Model Mathematics

Component: Environment

Component: Parameters

Component: PCA

ddtimeP_p=2Q_LpR_a-2P_p+2P_aR_aC_pddtimeQ_Lp=P_ai-P_p-Q_LpR_pL_p

Component: PCA_Components

C_p=3πr_p2r_ph_p+12E_p2r_ph_p+1l_pL_p=Rho_bπr_p2l_p0.0000075R_p=8Eta_bπr_p4l_p

Component: Arteriolar_Circulation

ddtimer_a=r_a0P_pR_a+R_vr_a+P_vR_ar_a-T_ae+T_am+P_icr_a+h_a2R_a+R_vr_a0r_a2K_VaR_aR_a+R_v+Eta_ah_a2R_a+R_vP_a=T_a+P_icr_a+h_ar_a

Component: AC_Components

R_a=K_Rar_a4C_a=1.0312R_a

Component: AC_Flow

Q_a=2P_a-P_vR_a+R_v

Component: Venous_Circulation

ddtimeP_v=2C_vP_a-P_vR_a+R_v-P_v-P_voR_v

Component: AC_Tension

T_a=T_ae+T_am+T_avT_ae=h_asigma_ae0K_a_sigmar_a-r_a0r_a0-1-sigma_acT_am=T_a_max-|r_a-r_amr_at-r_am|n_amT_av=Eta_ar_a0ddtimer_ah_a

Component: AC_Tension_Variables

h_a=r_a2+2r_a0h_a0+h_a02-r_aT_a_max=T_a_max01+M_s

Component: CBF_Regulation

M_s=2M_s1-12M_s1+1M_s1=G_myox_myo+G_shearx_shear+G_neurox_neuro+G_metax_meta+x_ini

Component: Myo_Regulation

A_myo=T_a-T_myo0T_myo_sddtimex_myo=A_myo-x_myoTau_myo

Component: Shear_Regulation

A_shear=K_shearQ_ar_a3-1ddtimex_shear=A_shear-x_shearTau_shear

Component: Neuro_Regulation

ddtimex_neuro=A_neuro-x_neuroTau_neuroA_neuro=1iftime10otherwise

Component: Meta_Regulation

A_Meta=G_a_Metaconc_CO2_t-conc_CO2_t_spddtimex_meta=A_Meta-x_metaTau_Meta

Component: Meta_CO2_Kinetics

ddtimeconc_CO2_t=1vol_PVCM_CO2-Q_aconc_CO2_v-conc_CO2_aconc_CO2_v=alpha_tvconc_CO2_t+beta_tv

Component: VC_Meta_Stim

M_CO2=M_CO2_0unity+A_neurof_Q-unityn_QM
Source
Derived from workspace Spronck, 2012 at changeset 02012ee8bbdf.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.