Model Mathematics

Component: environment

Component: parameters

Component: isotonic

isotonic_mode=1ifisotonic=1F_muscle>F_afterloadll_01+1 e -40otherwise

Component: parameters_izakov_et_al_1991

v_st=x_stv_max q_v=q_1-q_2vv_maxifv0q_4-q_3vv_st+q_3ifvv_st0<vq_41+beta_Qv-v_stv_maxalpha_Qotherwise v_1=v_max10

Component: force

F_CE=lambdap_vN F_muscle=F_XSE F_SE=beta_1alpha_1l_2-l_1-1 F_PE=beta_2alpha_2l_2-1 F_XSE=beta_3alpha_3l_3-1

Component: crossbridge_kinetics

M_A=AA_totmu1+k_mumuAA_totmu+k_mumu n_1=0ifg_1l_1+g_2<0g_1l_1+g_2ifg_1l_1+g_2<11otherwise L_oz=l_1+S_00.46+S_0ifl_1>0.55S_0+0.551otherwise k_p_v=kappakappa_0q_vm_0G_star k_m_v=kappa_0q_v1-kappam_0G_star K_kappa=k_p_vM_An_1L_oz1-N-k_m_vN ddtimeN=K_kappa

Component: length

l=l_2+l_3 dl_1_dt=v ddtimel_1=dl_1_dt dl_2_dt=phi_chi_2ifk_S_vis=0wotherwise ddtimel_2=dl_2_dt dl_3_dt=0ifisotonic_mode=1-phi_chi_2ifisotonic_mode=0k_S_vis=0-wifisotonic_mode=0k_S_vis0 ddtimel_3=-l_2+l_3-l_0stim_durationiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_durationdl_3_dtotherwise

Component: CE_velocity

alp_p=alpha_P_lengtheningifv0alpha_P_shorteningotherwise k_P_vis=beta_P_lengtheningalpha_P_lengtheningl_1ifv0beta_P_shorteningalpha_P_shorteningl_1otherwise phi_chi=-lambdaK_kappap_v+alp_pk_P_visv2+alpha_2beta_2alpha_2l_2wlambdaNp_prime_v+k_P_visifisotonic_mode=1-lambdaK_kappap_v+alp_pk_P_visv2+alpha_2beta_2alpha_2l_2+alpha_3beta_3alpha_3l_3wlambdaNp_prime_v+k_P_visotherwise phi_chi_2=alpha_1beta_1alpha_1l_2-l_1valpha_1beta_1alpha_1l_2-l_1+alpha_2beta_2alpha_2l_2ifisotonic_mode=1alpha_1beta_1alpha_1l_2-l_1valpha_1beta_1alpha_1l_2-l_1+alpha_2beta_2alpha_2l_2+alpha_3beta_3alpha_3l_3otherwise ddtimev=alpha_1beta_1alpha_1l_2-l_1phi_chi_2-v-lambdaK_kappap_v+alp_pk_P_visv2lambdaNp_prime_v+k_P_visifk_S_vis=0phi_chiotherwise

Component: PE_velocity

alp_s=alpha_S_lengtheningifwvalpha_S_shorteningotherwise k_S_vis=beta_S_lengtheningalpha_S_lengtheningl_2-l_1ifwvbeta_S_shorteningalpha_S_shorteningl_2-l_1otherwise ddtimew=k_S_visphi_chi-alp_sw-v2-alpha_1beta_1alpha_1l_2-l_1w-v-alpha_2beta_2alpha_2l_2wk_S_visifisotonic_mode=1k_S_vis0phi_chi-alp_sw-v2-alpha_1beta_1alpha_1l_2-l_1w-v+alpha_2beta_2alpha_2l_2+alpha_3beta_3alpha_3l_3wk_S_visifisotonic_mode=0k_S_vis00ifk_S_vis=0

Component: average_crossbridge_force

gamma=ad_hv_1v_max23ad_h-a+1v_1v_max P_star=a1+vv_maxa-vv_maxifv01+d_h-d_h2aad_hgammavv_max2+a+1vv_max+ad_hotherwise G_star=1+0.6vv_maxif-v_maxvv0P_star0.4a+1vav_max+1if0<vvv_1P_star-alpha_Gv-v_1v_maxalpha_P0.4a+1vav_max+1otherwise case_1=a0.4+0.4av_maxa+10.42 case_2=a11+0.4a+1.2vv_max+0.6vv_max2v_maxa-vv_max1+0.6vv_max2 case_3=0.4a+1av_max case_4=1v_max-alpha_Gvv_max-v_1v_maxalpha_P0.4a+1a+alpha_Galpha_P1+0.4a+1vav_maxvv_max-v_1v_maxalpha_P-1 p_v=P_starG_star p_prime_v=case_1ifv-v_maxcase_2if-v_max<vv0case_3if0<vvv_1case_4otherwise

Component: membrane

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-1Cmi_Stim+i_K1+i_to+i_Kr+i_Ks+i_NaK+i_Na+i_b_Na+i_p_Na+i_Ca_L_Na_cyt+i_Ca_L_Na_ds+i_NaCa_cyt+i_NaCa_ds+i_Ca_L_Ca_cyt+i_Ca_L_Ca_ds+i_Ca_L_K_cyt+i_Ca_L_K_ds+i_b_Ca

Component: reversal_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ks=RTFlnK_o+P_knaNa_oK_i+P_knaNa_i E_Ca=0.5RTFlnCa_oCa_i E_mh=RTFlnNa_o+0.12K_oNa_i+0.12K_i

Component: time_independent_potassium_current

i_K1=g_K1K_oK_o+K_mk1V-E_K1+V-E_K-10F1.25RT

Component: rapid_delayed_rectifier_potassium_current

i_Kr=g_Kr1xr1+g_Kr2xr211+V+922.4V-E_K

Component: rapid_delayed_rectifier_potassium_current_xr1_gate

alpha_xr1=501+-V-59 beta_xr1=0.05-V-2015 ddtimexr1=alpha_xr11-xr1-beta_xr1xr1

Component: rapid_delayed_rectifier_potassium_current_xr2_gate

alpha_xr2=501+-V-59 beta_xr2=0.4-V+30303 ddtimexr2=alpha_xr21-xr2-beta_xr2xr2

Component: slow_delayed_rectifier_potassium_current

i_Ks=g_Ksxs2V-E_Ks

Component: slow_delayed_rectifier_potassium_current_xs_gate

alpha_xs=141+-V-409 beta_xs=1-V45 ddtimexs=alpha_xs1-xs-beta_xsxs

Component: sodium_activated_potassium_current

i_KNa=g_K_NaNa_iNa_i+K_knaV-E_K

Component: fast_sodium_current

i_Na=g_Nam3hV-E_mh

Component: fast_sodium_current_m_gate

E0_m=V+41 alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwise beta_m=8000-0.056V+66 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=20-0.125V+75 beta_h=20001+320-0.1V+75 ddtimeh=alpha_h1-h-beta_hh

Component: persistent_sodium_current

i_p_Na=g_pna11+-V+528V-E_Na

Component: sodium_background_current

i_b_Na=g_bnaV-E_Na

Component: L_type_Ca_channel

i_Ca_L_Ca_cyt=1-FrICa4P_Ca_Ldff2V-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_cyt=1-FrICaP_CaKP_Ca_Ldff2V-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_cyt=1-FrICaP_CaNaP_Ca_Ldff2V-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L_Ca_ds=FrICa4P_Ca_Ldff2dsV-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_ds=FrICaP_CaKP_Ca_Ldff2dsV-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_ds=FrICaP_CaNaP_Ca_Ldff2dsV-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L=i_Ca_L_Ca_cyt+i_Ca_L_K_cyt+i_Ca_L_Na_cyt+i_Ca_L_Ca_ds+i_Ca_L_K_ds+i_Ca_L_Na_ds

Component: L_type_Ca_channel_d_gate

E0_d=V+24-5 alpha_d=120if|E0_d|<0.000130E0_d1--E0_d4otherwise beta_d=120if|E0_d|<0.000112E0_dE0_d10-1otherwise ddtimed=speed_dalpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

E0_f=V+34 alpha_f=25if|E0_f|<delta_f6.25E0_fE0_f4-1otherwise beta_f=121+-1V+344 ddtimef=speed_falpha_f1-f-beta_ff

Component: L_type_Ca_channel_f2_gate

ddtimef2=1-1Ca_iKm_f2+Ca_i+f2

Component: L_type_Ca_channel_f2ds_gate

ddtimef2ds=R_decay1-Ca_dsKm_f2ds+Ca_ds+f2ds

Component: calcium_background_current

i_b_Ca=g_bcaV-E_Ca

Component: transient_outward_current

i_to=g_tog_tos+s1-g_tosrV-E_K

Component: transient_outward_current_s_gate

alpha_s=0.033-V17 beta_s=331+-0.125V+10 ddtimes=alpha_s1-s-beta_ss

Component: transient_outward_current_r_gate

ddtimer=33311+-V+45-r

Component: sodium_potassium_pump

i_NaK=i_NaK_maxK_oK_mK+K_oNa_iK_mNa+Na_i

Component: sodium_calcium_exchanger

i_NaCa_cyt=1-FRiNaCak_NaCagamman_NaCa-2VFRTNa_in_NaCaCa_o-gamma-1n_NaCa-2VFRTNa_on_NaCaCa_i1+d_NaCaCa_iNa_on_NaCa+Ca_oNa_in_NaCa1+Ca_i0.0069 i_NaCa_ds=FRiNaCak_NaCagamman_NaCa-2VFRTNa_in_NaCaCa_o-gamma-1n_NaCa-2VFRTNa_on_NaCaCa_ds1+d_NaCaCa_dsNa_on_NaCa+Ca_oNa_in_NaCa1+Ca_ds0.0069 i_NaCa=i_NaCa_cyt+i_NaCa_ds

Component: sarcoplasmic_reticulum_calcium_pump

K_1=K_cycaK_xcsK_srca K_2=Ca_i+Ca_upK_1+K_cycaK_xcs+K_cyca i_up=Ca_iK_2alpha_up-Ca_upK_1K_2beta_upifflag_ingib=0Ca_iK_2alpha_up1+Ca_upK_inh-Ca_upK_1K_2beta_upotherwise

Component: calcium_translocation

i_trans=a_trCa_up-Ca_rel beta=beta_CaSalpha_CaS

Component: calcium_release

VoltDep=0.08V-40 CaiReg=Ca_iCa_i+K_m_Ca_cyt CadsReg=Ca_dsCa_ds+K_m_Ca_ds RegBindSite=CaiReg+1-CaiRegCadsReg ActRate=500RegBindSite2 InactRate=60+500RegBindSite2 SpeedRel=5ifV<-501otherwise PrecFrac=1-ActFrac-ProdFrac ddtimeActFrac=PrecFracSpeedRelActRate-ActFracSpeedRelInactRate ddtimeProdFrac=ActFracSpeedRelInactRate-SpeedRel0.6ProdFrac i_rel=ActFracActFrac+0.252K_m_rel+SRLeakCa_rel

Component: extracellular_sodium_concentration

Component: intracellular_sodium_concentration

ddtimeNa_i=-11V_iFi_Na+i_p_Na+i_b_Na+i_Ca_L_Na_cyt+i_Ca_L_Na_ds+n_NaKn_NaK-1i_NaK+n_NaCan_NaCa-2i_NaCa

Component: extracellular_calcium_concentration

Component: extracellular_potassium_concentration

ddtimeK_o=1i_Kr+i_Ks+i_K1+i_to-1n_NaK-1i_NaK+i_Ca_L_K_cyt+i_Ca_L_K_ds1V_eF-0.7K_o-K_b

Component: intracellular_potassium_concentration

ddtimeK_i=-11V_iFi_K1+i_Kr+i_Ks+i_Ca_L_K_cyt+i_Ca_L_K_ds+i_to-1n_NaK-1i_NaK

Component: intracellular_calcium_concentration

N_A=A_totNL_ozA pi_N_A=pi_minifN_A0pi_minN_AifN_A11otherwise ddtimeA=a_onA_tot-ACa_i-a_off-k_AApi_N_AA ddtimeB_1=b_1_onB_1_tot-B_1Ca_i-b_1_offB_1 ddtimeB_2=b_2_onB_2_tot-B_2Ca_i-b_2_offB_2 V_Cell=3.141592654radius10002length1000 V_i=V_CellV_i_ratio V_e=V_CellV_e_ratio ddtimeCa_i=-121V_iFi_Ca_L_Ca_cyt+i_b_Ca-2n_NaCa-2i_NaCa_cyt+Ca_dsV_ds_ratioKdecay+i_relV_rel_ratioV_i_ratio-ddtimeA-ddtimeB_1-ddtimeB_2-i_up ddtimeCa_ds=-1i_Ca_L_Ca_ds+2i_NaCa_dsn_NaCa-221V_ds_ratioV_iF-Ca_dsKdecay ddtimeCa_up=V_i_ratioV_up_ratioi_up-i_trans ddtimeCa_rel=V_up_ratioV_rel_ratioi_trans-i_rel1+betaCaS_totCa_rel+beta2

Component: fibroblast

i_fibro=g_fibroV_fibro+20+g_fibro_stretchV_fibro-E_fibro_stretch i_fibro_junct=-g_fibro_junctV-V_fibro ddtimeV_fibro=-i_fibro+i_fibro_junctc_fibro