A supervisor for volume-controlled tidal liquid

Biomedical Signal Processing and Control 2 (2007) 267–274 www.elsevier.com/locate/bspc

A supervisor for volume-controlled tidal liquid ventilator using independent piston pumps Raymond Robert a,*, Philippe Micheau a, Herve´ Walti b a

Department of Mechanical Engineering, University of Sherbrooke, Canada b Department of Paediatrics, University of Sherbrooke, Canada

Received 24 February 2007; received in revised form 17 July 2007; accepted 25 July 2007 Available online 4 September 2007

Abstract Liquid ventilation using perfluorochemicals (PFC) offers clear theoretical advantages over gas ventilation, such as decreased lung damage, recruitment of collapsed lung regions and lavage of inflammatory debris. This paper presents the control of a total liquid ventilator (TLV) dedicated to ventilate patients with completely filled lungs with a tidal volume of perfluorochemical liquid. The two independent piston pumps are volume controlled and pressure limited. Measurable pumping errors are corrected by a programmed supervisor module, which modifies the inserted or withdrawn volume. Pump independence also allows easy FRC modifications during ventilation. The prototype was tested on eight healthy term newborn lambs ( 0

(3)

Eqs. (2) and (3) in (1) lead to: FRC½k þ 1  FRC½k þ gi ðV t þ DV½k; T i Þ  ge ðV t ; T i Þ ifDV½k < 0 ¼ FRC½k þ ge ðV t ; T e Þ  ge ðV t  DV½k; T e Þ ifDV½k  0 (4) When the servo-control is perfect, gi(Vt + DV, Ti) = Vt  jDVj if DV  0 and ge(Vt + DV, Te) = Vt  jDVj if DV  0, the FRC is linearly commanded by the FRC correction DV[k]: FRC[k + 1] = FRC[k] + DV[k]. However, in fact, the assumptions are no longer valid: there are small errors, Ei and Ee such that gi(Vi, Ti) = Vi + Ei(Vi, Ti) and ge(Ve, Te) = Ve + Ee(Ve, Te). These errors lead to a slow time-varying FRC drift. To illustrate this point, let consider constant values of parameters (Vi[k] = Ve[k] = Vi, Ti[k] = Ti and Te[k] = Te); consequently, the errors are constant values, and the FRC drifts at the rate E/(Ti + Te + Teip + Teep) (in L/s, where Teip and Teep are the end-inspiratory and expiratory pause time) because FRC[k + 1] = FRC[k] + E* with E = Ei  Ee and the cycle duration Ti + Te + Teip + Teep. 2.5. The control of small errors In order to avoid an accumulation of small tracking errors due to the feedback loops, the proposed discrete control consists of correcting the inspiratory errors by controlling the expiratory volume: a control is added in Eq. (3). The desired expiratory volume Ve[k] is computed based on the tidal volume, Vt[k], the correction volume, DV (if it needs to be increased), the inspiratory measurable error volume, Ei[k], and the previous measurable expiratory error volume Ee[k  1] as follow:  V t ½k  Ei ½k þ Ee ½k  1 if DV½k  0 V e ½k ¼ V t ½k  Ei ½k þ Ee ½k  1  DV½k if DV½k > 0 (5) The measured inspiratory and expiratory errors are measurable. Hence, stochastic variables bi[k] and be[k] are added to represent the noise measurement or some bias on the measurement: Ei ½k ¼ gi ðV i ½k; T i ½kÞ  V t þ bi ½k

(6)

Ee ½k ¼ ge ðV e ½k; T e ½kÞ  V t þ be ½k

(7)

To demonstrate the convergence of the supervisor module, the following case is considered: a constant tidal volume Vi[k] = Vt, no compensation of FRC (DV = 0) and constant expiratory and inspiratory times. Because DV = 0, the desired inspiratory volume given by (2) is Vi[k] = Vt, and the desired expiratory volume computed with (4) is Ve[k] = Vt  Ei[k] + Ei[k  1]. Using relation (5)–(7) we obtain the following stochastic nonlinear equation: V e ½k ¼ V t  gi þ ge ðV e ½k  1Þ þ b½k with b[k] = be[k  1]  be[k].

(8)

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With a white measurement noise, E{b[k]} = 0, the expectance value of mean value of Ve[k], Ve ¼ EfV e ½kg, is the solution of EfVe g ¼ ge ðEfVe gÞ þ V t  gi . Hence, close to the equilibrium point, the discrete dynamic can be approximated by dge dV e ½k ¼ dV ðVe ÞdV e ½k  1 þ b½k where dV e ¼ V e  Ve is a e small disturbance close to the equilibrium point. The equilibrium point Ve is attractive (the discrete recurrence is stable), if and only if the slope of the curve respect the condition 1 < ðdge =dV e ÞðVe Þ < 1. By definition, ge(Ve) is a monotonous increasing positive function, ðdge =dV e Þ > 0. Hence, the stability condition implies to verify ðdge =dV e ÞðVe Þ < 1. In steady state condition, this corrected volume ensures the same expected value of inspiratory and expiratory volume, thus a constant FRC during ventilation. 2.6. Pressure limitations Lower and upper pressure limits are set to protect the patient’s lung. If the upper pressure Pmax is reached during the inspiration phase, P(t) > Pmax, the inspiratory pump is stopped, and the cycle switches to the end-inspiratory pause. In this case, due to Eq. (4), only the volume instilled in the lungs will be expired. Also, if the lower pressure limit, Pmin, is reached during the expiration phase with the risk of an airway closure, P(t) < Pmin, the expiratory pump is stopped, and the cycle switches to the end-expiratory pause. In such a case, the desired inspiratory volume for the next inspiration is equal to the volume expired from the lungs during the stopped expiratory cycle, Vi[k] = ye[k  1]. So, every time a pressure limit is reached, the volume inserted or expired from the lungs is adjusted to maintain the same FRC. Therefore, each pump is time-limited, volume-controlled and pressure-limited. 3. Experimentation 3.1. In vitro testing The supervisor module was tested to determine whether the algorithm converges and manages measurable pumping errors. A dSpace acquisition station (DS1003 processor board, DS2201, 12 bits I/O analog board) was used to precisely record the analog signals provided by the potentiometers of the expiratory and inspiratory pumps. In order to reflect the weight range of a term newborn infant during the first weeks of life four Vt were chosen: 75, 100, 125 and 150 ml. To test the operating capabilities of the expiratory and inspiratory piston pumps and their overall system control, in vivo TLV was mimicked by replacing the lungs with a fixed reservoir. The tidal ventilator delivers the tidal volumes at a rate of 5 breaths/min over a 2 h period which implies 480 cycles. The quantization error of the analog converter used by the PLC, is 0.14 ml; consequently the worst case of drift of FRC is estimated to be 0.14  480 cycles = 67.2 ml over 2 h. The means  S.D. inspired tidal volume in the reservoir were 75.06  0.16, 100.16  0.15, 125.19  0.17 and 150.22  0.15 ml. The means  S.D. expired tidal volume in the reservoir were 75.09  0.16, 100.19  0.43, 125.19  0.34 and 150.31  0.28 ml. At the end of a 2 h period, the computed

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FRC drifts were 14, 16, 1 and 31 ml for respectively the required tidal volumes of 75, 100, 125 and 150 ml. The supervisor module proved its effectiveness in managing measurable errors because the measured drifts over 2 h are below the worst estimated case. The standard deviations on the measured volumes are roughly close to the quantization error of the analog converter. 3.2. In vivo testing The experimental protocol was approved by our institutional Ethics Committee for Animal Care and Experimentation. The presented results were obtained in eight healthy term anaesthetized newborn lambs (age < 5 days, weight of 4.40  1.39 kg, 2 h TLV trial) [28]. A tracheotomy was then performed and a 6.0 G cuffed ETT placed into the trachea. The airway pressure was measured at the distal end of the ETT using a Mikro-Tip catheter 2.3 Fr (SPR524, Millar Instruments Inc., Houston, TX). The analog signals of trachea pressure, inspiratory volume and expiratory volume generated from the TLV ventilator were recorded using Signal Ranger I/O boards (SoftdB, Quebec, Canada). After the instillation of the PFC (PFOB from F2 Chemicals, Lancashire, UK), the tidal liquid ventilation was then initiated at a rate of 3–4 breaths/min, a Vt of 25 ml/kg and an inspiratory/expiratory (I/E) ratio of 1/3, with a FiO2 of 1.0. An exponential profile was used during expiration and a ramp profile during inspiration. The ventilator settings were then adjusted to maintain PaO2 > 100 mmHg and PaCO2 at 30–50 mmHg. The TLV ventilator maintained adequate gas exchange, normal acido-basis equilibrium, cardio-vascular stability and there was not different from results obtained in a similar gas-ventilated animal preparation (data not shown) [28]. Furthermore, airway pressure, lung volumes and ventilation scheme were maintained in the targeted range including the absence of any observed perfluorothorax.

Fig. 4 presents a typical pressure measurement in the trachea and volume variations in the pumps for a tidal volume of 120 ml. The exponential profile used during the expiration generates a slow decreasing airway pressure from 0 to 10 cm H2O. The quasi-static end-expiration pause allows the measurement of the PEEP at the end of expiration (this value is close to +5 cm H2O at time 64.05 min). During inspiration, the ramp volume profile included a 20% acceleration time and a 40% deceleration time. The inspiration generates a slow increasing airway pressure from 20 to 30 cm H2O. The quasistatic end-inspiration pause allows measuring the PEIP at the end of the inspiration (this value is close to +15 cm H2O at time 60.13 min). Fig. 5 presents the case of a chocked flow at time 25.2 min and the correction due to the supervisor. For the purpose of this example, the chocked flow is artificially generated by reducing the FRC to a critical low level. The pressure limit is set very low (below 45 cm H2O) to clearly show the drop pressure. Before time 25 min, the operator requests a 20 ml reduction of the FRC volume. To obtain this lung volume change, the supervisor controls the inspiratory pump to move from 100 to 20 ml (1a in Fig. 5). This point illustrates how the supervisor controls the residual liquid in the lungs. However, during the following expiratory phase (1b in Fig. 5) a chocked flow occurs, measured by the rapid decreasing of the airway pressure from 0 to 45 cm H2O. When the pressure limit is reached at 45 cm H2O, the supervisor immediately stops the expiratory phase. At this time, only 90 ml of PFC were expired and the supervisor memorizes this information for the following inspiratory phase which starts at time 25.2 min (3 in Fig. 5). Consequently, only 90 ml of PFC were inspired in order to maintain the FRC at the required level. To retrieve the initial lung volume (reinsert the 20 ml), the operator commands an FRC increase by step of 10 ml during the two next cycles (4 in Fig. 5).

Fig. 4. Typical pressure in the trachea, volumes in the inspiratory and expiratory pump vs. the time.

R. Robert et al. / Biomedical Signal Processing and Control 2 (2007) 267–274

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Fig. 5. Pressure in the trachea, volumes in the inspiratory and expiratory pump vs. the time when a collapse occurs during the expiration phase.

4. Discussion The in vitro experiments demonstrated the ability of the control (4) to compensate the measurable volume errors induced by the lack of precision in the servo-control of the two independent pumps. The accuracy of the pump volume compensator is limited by the accuracy of the volume measurement. For the presented experimental set-up, the 12 bits resolution of the analog-digital converter was the main limitation. A higher resolution may reduce the bias error. Another limitation of the supervisor is that the algorithm only corrects the measurable errors, meaning that it cannot compensate non-measurable added volume (such as the closing or opening of the pinch valves). Consequently, a slow FRC drift cannot be avoided for a long-term period. As an example, a repeated error of 0.14 ml at 5 breaths/min over a 10 min period, provokes a significant 7 ml FRC drift. However, there are two ways to observe this drift with the presented tidal liquid ventilator: (i) The buffer reservoir provides a mean to estimate visually the amount of PFC in the patient (after considering the PFC loss by evaporation). For example, if the measured PFC level in the buffer reservoir has increased by 7 ml, it indicates that the FRC has decreased by, at least, 7 ml. (ii) The airways pressure at the end of the expiration (PEEP, during the expiratory pause) is a measurement of the alveolar pressure, which is directly related to the amount of PFC in the lungs (via the lung compliance). With this measurable information, the clinician can decided to increase or decrease the amount of FRC in the lungs with the FRC correction, Eqs. (2) and (3). With this command, he can adjust the FRC in order to maintain a constant level of PFC in the buffer reservoir or a constant PEEP level. Those strategies were used during the in vivo experiments. The accuracy obtained with the supervisor allowed a reduction in the FRC correction at a low sampling period of 10 min.

The presented in vivo experiments with eight term newborn lambs (healthy lungs), demonstrate the supervisor reliability to perform tidal liquid ventilation. The special case presented in Fig. 5 illustrates the case of a chocked flow generated by an FRC reduction. This is a typical result obtained with different lambs at any time. In most of these cases, an FRC augmentation at the next cycle has always solved this chocked flow problem. Consequently, it suggests that a low FRC value may lead to a chocked flow in tidal liquid ventilation. So, it is critical to perfectly control the FRC level over a long period. If we compare the presented supervisor to the classical modes of ventilator operation [29,30], we can classify it as a volume-controlled, time driven and pressure-limited mode. Current developments include the design of a closed loop pressure control [31] in order to avoid airway collapses and optimize the liquid ventilation. Acknowledgments The authors would like to thank Valerie Cardinal, Johann Lebon, Valerie Provost, and Caroline Ouellet for their technical assistance supporting the in vivo experiments. The authors would also like to thank Remi Oddo and O. Berbuer for their technical assistance. References [1] L.C. Clark, F. Gollan, Survival of mammals breathing organic liquids equilibrated with oxygen at atmospheric pressure, Science 152 (730) (1966) 1755–1756. [2] C.A. Cox, M.R. Wolfson, T.H. Shaffer, Liquid ventilation: a comprehensive overview, Neonatal Network 15 (2) (1996) 31–43. [3] R. Foust 3rd, N.N. Tran, C. Cox, T.F. Miller Jr., J.S. Greenspan, M.R. Wolfson, et al., Liquid assisted ventilation: an alternative ventilatory strategy for acute meconium aspiration injury, Pediatr. Pulmonol. 21 (5) (1996) 316–322. [4] A.T. Rotta, D.M. Steinhorn, Partial liquid ventilation reduces pulmonary neutrophil accumulation in an experimental model of systemic endotoxemia and acute lung injury, Crit. Care Med. 26 (10) (1998) 1707–1715.

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