David J. Stevenson

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.

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Lumped parameter approaches for modelling the cardiovascular system typically have many parameters of which a significant percentage are often not identifiable from limited data sets. Hence, significant parts of the model are required to be simulated with little overall effect on the accuracy of data fitting, as well as dramatically increasing the complexity of parameter identification. This separates sub-structures of more complex cardiovascular system models to create uniquely identifiable simplified models that are one to one with the measurements. In addition, a new concept of parameter identification is presented where the changes in the parameters are treated as an actuation force into a feed back control system, and the reference output is taken to be steady state values of measured volume and pressure. The major advantage of the method is that when it converges, it must be at the global minimum so that the solution that best fits the data is always found. By utilizing continuous information from the arterial/pulmonary pressure waveforms and the end-diastolic time, it is shown that potentially, the ventricle volume is not required in the data set, which was a requirement in earlier published work. The simplified models can also act as a bridge to identifying more sophisticated cardiac models, by providing an initial set of patient specific parameters that can reveal trends and interactions in the data over time. The goal is to apply the simplified models to retrospective data on groups of patients to help characterize population trends or un-modelled dynamics within known bounds. These trends can assist in improved prediction of patient responses to cardiac disturbance and therapy intervention with potentially smaller and less invasive data sets. In this way a more complex model that takes into account individual patient variation can be developed, and applied to the improvement of cardiovascular management in critical care.

Clinical detection and monitoring of acute pulmonary embolism: proof of concept of a computer-based method

BackgroundThe diagnostic ability of computer-based methods for cardiovascular system (CVS) monitoring offers significant clinical potential. This research tests the clinical applicability of a newly improved computer-based method for the proof of concept case of tracking changes in important hemodynamic indices due to the influence acute pulmonary embolism (APE).MethodsHemodynamic measurements from a porcine model of APE were used to validate the method. Of these measurements, only those that are clinically available or inferable were used in to identify pig-specific computer models of the CVS, including the aortic and pulmonary artery pressure, stroke volume, heart rate, global end diastolic volume, and mitral and tricuspid valve closure times. Changes in the computer-derived parameters were analyzed and compared with experimental metrics and clinical indices to assess the clinical applicability of the technique and its ability to track the disease state.ResultsThe subject-specific computer models accurately captured the increase in pulmonary resistance (Rpul ), the main cardiovascular consequence of APE, in all five pigs trials, which related well (R2 = 0.81) with the experimentally derived pulmonary vascular resistance. An increase in right ventricular contractility was identified, as expected, consistent with known reflex responses to APE. Furthermore, the modeled right ventricular expansion index (the ratio of right to left ventricular end diastolic volumes) closely followed the trends seen in the measured data (R2 = 0.92) used for validation, with sharp increases seen in the metric for the two pigs in a near-death state. These results show that the pig-specific models are capable of tracking disease-dependent changes in pulmonary resistance (afterload), right ventricular contractility (inotropy), and ventricular loading (preload) during induced APE. Continuous, accurate estimation of these fundamental metrics of cardiovascular status can help to assist clinicians with diagnosis, monitoring, and therapy-based decisions in an intensive care environment. Furthermore, because the method only uses measurements already available in the ICU, it can be implemented with no added risk to the patient and little extra cost.ConclusionsThis computer-based monitoring method shows potential for real-time, continuous diagnosis and monitoring of acute CVS dysfunction in critically ill patients.

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.

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

The cardiac muscle activation or driver function, is a major determinant of cardiovascular dynamics, and is often approximated by the ratio of the left ventricle pressure to the left ventricle volume. In an intensive care unit, the left ventricle pressure is usually never measured, and the left ventricle volume is only measured occasionally by echocardiography, so is not available real-time. This paper develops a method for identifying the driver function based on correlates with geometrical features in the aortic pressure waveform. The method is included in an overall cardiovascular modelling approach, and is clinically validated on a porcine model of pulmonary embolism. For validation a comparison is done between the optimized parameters for a baseline model, which uses the direct measurements of the left ventricle pressure and volume, and the optimized parameters from the approximated driver function. The parameters do not significantly change between the two approaches thus showing that the patient specific approach to identifying the driver function is valid, and has potential clinically.

Beat-to-beat estimation of the continuous left and right cardiac elastance from metrics commonly available in clinical settings

IntroductionFunctional time-varying cardiac elastances (FTVE) contain a rich amount of information about the specific cardiac state of a patient. However, a FTVE waveform is very invasive to directly measure, and is thus currently not used in clinical practice. This paper presents a method for the estimation of a patient specific FTVE, using only metrics that are currently available in a clinical setting.MethodCorrelations are defined between invasively measured FTVE waveforms and the aortic and pulmonary artery pressures from 2 cohorts of porcine subjects, 1 induced with pulmonary embolism, the other with septic shock. These correlations are then used to estimate the FTVE waveform based on the individual aortic and pulmonary artery pressure waveforms, using the “other” dysfunction’s correlations as a cross validation.ResultsThe cross validation resulted in 1.26% and 2.51% median errors for the left and right FTVE respectively on pulmonary embolism, while the septic shock cohort had 2.54% and 2.90% median errors.ConclusionsThe presented method accurately and reliably estimated a patient specific FTVE, with no added risk to the patient. The cross validation shows that the method is not dependent on dysfunction and thus has the potential for generalisation beyond pulmonary embolism and septic shock.

Algorithmic processing of pressure waveforms to facilitate estimation of cardiac elastance

BackgroundCardiac elastances are highly invasive to measure directly, but are clinically useful due to the amount of information embedded in them. Information about the cardiac elastance, which can be used to estimate it, can be found in the downstream pressure waveforms of the aortic pressure (Pao) and the pulmonary artery (Ppa). However these pressure waveforms are typically noisy and biased, and require processing in order to locate the specific information required for cardiac elastance estimations. This paper presents the method to algorithmically process the pressure waveforms.MethodsA shear transform is developed in order to help locate information in the pressure waveforms. This transform turns difficult to locate corners into easy to locate maximum or minimum points as well as providing error correction.ResultsThe method located all points on 87 out of 88 waveforms for Ppa, to within the sampling frequency. For Pao, out of 616 total points, 605 were found within 1%, 5 within 5%, 4 within 10% and 2 within 20%.ConclusionsThe presented method provides a robust, accurate and dysfunction-independent way to locate points on the aortic and pulmonary artery pressure waveforms, allowing the non-invasive estimation of the left and right cardiac elastance.

Model-based Monitoring of Septic Shock Treated with Large-Pore Hemofiltration Therapy

Abstract The diagnostic ability of model-based monitoring systems offer significant clinical potential. This research tests, the clinical ability of a model-based system for tracking hemodynamic changes in a porcine study on septic shock and large pore hemofiltration (LPHF) therapy. Typically available or inferable intensive care unit (ICU) measurements are used to identify subject-specific models of the cardiovascular system (CVS). The approach accurately identified known trends of septic shock including a drop in systemic vascular resistance and right ventricular distension, and accurately predicted left and right ventricular volumes and pressures. The method also quantified each subjects individual response to the disease and corresponding LPHF therapy. These results indicate the clinical potential of using model-based methods for tracking acute hemodynamic changes in cardiovascular compromised individuals.

Estimating afterload, systemic vascular resistance and pulmonary vascular resistance in an intensive care setting

Abstract Poor management and delayed diagnosis for both pulmonary embolism and septic shock are common and lead to increased cost, length of stay and mortality. Despite a wealth of information coming from commonly placed catheters much of this information remains unknown to an intensive care clinician. Data was gather from two porcine trials, 5 subjects induced with pulmonary embolism, and 5 with septic shock (treated with haemofiltration). Methods for real-time estimating afterload, systemic vascular resistance and pulmonary vascular resistance are presented. Knowledge of these parameters would greatly increase management of patients with pulmonary embolism and septic shock, and help the accuracy and speed of diagnosis. All estimations tracked trends very well. The estimating for afterload has a percentage error of 21.6% in pulmonary embolism and 11.8% in septic shock, systemic vascular resistance has a percentage error of 12.51% and 13.5% for pulmonary embolism and septic shock respectively while pulmonary vascular resistance showed percentage errors of 12.2% and 44.5%. From these estimations, the drop in systemic vascular resistance and afterload can be clearly identified in the septic shock cohort, as well as the recovery after haemofiltration was started, while the pulmonary embolism cohort showed the expected increase in pulmonary vascular resistance.

Analysis of Aortic Energetics from Pulse Wave Examination in a Porcine Study of Septic Shock

Abstract Aortic pressure ( P ao ) can be separated into two components representing the wave phenomena of flow, called excess pressure ( P ex ), and the storage capacity of the elastic arteries, called reservoir pressure ( P wk ). Subject-specific aortic models, identified from measurements from a porcine study on septic shock, were used to calculate the hydraulic work associated with the excess and reservoir pressures ( W ex , W wk ). Changes in these energies were compared to a metrics derived from left ventricular pressure-volume analysis. Total aortic work ( W ao = W ex + W wk ) compared well to clinically assessed left ventricular work (R 2 =0.88). However, only a weak relationship of R 2 = 0.24 was found between ventricular arterial coupling ( E es / E a ) and W ex / W wk . Although a strong relationship (R 2 = 0.76) was noticed between the inverse of afterload (1/ E a ) and W ex . As septic shock progressed, a drop in W wk was seen, indicating the arterial system loses its ability to store the stoke volume (SV) from the ventricle for release during diastole, resulting in a flattening of the diastolic pressure. These results indicate that one of the main reasons left ventricular afterload decreases during septic shock is because arterial system loses its ability to act as a storage reservoir.