Estimation of cardiac function from computer analysis of the arterial pressure waveform

Review of the Development of Hemodynamic Modeling Techniques to Capture Flow Behavior in Arteries Affected by Aneurysm, Atherosclerosis, and Stenting

Cardiovascular diseases (CVDs) are the leading cause of death in the developed world. CVD can include atherosclerosis, aneurysm, dissection, or occlusion of the main arteries. Many CVDs are caused by unhealthy hemodynamics. Some CVDs can be treated with the implantation of stents and stent grafts. Investigations have been carried out to understand the effects of stents and stent grafts have on arteries and the hemodynamic changes post-treatment. Numerous studies on stent hemodynamics have been carried out using computational fluid dynamics (CFD) which has yielded significant insight into the effect of stent mesh design on near-wall blood flow and improving hemodynamics. Particle image velocimetry (PIV) has also been used to capture behavior of fluids that mimic physiological hemodynamics. However, PIV studies have largely been restricted to unstented models or intra-aneurysmal flow rather than peri or distal stent flow behaviors. PIV has been used both as a standalone measurement method and as a comparison to validate the CFD studies. This article reviews the successes and limitations of CFD and PIV-based modeling methods used to investigate the hemodynamic effects of stents. The review includes an overview of physiology and relevant mechanics of arteries as well as consideration of boundary conditions and the working fluids used to simulate blood for each modeling method along with the benefits and limitations introduced.

Parameter Identification of Cardiovascular System Model Used for Left Ventricular Assist Device Algorithms

Advancement of implanted left ventricular assist device (LVAD) technology includes modern sensing and control methods to enable online diagnostics and monitoring of patients using on-board sensors. These methods often rely on a cardiovascular system (CVS) model, the parameters of which must be identified for the specific patient. Some of these, such as the systemic vascular resistance (SVR), can be estimated online while others must be identified separately. This paper describes a three-staged approach for designing a parameter identification algorithm (PIA) for this problem. The approach is demonstrated using a two-element Windkessel model of the systemic circulation (SC) with a time-varying elastance for the left ventricle (LV). A parameter identifiability stage is followed by identification using an unscented Kalman filter (UKF), which uses measurements of LV pressure (P_lv), aortic pressure (P_ao), aortic flow (Q_a), and known input measurement of LVAD flowrate (Q_vad). Both simulation and experimental data from animal experiments were used to evaluate the presented methods. By bounding the initial guess for left ventricular volume, the identified CVS model is able to reproduce signals of P_lv, P_ao, and Q_a within a normalized root mean squared error (nRMSE) of 5.1%, 19%, and 11%, respectively, during simulations. Experimentally, the identified model is able to estimate SVR with an accuracy of 3.4% compared with values from invasive measurements. Diagnostics and physiological control algorithms on-board modern LVADs could use CVS models other than those shown here, and the presented approach is easily adaptable to them. The methods also demonstrate how to test the robustness and accuracy of the identification algorithm.

Sensitivity Analysis of a Left Ventricle Model in the Context of Intraventricular Dyssynchrony

The objective of the current study was to propose a sensitivity analysis of a 3D left ventricle model in order to assess the influence of parameters on myocardial mechanical dispersion. A finite element model of LV electro-mechanical activity was proposed and a screening method was used to evaluate the sensitivity of model parameters on the standard deviation of time to peak strain. Results highlight the importance of propagation parameters associated with septal and lateral segments activation. Simulated curves were compared to myocardial strains, obtained from echocardiography of one healthy subject and one patient diagnosed with intraventricular dyssynchrony and coronary artery disease. Results show a close match between simulation and clinical strains and illustrate the model ability to reproduce myocardial strains in the context of intraventricular dyssynchrony.

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

INTRODUCTION

Functional 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.

METHOD

Correlations 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.

RESULTS

The 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.

CONCLUSIONS

The 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

Background

Cardiac 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 (P_ao) and the pulmonary artery (P_pa). 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.

Methods

A 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.

Results

The method located all points on 87 out of 88 waveforms for P_pa, to within the sampling frequency. For P_ao, out of 616 total points, 605 were found within 1%, 5 within 5%, 4 within 10% and 2 within 20%.

Conclusions

The 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.

Effects of pressure-dependent segmental arterial compliance and postural changes on pulse wave transmission in an arterial model of the human upper limb

With increasing interest in the effect of postural changes on arterial blood pressure and vascular properties, it is important to understand effects of pressure-dependent arterial compliance. This study investigates effects of pressure-dependent compliance on pulse wave velocity (PWVar), pressure wave shape, and transmission characteristics in an arterial model of the human arm from heart to radial artery from supine to standing. Estimated central pressure waveform was used as the input for the model, calculated using a validated transfer function (SphygmoCor, AtCor Medical) from recorded radial pulses in 10 healthy male subjects (53.8 ± 7.9 years) during 0, 30, 60 and 90 degree head-up tilt. A 5-segment linear model was optimized using estimated central and recorded radial arterial pulse; each segment represented by an equivalent inductance, resistance and capacitance (compliance (C)) Pressure-dependent compliance (C(P)=a · e(b · P) was added to develop a nonlinear model, and the radial pulse calculated. Comparison of the radial pulse calculated by the linear and nonlinear models showed no statistical difference in systolic, diastolic, mean, and pulse pressure in any position of tilt. However, waveform shape was increasingly divergent at higher angles of tilt (RMS error 2.3 ± 1.2 mmHg supine, 6.5 ± 3.0 mmHg standing) as was PWVar (0% increase from supine to standing in the linear model, 16.7% increase in nonlinear model). Fourier analysis demonstrated peak amplitude of transmission being at higher frequencies and phase delay being lower in the nonlinear model relative to the linear model. Pressure-dependent arterial compliance, whilst having no effect on peak values of pressure, has significant effects on waveform shape and transmission speed, especially with a more upright position.

Continuous and less invasive central hemodynamic monitoring by blood pressure waveform analysis

Blood pressure waveform analysis may permit continuous (i.e., automated) and less invasive (i.e., safer and simpler) central hemodynamic monitoring in the intensive care unit and other clinical settings without requiring any instrumentation beyond what is already in use or available. This practical approach has been a topic of intense investigation for decades and may garner even more interest henceforth due to the evolving demographics as well as recent trends in clinical hemodynamic monitoring. Here, we review techniques that have appeared in the literature for mathematically estimating clinically significant central hemodynamic variables, such as cardiac output, from different blood pressure waveforms. We begin by providing the rationale for pursuing such techniques. We then summarize earlier techniques and thereafter overview recent techniques by our collaborators and us in greater depth while pinpointing both their strengths and weaknesses. We conclude with suggestions for future research directions in the field and a description of some potential clinical applications of the techniques.

A multiformalism and multiresolution modelling environment: application to the cardiovascular system and its regulation

The role of modelling and simulation in the systemic analysis of living systems is now clearly established. Emerging disciplines, such as systems biology, and worldwide research actions, such as the Physiome Project or the Virtual Physiological Human, are based on an intensive use of modelling and simulation methodologies and tools. One of the key aspects in this context is to perform an efficient integration of various models representing different biological or physiological functions, at different resolutions, spanning through different scales. This paper presents a multiformalism modelling and simulation environment (M2SL) that has been conceived to ease model integration. A given model is represented as a set of coupled and atomic model components that may be based on different mathematical formalisms with heterogeneous structural and dynamical properties. A co-simulation approach is used to solve these hybrid systems. The pioneering model of the overall regulation of the cardiovascular system proposed by Guyton and co-workers in 1972 has been implemented under M2SL and a pulsatile ventricular model based on a time-varying elastance has been integrated in a multi-resolution approach. Simulations reproducing physiological conditions and using different coupling methods show the benefits of the proposed environment.

A tissue-level electromechanical model of the left ventricle: application to the analysis of intraventricular pressure

The ventricular pressure profile is characteristic of the cardiac contraction progress and is useful to evaluate the cardiac performance. In this contribution, a tissue-level electromechanical model of the left ventricle is proposed, to assist the interpretation of left ventricular pressure waveforms. The left ventricle has been modeled as an ellipsoid composed of twelve mechano-hydraulic sub-systems. The asynchronous contraction of these twelve myocardial segments has been represented in order to reproduce a realistic pressure profiles. To take into account the different energy domains involved, the tissue-level scale and to facilitate the building of a modular model, multiple formalisms have been used: Bond Graph formalism for the mechano-hydraulic aspects and cellular automata for the electrical activation. An experimental protocol has been defined to acquire ventricular pressure signals from three pigs, with different afterload conditions. Evolutionary Algorithms have been used to identify the model parameters in order to minimize the error between experimental and simulated ventricular pressure signals. Simulation results show that the model is able to reproduce experimental ventricular pressure. In addition, electro-mechanical activation times have been determined in the identification process. For example, the maximum electrical activation time is reached, respectively, 96.5, 139.3 and 131.5 ms for the first, second, and third pigs. These preliminary results are encouraging for the application of the model on non-invasive data like ECG, arterial pressure or myocardial strain.

Continuous left ventricular ejection fraction monitoring by aortic pressure waveform analysis

We developed a technique to monitor left ventricular ejection fraction (EF) by model-based analysis of the aortic pressure waveform. First, the aortic pressure waveform is represented with a lumped parameter circulatory model. Then, the model is fitted to each beat of the waveform to estimate its lumped parameters to within a constant scale factor equal to the arterial compliance (C (a)). Finally, the proportional parameter estimates are utilized to compute beat-to-beat absolute EF by cancelation of the C (a) scale factor. In this way, in contrast to conventional imaging, EF may be continuously monitored without any ventricular geometry assumptions. Moreover, with the proportional parameter estimates, relative changes in beat-to-beat left ventricular end-diastolic volume (EDV), cardiac output (CO), and maximum left ventricular elastance (E (max)) may also be monitored. To evaluate the technique, we measured aortic pressure waveforms, reference EF and EDV via standard echocardiography, and other cardiovascular variables from six dogs during various pharmacological influences and total intravascular volume changes. Our results showed overall EF and calibrated EDV root-mean-squared-errors of 5.6% and 4.1 mL, and reliable estimation of relative E (max) and beat-to-beat CO changes. These results demonstrate, perhaps for the first time, the feasibility of estimating EF from only a blood pressure waveform.

Model-based analysis of myocardial strain data acquired by tissue Doppler imaging

OBJECTIVE

Tissue Doppler imaging (TDI) is commonly used to evaluate regional ventricular contraction properties through the analysis of myocardial strain. During the clinical examination, a set of strain signals is acquired concurrently at different locations. However, the joint interpretation of these signals remains difficult. This paper proposes a model-based approach in order to assist the clinician in making an analysis of myocardial strain.

METHODS AND MATERIALS

The proposed method couples a model of the left ventricle, which takes into account cardiac electrical, mechanical and hydraulic activities with an adapted identification algorithm, in order to obtain patient-specific model representations. The proposed model presents a tissue-level resolution, adapted to TDI strain analysis. The method is applied in order to reproduce TDI strain signals acquired from two healthy subjects and a patient presenting with dilated cardiomyopathy (DCM).

RESULTS

The comparison between simulated and experimental strains for the three subjects reflects a satisfying adaptation of the model on different strain morphologies. The mean error between real and synthesized signals is equal to 2.34% and 2.09%, for the two healthy subjects and 1.30% for the patient suffering from DCM. Identified parameters show significant electrical conduction and mechanical activation delays for the pathologic case and have shown to be useful for the localization of the failing myocardial segments, which are situated on the anterior and lateral walls of the ventricular base.

CONCLUSION

The present study shows the feasibility of a model-based method for the analysis of TDI strain signals. The identification of delayed segments in the pathologic case produces encouraging results and may represent a way to better utilize the information included in strain signals and to improve the therapy assistance.

The role of the autonomic nervous system in hypertension: a bond graph model study

A bond graph model of the cardiovascular system with embedded autonomic nervous regulation was developed for a better understanding of the role of the autonomic nervous system (ANS) in hypertension. The model is described by a pump model of the heart and a detailed representation of the head and neck, pulmonary, coronary, abdomen and extremity circulation. It responds to sympathetic and parasympathetic activities by modifying systemic peripheral vascular resistance, heart rate, ventricular end-systolic elastance and venous unstressed volumes. The impairment of ANS is represented by an elevation of the baroreflex set point. The simulation results show that, compared with normotensive, in hypertension the systolic and diastolic blood pressure (SBP/DBP) rose from 112/77 mmHg to 144/94 mmHg and the left ventricular wall thickness (LVWT) increased from 10 mm to 12.74 mm. In the case that ANS regulation was absent, both the SBP and DBP further increased by 8 mmHg and the LVWT increased to 13.22 mm. The results also demonstrate that when ANS regulation is not severely damaged, e.g. the baroreflex set point is 97 mmHg, it still has an effect in preventing the rapid rise of blood pressure in hypertension; however, with the worsening of ANS regulation, its protective role weakens. The results agree with human physiological and pathological features in hemodynamic parameters and carotid baroreflex function curves, and indicate the role of ANS in blood pressure regulation and heart protection. In conclusion, the present model may provide a valid approach to study the pathophysiological conditions of the cardiovascular system and the mechanism of ANS regulation.

Estimation of the total peripheral resistance baroreflex impulse response from spontaneous hemodynamic variability

We previously developed a mathematical analysis technique for estimating the static gain values of the arterial total peripheral resistance (TPR) baroreflex (G(A)) and the cardiopulmonary TPR baroreflex (G(C)) from small, spontaneous beat-to-beat fluctuations in arterial blood pressure, cardiac output, and stroke volume. Here, we extended the mathematical analysis so as to also estimate the entire arterial TPR baroreflex impulse response [h(A)(t)] as well as the lumped arterial compliance (AC). The extended technique may therefore provide a linear dynamic characterization of TPR baroreflex systems during normal physiological conditions from potentially noninvasive measurements. We theoretically evaluated the technique with respect to realistic spontaneous hemodynamic variability generated by a cardiovascular simulator with known system properties. Our results showed that the technique reliably estimated h(A)(t) [error = 30.2 +/- 2.6% for the square root of energy (E(A)), 19.7 +/- 1.6% for absolute peak amplitude (P(A)), 37.3 +/- 2.5% for G(A), and 33.1 +/- 4.9% for the overall time constant] and AC (error = 17.6 +/- 4.2%) under various simulator parameter values and reliably tracked changes in G(C). We also experimentally evaluated the technique with respect to spontaneous hemodynamic variability measured from seven conscious dogs before and after chronic arterial baroreceptor denervation. Our results showed that the technique correctly predicted the abolishment of h(A)(t) [E(A) = 1.0 +/- 0.2 to 0.3 +/- 0.1, P(A) = 0.3 +/- 0.1 to 0.1 +/- 0.0 s(-1), and G(A) = -2.1 +/- 0.6 to 0.3 +/- 0.2 (P < 0.05)] and the enhancement of G(C) [-0.7 +/- 0.44 to -1.8 +/- 0.2 (P < 0.05)] following the chronic intervention. Moreover, the technique yielded estimates whose values were consistent with those reported with more invasive and/or experimentally difficult methods.

A Kalman filtering approach to estimation of maximum ventricle elastance

In this paper a method for estimating maximum ventricular elastance through an extended Kalman filter is proposed, based on measurement of ventricular volume and aortic pressure. The Kalman filter is particularly well suited to this task, since it produces an optimal estimate (in the sense that the error is statistically minimized) given noise corrupted data. The EKF model is derived from an electrical-analog model of the left ventricle and systemic load. An observability study was a priori conducted on the model, restricted to the ejection phase, to validate the estimation procedure. The method has been evaluated with simulated data and produced good results (the estimate error was 7.14%).

Conceptual design of a multi-functional sphygmus detection system

From the energy point of view, obtaining simultaneous blood pressure and flow rate of the radial artery at the wrist is very important for sphygmic diagnosis in medicine. This work depicts the conceptual design for a noninvasive multi-functional sphygmus detection system. According to Y. C. Fung's flow rate equation, flow rate is a function of the diameter of the blood vessel, two adjacent pressures, arterial compliance, the distance between the two adjacent pressures and the viscosity of the blood. Because the distance between the two adjacent pressures is preset and the viscosity is obtained from either a data bank or viscometer, four measuring techniques are proposed to realize the calculation of the flow rate. First, use thermal array sensors and a thermal image identification technique to locate the artery for positioning the sphygmus detection head at wrist and to estimate the diameter of blood vessel as well. Second, detect the delay time between the two adjacent pressures, and then compute the downstream pressure in accordance with the sampled upstream pressure and delay time. Third, employ pressure feedback control to determine the variation of the vessel diameter that in turn can be used to compute the dynamic arterial compliance. Finally, use the nonlinear flow rate equation to calculate the blood flow rate.

A tissue-level model of the left ventricle for the analysis of regional myocardial function

This paper presents a model-based method for the analysis of regional myocardial strain, based on echocardiography and Tissue Doppler Imaging (TDI). A multi-formalism, tissue-level electromechanical model of the left ventricle is proposed. The parameters of the model are identified in order to reproduce regional strain signal morphologies obtained from a healthy subject and a patient presenting a dilated cardiomyopathy. The parameters identified for the DCM patient allow the localization of the failing myocardial segments and may be useful for a better design of cardiac resynchronization therapy on heart failure patients.

A bond graph model of the cardiovascular system

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals.

Model based analysis of the variation in Korotkoff sound onset time during exercise

In this study, a minimal mathematical model of the cardiovascular system is used to study the effects of changes in arterial compliance and cardiac contractility on the onset time of Korotkoff sounds during an auscultatory procedure. The model provides blood pressure waveforms in the ventricle, the aorta and the brachial artery. From these waveforms, pre-ejection time, pulse propagation time and rise time of the blood pressure at the brachial artery can be computed. The time delay between onset time of ECG Q wave and onset time of Korotkoff sound is the sum of these three times. Rise time is zero and the time delay is minimal when the cuff pressure is slightly above the diastolic pressure. This minimum time delay is represented by QKD. Simulation results suggest that during the Bruce exercise protocol QKD decreases to one-third of its pre-exercise value if the cardiac contractility increases threefold. The effect of arterial compliance is not as significant as that of the cardiac contractility. From data recorded during an exercise test, it is observed that QKD decreases considerably as the test load is increased. We show in this study that the amount of decrease in QKD can be used as an index of the amount of increase in cardiac contractility during an exercise ECG test. Use of signal averaging for reducing the effect of motion artifacts during an exercise test is also shown to be very instrumental for making accurate QKD measurements.