混合尖峰发放模型-神经科学课件

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,混合尖峰发放,模型,To understand how the brain works, we need to combine experimentalstudies of animal and human nervous systems with numerical simulation of large-scale brain models.,E.M. Izhikevich,神经元是生物体中信息传递的基本单元。,文章解读（,Hybrid spiking models,）,several kinds of models,simulation methods of simple model of spiking neurons,问题探究,重现图,2,中不同神经元的活动模式，并指出,相应活动模式的参数,统计各种模式下发放率与输入刺激的强度之,间的关系,输入均值为,符合泊松分布的随机电脉冲，,考察均值与发放率之间关系,The leaky integrate-and-fire model,v:membrane potential,C:memberane capacitance,g,leak,:leaky ohmic conductance,E,leak,:leaky reverse potential,I:input current,It lacks an intrinsic spike-generation mechanism, and hence is just a threshold model.,The quadratic integrate-and-fire model,v:membrane potential,C:memberane capacitance,I:input current,K:a positive parameter,Vrest:resting potentials,Vthresh:,instantaneous,threshold potentials,A hybrid spiking modelas it combines a smooth spike-generation mechanism with autocatalytic upstroke of the spike and a hard after-spike reset.,Simple model of spiking neurons,U:a recovery variable,a: the time scale of u,b: the sensitivity of u,c:,the after-spike reset value of,v,d: the after-spike reset of u,Simple model of spiking neurons,U:a recovery variable,a: the time scale of u,b: the sensitivity of u,c: the after-spike reset value of v,d: the after-spike reset of u,Other hybrid spiking models,All after-spiking resetting are the same.,U,：,a conductance,E:the reverse potential of u,Simple model of spiking neurons,Simulation methods,1)How to detect V,peak,crossing?,2)Strong,synaptic conductances cause numerical,instability. How to avoid numerical instability?,Simple model of spiking neurons,Simulation methods,Detecting V,peak,crossing:,linear,interpolation,Avoiding,numerical,instability:,Simple model of spiking neurons,Simulation methods,time-varying conductance,the reverse potential for,a particular,synaptic current,i,e.g,.,i,= NMDA, AMPA, GABAA and GABAB,Avoiding,numerical,instability:,Simple model of spiking neurons,Simulation methods,The total conductance,The total,reverse potential,Avoiding,numerical,instability:,Simple model of spiking neurons,Simulation methods,Indeed, positive,values of,g(t) push the,membrane,voltage towards the reverse potential,E(t).,However, when g(t) is large, the term,t,g,(t)E(t) v(t) becomes large, resulting in,overshoot and,divergence,from,E(t). Notice that, no matter how small the simulation step t is,the,conductance variable could always become so large as to create the,instability,.,Avoiding,numerical,instability:,Simple model of spiking neurons,Simulation methods,Finally,，,Since the numerical instability is caused by the linear term, one can use,the hybrid,numerical,method,that combines the simplicity and efficiency of explicit methods and the,numerical stability,of implicit methods,.,Avoiding,numerical,instability:,Simple model of spiking neurons,Simulation methods,Left:,Right:,问题探究一,重现图,2,中不同神经元的活动模式，并指出相应活动模式的参数, form,“,Simple model of spiking neurons,”,问题探究一,:,程序示例,subplot(5,4,1),a=0.02; b=0.2; c=-65; d=6;,V=-70; u=b*V;,VV=;,uu,=;,tau = 0.25;,tspan,= 0:tau:100;,T1=,tspan,(end)/10;,for t=,tspan,if (tT1),I=14;,else,I=0;,end;,V = V + tau*(0.04*V2+5*V+140-u+I);,u = u + tau*a*(b*V-u);,if V 30,VV(end+1)=30;,V = c;,u = u + d;,else,VV(end+1)=V;,end;,uu,(end+1)=u;,end;,plot(tspan,VV,0 T1 T1 max(tspan),-90+0 0 10 10);,axis(0 max(,tspan,) -90 30),axis off;,title(A) tonic spiking);,问题探究一,:figure,1,问题探究一,:figure,2,问题探究一,:,参数,模式,/,参数,a,b,c,d,V0,A,0.02,0.2,-65,6,-70,B,0.02,0.25,-65,6,-64,C,0.02,0.2,-50,2,-70,D,0.02,0.25,-55,0.05,-64,E,0.02,0.2,-55,4,-70,F,0.01,0.2,-65,8,-70,G,0.02,-0.1,-55,6,-60,H,0.2,0.26,-65,0,-64,I,0.02,0.2,-65,6,-70,J,0.05,0.26,-60,0,-62,问题探究一,:,参数,模式,/,参数,a,b,c,d,V0,K,0.1,0.26,-60,-1,-62,L,0.02,-0.1,-55,6,-60,M,0.03,0.25,-60,4,-64,N,0.03,0.25,-52,0,-64,O,0.03,0.25,-60,4,-64,P,0.1,0.26,-60,0,-61,Q,1,0.2,-60,-21,-70,R,0.02,1,-25,4,-65,S,-0.02,-1,-60,8,-63.8,T,-0.026,-1,-45,-2,-63.8,问题探究二,统计各种模式下发放率和输入刺激的强度之间的关系,1,）在不同模式下，改变输入刺激电流,I,的大小，并统计不同的输入电流,I,对应,的发放率,r,，利用,plot,函数绘制不同模式下的“,r-I,”关系图,2,）对,A,模式（,tonic spiking,）的“,r-I,”关系图进行拟合，得出其对应表达式,注：统计发放率方法众多，此处采用较为简便的“时间平均法”,问题探究二：程序示例,V = V + tau*(0.04*V2+5*V+140-u+I);,u = u + tau*a*(b*V-u);,if V 30,VV(end+1)=30;,V = c;,u = u + d;,else,VV(end+1)=V;,end;,uu,(end+1)=u;,end;,ffl,(,i,)=,histc,(VV,30)/100;,end,figure,plot(,dl,ffl,-o),title(A) tonic spiking);,subplot(5,4,1),a=0.02; b=0.2;,c=-65; d=6;,V=-70; u=b*V;,VV=;,uu,=;,tau = 0.25;,tspan,= 0:tau:100;,T1=,tspan,(end)/10;,dl=1:50;,ffl,=zeros(1,length(dl);,for,i,=1:length(dl),for t=,tspan,if (tT1),I=dl(,i,);,else,I=0;,end;,问题探究二：“,r-I,”关系图,问题探究二,对,A,模式（,tonic spiking,）的“,r-I,”关系图进行拟合,Linear model Poly2:,f(x) = p1*x2 + p2*x + p3,Coefficients (with 95% confidence bounds):,p1 = 0.001364 (0.001358, 0.001369),p2 = 6.425e-005 (-0.0002163, 0.0003448),p3 = -0.007935 (-0.01104, -0.004833),即：,问题探究三,输入均值为 符合泊松分布的随机电脉冲，考察均值和发放率之间的关系,(1),选择“,tonic spiking,”的脉冲为基本脉冲单元，在一个单位的时间内有,n,个基本脉冲单元依次输入（,n,服从均值为,u,的泊松分布），则在此单位时间内的总输入为,n,个基本脉冲单元的累加,总电流。,如右图例示（,n=5,）,问题探究二,(2),当,u=5,时，得出 发放率与输入刺激,I,的关系如右图所示：,问题探究二,(3),对于不同的,u,值，分别统计发放率，最终得到“,r-u,”关系图：,THANK YOU !,