{"title": "Flight Control in the Dragonfly: A Neurobiological Simulation", "book": "Advances in Neural Information Processing Systems", "page_first": 514, "page_last": 520, "abstract": null, "full_text": "Flight Control in the Dragonfly: \nA Neurobiological Simulation \n\nWilliam  E.  Faller  and  Marvin  W.  Luttges \n\nAerospace Engineering Sciences, \n\nUniversity of Colorndo, Boulder, Colorado 80309-0429. \n\nABSTRACT \n\nNeural network simulations of the dragonfly flight neurocontrol system \nhave  been  developed  to  understand  how  this  insect  uses  complex, \nunsteady  aerodynamics.  The  simulation  networks  account  for  the \nganglionic  spatial  distribution  of  cells  as  well  as  the  physiologic \noperating range and the stochastic cellular fIring history of each neuron. \nIn  addition  the  motor  neuron  firing  patterns,  \"flight  command \nsequences\", were utilized. Simulation training was targeted against both \nthe  cellular  and  flight  motor  neuron  firing  patterns.  The  trained \nnetworks  accurately  resynthesized  the  intraganglionic  cellular firing \npatterns. These in  tum controlled the  motor neuron fIring patterns that \ndrive  wing  musculature  during  flight.  Such  networks  provide  both \nneurobiological analysis tools and fIrst  generation controls for  the  use \nof \"unsteady\" aerodynamics. \n\n1  INTRODUCTION \n\nHebb (1949) proposed a theory of inter-neuronal learning. \"Hebbian Learning\", in which \ncells acting  together as assemblies alter the  effIcacy of mutual interconnections.  These \nneural \"cell assemblies\"  presumably comprise the information processing \"units\"  of the \nnervous system. \n\nTo provide one framework  within  which  to perform detailed analyses  of these cellular \norganizational  \"rules\"  a  new  analytical  technique  based  on  neural  networks  is  being \nexplored.  The neurobiological data analyzed was  obtained from  the  neurnl  cells of the \ndrngonfly ganglia. \n\n514 \n\n\fFlight Control in the Dragonfly: A Neurobiological Simulation \n\n515 \n\nThe dragonfly use of unsteady separated flows  to generate highly maneuverable flight is \ngoverned  by  the  control  sequences  that originate  in  the  thoracic  ganglia  flight  motor \nneurons  (MN).  To  provide  this  control  the  roughly  2200  cells  of  the  meso- and \nmetathoracic ganglia integrate environmental cues that include visual  input. wind shear, \nvelocity and acceleration. The cellular flring patterns coupled with proprioceptive feedback \nin turn drive elevator/depressor flight MNs which typically produce a 25-37 Hz wingbeat \ndepending on the flight mode (Luttges 1989; Kliss  1989). \n\nThe neural networks utilized in the analyses incorporate the spatial distribution of cells, \nthe physiologic operating range of each neuron and the stochastic history of the cellular \nspike trains (Faller and Luttges  1990). The present work describes two neural networks. \nThe simultaneous Single-unit firing  patterns at time (t)  were used  to  predict the cellular \nftring patterns at time (t+~). And, the simultaneous single-unit frring patterns were used \nto \"drive\" flight-MN frring patterns at a 37 Hz wingbeat frequency. \n\n2  METHODS \n\n2.1  BIOLOGICAL  DATA \n\nRecordings were obtained from  the mesothoracic ganglion of the dragonfly Aeshna  in the \nganglionic regions known  to  contain the cell  bodies of flight MNs as  well as small and \nlarge cell bodies (Simmons 1977; Kliss  1989). Multiple-unit recordings from  many cells \n(-40-80) were systematically decomposed to yield simultaneously active single-unit ftring \npatterns. The technique has been described elsewhere (Faller and Luttges in press). \n\nDuring  the recording of neural activity spontaneous flight episodes commonly occurred. \nThese events were consistent with typical flight episodes (2-3  secs duration) observed in \nthe tethered dragonfly  (Somps and Luttges  1985). For analysis, a  12 second record was \nobtained from  58  single units, 26 rostral cells and 32 caudal cells. The continuous record \nwas separated into 4 second behavioral epochs: pre-flight, flight and post-flight. \n\nA simplified model of one flight mode was assumed. Each forewing  is driven by 3 main \nelevator and 2 main depressor muscles, innervated by 11  and 14 MNs, respectively. A 37 \nHz MN firing frequency,  3-5 spikes per output burst, and 180 degree phase shift between \nantagonistic  MNs was  assumed.  Given  the  symmetrical nature of the elevator/depressor \noutput patterns only the  11  elevator MNs were simulated. \n\nPrior to  analysis  the  ganglionic  spatial  distribution  of neurons  was  reconstructed.  The \nimportance of this is reserved for later discussion. A method has been described (Faller and \nLuttges submitted:a) that resolves the spatial distribution based on two distancing criteria: \nthe amplitude ratio across electrodes and the spike angle (width) for each cell. Cells were \nsorted along a rostral, cell 1, to caudal, cell 58 continuum based on this infonnation. \n\nThe  middle 2  seconds  of the  flight  data was  simulated.  This  was  consistent with  the \nknown duration of spontaneous flight episodes. Within these 2 seconds, 44 cells remained \nactive, 19 rostral and 25 caudal. The cell numbering (1-58) derived for the biological data \nwas not altered. The remaining 14 inactive cells/units carry zeros in all analyses. \n\n\f516 \n\nFaller and Luttges \n\n2.2  MIMICKING  THE  SINGLE  CELLS \n\nEach  neuron  was  represented  by  a  unique  unit  that  mimicked  both  the  mean  fIring \nfrequency and dynamic range of the physiologic cell. The activation value ranged from \nzero to twice the nonnalized mean fIring frequency for each cell. The dynamic range was \ncalculated as a unique thermodynamic profile for each sigmoidal activation function. The \ntechnique has been described fully elsewhere (Faller and Luttges 1990). \n\n2.3  SPIKE  TRAIN  REPRESENT A TION \n\nThe  spike  trains  and  MN  firing  patterns  were  represented  as  iteratively  continuous \n\"analog\" gradients (Faller and Luttges 1990 &  submitted:b). Briefly. each spike train was \nrepresented in  two-dimensions based on the following assumptions:  (1) the mean fIring \nfrequency  reflects  the  inherent physiology  of each cell and (2)  the  interspike intervals \nencode the information transferred to other cells. Exponential functions were mapped into \nthe  intervals  between consecutive spikes  and  these  functions  were  then  discretized  to \nprovide  the  spike  train  inputs  to  the  neural  network.  These  functions  retain  the  exact \nspiking times and the temporal modulations (interval code) of cell fIring histories. \n\n2.4  ARCHITECTURE \n\nThe two simulation architectures were as follows: \n\nSimulation  1 \n\nSimulation  2 \n\n1 cell:l  unit (44  units) \n1 ceU:2  units (88  units) \n1 cell: 1 unit (44  total units) \n\nInput layer \nHidden layer \nOutput layer \nThe hidden units were recurrently connected and the interconnections between units were \nbased on a 1st order exponential rise and decay. The general architecture has been described \nelsewhere (Faller and Luttges 1990). \n\n1 cell:l  unit (44  units) \n1 cell:2 unit (88  units) \n11  main elevator MNs \n\nFor  the  cell-to-cell  simulation  no  bias  units  were  utilized.  Since  the  MNs  fire  both \nsynchronously and infrequently bias units were incorporated in the MN simulation. These \nunits  were  constrained  to  function  synchronously  at  the  MN  fuing  frequency.  This \nconstraining technique pennitted the network to be trained despite the sparsity of the MN \ndataset \n\nTraining was perfonned using a  supervised backpropagation algorithm in  time.  All 44 \ncells.  2000  points  per  discretized  gradient  (~=1  msec  real-time)  were  presented \nsynchronously to the network.  The results were consistent for L\\=2-5  msec  in  all  cases. \nThe simulation paradigms were as follows: \n\nSimulation  1 \n\nNeural activity at time (t) \n\nlnmJ.t \nOutput/Target  Neural activity at time (t+~) \nInitial weights were random. -0.3 and 0.3. and the learning rate was 1l=O.2. Training was \nperformed until  the  temporal  reproduction of cell  spiking patterns was  verified for  all \ncells. Following training. the network was \"run\". 1l  = o. \n\nNeural activity at time (t) \nMN activity at time (t) \n\nSimulation  2 \n\n\fFlight Control in the Dragonfly: A Neurobiological Simulation \n\n517 \n\nSum squared errors for aU  units were calculated and normalized to an activation value of 0 \nto  1. The temporal reproduction of the output patterns was  verified by  linear correlation \nagainst  the  targeted spike  trains.  The \"effective\"  contribution  of each  unit to  the  flight \npattern  was  then  determined by  \"lesioningrt  individual  cells  from  the  network  prior  to \npresenting the  input pattern. The effects of lesioning  were judged by the change in error \nrelative to the unlesioned network. \n\n3  RESULTS \n\n3.1  CELL\u00b7TO-CELL  SIMULATION \n\nFollowing training the complete pattern set was presented  to  the network. And. the sum \nsquared error was  averaged over aU  units.  Fig.  1.  Clearly  the  network  has a  different \n\"interpretationrt  of  the  data  at  certain  time  steps.  This  is  due  both  to  the \nomission/commission of spikes  as  well as  timing errors.  However.  the data  needed  to \nreproduce overall cell firing patterns is clearly available. \n\nc:t:l  ~ 1 \n\no~O~--------------------------------------------------~ \n00-20t \nffio.tO- ~ \n(zoo \n\nI  ~ \n\nI t 0'00 I \n\nJOOO I \n\n:to \n\n0.00 \n\nI \n\n, \n\nI \n\nI \n\nI \n\nI \n\nI \n\nI \n\nTIM!:  t4JWSECONDS) \n\nFigure  1:  The network error \n\nUnit sum squared errors were also averaged over the 2 second simulation. Fig. 2. Clearly \nthe network predicted some unil/cell flring patterns e:lSier than others. \n\n! ~ t. 0,0,0,0, ,ctili,D1dJlitIm, , ' , ,.DJlI1.1bdJJjJ,llilli),dli \n\n~ \n\n0 \n\n10 \n\n10 \n40 \nUNIT (SHOWN  BY  caJ.. NUYSER) \n\n~o \n\n~ \n\nso \n\nFigure  2:  The unit errors \n\nThe  temporal reproduction  of the cell firing  patterns was  verified by  linear correlation \nbetween the network outputs and the biological spike train representations. If the network \naccurately reproduces  the temporal history of the spike trains these functions should be \nidentical. r=1. Fig. 3. Clearly the network reproduces the temporal coding inherent within \neach spike train. The lowest correlation of roughly 0.85 is highly signffic:ult. (p<O.Ol). \n\nFigure 3:  The unit temporal errors \n\n\f518 \n\nFaller and Luttges \n\nOne  way  to  measure  the  relative  importance  of each  unit/cell  to  the  network  is  to \nomit/\"lesion It  each unit prior to  presenting the cell firing patterns to  the trained network. \nThe data shown was collected by  lesioning each unit individually, Fig. 4. The unlesioned \nnetwork  error  is  shown  as  the  \"0\"  cell.  Overall  the  degradation  of the  network  was \nminimal. Clearly some units provide more information to  the network in reproducing the \ncell fuing histories. Units that caused relatively large errors when \"lesioned\" were defmed \nas primary units. The other units were defined as secondary units. \n\n! ~t'Q.O'Q'QI'~'~'I\" '~'I'I'I.J1bJJ.Jl.JJ.1 \n\n20 \n40 \nUNIT (SHOWN  BY CElL NUMBER) \n\nto \n\no \n\nJO \n\n10 \n\n~O \n\n::I \n\nFigure  4:  Lesion  studies \n\nThe  primary  units  (cells)  form  what  might  classically  be  termed  a  central  pattern \ngenerator. These units can provide a relatively gross representation of both cellular and \nMN firing patterns. The generation of dynamic cellular and MN firing patterns. however 9 \nis  apparently  dependent  on  both  primary  and  secondary  units.  It  appears  that  the \ngeneration  of functional activity patterns within  the ganglia is  largely controlled by the \ndynamic  interactions  between  large  groups  of cells.  ie.  the  \"whole\"  network.  This  is \nconsistent with other results derived from  both  neural network and statistical analyses of \nthe biological data (Faller and Luttges 1990 & submitted:b). \n\n3.2  MOTOR  NEURON  FIRING  PATTERNS \n\nThe 44 cellular frring patterns were then  used to drive the MN ruing patterns. Following \ntraining. the cell fIring pattern set was presented to the network and the sum squared error \nwas averaged over the  output MNs. Fig. 5. The error in this case oscillates in time at the \nwingbeat  frequency  of 37  Hz.  As  will  be  shown.  however.  this  is  an artifact and  the \nnetwork does accurately drive the MNs. \n\n~ Iml \nIII om~ \u2022\u2022  ,  o  JIIIII U IIUllll!llllUllul II II U!lU 111111111 Uh Ulllilu 1111 IlluUIIL  , \n\nJobo  \" ~l \n\nnUE (t.IlWSfCONOS) \n\no \n0::  ~o \n\n1  00 \n\n2000 \n\nFigure 5:  The network error \n\nFor each MN the sum squared error was also averaged over the 2 second simulation. Fig. \n6. Clearly individual MNs contribute nearly equally to the network error. \n\n~ o~I-r==~==~==~==~==~==~==~==~==~~~~~:l \n\n~ ~t -+---L-I ~. I ~. I _____.. I ~. I ~. I + - - - ' - -1  I ~o I ~. I ,~I ,~I ,-'--tIl \n\n::::I \n\nQ \n\n12 \n\nUOTOR  NEURON  NUUBER \n\nI \n\nFigure  6:  The unit errors \n\n\fFlight Control in the Dragonfly: A Neurobiological Simulation \n\n519 \n\nThe temporal  reproduction  of the  MN  ftring  patterns  was  verifted  by  linear correlation \nbetween the output and targeted MN ftring patterns of the network. This is shown in Fig. \n7.  Clearly  the  cell  inputs  to  the  network  have  the  spiking  characteristics  needed  for \ndriving the temporal  ftring  sequences of the  MNs  innervating  the  wing musculature.  All \ncorrelations  are roughly  0.80.  highly  signiftcant.  (p<O.Ol).  The output  for  one  MN  is \nshown relative to  the  targeted MN output in  Fig.  8.  Clearly  the network does  drive  the \nMNs correctly. \n\n11.10.90 \nu \n\ng ,.oa! \ni~  I. \nE; \nu \n\na \n\n.1.1  \u2022 .  111.1. \n\nI  I \n\nI  I \n\nI \n\nI \n\nWOTOR  NEURON  NUUBER \n\nFigure 7:  The unit temporal errors \n\n12 \n\n~'AO~--------~------------~------------~~----------' \n~o.~ \n~o~o \n~ O.2! \n~ \nGO.OO~--~~~~20~--~~--~~--~----~6~~--~----teo~--~--~1~O \n~ \n\n-- TARGETED  MOTOR  NEURON  OUTPUT \n\n__  _UU' \u2022 .'\"ON  OUTPUT \n\nllUE CMIUJSECONDS} \n\n.;>...  \"\" .. \n\nFigure  8:  The  MN  flring  patterns \n\n3.3  SUMMARY \n\nThe  re~ults indicate  that synthetic  networks  can  learn  and  then  synthesize patterns  of \nneural  spiking  activity  needed  for  biological  function.  In  this  case,  cell and  MN  fIring \npatterns occurring in the dragonfly ganglia during a spontaneous flight episode. \n\n4  DISCUSSION \n\nRecordings  from  more  than  50  spatially  unique cells  that reflect the complex  network \ncharacteristics of a small. intact neural tissue were  used to successfully train two neural \nnetworks. Unit sum squared errors were less than 0.003 and spike train temporal histories \nwere accurately reproduced. There was little evidence for unexpected \"cellular behavior\". \nFunctional  lesioning  of single  units  in  the  network  caused  minimal  degradation  of \nnetwork performance. however. some lesioned cells were more important than others to \noverall network performance. \n\nThe  capability  to  lesion  cells  permitted  the  contribution  of individual  cells  to  the \nproduction of the flight rhythm to be detennined. The detection of primary and secondary \ncells  underlying  the dynamic  generation of both cellular and  MN  firing patterns  is  one \nexample.  Such  results  may  encourage  neurobiologists  to  adopt  neural  networks  as \neffective analytical tools with which to study and analyze spike train data. \n\nClearly  the  solution  arrived  at  is  not  the  biological  one.  However.  the  networks  do \naccurately predict the future cell firing patterns based on past flring  history information. It \n\n\f520 \n\nFaller and L u ttges \n\nis asserted that the network must therefore contain the majority of infonnation required to \nresolve  biological  cell  interactions  during  flight  in  the  dragonfly.  A  sample  of  58 \nganglionic cells was utilized. the remaining cells functional contributions are presumably \nstatistically  accounted  for  by  this  small  sampling.  The  inherent  \"infonnation\"  of the \nbiological network is presumably stored in  the weight matrices as a generalized statistical \nrepresentation of the \"rules\" through which cells participate in biological assemblies. \n\nAnalyses  of  the  weight  matrices  in  turn  may  permit  the  operational  \"rules\"  of cell \nassemblies to be defined. Questions about the effects of cell size. the spatial architecture \nof the network and the temporal interactions between cells as they relate to cell assembly \nfunction can be addressed. For this reason the individuality of cells. the spatial architecture \nand the stochastic cellular firing histories of the individual cells were retained within  the \nnetwork  architectures  utilized.  Crucial  to  these  analyses  will  be  methods  that permit \ndirect, time-incrementing evaluations of the weight matrices following training. \n\nBiological nervous system function can now be analyzed from  two points of view: direct \nanalyses of the biological data and indirect, but potentially more approachable, analyses of \nthe weight matrices from trained neural networks such as the ones described. \n\nREFERENCES \n\nFaller WE, Luttges MW (1990) A Neural  Network Simulation of Simultaneous Single(cid:173)\nUnit Activity Recorded from  the Dragonfly Ganglia. ISA Paper #90-033 \n\nFaller WE,  Luttges  MW (in  press)  Recording of Simultaneous Single-Unit Activity  in \nthe Dragonfly Ganglia. J Neurosci Methods \n\nFaller WE, Luttges MW (Submitted:a) Spatiotemporal Analysis of Simultaneous Single(cid:173)\nUnit Activity in the Dragonfly:  1.  Cellular Activity Patterns. Bioi Cybem \n\nFaller WE, Luttges MW (Submitted:b) Spatiotemporal Analysis of Simultaneous Single(cid:173)\nUnit Activity in  the Dragonfly: II. Network Connectivity. Bioi Cybem \n\nHebb DO (1949) The Organization of Behavior:  A Neuropsychological Theory.  Wiley, \nNew York, Chapman and Hall, London \n\nKliss  MH  (1989)  Neurocontrol  Systems  and  Wing-Fluid  Interactions  Underlying \nDragonfly Flight Ph.D. Thesis, University of Colorado. Boulder, pp 70-80 \n\nLuttges  MW  (1989)  Accomplished  Insect Fliers.  In:  Gad-el-Hale  M  (ed)  Frontiers  in \nExperimental Fluid Mechanics. Springer-Verlag, Berlin Heidelberg. pp 429-456 \n\nSimmons P  (1977) The Neuronal Control  of Dragonfly  Flight I. Anatomy.  J  exp  Bioi \n71:123-140 \n\nSomps C, Luttges MW (1985) Dragonfly flight: Novel uses of unsteady separated flows. \nScience 228:1326-1329 \n\n\fPart IX \n\nApplications \n\n\f\f", "award": [], "sourceid": 326, "authors": [{"given_name": "William", "family_name": "Faller", "institution": null}, {"given_name": "Marvin", "family_name": "Luttges", "institution": null}]}