The careful reader might notice that many of the algebraic variables are not strictly necessary to the model evolution - rather they are simply variables of convenience capturing intermediate steps in some calculation. For example the variables and
- conductivities of calcium channels in vascular smooth muscle serve only as intermediates to determine
and
, the rates of calcium entry into smooth muscle cells. However, in keeping with our philosophy of conceptual simplicity we have included such variables. Eliminating some of these non-crucial model variables, adds little to simulation speed, while making the model harder to understand and alter.
variable (click for evolution) | code version | brief description | default initial value | other comments |
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C_vi | venous compliance | 4.5930e-01 (fcn) | see (1) |
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G_1 | conductance of the proximal arterial segment | 4.3619e-01 (fcn) | see (1) |
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G_2 | conductance of the distal arterial segment | 2.6932e-01 (fcn) | see (1) |
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G_vs | conductance of the terminal veins | 1.5740e+00 (fcn) | see (1) |
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M_1 | level of muscle activation in proximal arterial segment | 1.0000e+00 (fcn) | normal value = 1 |
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M_2 | level of muscle activation in distal arterial segment | 1.0000e+00 (fcn) | normal value = 1 |
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PD_K | membrane potential for potassium ions in both VSM segments | -1.1129e+02 (fcn) | assumed to be the same in each segment since it is dependent primarily on the concentration of extracellular potassium |
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PD_Ca2 | membrane potential for calcium ions in the distal VSM segment | 1.5387e+02 (fcn) | |
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PD_Ca1 | membrane potential for calcium ions in the proximal VSM segment | 1.5387e+02 (fcn) | |
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PD_mem1 | membrane potential of cells in the proximal VSM segment | -5.0000e+01 (fcn) | |
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PD_mem2 | membrane potential of cells in the distal VSM segment | -5.3000e+01 (fcn) | |
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PMF | the proton motive force across the mitochondrial inner membrane | 1.8693e+02 (fcn) | |
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P_1 | blood pressure at the midpoint of the proximal arterial segment | 8.5671e+01 (fcn) | see (1) |
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P_2 | blood pressure at the midpoint of the distal arterial segment | 4.8136e+01 (fcn) | see (1) |
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P_c | capillary blood pressure | 2.4929e+01 (fcn) | see (1) |
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P_v | cerebral venous pressure | 1.3937e+01 (fcn) | see (1) |
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P_ic | intracranial pressure | 9.4265e+00 (fcn) | see (1) |
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P_vs | venous sinus pressure | 5.9997e+00 (fcn) | see (1) |
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Pbuf | Sites on cellular proteins capable of binding protons | 1.0000e+01 (fcn) | |
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PbufH | Sites on cellular proteins bound to protons | 2.0000e+00 (fcn) | |
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T_e1 | elastic tension in the vessel walls of the proximal arterial segment | -4.3856e-02 (fcn) | see (1) |
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T_e2 | elastic tension in the vessel walls of the distal arterial segment | -1.1205e-01 (fcn) | see (1) |
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T_m1 | active tension in the vessel walls of the proximal arterial segment | 1.8087e+00 (fcn) | see (1) |
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T_m2 | active tension in the vessel walls of the distal arterial segment | 3.6079e-01 (fcn) | see (1) |
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T_max1 | maximum active muscle tension in the proximal arterial segment | 2.1600e+00 (fcn) | |
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T_max2 | maximum active muscle tension in the distal arterial segment | 1.5000e+00 (fcn) | |
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T_v1 | viscous tension in the vessel walls of the proximal arterial segment | 0.0000e+00 (fcn) | see (1) |
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T_v2 | viscous tension in the vessel walls of the distal arterial segment | 0.0000e+00 (fcn) | see (1) |
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V_1 | blood volume in the proximal arterial segment | 2.5626e+00 (fcn) | see (1) |
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V_2 | blood volume in the distal arterial segment | 7.9286e+00 (fcn) | see (1) |
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V_mca | approximate velocity of the blood in the middle cerebral artery | 5.8946e+01 (fcn) | see (1) |
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Vmax_glucN | Vmax for glycolysis | 1.2973e-01 (fcn) | a function of ATP and AMP concentrations |
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Vol_art | proportion of total brain volume which is arterial blood | 1.0491e+01 (fcn) | see (1) |
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Vol_ven | proportion of total brain volume which is venous blood | 3.0834e+01 (fcn) | see (1) |
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_ADP | ADP concentration in cytoplasm | 3.5000e-01 (fcn) | |
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_mADP | ADP concentration in mitochondria | 8.2677e-01 (fcn) | |
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_AMP | AMP concentration in cytoplasm | 1.1367e-01 (fcn) | |
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_ATP | ATP concentration in cytoplasm | 3.0000e+00 (fcn) | |
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_mATP | ATP concentration in mitochondria | 1.4173e+01 (fcn) | |
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_Ad | adenosine concentration in cytoplasm | 1.0000e-05 (fcn) | |
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_eAd | adenosine concentration in extracellular space | 1.0000e-05 (fcn) | |
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_CO2 | carbon dioxide concentration in cytoplasm | 2.0520e+00 (fcn) | |
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CO2 | carbon dioxide concentration in capillary blood | 1.5157e+00 (fcn) | |
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_eCO2 | carbon dioxide concentration in extracellular space | 1.7838e+00 (fcn) | |
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_mCO2 | carbon dioxide concentration in mitochondria | 2.4624e+00 (fcn) | |
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CO2_v | carbon dioxide concentration in venous blood | 2.0200e+00 | |
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Ca_i1 | intracellular calcium ion concentration in proximal VSM segment | 1.0000e-04 (fcn) | |
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Ca_i2 | intracellular calcium ion concentration in distal VSM segment | 1.0000e-04 (fcn) | |
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_Cr | creatine concentration in cytoplasm | 3.9000e+00 (fcn) | |
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_mFADH |
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1.2200e+00 (fcn) | |
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_mFAD | FAD concentration in mitochondria | 1.0000e-01 (fcn) | |
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_BiC | bicarbonate ion concentration in cytoplasm | 1.9046e+01 (fcn) | |
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BiC | bicarbonate ion concentration in capillary blood | 2.5760e+01 (fcn) | |
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_eBiC | bicarbonate ion concentration in extracellular space | 2.5060e+01 (fcn) | |
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_mBiC | bicarbonate ion concentration in mitochondria | 9.0988e+01 (fcn) | |
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BiC_v | bicarbonate ion concentration in venous blood | 2.5550e+01 | |
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_Hy | hydrogen ion concentration in cytoplasm | 8.5114e-05 (fcn) | |
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Hy | hydrogen ion concentration in capillary blood | 4.4157e-05 (fcn) | |
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_eHy | hydrogen ion concentration in extracellular space | 5.6234e-05 (fcn) | |
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_mHy | hydrogen ion concentration in mitochondria | 2.1380e-05 (fcn) | |
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Hy_v | hydrogen ion concentration in venous blood | 6.2500e-05 | |
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X_H | concentration of capillary haemoglobin combined with protons | 3.1960e-01 (fcn) | |
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X_H_v | concentration of venous haemoglobin combined with protons | 5.4000e-01 | |
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X_O4_H | concentration of capillary haemoglobin combined with oxygen and protons | 3.3572e-01 (fcn) | |
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X_O4_H_v | concentration of venous haemoglobin combined with oxygen and protons | 8.3500e-02 | |
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X_O4 | concentration of capillary haemoglobin combined with four oxygen molecules | 1.5206e+00 (fcn) | |
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X_O4_v | concentration of venous haemoglobin combined with four oxygen molecules | 1.5300e+00 | |
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CY | concentration of
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3.0181e+00 (fcn) | |
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CY_v | concentration of
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3.3500e+00 | |
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X | concentration of capillary haemoglobin (not combined with oxygen or protons) | 9.4093e-02 (fcn) | |
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Y | concentration of empty
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6.0619e+00 (fcn) | |
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X_v | concentration of venous haemoglobin (not combined with oxygen or protons) | 1.2000e-01 | |
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Y_v | concentration of empty
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5.7300e+00 | |
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_K | potassium ion concentration in cytoplasm | 1.8000e+02 (fcn) | |
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K | potassium ion concentration in capillary blood | 4.0700e+00 (fcn) | |
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_eK | potassium ion concentration in extracellular space | 2.8000e+00 (fcn) | |
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K_v | potassium ion concentration in venous blood | 0.0000e+00 | |
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MLC1 | concentration of unphosphorylated crossbridge heads of myosin in the proximal VSM segment | 4.4800e-02 (fcn) | |
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MLC2 | concentration of unphosphorylated crossbridge heads of myosin in the distal VSM segment | 4.7600e-02 (fcn) | |
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MLCp1 | concentration of phosphorylated crossbridge heads of myosin in the proximal VSM segment | 1.1200e-02 (fcn) | |
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MLCp2 | concentration of phosphorylated crossbridge heads of myosin in the distal VSM segment | 8.4000e-03 (fcn) | |
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_NADH | NADH concentration in cytoplasm | 2.9703e-03 (fcn) | |
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_mNADH | NADH concentration in mitochondria | 9.0909e-01 (fcn) | |
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_NAD | NAD concentration in cytoplasm | 2.9703e-01 (fcn) | |
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_mNAD | NAD concentration in mitochondria | 9.0909e+00 (fcn) | |
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NO1 | nitric oxide concentration in proximal VSM segment | 2.0000e-06 (fcn) | |
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NO2 | nitric oxide concentration in distal VSM segment | 2.0000e-06 (fcn) | |
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_Na | sodium ion concentration in cytoplasm | 1.5000e+01 (fcn) | |
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Na | sodium ion concentration in capillary blood | 1.3800e+02 (fcn) | |
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_eNa | sodium ion concentration in extracellular space | 1.3800e+02 (fcn) | |
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Na_v | sodium ion concentration in venous blood | 0.0000e+00 | |
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_O2 | oxygen concentration in cytoplasm | 4.5500e-02 (fcn) | |
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O2 | dissolved oxygen concentration in capillary blood | 6.8000e-02 (fcn) | |
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_mO2 | oxygen concentration in mitochondria | 2.2750e-02 (fcn) | |
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O2_v | dissolved oxygen concentration in venous blood | 6.2500e-02 | |
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_eO2 | oxygen concentration in extracellular space | 5.0000e-02 (fcn) | |
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_Ox | oxaloacetate concentration in mitochondria | 5.4000e-01 (fcn) | |
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_PCr | phosphocreatine concentration in cytoplasm | 5.8500e+00 (fcn) | |
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_Phos | inorganic phosphate concentration in cytoplasm | 1.5000e+00 (fcn) | |
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_mPhos | inorganic phosphate concentration in mitochondria | 3.2000e+00 (fcn) | |
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_AKG | alpha-ketoglutarate concentration in mitochondria | 1.0000e-01 (fcn) | |
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_gluc | glucose concentration in cytoplasm | 1.4000e+00 (fcn) | |
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gluc | glucose concentration in capillary blood | 4.8396e+00 (fcn) | |
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_egluc | glucose concentration in extracellular space | 2.0879e+00 (fcn) | |
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gluc_v | glucose concentration in venous blood | 0.0000e+00 | |
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_L0 | lactate concentration in cytoplasm | 2.0000e+00 (fcn) | |
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L0 | lactate ion concentration in capillary blood | 1.0200e+00 (fcn) | |
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_eL0 | lactate ion concentration in extracellular space | 1.9020e+00 (fcn) | |
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L0_v | lactate ion concentration in venous blood | 1.0300e+00 | |
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_lac | lactic acid concentration in cytoplasm | 1.2335e-03 (fcn) | |
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L | lactic acid concentration in capillary blood | 3.2638e-04 (fcn) | |
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_eL | lactic acid concentration in extracellular space | 7.7505e-04 (fcn) | |
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L_v | lactic acid concentration in venous blood | 4.6000e-04 | |
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_Py0 | pyruvate concentration in cytoplasm | 1.2000e-01 (fcn) | |
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_ePy0 | pyruvate concentration in extracellular space | 1.2000e-01 (fcn) | |
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_mPy0 | pyruvate concentration in mitochondria | 3.8218e-01 (fcn) | |
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_suc | succinate concentration in mitochondria | 1.0000e-01 (fcn) | |
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PD_mit | membrane potential for the mitochondrial inner membrane (multiplied by membrane capacitance) | 1.5000e+02 (fcn) | |
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sigma_e1 | elastic stress in the vessel walls of the proximal arterial segment | -2.1716e+01 (fcn) | see (1) |
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sigma_e2 | elastic stress in the vessel walls of the distal arterial segment | -4.3339e+01 (fcn) | see (1) |
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sigma_v1 | viscous stress in the vessel walls of the proximal arterial segment | 0.0000e+00 (fcn) | see (1) |
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sigma_v2 | viscous stress in the vessel walls of the distal arterial segment | 0.0000e+00 (fcn) | see (1) |
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gCa1 | conductivity of calcium channels in the proximal VSM segment | 6.7999e-08 (fcn) | |
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gCa2 | conductivity of calcium channels in the distal VSM segment | 6.7999e-08 (fcn) | |
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gK1 | total conductivity of all potassium channels in the proximal VSM segment | 3.9161e-02 (fcn) | |
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gK2 | total conductivity of all potassium channels in the distal VSM segment | 4.3235e-02 (fcn) | |
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gKATP1 | conductivity of the ATP and pH sensitive potassium channels in the proximal VSM segment | 7.8321e-03 (fcn) | |
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gKATP2 | conductivity of the ATP and pH sensitive potassium channels in the distal VSM segment | 1.2971e-02 (fcn) | |
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gKpres1 | conductivity of the pressure sensitive potassium channels in the proximal VSM segment | 1.9580e-02 (fcn) | |
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gKpres2 | conductivity of the pressure sensitive potassium channels in the distal VSM segment | 1.7294e-02 (fcn) | |
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gKpot1 | conductivity of the potassium sensitive potassium channels in the proximal VSM segment | 7.8321e-03 (fcn) | |
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gKpot2 | conductivity of the potassium sensitive potassium channels in the distal VSM segment | 8.6470e-03 (fcn) | |
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gKV1 | conductivity of the voltage gated potassium channels in the proximal VSM segment | 3.9161e-03 (fcn) | |
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gKV2 | conductivity of the voltage gated potassium channels in the distal VSM segment | 4.3235e-03 (fcn) | |
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h_1 | vessel wall thickness in the proximal arterial segment | 2.0195e-03 (fcn) | see (1) |
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h_2 | vessel wall thickness in the distal arterial segment | 2.5854e-03 (fcn) | see (1) |
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k_CC | rate constant for the diffusion of carbon dioxide between blood and extracellular space | 1.4713e+02 (fcn) | perhaps dependent on transmural pressure |
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k_Cain1 | rate constant for the inflow of calcium into the proximal VSM segment | 1.3863e-05 (fcn) | dependent on conductance of calcium channels |
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k_Cain2 | rate constant for the inflow of calcium into the distal VSM segment | 1.3863e-05 (fcn) | dependent on conductance of calcium channels |
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k_MLC1ac | rate of phosphorylation of dephosphorylated myosin heads in the proximal VSM segment | 1.3863e-01 (fcn) | |
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k_MLC2ac | rate of phosphorylation of dephosphorylated myosin heads in the distal VSM segment | 1.0397e-01 (fcn) | |
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k_MLC1inac | rate of dephosphorylation of phosphorylated myosin heads in the proximal VSM segment | 5.5452e-01 (fcn) | |
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k_MLC2inac | rate of dephosphorylation of phosphorylated myosin heads in the distal VSM segment | 5.8918e-01 (fcn) | |
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k_NOprod1 | rate constant for the inflow of nitric oxide into the proximal VSM segment | 1.3863e-08 (fcn) | dependent on shear stress and pH |
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k_NOprod2 | rate constant for the inflow of nitric oxide into the distal VSM segment | 1.3863e-08 (fcn) | dependent on shear stress and pH |
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k_OO | rate constant for the diffusion of oxygen between blood and extracellular space | 2.4112e+03 (fcn) | perhaps dependent on transmural pressure, though currently no effects are included. |
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q | cerebral blood flow | 1.2500e+01 (fcn) | see (1) |
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r_1 | radius of the larger (proximal) cerebral arteries | 2.3501e-02 (fcn) | see (1) |
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r_2 | radius of the smaller (distal) cerebral arteries | 7.1683e-03 (fcn) | see (1) |
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r_mca | approximate radius of the middle cerebral artery | 1.5000e-01 (fcn) | see (1) |
variable table ends |