A graphical method for practical and informative identifiability analyses of physiological models: a case study of insulin kinetics and sensitivity

Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Model-based subcutaneous insulin for glycemic control of pre-term infants in the neonatal intensive care unit

Hyperglycaemia is a common problem in neonatal intensive care units (NICUs). Achieving good control can result in better outcomes for patients. However, good control is difficult, where poor control and resulting hypoglycaemia reduces outcomes and confounds results. Clinically validated models can provide good control, and subcutaneous insulin delivery can provide more options for insulin therapy for clinicians. However, this combination has only been significantly utilised in adult outpatient diabetes, but could hold benefit for treating NICU infants. This research combines a well-validated NICU metabolic model with subcutaneous insulin kinetics models to assess the feasibility of a model-based approach. Clinical data from 12 very/extremely pre-mature infants was collected for an average study duration of 10.1 days. Blood glucose, interstitial and plasma insulin, as well as subcutaneous and local insulin were modelled, and patient-specific insulin sensitivity profiles were identified for each patient. Modelling error was low, where the cohort median [IQR] mean percentage error was 0.8 [0.3 3.4] %. For external validation, insulin sensitivity was compared to previous NICU cohorts using the same metabolic model, where overall levels of insulin sensitivity were similar. Overall, the combined system model accurately captured observed glucose and insulin dynamics, showing the potential for a model-based approach to glycaemic control using subcutaneous insulin in this cohort. The results justify further model validation and clinical trial research to explore a model-based protocol.

Estimating Enhanced Endogenous Glucose Production in Intensive Care Unit Patients with Severe Insulin Resistance

BACKGROUND

Critically ill ICU patients frequently experience acute insulin resistance and increased endogenous glucose production, manifesting as stress-induced hyperglycemia and hyperinsulinemia. STAR (Stochastic TARgeted) is a glycemic control protocol, which directly manages inter- and intra- patient variability using model-based insulin sensitivity (SI). The model behind STAR assumes a population constant for endogenous glucose production (EGP), which is not otherwise identifiable.

OBJECTIVE

This study analyses the effect of estimating EGP for ICU patients with very low SI (severe insulin resistance) and its impact on identified, model-based insulin sensitivity identification, modeling accuracy, and model-based glycemic clinical control.

METHODS

Using clinical data from 717 STAR patients in 3 independent cohorts (Hungary, New Zealand, and Malaysia), insulin sensitivity, time of insulin resistance, and EGP values are analyzed. A method is presented to estimate EGP in the presence of non-physiologically low SI. Performance is assessed via model accuracy.

RESULTS

Results show 22%-62% of patients experience 1+ episodes of severe insulin resistance, representing 0.87%-9.00% of hours. Episodes primarily occur in the first 24 h, matching clinical expectations. The Malaysian cohort is most affected. In this subset of hours, constant model-based EGP values can bias identified SI and increase blood glucose (BG) fitting error. Using the EGP estimation method presented in these constrained hours significantly reduced BG fitting errors.

CONCLUSIONS

Patients early in ICU stay may have significantly increased EGP. Increasing modeled EGP in model-based glycemic control can improve control accuracy in these hours. The results provide new insight into the frequency and level of significantly increased EGP in critical illness.

The Impact of Exogenous Insulin Input on Calculating Hepatic Clearance Parameters

OBJECTIVE

Model-based metabolic tests require accurate identification of subject-specific parameters from measured assays. Insulin assays are used to identify insulin kinetics parameters, such as general and first-pass hepatic clearances. This study assesses the impact of intravenous insulin boluses on parameter identification precision.

METHOD

Insulin and C-peptide data from two intravenous glucose tolerance test (IVGTT) trials of healthy adults (N = 10 × 2; denoted A and B), with (A) and without (B) insulin modification, were used to identify insulin kinetics parameters using a grid search. Monte Carlo analysis (N = 1000) quantifies variation in simulation error for insulin assay errors of 5%. A region of parameter values around the optimum was identified whose errors are within variation due to assay error. A smaller optimal region indicates more precise practical identifiability. Trial results were compared to assess identifiability and precision.

RESULTS

Trial B, without insulin modification, has optimal parameter regions 4.7 times larger on average than Trial A, with 1-U insulin bolus modification. Ranges of optimal parameter values between trials A and B increase from 0.04 to 0.12 min^-1 for hepatic clearance and from 0.07 to 0.14 for first-pass clearance on average. Trial B's optimal values frequently lie outside physiological ranges, further indicating lack of distinct identifiability.

CONCLUSIONS

A small 1-U insulin bolus improves identification of hepatic clearance parameters by providing a smaller region of optimal parameter values. Adding an insulin bolus in metabolic tests can significantly improve identifiability and outcome test precision. Assay errors necessitate insulin modification in clinical tests to ensure identifiability and precision.

Determining Losses in Jet Injection Subcutaneous Insulin Delivery: A Model-Based Approach

OBJECTIVE

Accurate, safe glycemic management requires reliable delivery of insulin doses. Insulin can be delivered subcutaneously for action over a longer period of time. Needle-free jet injectors provide subcutaneous (SC) delivery without requiring needle use, but the volume of insulin absorbed varies due to losses associated with the delivery method. This study employs model-based methods to determine the expected proportion of active insulin present from a needle-free SC dose.

METHODS

Insulin, C-peptide, and glucose assay data from a frequently sampled insulin-modified oral glucose tolerance test trial with 2U SC insulin delivery, paired with a well-validated metabolic model, predict metabolic outcomes for N = 7 healthy adults. Subject-specific nonlinear hepatic clearance profiles are modeled over time using third-order basis splines with knots located at assay times. Hepatic clearance profiles are constrained within a physiological rate of change, and relative to plasma glucose profiles. Insulin loss proportions yielding optimal insulin predictions are then identified, quantifying delivery losses.

RESULTS

Optimal parameter identification suggests losses of up to 22% of the nominal 2U SC dose. The degree of loss varies between subjects and between trials on the same subject. Insulin fit accuracy improves where loss greater than 5% is identified, relative to where delivery loss is not modeled.

CONCLUSIONS

Modeling shows needle-free SC jet injection of a nominal dose of insulin does not necessarily provide metabolic action equivalent to total dose, and this availability significantly varies between trials. By quantifying and accounting for variability of jet injection insulin doses, better glycemic management outcomes using SC jet injection may be achieved.

Quantifying ventilator unloading in CPAP ventilation

BACKGROUND

The intrinsic (muscular) patient effort driving inspiration in non-invasive ventilation modes, such as continuous positive airway pressure (CPAP) therapy, has not been identified from non-invasive data. Current CPAP settings are based on clinical judgment and assessment of symptoms of respiratory distress. Non-optimal settings, including too much positive end expiratory pressure (PEEP) can cause unintended lung injury and ventilator unloading, where patient effort drops and the CPAP device enables too much work being imposed on the injured lung. Currently, there is no non-invasive means of quantifying or identifying these effects.

METHODS

A novel model-based method of ascertaining intrinsic patient work of breathing (WOB) in CPAP is developed based on linear single compartment and 2nd order b-spline models previously used in invasive ventilation modes. Results are compared to current clinical indications, such as total Imposed WOB from the CPAP device and beak length, the latter of which is the clinical metric used to indicate alveolar overdistension. Intrinsic and Imposed WOB are compared. The hypothesis is that ventilator unloading can be assessed as a decrease in Intrinsic WOB relative to Imposed WOB, as PEEP and associated ventilator unloading rise. This hypothesis is tested using 14 subjects from a CPAP trial of several breathing rates at two PEEP levels.

RESULTS

The ratio of Intrinsic to Imposed WOB, normalised per unit tidal volume, decreased with increasing PEEP (4-7 cm H₂O), capturing the expected trend of ventilator unloading. Ventilator unloading was observed across all breathing rates. Beak length measurements showed no conclusive evidence of capturing overdistension at higher PEEP or ventilator unloading.

CONCLUSIONS

Patient Intrinsic WOB in CPAP was non-invasively quantified using model-based methods, based on pressure and flow measurements. The ratio of Intrinsic to Imposed WOB per unit tidal volume clearly and consistently showed ventilator unloading across all patients and breathing rates, with Intrinsic WOB decreasing with increasing PEEP. This trend was not observed in the current clinical metric of beak length. Non-invasively quantifying Intrinsic WOB and ventilator unloading is the critical first step to objectively optimising clinical CPAP settings, patient care, and outcomes.

Model-based estimation of negative inspiratory driving pressure in patients receiving invasive NAVA mechanical ventilation

BACKGROUND

Optimisation of mechanical ventilation (MV) and weaning requires insight into underlying patient breathing effort. Current identifiable models effectively describe lung mechanics, such as elastance (E) and resistance (R) at the bedside in sedated patients, but are less effective when spontaneous breathing is present. This research derives and regularises a single compartment model to identify patient-specific inspiratory effort.

METHODS

Constrained second-order b-spline basis functions (knot width 0.05 s) are used to describe negative inspiratory drive (Pp, cmH₂O) as a function of time. Breath-breath Pp are identified with single E and R values over inspiration and expiration from n = 20 breaths for N = 22 patients on NAVA ventilation. Pp is compared to measured electrical activity of the diaphragm (Eadi) and published results.

RESULTS

Average per-patient root-mean-squared model fit error was (median [interquartile range, IQR]) 0.9 [0.6-1.3] cmH₂O, and average per-patient median Pp was -3.9 [-4.5- -3.0] cmH₂O, with range -7.9 - -1.9 cmH₂O. Per-patient E and R were 16.4 [13.6-21.8] cmH₂O/L and 9.2 [6.4-13.1] cmH₂O.s/L, respectively. Most patients showed an inspiratory volume threshold beyond which Pp started to return to baseline, and Pp at peak Eadi (end-inspiration) was often strongly correlated with peak Eadi (R²=0.25-0.86). Similarly, average transpulmonary pressure was consistent breath-breath in most patients, despite differences in peak Eadi and thus peak airway pressure.

CONCLUSIONS

The model-based inspiratory effort aligns with electrical muscle activity and published studies showing neuro-muscular decoupling as a function of pressure and/or volume. Consistency in coupling/dynamics were patient-specific. Quantification of patient and ventilator work of breathing contributions may aid optimisation of MV modes and weaning.

Estimating Increased EGP During Stress Response in Critically Ill Patients

BACKGROUND

Stress-induced hyperglycemia is frequently experienced by critically ill patients and the use of glycemic control (GC) has been shown to improve patient outcomes. For model-based approaches to GC, it is important to understand and quantify model parameter assumptions. This study explores endogenous glucose production (EGP) and the use of a population-based parameter value in the intensive care unit context.

METHOD

Hourly insulin sensitivity (SI) was fit to clinical data from 145 patients on the Specialized Relative Insulin and Nutrition Titration GC protocol for at least 24 hours. Constraint of SI at a lower bound was used to explore likely EGP variability due to stress response. Minimum EGP was estimated during times when the model SI was constrained, and time and duration of events were examined.

RESULTS

Constrained events occur for 1.6% of patient hours. About 70% of constrained events occur in the first 12 hours and most events (~80%) occur when there is no exogenous nutrition given. Enhanced EGP values ranged from 1.16 mmol/min (current population value) to 2.75 mmol/min, with most being below 1.5 mmol/min (21% increase).

CONCLUSION

The frequency of constrained events is low and the current population value of 1.16 mmol/min is sufficient for more than 98% of patient hours, however, some patients experience significantly raised EGP probably due to an extreme stress response early in patient stay.

Virtual patients for mechanical ventilation in the intensive care unit

BACKGROUND

Mechanical ventilation (MV) is a core intensive care unit (ICU) therapy. Significant inter- and intra- patient variability in lung mechanics and condition makes managing MV difficult. Accurate prediction of patient-specific response to changes in MV settings would enable optimised, personalised, and more productive care, improving outcomes and reducing cost. This study develops a generalised digital clone model, or in-silico virtual patient, to accurately predict lung mechanics in response to changes in MV.

METHODS

An identifiable, nonlinear hysteresis loop model (HLM) captures patient-specific lung dynamics identified from measured ventilator data. Identification and creation of the virtual patient model is fully automated using the hysteresis loop analysis (HLA) method to identify lung elastances from clinical data. Performance is evaluated using clinical data from 18 volume-control (VC) and 14 pressure-control (PC) ventilated patients who underwent step-wise recruitment maneuvers.

RESULTS

Patient-specific virtual patient models accurately predict lung response for changes in PEEP up to 12 cmH₂O for both volume and pressure control cohorts. R² values for predicting peak inspiration pressure (PIP) and additional retained lung volume, V_frc in VC, are R²=0.86 and R²=0.90 for 106 predictions over 18 patients. For 14 PC patients and 84 predictions, predicting peak inspiratory volume (PIV) and V_frc yield R²=0.86 and R²=0.83. Absolute PIP, PIV and V_frc errors are relatively small.

CONCLUSIONS

Overall results validate the accuracy and versatility of the virtual patient model for capturing and predicting nonlinear changes in patient-specific lung mechanics. Accurate response prediction enables mechanically and physiologically relevant virtual patients to guide personalised and optimised MV therapy.

Stochastic Modelling of Respiratory System Elastance for Mechanically Ventilated Respiratory Failure Patients

While lung protective mechanical ventilation (MV) guidelines have been developed to avoid ventilator-induced lung injury (VILI), a one-size-fits-all approach cannot benefit every individual patient. Hence, there is significant need for the ability to provide patient-specific MV settings to ensure safety, and optimise patient care. Model-based approaches enable patient-specific care by identifying time-varying patient-specific parameters, such as respiratory elastance, E_rs, to capture inter- and intra-patient variability. However, patient-specific parameters evolve with time, as a function of disease progression and patient condition, making predicting their future values crucial for recommending patient-specific MV settings. This study employs stochastic modelling to predict future E_rs values using retrospective patient data to develop and validate a model indicating future intra-patient variability of E_rs. Cross validation results show stochastic modelling can predict future elastance ranges with 92.59 and 68.56% of predicted values within the 5-95% and the 25-75% range, respectively. This range can be used to ensure patients receive adequate minute ventilation should elastance rise and minimise the risk of VILI should elastance fall. The results show the potential for model-based protocols using stochastic model prediction of future E_rs values to provide safe and patient-specific MV. These results warrant further investigation to validate its clinical utility.

Capacity of Infusion Lines for Insulin Adsorption: Effect of Flow Rate on Total Adsorption

BACKGROUND

Insulin adsorption to clinical materials has been well observed, but not well quantified. Insulin adsorption reduces expected and actual insulin delivery and is unaccounted for in insulin therapy or glycemic control. It may thus contribute to poor control and high glycemic variability. This research quantifies the problem in the context of clinical use.

METHOD

Experimental insulin adsorption data from literature is used to calculate insulin delivery and total insulin adsorption capacities for polyethylene (PE) and polyvinal chloride (PVC) lines at clinically relevant flow rates and concentrations.

RESULTS

Insulin adsorption capacity decreased hyperbolically with flow rate for both PE and PVC, where low flow scenarios result in greater insulin adherence to infusion lines. When the infusion flow rate was halved from 1 to 0.5 mL/h, twice as much insulin adsorbed to the line. Insulin loss to adsorption resulted in up to ~50% of intended insulin not delivered over 24 hours in a low flow and low concentration context.

CONCLUSION

Material capacity for insulin adsorption is not constant, but increases with decreasing flow. Different materials have different adsorption capacities. In low flow and low concentration contexts, such as in neonatal or pediatric intensive care, insulin loss to adsorption represents a significant proportion of daily insulin delivery, which needs to be accounted for.

Measuring lung mechanics of expiratory tidal breathing with non-invasive breath occlusion

Background and objective

Lung mechanics measurements provide clinically useful information about disease progression and lung health. Currently, there are no commonly practiced methods to non-invasively measure both resistive and elastic lung mechanics during tidal breathing, preventing the important information provided by lung mechanics from being utilised. This study presents a novel method to easily assess lung mechanics of spontaneously breathing subjects using a dynamic elastance, single-compartment lung model.

Methods

A spirometer with a built-in shutter was used to occlude expiration during tidal breathing, creating exponentially decaying flow when the shutter re-opened. The lung mechanics measured were respiratory system elastance and resistance, separated from the exponentially decaying flow, and interrupter resistance calculated at shutter closure. Progressively increasing resistance was added to the spirometer mouthpiece to simulate upper airway obstruction. The lung mechanics of 17 healthy subjects were successfully measured through spirometry.

Results

N = 17 (8 female, 9 male) healthy subjects were recruited. Measured decay rates ranged from 5 to 42/s, subjects with large variation of decay rates showed higher muscular breathing effort. Lung elastance measurements ranged from 3.9 to 21.2 cmH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2O/L, with no clear trend between change in elastance and added resistance. Resistance calculated from decay rate and elastance ranged from 0.15 to 1.95 cmH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2Os/L. These very small resistance values are due to the airflow measured originating from low-resistance areas in the centre of airways. Occlusion resistance measurements were as expected for healthy subjects, and increased as expected as resistance was added.

Conclusions

This test was able to identify reasonable dynamic lung elastance and occlusion resistance values, providing new insight into expiratory breathing effort. Clinically, this lung function test could impact current practice. It does not require high levels of cooperation from the subject, allowing a wider cohort of patients to be assessed more easily. Additionally, this test can be simply implemented in a small standalone device, or with standard lung function testing equipment.

Mechanically ventilated premature babies have sex differences in specific elastance: A pilot study

OBJECTIVES

A pilot study to compare pulmonary mechanics in a neonatal intensive care unit (NICU) cohort, specifically, comparing lung elastance between male and female infants in the NICU.

HYPOTHESIS

Anecdotally, male infants are harder to ventilate than females. We hypothesize that males have higher model-based elastance (converse: lower specific compliance) compared to females, reflecting underlying stiffer lungs.

STUDY DESIGN

A clinically validated, single-compartment model is used to identify specific elastance (inverse of specific compliance) and resistance for each breath. Specific elastance accounts for weight differences when comparing male and female infants. Relative percent breath-to-breath variability (%ΔE) in specific elastance is also compared. Level of asynchrony was also determined.

PATIENT-SUBJECT SELECTION

Ten invasively mechanically ventilated patients from Christchurch Women's Hospital.

METHODOLOGY

Airway pressure and flow data from 10 invasive mechanical ventilation (MV) infants from Christchurch Women's Hospital Neonatal Intensive Care Unit, New Zealand was prospectively recorded under standard MV care. Model-based specific elastance and resistance are identified for each breath, as well as relative percent breath-to-breath variability (%ΔE) in specific elastance.

RESULTS

Male infants overall had higher specific elastance compared to females infants (P ≤ .01), with median (interquartile range) for males of 1.91 (1.33-2.48) cmH₂ O·kg/mL compared to 1.31 (0.86-2.02) cmH₂ O·kg/mL in females. Male infants had lower variability with %ΔE of -0.03 (-7.56 to 8.01)% vs female infants of -0.59 (12.56-12.86)%. Males had 14.75% asynchronous breaths whereas females had 17.54%.

CONCLUSION

Overall, males had higher specific elastance and correspondingly lower breath-to-breath variability. These results indicate male and female infants may require different MV settings, mode, and monitoring.

Multi-input stochastic prediction of insulin sensitivity for tight glycaemic control using insulin sensitivity and blood glucose data

BACKGROUND

Glycaemic control in the intensive care unit is dependent on effective prediction of patient insulin sensitivity (SI). The stochastic targeted (STAR) controller uses a 2D stochastic model for prediction, with current SI as an input and future SI as an output.

METHODS

This paper develops an extension of the STAR 2D stochastic model into 3D by adding blood glucose (G) as an input. The performance of the 2D and 3D stochastic models is compared over a retrospective cohort of 65,269 data points across 1525 patients.

RESULTS

Under five-fold cross-validation, the 3D model was found to better match the expected potion of data points within, above and below various credible intervals, suggesting it provided a better representation of the underlying probability field. The 3D model was also found to provide an 18.1% narrower 90% credible interval on average, and a narrower 90% credible interval in 96.4% of cases, suggesting it provided more accurate predictions of future SI. Additionally, the 3D stochastic model was found to avoid the undesirable tendency of the 2D model to overestimate SI for patients with high G, and underestimate SI for patients with low G.

CONCLUSIONS

Overall, the 3D stochastic model is shown to provide clear potential benefits over the 2D model for minimal clinical cost or effort, though further exploration into whether these improvements in SI prediction translate into improved clinical outcomes is required.

A subcutaneous insulin pharmacokinetic model for insulin Detemir

BACKGROUND AND OBJECTIVE

Type 2 diabetes (T2D) is rapidly increasing in incidence and has significant social and economic costs. Given the increasing cost of complications, even relatively short delays in the onset of T2D can significantly reduce long-term complications and costs. Equally, recent studies have shown the onset of T2D can be delayed by use of long-acting insulin, despite the risk and concomitant low adherence. Thus, there is a strong potential motivation to develop models of long-acting insulin analogues to enable safe, effective use in model-based dosing systems. In particular, there are no current models of long-acting insulin Detemir and its unique action for model-based control. The objective of this work is to develop a first model of insulin Detemir and its unique action, and validate it against existing data in the literature.

METHODS

This study develops a detailed compartment model for insulin Detemir. Model specific parameters are identified using data from a range of published clinical studies on the pharmacokinetic of insulin Detemir. Model validity and robustness are assessed by identifying the model for each study and using average identified parameters over several dose sizes and study cohorts. Comparisons to peak concentration, time of peak concentration and overall error versus measured plasma concentrations are used to assess model accuracy and validity.

RESULTS

Almost all studies and cohorts fit literature data to within one standard deviation of error, even when using averaged identified model parameters. However, there appears to be a noticeable dose dependent dynamic not included in this first model, nor reported in the literature studies.

CONCLUSIONS

A first model of insulin Detemir including its unique albumin binding kinetics is derived and provisionally validated against clinical pharmacokinetic data. The pharmacokinetic curves are suitable for model-based control and general enough for use. While there are limitations in the studies used for validation that prevent a more complete understanding, the results provide an effective first model and justify the design and implementation of further, more precise human trials.

Model-based glycemic control in a Malaysian intensive care unit: performance and safety study

Background: Stress-induced hyperglycemia is common in critically ill patients. A few forms of model-based glycemic control have been introduced to reduce this phenomena and among them is the automated STAR protocol which has been used in the Christchurch and Gyulá hospitals' intensive care units (ICUs) since 2010. Methods: This article presents the pilot trial assessment of STAR protocol which has been implemented in the International Islamic University Malaysia Medical Centre (IIUMMC) Hospital ICU since December 2017. One hundred and forty-two patients who received STAR treatment for more than 20 hours were used in the assessment. The initial results are presented to discuss the ability to adopt and adapt the model-based control framework in a Malaysian environment by analyzing its performance and safety. Results: Overall, 60.7% of blood glucose measurements were in the target band. Only 0.78% and 0.02% of cohort measurements were below 4.0 mmol/L and 2.2 mmol/L (the limitsfor mild and severe hypoglycemia, respectively). Treatment preference-wise, the clinical staff were favorable of longer intervention options when available. However, 1 hourly treatments were still used in 73.7% of cases. Conclusion: The protocol succeeded in achieving patient-specific glycemic control while maintaining safety and was trusted by nurses to reduce workload. Its lower performance results, however, give the indication for modification in some of the control settings to better fit the Malaysian environment.

Parameter estimation in a minimal model of cardio-pulmonary interactions

Mechanical ventilation is a widely used breathing support for patients in intensive care. Its effects on the respiratory and cardiovascular systems are complex and difficult to predict. This work first presents a minimal mathematical model representing the mechanics of both systems and their interaction, in terms of flows, pressures and volumes. The aim of this model is to get insight on the two systems' status when mechanical ventilation settings, such as positive end-expiratory pressure, are changing. The parameters of the model represent cardiac elastances and vessel compliances and resistances. As a second step, these parameters are estimated from 16 experimental datasets. The data come from three pig experiments reproducing intensive care conditions, where a large range of positive end-expiratory pressures was imposed by the mechanical ventilator. The data used for parameter estimation is limited to information available in the intensive care unit, such as stroke volume, central venous pressure and systemic arterial pressure. The model is able to satisfactorily reproduce this experimental data, with mean relative errors ranging from 1 to 26%. The model also reproduces the dynamics of the cardio-vascular and respiratory systems, and their interaction. By looking at the estimated parameter values, one can quantitatively track how the two coupled systems mechanically react to changes in external conditions imposed by the ventilator. This work thus allows real-time, model-based management of ventilator settings.

Optimising mechanical ventilation through model-based methods and automation

Mechanical ventilation (MV) is a core life-support therapy for patients suffering from respiratory failure or acute respiratory distress syndrome (ARDS). Respiratory failure is a secondary outcome of a range of injuries and diseases, and results in almost half of all intensive care unit (ICU) patients receiving some form of MV. Funding the increasing demand for ICU is a major issue and MV, in particular, can double the cost per day due to significant patient variability, over-sedation, and the large amount of clinician time required for patient management. Reducing cost in this area requires both a decrease in the average duration of MV by improving care, and a reduction in clinical workload. Both could be achieved by safely automating all or part of MV care via model-based dynamic systems modelling and control methods are ideally suited to address these problems. This paper presents common lung models, and provides a vision for a more automated future and explores predictive capacity of some current models. This vision includes the use of model-based methods to gain real-time insight to patient condition, improve safety through the forward prediction of outcomes to changes in MV, and develop virtual patients for in-silico design and testing of clinical protocols. Finally, the use of dynamic systems models and system identification to guide therapy for improved personalised control of oxygenation and MV therapy in the ICU will be considered. Such methods are a major part of the future of medicine, which includes greater personalisation and predictive capacity to both optimise care and reduce costs. This review thus presents the state of the art in how dynamic systems and control methods can be applied to transform this core area of ICU medicine.

Practical identifiability analysis of a minimal cardiovascular system model

BACKGROUND AND OBJECTIVE

Parameters of mathematical models of the cardiovascular system can be used to monitor cardiovascular state, such as total stressed blood volume status, vessel elastance and resistance. To do so, the model parameters have to be estimated from data collected at the patient's bedside. This work considers a seven-parameter model of the cardiovascular system and investigates whether these parameters can be uniquely determined using indices derived from measurements of arterial and venous pressures, and stroke volume.

METHODS

An error vector defined the residuals between the simulated and reference values of the seven clinically available haemodynamic indices. The sensitivity of this error vector to each model parameter was analysed, as well as the collinearity between parameters. To assess practical identifiability of the model parameters, profile-likelihood curves were constructed for each parameter.

RESULTS

Four of the seven model parameters were found to be practically identifiable from the selected data. The remaining three parameters were practically non-identifiable. Among these non-identifiable parameters, one could be decreased as much as possible. The other two non-identifiable parameters were inversely correlated, which prevented their precise estimation.

CONCLUSIONS

This work presented the practical identifiability analysis of a seven-parameter cardiovascular system model, from limited clinical data. The analysis showed that three of the seven parameters were practically non-identifiable, thus limiting the use of the model as a monitoring tool. Slight changes in the time-varying function modeling cardiac contraction and use of larger values for the reference range of venous pressure made the model fully practically identifiable.

Modelling intestinal glucose absorption in premature infants using continuous glucose monitoring data

BACKGROUND

Model-based glycaemic control protocols have shown promise in neonatal intensive care units (NICUs) for reducing both hyperglycaemia and insulin-therapy driven hypoglycaemia. However, current models for the appearance of glucose from enteral feeding are based on values from adult intensive care cohorts. This study aims to determine enteral glucose appearance model parameters more reflective of premature infant physiology.

METHODS

Peaks in CGM data associated with enteral milk feeds in preterm and term infants are used to fit a two compartment gut model. The first compartment describes glucose in the stomach, and the half life of gastric emptying is estimated as 20 min from literature. The second compartment describes glucose in the small intestine, and absorption of glucose into the blood is fit to CGM data. Two infant cohorts from two NICUs are used, and results are compared to appearances derived from data in highly controlled studies in literature.

RESULTS

The average half life across all infants for glucose absorption from the gut to the blood was 50 min. This result was slightly slower than, but of similar magnitude to, results derived from literature. No trends were found with gestational or postnatal age. Breast milk fed infants were found to have a higher absorption constant than formula fed infants, a result which may reflect known differences in gastric emptying for different feed types.

CONCLUSIONS

This paper presents a methodology for estimation of glucose appearance due to enteral feeding, and model parameters suitable for a NICU model-based glycaemic control context.

Predictive Virtual Patient Modelling of Mechanical Ventilation: Impact of Recruitment Function

Mechanical ventilation is a life-support therapy for intensive care patients suffering from respiratory failure. To reduce the current rate of ventilator-induced lung injury requires ventilator settings that are patient-, time-, and disease-specific. A common lung protective strategy is to optimise the level of positive end-expiratory pressure (PEEP) through a recruitment manoeuvre to prevent alveolar collapse at the end of expiration and to improve gas exchange through recruitment of additional alveoli. However, this process can subject parts of the lung to excessively high pressures or volumes. This research significantly extends and more robustly validates a previously developed pulmonary mechanics model to predict lung mechanics throughout recruitment manoeuvres. In particular, the process of recruitment is more thoroughly investigated and the impact of the inclusion of expiratory data when estimating peak inspiratory pressure is assessed. Data from the McREM trial and CURE pilot trial were used to test model predictive capability and assumptions. For PEEP changes of up to and including 14 cmH₂O, the parabolic model was shown to improve peak inspiratory pressure prediction resulting in less than 10% absolute error in the CURE cohort and 16% in the McREM cohort. The parabolic model also better captured expiratory mechanics than the exponential model for both cohorts.

Determining minimal output sets that ensure structural identifiability

The process of inferring parameter values from experimental data can be a cumbersome task. In addition, the collection of experimental data can be time consuming and costly. This paper covers both these issues by addressing the following question: “Which experimental outputs should be measured to ensure that unique model parameters can be calculated?”. Stated formally, we examine the topic of minimal output sets that guarantee a model’s structural identifiability. To that end, we introduce an algorithm that guides a researcher as to which model outputs to measure. Our algorithm consists of an iterative structural identifiability analysis and can determine multiple minimal output sets of a model. This choice in different output sets offers researchers flexibility during experimental design. Our method can determine minimal output sets of large differential equation models within short computational times.

Identifiability Analysis of Three Control-Oriented Models for Use in Artificial Pancreas Systems

OBJECTIVE

Our aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).

METHODS

Structural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.

RESULTS

A reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.

CONCLUSION

This study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

Assessing mechanical ventilation asynchrony through iterative airway pressure reconstruction

BACKGROUND AND OBJECTIVE

Respiratory mechanics estimation can be used to guide mechanical ventilation (MV) but is severely compromised when asynchronous breathing occurs. In addition, asynchrony during MV is often not monitored and little is known about the impact or magnitude of asynchronous breathing towards recovery. Thus, it is important to monitor and quantify asynchronous breathing over every breath in an automated fashion, enabling the ability to overcome the limitations of model-based respiratory mechanics estimation during asynchronous breathing ventilation.

METHODS

An iterative airway pressure reconstruction (IPR) method is used to reconstruct asynchronous airway pressure waveforms to better match passive breathing airway waveforms using a single compartment model. The reconstructed pressure enables estimation of respiratory mechanics of airway pressure waveform essentially free from asynchrony. Reconstruction enables real-time breath-to-breath monitoring and quantification of the magnitude of the asynchrony (M_Asyn).

RESULTS AND DISCUSSION

Over 100,000 breathing cycles from MV patients with known asynchronous breathing were analyzed. The IPR was able to reconstruct different types of asynchronous breathing. The resulting respiratory mechanics estimated using pressure reconstruction were more consistent with smaller interquartile range (IQR) compared to respiratory mechanics estimated using asynchronous pressure. Comparing reconstructed pressure with asynchronous pressure waveforms quantifies the magnitude of asynchronous breathing, which has a median value M_Asyn for the entire dataset of 3.8%.

CONCLUSION

The iterative pressure reconstruction method is capable of identifying asynchronous breaths and improving respiratory mechanics estimation consistency compared to conventional model-based methods. It provides an opportunity to automate real-time quantification of asynchronous breathing frequency and magnitude that was previously limited to invasively method only.

Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them

Critical care, like many healthcare areas, is under a dual assault from significantly increasing demographic and economic pressures. Intensive care unit (ICU) patients are highly variable in response to treatment, and increasingly aging populations mean ICUs are under increasing demand and their cohorts are increasingly ill. Equally, patient expectations are growing, while the economic ability to deliver care to all is declining. Better, more productive care is thus the big challenge. One means to that end is personalised care designed to manage the significant inter- and intra-patient variability that makes the ICU patient difficult. Thus, moving from current "one size fits all" protocolised care to adaptive, model-based "one method fits all" personalised care could deliver the required step change in the quality, and simultaneously the productivity and cost, of care. Computer models of human physiology are a unique tool to personalise care, as they can couple clinical data with mathematical methods to create subject-specific models and virtual patients to design new, personalised and more optimal protocols, as well as to guide care in real-time. They rely on identifying time varying patient-specific parameters in the model that capture inter- and intra-patient variability, the difference between patients and the evolution of patient condition. Properly validated, virtual patients represent the real patients, and can be used in silico to test different protocols or interventions, or in real-time to guide care. Hence, the underlying models and methods create the foundation for next generation care, as well as a tool for safely and rapidly developing personalised treatment protocols over large virtual cohorts using virtual trials. This review examines the models and methods used to create virtual patients. Specifically, it presents the models types and structures used and the data required. It then covers how to validate the resulting virtual patients and trials, and how these virtual trials can help design and optimise clinical trial. Links between these models and higher order, more complex physiome models are also discussed. In each section, it explores the progress reported up to date, especially on core ICU therapies in glycemic, circulatory and mechanical ventilation management, where high cost and frequency of occurrence provide a significant opportunity for model-based methods to have measurable clinical and economic impact. The outcomes are readily generalised to other areas of medical care.

Generalisability of a Virtual Trials Method for Glycaemic Control in Intensive Care

BACKGROUND

Elevated blood glucose (BG) concentrations (Hyperglycaemia) are a common complication in critically ill patients. Insulin therapy is commonly used to treat hyperglycaemia, but metabolic variability often results in poor BG control and low BG (hypoglycaemia).

OBJECTIVE

This paper presents a model-based virtual trial method for glycaemic control protocol design, and evaluates its generalisability across different populations.

METHODS

Model-based insulin sensitivity (SI) was used to create virtual patients from clinical data from three different ICUs in New Zealand, Hungary, and Belgium. Glycaemic results from simulation of virtual patients under their original protocol (self-simulation) and protocols from other units (cross simulation) were compared.

RESULTS

Differences were found between the three cohorts in median SI and inter-patient variability in SI. However, hour-to-hour intra-patient variability in SI was found to be consistent between cohorts. Self and cross-simulation results were found to have overall similarity and consistency, though results may differ in the first 24-48 h due to different cohort starting BG and underlying SI.

CONCLUSIONS AND SIGNIFICANCE

Virtual patients and the virtual trial method were found to be generalisable across different ICUs. This virtual trial method is useful for in silico protocol design and testing, given an understanding of the underlying assumptions and limitations of this method.

Evaluating different approaches to identify a three parameter gas exchange model

Mathematical models can be employed to simulate a patient’s individual physiology and can therefore be used to predict reactions to changes in the therapy. To be clinically useful, those models need to be identifiable from data available at the bedside. Gradient based methods to identify the values of the model parameters that represent the recorded data highly depend on the initial estimates. The proposed work implements a previously developed method to overcome those dependencies to identify a three parameter model of gas exchange. The proposed hierarchical method uses models of lower order related to the three parameter model to calculate valid initial estimates for the parameter identification. The presented approach was evaluated using 12 synthetic patients and compared to a traditional direct approach as well as a global search method. Results show that the direct approach is highly dependent on how well the initial estimates are selected, while the hierarchical approach was able to find correct parameter values in all tested patients.

Insulin kinetics and the Neonatal Intensive Care Insulin-Nutrition-Glucose (NICING) model

BACKGROUND

Models of human glucose-insulin physiology have been developed for a range of uses, with similarly different levels of complexity and accuracy. STAR (Stochastic Targeted) is a model-based approach to glycaemic control. Elevated blood glucose concentrations (hyperglycaemia) are a common complication of stress and prematurity in very premature infants, and have been associated with worsened outcomes and higher mortality. This research identifies and validates the model parameters for model-based glycaemic control in neonatal intensive care.

METHODS

C-peptide, plasma insulin, and BG from a cohort of 41 extremely pre-term (median age 27.2 [26.2-28.7] weeks) and very low birth weight infants (median birth weight 839 [735-1000] g) are used alongside C-peptide kinetic models to identify model parameters associated with insulin kinetics in the NICING (Neonatal Intensive Care Insulin-Nutrition-Glucose) model. A literature analysis is used to determine models of kidney clearance and body fluid compartment volumes. The full, final NICING model is validated by fitting the model to a cohort of 160 glucose, insulin, and nutrition data records from extremely premature infants from two different NICUs (neonatal intensive care units).

RESULTS

Six model parameters related to insulin kinetics were identified. The resulting NICING model is more physiologically descriptive than prior model iterations, including clearance pathways of insulin via the liver and kidney, rather than a lumped parameter. In addition, insulin diffusion between plasma and interstitial spaces is evaluated, with differences in distribution volume taken into consideration for each of these spaces. The NICING model was shown to fit clinical data well, with a low model fit error similar to that of previous model iterations.

CONCLUSIONS

Insulin kinetic parameters have been identified, and the NICING model is presented for glycaemic control neonatal intensive care. The resulting NICING model is more complex and physiologically relevant, with no loss in bedside-identifiability or ability to capture and predict metabolic dynamics.

Incorporating bolus and infusion pharmacokinetics into the ICING insulin model

The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivity and Secretion Tests (DISST) and 36 Intravenous Glucose Tolerance Tests (IVGTT) from independent dietary intervention studies was used to fit model parameters to a model structure that conforms to known behaviour. The DISST tests measured both endogenous and exogenous IV insulin bolus responses, while the IVGTT measured exogenous IV insulin infusion dynamics. Unidentifiable parameters were given physiologically justified values, with knowledge on relative insulin clearance rates used to constrain parameter values. The resulting whole-cohort description was able to simultaneously describe both IV bolus and infusion dynamics, and improves ICING model descriptive capability. Improved infusion dynamics will allow better description of subcutaneous insulin, the insulin administration route favoured in outpatient care of diabetes.

The necessity of identifying the basal glucose set-point in the IVGTT for patients with Type 2 Diabetes

Background

The model-based dynamic insulin sensitivity and secretion test (DISST) uses fasting glucose (G₀) as the basal glucose (G_B) concentration when assessing insulin sensitivity (SI). However, this model was developed in a healthy, normoglycaemic cohort. We sought to determine the suitability the DISST model has for individuals with established type 2 diabetes (T2D).

Methods

14 participants with established T2D were recruited to take part in a dietary intervention study. Insulin-modified intravenous glucose tolerance tests (IM-IVGTT) were undertaken at week 0, 12 and 24 and were used with DISST model to identify G_B. A total of 36 tests were conducted across 12 participants throughout the study. Measured G₀ and identified G_B values were compared using a Kolmogorov-Smirnov (KS) and signed rank (RS) test for the cohort.

Results

There were significant differences between the G₀ and identified G_B values in this cohort (p_rs and p_ks < 0.0001), although both values were well correlated (R = 0.70). The residual plot demonstrates that the modified model captures the behaviour of the participants more accurately than the original model.

Conclusions

This analysis has shown that G_B is an important variable for modelling the glycaemic behaviour in T2D. These findings suggest that the original DISST model, while appropriate for normoglycaemic cohorts, needs to model basal glucose level as a variable for assessing individuals with established T2D.

Continuous stroke volume estimation from aortic pressure using zero dimensional cardiovascular model: proof of concept study from porcine experiments

Introduction

Accurate, continuous, left ventricular stroke volume (SV) measurements can convey large amounts of information about patient hemodynamic status and response to therapy. However, direct measurements are highly invasive in clinical practice, and current procedures for estimating SV require specialized devices and significant approximation.

Method

This study investigates the accuracy of a three element Windkessel model combined with an aortic pressure waveform to estimate SV. Aortic pressure is separated into two components capturing; 1) resistance and compliance, 2) characteristic impedance. This separation provides model-element relationships enabling SV to be estimated while requiring only one of the three element values to be known or estimated. Beat-to-beat SV estimation was performed using population-representative optimal values for each model element. This method was validated using measured SV data from porcine experiments (N = 3 female Pietrain pigs, 29–37 kg) in which both ventricular volume and aortic pressure waveforms were measured simultaneously.

Results

The median difference between measured SV from left ventricle (LV) output and estimated SV was 0.6 ml with a 90% range (5^th–95^th percentile) −12.4 ml–14.3 ml. During periods when changes in SV were induced, cross correlations in between estimated and measured SV were above R = 0.65 for all cases.

Conclusion

The method presented demonstrates that the magnitude and trends of SV can be accurately estimated from pressure waveforms alone, without the need for identification of complex physiological metrics where strength of correlations may vary significantly from patient to patient.

Utility of a novel error-stepping method to improve gradient-based parameter identification by increasing the smoothness of the local objective surface: a case-study of pulmonary mechanics

Accurate model parameter identification relies on accurate forward model simulations to guide convergence. However, some forward simulation methodologies lack the precision required to properly define the local objective surface and can cause failed parameter identification. The role of objective surface smoothness in identification of a pulmonary mechanics model was assessed using forward simulation from a novel error-stepping method and a proprietary Runge-Kutta method. The objective surfaces were compared via the identified parameter discrepancy generated in a Monte Carlo simulation and the local smoothness of the objective surfaces they generate. The error-stepping method generated significantly smoother error surfaces in each of the cases tested (p<0.0001) and more accurate model parameter estimates than the Runge-Kutta method in three of the four cases tested (p<0.0001) despite a 75% reduction in computational cost. Of note, parameter discrepancy in most cases was limited to a particular oblique plane, indicating a non-intuitive multi-parameter trade-off was occurring. The error-stepping method consistently improved or equalled the outcomes of the Runge-Kutta time-integration method for forward simulations of the pulmonary mechanics model. This study indicates that accurate parameter identification relies on accurate definition of the local objective function, and that parameter trade-off can occur on oblique planes resulting prematurely halted parameter convergence.

Non-identifiability of the Rayleigh damping material model in magnetic resonance elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, μI and ρI. Results show the non-identifiability of the RD model at a single input frequency based on a structural analysis with a series of supporting experimental phantom results. The estimated real shear modulus values (μR) were substantially correct in characterising various material types and correlated well with the expected stiffness contrast of the physical phantoms. However, estimated RD parameters displayed consistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To overcome this issue, two alternative approaches were developed: (1) simultaneous multi-frequency inversion; and (2) parametric-based reconstruction. Overall, the RD model estimates the real shear shear modulus (μR) well, but identifying damping parameters (μI and ρI) is not possible without an alternative approach.