Mathematical modeling of septic shock based on clinical data

Yamanaka, Yukihiro; Uchida, Kenko; Akashi, Momoka; Watanabe, Yuta; Yaguchi, Arino; Shimamoto, Shuji; Shimoda, Shingo; Yamada, Hitoshi; Yamashita, Masashi; Kimura, Hidenori

doi:10.1186/s12976-019-0101-9

Theoretical Biology and Medical Modelling

Table 4 Cardio vascular system model (Ursino model) parameters

From: Mathematical modeling of septic shock based on clinical data

Parameter	Value	Description	Source
C _sa	4ml/mmHg	Compliance of sa	[16]
C _sv	111.11ml/mmHg	Compliance of sv	[16]
C _ra	31.25ml/mmHg	Compliance of ra	[16]
C _pa	6.56ml/mmHg	Compliance of pa	[16]
C _pv	25.37ml/mmHg	Compliance of pv	[16]
C _la	19.23ml/mmmHg	Compliance of la	[16]
R _s2	0.2247mmHg∙ s/ml	Hydraulic resistance of the systemic circulation upstream of arteriolar capillaries	[16]
R _s3	0.1124mmHg∙ s/ml	Hydraulic resistance of the systemic circulation downstream of arteriolar capillaries	[16]
R _sv	0.011mmHg∙ s/ml	Hydraulic resistance of sv	[16]
R _pa	0.1124mmHg∙ s/ml	Hydraulic resistance of pa	[16]
R _pv	0.0056mmHg∙ s/ml	Hydraulic resistance of pv	[16]
L _a	0.01ml/mmHg/s	Permeability coefficient of arterial capillaries	[16]
L _v	0.062ml/mmHg/s	Permeability coefficient of venular capillaries	[16]
V _usa	611.3ml	Unstressed volume of sa	[16]
V _ura	25ml	Unstressed volume of ra	[16]
V _upa	124ml	Unstressed volume of pa	[16]
V _upv	120ml	Unstressed volume of pv	[16]
V _ula	25ml	Unstressed volume of la	[16]
k _l	20ml/mmHg	Slope of the stroke volume versus the atrial pressure relationship for the left heart	[16]
k _r	34.028ml/mmHg	Slope of the stroke volume versus the atrial pressure relationship for the right heart	[16]
p _la0	2.8mmHg	x -axis intercept of the stroke volume versus atrial pressure relationship for the left heart	[16]
p _ra0	1.82mmHg	x -axis intercept of the stroke volume versus atrial pressure relationship for the right heart	[16]
V _n	5300ml	Total blood volume in the basal condition	[16]
V _rc	1300ml	Red blood cell volume	[16]
p _san	100mmHg	Intravascular pressure in the sa in the basal condition	[16]
p _svn	5mmHg	Intravascular pressure in the sv in the basal condition	[16]
p _ran	4mmHg	Intravascular pressure in the ra in the basal condition	[16]
p _pan	17mmHg	Intravascular pressure in the pa in the basal condition	[16]
p _pvn	7mmHg	Intravascular pressure in the pv in the basal condition	[16]
p _lan	6.5mmHg	Intravascular pressure in the la in the basal condition	[16]
k _Na	25ml/s	Mass transfer coefficient of the cellular membrane for sodium	[16]
β _Na	0.0704	Mass transfer coefficient of the cellular membrane for sodium	[16]
k _K	6.67 ∙ 10⁻²ml/s	Mass transfer coefficient of the cellular membrane for potassium	[16]
β _K	28.2	Mass transfer coefficient of the cellular membrane for potassium	[16]
k _U	13ml/s	Mass transfer coefficient of the cellular membrane for urea	[16]
β _U	1	Mass transfer coefficient of the cellular membrane for urea	[16]
k _f	4 ∙ 10⁻³L²/s/mmol	Water exchange coefficient of the cellular membrane	[16]
M _eq,ic	150mmol	Amount of other osmotically efficient solutes in the intracellular compartment	[16]
M _eq,ex	150mmol	Amount of other osmotically efficient solutes in the extracellular compartment	[16]
E _is	24.5mmHg/L	Interstitial space elastance	[16]
V _isn	11L	Basal volume of the interstitial fluid	[16]
V _icn	25L	Basal volume of the intracellular fluid	[16]
c _p,pin	7.4g/dl	Basal protein concentration in the plasma	[16]
c _p,isn	1.37g/dl	Basal protein concentration in the interstitial fluid	[16]
M_k,ic(0)	3535mEq	Initial amount of potassium in the intracellular fluid	[16]
Mk,ex(0)	75mEq	Initial amount of potassium in the extracellular fluid	[16]
M_Na,ic(0)	250mEq	Initial amount of sodium in the intracellular fluid	[16]
M_Na,ex(0)	2130mEq	Initial amount of sodium in the intracellular fluid	[16]
M_U,ic(0)	2130mEq	Initial amount of urea in the intracellular fluid	[16]
M_U,ex(0)	375mmol	Initial amount of urea in the extracellular fluid	[16]
Q _F	0.2083ml/s	Ultrafiltration rate of the replacement fluid	[16]
Q _inf	0ml/s	Ultrafiltration rate of the replacement fluid	[16]
c _Na,d	142mEq/L	Ultrafiltration rate of the replacement fluid	[16]
c _Kd	62mEq/L	Ultrafiltration rate of the replacement fluid	[16]
c _Ud	0	Concentration of urea in the dialysate	[16]
F _p	0.94	Plasma fractions	[16]
F _R	0.72	Red blood cell water fractions	[16]
γ _U	1	Fraction of red blood cell water that participates in the transfer through the dialyzer	[16]
R _DU	1	Donnan ratio for urea in red cells	[16]
γ _Na	0	Fraction of red blood cell water that participates in the transfer through the dialyzer	[16]
γ _K	0	Fraction of red blood cell water that participates in the transfer through the dialyzer	[16]
Q _B	3ml/s	Bulk blood flow through the dialyzer	[16]
D _Na	2.67ml/s	Dialysance (or clearance) of sodium	[16]
D _K	2.67ml/s	Dialysance (or clearance) of potassium	[16]
D _U	2.67ml/s	Dialysance (or clearance) of urea	[16]
σ _Rn	0.7303mmHg∙ s/ml	Basal value of the sigmodideal static characteristic for the mechanism of systemic resistance control	[16]
Δ_σR	1.4mmHg∙ s/ml	Amplitude of the sigmodideal static characteristic for the mechanism of systemic resistance control	[16]
τ _R	6s	Time constant of the mechanism of systemic resistance control	[16]
G _aR	0.02/mmHg	Central gain of the arterial controls for the mechanism of systemic resistance control	[16]
G _cR	0.7/mmHg	Central gain of the cardiopulmonary controls for the mechanism of systemic resistance control	[16]
σ _{V n}	2900ml	Basal value of the sigmodideal static characteristic for the mechanism of venous unstressed volume control	[16]
Δ_σV	500ml	Amplitude of the sigmodideal static characteristic for the mechanism of venous unstressed volume control	[16]
τ _V	20s	Time constant of the mechanism of venous unstressed volume control	[16]
G _aV	10.8/mmHg	Central gain of the arterial controls for the mechanism of venous unstressed volume control	[16]
G _cV	417/mmHg	Central gain of the cardiopulmonary controls for the mechanism of venous unstressed volume control	[16]
σ _Tn	0.833s	Basal value of the sigmodideal static characteristic for the mechanism of heart period control	[16]
Δ_σT	0.75s	Amplitude of the sigmodideal static characteristic for the mechanism of heart period control	[16]
τ _T	2s	Time constant of the mechanism of heart period control	[16]
G _aT	0.015/mmHg	Central gain of the arterial controls for the mechanism of heart period control	[16]
G _cT	0/mmHg	Central gain of the cardiopulmonary controls for the mechanism of heart period control	[16]
p _lat	4.5mmHg	Threshold value of left atrial pressure for activation of the sympathoinhibitory mechanism	[16]
G _σ	4.5mmHg	Gain constant of the sympathoinhibitory mechanism	[16]
τ _σ	120s	Time constant of the sympathoinhibitory mechanism	[16]
τ _ϵ	2700s(acetate dialysis only)	Time constant of the acetate effect upon peripheral vessels	[16]

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