchronous thorax in the dorsal-ventral direction. Differences in thorax stiffness and forces acting at the wing hinge led us to hypothesize about differing roles of series and parallel elasticity in the thoraxes of insects with synchronous and asynchronous musculature. Specifically, wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature. 3.1 Introduction Flying insects are a diverse group with astounding ranges in body mass (approximately µg to g) [1,2], wingbeat frequency (15 to 1000 Hz) [3,4] and flying abilities (e.g., hovering, aerial maneuvers, sustained flight) [5]. Most insects realize flight through “indirect actuation”, 41 whereby the flight muscles pull directly on the exoskeletal shell surrounding the thorax rather than at the wing base. The thorax deformation is then transformed into flapping via a complex linkage called the wing hinge [6–8]. Indirect actuation is hypothesized to improve the energetic economy of flight by allowing elastic energy to be stored in the thorax between wing flaps [9]. Thorax elasticity is therefore of fundamental importance to efficient flight. Beyond indirect actuation, some insects possess specialized flight muscles believed to enhance flight efficiency. Many insects have “asynchronous” flight muscles, where one neurological signal generates several wingbeats [10]. This differs from the one-to-one ratio between muscle signaling and wingbeat observed in insects with “synchronous” flight muscles [10]. Asynchronous muscle function is enabled by stretch activation, where the tension caused by elongating one set of flight muscles triggers the antagonistic set of muscles to activate, thereby allowing mechanical muscle activation between neurological signals [11]. For synchronous muscle to activate, calcium must be cycled across the sarcoplasmic reticulum, which requires both time and energy [12]. Asynchronous muscles’ ability to activate without an action potential removes the need for extensive sarcoplasmic reticulum and calcium pumping. This allows more space for muscle fibers and enables higher wingbeat frequencies [12]. The evolution of asynchronous muscle may be accompanied by other physiological adaptations as well. For example, wing density per unit area is generally higher in insects with asynchronous musculature compared to those with synchronous musculature [4]. As a result, the inertial forces generated by the flapping wings are believed to be higher in insects with asynchronous musculature [13]. Aerodynamic forces generated by the flapping wings may also vary between asynchronous and synchronous groups, but they are generally on the same order as 42 the weight of the insect to produce sufficient lift for hover [14]. Unlike the flight muscle forces, which are applied at the dorsal/ventral and anterior/posterior thoracic walls, the aerodynamic and inertial forces generated by the flapping wing act at the fulcrum formed by the thoracic walls near the wing base. Though it is often thought that muscle action is the dominant source of thorax deformation, wing aerodynamic and inertial forces may deform the thoracic exoskeleton locally at the fulcrum. Consequently, recent studies have imagined the thorax as a system with elasticity distributed in two primary regions: a parallel elastic element, representative of the combined elasticity of the primary flight muscles and/or the compliant thorax walls they act on, and a series elastic element, representative of the (usually rotational) elasticity of the wing hinge and the thoracic exoskeleton immediately surrounding the wing base (Figure 3.1) [13]. Mathematical modeling has demonstrated the importance of both elastic elements to flight energetics [15], though there are few experimental studies that address elasticity distributions in real insects. 43 Figure 3.1 The insect thorax (left) can be idealized as a two degree-of-freedom mechanical model (right). Within the mechanical model, the elasticity is lumped into two components: a parallel elastic element of stiffness 𝑘𝑝 that represents the flight muscles and the thorax exoskeleton (highlighted in red), and a series elastic element of torsional stiffness 𝑘𝑠 that represents the rotational elasticity of the wing hinge and the thorax exoskeleton immediately surrounding the wing base (highlighted in blue). The parallel element deforms a distance 𝑥 directly under muscle force 𝐹, which causes the wing to rigidly rotate an amount θ. The wing may rotate an additional amount Φ about the wing hinge if the series element deforms under the inertial and aerodynamic loading of the wing. Left image adapted from [13,16]. Despite advances in our understanding of insect thorax mechanics and muscle physiology, there remain the questions: how is elasticity distributed throughout an insect thorax, and does this distribution differ between insects with synchronous and asynchronous flight musculature? The goal of the current study is to provide evidence for elasticity distributions in these two insect groups. Within this work, thorax elasticity is assumed to be lumped into series and parallel elements to remain consistent with recent modeling efforts [13,15]. The stiffness of the parallel elastic element can be measured directly via force-displacement testing on sacrificed insects. Conversely, the series element is more challenging to measure directly, as many insects 44 disengage their wings their wings post sacrifice. This renders the moment-angular displacement tests that are necessary to assess series element stiffness inaccessible. The two studies presented here estimate elasticity distributions in the thoraxes of insects with synchronous and asynchronous flight musculature. In the first study, thorax deformations and aerodynamic/inertial forces generated by the flapping wings are simultaneously measured in tethered flying insects. While this study does not directly measure stiffness of the series elastic element, it provides a quantitative measure of the forces that deform this element. Assuming that the wing hinge region and surrounding exoskeletal cuticle are similarly stiff across insects, the series elastic element will deform more when wing-generated forces are larger. While difficult to assess this assumption directly, thorax cuticle modulus is similar between hawkmoths and honeybees, which have synchronous and asynchronous flight musculature, respectively [17]. Thorax cuticle normalized by thorax diameter is similar between these species as well (unpublished data). This provides evidence that the relative series element stiffness is similar across insects, though additional studies that account for wing hinge soft tissue material properties and geometry are required to address this quantitatively. Within this work, the total wing generated force swill be used as a proxy for the relative influence of the series element. A second study is used to directly measure the stiffness of the parallel elastic element in multiple insect species. Insect thoraxes are quasi-statically compressed using the deformation amplitudes measured during the first study and the stiffness of the parallel elastic element is estimated via the slope of the resulting force-displacement curve. Together, these studies provide evidence that the relative influence of parallel and series elasticity in flapping wing insects differs between those with synchronous and asynchronous flight muscles. 45 3.2 Methods 3.2.1 Specimen Collection and Care Experiments were conducted on six insect species with synchronous and asynchronous musculature that spanned two orders of magnitude in mass (~10-2 to 100 grams). Species with asynchronous musculature included Bombus centralis (bumble bee), Xylocopa califo