. Author manuscript; available in PMC: 2014 Oct 2.

Published in final edited form as: Math Biosci. 2012 Oct 6;241(1):56–74. doi: 10.1016/j.mbs.2012.09.003

Table 4.

Nominal parameters and initial conditions for the respiratory model. Top: auxiliary parameters, center: model parameters, bottom: initial values for ODE's.

Parameter	Physiologic description	Nominal value or formula	Reference
w [kg]	Body weight	83.2	meas
M_CO₂ [ml_stpd/s]	Body CO₂ tissue metabolism	0.85 M_O₂ = 4.42	[1, 36, 37]
M_O₂ [ml_stpd/s]	Body O₂ tissue metabolism	5.2	[1, 36, 37]
V_CO₂ [ml_stpd]	Body CO₂ tissue volume	15,000	[1, 36, 37]
V_O₂ [ml_stpd]	Body CO₂ tissue volume	6,000	[1, 36, 37]

M_B,CO₂ [ml_stpd/s]	Brain CO₂ tissue metabolism	0.2 M_O₂ = 1.04	[1, 36, 37]
M_B,O₂ [ml_stpd/s]	Brain O₂ tissue metabolism	M_B,CO₂ = 1.04	[1, 36, 37]
M_S,CO₂ [ml_stpd/s]	Systemic CO₂ tissue metabolism	M_CO₂ – M_B, CO₂ = 3.38	[1, 36, 37]
M_S, O₂ [ml_stpd/s]	Systemic O₂ tissue metabolism	M_O₂ – M_B, O₂ = 4.16	[1, 36, 37]
V_{Btis, CO₂} [ml_stpd]	Cerebral tissue CO₂ volume	900	[1, 36, 37]
V_Btis,O₂ [ml_stpd]	Cerebral tissue O₂ volume	1,000	[1, 36, 37]
V_Stis,CO₂ [ml_stpd]	Systemic tissue CO₂ volume	V_CO₂ – V_Btis,CO₂ = 14,100	[1, 36, 37]
V_Stis,O₂ [ml_stpd]	Systemic tissue O₂ volume	V_O₂ – V_Btis,CO₂ = 5,000	[1, 36, 37]
V_Bcap,CO₂ [ml_stpd]	Cerebral capillary CO₂ volume	f_V,cap V_Btis,CO₂ = 9	[21]
V_Scap,CO₂ [ml_stpd]	Systemic capillary CO₂ volume	f_V,cap V_Stis,CO₂ = 141	est [21]
V_Bcap,O₂ [ml_stpd]	Cerebral capillary O₂ volume	f_V,cap V_Btis,O₂ = 10	[21]
V_Scap,O₂ [ml_stpd]	Systemic capillary O₂ volume	f_V,cap V_Stis,O₂ = 50	est [21]
V_D [ml_btps]	Total dead space volume	181	[38, 36, 37]
K_O₂ [ml_stpd/ml]	O₂ dissociation coefficient	0.200	[1, 36, 37]
k_O₂ [mmHg^–¹]	O₂ dissociation coefficient	0.046	[1, 36, 37]
K_CO₂ [ml_stpd /mmHg/ml]	CO₂ dissociation coefficient	0.0065	[1, 36, 37]
k_CO₂ [ml_stpd/ml]	CO₂ dissociation coefficient	0.244	[1, 36, 37]
K̃_O₂ [ml_stpd /mmHg/ml]	O₂ linearized dissociation coefficient	0.0025	[1, 36, 37]
D_T,CO₂ [ml/s]	CO₂ diffusion coefficient	9/60 w/K_CO₂ = 1899	[21]
D_T,O₂ [ml/s]	O₂ diffusion coefficient	9/60 w/K̃_O₂ = 4938	[21]
f_V,cap [N.D.]	Tissue-capillary volume fraction	0.01	[21]

$p_{D 1, {CO}_{2}}^{I}$ [mmHg]	Initial CO₂ partial pressure dead space 1	5	[37, 38]
$p_{D 1, O_{2}}^{I}$ [mmHg]	Initial O₂ partial pressure dead space 1	159	[37, 38]
$p_{D 2, {CO}_{2}}^{I}$ [mmHg]	Initial CO₂ partial pressure dead space 2	6	[37, 38]
$p_{D 2, O_{2}}^{I}$ [mmHg]	Initial O₂ partial pressure dead space 2	158	[37, 38]
$p_{D 3, {CO}_{2}}^{I}$ [mmHg]	Initial CO₂ partial pressure dead space 3	7	[37, 38]
$p_{D 3, O_{2}}^{I}$ [mmHg]	Initial O₂ partial pressure sdead space 3	157	[37, 38]
$p_{a, {CO}_{2}}^{I}$ [mmHg]	Initial systemic arterial CO₂ partial pressure	40	[39]
$p_{a, O_{2}}^{I}$ [mmHg]	Initial systemic arterial O₂ partial pressure	100	[40]
$c_{S t i s, {CO}_{2}}^{I}$ [ml_stpd/ml]	Initial systemic tissue CO₂ concentration	0.543	[40]
$c_{S t i s, O_{2}}^{I}$ [ml_stpd/ml]	Initial systemic tissue MO₂ concentration	0.128	[40]
$c_{B t i s, {CO}_{2}}^{I}$ [ml_stpd/ml]	Initial brain tissue CO₂ concentration	0.569	[37, 38]
$c_{B t i s, O_{2}}^{I}$ [ml_stpd/ml]	Initial brain tissue O₂ concentration	0.112	[37, 38]
$c_{S c a p, {CO}_{2}}^{I}$ [ml_stpd/ml]	Initial systemic capillary CO₂ concentration	c_Stis,CO₂ – M_S,CO₂ /D_T,CO₂ = 0.541	(23)
$c_{S c a p, O_{2}}^{I}$ [ml_stpd/ml]	Initial systemic capillary O₂ concentration	c_Stis,O₂ – M_S,O₂ /D_T,O₂ = 0.127	(23)
$c_{B c a p, {CO}_{2}}^{I}$ [ml_stpd/ml]	Initial cerebral capillary CO₂ concentration	c_Btis,CO₂ – M_B,CO₂ /D_T,CO₂ = 0.568	(23)
$c_{B c a p, O_{2}}^{I}$ [ml_stpd/ml]	Initial cerebral capillary O₂ concentration	c_Btis,O₂ – M_B,O₂ /D_T,O₂ = 0.111	(23)