An Analog VLSI Model of Central Pattern 
Generation in the Leech 
Micah S. Siegel* 
Department of Electrical Engineering 
Yale University 
New Haven, CT 06520 
Abstract 
I detail the design and construction of an analog VLSI model of the 
neural system responsible for swimming behaviors of the leech. Why 
the leech? The biological network is small and relatively well 
understood, and the silicon model can therefore span three levels of 
organization in the leech nervous system (neuron, ganglion, system); it 
represents one of the first comprehensive models of leech swimming 
operating in real-time. The circuit employs biophysically motivated 
analog neurons networked to form multiple biologically inspired silicon 
ganglia. These ganglia are coupled using known interganglionic 
connections. Thus the model retains the flavor of its biological 
counterpart, and though simplified, the output of the silicon circuit is 
similar to the output of the leech swim central pattern generator. The 
model operates on the same time- and spatial-scale as the leech nervous 
system and will provide an excellent platform with which to explore 
real-time adaptive locomotion in the leech and other "simple" 
invertebrate nervous systems. 
1. INTRODUCTION 
A Central Pattern Generator (CPG) is a network of neurons that generates rhythmic 
output in the absence of sensory input (Rowat and Selverston, 1991). It has been 
Present address: Micah Siegel, Computation and Neural Systems, Mail Stop 139-74 
California Institute of Technology, Pasadena, CA 91125. 
622 
An Analog VLSI Model of Central Pattern Generation in the Leech 623 
I tonic 
width 
Figure 1. Silicon neuromime. The circuit includes tonic excitation, inhibitory synapses 
and an inhibitory recovery time. Note that there are two inhibitory synapses per device. 
Iionic sets the level of tonic excitatory input; Vinhib sets the synaptic strength; Irecoy 
.determines the inhibitory recovery time. 
suggested that invertebrate central pattern generation may represent an excellent theatre 
within which to explore silicon implementations of adaptive neural systems: invertebrate 
CPG networks are orders of magnitude smaller than their vertebrate counterparts, much 
detailed information is available about them, and they guide behaviors that may be of 
technological interest (Ryckebusch et al., 1989). Furthermore, CPG networks are 
typically embedded in larger neural circuits and are integral to the neural correlates of 
adaptive behavior in many natural organisms (Friesen, 1989). 
On strategy for modeling "simple" adaptive behaviors is first to evolve a biologically 
plausible framework within which to include increasingly more sophisticated and 
verisimilar adaptive mechanisms; because the model of leech swimming presented in this 
paper encompasses three levels of organization in the leech central nervous system, it 
may provide an ideal such structure with which to explore potentially useful adaptive 
mechanisms in the leech behavioral repertoire. Among others, these mechanisms include: 
habituation of the swim response (Debski and Friesen, 1985), the local bending reflex 
(Lockery and Kristan, 1990), and conditioned learning of the stepping and shortening 
behaviors (Sahley and Ready, 1988). 
624 Siegel 
B 
phase 
$0  
100  
123  t L. 
282 t , 
c 
Figure 2. The individual ganglion. (A) Cycle phases of the 
oscillator neurons in the biological ganglion (from Friesen, 
1989). (B) Somatic potential of the simplified silicon 
ganglion. (C) Circuit diagram of silicon ganglion using cells 
and synaptic connections identified in the leech ganglion. 
2. LOCOMOTORY CPG IN THE LEECH 
As a first step toward modeling a full repertoire of adaptive behavior in the medicinal 
leech (Hirundo medicinalis), I have designed, fabricated, and successfully tested an analog 
silicon model of one critical neural subsystem w the coupled oscillatory central pattern 
generation network responsible for swimming. A leech swims by undulating its 
segmented body to form a rearward-progressing body wave. This wave is analogous to 
the locomotory undulations of most elongated aquatic animals (e.g. fish), and some 
terrestrial amphibians and reptiles (including salamanders and snakes) (Friesen, 1989). 
The moving crests and troughs in the body wave are produced by phase-delayed contractile 
rhythms of the dorsal and ventral body wall along successive segments (Stent and Kristan, 
1981). The interganglionic neural subsystem that subserves this behavior constitutes an 
important modeling platform because it guides locomotion in the leech over a wide range 
of frequencies and adapts to varying intrinsic and extrinsic conditions (Debski and Friesen, 
1985). 
In the medicinal leech, interneurons that coordinate the rearward-progressing swimming 
contractions undergo oscillations in membrane potential and fire impulses in bursts. It 
appears that the oscillatory activity of these interneurons arises from a network rhythm 
that depends on synaptic interaction between neurons rather than from an endogenous 
polarization rhythm arising from inherently oscillatory membrane potentials in individual 
An Analog VLSI Model of Central Pattern Generation in the Leech 625 
A 
ganglion: 9 10 11 
head tail 
B 
28 
9{27 
123 :_ 
123 
28 
103 ms 
Figure 3. The complete silicon model. (A) Coupled oscillatory ganglia. As in the leech 
nervous system, interganglionic connections employ conduction delays. (B) Somatic 
recording of cells (28, 27, 123) from three midbody ganglia (9,10,11) in the silicon 
model. Notice the phase-delay in homologous cells of successive ganglia. (The apparent 
"beat" frequencies riding on the spike bursts are an aliasing artifact of the digital 
oscilloscope measurement and the time-scale; all spikes are approximately the same 
height.) 
neurons (Friesen, 1989). The phases of the oscillatory interneurons form groups clustered 
about three phase points spaced equally around the activity cycle. To first 
approximation, all midbody ganglia of the leech nerve cord express an identical activity 
rhythm. However, activity in each ganglion is phase-delayed with respect to more 
anterior ganglia (Friesen, 1989); presumably this is responsible for the undulatory body 
wave characteristic of leech swimming. 
626 Siegel 
3. THE SILICON MODEL 
The silicon analog model employs biophysically realistic neural elements (neuromimes), 
connected into biologically realistic ganglion circuits. These ganglion circuits are 
coupled together using known interganglionic connections. This silicon model thus 
spans three levels of organization in the nervous system of the leech (neuron, 
ganglion, system), and represents one of the first comprehensive models of leech 
swimming (see also Friesen and Stent, 1977). The hope is that this model will provide a 
framework for the implementation of adaptive mechanisms related to undulatory 
locomotion in the leech and other invertebrates. 
The building block of the model CPG is the analog neuromime (see figure 1); it exhibits 
many essential similarities to its biological counterpart. Like CPG interneurons in the 
leech swim system, the silicon neuromime integrates current across a somatic 
"capacitance" and uses positive feedback to generate action potentials whose frequency is 
determined by the magnitude of excitatory current input (Mead, 1989). In the leech swim 
system, nearly tonic excitatory input is transformed by a system of inhibition to produce 
the swim pattern (Friesen, 1989); adjustable tonic excitation is therefore included in 
the individual silicon neuromime. 
Inhibitory synapses with adjustable weights are also implemented. Like its 
biological counterpart, the silicon neuromime includes a characteristic recovery time from 
inhibition. From theoretical and experimental studies, such inhibition recovery time is 
thought to play an important functional role in the interneurons that constitute the leech 
swim system (Friesen and Stent, 1977). Axonal delays have been demonstrated in the 
intersegmental interaction between ganglia in the leech. Similar axonal delays have been 
implemented in the silicon model using shifting delay lines. 
The building block of the distributed model for the leech swim system is the ganglion. 
These biologically motivated silicon ganglia are constructed using only (though not all) 
identified cells and synaptic connections between cells in the biological system. Cells 
27, 28, and 123 constitute a central inhibitory loop within each ganglion. Figure 2 
exhibits the simplified diagram and the cycle phases of oscillatory interneurons in both 
the biological and the silicon ganglion. As in the leech ganglion, the phase relationships 
in the model ganglion fall into three groups, with cells 27, 28, and 123 participating each 
in the appropriate group of the oscillatory cycle. It is interesting that, though the silicon 
model captures the spirit of the tri-phasic output, the model is imprecise with respect to 
the exact phase locations of cells 27, 28, and 123 within their respective groups. This 
discrepancy between the silicon model and the biological system may point to the 
significance of other swim interneurons for swim pattern generation in the leech. 
Undoubtedly, the additional oscillatory interneurons sculpt this tri-phasic output 
significantly. 
The silicon model of coupled successive segments in the leech is implemented using 
these silicon neurons and biologically motivated ganglia. The model employs 
interganglionic connections known to exist in the biological system and generates 
qualitatively similar output at the same time-scale as the leech system. It appears in the 
leech that synchronization between ganglia is governed by the interganglionic synaptic 
interaction of interneurons involved in the oscillatory pattern rather than by autonomous 
An Analog VLSI Model of Central Pattern Generation in the Leech 627 
coordinating neurons (Friesen, 1989). In the silicon model, interganglionic interaction is 
represented by a projection from more anterior cell 123 to more posterior cell 28; this 
B 
100 ms 
7igure 4. Phase lag between more anterior and more posterior 
segments in both systems. (A) Intersegmental phase lag in 
the leech swim system (from Friesen, 1989). (B) 
Intersegmental phase lag in the silicon model. Though not 
shown in the figure, this cycle repeats at the same frequency as 
the cycle in A. (Note change of time scale.) 
projection is also observed between cells 123 and 28 of successive ganglia in the leech 
(Friesen, 1989), however it is by no means the only such interganglionic connection. In 
addition, the biological system utilizes conduction delays in its interganglionic 
projections; each of these is modeled in the silicon system by a delay line (Friesen and 
Stent, 1977) analogous to an active cable with adjustable propagation speed. Figure 3 
demonstrates the silicon model of three coupled ganglia with transmission delays. Notice 
that neuromimes in each successive ganglion are phase-delayed from homologous 
neuromimes in more anterior ganglia. Figure 4 shows this phase delay more explicitly. 
4. DISCUSSION 
The analog silicon model of central pauern generation in the leech successfully captures 
design principles from three levels of organization in the leech nervous system and has 
been tested over a wide range of network parameter values. It operates on the same time- 
scale as its biological counterpart and gives rise to ganglionic activity that is qualitatively 
similar to activity in the leech ganglion. Furthermore, it maintains biologically 
plausible phase relationship between homologous elements of successive ganglia. The 
design of the silicon model is intentionally compatible with analog Very Large Scale 
Integration (VLSI) technology, making its integrated spatial-scale close to that of the 
leech nervous system. It is interesting that this highly simplified model captures 
qualitatively the output both within and between ganglia of the leech; it may be 
illuminating to explore the functional significance of other swim interneurons by their 
inclusion in similar silicon networks. The current model provides an important platform 
for future implementations of invertebrate adaptive behaviors, especially those behaviors 
related to swim and other locomotory pattern generation. The hope is that such behaviors 
628 Siegel 
can be evolved incrementally using neuromime models of identified adaptive interneurons 
to modulate the swim central pattern generating network. 
Acknowledgments 
I would like to thank the department of Electrical Engineering at Yale University for 
encouraging and generously supporting independent undergraduate research. 
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