Respiratory control model with brainstem CPG and sensory feedback (Diekman, Thomas, and Wilson 2017)

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Accession:229640
This is a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. The closed-loop system exhibits bistability of bursting and tonic spiking. Bursting corresponds to coexistence of eupnea-like breathing, with normal minute ventilation and blood oxygen level. Tonic spiking corresponds to a tachypnea-like state, with pathologically reduced minute ventilation and critically low blood oxygen. In our paper, we use the closed-loop system to demonstrate robustness to changes in metabolic demand, spontaneous autoresuscitation in response to hypoxia, and the distinct mechanisms that underlie rhythmogenesis in the intact control circuit vs. the isolated, open-loop CPG.
Reference:
1 . Diekman CO, Thomas PJ, Wilson CG (2017) Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model. J Neurophysiol 118:2194-2215 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Brainstem;
Cell Type(s): Respiratory column neuron; PreBotzinger complex neuron;
Channel(s): I Na,p; I Na,t; I K;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB; XPP;
Model Concept(s): Pacemaking mechanism; Respiratory control;
Implementer(s): Diekman, Casey O. [casey.o.diekman at njit.edu];
Search NeuronDB for information about:  I Na,p; I Na,t; I K;
% Script to reproduce Figure A1
% calls 'closedloop.m'

clear all

%% Initial conditions [V n h alpha vollung PO2lung PO2blood]

initsA = [-58.5754 0.0006 0.7252 0.0010 2.2665 103.3461 102.2229];

tf = 8000;

options = odeset('RelTol',1e-9,'AbsTol',1e-9);

[t,u] = ode15s('closedloop',[0 tf],initsA,options);

v=u(:,1);
n=u(:,2);
h=u(:,3);
alpha=u(:,4);
vollung=u(:,5);
po2lung=u(:,6);
po2blood=u(:,7);

%% Calculate derivatives

% Parameters

taulb=500;
M=8e-6;

gnap=2.8; gna=28; gk=11.2; gl=2.8; 
Ena=50; Ek=-85; El=-65; Esyn=0;

r=0.001; Tmax=1; VT=2; Kp=5;
E1=0.0025; E2=0.4;

PO2ext=(760-47)*.21; Vol0=2; R=62.364; Temp=310; 
Hb=150; volblood=5; eta=Hb*1.36; gamma=volblood/22400; betaO2=0.03;

c=2.5; K=26;
SaO2=(po2blood.^c)./(po2blood.^c+K^c);
CaO2=eta*SaO2+betaO2*po2blood;
partial=(c*po2blood.^(c-1)).*(1./(po2blood.^c+K^c)-(po2blood.^c)./((po2blood.^c+K^c).^2));

gtonic=0.3*(1-tanh((po2blood-85)./30));

Jlb=(1/taulb)*(po2lung-po2blood).*(vollung/(R*Temp));
Jbt=M*CaO2*gamma;

C=21;  %pF

theta_mp=-40;  %mV
sigma_mp=-6;  %mV
taumax_h=10000;  %ms
theta_h=-48;  %mV
sigma_h=6;  %mV

theta_m=-34;  %mV
sigma_m=-5;  %mV

taumax_n=10;  %ms
theta_n=-29; %mV
sigma_n=-4;  %mV


% Steady state values and time constants
mp_inf=1./(1+exp((v-theta_mp)./sigma_mp));

m_inf=1./(1+exp((v-theta_m)./sigma_m));

h_inf=1./(1+exp((v-theta_h)./sigma_h));
tau_h=taumax_h./cosh((v-theta_h)./(2*sigma_h));

n_inf=1./(1+exp((v-theta_n)./sigma_n));
tau_n=taumax_n./cosh((v-theta_n)./(2*sigma_n));


% Currents

Inap=gnap*mp_inf.*h.*(v-Ena);
Ina=gna*(m_inf.^3).*(1-n).*(v-Ena);
Ik=gk*(n.^4).*(v-Ek);
Il=gl*(v-El);
Itonic=gtonic.*(v-Esyn);

NT=Tmax./(1+exp(-(v-VT)./Kp));

% Lung Volume

dvolrhs=max(0,-E1*(vollung-Vol0)+E2*alpha);

% Differential equations

dv=(-Inap-Ina-Ik-Il-Itonic)/C;
dh=(h_inf-h)./tau_h;
dn=(n_inf-n)./tau_n;
dalpha=r*NT.*(1-alpha)-r*alpha;
dvollung=-E1*(vollung-Vol0)+E2*alpha;
dpo2lung=(1./vollung).*(PO2ext-po2lung).*dvolrhs-Jlb.*(R*Temp./vollung);
dpo2blood=(Jlb-Jbt)./(gamma*(betaO2+eta*partial));

% get max speed

vx_po2blood=max(abs(dpo2blood))/(max(po2blood)-min(po2blood));
vx_vollung=max(abs(dvollung))/(max(vollung)-min(vollung));
vx_po2lung=max(abs(dpo2lung))/(max(po2lung)-min(po2lung));
vx_h=max(abs(dh))/(max(h)-min(h));
vx_alpha=max(abs(dalpha))/(max(alpha)-min(alpha));
vx_v=max(abs(dv))/(max(v)-min(v));
vx_n=max(abs(dn))/(max(n)-min(n));

vx_po2blood_ind=find(abs(dpo2blood)/(max(po2blood)-min(po2blood))==vx_po2blood);
vx_vollung_ind=find(abs(dvollung)/(max(vollung)-min(vollung))==vx_vollung);
vx_po2lung_ind=find(abs(dpo2lung)/(max(po2lung)-min(po2lung))==vx_po2lung);
vx_h_ind=find(abs(dh)/(max(h)-min(h))==vx_h);
vx_alpha_ind=find(abs(dalpha)/(max(alpha)-min(alpha))==vx_alpha);
vx_v_ind=find(abs(dv)/(max(v)-min(v))==vx_v);
vx_n_ind=find(abs(dn)/(max(n)-min(n))==vx_n);


%% make plots

close all

set(0,'DefaultAxesFontSize',24)

lw=3;
ms=10;

figure(1)
subplot(2,3,2)
plot(v,dv/(max(v)-min(v)),'k','Linewidth',lw)
hold on
plot(v(vx_v_ind),vx_v,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$V$','Interpreter','latex')
ylabel('normalized $V''(t)$','Interpreter','latex')
xlim([-65 20])
ylim([-.5 1.2])

subplot(2,3,1)
plot(n,dn/(max(n)-min(n)),'k','Linewidth',lw)
hold on
plot(n(vx_n_ind),vx_n,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$n$','Interpreter','latex')
ylabel('normalized $n''(t)$','Interpreter','latex')
xlim([-.05 1])
ylim([-0.5 2])

subplot(2,3,4)
plot(h,dh/(max(h)-min(h)),'k','Linewidth',lw)
hold on
plot(h(vx_h_ind),-vx_h,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$h$','Interpreter','latex')
ylabel('normalized $h''(t)$','Interpreter','latex')
xlim([0.65 0.78])
ylim([-0.045 0.005])

subplot(2,3,3)
plot(alpha,dalpha/(max(alpha)-min(alpha)),'k','Linewidth',lw)
hold on
plot(alpha(vx_alpha_ind),vx_alpha,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$\alpha$','Interpreter','latex')
ylabel('normalized $\alpha''(t)$','Interpreter','latex')
xlim([-0.001 0.01])
ylim([-.005 .081])

subplot(2,3,5)
plot(vollung,dvollung/(max(vollung)-min(vollung)),'k','Linewidth',lw)
hold on
plot(vollung(vx_vollung_ind),vx_vollung,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$\mathrm{vol}_\mathrm{L}$','Interpreter','latex')
ylabel('normalized $\mathrm{vol}_\mathrm{L}''(t)$','Interpreter','latex')
xlim([1.9 3.1])
ylim([-.0008 .003])

subplot(2,3,6)
plot(po2lung,dpo2lung/(max(po2lung)-min(po2lung)),'b','Linewidth',lw)
hold on
plot(po2blood,dpo2blood/(max(po2blood)-min(po2blood)),'r','Linewidth',lw)
plot(po2lung(vx_po2lung_ind),vx_po2lung,'go','MarkerFaceColor','g','MarkerSize',ms)
plot(po2blood(vx_po2blood_ind),vx_po2blood,'go','MarkerFaceColor','g','MarkerSize',ms)
xlabel('$P\mathrm{O}_2$','Interpreter','latex')
ylabel('normalized $P\mathrm{O}_2''(t)$','Interpreter','latex')
h=legend('$P_\mathrm{A}\mathrm{O}_2$','$P_\mathrm{a}\mathrm{O}_2$','Location','South','Orientation','Horizontal');
legend('boxoff')
set(h,'Interpreter','latex')
ylim([-.0008 .003])
xlim([92 108])

set(gcf,'position',get(0,'screensize'))


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