Patient specific identification of the cardiac driver function in a cardiovascular system model

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Cardiovascular models for personalised medicine: Where now and where next?

The aim of this position paper is to provide a brief overview of the current status of cardiovascular modelling and of the processes required and some of the challenges to be addressed to see wider exploitation in both personal health management and clinical practice. In most branches of engineering the concept of the digital twin, informed by extensive and continuous monitoring and coupled with robust data assimilation and simulation techniques, is gaining traction: the Gartner Group listed it as one of the top ten digital trends in 2018. The cardiovascular modelling community is starting to develop a much more systematic approach to the combination of physics, mathematics, control theory, artificial intelligence, machine learning, computer science and advanced engineering methodology, as well as working more closely with the clinical community to better understand and exploit physiological measurements, and indeed to develop jointly better measurement protocols informed by model-based understanding. Developments in physiological modelling, model personalisation, model outcome uncertainty, and the role of models in clinical decision support are addressed and 'where-next' steps and challenges discussed.

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.

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.

Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).

Bridging the gap between measurements and modelling: a cardiovascular functional avatar

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

Data assimilation and modelling of patient-specific single-ventricle physiology with and without valve regurgitation

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

A novel method for pulmonary embolism detection in CTA images

In this paper, we propose a new computer-aided detection (CAD) - based method to detect pulmonary embolism (PE) in computed tomography angiography images (CTAI). Since lung vessel segmentation is the main objective to provide high sensitivity in PE detection, this method performs accurate lung vessel segmentation. To concatenate clogged vessels due to PEs, the starting region of PEs and some reference points (RPs) are determined. These RPs are detected according to the fixed anatomical structures. After lung vessel tree is segmented, the region, intensity, and size of PEs are used to distinguish them. We used the data sets that have heart disease or abnormal tissues because of lung disease except PE in this work. According to the results, 428 of 450 PEs, labeled by the radiologists from 33 patients, have been detected. The sensitivity of the developed system is 95.1% at 14.4 false positive per data set (FP/ds). With this performance, the proposed CAD system is found quite useful to use as a second reader by the radiologists.

Evaluation of a model-based hemodynamic monitoring method in a porcine study of septic shock

INTRODUCTION

The accuracy and clinical applicability of an improved model-based system for tracking hemodynamic changes is assessed in an animal study on septic shock.

METHODS

This study used cardiovascular measurements recorded during a porcine trial studying the efficacy of large-pore hemofiltration for treating septic shock. Four Pietrain pigs were instrumented and induced with septic shock. A subset of the measured data, representing clinically available measurements, was used to identify subject-specific cardiovascular models. These models were then validated against the remaining measurements.

RESULTS

The system accurately matched independent measures of left and right ventricle end diastolic volumes and maximum left and right ventricular pressures to percentage errors less than 20% (except for the 95th percentile error in maximum right ventricular pressure) and all R(2) > 0.76. An average decrease of 42% in systemic resistance, a main cardiovascular consequence of septic shock, was observed 120 minutes after the infusion of the endotoxin, consistent with experimentally measured trends. Moreover, modelled temporal trends in right ventricular end systolic elastance and afterload tracked changes in corresponding experimentally derived metrics.

CONCLUSIONS

These results demonstrate that this model-based method can monitor disease-dependent changes in preload, afterload, and contractility in porcine study of septic shock.

Validation of subject-specific cardiovascular system models from porcine measurements

A previously validated mathematical model of the cardiovascular system (CVS) is made subject-specific using an iterative, proportional gain-based identification method. Prior works utilised a complete set of experimentally measured data that is not clinically typical or applicable. In this paper, parameters are identified using proportional gain-based control and a minimal, clinically available set of measurements. The new method makes use of several intermediary steps through identification of smaller compartmental models of CVS to reduce the number of parameters identified simultaneously and increase the convergence stability of the method. This new, clinically relevant, minimal measurement approach is validated using a porcine model of acute pulmonary embolism (APE). Trials were performed on five pigs, each inserted with three autologous blood clots of decreasing size over a period of four to five hours. All experiments were reviewed and approved by the Ethics Committee of the Medical Faculty at the University of Liege, Belgium. Continuous aortic and pulmonary artery pressures (P(ao), P(pa)) were measured along with left and right ventricle pressure and volume waveforms. Subject-specific CVS models were identified from global end diastolic volume (GEDV), stroke volume (SV), P(ao), and P(pa) measurements, with the mean volumes and maximum pressures of the left and right ventricles used to verify the accuracy of the fitted models. The inputs (GEDV, SV, P(ao), P(pa)) used in the identification process were matched by the CVS model to errors <0.5%. Prediction of the mean ventricular volumes and maximum ventricular pressures not used to fit the model compared experimental measurements to median absolute errors of 4.3% and 4.4%, which are equivalent to the measurement errors of currently used monitoring devices in the ICU (∼5-10%). These results validate the potential for implementing this approach in the intensive care unit.

Assessment of cardiovascular function by combining clinical data with a computational model of the cardiovascular system

OBJECTIVE

A sufficient understanding of patients' cardiovascular status is necessary for doctors to make the best decisions with regard to the treatment of cardiovascular disease; however, it is often not available because of the limitation of clinical measurements. The objective of this study was to examine whether cardiovascular function can be assessed quantitatively and for specific patients by combining clinical data with a computational model of the cardiovascular system.

METHODS

Seven consecutive patients undergoing off-pump coronary artery bypass grafting were enrolled in this study. The clinical data were collected both during the preoperative diagnosis and during the operation. Sensitivity analysis was performed to select the major model parameters most relevant to the measured data. The major model parameters were then estimated through a data-fitting procedure, enabling a patient-specific quantitative assessment of various aspects of cardiovascular function.

RESULTS

The results revealed the prevalence of left ventricular diastolic dysfunction in the patients, although the severity of dysfunction exhibits significant interpatient variability (the estimated left ventricular passive elastance varies from 194% to 540% of its reference value). Moreover, 4 of the 7 patients studied had impaired left ventricular systolic function.

CONCLUSIONS

The current study demonstrates the feasibility of assessing cardiovascular function quantitatively by combining clinical data with a cardiovascular model. In particular, the assessment utilizes the measurements already in use or available in clinical settings, enhancing the clinical potential of the proposed method.