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More attention should be paid to the neural system, which is a quantitative system. There are few reports about the quantitative research on neural system. It will hinder the quantitative studies on animal binaural sound localization. The existing physiological experiments have found that there is a monotonic increase/decrease relationship between the input sound levels and the output spike frequencies of auditory neurons, so the variations of input sound level can be simplified into the change of output spike frequency of auditory neurons. In this paper, based on the theory of circle map and symbolic dynamics, a quantitative model of auditory neural circuitry is presented. In this neural circuit model, the neurons of ipsilateral input circuit propagate the action potentials as excitatory inputs, the neurons of heterolateral input one propagate the action potentials as inhibitory inputs. We also use a chemical neuronal model, which shows that the neurotransmitters released from pre-synapse vesicles have characteristics of quantitative release. The strength of the coupling between two neurons is represented by a coupling coefficient. The relationship between the input/output spike sequences of neural circuitry is simulated by using an Hodgkin-Huxley equation. In the range of simulating parameters, there is a monotonic increase/decrease phenomenon between input and output spike frequency. For the neuron with a single input and output structure, it is symbolized according to the method of symbolic dynamics; for the neurons with multi-input and single output structure, the output spike time will be used to detect the input spike frequency variations which are caused by the changes of interaural level difference (ILD), and the binaural level differences from those spike sequences are analyzed to locate the source of the sounds. With the increase of output spikes, the length of symbolic sequence increases, the symbolic sequence is sensitive to the variation of input signal. The simulation results show that the quantitative model proposed in this paper is able to detect the ILD signals by neural spike sequences.
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Keywords:
- biosonar /
- interaural level difference /
- circle map /
- symbolic dynamics
[1] Jeffress L A 1948 J. Comp. Physiol. Psych. 41 35
[2] Joris P X, Smith P H, Yin T C T 1998 Neuron 21 1235
[3] Moiseff A, Konishi M 1981 J. Neurosci. 1 40
[4] Massoud S, Aiken S J, Newmann A J, Phillips D P, Bance M 2011 Ear and Hearing 32 114
[5] Tollin D J 2003 The Neuroscientist 9 127
[6] Konishi M 1993 Sci. Am. 268 34
[7] Nicholls J G, Martin A R, Wallace B G, Fuchs P A (translated by Yang X L) 2003 From Neuron to Brain (4th Ed.) (Beijing: Science Press) pp430-442 (in Chinese) [尼克尔斯 J G, 马丁 A R, 华莱士 B G, 富克斯 P A 著(杨雄里 等译) 2003 神经生物学——从神经元到脑 (北京: 科学出版社)第430–442页]
[8] Campbell R A A, King A J 2004 Current Biol. 14 886
[9] Rose J E, Hind J E, Anderson D J 1971 J. Neurophys. 34 685
[10] Zhang H, Mo J, Tong Q Y 2007 Acta Biophys. Sin. 23 455(in Chinese) [张宏, 莫珏, 童勤业 2007 生物物理学报 23 455]
[11] Tong Q Y, Qian M Q, Li X, Gu H J, Han X P, Li G, Shen G Y 2006 Sci. Sin. 36 449(in Chinese) [童勤业, 钱鸣奇, 李绪, 郭宏记, 韩晓鹏, 李光, 沈公羽 2006 中国科学E辑 信息科学 36 449]
[12] Zhang H, Fang L P, Tong Q Y 2007 Acta Phys. Sin. 56 7339(in Chinese) [张宏, 方路平, 童勤业 2007 物理学报 56 7339]
[13] Destexhe A, Contreras D, Steriade M, Sejnowski T J, Huguenard J R 1996 J. Neurosci. 16 169
[14] Destexhe A, Contreras D, Sejnowski T J, Steriade M 1994 J. Neurophysiol. 72 803
[15] Mountcastle V B 1978 The Mindful Brain (Cambridge: MIT Press) pp7-50
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[1] Jeffress L A 1948 J. Comp. Physiol. Psych. 41 35
[2] Joris P X, Smith P H, Yin T C T 1998 Neuron 21 1235
[3] Moiseff A, Konishi M 1981 J. Neurosci. 1 40
[4] Massoud S, Aiken S J, Newmann A J, Phillips D P, Bance M 2011 Ear and Hearing 32 114
[5] Tollin D J 2003 The Neuroscientist 9 127
[6] Konishi M 1993 Sci. Am. 268 34
[7] Nicholls J G, Martin A R, Wallace B G, Fuchs P A (translated by Yang X L) 2003 From Neuron to Brain (4th Ed.) (Beijing: Science Press) pp430-442 (in Chinese) [尼克尔斯 J G, 马丁 A R, 华莱士 B G, 富克斯 P A 著(杨雄里 等译) 2003 神经生物学——从神经元到脑 (北京: 科学出版社)第430–442页]
[8] Campbell R A A, King A J 2004 Current Biol. 14 886
[9] Rose J E, Hind J E, Anderson D J 1971 J. Neurophys. 34 685
[10] Zhang H, Mo J, Tong Q Y 2007 Acta Biophys. Sin. 23 455(in Chinese) [张宏, 莫珏, 童勤业 2007 生物物理学报 23 455]
[11] Tong Q Y, Qian M Q, Li X, Gu H J, Han X P, Li G, Shen G Y 2006 Sci. Sin. 36 449(in Chinese) [童勤业, 钱鸣奇, 李绪, 郭宏记, 韩晓鹏, 李光, 沈公羽 2006 中国科学E辑 信息科学 36 449]
[12] Zhang H, Fang L P, Tong Q Y 2007 Acta Phys. Sin. 56 7339(in Chinese) [张宏, 方路平, 童勤业 2007 物理学报 56 7339]
[13] Destexhe A, Contreras D, Steriade M, Sejnowski T J, Huguenard J R 1996 J. Neurosci. 16 169
[14] Destexhe A, Contreras D, Sejnowski T J, Steriade M 1994 J. Neurophysiol. 72 803
[15] Mountcastle V B 1978 The Mindful Brain (Cambridge: MIT Press) pp7-50
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