Keywords

1 Introduction

Biological model systems are studied to understand distinctive biological processes and mechanisms. Along these lines various species are investigated because it is believed that explorations made in the model organism will render insight into the working principles of other organisms, including humans. Well known examples which have been extensively studied are mice, rats, zebrafish, the fruit fly Drosophila melanogaster and the nematode worm Caenorhabditis elegans [1,2,3,4]. Despite the immense differences in the details, it is believed that the most basal mechanisms of development are recapitulated in all animals and are evolved from the earliest animal ancestors. Hence, the elucidation of a developmental process in one animal is often of importance for understanding development in another [5]. Despite the significance of model systems for comparative studies in biology, they may also present novel guidelines for the field of bio-inspired engineering. The goal hereby is to extract evolutionary shaped basal biological mechanisms from the point of power efficiency and sensitivity and transfer those to technology. Visual information processing in the relatively simple T. cystophora nervous system offers a unique opportunity to reverse engineer pattern recognition electronic hardware, and thereby circumvent the need for processing computers to run pattern recognition software. Fast responding pattern recognition hardware could support self-guiding robotic vehicles or automated driving assistants. Here, we consider the visual system of the box jellyfish and realize their optical communication principles in electronic circuitry comprising a set of coupled relaxation-type oscillators [6, 7]. In the first stage we simulate the circuitry by LTSpice XVII [8]. In the present theoretical study, coupled relaxation-type oscillators with a fixed topology enabled essential box jellyfish motor effector activation used in coordinated swimming, hovering, and turning [9].

2 The Box Jellyfish: Anatomy, Dynamic and Behavior

The box jellyfish Tripedalia cystophora is emerging as a new model system for basic visual information processing. Photographs of the visual system and nervous system of T. cystophora are shown in Fig. 1 [10]. The T. cystophora model system is attractive due to its vertebrate like camera type eyes [11, 12], multiple distinct visual behaviors [13,14,15,16], and an experimentally tractable central nervous system comprising approximately 1000–1500 processing neurons [17, 18].

Fig. 1
figure 1

Figure adapted from [10]

The visual system and nervous system of Tripedalia cystophora. a An adult specimen of the mangrove dwelling box jellyfish Tripedalia cystophora has a bell diameter of about 10 mm. b, c The eye-brain complexes (rhopalia) each carries 6 eyes, of four morphological different types, and the processing neural circuitry. The four rhopalia are suspended from the sides of the bell by a flexible stalk and weighed down by a crystal on the distal end. The epidermal stalk nerve conveying the motor signal is located in the medial side of the stalk. A circumnavigating ring nerve enables inter-rhopalial communication (a). PE: pit eye, SE: slit eye, ULE: upper lens eye, LLE: lower lens eye.

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2.1 Visual system

The visual system of T. cystophora, and box jellyfish in general, comprises 24 eyes of four distinct different types. Eight of these are vertebrate like camera type lens eyes complete with ‘Matthiessen’s ratio’ lens with graded refractive index, retina with opsin-based photoreceptors, and pigment screen to accommodate directional vision [12, 19, 20]. The eyes are distributed on four sensory structures termed rhopalia (see Fig. 1b and c), each of which is carrying two lens eyes and four ‘lesser’ eyes [12, 20]. The rhopalium also carries the processing neuronal circuitry used to process the visual information collected from the eyes. The rhopalia are suspended from the sides of the animal by a flexible stalk, which contains the efferent epidermal motor nerve, and are inter-connected through a ring nerve that circumnavigates the medusoid bell (Fig. 1a) [21]. It is thought that the ring nerve is involved in inter-rhopalial communication and, at least to some degree, coordinates the contraction of the bell [22]. A calcium sulphate hemihydrate crystal [23] at the distal end ensures a constant vertical orientation of the rhopalium and thereby constant field of view of the lens eyes [15, 24]. The lens eyes are thought to be special purpose eyes modulating specific visual behaviors. The upper lens eye is directed out of the water and into Snell’s window. Snell’s window is a physical phenomenon created by the difference in refractive indices between air and water that visually compresses the 180\(^\circ \) hemisphere above water into an approximately 97\(^\circ \) underwater cone. The visual field of just below 100\(^\circ \) perfectly matches the upper lens eye to Snell’s window [12]. By adjusting the direction and angle of the visual field to accommodate visual information received from Snell’s window, the upper lens eye can detect the contrast line between the mangrove canopy and the open sky as a bright line on a dark background [24]. T. cystophora can thereby use terrestrial cues for long distance navigation [15]. Tidal currents constantly pose the risk of sweeping T. cystophora into the middle of the mangrove creek lagoon and subsequently to the open sea. Being swept away from the primary habitat would prove fatal to the animal since T. cystophora forage in light shafts created by sunlight shining through the mangrove tree foliage and between the prop roots [16], where their photo tactic copepod prey is abundant. Therefore, if the animal finds itself under the open sky, it will quickly turn and swim back under the canopy [15]. The lower lens eye is directed 60\(^\circ \) into the water and with a visual field of approximately 170\(^\circ \) scans the underwater environment for potentially dangerous objects [12, 13]. It has been shown that the lower lens eye overrides the upper lens eye, indicating that underwater input is regarded of higher importance than above water input [25]. Intuitively a sensible prioritization since collision with the prop roots of the mangrove trees poses an immediate danger of inflicting fatal damage to the fragile box jellyfish bell. As mentioned, the rhopalia are interconnected through the ring nerve and the overall behavior of the animal results from coordination between the rhopalia, prioritizing the rhopalium that detect changes in the visual environment [26,27,28].

2.2 Obstacle Avoidance Behavior

When T. cystophora encounters an underwater obstacle it will perform 4–5 fast bell contractions, turn 120–180\(^\circ \) and swim away (Fig. 2) [13]. This distinct visual behavior is modulated by the lower lens eye and is based on true spatial vision. The animal shows a graded avoidance response to varying contrasts of the obstacles, higher contrast yielding greater response–presumably an inherent gauge of distance under water [14]. Under the canopy, T. cystophora explores the mangrove habitat in search of foraging opportunities in the light shafts (Fig. 2a). When the animal encounters an underwater object, it will estimate the distance by the contrast of the object compared to the surrounding water. When the contrast surpasses the response threshold (Fig. 2b), the obstacle avoidance behavior will be initiated, which, as mentioned, consists of 4–5 fast bell contractions and directional control of the velarium (Fig. 2c). The velarium is a membrane-like constriction of the oral opening of the box jellyfish bell that can be asymmetrically constricted to form directionally controlled jet propulsion of the water flow created by the bell contraction [26]. This enables the animal to turn 180\(^\circ \) within 2–3 bell contractions. The bell contracting motor output signal is generated by oscillatory, or pacemaker, cells located on the rhopalium at the base of the stalk [18, 29]. The pacemaker cells have never been unequivocally identified but are thought to be what has been described as ‘giant neurons’ in the literature [17, 18]. Regardless of location in the rhopalial nervous system (RNS), the pacemaker cells produce a swim pacemaker signal that contracts the box jellyfish bell in a 1:1 manner. The intrinsic pacemaker cell frequency is 3–4 Hz, which is suppressed by neuropeptidergic mediation [30] to approximately 0.5–1 Hz. The latter corresponds to leisurely swimming and foraging in the mangrove habitat. The duration of one bell contraction from fully expanded bell to fully expanded bell is approximately 250 ms, corresponding to an absolute physiological relevant maximum of 4 Hz. Usually the animals display swim contractions of less than 3 Hz even during obstacle avoidance events.

Fig. 2
figure 2

Obstacle avoidance behavior. a Tripedalia cystophora navigating the mangrove habitat must avoid collision with underwater object to prevent damaging the fragile bell. b When the box jellyfish encounters an obstacle estimated close enough to pose an immediate danger, the animal will initiate obstacle avoidance behavior. c Obstacle avoidance behavior comprises 4-5 fast bell contractions, turning 120–180\(^\circ \)  and swimming away from the obstacle

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2.3 Pacemaker Activity Represents Behavior

The swim pacemaker signals can be recorded from the efferent epidermal stalk nerve (Fig. 3) by a suction electrode (extracellular electrophysiology). The pacemaker signals are 45 ms signals with a profile easily discernable from regular action potentials (Fig. 3d). Since swim contractions are the only means of locomotion in T. cystophora the pacemaker signals characterize the behavior of the entire animal. This correlation is prominent when presenting light-ON and light-OFF stimuli to the lower lens eye. If a rhopalium is kept in the dark for a few minutes the pacemaker signal frequency will stabilize around 0.5–1 Hz. If subsequently the lower lens eye is presented with a light ON stimulus, the pacemaker signal frequency will suddenly decrease and sometimes completely cease. Conversely, a light-OFF stimulus to a light adapted lower lens eye will result in a sudden increase in pacemaker signal frequency. Whereas the light-ON response is long lasting (scale of minutes), the light-OFF response is transient and lasts about 10 s [25]. The pacemaker signal response is directly related to the foraging behavior of T. cystophora. When the box jellyfish enters a light shaft (light-ON), where phototactic copepod prey is abundant, the animal will cease swimming and start fishing by passively sinking with outstretched tentacles. If T. cystophora inadvertently swims out of the light shaft (light-OFF) it will perform a number of high frequency swim bell contractions, turn, and try to relocate the light shaft [16].

Fig. 3
figure 3

Figure adapted from [30]

Pacemaker signals predict the behavior of Tripedalia cystophora. a To record the motor neuron output signals (pacemaker signals) the stalk is transected at about 2/3 of the distance to the bell. b This section reveals the two medially located epidermal stalk nerves (EN) where an extracellular electrophysiological suction electrode can be attached. c With the electrode in place, visual stimulation of the lower lens eye (LLE) can be performed and the responding pacemaker activity recorded. d Intrinsic pacemaker signal activity recorded from the EN (red arrowheads). The pacemaker signals have significant longer duration (45 ms) than normal action potentials. ULE: upper lens eye.

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2.4 Lens Eye Morphology and Activity

Light entering the lens eye is first refracted by the lens and focused onto the retina. The lenses of the upper and lower lens eyes are of remarkable high quality and capable of producing images on the retina with high spatial resolution. However, the retinas of the lens eyes are displaced closer to the lens than the focal plane of the lens. This severe under-focus is thought to remove fine image details to avoid overloading the processing circuitry. With this under-focus the receptive fields of the photoreceptors are 15–20\(^\circ \) depending on their location in the retina [12]. The upper and lower lens eyes comprise 400 and 600 cone-like photoreceptors respectively. The light sensitivity is accomplished through a c type opsin (cnidops), cAMP, and an opsin Gs pathway which hyperpolarizes the photoreceptor membrane [31, 32]. The photoreceptors are interconnected through invaginated chemical synapses [33] and, since the box jellyfish retina is everted, articulate directly on putative second order neurons. The everted retina means that the light strikes the outer photoreceptive signals directly and that the animals do not have blind spots as in vertebrate eyes, where the afferent optic nerve exits the retina (optic disk).

2.5 Rhopalial Nervous System Organisation

The organization of the RNS is not yet understood in detail. However, visual information, detected by the lens eyes, is processed in putative second order neurons and subsequently applied to modulate swim pacemaker signal frequency. The swim pacemaker cell cluster is a central convergent and translatory hub for processed sensory information. The visual input in turn modulates the pacemaker cell cluster activity and is here translated into the motor signal that controls the motor effectors of the box jellyfish bell. The swim bell contractions are the only means of locomotion for the box jellyfish so the swim pacemaker signals can be used as indication of the behaviour of the animal. The advantage is, as mentioned, that we do not need to examine the entire animal to determine a behavioural reaction to a given visual stimulus [25, 34].

2.6 Retinal Organization, Bipolar Cells Connectivity to ON- and OFF- Ganglion Cells

Vertebrate photoreceptors signal through a type c-opsin and a G-protein cGMP transduction cascade [35] and the photoreceptors thereby hyperpolarize in response to light ON stimuli [36]. In mammalian retinas, bipolar cells respond selectively to the photoreceptor activity. In the dark, the constant release of glutamate from the cone cells keep ON-bipolar cell membranes hyperpolarized, but at light-ON hyperpolarization of the photoreceptor membrane reduces glutamate release, inducing depolarization of the bipolar cell membrane. In contrast OFF-bipolar cells remain hyperpolarized in light-ON conditions and depolarizes in response to light-OFF events. Retinal ganglion cells subsequently integrate neuronal information from several bipolar cells to produce firing rates corresponding to the received information. Ganglion cells have circular receptive fields with specialized center and antagonistic surround regions (eg. ON-center–OFF-surround). Depending on the type of ganglion cell the firing rate is modulated by light illumination of the center- or surround region. ON-center ganglion cells have low rates of firing under dim illumination and rapidly increase firing in response to light-ON stimulus in the center of their receptive field. In contrast, OFF-center ganglion cells discharge at low rates under light conditions and rapidly increase firing rates by light-OFF stimulus to their receptive field center [36]. The corresponding classes of bipolar and ganglion cells have excitatory connections so that an ON-center bipolar cell depolarization increases ON-center ganglion cell firing rate. The same is true for the OFF-center bipolar and OFF-center ganglions cell connection. There are species differences across the mammalian class but bipolar cells commonly integrate visual information from several light sensitive photoreceptors and, similar to the ganglion cells, have antagonistic center-surround receptive field organization [36].

2.7 Retinal Pre-processing of Basic Shapes (Bars, Contrast Lines, etc.)

The firing rate of ganglion cells provides a measure of the difference in the intensities of light illuminating the center and surround regions. Information about small differences in intensities and the center-surround organization of the ganglion cells receptive fields are therefore designed to report principally on contrast lines rather than absolute intensity [36]. Retinas adapted to optimally scan the appropriate environments and pattern recognition are inherent functions in visual systems across the animal kingdom [36, 37]. Unlike the human general-purpose eyes, that guide all our visual behavior, box jellyfish have special-purpose eyes, which scan the visual field for specific visual information (cf. matched filters) [37]. A visual strategy based on multiple special purpose eyes may seem energetically expensive, but requires far fewer computational circuits in the central nervous system. Based on immunohistochemical staining, it is estimated that T. cystophora has approximately one thousand neurons available to process visual information from all six eyes on the rhopalium and to modulate several visual behaviors [17]. Accordingly, the rhopalial nervous system (RNS) is presumed highly compartmentalized, indicating that the actual neuronal network serving one particular eye is considerably smaller [24, 30]. For the transfer into electronics, the pacemakers can be viewed as oscillators with a certain intrinsic frequency that is modulated by visual input. For Tripedalia cystophora it would be advantageous to have this type of matched filter in the lower lens eye to scan the retina for contrast lines that would imply an oncoming underwater obstacle. This could initiate evasive actions and steer the animal clear of collision. Presently, we have little knowledge of the cellular mechanisms involved in obstacle avoidance behavior but from previous work we can form an idea of how obstacle detection – or pattern recognition – can be accomplished in the box jellyfish visual system, and how the motor signal is generated. In the everted retina of T. cystophora the photoreceptors directly articulate on second order neurons, which could then be similar in function to the bipolar cells in the human retina. The second order neurons could translate the hyperpolarizing photoreceptor signal into ON- and OFF-center excitatory signals to the pacemaker cells. Three sets of giant neurons, presumably pacemaker cell clusters, have been identified in the T. cystophora RNS in the proximal part of the stalk region. Each set has positive immunoreactivity (ir+) to a specific neuropeptide [18]. Since ir+ has been discovered for three specific neuropeptides in three distinct different pacemaker clusters and swim pacemaker signals (Fig. 3d) can be recorded from the efferent epidermal stalk nerve (Fig. 3c), it is attractive to suggest that two subordinate pacemaker cell clusters converge into a terminal pacemaker cell cluster, which produces the motor signal for the effectors. Additionally, it stands to reason that, due to general morphology of photoreceptor cells and the distance from the lens eyes to the putative pacemaker cell clusters, at least one level of interneurons is present between the two cell types. This again supports the presumption of bipolar cell organizational analogy. Assuming two major control units in the rhopalium; the upper and the lower lens eyes, second order neurons from each eye could converge onto one giant neurons/pacemaker cell cluster (sub-cluster) analogous to retinal ganglion cells in mammals. The sub clusters would converge onto the terminal pacemaker cell cluster that would integrate the signal from the entire RNS and produce the appropriate behavioral modulatory motor signal of the epidermal stalk nerve. The convergence of signaling from the two lens eyes and the bias of the two potential cluster outputs in the terminal cluster is beyond the scope of this chapter, but there is evidence that sensory input from the lower lens eye has priority over the other eyes on the rhopalium [25]. Theoretically, this bias could be integrated at the level of the sub-cluster–terminal cluster junction.

2.8 Modeling RNS Visual Information Processing to the Mammalian Retina

Here we will consider the modulation of obstacle avoidance behavior by the lower lens eye. Putatively this could be based on pattern recognition in the retina and oscillator frequency synchrony in the pacemaker cell clusters. Consider the photoreceptors of the lower lens eye, the second order neurons, and the corresponding pacemaker cell cluster in T. cystophora to be three levels of matrices analogues to the photoreceptors, bipolar cells, and ganglion cells of the mammalian retina.

Matrix level I: photoreceptors

Approximately 600 photoreceptors make up the retina of the lower lens eye in the box jellyfish, each with an acceptance angle of about 20\(^\circ \) [12]. As mentioned, photoreceptors with c type opsins hyperpolarize in response to a light-ON stimulus and assumedly this is the case for box jellyfish as well [31, 32]. A light-ON response implies that the photoreceptors only register a change in light intensity, whereas constant light causes adaptation and image fading or blindness [38]. Adaptation occurs in photoreceptors across the Metazoa regardless of opsin type, and animals must have strategies in place to counteract adaptation. In mammals, oculomotor generated fixational eye movements constantly refresh the retinal image to avoid immobility blindness [39]. The box jellyfish utilizes the bell contractions as fixational eye movements and can in this way detect immobile objects in their visual field [24].

Matrix level II: second order neurons

The photoreceptors articulate directly on second order neurons in the T. cystophora everted retina. Potentially, and similar to bipolar cells, OFF-center second order neurons respond to depolarized photoreceptors (light-OFF) by remaining in a depolarized state, and hyperpolarize in response to hyperpolarized photoreceptors (light-ON). Conversely, ON-center second order neurons depolarize in response to hyperpolarized photoreceptors (light-ON) and hyperpolarize with depolarized photoreceptors (light-OFF) [36]. In short, ON-center second order neurons signal in response to light-ON, OFF-center neurons signal in response to light-OFF. Applied to a matrix, we would now have an array of second order neurons activated when a suitable visual stimulus (light or dark) is applied to their respective field of view (acceptance angle). When in the second order neurons a ‘pre-programmed’ visual image fills the field of view of the lower lens eye, all second order neurons could potentially depolarize simultaneously. So, if T. cystophora would encounter a speed limit sign (Fig. 4), the image would dovetail the matrix of ON- and OFF-center second order neurons and entirely excitatory signals would be relayed to the respective ON- and OFF-center sub-cluster pacemaker cells. One important aspect of the pattern detection is that since the photoreceptors are binary in nature (either responding to a stimulus or not) the response threshold is important. If the threshold is too low, too much redundant information will be relayed to the processing circuitry–if the threshold is too high, important information could be lost. Figure 4c displays a threshold of sufficient sensitivity to detect a speed limit sign in a cluttered visual environment (numbers within a circle). The T. cystophora response to the speed limit sign is an approximation since their photoreceptors do not respond to red light, but this problem will not be encountered in a CCD or CMOS monochrome sensor.

Matrix level III: pacemaker cells

Hypothetically, and similar to bipolar and ganglion cell connectivity in the mammalian retina, several second order neurons converge on the sub-cluster pacemaker cells. This neuronal circuit architecture seems logical in that there are considerably more neurons in the neuropil than there are pacemaker cells. This morphology suggests a matrix of i.e. ON-center second order neurons to converge on one ON-center sub-cluster pacemaker cell. Likewise the OFF-center second order neurons converge on OFF-center sub-cluster pacemaker cells. The ON- and OFF-center second order neurons form excitatory synapses with ON- and OFF-center sub-cluster pacemaker cells respectively. This results in sub-cluster pacemaker cells (oscillators) high frequency firing in response to excitatory presynaptic potentials from the second order neurons [36]. Following this line of reasoning when recognizing a pre-encoded pattern, such as the 60 km/h speed limit sign (Fig. 4), under water, all sub-cluster pacemaker cells synchronize to high frequency firing, terminal pacemaker cells initiates obstacle avoidance motor signal. In our automated driving assistant analogy, a potential vehicle would be slowed (or accelerated) to 60 km/h.

Fig. 4
figure 4

Representation of the image quality perceived by the Tripadalia cystophora retina. a Speed limit sign 60 km/h. b The same image as in (a) monochrome (single opsin), and adjusted for the approximately 600 pixels/photoreceptors resolution in the lower lens eye of T. cystophora. c Same image as in (b) with adjusted response threshold

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3 An Engineered Box Jellyfish by an Ensemble of Pulsed-Coupled Oscillators

As described previously, the box jellyfish’s visual system and rhopalial nervous system (RNS) can be viewed as an actuator coupled vertebrate-like retina. The level of visual information processing in the RNS is comparable to the pre-processing in a human retina in regard to pattern recognition, contrast line detection, and contrast estimation. The difference is that where human retinal information is sent to higher processing centers in the brain to actuate behavioral actions, in box jellyfish the motor effector signal is created directly within the RNS. In the present work, we modeled the described pattern recognition and oscillator synchrony to achieve the terminal pacemaker cluster output necessary for obstacle avoidance behavior. To simplify, we used the humblest pattern possible: one white pixel, one black. The light intensity of each pixel was monitored by a sensory oscillator, which would increase firing frequency when an internal criterion was met. In our experiment, the pattern of the two pixels could be varied in four ways: ON-OFF, ON-ON, OFF-ON, OFF-OFF. By using one ON-center and one OFF-center sensory oscillator (sub-cluster pacemaker cell equivalents) to monitor the presented patterns, the pattern meeting the criteria of both oscillators simultaneously would be the ON-OFF combination. In Fig. 5 this functionality is portrayed in an abstract view graph comprising two interacting input oscillators for the stimulus 1 (ON-oscillator) and stimulus 2 (OFF-oscillator). These oscillators were coupled and connected to a “Sync” oscillator unit (terminal cluster pacemaker cell equivalent). When the two sensory oscillators recognized the ON-OFF pattern simultaneously, the oscillators fired in phase and produced increased signal amplitude. The sync oscillator responded to the increased amplitude by commencing firing and producing the motor signal needed to initiate obstacle avoidance behavior. When the oscillators were uncoupled no increased amplitude could be observed, and the sync oscillator remained silent. The technical realization of this process is discussed below.

Fig. 5
figure 5

Abstract functional diagram to mimic visual information processing in T. cystophora. The two input oscillators respond to the light intensity on the photodiode (sensor input). When both input oscillators are activated in response to the appropriate visual stimulus, the sync oscillator initiates an activation sequence of 2 Hz spikes. See also Fig. 10

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This sensory oscillatory experiment is a proof of principle that the rhopalial nervous system can accomplish pattern recognition and respond with evasive action by utilizing interconnected sensory modulated sub-cluster pacemaker cells. The terminal cluster pacemaker cell firing activity is in turn modulated by the synchronized activity (and thereby signals amplitude) of the sub-cluster pacemaker cells. In order to partly mimic the complex functionalities of the box jellyfish neuronal network in electronic hardware, an ensemble of relaxation-type oscillators were applied and simulated by LTspice XVII (Linear Technology). Relaxation-type oscillators exhibit the leaky integrate and firing (LIF) mechanism of a neuron and therefore were applied to electronically mimic basic neuronal functions [40].

Fig. 6
figure 6

A mechanical (a) and an electronic version (b) of relaxation-type oscillators

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To explain the basic function of such oscillators a mechanical and an electrical version of relaxation-type oscillators are sketched in Fig. 6a and b, respectively. The mechanical model (Fig. 6a) is based on a seesaw comprising a mass on one wing (left) and a permanent charging (here water) on the right wing. In case the mass in the right container becomes larger than that on the left wing, the seesaw suddenly, seeps and the water container empties. The seesaw turns back to its original position and the procedure repeats again in a self-sustained way. The electronic version (Fig. 6b) consists of a constant voltage source \(V_0\), a resistor R, a capacitor C and a glow discharge lamp. The capacitor is charged by the current I via the resistor. If the threshold voltage of the glow lamp is reached, the lamp discharges the capacitor, accompanied by a short visible light spark and the entire process starts again [41]. The period of the pulse are set by the resistor, the capacitor and the threshold voltage of the lamp. The similarity to the leaky-integrate and firing (LIF) model for neurons is obvious. In this work semiconductor based relaxation-type van der Pol oscillators (programmable unijunction transistors) were applied [42]. The programmable unijunction transistor (PUT) 2N6027 functions as an electrical switch [43]. The PUT is part of a small circuitry comprising passive devices. The basic circuit is sketched in Fig. 7a. The three terminals of a PUT are the gate G, the cathode C and the anode A. With a constant supply voltage V, a current flows through R1. This current charges the capacitor C1 and the voltage at the anode of the PUT increases. If it reaches the threshold voltage of the PUT, the PUT will switch into the conducting state. Hence, the capacitor gets discharged by a current flow from anode to cathode. At the resistor R4 this discharge can be measured in form of a voltage spike. If the voltage from anode to cathode is sufficiently high, a current can flow. The threshold voltage depends on the voltage divider consisting of the resistors R2 and R3 and hence can be adjusted. The spiking frequency of the oscillator varies in dependence of its circuit parameters. The time constant \(\tau = R_1*C_1\) as well as the voltage divider R2 and R3 define the pulse frequency \(f_{osc}\) of the oscillator. The voltage traces at the anode terminal \(V_A\) and at the cathode terminal \(V_C\) are depicted qualitatively in Fig. 7b. Three of such PUT-based oscillators were coupled to mimic basal mechanisms of the box jellyfish‘s visual system.

Fig. 7
figure 7

Electrical circuit of a relaxation-type van der Pol oscillator (a), and the corresponding voltage curves (b). \(V_A\) shows the charging curve of the capacitor C1 and the instant discharge when the threshold voltage of the PUT is reached. The voltage \(V_C\) shows the discharge spikes of the capacitor at the cathode of the PUT

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As coupling mechanism between the oscillators, a gate to gate coupling is used (Fig. 8). The voltage at the gate is constant when the threshold voltage of the PUT is not reached. When the PUT switches, a current can flow and the voltage breaks down for a short moment in form of the reversed voltage spike at the cathode. The capacitors in the coupling are used to filter low frequencies, especially the DC part of the voltage. In the moment of a spike the capacitors are equivalent to short circuits and a current can flow. This means that the voltage divider changes its value and it is more likely for the second oscillator to fire, too. Therefore the two oscillators are pulsed-coupled [44,45,46,47]. If the frequency difference between both oscillators is small enough a synchronization will occur. Synchronization can only be achieved with oscillators that are similar enough to each other in regards of their frequencies. If the difference is too high even with a strong coupling no synchronization can occur. In this work the coupled oscillator scheme as shown in Fig. 5 has between transferred to an electronic circuitry design and in the first stage simulated correspondently by LTspice XVII [8]. The pattern recognition functions with three oscillators and persists of two stages. The visual stimuli are encoded in the voltages V1 and V2. A high voltage is equal to an ON pattern and a voltage of 0V equals an OFF pattern. Both voltage sources are chosen in a way that all possible combinations of two binary inputs (OFF-OFF, OFF-ON, ON-OFF, ON-ON) occur over time (Fig. 9).

Fig. 8
figure 8

Electrical circuit of two coupled relaxation-type van der Pol oscillators. The two oscillators are coupled via a RC circuit. The capacitors serve as a DC-de-coupling between the oscillators. A firing of one oscillator leads to a phase shift of the other oscillator and may lead to synchrony in case the coupling resistance is finite

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Fig. 9
figure 9

Electrical circuit of the complete setup. The ON- and OFF-oscillator are on the left and receive their input from V1 and V2. With the coupling element in place and the right input pattern synchronization can occur and the synchronization oscillator on the right starts to spike. Chosen Values: \(R1 = 1\ M\Omega \), \(R2 = 750\ k\Omega \), \(R3 = R7 = R17 = 100\ k\Omega \), \(R4 = R10 = R18 = 200\ k\Omega \), \(R5 = R8 = R12 = R13 = 1\ k\Omega \), \(R6 = 420\ k\Omega \), \(R9 = 1.6\ M\Omega \), \(R11 = 2\ M\Omega \), \(R14 = R16 = 10\ k\Omega \), \(R15 = 9\ M\Omega \), \(C1 = C2 = C5 = 0.1\ \mu F\), \(C3 = C4 = 1\ \mu F\), \(V3 = V4 = V5 = 10\ V\)

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For the charging resistors R2 and R6 of the two oscillators the values \(750\ k\Omega \) and \(420\ k\Omega \)) are chosen in a way that no synchronization can occur without the right stimuli from V1 and V2. The 2N7002 are n-mosfets and function as voltage-controlled switches. If a positive voltage is applied by V1 or V2, the corresponding n-MOSFET switches and a current can flow through the device. The oscillator influenced by V1 is called the ON-oscillator. If a positive voltage is applied to the n-MOSFET, it switches and a second resistor is parallel connected to the charging resistor. The new value of the overall charging resistor can be calculated with \(R_{ges}= {R_1 * R_2}/{R_1+ R_2}\). The second resistor is chosen in a way that the overall resistance \(R_{ges}\) is almost equal to the charging resistor of the OFF-oscillator. Therefore, in the moment of a stimulus synchronization of the two oscillators becomes possible. The second oscillator is called OFF-oscillator because synchronization is only possible in absence of a stimulus from V2. When a positive voltage is applied as stimulus by V2, the n-MOSFET switches into the on state and now a resistor is parallel connected to the capacitor. This leads to a leaky-current through the resistor and less current arrives at the capacitor. Therefore, the charging process of the capacitor takes longer than before and the frequency of the oscillator drops. This drop is so high, that again no synchronization is possible between the two oscillators. The at the cathodes generated voltage spikes are the input for the second stage. The second stage consists of only one oscillator: It only spikes when the oscillators of the first stage are firing in synchrony. Two optocouplers (PC817A) are applied as voltage dependent switches and likewise to realize a potential decoupling from the input circuit. Both optocouplers are connected with a cathode of one of the PUTs. Hence, the generated voltage spikes of the oscillators are the inputs of the optocouplers. Only when both optocouplers are switched on simultaneously, a current charges the capacitor of the sync oscillator. Therefore, only when the optocouplers receive a voltage spike at the same time from their input-oscillators can the synchronization oscillator generate spikes–which is equivalent for synchronization of the input oscillators.

Fig. 10
figure 10

The first two panels show the input variation over time (V1 and V2 in Fig. 9). Panel 3 shows the frequency of the ON and OFF oscillator in dependence of the input stimulus. Panel 4 shows the spiking behavior of the synchronization oscillator that only spikes when the right input pattern occurs and induces a synchronization of the ON and OFF oscillator

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4 Conclusion

Biological model systems offer attractive guidelines to develop novel computing architectures, which may exhibit enhanced pattern recognition capabilities, by equally low power dissipation. In this work, we demonstrate how two input oscillators and a sync oscillator can mimic basal visual information processing in the T. cystophora rhopalial nervous system. The sync oscillator fires only when the two input oscillators achieve the correct input pattern and subsequently initiates the activation sequence (2 Hz spiking signal) (Fig. 10). This validates not only that pattern recognition functionality in the box jellyfish nervous system can be accomplished by sequentially connected oscillators, but also that this functionality can be reversed engineered into hardware electronics. The present work considers a very humble pattern of just two pixels but with a bit of engineering effort, hardware components can be extended to support the approximately 600 pixels in the box jellyfish retinal sensor. This would enable extraction of specific visual information (such as speed limits) from a complex visual environment (Fig. 4). Pattern recognition filters for each possible speed limit inserted in parallel would then instantaneously report on the specific speed allowed, since only the sync oscillator recognizing the accurate visual cue would initiate the activation sequence. Subsequently, an autonomously driving vehicle would then be able to maintain correct speed using hardware units rather than occupying processing capacity on an on-board computer. Integrated in the T. cystophora model system is an override mechanism favoring sensory information of the most present danger. The special purpose lens eyes, upper and lower lens eyes, each has pattern recognition function but for vastly different visual input. The upper lens eye is directed out of the water column and concerned about the keeping the contrast line between the mangrove canopy and the open sky in the periphery of the visual field, indicating that the animal is nested well within the habitat [15]. The lower lens eye is directing obstacle avoidance behavior and is responsible for keeping a safe distance to underwater obstacles that could damage the fragile bell of the animal [13]. Collision with obstacles present greater danger and avoidance is more time critical than to adjust the position of the animal in respect to the habitat. It is then logical that the lower lens eye has override privileges compared to the upper lens eye [25]. By adding pattern recognition filters with overriding privileges, of e.g. pedestrians or approaching vehicles, our hardware model would then have built in safety measures for clear and present danger – if the sync oscillators monitoring the override filters would initiate an activation sequence, the vehicle could be brought to an abrupt stop regardless of the input from the speed limit sync oscillators. The T. cystophora neuronal network integrates the bias of the sub cluster pacemaker cells into the terminal cluster pacemaker cells, but for the technical modeling we need another layer of sync oscillators to accomplish the decision making functionality (Fig. 11).

Fig. 11
figure 11

The T. cystophora nervous system contains an intrinsic terminal pacemaker override mechanism to avoid immediate danger. For transference into electronic circuitry an extra decision making oscillator level must be added to accomplish this intrinsic override function. In this figure, “visual stimuli” represent the photoreceptor and second order neuron layers. The input layer comprises the sub-cluster pacemaker cells which respond to the appropriate visual input by high frequency firing. The sync oscillators in turn produce the 2 Hz activation sequence in response to aligned spiking from the sync oscillators. Here Sync2 has override privileges in case Sync1 and Sync2 are simultaneously activated, and an added decision making oscillatory circuit would evaluate this bias and produce the activation sequence appropriate for Sync2

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