{"title": "Chemosensory Processing in a Spiking Model of the Olfactory Bulb: Chemotopic Convergence and Center Surround Inhibition", "book": "Advances in Neural Information Processing Systems", "page_first": 1105, "page_last": 1112, "abstract": null, "full_text": " Chemosensory processing in a spiking \n model of the olfactory bulb: chemotopic \n convergence and center surround \n inhibition \n\n\n \n Baranidharan Raman and Ricardo Gutierrez-Osuna \n Department of Computer Science \n Texas A&M University \n College Station, TX 77840 \n {barani,rgutier}@cs.tamu.edu \n \n\n\n\n Abstract \n\n This paper presents a neuromorphic model of two olfactory signal-\n processing primitives: chemotopic convergence of olfactory \n receptor neurons, and center on-off surround lateral inhibition in \n the olfactory bulb. A self-organizing model of receptor \n convergence onto glomeruli is used to generate a spatially \n organized map, an olfactory image. This map serves as input to a \n lattice of spiking neurons with lateral connections. The dynamics \n of this recurrent network transforms the initial olfactory image into \n a spatio-temporal pattern that evolves and stabilizes into odor- and \n intensity-coding attractors. The model is validated using \n experimental data from an array of temperature-modulated gas \n sensors. Our results are consistent with recent neurobiological \n findings on the antennal lobe of the honeybee and the locust. \n\n\n1 Introduction \nAn artificial olfactory system comprises of an array of cross-selective chemical \nsensors followed by a pattern recognition engine. An elegant alternative for the \nprocessing of sensor-array signals, normally performed with statistical pattern \nrecognition techniques [1], involves adopting solutions from the biological olfactory \nsystem. The use of neuromorphic approaches provides an opportunity for \nformulating new computational problems in machine olfaction, including mixture \nsegmentation, background suppression, olfactory habituation, and odor-memory \nassociations. \n\nA biologically inspired approach to machine olfaction involves (1) identifying key \nsignal processing primitives in the olfactory pathway, (2) adapting these primitives \nto account for the unique properties of chemical sensor signals, and (3) applying the \nmodels to solving specific computational problems. \n\n\f\n \n\n\nThe biological olfactory pathway can be divided into three general stages: (i) \nolfactory epithelium, where primary reception takes place, (ii) olfactory bulb (OB), \nwhere the bulk of signal processing is performed and, (iii) olfactory cortex, where \nodor associations are stored. A review of literature on olfactory signal processing \nreveals six key primitives in the olfactory pathway that can be adapted for use in \nmachine olfaction. These primitives are: (a) chemical transduction into a \ncombinatorial code by a large population of olfactory receptor neurons (ORN), (b) \nchemotopic convergence of ORN axons onto glomeruli (GL), (c) logarithmic \ncompression through lateral inhibition at the GL level by periglomerular \ninterneurons, (d) contrast enhancement through lateral inhibition of mitral (M) \nprojection neurons by granule interneurons, (e) storage and association of odor \nmemories in the piriform cortex, and (f) bulbar modulation through cortical \nfeedback [2, 3]. \n\nThis article presents a model that captures the first three abovementioned \nprimitives: population coding, chemotopic convergence and contrast enhancement. \nThe model operates as follows. First, a large population of cross-selective pseudo-\nsensors is generated from an array of metal-oxide (MOS) gas sensors by means of \ntemperature modulation. Next, a self-organizing model of convergence is used to \ncluster these pseudo-sensors according to their relative selectivity. This clustering \ngenerates an initial spatial odor map at the GL layer. Finally, a lattice of spiking \nneurons with center on-off surround lateral connections is used to transform the GL \nmap into identity- and intensity-specific attractors. \n\nThe model is validated using a database of temperature-modulated sensor patterns \nfrom three analytes at three concentration levels. The model is shown to address the \nfirst problem in biologically-inspired machine olfaction: intensity and identity \ncoding of a chemical stimulus in a manner consistent with neurobiology [4, 5]. \n\n2 Modeling chemotopic convergence \n\nThe projection of sensory signals onto the olfactory bulb is organized such that \nORNs expressing the same receptor gene converge onto one or a few GLs [3]. This \nconvergence transforms the initial combinatorial code into an organized spatial \npattern (i.e., an olfactory image). In addition, massive convergence improves the \nsignal to noise ratio by integrating signals from multiple receptor neurons [6]. \nWhen incorporating this principle into machine olfaction, a fundamental difference \nbetween the artificial and biological counterparts must be overcome: the input \ndimensionality at the receptor/sensor level. The biological olfactory system employs \na large population of ORNs (over 100 million in humans, replicated from 1,000 \nprimary receptor types), whereas its artificial analogue uses a few chemical sensors \n(commonly one replica of up to 32 different sensor types). \n\nTo bridge this gap, we employ a sensor excitation technique known as temperature \nmodulation [7]. MOS sensors are conventionally driven in an isothermal fashion by \nmaintaining a constant temperature. However, the selectivity of these devices is a \nfunction of the operating temperature. Thus, capturing the sensor response at \nmultiple temperatures generates a wealth of additional information as compared to \nthe isothermal mode of operation. If the temperature is modulated slow enough \n(e.g., mHz), the behavior of the sensor at each point in the temperature cycle can \nthen be treated as a pseudo-sensor, and thus used to simulate a large population of \ncross-selective ORNs (refer to Figure 1(a)). \n\nTo model chemotopic convergence, these temperature-modulated pseudo-sensors \n(referred to as ORNs in what follows) must be clustered according to their \n\n\n\n\n\n \n\n\f\n \n\n\nselectivity [8]. As a first approximation, each ORN can be modeled by an affinity \nvector [9] consisting of the responses across a set of C analytes: \n r\n K K1\n = , K 2,..., K (1) \n i [ C\n i i i ]\n\nwhere a\n K is the response of the ith ORN to analyte a. The selectivity of this ORN \n i r\nis then defined by the orientation of the affinity vector . \n i\n\nA close look at the OB also shows that neighboring GLs respond to similar odors \n[10]. Therefore, we model the ORN-GL projection with a Kohonen self-organizing \nmap (SOM) [11]. In our model, the SOM is trained to model the distribution of \n r\nORNs in chemical sensitivity space, defined by the affinity vector . Once the \n i\ntraining of the SOM is completed, each ORN is assigned to the closest SOM node (a \nsimulated GL) in affinity space, thereby forming a convergence map. The response \nof each GL can then be computed as \n\n a\n G = W ORN (2) \n j (N a\n i= ij i\n 1 )\nwhere a\n ORN is the response of pseudo-sensor i to analyte a, W\n i ij=1 if pseudo-sensor i \nconverges to GL j and zero otherwise, and () is a squashing sigmoidal function \nthat models saturation. \n\nThis convergence model works well under the assumption that the different sensory \ninputs are reasonably uncorrelated. Unfortunately, most gas sensors are extremely \ncollinear. As a result, this convergence model degenerates into a few dominant GLs \nthat capture most of the sensory activity, and a large number of dormant GLs that do \nnot receive any projections. To address this issue, we employ a form of competition \nknown as conscience learning [12], which incorporates a habituation mechanism to \nprevent certain SOM nodes from dominating the competition. In this scheme, the \nfraction of times that a particular SOM node wins the competition is used as a bias \nto favor non-winning nodes. This results in a spreading of the ORN projections to \nneighboring units and, therefore, significantly reduces the number of dormant units. \n\nWe measure the performance of the convergence mapping with the entropy across \nthe lattice, H = - P log P , where P\n i i i is the fraction of ORNs that project to SOM \nnode i [13]. To compare Kohonen and conscience learning, we built convergence \nmappings with 3,000 pseudo-sensors and 400 GL units (refer to section 4 for \ndetails). The theoretical maximum of the entropy for this network, which \ncorresponds to a uniform distribution, is 8.6439. When trained with Kohonen's \nalgorithm, the entropy of the SOM is 7.3555. With conscience learning, the entropy \nincreases to 8.2280. Thus, conscience is an effective mechanism to improve the \nspreading of ORN projections across the GL lattice. \n\n3 Modeling the olfactory bulb network \n\nMitral cells, which synapse ORNs at the GL level, transform the initial olfactory \nimage into a spatio-temporal code by means of lateral inhibition. Two roles have \nbeen suggested for this lateral inhibition: (a) sharpening of the molecular tuning \nrange of individual M cells with respect to that of their corresponding ORNs [10], \nand (b) global redistribution of activity, such that the bulb-wide representation of an \nodorant, rather than the individual tuning ranges, becomes specific and concise over \ntime [3]. More recently, center on-off surround inhibitory connections have been \nfound in the OB [14]. These circuits have been suggested to perform pattern \nnormalization, noise reduction and contrast enhancement of the spatial patterns. \n\n\n\n\n\n \n\n\f\n \n\n\nWe model each M cell using a leaky integrate-and-fire spiking neuron [15]. The \ninput current I(t) and change in membrane potential u(t) of a neuron are given by: \n\n u(t) du\n I (t) = + C\n R dt (3) \n du\n = -u(t) + R I(t) [ = RC]\n dt\nEach M cell receives current Iinput from ORNs and current Ilateral from lateral \nconnections with other M cells: \n\n I ( j) =\n input W ORN\n ij i\n i (4) \n I ( j,t) = \n lateral L (k,t - )1\n kj\n k\n\nwhere Wij indicates the presence/absence of a synapse between ORNi and Mj, as \ndetermined by the chemotopic mapping, Lkj is the efficacy of the lateral connection \nbetween Mk and Mj, and (k,t-1) is the post-synaptic current generated by a spike at \nMk: \n (k,t - )\n 1 = -g(k,t - )\n 1 [u( j,t - )\n 1 - E ]\n + (5) \n syn\n\ng(k,t-1) is the conductance of the synapse between Mk and Mj at time t-1, u(j,t-1) is \nthe membrane potential of Mj at time t-1 and the + subscript indicates this value \nbecomes zero if negative, and Esyn is the reverse synaptic potential. The change in \nconductance of post-synaptic membrane is: \n\n dg(k,t) -g(k,t)\n g&(k,t) = = + z(k,t)\n dt \n syn (6) \n dz(k,t) - z(k,t)\n z&(k,t) = = + g spk(k,t)\n dt norm\n syn\n\nwhere z(.) and g(.) are low pass filters of the form exp(-t/syn) and t exp( t\n - / ) , \n syn\nrespectively, syn is the synaptic time constant, gnorm is a normalization constant, and \nspk(j,t) marks the occurrence of a spike in neuron i at time t: \n\n 1 u( j,t) = Vspike\n spk( j,t) = (7) \n 0 u( j,t) Vspike\nCombining equations (3) and (4), the membrane potential can be expressed as: \n\n du( j,t) - u( j,t) I ( j,t) I ( j)\n u&( j,t) = = + lateral + input\n dt RC C C\n (8) \n u( j,t - )\n 1 + u&( j,t - )\n 1 dt u( j,t) < Vthreshold \n u( j,t) = \n V u( j,t) V\n spike threshold \n\nWhen the membrane potential reaches Vthreshold, a spike is generated, and the \nmembrane potential is reset to Vrest. Any further inputs to the neuron are ignored \nduring the subsequent refractory period. \n\nFollowing [14], lateral interactions are modeled with a center on-off surround \nmatrix Lij. Each M cell makes excitatory synapses to nearby M cells (d