Model Mathematics

Component: environment

Component: parameters

Component: isotonic

flag=0ifll_0time<0.151otherwise isotonic_mode=0ifisotonic=01ifisotonic=1F_muscleF_afterload0ifisotonic=1ll_0flag=1

Component: parameters_izakov_et_al_1991

q_v=q_1-q_2vv_maxifv0q_4-q_3vv_star+q_3ifvv_star0<vq_41+beta_Qv-v_starv_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=AmuAmu+A_halfmu n_1=0.6l_1+0.5 L_oz=l_1+S_00.46+S_0 k_p_v=chichi_0q_vm_0G_star k_m_v=chi_0q_v1-chim_0G_starifvv_starchi_0q_41-chim_0G_star+q_starv-v_starv_0-v_starotherwise K_chi=k_p_vM_An_1L_oz1-N-k_m_vN ddtimeN=K_chi

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-wotherwise ddtimel_3=dl_3_dt

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_chip_v+alp_pk_P_visv2+alpha_2beta_2alpha_2l_2wlambdaNp_prime_v+k_P_visifisotonic_mode=1-lambdaK_chip_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_chip_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=1phi_chi-alp_sw-v2-alpha_1beta_1alpha_1l_2-l_1w-v+alpha_2beta_2alpha_2l_2+alpha_3beta_3alpha_3l_3wk_S_visotherwise

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: calcium_handling

N_A=NL_ozA pi_N_A=1ifN_A10.02N_Aotherwise dA_dt=a_onA_tot-ACa_C-a_off-k_AApi_N_AA ddtimeA=dA_dt dB_dt=b_onB_tot-BCa_C-b_offB ddtimeB=dB_dt ddtimeCa_C=4a_cCa_mtime1--a_ctime2-a_ctime2iftime<t_d-dA_dt-dB_dt-r_Ca-q_CaCa_CCa_Cotherwise