Physiological closed-loop control of mechanical ventilation and extracorporeal membrane oxygenation

Christian Brendle; Thorsten Mülders; Jan Kühn; Thorsten Janisch; Rüdger Kopp; Rolf Rossaint; Andre Stollenwerk; Stefan Kowalewski; Berno Misgeld; Steffen Leonhardt; Marian Walter

doi:10.1515/bmt-2016-0077

Published by De Gruyter January 25, 2017

Physiological closed-loop control of mechanical ventilation and extracorporeal membrane oxygenation

Christian Brendle , Thorsten Mülders , Jan Kühn , Thorsten Janisch , Rüdger Kopp , Rolf Rossaint , Andre Stollenwerk , Stefan Kowalewski , Berno Misgeld , Steffen Leonhardt and Marian Walter

From the journal Biomedical Engineering / Biomedizinische Technik

https://doi.org/10.1515/bmt-2016-0077

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Abstract

A new concept is presented for cooperative automation of mechanical ventilation and extracorporeal membrane oxygenation (ECMO) therapy for treatment of acute respiratory distress syndrome (ARDS). While mechanical ventilation is continuously optimized to promote lung protection, extracorporeal gas transfer rates are simultaneously adjusted to control oxygen supply and carbon dioxide removal using a robust patient-in-the-loop control system. In addition, the cooperative therapy management uses higher-level algorithms to adjust both therapeutic approaches. The controller synthesis is derived based on the introduced objectives, the experimental setup and the uncertain models. Finally, the autonomous ARDS therapy system capabilities are demonstrated and discussed based on in vivo data from animal experiments.

Keywords: acute respiratory distress syndrome; extracorporeal membrane oxygenation; gas exchange; lung protection; mechanical ventilation; patient-in-the-loop

Acknowledgment

The authors gratefully acknowledge the contribution of the German Research Foundation DFG (Grant PAK 138/2; LE 817/15-1; KO 1430/14-1; RO 2000/18-1).

Appendix

A Equations and parameters

A.1 Extracorporeal gas transfer

Time delays: TQO2,d=14.92 s and TQCO2,d=5.03 s; variable range of in silico study: QCO2∈[0.15, 0.3] l/min, QO2∈[0, 0.25] l/min, Sv,O2∈[45, 70]%, and pv,CO2∈[44, 70] mm Hg; parameters are presented in Tables 2 and 3.

(7)GQ,nom=KQ⋅(1+sz0,Q)TQ2⋅s2+2⋅TQ⋅DQ⋅s+1,

(8)WQ=∑i = 0Nbi⋅si∑i = 0Nai⋅si.

Table 2:

Nominal transfer function parameter (see Eq. 7).

Gas	K_{_Q}	z_{0,_Q}	T_{_Q}	D_{_Q}
CO₂	0.996	0.231 s⁻¹	0.913 s	45.74
O₂	0.987	0.0995 s⁻¹	26.03 s	0.795

Table 3:

Weight function parameter (see Eq. 8).

i	O₂: a_{_i}	O₂: b_{_i}	CO₂: a_{_i}	CO₂: b_{_i}
0	4.05·10⁻⁶	2.33·10⁻⁷	0.0386	0.00285
1	0.000406	0.000136	88.0	9.25
2	0.0174	0.0105	1.68·10⁴	1.02·10⁴
3	0.161	0.194	1.01·10⁵	3.59·10⁵
4	0.673	0.606	1.99·10⁵	4.59·10⁵
5	0.771	0.864	8.55·10⁴	1.07·10⁵
6	1	0.948	2690	3218
7	–	–	1	28.47

A.2 Circulatory gas exchange model

Concentration c=[cCO2, cO2]T; time delays: TO2,d,pat=27.4 s and TCO2,d,pat=28 s; parameters are presented in Table 4; variable range of in silico study:

(9)Sp,O2∈[88, 98]%; pv,CO2∈[44, 70] mm Hg;QCO∈[6, 10] l/min; QT,O2∈[0.27, 0.29] l/min;VA∈[2.5, 3.5] l; Vt∈[31.2, 46.8] l; hct∈[19, 21]%.

(10)Td,a=Va/QCO∧Td,v=Vv/QCO,

(11)F˙A=1VA⋅[863⋅(1−fs)pbar−pH2O⋅QCO⋅(cmv−ca∗),+RR⋅Vt⋅fd⋅(Finsp−FA)]

(12)pa*=pA=(pbar−pH2O)⋅FA,

(13)ca=ca*⋅(1−fs)+cmv⋅fs,

(14)c˙v=1VT[(QT,O2Vmol⋅RQ−QO2,TVmol)+QCO⋅(ca−cv)],

(15)c˙mv=1Voxy⋅[(−QCO2,yVmolQO2,yVmol)+QCO⋅(cv−cmv)].

Table 4:

Patient model parameters.

Parameter	Value	Description
f_s	0.23	Pulmonary blood shunt
f_d	0.8	Reduced alveolar space
QO2,T	0.27 l/min	Cell’s O₂ consumption
p_bar	760 mm Hg	Ambient pressure [38]
pH2O	47 mm Hg	Vapor pressure [38]
RQ	0.9	Respiratory quotient
V_A	3 l	Alveolar volume [12]
V_a	1.82 l	Arterial volume [12]
V_T	39 l	Tissue volume [12]
V_oxy	0.2 l	Oxygenator blood volume
V_v	3.188 l	Venous volume [12]

A.3 Sensor models

(16)GSp,O2(s)=11⋅s+1⋅e−5⋅ss,

(17)Gpv,CO2(s)=120⋅s+1⋅e−10⋅s⋅e−6⋅ss.

A.4 Physiological target controller

KPID(s)=Kp+KI⋅s−1+KD⋅sTf⋅s+1 (see Table 5).(18)

Table 5:

Controller parameters.

	Kp(mlmin)	Ki(mlmin2)	KD(ml%)	T_{_f} (min)
KO2,low	3.41%	1.81%	0.072	17.5
KO2,high	31%	3.481%	0.048	7.77
KCO2	− 0.0511mm Hg	− 3.3361mm Hg	−	−

A.5 PEEP titration protocol

The PEEP titration protocol length has been limited to a minimal number of breath cycles required for reliable parameter estimation (see Table 6). A minimum compliance difference of 0.5 ml/mbar is significantly distinguishable using 5 samples assuming a test power of 80% and a normal distributed compliance noise with a standard deviation of 0.278 ml/mbar (measured steady-state value).

Table 6:

PEEP titration protocol parameters.

PEEP	PEEP range	Step size (mbar)	Step length (breath cycles)
Titration	[PEEP_min , PEEP_max ]	−2	6
Review	PEEP_best ± 2 mbar	−0.5	6

whiletruedo

open lung: 10 breath cycles PEEP= PEEP_max;

decremental PEEP titration;

reopen lung: PEEP=PEEP_max for 1 min;

set best PEEP={PEEP_best|max(C̅_rs,step)};

wait 1 min; set t_start=t_act; set review=true;

whileC¯rs,10(tact)>maxt ∈ [tstart,tact]C¯rs,10(t)⋅0.8do

ifreviewthen

PEEP review;

set review=false; set t_rev=t_act;

else ift_act−t_rev> 5 min then

set review=true;

end if

end while

A.6 Blood gas values

Used constants are presented in Table 7.

(19)cH+=KCO2⋅αCO2⋅pCO2cCO2−αCO2⋅pCO2,

(20)pH=9−log(cH+⋅lnmol),

(21)cCO2=cCO2ery⋅cHbcHbery+cCO2pla⋅(1−cHbcHbery),

(22)cCO2ery=αCO2ery⋅pO2⋅(1+10pHery − pKery),

(23)pKery=6,125−log(1+10pHery − 7,84 − 0,06 ⋅ SO2),

(24)pHery=7,19+0,77⋅(pH−7,4),+0,035⋅(1−SO2)

(25)cCO2pla=αCO2pla⋅pO2⋅(1+10pH−pKpla),

(26)pKpla=6,125−log(1+10pH − 8,7),

(27)cO2=αO2⋅pO2+capO2⋅SO2,

(28)capO2=kH⋅MCHC⋅hctVmol,

(29)SO2=ef(pO2)⋅1001+ef(pO2),

(30)f(pO2)=ln(SO2,01−SO2,0)+ln(pO2PO2,0)+k⋅tanh(h−1k⋅ln(pO2PO2,0)),

(31)pO2,0=1,955⋅p507,4⋅10pH − 7,4,

(32)pO2=p507,4⋅10pH − 7,4⋅SO2100−SO2h.

Table 7:

Blood gas parameters.

Parameter	Value	Description
αCO2	32.6598 μmoll⋅mm Hg	Solubility of CO₂ in water [42]
αCO2ery	0.195 mmoll⋅kPa	Solubility of CO₂ in erythrocyte [42]
αCO2pla	0.23 mmoll⋅kPa	Solubility of CO₂ in plasma [42]
αO2	1.457 μmoll⋅mm Hg	Solubility of O₂ in water [42]
c_Hb	9.3 mmoll	Hemoglobin concentration in blood [42]
cHbery	21 mmoll	Hemoglobin concentration in erythrocyte [42]
h	2.87	Hill coefficient [42]
KCO2	795 mmol/l	Dissociation constant of carbonic acid [12]
k_H	1.34 ml/g	Maximum O₂ uptake [26]
k	3.5	Half horizontal distance [42]
MCHC	340 g/l	Mean corpuscular hemoglobin concentration [26]
p507,4	26.86 mm Hg	Half O₂ saturation pressure [42]
SO2,0	0.867	Maximum of Hill slope [42]
V_mol	22.414 l/mol	Molar volume

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Received: 2016-3-29

Accepted: 2016-11-28

Published Online: 2017-1-25

Published in Print: 2017-4-1

Physiological closed-loop control of mechanical ventilation and extracorporeal membrane oxygenation

Abstract

Acknowledgment

Appendix

A Equations and parameters

A.1 Extracorporeal gas transfer

A.2 Circulatory gas exchange model

A.3 Sensor models

A.4 Physiological target controller

A.5 PEEP titration protocol

A.6 Blood gas values

References

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