Physiologic Data-Driven Iterative Learning Control for Left Ventricular Assist Devices

Figures

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  Figure 1. Schematic overview of the physiological data-driven iterative learning controller. The input signals LVP and PF are filtered and the EDP and SP indices are extracted from the LVP. Based on the Frank-starling mechanism, the desired average PF is calculated based on the LV-EDP that is used as a preload surrogate, and the reference pulsatile PF trajectory is obtained based on the objectives of the therapy. A data-driven iterative learning controller is implemented to achieve accurate tracking of the reference PF without requiring modeling of the CVS or the pump. Finally, a proportional-derivative (PD) controller is coupled coupled to enable feedback in the time-domain. The desired pump speed is the output of the controller. Bold letters define vectors. LVP, left ventricular pressure; EDP, end-diastolic pressure; SP, systolic pressure; PF, pump flow; qbp, measured pump flow; q¯bp*, heart cycle average pump flow; qbp*, time vector of the desired pump flow trajectory; nbp,FF*, feed forward desired pump speed; nbp,FB*, feedback desired pump speed; nbp*, desired pump speed output.

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  Figure 2. Schematic representation of the LV-EDP extraction process and the extension for the minimization of misdetections. (A) Identification of all local minima (cyan circles) and inflection points (red rectangles) as LV-EDP candidates. The inflection points with large first LVP derivative (dLVP/dt > 40 mmHg/s) are excluded and the candidate with the smaller distance from the SP index (dtmin) is identified as the LV-EDP. (B) Comparison of the identified LV-EDP (filled circles) with the LV-EDP estimated (filled rectangles) based on linear regression of the LV-EDP extracted on the previous three heartbeats. If the identified LV-EDP is within the boundaries, it is extracted as LV-EDP value. (C) Based on the comparison described in b, if the identified LV-EDP is outside the boundaries it is considered an outlier and the mean value of the last three LV-EDPs is extracted as LV-EDP (filled triangles) of the investigated heartbeat. The outliers are stored in memory and if three consecutive identified LV-EDPs constitute outliners a flag is raised and the new LV-EDP estimate is based on the outliers (LRn+3) instead of the extracted LV-EDPs. In this way, physiological rapid changes in preload are…

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  Figure 3. Reference PF trajectories that incorporate a physiological response to preload changes based on the Frank-Starling mechanism and therapy-oriented pulsatile PF profiles. A copulsation and a counterpulsation PF trajectory along with the LVP for one cardiac cycle are depicted. For both PF trajectories, the minimum PF is qbp,min*=20 mL/s and the maximum PF is calculated based on the qbp,min* and the necessary average PF provided by the starling-relation (q¯bp*). PF, pump flow; LVP, left ventricular pressure; Co-PF, copulsation pump flow; Counter-PF, counterpulsation pump flow.

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  Figure 4. Schematic overview of the DD-ILC algorithm. The pump speed setpoint and the PF are stored in a memory block. Then, they are used at the beginning of each cycle to update the system model through dynamic linearization. The model is used in a quadratic optimization problem to minimize the PF tracking error under pump speed constraints. The time index counter operates continuously to extract and output the feedforward pump speed setpoint at every time step within an iteration. Bold letters define vectors. nbp,j*, pump speed setpoint vector of the jth cycle; qbp,j, measured PF vector of the jth cycle; Φ^j, pseudo partial derivative denoting the linearized system model; qbp,j+1*, PF reference trajectory; nbp,FF*, feedforward pump speed setpoint in the time domain.

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  Figure 5. Schematic overview of the physiological flow PID controller. The input signals LVP and PF are filtered and the EDP and SP indices are extracted from the LVP. Based on the Frank-Starling mechanism, the average PF is calculated based on the LV-EDP that is used as a preload surrogate, and the reference pulsatile PF trajectory is obtained based on the objectives of the therapy. A time index counter operates continuously to extract and output the feedforward PF setpoint at every time step. A PID flow controller (included in the orange dashed-line box) provides the necessary change in the pump speed setpoint based on the error between the measured and the desired PF. The desired pump speed is the output of the controller. Bold letters define vectors. LVP, left ventricular pressure; EDP, end-diastolic pressure; SP, systolic pressure; PF, pump flow; PID, proportional-integral-derivative; qbp, measured pump flow; q¯bp*, heart cycle average pump flow; qbp*, time vector of the desired pump flow trajectory; qbp,FF*, feed forward desired pump flow; eq, bp, feedback error between the measured and the desired PF; Δnbp*, desired pump speed change; nbp,constant, pump speed constant; nbp*, desired…

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  Figure 6. Reference trajectory tracking performance of the PDD-ILC and the PF-PIDC during one cardiac cycle of the rest-conditions experiment (Exp0, Supplementary Table S1, Supplementary Material) under (A) copulsation and (B) counterpulsation. The reference trajectories, along with the left ventricular pressure profile that corresponds to the main source of disturbance are given for both modes. Both controllers are able to track accurately the reference trajectory during copulsation, reaching the maximum and minimum PF values without time lag. During the counterpulsation, the high disturbance of the fast change in LVP cannot be compensated completely from any of the controllers, however, the overall tracking is adequate. PDD-ILC, physiologic data-driven iterative learning controller; PF-PIDC, pump flow proportional-integral-derivative controller; Ref. Traj., reference trajectory; LVP, left ventricular pressure.

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  Figure 7. Transient performance of the PDD-ILC and the PF-PIDC in terms of RMSE and maximum instantaneous error in tracking the reference trajectory under all physiological conditions and scenarios executed with the copulsation mode. (A) Rest-conditions (Exp0): The PDD-ILC converged after 100 iterations, obtaining an RMSE of 0.07 L min-1 and maximum error of 0.19 L min-1. The PF-PIDC obtained an RMSE of 0.06 L min-1 and maximum error of 0.11 L min-1. (B) Preload variation (Exp1): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.07 L min-1 and 0.23 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.05 L min-1 and 0.08 L min-1, respectively. (C) Afterload variation (Exp2): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.20 L min-1 and 0.73 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.11 L min-1 and 0.38 L min-1, respectively. (D) Sleep-to-wake (Exp3): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.05 L min-1 and 0.21 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.06 L min-1 and 0.11 L min-1,…

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  Figure 8. Transient performance of the PDD-ILC and the PF-PIDC in terms of RMSE and maximum instantaneous error in tracking the reference trajectory under all physiological conditions and scenarios executed with the counterpulsation mode selected. (A) Rest-conditions (Exp0): The PDD-ILC converged after 50 iterations, obtaining an RMSE of 0.88 L min-1 and maximum error of 2.64 L min-1. The PF-PIDC obtained an RMSE of 0.42 L min-1 and maximum error of 1.32 L min-1. (B) Preload variation (Exp1): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.94 L min-1 and 2.60 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.43 L min-1 and 1.32 L min-1, respectively. (C) Afterload variation (Exp2): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.50 L min-1 and 1.67 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.19 L min-1 and 0.50 L min-1, respectively. (D) Sleep-to-wake (Exp3): Last variation at 85 seconds. The converged RMSE and maximum error for the PDD-ILC was 0.90 L min-1 and 2.30 L min-1, respectively. The RMSE and maximum error for the PF-PIDC was 0.43 L min-1 and 1.34 L…

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  Figure 9. Influence of the copulsation and counterpulsation modes on the left ventricular stroke work (LVSW) of the diseased heart (DH) during: (A) Rest-conditions (Exp0), (B) Preload variation (Exp1 (C) Afterload variation (Exp2) (D) Sleep-to-wake (Exp3) (E) Contractility variation (Exp4) (F) Rest-to-exercise (Exp5). DH, diseased heart; CS, constant speed control; PDD-ILCco, physiologic data-driven iterative learning controller copulsation; PF-PIDCco, pump flow proportional-integral-derivative controller copulsation; PDD-ILCcc, physiologic data-driven iterative learning controller counterpulsation; PF-PIDCcc, pump flow proportional-integral-derivative controller counterpulsation.

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  Figure 10. Influence of the copulsation and counterpulsation modes on the aortic pulse pressure (PP) of the diseased heart (DH) during: (A) Rest-conditions (Exp0), (B) Preload variation (Exp1) (C) Afterload variation (Exp2) (D) Sleep-to-wake (Exp3) (E) Contractility variation (Exp4) (F) Rest-to-exercise (Exp5). HH, healthy heart; DH, diseased heart; CS, constant speed control; PF-PIDCco, pump flow proportional-integral-derivative controller copulsation; PDD-ILCcc, physiologic data-driven iterative learning controller counterpulsation; PF-PIDCcc, pump flow proportional-integral-derivative controller counterpulsation.