/* * An integrative dynamic model of brain energy metabolism using * in vivo neurochemical measurements * * Model Status * * This CellMl model runs in OpenCell to recreate the published * results. The units are balanced. Thank you to the original author * Mathieu Cloutier for his invaluable help in the final stages * of model curation. We recommend the followin simulation conditions: * a duration of 2500 seconds with a an increase in neuronal activity * at 200 seconds. * * Model Structure * * ABSTRACT: An integrative, systems approach to the modelling * of brain energy metabolism is presented. Mechanisms such as * glutamate cycling between neurons and astrocytes and glycogen * storage in astrocytes have been implemented. A unique feature * of the model is its calibration using in vivo data of brain * glucose and lactate from freely moving rats under various stimuli. * The model has been used to perform simulated perturbation experiments * that show that glycogen breakdown in astrocytes is significantly * activated during sensory (tail pinch) stimulation. This mechanism * provides an additional input of energy substrate during high * consumption phases. By way of validation, data from the perfusion * of 50 microM propranolol in the rat brain was compared with * the model outputs. Propranolol affects the glucose dynamics * during stimulation, and this was accurately reproduced in the * model by a reduction in the glycogen breakdown in astrocytes. * The model's predictive capacity was verified by using data from * a sensory stimulation (restraint) that was not used for model * calibration. Finally, a sensitivity analysis was conducted on * the model parameters, this showed that the control of energy * metabolism and transport processes are critical in the metabolic * behaviour of cerebral tissue. * * model diagram * * [[Image file: cloutier_2009.png]] * * Schematic diagram of the model for astrocyte-neuron metabolism * * The original paper reference is cited below: * * An integrative dynamic model of brain energy metabolism using * in vivo neurochemical measurements, Mathieu Cloutier, Fiachra * B. Bolger, John P. Lowry and Peter Wellstead, 2009, Journal * of Computational Neuroscience, 27, 391-414. PubMed ID: 19396534 */ import nsrunit; unit conversion on; unit s=1 second^1; unit mM=1 meter^(-3)*mole^1; unit per_mM=1 meter^3*mole^(-1); unit mM_per_s=1 meter^(-3)*second^(-1)*mole^1; unit per_mM_per_s=1 meter^3*second^(-1)*mole^(-1); unit per_s=1 second^(-1); unit cm_per_mM_per_s=.01 meter^4*second^(-1)*mole^(-1); unit per_cm=100 meter^(-1); unit C_per_mole=1 second^1*ampere^1*mole^(-1); unit L_per_millimole=1 meter^3*mole^(-1); unit mS_per_cm2=10 kilogram^(-1)*meter^(-4)*second^3*ampere^2; unit mV=.001 kilogram^1*meter^2*second^(-3)*ampere^(-1); unit mV_C_per_mol=.001 kilogram^1*meter^2*second^(-2)*mole^(-1); math main { realDomain time s; time.min=0; extern time.max; extern time.delta; real NAn(time) mM; when(time=time.min) NAn=15.533; real Vn_leak_Na(time) mM_per_s; real Vn_pump(time) mM_per_s; real Vn_stim(time) mM_per_s; real GLCn(time) mM; when(time=time.min) GLCn=0.2633; real V_en_GLC(time) mM_per_s; real Vn_hk(time) mM_per_s; real G6Pn(time) mM; when(time=time.min) G6Pn=0.7275; real Vn_pgi(time) mM_per_s; real F6Pn(time) mM; when(time=time.min) F6Pn=0.1091; real Vn_pfk(time) mM_per_s; real GAPn(time) mM; when(time=time.min) GAPn=0.0418; real Vn_pgk(time) mM_per_s; real PEPn(time) mM; when(time=time.min) PEPn=0.0037; real Vn_pk(time) mM_per_s; real PYRn(time) mM; when(time=time.min) PYRn=0.0388; real Vn_ldh(time) mM_per_s; real Vn_mito(time) mM_per_s; real LACn(time) mM; when(time=time.min) LACn=0.3856; real Vne_LAC(time) mM_per_s; real NADHn(time) mM; when(time=time.min) NADHn=0.0319; real ATPn(time) mM; when(time=time.min) ATPn=2.2592; real nOP dimensionless; nOP=15.0; real Vn_ATPase(time) mM_per_s; real Vn_ck(time) mM_per_s; real dAMP_dATPn(time) dimensionless; real PCrn(time) mM; when(time=time.min) PCrn=4.2529; real O2n(time) mM; when(time=time.min) O2n=0.0975; real NAero dimensionless; NAero=3.0; real Vcn_O2(time) mM_per_s; real GLUn(time) mM; when(time=time.min) GLUn=3.0; real Rng dimensionless; Rng=1.8; real Vg_gs(time) mM_per_s; real Vn_stim_GLU(time) mM_per_s; real NAg(time) mM; when(time=time.min) NAg=13.36; real Vg_leak_Na(time) mM_per_s; real Vg_pump(time) mM_per_s; real Veg_GLU(time) mM_per_s; real GLCg(time) mM; when(time=time.min) GLCg=0.1656; real Vcg_GLC(time) mM_per_s; real Veg_GLC(time) mM_per_s; real Vg_hk(time) mM_per_s; real G6Pg(time) mM; when(time=time.min) G6Pg=0.7326; real Vg_pgi(time) mM_per_s; real Vg_glys(time) mM_per_s; real Vg_glyp(time) mM_per_s; real F6Pg(time) mM; when(time=time.min) F6Pg=0.1116; real Vg_pfk(time) mM_per_s; real GAPg(time) mM; when(time=time.min) GAPg=0.0698; real Vg_pgk(time) mM_per_s; real PEPg(time) mM; when(time=time.min) PEPg=0.0254; real Vg_pk(time) mM_per_s; real PYRg(time) mM; when(time=time.min) PYRg=0.1711; real Vg_ldh(time) mM_per_s; real Vg_mito(time) mM_per_s; real LACg(time) mM; when(time=time.min) LACg=0.4651; real Vge_LAC(time) mM_per_s; real Vgc_LAC(time) mM_per_s; real NADHg(time) mM; when(time=time.min) NADHg=0.0445; real ATPg(time) mM; when(time=time.min) ATPg=2.24; real Vg_ATPase(time) mM_per_s; real Vg_ck(time) mM_per_s; real dAMP_dATPg(time) dimensionless; real PCrg(time) mM; when(time=time.min) PCrg=4.6817; real O2g(time) mM; when(time=time.min) O2g=0.1589; real Vcg_O2(time) mM_per_s; real GLYg(time) mM; when(time=time.min) GLYg=2.5; real GLUg(time) mM; when(time=time.min) GLUg=0.0; real GLCe(time) mM; when(time=time.min) GLCe=0.3339; real Reg dimensionless; Reg=0.8; real Ren dimensionless; Ren=0.4444444444444444; real Vce_GLC(time) mM_per_s; real LACe(time) mM; when(time=time.min) LACe=0.3986; real Vec_LAC(time) mM_per_s; real GLUe(time) mM; when(time=time.min) GLUe=0.0; real O2c(time) mM; when(time=time.min) O2c=7.4201; real Rcn dimensionless; Rcn=0.01222; real Rcg dimensionless; Rcg=0.022; real Vc_O2(time) mM_per_s; real GLCc(time) mM; when(time=time.min) GLCc=4.6401; real Rce dimensionless; Rce=0.0275; real Vc_GLC(time) mM_per_s; real LACc(time) mM; when(time=time.min) LACc=0.3251; real Vc_LAC(time) mM_per_s; real CO2c(time) mM; when(time=time.min) CO2c=2.12; real Vnc_CO2(time) mM_per_s; real Vc_CO2(time) mM_per_s; real Vgc_CO2(time) mM_per_s; real Vv(time) dimensionless; when(time=time.min) Vv=0.0237; real Fin_t(time) per_s; real Fout_t(time) per_s; real dHb(time) mM; when(time=time.min) dHb=0.0218; real O2a mM; O2a=8.34; real gn_NA mS_per_cm2; gn_NA=0.0039; real Sm_n per_cm; Sm_n=40500; real Vm mV; Vm=-70; real Vn dimensionless; Vn=0.45; real RT mV_C_per_mol; RT=2577340; real F C_per_mole; F=96500; real NAe mM; NAe=150.0; real kpump cm_per_mM_per_s; kpump=3.17e-7; real Km_pump mM; Km_pump=0.4243; real v_stim(time) mM_per_s; real Km_en_GLC mM; Km_en_GLC=5.32; real Vm_en_GLC mM_per_s; Vm_en_GLC=0.50417; real Vmax_n_hk mM_per_s; Vmax_n_hk=0.0513; real Km_GLC mM; Km_GLC=0.105; real G6P_inh_hk mM; G6P_inh_hk=0.6; real aG6P_inh_hk dimensionless; aG6P_inh_hk=20.0; real Vmaxf_n_pgi mM_per_s; Vmaxf_n_pgi=0.5; real Vmaxr_n_pgi mM_per_s; Vmaxr_n_pgi=0.45; real Km_G6P mM; Km_G6P=0.5; real Km_F6P_pgi mM; Km_F6P_pgi=0.06; real kn_pfk per_s; kn_pfk=0.55783; real Km_F6P_pfk mM; Km_F6P_pfk=0.18; real Ki_ATP mM; Ki_ATP=0.7595; real nH dimensionless; nH=4.0; real kn_pgk per_mM_per_s; kn_pgk=0.4287; real ADPn(time) mM; real NADn(time) mM; real kn_pk per_mM_per_s; kn_pk=28.6; real kfn_ldh per_mM_per_s; kfn_ldh=5.30; real krn_ldh per_mM_per_s; krn_ldh=0.1046; real Vmax_n_mito mM_per_s; Vmax_n_mito=0.05557; real Km_O2 mM; Km_O2=0.0029658; real Km_ADP mM; Km_ADP=0.00107; real Km_PYR mM; Km_PYR=0.0632; real rATP_mito dimensionless; rATP_mito=20.0; real aATP_mito dimensionless; aATP_mito=5.0; real Vmax_ne_LAC mM_per_s; Vmax_ne_LAC=0.1978; real Km_ne_LAC mM; Km_ne_LAC=0.09314; real Vmax_n_ATPase mM_per_s; Vmax_n_ATPase=0.04889; real krn_ck per_mM_per_s; krn_ck=0.015; real kfn_ck per_mM_per_s; kfn_ck=0.0524681; real CRn(time) mM; real Vcn_O2.nh_O2 dimensionless; Vcn_O2.nh_O2=2.7; real PScapn per_s; PScapn=0.2202; real Ko2 mM; Ko2=0.089733; real HbOP mM; HbOP=8.6; real gg_NA mS_per_cm2; gg_NA=0.00325; real Sm_g per_cm; Sm_g=10500; real Vg dimensionless; Vg=0.25; real Km_eg_GLC mM; Km_eg_GLC=3.53; real Vm_eg_GLC mM_per_s; Vm_eg_GLC=0.038089; real KO1 dimensionless; KO1=1.0; real Km_cg_GLC mM; Km_cg_GLC=9.92; real Vm_cg_GLC mM_per_s; Vm_cg_GLC=0.0098394; real Vmax_g_hk mM_per_s; Vmax_g_hk=0.050461; real Vmaxf_g_pgi mM_per_s; Vmaxf_g_pgi=0.5; real Vmaxr_g_pgi mM_per_s; Vmaxr_g_pgi=0.45; real kg_pfk per_s; kg_pfk=0.403; real kg_pgk per_mM_per_s; kg_pgk=0.2514; real ADPg(time) mM; real NADg(time) mM; real kg_pk per_mM_per_s; kg_pk=2.73; real kfg_ldh per_mM_per_s; kfg_ldh=6.2613; real krg_ldh per_mM_per_s; krg_ldh=0.54682; real Vmax_g_mito mM_per_s; Vmax_g_mito=0.008454; real Vmax_ge_LAC mM_per_s; Vmax_ge_LAC=0.086124; real Km_ge_LAC mM; Km_ge_LAC=0.22163; real Vmax_gc_LAC mM_per_s; Vmax_gc_LAC=0.00021856; real Km_gc_LAC mM; Km_gc_LAC=0.12862; real Vmax_g_ATPase mM_per_s; Vmax_g_ATPase=0.035657; real krg_ck per_mM_per_s; krg_ck=0.02073; real kfg_ck per_mM_per_s; kfg_ck=0.0243; real CRg(time) mM; real PScapg per_s; PScapg=0.2457; real Vcg_O2.nh_O2 dimensionless; Vcg_O2.nh_O2=2.7; real Vc dimensionless; Vc=0.0055; real GLCa mM; GLCa=4.8; real Km_ce_GLC mM; Km_ce_GLC=8.4568; real Vm_ce_GLC mM_per_s; Vm_ce_GLC=0.0489; real LACa mM; LACa=0.313; real Km_ec_LAC mM; Km_ec_LAC=0.764818; real Vm_ec_LAC mM_per_s; Vm_ec_LAC=0.0325; real R_GLU_NA dimensionless; R_GLU_NA=0.075; real Km_GLU mM; Km_GLU=0.05; real KO2 dimensionless; KO2=1; real Vmax_g_gs mM_per_s; Vmax_g_gs=0.3; real Km_ATP mM; Km_ATP=0.01532; real Vmax_eg_GLU mM_per_s; Vmax_eg_GLU=0.0208; real CO2a mM; CO2a=1.2; real Vmax_glys mM_per_s; Vmax_glys=0.0001528; real Km_G6P_glys mM; Km_G6P_glys=0.5; real GLY_inh mM; GLY_inh=4.2; real aGLY_inh dimensionless; aGLY_inh=20.0; real Vmax_glyp mM_per_s; Vmax_glyp=4.922e-5; real Km_GLY mM; Km_GLY=1.0; real deltaVt_GLY(time) dimensionless; real unitstepSB2(time) dimensionless; real stim dimensionless; stim=1; real was_to s; was_to=200; real to_GLY s; to_GLY=83; real tend_GLY s; tend_GLY=440; real sr_GLY dimensionless; sr_GLY=4; real t1 s; t1=2; real delta_GLY dimensionless; delta_GLY=62; real KO3 dimensionless; KO3=1; real Fin_t.CBF0 per_s; Fin_t.CBF0=0.012; real tend s; tend=300; real sr dimensionless; sr=4.59186; real deltaf dimensionless; deltaf=0.42; real Fout_t.CBF0 per_s; Fout_t.CBF0=0.012; real Vv0 dimensionless; Vv0=0.0236; real tv s; tv=35.0; real NADH_n_tot mM; NADH_n_tot=0.22; real NADH_g_tot mM; NADH_g_tot=0.22; real PCrn_tot mM; PCrn_tot=5.0; real PCrg_tot mM; PCrg_tot=5.0; real ATPtot mM; ATPtot=2.379; real qak dimensionless; qak=0.92; real u_n(time) dimensionless; real u_g(time) dimensionless; real AMPn(time) mM; real AMPg(time) mM; real BOLD(time) dimensionless; real k1 dimensionless; k1=2.22; real k2 dimensionless; k2=0.46; real k3 dimensionless; k3=0.43; real dHb0 mM; dHb0=0.064; real unitpulseSB(time) dimensionless; real t_n_stim s; t_n_stim=2; real v1_n mM_per_s; v1_n=0.041; real v2_n mM_per_s; v2_n=2.55; real unitstepSB(time) dimensionless; // // NAn:time=(Vn_leak_Na+Vn_stim-3*Vn_pump); // GLCn:time=(V_en_GLC-Vn_hk); // G6Pn:time=(Vn_hk-Vn_pgi); // F6Pn:time=(Vn_pgi-Vn_pfk); // GAPn:time=(2*Vn_pfk-Vn_pgk); // PEPn:time=(Vn_pgk-Vn_pk); // PYRn:time=(Vn_pk-(Vn_ldh+Vn_mito)); // LACn:time=(Vn_ldh-Vne_LAC); // NADHn:time=(Vn_pgk-(Vn_ldh+Vn_mito)); // ATPn:time=((Vn_pgk+Vn_pk+nOP*Vn_mito+Vn_ck-(Vn_hk+Vn_pfk+Vn_ATPase+Vn_pump))*(1-dAMP_dATPn)^(-1)); // PCrn:time=((-1)*Vn_ck); // O2n:time=(Vcn_O2-NAero*Vn_mito); // GLUn:time=(Vg_gs*(1/Rng)-Vn_stim_GLU); // NAg:time=(Vg_leak_Na+3*Veg_GLU-3*Vg_pump); // GLCg:time=(Vcg_GLC+Veg_GLC-Vg_hk); // G6Pg:time=(Vg_hk+Vg_glyp-(Vg_pgi+Vg_glys)); // F6Pg:time=(Vg_pgi-Vg_pfk); // GAPg:time=(2*Vg_pfk-Vg_pgk); // PEPg:time=(Vg_pgk-Vg_pk); // PYRg:time=(Vg_pk-(Vg_ldh+Vg_mito)); // LACg:time=(Vg_ldh-(Vge_LAC+Vgc_LAC)); // NADHg:time=(Vg_pgk-(Vg_ldh+Vg_mito)); // ATPg:time=((Vg_pgk+Vg_pk+nOP*Vg_mito+Vg_ck-(Vg_hk+Vg_pfk+Vg_ATPase+Vg_pump+Vg_gs))*(1-dAMP_dATPg)^(-1)); // PCrg:time=((-1)*Vg_ck); // O2g:time=(Vcg_O2-NAero*Vg_mito); // GLYg:time=(Vg_glys-Vg_glyp); // GLUg:time=(Veg_GLU-Vg_gs); // GLCe:time=(Vce_GLC-(Veg_GLC*(1/Reg)+V_en_GLC*(1/Ren))); // LACe:time=(Vne_LAC*(1/Ren)+Vge_LAC*(1/Reg)-Vec_LAC); // GLUe:time=(Vn_stim_GLU*(1/Ren)-Veg_GLU*(1/Reg)); // O2c:time=(Vc_O2-(Vcn_O2*(1/Rcn)+Vcg_O2*(1/Rcg))); // GLCc:time=(Vc_GLC-(Vce_GLC*(1/Rce)+Vcg_GLC*(1/Rcg))); // LACc:time=(Vc_LAC+(Vec_LAC*(1/Rce)+Vgc_LAC*(1/Rcg))); // CO2c:time=(Vnc_CO2*(1/Rcn)+Vgc_CO2*(1/Rcg)-Vc_CO2); // Vv:time=(Fin_t-Fout_t); // dHb:time=(Fin_t*(O2a-O2c)-Fout_t*(dHb/Vv)); // Vn_leak_Na=(Sm_n/Vn*(gn_NA/F)*(RT/F*ln(NAe/NAn)-Vm)); // Vn_pump=(Sm_n/Vn*kpump*ATPn*NAn*(1+ATPn/Km_pump)^(-1)); // Vn_stim=v_stim; // V_en_GLC=(Vm_en_GLC*(GLCe/(GLCe+Km_en_GLC)-GLCn/(GLCn+Km_en_GLC))); // Vn_hk=(Vmax_n_hk*ATPn*(GLCn/(GLCn+Km_GLC))*((1 per_mM)-(1 per_mM)/(1+exp((-1)*aG6P_inh_hk*((1 per_mM)*(G6Pn-G6P_inh_hk)))))); // Vn_pgi=(Vmaxf_n_pgi*(G6Pn/(G6Pn+Km_G6P))-Vmaxr_n_pgi*(F6Pn/(F6Pn+Km_F6P_pgi))); // Vn_pfk=(kn_pfk*ATPn*(F6Pn/(F6Pn+Km_F6P_pfk))*(1+(ATPn/Ki_ATP)^nH)^(-1)); // Vn_pgk=(kn_pgk*GAPn*ADPn*(NADn/NADHn)); // Vn_pk=(kn_pk*PEPn*ADPn); // Vn_ldh=(kfn_ldh*PYRn*NADHn-krn_ldh*LACn*NADn); // Vn_mito=(Vmax_n_mito*(O2n/(O2n+Km_O2))*(ADPn/(ADPn+Km_ADP))*(PYRn/(PYRn+Km_PYR))*(1-1/(1+exp((-1)*aATP_mito*(1*(ATPn/ADPn-1*rATP_mito)))))); // Vne_LAC=(Vmax_ne_LAC*(LACn/(LACn+Km_ne_LAC)-LACe/(LACe+Km_ne_LAC))); // Vn_ATPase=(Vmax_n_ATPase*(ATPn/(ATPn+(.001 mM)))); // Vn_ck=(kfn_ck*PCrn*ADPn-krn_ck*CRn*ATPn); // Vcn_O2=(PScapn/Vn*(Ko2*(HbOP/O2c-1)^((-1)/Vcn_O2.nh_O2)-O2n)); // Vg_leak_Na=(Sm_g/Vg*(gg_NA/F)*(RT/F*ln(NAe/NAg)-Vm)); // Vg_pump=(Sm_g/Vg*kpump*ATPg*NAg*(1+ATPg/Km_pump)^(-1)); // Veg_GLC=(KO1*Vm_eg_GLC*(GLCe/(GLCe+Km_eg_GLC)-GLCg/(GLCg+Km_eg_GLC))); // Vcg_GLC=(Vm_cg_GLC*(GLCc/(GLCc+Km_cg_GLC)-GLCg/(GLCg+Km_cg_GLC))); // Vg_hk=(Vmax_g_hk*ATPg*(GLCg/(GLCg+Km_GLC))*((1 per_mM)-(1 per_mM)/(1+exp((-1)*aG6P_inh_hk*((1 per_mM)*(G6Pg-G6P_inh_hk)))))); // Vg_pgi=(Vmaxf_g_pgi*(G6Pg/(G6Pg+Km_G6P))-Vmaxr_g_pgi*(F6Pg/(F6Pg+Km_F6P_pgi))); // Vg_pfk=(kg_pfk*ATPg*(F6Pg/(F6Pg+Km_F6P_pfk))*(1+(ATPg/Ki_ATP)^nH)^(-1)); // Vg_pgk=(kg_pgk*GAPg*ADPg*(NADg/NADHg)); // Vg_pk=(kg_pk*PEPg*ADPg); // Vg_ldh=(kfg_ldh*PYRg*NADHg-krg_ldh*LACg*NADg); // Vg_mito=(Vmax_g_mito*(O2g/(O2g+Km_O2))*(ADPg/(ADPg+Km_ADP))*(PYRg/(PYRg+Km_PYR))*(1-1/(1+exp(1*((-1)*aATP_mito)*(ATPg/ADPg-1*rATP_mito))))); // Vge_LAC=(Vmax_ge_LAC*(LACg/(LACg+Km_ge_LAC)-LACe/(LACe+Km_ge_LAC))); // Vgc_LAC=(Vmax_gc_LAC*(LACg/(LACg+Km_gc_LAC)-LACc/(LACc+Km_gc_LAC))); // Vg_ATPase=(Vmax_g_ATPase*(ATPg/(ATPg+(.001 mM)))); // Vg_ck=(kfg_ck*PCrg*ADPg-krg_ck*CRg*ATPg); // Vcg_O2=(PScapg/Vg*(Ko2*(HbOP/O2c-1)^((-1)/Vcg_O2.nh_O2)-O2g)); // Vc_O2=(2*(Fin_t/Vc)*(O2a-O2c)); // Vc_GLC=(2*(Fin_t/Vc)*(GLCa-GLCc)); // Vce_GLC=(Vm_ce_GLC*(GLCc/(GLCc+Km_ce_GLC)-GLCe/(GLCe+Km_ce_GLC))); // Vc_LAC=(2*(Fin_t/Vc)*(LACa-LACc)); // Vec_LAC=(Vm_ec_LAC*(LACe/(LACe+Km_ec_LAC)-LACc/(LACc+Km_ec_LAC))); // Vnc_CO2=(3*Vn_mito); // Vgc_CO2=(3*Vg_mito); // Vn_stim_GLU=(Vn_stim*R_GLU_NA*KO2*(GLUn/(GLUn+Km_GLU))); // Vg_gs=(Vmax_g_gs*(GLUg/(GLUg+Km_GLU)*(ATPg/(ATPg+Km_ATP)))); // Veg_GLU=(Vmax_eg_GLU*(GLUe/(GLUe+Km_GLU))); // Vc_CO2=(2*(Fin_t/Vc)*(CO2c-CO2a)); // Vg_glys=(Vmax_glys*(G6Pg/(G6Pg+Km_G6P_glys))*(1-1/(1+exp((-1)*aGLY_inh*((1 per_mM)*(GLYg-GLY_inh)))))); // Vg_glyp=(Vmax_glyp*(GLYg/(GLYg+Km_GLY))*deltaVt_GLY); deltaVt_GLY=(1+stim*(delta_GLY*KO3*(1/(1+exp((1 per_s)*((-1)*sr_GLY)*(time-(was_to+to_GLY)))))*(1-unitstepSB2))); // Fin_t=(Fin_t.CBF0+(stim*Fin_t.CBF0*deltaf*(1/(1+exp((1 per_s)*((-1)*sr)*(time-(was_to+t1-(3 second))))))-stim*Fin_t.CBF0*deltaf*(1/(1+exp((1 per_s)*((-1)*sr)*(time-(was_to+tend+t1+(3 second)))))))); // Fout_t=(Fout_t.CBF0*(((Vv/Vv0)^2+tv*(Vv/Vv0)^(-0.5)*(Fin_t/Vv0))/(1+Fout_t.CBF0*tv*(Vv/Vv0)^(-0.5)*(1/Vv0)))); // NADn=(NADH_n_tot-NADHn); // NADg=(NADH_g_tot-NADHg); // CRn=(PCrn_tot-PCrn); // CRg=(PCrg_tot-PCrg); // ADPn=(ATPn/2*((-1)*qak+sqrt(qak^2+4*qak*(ATPtot/ATPn-1)))); // ADPg=(ATPg/2*((-1)*qak+sqrt(qak^2+4*qak*(ATPtot/ATPg-1)))); // u_n=(qak^2+4*qak*(ATPtot/ATPn-1)); // u_g=(qak^2+4*qak*(ATPtot/ATPg-1)); // dAMP_dATPn=(qak/2+qak*(ATPtot/(ATPn*sqrt(u_n)))-(1+.5*sqrt(u_n))); // dAMP_dATPg=(qak/2+qak*(ATPtot/(ATPg*sqrt(u_g)))-(1+.5*sqrt(u_g))); // AMPn=(ATPtot-(ATPn+ADPn)); // AMPg=(ATPtot-(ATPg+ADPg)); // BOLD=(Vv0*((k1+k2)*(1-dHb/dHb0)-(k2+k3)*(1-Vv/Vv0))); // v_stim=(stim*(v1_n+v2_n*((time-was_to)/t_n_stim)*exp((-1)*((time-was_to)*(unitpulseSB/t_n_stim))))*unitpulseSB); unitpulseSB=(if ((time>=was_to) and (time<=(was_to+tend))) 1 else 0); // unitstepSB=(if ((time-(tend+was_to))>=(0 second)) 1 else 0); // // unitstepSB2=(if ((time-(tend_GLY+was_to+to_GLY))>=(0 second)) 1 else 0); }