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

An algorithm to detect dicrotic notch in arterial blood pressure and photoplethysmography waveforms using the iterative envelope mean method

Background and Objective

Detection of the dicrotic notch (DN) within a cardiac cycle is essential for assessment of cardiac output, calculation of pulse wave velocity, estimation of left ventricular ejection time, and supporting feature-based machine learning models for noninvasive blood pressure estimation, and hypotension, or hypertension prediction. In this study, we present a new algorithm based on the iterative envelope mean (IEM) method to detect automatically the DN in arterial blood pressure (ABP) and photoplethysmography (PPG) waveforms.

Methods

The algorithm was evaluated on both ABP and PPG waveforms from a large perioperative dataset (MLORD dataset) comprising 17,327 patients. The analysis involved a total of 1,171,288 cardiac cycles for ABP waveforms and 3,424,975 cardiac cycles for PPG waveforms. To evaluate the algorithm's performance, the systolic phase duration (SPD) was employed, which represents the duration from the onset of the systolic phase to the DN in the cardiac cycle. Correlation plots and regression analysis were used to compare the algorithm with an established DN detection technique (second derivative). The marking of the DN temporal location was carried out by an experienced researcher using the help of the 'find_peaks' function from the scipy PYTHON package, serving as a reference for the evaluation. The marking was visually validated by both an engineer and an anesthesiologist. The robustness of the algorithm was evaluated as the DN was made less visually distinct across signal-to-noise ratios (SNRs) ranging from -30 dB to -5 dB in both ABP and PPG waveforms.

Results

The correlation between SPD estimated by the algorithm and that marked by the researcher is strong for both ABP (R2(87343) =.99, p<.001) and PPG (R2(86764) =.98, p<.001) waveforms. The algorithm had a lower mean error of dicrotic notch detection (s): 0.0047 (0.0029) for ABP waveforms and 0.0046 (0.0029) for PPG waveforms, compared to 0.0693 (0.0770) for ABP and 0.0968 (0.0909) for PPG waveforms for the established 2nd derivative method. The algorithm has high accuracy of DN detection for SNR of >= -9 dB for ABP waveforms and >= -12 dB for PPG waveforms indicating robust performance in detecting the DN when it is less visibly distinct.

Conclusion

Our proposed IEM- based algorithm can detect DN in both ABP and PPG waveforms with low computational cost, even in cases where it is not distinctly defined within a cardiac cycle of the waveform ('DN-less signals'). The algorithm can potentially serve as a valuable, fast, and reliable tool for extracting features from ABP and PPG waveforms. It can be especially beneficial in medical applications where DN-based features, such as SPD, diastolic phase duration, and DN amplitude, play a significant role.

Non-invasive pressure-volume loops using the elastance model and CMR: a porcine validation at transient pre-loads

Aims

Pressure-volume (PV) loops have utility in the evaluation of cardiac pathophysiology but require invasive measurements. Recently, a time-varying elastance model to derive PV loops non-invasively was proposed, using left ventricular (LV) volume by cardiovascular magnetic resonance (CMR) and brachial cuff pressure as inputs. Validation was performed using CMR and pressure measurements acquired on the same day, but not simultaneously, and without varying pre-loads. This study validates the non-invasive elastance model used to estimate PV loops at varying pre-loads, compared with simultaneous measurements of invasive pressure and volume from real-time CMR, acquired concurrent to an inferior vena cava (IVC) occlusion.

Methods and results

We performed dynamic PV loop experiments under CMR guidance in 15 pigs (n = 7 naïve, n = 8 with ischaemic cardiomyopathy). Pre-load was altered by IVC occlusion, while simultaneously acquiring invasive LV pressures and volumes from real-time CMR. Pairing pressure and volume signals yielded invasive PV loops, and model-based PV loops were derived using real-time LV volumes. Haemodynamic parameters derived from invasive and model-based PV loops were compared. Across 15 pigs, 297 PV loops were recorded. Intra-class correlation coefficient (ICC) agreement was excellent between model-based and invasive parameters: stroke work (bias = 0.007 ± 0.03 J, ICC = 0.98), potential energy (bias = 0.02 ± 0.03 J, ICC = 0.99), ventricular energy efficiency (bias = -0.7 ± 2.7%, ICC = 0.98), contractility (bias = 0.04 ± 0.1 mmHg/mL, ICC = 0.97), and ventriculoarterial coupling (bias = 0.07 ± 0.15, ICC = 0.99). All haemodynamic parameters differed between naïve and cardiomyopathy animals (P < 0.05). The invasive vs. model-based PV loop dice similarity coefficient was 0.88 ± 0.04.

Conclusion

An elastance model-based estimation of PV loops and associated haemodynamic parameters provided accurate measurements at transient loading conditions compared with invasive PV loops.

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.

Non-invasive left ventricular pressure-volume loops from cardiovascular magnetic resonance imaging and brachial blood pressure: validation using pressure catheter measurements

Aims

Left ventricular (LV) pressure-volume (PV) loops provide gold-standard physiological information but require invasive measurements of ventricular intracavity pressure, limiting clinical and research applications. A non-invasive method for the computation of PV loops from magnetic resonance imaging and brachial cuff blood pressure has recently been proposed. Here we evaluated the fidelity of the non-invasive PV algorithm against invasive LV pressures in humans.

Methods and results

Four heart failure patients with EF < 35% and LV dyssynchrony underwent cardiovascular magnetic resonance (CMR) imaging and subsequent LV catheterization with sequential administration of two different intravenous metabolic substrate infusions (insulin/dextrose and lipid emulsion), producing eight datasets at different haemodynamic states. Pressure-volume loops were computed from CMR volumes combined with (i) a time-varying elastance function scaled to brachial blood pressure and temporally stretched to match volume data, or (ii) invasive pressures averaged from 19 to 30 sampled beats. Method comparison was conducted using linear regression and Bland-Altman analysis. Non-invasively derived PV loop parameters demonstrated high correlation and low bias when compared to invasive data for stroke work (R2 = 0.96, P < 0.0001, bias 4.6%), potential energy (R2 = 0.83, P = 0.001, bias 1.5%), end-systolic pressure-volume relationship (R2 = 0.89, P = 0.0004, bias 5.8%), ventricular efficiency (R2 = 0.98, P < 0.0001, bias 0.8%), arterial elastance (R2 = 0.88, P = 0.0006, bias -8.0%), mean external power (R2 = 0.92, P = 0.0002, bias 4.4%), and energy per ejected volume (R2 = 0.89, P = 0.0001, bias 3.7%). Variations in estimated end-diastolic pressure did not significantly affect results (P > 0.05 for all). Intraobserver analysis after one year demonstrated 0.9-3.4% bias for LV volumetry and 0.2-5.4% for PV loop-derived parameters.

Conclusion

Pressure-volume loops can be precisely and accurately computed from CMR imaging and brachial cuff blood pressure in humans.

Imaging in Pulmonary Vascular Disease-Understanding Right Ventricle-Pulmonary Artery Coupling

The right ventricle (RV) and pulmonary arterial (PA) tree are inextricably linked, continually transferring energy back and forth in a process known as RV-PA coupling. Healthy organisms maintain this relationship in optimal balance by modulating RV contractility, pulmonary vascular resistance, and compliance to sustain RV-PA coupling through life's many physiologic challenges. Early in states of adaptation to cardiovascular disease-for example, in diastolic heart failure-RV-PA coupling is maintained via a multitude of cellular and mechanical transformations. However, with disease progression, these compensatory mechanisms fail and become maladaptive, leading to the often-fatal state of "uncoupling." Noninvasive imaging modalities, including echocardiography, magnetic resonance imaging, and computed tomography, allow us deeper insight into the state of coupling for an individual patient, providing for prognostication and potential intervention before uncoupling occurs. In this review, we discuss the physiologic foundations of RV-PA coupling, elaborate on the imaging techniques to qualify and quantify it, and correlate these fundamental principles with clinical scenarios in health and disease. © 2022 American Physiological Society. Compr Physiol 12: 1-26, 2022.

Estimation of left ventricular stroke work based on a large cohort of healthy children

Left ventricular stroke work is an important prognostic marker to analyze cardiac function. Standard values for children are, however, missing. For clinicians, standards can help to improve the treatment decision of heart failures. For engineers, they can help to optimize medical devices. In this study, we estimated the left ventricular stroke work for children based on modeled pressure-volume loops. A lumped parameter model was fitted to clinical data of 340 healthy children. Reference curves for standard values were created over age, weight, and height. Left ventricular volume was measured with 3D echocardiography, while maximal ventricular pressure was approximated with a regression model from the literature. For validation of this method, we used 18 measurements acquired by a conductance catheter in 11 patients. The method demonstrated a low absolute mean difference of 0.033 J (SD: 0.031 J) for stroke work between measurement and estimation, while the percentage error was 21.66 %. According to the resulting reference curves, left ventricular stroke work of newborns has a median of 0.06 J and increases to 1.15 J at the age of 18 years. Stroke work increases over weight and height in a similar trend. The percentile curves depict the distribution. We demonstrate how reference curves can be used for quantification of differences and comparison in patients.

Accurate end systole detection in dicrotic notch-less arterial pressure waveforms

Identification of end systole is often necessary when studying events specific to systole or diastole, for example, models that estimate cardiac function and systolic time intervals like left ventricular ejection duration. In proximal arterial pressure waveforms, such as from the aorta, the dicrotic notch marks this transition from systole to diastole. However, distal arterial pressure measures are more common in a clinical setting, typically containing no dicrotic notch. This study defines a new end systole detection algorithm, for dicrotic notch-less arterial waveforms. The new algorithm utilises the beta distribution probability density function as a weighting function, which is adaptive based on previous heartbeats end systole locations. Its accuracy is compared with an existing end systole estimation method, on dicrotic notch-less distal pressure waveforms. Because there are no dicrotic notches defining end systole, validating which method performed better is more difficult. Thus, a validation method is developed using dicrotic notch locations from simultaneously measured aortic pressure, forward projected by pulse transit time (PTT) to the more distal pressure signal. Systolic durations, estimated by each of the end systole estimates, are then compared to the validation systolic duration provided by the PTT based end systole point. Data comes from ten pigs, across two protocols testing the algorithms under different hemodynamic states. The resulting mean difference ± limits of agreement between measured and estimated systolic duration, of [Formula: see text] versus [Formula: see text], for the new and existing algorithms respectively, indicate the new algorithms superiority.

Patient-Specific Monitoring and Trend Analysis of Model-Based Markers of Fluid Responsiveness in Sepsis: A Proof-of-Concept Animal Study

Total stressed blood volume ([Formula: see text]) and arterial elastance ([Formula: see text]) are two potentially important, clinically applicable metrics for guiding treatment in patients with altered hemodynamic states. Defined as the total pressure generating blood in the circulation, [Formula: see text] is a potential direct measurement of tissue perfusion, a critical component in treatment of sepsis. [Formula: see text] is closely related to arterial tone thus provides insight into cardiac efficiency. However, it is not clinically feasible or ethical to measure [Formula: see text] in patients, so a three chambered cardiovascular system model using measured left ventricle pressure and volume, aortic pressure and central venous pressure is implemented to identify [Formula: see text] and [Formula: see text] from clinical data. [Formula: see text] and [Formula: see text] are identified from clinical data from six (6) pigs, who have undergone clinical procedures aimed at simulating septic shock and subsequent treatment, to identify clinically relevant changes. A novel, validated trend analysis method is used to adjudge clinically significant changes in state in the real-time [Formula: see text] and [Formula: see text] traces. Results matched hypothesised increases in [Formula: see text] during fluid therapy, with a mean change of + 21% during initial therapy, and hypothesised decreases during endotoxin induced sepsis, with a mean change of - 29%. [Formula: see text] displayed the hypothesised reciprocal behaviour with a mean changes of - 12 and + 30% during initial therapy and endotoxin induced sepsis, respectively. The overall results validate the efficacy of [Formula: see text] in tracking changes in hemodynamic state in septic shock and fluid therapy.

A Zero-Dimensional Model and Protocol for Simulating Patient-Specific Pulmonary Hemodynamics From Limited Clinical Data

In pulmonary hypertension (PH) diagnosis and management, many useful functional markers have been proposed that are unfeasible for clinical implementation. For example, assessing right ventricular (RV) contractile response to a gradual increase in pulmonary arterial (PA) impedance requires simultaneously recording RV pressure and volume, and under different afterload/preload conditions. In addition to clinical applications, many research projects are hampered by limited retrospective clinical data and could greatly benefit from simulations that extrapolate unavailable hemodynamics. The objective of this study was to develop and validate a 0D computational model, along with a numerical implementation protocol, of the RV-PA axis. Model results are qualitatively compared with published clinical data and quantitatively validated against right heart catheterization (RHC) for 115 pediatric PH patients. The RV-PA circuit is represented using a general elastance function for the RV and a three-element Windkessel initial value problem for the PA. The circuit mathematically sits between two reservoirs of constant pressure, which represent the right and left atriums. We compared Pmax, Pmin, mPAP, cardiac output (CO), and stroke volume (SV) between the model and RHC. The model predicted between 96% and 98% of the variability in pressure and 98-99% in volumetric characteristics (CO and SV). However, Bland Altman plots showed the model to have a consistent bias for most pressure and volumetric parameters, and differences between model and RHC to have considerable error. Future studies will address this issue and compare specific waveforms, but these initial results are extremely promising as preliminary proof of concept of the modeling approach.

Beat-by-Beat Estimation of the Left Ventricular Pressure-Volume Loop Under Clinical Conditions

This paper develops a method for the minimally invasive, beat-by-beat estimation of the left ventricular pressure-volume loop. This method estimates the left ventricular pressure and volume waveforms that make up the pressure-volume loop using clinically available inputs supported by a short, baseline echocardiography reading. Validation was performed across 142,169 heartbeats of data from 11 Piétrain pigs subject to two distinct protocols encompassing sepsis, dobutamine administration and clinical interventions. The method effectively located pressure-volume loops, with low overall median errors in end-diastolic volume of 8.6%, end-systolic volume of 17.3%, systolic pressure of 19.4% and diastolic pressure of 6.5%. The method further demonstrated a low overall mean error of 23.2% predicting resulting stroke work, and high correlation coefficients along with a high percentage of trend compass 'in band' performance tracking changes in stroke work as patient condition varied. This set of results forms a body of evidence for the potential clinical utility of the method. While further validation in humans is required, the method has the potential to aid in clinical decision making across a range of clinical interventions and disease state disturbances by providing real-time, beat-to-beat, patient specific information at the intensive care unit bedside without requiring additional invasive instrumentation.

Minimally invasive estimation of ventricular dead space volume through use of Frank-Starling curves

This paper develops a means of more easily and less invasively estimating ventricular dead space volume (V_d), an important, but difficult to measure physiological parameter. V_d represents a subject and condition dependent portion of measured ventricular volume that is not actively participating in ventricular function. It is employed in models based on the time varying elastance concept, which see widespread use in haemodynamic studies, and may have direct diagnostic use. The proposed method involves linear extrapolation of a Frank-Starling curve (stroke volume vs end-diastolic volume) and its end-systolic equivalent (stroke volume vs end-systolic volume), developed across normal clinical procedures such as recruitment manoeuvres, to their point of intersection with the y-axis (where stroke volume is 0) to determine V_d. To demonstrate the broad applicability of the method, it was validated across a cohort of six sedated and anaesthetised male Pietrain pigs, encompassing a variety of cardiac states from healthy baseline behaviour to circulatory failure due to septic shock induced by endotoxin infusion. Linear extrapolation of the curves was supported by strong linear correlation coefficients of R = 0.78 and R = 0.80 average for pre- and post- endotoxin infusion respectively, as well as good agreement between the two linearly extrapolated y-intercepts (V_d) for each subject (no more than 7.8% variation). Method validity was further supported by the physiologically reasonable V_d values produced, equivalent to 44.3–53.1% and 49.3–82.6% of baseline end-systolic volume before and after endotoxin infusion respectively. This method has the potential to allow V_d to be estimated without a particularly demanding, specialised protocol in an experimental environment. Further, due to the common use of both mechanical ventilation and recruitment manoeuvres in intensive care, this method, subject to the availability of multi-beat echocardiography, has the potential to allow for estimation of V_d in a clinical environment.

Minimally invasive, patient specific, beat-by-beat estimation of left ventricular time varying elastance

Background

The aim of this paper was to establish a minimally invasive method for deriving the left ventricular time varying elastance (TVE) curve beat-by-beat, the monitoring of which’s inter-beat evolution could add significant new data and insight to improve diagnosis and treatment. The method developed uses the clinically available inputs of aortic pressure, heart rate and baseline end-systolic volume (via echocardiography) to determine the outputs of left ventricular pressure, volume and dead space volume, and thus the TVE curve. This approach avoids directly assuming the shape of the TVE curve, allowing more effective capture of intra- and inter-patient variability.

Results

The resulting TVE curve was experimentally validated against the TVE curve as derived from experimentally measured left ventricular pressure and volume in animal models, a data set encompassing 46,318 heartbeats across 5 Piétrain pigs. This simulated TVE curve was able to effectively approximate the measured TVE curve, with an overall median absolute error of 11.4% and overall median signed error of −2.5%.

Conclusions

The use of clinically available inputs means there is potential for real-time implementation of the method at the patient bedside. Thus the method could be used to provide additional, patient specific information on intra- and inter-beat variation in heart function.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-017-0338-7) contains supplementary material, which is available to authorized users.

Simulation of left atrial function using a multi-scale model of the cardiovascular system

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors.

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.