Flight Control in the Dragonfly: 
A Neurobiological Simulation 
William E. Failer and Marvin W. Luttges 
Aerospace Engineering Sciences, 
University of Colorado, Boulder, Colorado 80309-0429. 
ABSTRACT 
Neural network simulations of the dragonfly flight neurocontrol system 
have been developed to understand how this insect uses complex, 
unsteady aerodynamics. The simulation networks account for the 
ganglionic spatial distribution of cells as well as the physiologic 
operating range and the stochastic cellular firing history of each neuron. 
In addition the motor neuron firing patterns, "flight command 
sequences", were utilized. Simulation training was targeted against both 
the cellular and flight motor neuron firing patterns. The trained 
networks accurately resynthesized the intraganglionic cellular firing 
patterns. These in turn controlled the motor neuron firing patterns that 
drive wing musculature during flight. Such networks provide both 
neurobiological analysis tools and first generation controls for the use 
of "unsteady" aerodynamics. 
1 INTRODUCTION 
Hebb (1949) proposed a theory of inter-neuronal learning, "Hebbian Learning", in which 
cells acting together as assemblies alter the efficacy of mutual interconnections. These 
neural "cell assemblies" presumably comprise the infomarion processing "units" of the 
nervous system. 
To provide one framework within which to perform detailed analyses of these cellular 
organizational "rules" a new analytical technique based on neural networks is being 
explored. The neurobiological data analyzed was obtained from the neural cells of the 
dragonfly ganglia. 
514 
Flight Control in the Dragonfly: A Neurobiological Simulation 515 
The dragonfly use of unsteady separated flows to generate highly maneuverable flight is 
governed by the control sequences that originate in the thoracic ganglia flight motor 
neurons (MN). To provide this control the roughly 2200 cells of the meso- and 
metathoracic ganglia integrate environmental cues that include visual input, wind shear, 
velocity and acceleration. The cellular f'tring pauems coupled with propfiocepfive feedback 
in turn drive elevator/depressor flight MNs which typically produce a 25-37 Hz wingbeat 
depending on the flight mode (Luttges 1989; Kliss 1989). 
The neural networks utilized in the analyses incorporate the spatial distribution of cells, 
the physiologic operating range of each neuron and the stochastic history of the cellular 
spike trains (Faller and Luttges 1990). The present work describes two neural networks. 
The simultaneous single-unit firing patterns at time (t) were used to predict the cellular 
firing patterns at time (t+A). And, the simultaneous single-unit firing patterns were used 
to "drive" flight-MN firing patterns at a 37 Hz wingbeat frequency. 
2 METHODS 
2.1 BIOLOGICAL DATA 
Recordings were obtained from the mesothoracic ganglion of the dragonfly Aeshna in the 
ganglionic regions known to contain the cell bodies of flight MNs as well as small and 
large cell bodies (Simmons 1977; Kliss 1989). Multiple-unit recordings from many cells 
(-40-80) were systematically decomposed to yield simultaneously active single-unit firing 
pauems. The technique has been described elsewhere (Failer and Lunges in press). 
During the recording of neural activity spontaneous flight episodes commonly occurred. 
These events were consistent with typical flight episodes (2-3 secs duration) observed in 
the tethered dragonfly (Somps and Luttges 1985). For analysis, a 12 second record was 
obtained from 58 single units, 26 rostral cells and 32 caudal cells. The continuous record 
was separated into 4 second behavioral epochs: pre-flight, flight and post-flight. 
A simplified model of one flight mode was assumed. Each forewing is driven by 3 main 
elevator and 2 main depressor muscles, innervated by 11 and 14 MNs, respectively. A 37 
Hz MN firing frequency, 3-5 spikes per output burst, and 180 degree phase shift between 
antagonistic MNs was assumed. Given the symmetrical nature of the elevator/depressor 
output patterns only the 11 elevator MNs were simulated. 
Prior to analysis the ganglionic spatial distribution of neurons was reconstructed..The 
importance of this is reserved for later discussion. A method has been described (Faller and 
Luttges submitted:a) that resolves the spatial distribution based on two distancing criteria: 
the amplitude ratio across electrodes and the spike angle (width) for each cell. Cells were 
sorted along a rostral, cell 1, to caudal, cell 58 continuum based on this information. 
The middle 2 seconds of the flight data was simulated. This was consistent with the 
known duration of spontaneous flight episodes. Within these 2 seconds, 44 cells remained 
active, 19 rostral and 25 caudal. The cell numbering (1-58) derived for the biological data 
was not altered. The remaining 14 inactive cells/units carry zeros in all analyses. 
516 Faller and Luttges 
2.2 MIMICKING THE SINGLE CELLS 
Each neuron was represented by a unique unit that mimicked both the mean firing 
frequency and dynamic range of the physiologic cell. The activation value ranged from 
zero to twice the normalized mean firing frequency for each cell. The dynamic range was 
calculated as a unique thermodynamic profile for each sigmoidal activation function. The 
technique has been described fully elsewhere (Failer and Luuges 1990). 
2.3 SPIKE TRAIN REPRESENTATION 
The spike trains and MN firing patterns were represented as iteratively continuous 
"analog" gradients (Failer and Luttges 1990 & submitted:b). Briefly, each spike train was 
represented in two-dimensions based on the following assumptions: (1) the mean firing 
frequency reflects the inherent physiology of each cell and (2) the interspike intervals 
encode the information transferred to other cells. Exponential functions were mapped into 
the intervals between consecutive spikes and these functions were then discretized to 
provide the spike train inputs to the neural network. These functions retain the exact 
spiking times and the temporal modulations (interval code) of cell firing histories. 
2.4 ARCHITECTURE 
The two simulation architectures were as follows: 
Simulation I 
Input laver 
Hidclen layer 
Outout laver 
1 cell: 1 unit (44 units) 
1 cell:2 units (88 units) 
1 cell  1 unit (44 total units) 
Simulation 2 
1 cell: 1 unit (44 units) 
1 cell:2 unit (88 units) 
11 main elevator MNs 
The hidden units were recurrently connected and the interconnections between units were 
based on a 1st order exponential rise and decay. The general architecture has been described 
elsewhere (Failer and Luttges 1990). 
For the cell-to-cell simulation no bias units were utilized. Since the MNs fire both 
synchronously and infrequently bias units were incorporated in the MN simulation. These 
units were consmined to function synchronously at the MN firing frequency. This 
constraining technique permitted the network to be trained despite the sparsity of the MN 
data set. 
Training was performed using a supervised backpropagation algorithm in time. All 44 
cells, 2000 points per discretized gradient (A=I msec real-time) were presefited 
synchronously to the network. The results were consistent for A=2-5 msec in all cases. 
The simulation paradigms were as follows: 
Simulation 1 Simulation 2 
Input Neural activity at time (0 Neural activity at time (0 
 Neural activity at time (t+A) MN activity at time (t) 
Initial weights were random, -0.3 and 0.3, and the learning rate was q=0.2. Training was 
performed until the temporal reproduction of cell spiking patterns was verified for all 
cells. Following training, the network was "run", q = 0. 
Flight Control in the Dragonfly: A Neurobiological Simulation 517 
Sum squared errors for all units were calculated and normalized to an activation value of 0 
to 1. The temporal reproduction of the output patterns was verified by linear correlation 
against the targeted spike trains. The 'effective" contribution of each unit to the flight 
pattern was then determined by 'esioning" individual cells from the network prior to 
presenting the input pattern. The effects of lesionlag were judged by the change in error 
relative to the unlesioned network. 
3 RESULTS 
3.1 CELL-TO-CELL SIMULATION 
Following training the complete pattern set was presented to the network. And, the sum 
squared error was averaged over all units, Fig. 1. Clearly the network has a different 
'interpretation" of the data at certain time steps. This is due both to the 
omission/commission of spikes as well as timing errors. However, the data needed to 
reproduce overall cell f'wing patterns is clearly available. 
nM (UlI.LI[L"OND) 
Figure 1: The network error 
Unit sum squared errors were also averaged over the 2 second simulation, Fig. 2. Clearly 
the network predicted some unit/cell f'mng patterns easier than others. 
n,, (2.002 t - 
o ool 
:2 0 10 20 20 4.0 0 60 
UNIT (,.IOWN Err'  NUUBE) 
Figure 2: The unit errors 
The temporal reproduction of the cell firing patterns was verified by linear correlation 
between the network outputs and the biological spike train representations. If the network 
accurately reproduces the temporal history of the spike wains these functions should be 
identical, r=-l, Fig. 3. Clearly the network reproduces the temporal coding inherent within 
each spike wain. The lowest correlation of roughly 0.85 is highly significant, (p<0.01). 
Figure 3: The unit temporal errors 
518 Faller and Luttges 
One way to measure the relative importance of each unit/cell to the network is to 
omit/"lesion" each unit prior to presenting the cell firing patterns to the trained network. 
The data shown was collected by lesioning each unit individually, Fig. 4. The unlesioned 
network error is shown as the "0" cell. Overall the degradation of the network was 
minimal. Clearly some units provide more information to the network in reproducing the 
cell f'u'ing histories. Units that caused relatively large errors when "lesioned" were deftned 
as primary units. The other units were defined as secondary units. 
0.4 
o.1 .m..m.m I . .r171 
.0 .............. '- ........... :|::: .............. : ..... :--: 
UNIT (SHOWN BY CELL NUMBEr) 
Figure 4: Lesion studies 
The primary units (cells) form what might classically be termed a central pattern 
generator. These units can provide a relatively gross representation of both cellular and 
MN firing patterns. The generation of dynamic cellular and MN f'u'ing patterns, however, 
is apparenQy dependent on both primary and secondary units. It appears that the 
generation of functional activity patterns within the ganglia is largely controlled by the 
dynamic interactions between large groups of cells, ie. the "whole" network. This is 
consistent with other results derived from both neural network and statisdcal analyses of 
the biological data (Failer and Luttges 1990 & submitted:b). 
3.2 MOTOR NEURON FIRING PATTERNS 
The 44 cellular f'mng patterns were then used to drive the MN f'u'ing patterns. Following 
training, the cell f'mng pattern set was presented to the network and the sum squared error 
was averaged over the output MNs, Fig. 5. The error in this case oscillates in time at the 
wingbeat frequency of 37 Hz. As will be shown, however, this is an artifact and the 
network does accurately drive the MNs. 
La o.oo b. ' .. : : l boO ' ' ' ' ......... ' .... oto: : : oo 
2000 
UE (WLUSEONO) 
Figure : The network error 
For each MN the sum squared error was also averaged over the 2 second simulation, Fig. 
6. Clearly individual MNs contribute nearly equally to the network error. 
0.002 
0.001 
0.000 
0 6 
MOTOR NEURON NUMBER 
Figure 6: The unit errors 
12 
Flight Control in the Dragonfly: A Neurobiological Simulation 519 
The temporal reproduction of the MN firing pauems was verified by linear correlation 
between the output and targeted MN firing patterns of the network. This is shown in Fig. 
7. Clearly the cell inputs to the network have the spiking characteristics needed for 
driving the temporal fining sequences of the MNs innervating the wing musculature. All 
correlations are roughly 0.80, highly significant, (p<0.01). The output for one MN is 
shown relative to the targeted MN output in Fig. 8. Clearly the network does drive the 
MNs correctly. 
la 
 O.80 
i 0'7O 6 
ca MOTOR lIB.IRON NUMBER 
Figure 7: The unit temporal errors 
12 
,11.oo 
0.7 
0.50 
0.2 
0.00 0 
Figure 8: The MN firing patterns 
3.3 SUMMARY 
The results indicate that synthetic networks can learn and then synthesize patterns of 
neural spiking activity needed for biological function. In this case, cell and MN f'mng 
patterns occumng in the dragonfly ganglia during a spontaneous flight episode. 
4 DISCUSSION 
Recordings from more than 50 spatially unique cells that reflect the complex network 
characteristics of a small, intact neural tissue were used to successfully train two neural 
networks. Unit sum squared errors were less than 0.003 and spike train temporal histories 
were accurately reproduced. There was little evidence for unexpected "cellular behavior". 
Functional lesioning of single units in the network caused minimal degradation of 
network performance, however, some lesioned cells were more important than others to 
overall network performance. 
The capability to lesion cells permitted the contribution of individual cells to the 
production of the flight rhythm to be determined. The detection of primary and secondary 
cells underlying the dynamic generation of both cellular and MN firing patterns is one 
example. Such results may encourage neurobiologists to adopt neural networks as 
effective analytical tools with which to study and analyze spike wain data. 
Clearly the solution arrived at is not the biological one. However, the networks do 
accurately predict the future cell faring patterns based on past firing history information. It 
520 Faller and Luttges 
is asserted that the network must therefore contain the majority of information required to 
resolve biological cell interactions during flight in the dragonfly. A sample of 58 
ganglionic cells was utilized, the remaining cells functional contributions are presumably 
statistically accounted for by this small sampling. The inherent "information" of the 
biological network is presumably stored in the weight matrices as a generalized statistical 
representation of the "rules" through which cells participate in biological assemblies. 
Analyses of the weight matrices in turn may permit the operational "rules" of cell 
assemblies to be defined. Questions about the effects of cell size, the spatial architecture 
of the network and the temporal interactions between cells as they relate to cell assembly 
function can be addressed. For this reason the individuality of cells, the spatial architecture 
and the stochastic cellular firing histories of the individual cells were retained within the 
network architectures utilized. Crucial to these analyses will be methods that permit 
direct, time-incrementing evaluations of the weight matrices following training. 
Biological nervous system function can now be analyzed from two points of view: direct 
analyses of the biological data and indirect, but potentially more approachable, analyses of 
the weight matrices from trained neural networks such as the ones described. 
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Unit Activity Recorded from the Dragonfly Ganglia. ISA Paper g90-033 
Faller WE, Luttges MW (in press) Recording of Simultaneous Single-Unit Activity in 
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Failer WE, Luttges MW (Submitted:a) Spatiotemporal Analysis of Simultaneous Single- 
Unit Activity in the Dragonfly: I. Cellular Activity Patterns. Biol Cybern 
Failer WE, Luttges MW (Submitted:b) Spafiotemporal Analysis of Simultaneous Single- 
Unit Activity in the Dragonfly: II. Network Connectivity. Biol Cybern 
Hebb DO (1949) The Organization of Behavior: A Neuropsychological Theory. Wiley, 
New York, Chapman and Hall, London 
Kliss MH (1989) Neurocontrol Systems and Wing-Fluid Interactions Underlying 
Dragonfly Flight. Ph.D. Thesis, University of Colorado, Boulder, pp 70-80 
Luttges MW (1989) Accomplished Insect Fliers. In: Gad-el-Hak M (ed) Frontiers in 
Experimental Fluid Mechanics. Springer-Verlag, Berlin Heidelberg, pp 429456 
Simmons P (1977) The Neuronal Control of Dragonfly Flight I. Anatomy. J exp Biol 
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Science 228:1326-1329 
Part IX 
Applications 
