海马CA3SWNN模型及神经元集群编码刺激的研究
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摘要
目的：
本论文基于海马CA3区神经元发放的稀疏分布，构建了海马CA3区神经元发放的小世界神经网络(Small World Neural Network，SWNN)模型。应用该模型，仿真了在脉冲输入、Gaussian白噪声输入和两者线性叠加的输入条件下，海马CA3区神经元群电活动的时空序列。应用两种神经元集群编码：频率编码(ratecoding)和基于神经元放电峰峰间隔序列(ISI)相关编码。研究了海马CA3区神经元集群对这三类信息(刺激)的编码，为研究海马神经元集群编码(信息)的研究，提供神经计算的支持。
方法：
1．海马CA3区神经元群小世界神经网络模型的构建
根据海马CA3区特点：兴奋性神经元与抑制性神经元的数量比大约为5：1，海马CA3区神经元群体的稀疏发放(平均发放率小于10％)。在Matlab7．4仿真平台上，构建海马CA3区神经元群小世界神经网络模型。仿真海马CA3区神经元群体放电活动的时空序列。在小世界神经网络模型中每个神经元发放的模型是Hindmarsh-Rose(HR)模型，通过改变HR模型中的γ参数，可以得到兴奋性神经元和抑制性神经元的放电序列。海马CA3区神经元群小世界神经网络模型包含120个神经元，其中兴奋性神经元100个，抑制性神经元20个。神经元之间的联系按WS小世界网络的构建算法生成。
2．应用小世界网络模型对海马CA3区神经元群放电时空序列的动态仿真
设定三类典型的输入刺激模式：脉冲刺激、Gaussian白噪声刺激和以上两类刺激的线性叠加信号。在Matlab7．4平台上，对所构建的海马CA3区小世界神经网络模型分别施加上述三种不同的刺激模式，仿真在三种刺激条件下海马CA3区神经元群发放的时空序列40秒时间段，并获取在这三类刺激模式作用下序列中每个神经元放电的峰峰间隔(Inter-Spike Interval，ISI)序列，组成ISIs时空序列。
3．仿真的海马CA3区神经元集群电活动对刺激的编码
研究在不同的刺激模式下动态神经元集群对刺激的编码。采用两种神经元集群编码的表达方法：频率编码和ISI相关编码。比较频率编码和ISI相关编码，
对三类特定刺激神经元集群编码的表征效能。
对在不同刺激模式下获得的仿真神经元群体发放时空序列，分别应用频率编码和ISI相关编码来划分功能神经元集群。
(1)神经元集群电活动的频率编码
时间窗口为200ms(生理窗口)，窗口移动步长设置为50ms，统计时空序列中每个神经元在每个移动窗口内的神经元发放的个数。进行归一化处理后，获得表征神经元群体发放时空模式的动态“地形图”。
(2)基于放电峰峰间隔序列(ISI)的神经元集群相关编码
①对神经元群体放电时空序列(spike trains)中每个神经元的放电序列，计算放电脉冲间隔序列ISIs。
②连接N个神经元发放时空序列中每个神经元的离散ISIs点，经过曲线拟合后得到N条神经元发放ISI序列的连续曲线。
③选取在刺激后神经元平均发放频率最高的神经元发放序列作为参考序列。
④设定窗口宽度(选择小于50ms的小窗口)，在第k个窗口中计算其它N-1个ISI序列对参考序列的相关值。
⑤选择步长为1／3窗口宽度，计算每个移动窗口中ISI中的N-1个相关值。
⑥绘制在时间、空间上神经元群体放电的“地形图”，划分编码特定刺激模式的动态神经元集群。
结果：
1．本论文在Matlab7．4仿真平台上构建了海马CA3区小世界神经网络模型。应用该模型可以成功仿真海马CA3区神经元群体的放电特性。
2．在没有刺激输入时，海马CA3区小世界神经网络模型输出的神经元群动作电位发放平均发放率为7．8％，符合海马CA3区神经元群放电的稀疏发放特性(平均发放率小于10％)。
3．在三类刺激输入模式(脉冲刺激、Gaussian白噪声刺激和上述两类刺激的线性叠加)下，模型输出的神经元群体动作电位发放的特征模式不同。
对应的神经元集群编码模式如下：
①神经元集群频率编码
(a)在脉冲刺激输入条件下，各个神经元的放电频率范围为[5．14～21．52]Hz，群体(120个神经元)平均放电频率为10．43±0．38 Hz。神经元集群频率编码能够编码脉冲刺激输入模式。
(b)在Gaussian白噪声刺激信号作用下，各个神经元的放电频率范围为[3．02～15．28]Hz，群体平均放电频率为7．59±0．62Hz。神经元集群频率编码能够编码Gaussian白噪声刺激输入模式。
(c)在以上两类刺激的线性叠加条件下，神经元的放电频率为[2．27～55．21]Hz，平均放电频率为15．52±0．84Hz。神经元集群频率编码不能编码脉冲刺激和Gaussian白噪声刺激线性叠加输入模式。
②神经元集群的ISI相关编码
(a)神经元集群ISI相关编码能够编码脉冲刺激输入模式。
(b)神经元集群ISI相关编码能够编码Gaussian白噪声刺激输入模式。
(c)神经元集群ISI相关编码对脉冲刺激和Gaussian白噪声刺激线性叠加输入模式编码效果不明显。
结论：
1．本论文建立的海马CA3区神经元群小世界神经网络模型能够有效地仿真海马CA3区神经元群体电活动，反映其稀疏特性(平均发放率小于10％)。
2．在三种不同的刺激模式下(脉冲刺激、Gaussian白噪声刺激和上述两类刺激的线性叠加)，海马CA3区神经元群动作电位发放的时空序列特征模式不同。
3．在脉冲刺激和Gaussian白噪声刺激下，频率编码可以划分表征不同单个刺激的神经元集群，神经元集群频率编码只能编码单个刺激模式，对于混合刺激模式，不能编码混合刺激模式中不同的刺激模式。ISI相关编码效能优于频率编码，可以划分表征不同单个刺激的神经元集群，对于两类刺激的线性叠加，编码效果不明显，有待进一步研究。
Objective
In this paper,a hippocampus CA3 neurons spiking small world neural network(SWNN)model is established on the Matlab7.4 platform based on sparse activity ofhippocampus CA3 neurons.The temporal-spatial sequences of the hippocampus CA3area neurons firing activity are simulated under the stimulus of pulse input,Gaussianwhite noise input and the linear superposition input of the two conditions on theSWNN model.The neuronal ensemble rate coding and ISI correlation codingmethods are used to analyze the simulated spiking trains.The hippocampus CA3 areaneurons ensemble coding of the three types stimulus are investigated in this paper.The results may provide neural computation support for hippocampus neuronalensemble coding.
Methods
1.Construction of hippocampus CA3 area neurons spiking SWNN model
According to the anatomical characteristics of hippocampus CA3 area,the ratioof the excitatory to inhibitory neurons is about 5 to 1.The activity of hippocampusCA3 area neurons is sparse firing (less than 10%).A hippocampus CA3 neuronsspiking small world neural network (SWNN)model is established on the Matlab7.4platform.The temporal-spatial sequences of hippocampus CA3 area neurons firingactivity are simulated by the SWNN model.The Hindmarsh-Rose (HR)modelcould describe different discharge property of an excitatory or inhibitory neuron bychanging the parameterγ.In this paper,HR model is used to be the dynamicalequations of the spiking model neurons.The SWNN model is composed of 120neurons,in which 100 neurons are excitatory and 20 are inhibitory.The differentneurons in the SWNN model are connected with WS small-world network.
2.The dynamic simulation of hippocampus CA3 area neurons spikingtemporal-spatial sequences by using the SWNN model.
Set up three types of stimulus input patterns:pulse input,Gaussian white noiseinput and the linear superposition input of the two conditions.The 40 seconds temporal-spatial sequences of hippocampus CA3 area neurons are achieved under thethree different stimulus patterns imposed on the SWNN model.At the same time theinter-spike interval (ISI)of each neuron is get to make up the ISIs temporal-spatialsequences.
3.The hippocampus CA3 neurons ensemble coding of three types of stimulus
The dynamic neuronal ensemble coding is investigated under the differentstimulus input pattern.The neuronal ensemble rate coding and ISI correlation codingmethods are used to analyze the simulated temporal-spatial sequences.Theeffectiveness of the above neuronal ensemble coding methods are compared under thethree different stimulus input pattern.
For the neuronal population firing temporal-spatial sequences simulation dataunder the different stimulus pattern,adopt the rate coding and ISI correlation codingmethods to measure the functional neuronal ensembles.
(1)The rate coding of neuronal ensemble firing activity
The bin window is set to be 200ms (physiological window)and the step lengthof bin window is set to be 50ms.The spiking numbers are counted in the movingwindow of each neuron temporal-spatial sequence.The dynamic topography maps ofneuronal population spike trains are achieved after normalizing the spiking numbers.
(2)The ISI correlation coding of neuronal ensemble firing activity
①The inter-spike intervals (ISis)of each neuron firing sequence are computedamong the neuronal population spike trains.
②Connect the discrete ISis point of each neuron and get the N continuouscurves of ISI sequence by curve fitting.
③The maximum mean firing rate neuronal firing sequence is selected to be thereference sequence.
④The bin window length is set to be small scale (less than 50ms)and the ISIcorrelation values are computed in the kth window of N-1 ISI sequence withreference ISI sequence.
⑤The step length is set to be 1/3 bin window,and the N-1 ISI correlationvalues are computed in each moving window.
⑥The dynamic topography maps of neuronal population spike trains areachieved after normalizing the ISI correlation value.
Results
1.A hippocampus CA3 neurons spiking small world neural network (SWNN)model is established on the Matlab7.4 platform in this paper.The SWNN model cansimulate the sparse activity of hippocampus CA3 area neurons successfully.
2.The mean population firing rate of hippocampus CA3 area is 7.8% when nostimulus acts on the SWNN model.The result is in accordance with the sparse spikefiring characteristic of hippocampus CA3 area (the mean firing rate is less than 10%).
3.The hippocampus CA3 neuronal population firing patterns are different under thethree types of stimulus input(pulse input,Gaussian white noise input and the linearsuperposition input of the two conditions).The neuronal ensemble coding patterns areas followed:
①Neuronal ensemble rate coding
(a)The firing rate range of neuron is [5.14～21.52] Hz under the pulse inputstimulus acts on the SWNN model.The mean firing rate of neuronal population(120neurons)is 10.43±0.38 Hz.The neuronal ensemble rate coding method canencode the pulse input stimulus pattern.
(b)The firing rate range of neuron is [3.02～15.28] Hz under the Gaussian whitenoise input stimulus acts on the SWNN model.The mean firing rate of neuronalpopulation is 7.59±0.62 Hz.The neuronal ensemble rate coding method can encodethe Gaussian white noise input stimulus pattern.
(c)The firing rate range of neuron is [2.27～55.21] Hz under the linearsuperposition input of the pulse input and Gaussian white noise input stimulus acts onthe SWNN model.The mean firing rate of neuronal population is 15.52±0.84 Hz.The neuronal ensemble rate coding method can not distinguish between the pulseinput and Gaussian white noise input stimulus pattern.
②Neuronal ensemble ISI correlation coding
(a)The neuronal ensemble ISI correlation coding method can encode the pulseinput stimulus pattern.
(b)The neuronal ensemble ISI correlation coding method can encode theGaussian white noise input stimulus pattern.
(c)The encoding effect of the mix stimulus pattern by the neuronal ensemblerate coding method is not obvious.
Conclusions
1.The hippocampus CA3 neurons spiking small world neural network (SWNN)model can simulate the sparse activity of hippocampus CA3 area neuronssuccessfully.The simulation result is accordance with the sparse firing (mean firingrate is less than 10%)character of hippocampus CA3 area.
2.The temporal-spatial sequence patterns of hippocampus CA3 neurons aredifferent under the three different types of stimulus input pattern (pulse input,Gaussian white noise input and the linear superposition input of the above stimulusinput).
3.The neuronal ensemble rate coding method can encode the pulse inputstimulus pattern and the Gaussian white noise stimulus pattern.The neuronalensemble rate coding method can not distinguish between the pulse input andGaussian white noise input stimulus pattern.The coding effect of ISI correlation isbetter than the rate coding.The neuronal ensemble ISI correlation coding method canencode the pulse input stimulus pattern and the Gaussian white noise stimulus pattern.But the encoding effect of the mix stimulus pattern by the neuronal ensemble ratecoding method is not obvious.
本论文基于海马CA3区神经元发放的稀疏分布，构建了海马CA3区神经元发放的小世界神经网络(Small World Neural Network，SWNN)模型。应用该模型，仿真了在脉冲输入、Gaussian白噪声输入和两者线性叠加的输入条件下，海马CA3区神经元群电活动的时空序列。应用两种神经元集群编码：频率编码(ratecoding)和基于神经元放电峰峰间隔序列(ISI)相关编码。研究了海马CA3区神经元集群对这三类信息(刺激)的编码，为研究海马神经元集群编码(信息)的研究，提供神经计算的支持。
方法：
1．海马CA3区神经元群小世界神经网络模型的构建
根据海马CA3区特点：兴奋性神经元与抑制性神经元的数量比大约为5：1，海马CA3区神经元群体的稀疏发放(平均发放率小于10％)。在Matlab7．4仿真平台上，构建海马CA3区神经元群小世界神经网络模型。仿真海马CA3区神经元群体放电活动的时空序列。在小世界神经网络模型中每个神经元发放的模型是Hindmarsh-Rose(HR)模型，通过改变HR模型中的γ参数，可以得到兴奋性神经元和抑制性神经元的放电序列。海马CA3区神经元群小世界神经网络模型包含120个神经元，其中兴奋性神经元100个，抑制性神经元20个。神经元之间的联系按WS小世界网络的构建算法生成。
2．应用小世界网络模型对海马CA3区神经元群放电时空序列的动态仿真
设定三类典型的输入刺激模式：脉冲刺激、Gaussian白噪声刺激和以上两类刺激的线性叠加信号。在Matlab7．4平台上，对所构建的海马CA3区小世界神经网络模型分别施加上述三种不同的刺激模式，仿真在三种刺激条件下海马CA3区神经元群发放的时空序列40秒时间段，并获取在这三类刺激模式作用下序列中每个神经元放电的峰峰间隔(Inter-Spike Interval，ISI)序列，组成ISIs时空序列。
3．仿真的海马CA3区神经元集群电活动对刺激的编码
研究在不同的刺激模式下动态神经元集群对刺激的编码。采用两种神经元集群编码的表达方法：频率编码和ISI相关编码。比较频率编码和ISI相关编码，
对三类特定刺激神经元集群编码的表征效能。
对在不同刺激模式下获得的仿真神经元群体发放时空序列，分别应用频率编码和ISI相关编码来划分功能神经元集群。
(1)神经元集群电活动的频率编码
时间窗口为200ms(生理窗口)，窗口移动步长设置为50ms，统计时空序列中每个神经元在每个移动窗口内的神经元发放的个数。进行归一化处理后，获得表征神经元群体发放时空模式的动态“地形图”。
(2)基于放电峰峰间隔序列(ISI)的神经元集群相关编码
①对神经元群体放电时空序列(spike trains)中每个神经元的放电序列，计算放电脉冲间隔序列ISIs。
②连接N个神经元发放时空序列中每个神经元的离散ISIs点，经过曲线拟合后得到N条神经元发放ISI序列的连续曲线。
③选取在刺激后神经元平均发放频率最高的神经元发放序列作为参考序列。
④设定窗口宽度(选择小于50ms的小窗口)，在第k个窗口中计算其它N-1个ISI序列对参考序列的相关值。
⑤选择步长为1／3窗口宽度，计算每个移动窗口中ISI中的N-1个相关值。
⑥绘制在时间、空间上神经元群体放电的“地形图”，划分编码特定刺激模式的动态神经元集群。
结果：
1．本论文在Matlab7．4仿真平台上构建了海马CA3区小世界神经网络模型。应用该模型可以成功仿真海马CA3区神经元群体的放电特性。
2．在没有刺激输入时，海马CA3区小世界神经网络模型输出的神经元群动作电位发放平均发放率为7．8％，符合海马CA3区神经元群放电的稀疏发放特性(平均发放率小于10％)。
3．在三类刺激输入模式(脉冲刺激、Gaussian白噪声刺激和上述两类刺激的线性叠加)下，模型输出的神经元群体动作电位发放的特征模式不同。
对应的神经元集群编码模式如下：
①神经元集群频率编码
(a)在脉冲刺激输入条件下，各个神经元的放电频率范围为[5．14～21．52]Hz，群体(120个神经元)平均放电频率为10．43±0．38 Hz。神经元集群频率编码能够编码脉冲刺激输入模式。
(b)在Gaussian白噪声刺激信号作用下，各个神经元的放电频率范围为[3．02～15．28]Hz，群体平均放电频率为7．59±0．62Hz。神经元集群频率编码能够编码Gaussian白噪声刺激输入模式。
(c)在以上两类刺激的线性叠加条件下，神经元的放电频率为[2．27～55．21]Hz，平均放电频率为15．52±0．84Hz。神经元集群频率编码不能编码脉冲刺激和Gaussian白噪声刺激线性叠加输入模式。
②神经元集群的ISI相关编码
(a)神经元集群ISI相关编码能够编码脉冲刺激输入模式。
(b)神经元集群ISI相关编码能够编码Gaussian白噪声刺激输入模式。
(c)神经元集群ISI相关编码对脉冲刺激和Gaussian白噪声刺激线性叠加输入模式编码效果不明显。
结论：
1．本论文建立的海马CA3区神经元群小世界神经网络模型能够有效地仿真海马CA3区神经元群体电活动，反映其稀疏特性(平均发放率小于10％)。
2．在三种不同的刺激模式下(脉冲刺激、Gaussian白噪声刺激和上述两类刺激的线性叠加)，海马CA3区神经元群动作电位发放的时空序列特征模式不同。
3．在脉冲刺激和Gaussian白噪声刺激下，频率编码可以划分表征不同单个刺激的神经元集群，神经元集群频率编码只能编码单个刺激模式，对于混合刺激模式，不能编码混合刺激模式中不同的刺激模式。ISI相关编码效能优于频率编码，可以划分表征不同单个刺激的神经元集群，对于两类刺激的线性叠加，编码效果不明显，有待进一步研究。
Objective
In this paper,a hippocampus CA3 neurons spiking small world neural network(SWNN)model is established on the Matlab7.4 platform based on sparse activity ofhippocampus CA3 neurons.The temporal-spatial sequences of the hippocampus CA3area neurons firing activity are simulated under the stimulus of pulse input,Gaussianwhite noise input and the linear superposition input of the two conditions on theSWNN model.The neuronal ensemble rate coding and ISI correlation codingmethods are used to analyze the simulated spiking trains.The hippocampus CA3 areaneurons ensemble coding of the three types stimulus are investigated in this paper.The results may provide neural computation support for hippocampus neuronalensemble coding.
Methods
1.Construction of hippocampus CA3 area neurons spiking SWNN model
According to the anatomical characteristics of hippocampus CA3 area,the ratioof the excitatory to inhibitory neurons is about 5 to 1.The activity of hippocampusCA3 area neurons is sparse firing (less than 10%).A hippocampus CA3 neuronsspiking small world neural network (SWNN)model is established on the Matlab7.4platform.The temporal-spatial sequences of hippocampus CA3 area neurons firingactivity are simulated by the SWNN model.The Hindmarsh-Rose (HR)modelcould describe different discharge property of an excitatory or inhibitory neuron bychanging the parameterγ.In this paper,HR model is used to be the dynamicalequations of the spiking model neurons.The SWNN model is composed of 120neurons,in which 100 neurons are excitatory and 20 are inhibitory.The differentneurons in the SWNN model are connected with WS small-world network.
2.The dynamic simulation of hippocampus CA3 area neurons spikingtemporal-spatial sequences by using the SWNN model.
Set up three types of stimulus input patterns:pulse input,Gaussian white noiseinput and the linear superposition input of the two conditions.The 40 seconds temporal-spatial sequences of hippocampus CA3 area neurons are achieved under thethree different stimulus patterns imposed on the SWNN model.At the same time theinter-spike interval (ISI)of each neuron is get to make up the ISIs temporal-spatialsequences.
3.The hippocampus CA3 neurons ensemble coding of three types of stimulus
The dynamic neuronal ensemble coding is investigated under the differentstimulus input pattern.The neuronal ensemble rate coding and ISI correlation codingmethods are used to analyze the simulated temporal-spatial sequences.Theeffectiveness of the above neuronal ensemble coding methods are compared under thethree different stimulus input pattern.
For the neuronal population firing temporal-spatial sequences simulation dataunder the different stimulus pattern,adopt the rate coding and ISI correlation codingmethods to measure the functional neuronal ensembles.
(1)The rate coding of neuronal ensemble firing activity
The bin window is set to be 200ms (physiological window)and the step lengthof bin window is set to be 50ms.The spiking numbers are counted in the movingwindow of each neuron temporal-spatial sequence.The dynamic topography maps ofneuronal population spike trains are achieved after normalizing the spiking numbers.
(2)The ISI correlation coding of neuronal ensemble firing activity
①The inter-spike intervals (ISis)of each neuron firing sequence are computedamong the neuronal population spike trains.
②Connect the discrete ISis point of each neuron and get the N continuouscurves of ISI sequence by curve fitting.
③The maximum mean firing rate neuronal firing sequence is selected to be thereference sequence.
④The bin window length is set to be small scale (less than 50ms)and the ISIcorrelation values are computed in the kth window of N-1 ISI sequence withreference ISI sequence.
⑤The step length is set to be 1/3 bin window,and the N-1 ISI correlationvalues are computed in each moving window.
⑥The dynamic topography maps of neuronal population spike trains areachieved after normalizing the ISI correlation value.
Results
1.A hippocampus CA3 neurons spiking small world neural network (SWNN)model is established on the Matlab7.4 platform in this paper.The SWNN model cansimulate the sparse activity of hippocampus CA3 area neurons successfully.
2.The mean population firing rate of hippocampus CA3 area is 7.8% when nostimulus acts on the SWNN model.The result is in accordance with the sparse spikefiring characteristic of hippocampus CA3 area (the mean firing rate is less than 10%).
3.The hippocampus CA3 neuronal population firing patterns are different under thethree types of stimulus input(pulse input,Gaussian white noise input and the linearsuperposition input of the two conditions).The neuronal ensemble coding patterns areas followed:
①Neuronal ensemble rate coding
(a)The firing rate range of neuron is [5.14～21.52] Hz under the pulse inputstimulus acts on the SWNN model.The mean firing rate of neuronal population(120neurons)is 10.43±0.38 Hz.The neuronal ensemble rate coding method canencode the pulse input stimulus pattern.
(b)The firing rate range of neuron is [3.02～15.28] Hz under the Gaussian whitenoise input stimulus acts on the SWNN model.The mean firing rate of neuronalpopulation is 7.59±0.62 Hz.The neuronal ensemble rate coding method can encodethe Gaussian white noise input stimulus pattern.
(c)The firing rate range of neuron is [2.27～55.21] Hz under the linearsuperposition input of the pulse input and Gaussian white noise input stimulus acts onthe SWNN model.The mean firing rate of neuronal population is 15.52±0.84 Hz.The neuronal ensemble rate coding method can not distinguish between the pulseinput and Gaussian white noise input stimulus pattern.
②Neuronal ensemble ISI correlation coding
(a)The neuronal ensemble ISI correlation coding method can encode the pulseinput stimulus pattern.
(b)The neuronal ensemble ISI correlation coding method can encode theGaussian white noise input stimulus pattern.
(c)The encoding effect of the mix stimulus pattern by the neuronal ensemblerate coding method is not obvious.
Conclusions
1.The hippocampus CA3 neurons spiking small world neural network (SWNN)model can simulate the sparse activity of hippocampus CA3 area neuronssuccessfully.The simulation result is accordance with the sparse firing (mean firingrate is less than 10%)character of hippocampus CA3 area.
2.The temporal-spatial sequence patterns of hippocampus CA3 neurons aredifferent under the three different types of stimulus input pattern (pulse input,Gaussian white noise input and the linear superposition input of the above stimulusinput).
3.The neuronal ensemble rate coding method can encode the pulse inputstimulus pattern and the Gaussian white noise stimulus pattern.The neuronalensemble rate coding method can not distinguish between the pulse input andGaussian white noise input stimulus pattern.The coding effect of ISI correlation isbetter than the rate coding.The neuronal ensemble ISI correlation coding method canencode the pulse input stimulus pattern and the Gaussian white noise stimulus pattern.But the encoding effect of the mix stimulus pattern by the neuronal ensemble ratecoding method is not obvious.
引文
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