Learning pharmacometric covariate model structures with symbolic regression networks

Efficiently finding covariate model structures that minimize the need for random effects to describe pharmacological data is challenging. The standard approach focuses on identification of relevant covariates, and present methodology lacks tools for automatic identification of covariate model structures. Although neural networks could potentially be used to approximate covariate-parameter relationships, such approximations are not human-readable and come at the risk of poor generalizability due to high model complexity.In the present study, a novel methodology for the simultaneous selection of covariate model structure and optimization of its parameters is proposed. It is based on symbolic regression, posed as an optimization problem with a smooth loss function. This enables training of the model through back-propagation using efficient gradient computations.Feasibility and effectiveness are demonstrated by application to a clinical pharmacokinetic data set for propofol, containing infusion and blood sample time series from 1031 individuals. The resulting model is compared to a published state-of-the-art model for the same data set. Our methodology finds a covariate model structure and corresponding parameter values with a slightly better fit, while relying on notably fewer covariates than the state-of-the-art model. Unlike contemporary practice, finding the covariate model structure is achieved without an iterative procedure involving manual interactions.

Ex Vivo Working Porcine Heart Model

Ex vivo working porcine heart models allow for the study of a heart's function and physiology outside the living organism. These models are particularly useful due to the anatomical and physiological similarities between porcine and human hearts, providing an experimental platform to investigate cardiac disease or assess donor heart viability for transplantation. This chapter presents an in-depth discussion of the model's components, including the perfusate, preload, and afterload. We explore the challenges of emulating cardiac afterload and present a historical perspective on afterload modeling, discussing various methodologies and their respective limitations. An actively controlled afterload device is introduced to enhance the model's ability to rapidly adjust pressure in the large arteries, thereby providing a more accurate and dynamic experimental model. Finally, we provide a comprehensive experimental protocol for the ex vivo working porcine heart model.

A novel nonlinear afterload for ex vivo heart evaluation: porcine experimental results

Background

Existing working heart models for ex vivo functional evaluation of donor hearts often use cardiac afterloads made up of discrete resistive and compliant elements. This approach limits the practicality of independently controlling systolic and diastolic aortic pressure to safely test the heart under multiple loading conditions. We present and investigate a novel afterload concept designed to enable such control.

Methods

Six ∼70 kg pig hearts were evaluated in vivo, then ex vivo in left‐ventricular working mode using the presented afterload. Both in vivo and ex vivo, the hearts were evaluated at two exertion levels: at rest and following a 20 μg adrenaline bolus, while measuring aortic pressure and flow, left ventricular pressure and volume, and left atrial pressure.

Results

The afterload gave aortic pressure waveforms that matched the general shape of the in vivo measurements. A wide range of physiological systolic pressures (93 to 160 mm Hg) and diastolic pressures (73 to 113 mm Hg) were generated by the afterload.

Conclusions

With the presented afterload concept, multiple physiological loading conditions could be tested ex vivo, and compared with the corresponding in vivo data. An additional control loop from the set pressure limits to the measured systolic and diastolic aortic pressure is proposed to address discrepancies observed between the set limits and the measured pressures.

Nowcasting (Short-Term Forecasting) of COVID-19 Hospitalizations Using Syndromic Healthcare Data, Sweden, 2020

We report on local nowcasting (short-term forecasting) of coronavirus disease (COVID-19) hospitalizations based on syndromic (symptom) data recorded in regular healthcare routines in Östergötland County (population ≈465,000), Sweden, early in the pandemic, when broad laboratory testing was unavailable. Daily nowcasts were supplied to the local healthcare management based on analyses of the time lag between telenursing calls with the chief complaints (cough by adult or fever by adult) and COVID-19 hospitalization. The complaint cough by adult showed satisfactory performance (Pearson correlation coefficient r>0.80; mean absolute percentage error <20%) in nowcasting the incidence of daily COVID-19 hospitalizations 14 days in advance until the incidence decreased to <1.5/100,000 population, whereas the corresponding performance for fever by adult was unsatisfactory. Our results support local nowcasting of hospitalizations on the basis of symptom data recorded in routine healthcare during the initial stage of a pandemic.

Identifiability issues in estimating the impact of interventions on Covid-19 spread

The Covid-19 pandemic has spawned numerous dynamic modeling attempts aimed at estimation, prediction, and ultimately control. The predictive power of these attempts has varied, and there remains a lack of consensus regarding the mechanisms of virus spread and the effectiveness of various non-pharmaceutical interventions that have been enforced regionally as well as nationally. Setting out in data available in the spring of 2020, and with a now-famous model by Imperial College researchers as example, we employ an information-theoretical approach to shed light on why the predictive power of early modeling approaches have remained disappointingly poor.

Prevention of Ischemic Myocardial Contracture Through Hemodynamically Controlled DCD

Purpose

Ischemic myocardial contracture (IMC) or “stone heart” is a condition with rapid onset following circulatory death. It inhibits transplantability of hearts donated upon circulatory death (DCD). We investigate the effectiveness of hemodynamic normalization upon withdrawal of life-sustaining therapy (WLST) in a large-animal controlled DCD model, with the hypothesis that reduction in cardiac work delays the onset of IMC.

Methods

A large-animal study was conducted comprising of a control group (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=6$$\end{document}n=6) receiving no therapy upon WLST, and a test group (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=6$$\end{document}n=6) subjected to a protocol for fully automated computer-controlled hemodynamic drug administration. Onset of IMC within 1 h following circulatory death defined the primary end-point. Cardiac work estimates based on pressure-volume loop concepts were developed and used to provide insight into the effectiveness of the proposed computer-controlled therapy.

Results

No test group individual developed IMC within \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1} \text { h}$$\end{document}1h, whereas all control group individuals did (4/6 within \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${30}{\text { min}}$$\end{document}30min).

Conclusion

Automatic dosing of hemodynamic drugs in the controlled DCD context has the potential to prevent onset of IMC up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1}{\text { h}}$$\end{document}1h, enabling ethical and medically safe organ procurement. This has the potential to increase the use of DCD heart transplantation, which has been widely recognized as a means of meeting the growing demand for donor hearts.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13239-021-00537-8.

Robust PID control of propofol anaesthesia: Uncertainty limits performance, not PID structure

BACKGROUND AND OBJECTIVE

New proposals to improve the regulation of hypnosis in anaesthesia based on the development of advanced control structures emerge continuously. However, a fair study to analyse the real benefits of these structures compared to simpler clinically validated PID-based solutions has not been presented so far. The main objective of this work is to analyse the performance limitations associated with using a filtered PID controller, as compared to a high-order controller, represented through a Youla parameter.

METHODS

The comparison consists of a two-steps methodology. First, two robust optimal filtered PID controllers, considering the effect of the inter-patient variability, are synthesised. A set of 47 validated paediatric pharmacological models, identified from clinical data, is used to this end. This model set provides representative inter-patient variability Second, individualised filtered PID and Youla controllers are synthesised for each model in the set. For fairness of comparison, the same performance objective is optimised for all designs, and the same robustness constraints are considered. Controller synthesis is performed utilising convex optimisation and gradient-based methods relying on algebraic differentiation. The worst-case performance over the patient model set is used for the comparison.

RESULTS

Two robust filtered PID controllers for the entire model set, as well as individual-specific PID and Youla controllers, were optimised. All considered designs resulted in similar frequency response characteristics. The performance improvement associated with the Youla controllers was not significant compared to the individually tuned filtered PID controllers. The difference in performance between controllers synthesized for the model set and for individual models was significantly larger than the performance difference between the individual-specific PID and Youla controllers. The different controllers were evaluated in simulation. Although all of them showed clinically acceptable results, the robust solutions provided slower responses.

CONCLUSION

Taking the same clinical and technical considerations into account for the optimisation of the different controllers, the design of individual-specific solutions resulted in only marginal differences in performance when comparing an optimal Youla parameter and its optimal filtered PID counterpart. The inter-patient variability is much more detrimental to performance than the limitations imposed by the simple structure of the filtered PID controller.

Individualized closed-loop anesthesia through patient model partitioning

Closed-loop controlled drug dosing has the potential of revolutionizing clinical anesthesia. However, inter-patient variability in drug sensitivity poses a central challenge to the synthesis of safe controllers. Identifying a full individual pharmacokinetic-pharmacodynamic (PKPD) model for this synthesis is clinically infeasible due to limited excitation of PKPD dynamics and presence of unmodeled disturbances. This work presents a novel method to mitigate inter-patient variability. It is based on: 1) partitioning an a priori known model set into subsets; 2) synthesizing an optimal robust controller for each subset; 3) classifying patients into one of the subsets online based on demographic or induction phase data; 4) applying the associated closed-loop controller. The method is investigated in a simulation study, utilizing a set of 47 clinically obtained patient models. Results are presented and discussed.Clinical relevance-The proposed method is easy to implement in clinical practice, and has potential to reduce the impact from surgical stimulation disturbances, and to result in safer closed-loop anesthesia with less risk of under- and over dosing.

Optimizing Robust PID Control of Propofol Anesthesia for Children: Design and Clinical Evaluation

OBJECTIVE

The goal of this paper was to optimize robust PID control for propofol anesthesia in children aged 5-10 years to improve performance, particularly to decrease the time of induction of anesthesia while maintaining robustness.

METHODS

We analyzed results of a previous study conducted by our group to identify opportunities for system improvement. Allometric scaling was introduced to reduce the interpatient variability and a new robust PID controller was designed using an optimization-based method. We evaluated this optimized design in a clinical study involving 16 new cases.

RESULTS

The optimized controller design achieved the performance predicted in simulation studies in the design stage. Time of induction of anesthesia was median [Q1, Q3] 3.7 [2.3, 4.1] min and the achieved global score was 13.4 [9.9, 16.8].

CONCLUSION

Allometric scaling reduces the interpatient variability in this age group and allows for improved closed-loop performance. The uncertainty described by the model set, the predicted closed-loop responses, and the predicted robustness margins are realistic. The system meets the design objectives of improved speed of induction of anesthesia while maintaining robustness and improving clinically relevant system behavior.

SIGNIFICANCE

Control system optimization and ongoing system improvements are essential to the development of a clinically relevant commercial device. This paper demonstrates the validity of our approach, including system modeling, controller optimization, and pre-clinical testing in simulation.

Closed-Loop Prevention of Hypotension in the Heartbeating Brain-Dead Porcine Model

Objective: The purpose of this paper is to demonstrate feasibility of a novel closed-loop controlled therapy for prevention of hypertension in the heartbeating brain-dead porcine model.

METHODS

Dynamic modeling and system identification were based on in vivo data. A robust controller design was obtained for the identified models. Disturbance attenuation properties and reliability of operation of the resulting control system were evaluated in vivo.

RESULTS

The control system responded both predictably and consistently to external disturbances. It was possible to prevent mean arterial pressure to fall below a user-specified reference throughout 24 h of completely autonomous operation.

CONCLUSION

Parameter variability in the identified models confirmed the benefit of closed-loop controlled administration of the proposed therapy. The evaluated robust controller was able to mitigate both process uncertainty and external disturbances.

SIGNIFICANCE

Prevention of hypertension is critical to the care of heartbeating brain-dead organ donors. Its automation would likely increase the fraction of organs suitable for transplantation from this patient group.

Robust closed-loop control of induction and maintenance of propofol anesthesia in children

BACKGROUND

During closed-loop control, a drug infusion is continually adjusted according to a measure of clinical effect (e.g., an electroencephalographic depth of hypnosis (DoH) index). Inconsistency in population-derived pediatric pharmacokinetic/pharmacodynamic models and the large interpatient variability observed in children suggest a role for closed-loop control in optimizing the administration of intravenous anesthesia.

OBJECTIVE

To clinically evaluate a robustly tuned system for closed-loop control of the induction and maintenance of propofol anesthesia in children undergoing gastrointestinal endoscopy.

METHODS

One hundred and eight children, aged 6-17, ASA I-II, were enrolled. Prior to induction of anesthesia, NeuroSENSE™ sensors were applied to obtain the WAVCNS DoH index. An intravenous cannula was inserted and lidocaine (0.5 mg·kg(-1) ) administered. Remifentanil was administered as a bolus (0.5 μg·kg(-1) ), followed by continuous infusion (0.03 μg·kg(-1) ·min(-1) ). The propofol infusion was closed-loop controlled throughout induction and maintenance of anesthesia, using WAVCNS as feedback.

RESULTS

Anesthesia was closed-loop controlled in 102 cases. The system achieved and maintained an adequate DoH without manual adjustment in 87/102 (85%) cases. Induction of anesthesia (to WAVCNS  ≤ 60) was completed in median 3.8 min (interquartile range (IQR) 3.1-5.0), culminating in a propofol effect-site concentration (Ce ) of median 3.5 μg·ml(-1) (IQR 2.7-4.5). During maintenance of anesthesia, WAVCNS was measured within 10 units of the target for median 89% (IQR 79-96) of the time. Spontaneous breathing required no manual intervention in 91/102 (89%) cases.

CONCLUSIONS

A robust closed-loop system can provide effective propofol administration during induction and maintenance of anesthesia in children. Wide variation in the calculated Ce highlights the limitation of open-loop regimes based on pharmacokinetic/pharmacodynamic models.