Estimation of cardiac output and peripheral resistance using square-wave-approximated aortic flow signal

An intelligent aortic valve model for complete cardiac cycle

The aortic valve (AV) is crucial for cardiovascular (CV) hemodynamic, impacting cardiac output (CO) and left ventricular volumetric flow rate (LVQ). Its nonlinear behavior challenges standard LVQ prediction methods as well as CO one. This study presents a novel approach for modeling the AV in the CV system, offering an improved method for estimating crucial parameters like LVQ across various AV conditions, including aortic stenosis (AS). The model, based on AV channel length during the entire cardiac phase, introduces a time-varying AV resistance (TV-AVR) parameterized by the pressure ratio across the AV and LVQ, enabling the simulation of both healthy and AS-related conditions. To validate this model, in vitro measurements are compared using a hybrid mock circulatory loop device. An unconventional use of a convolutional neural network (CNN) corrects the model's estimates, eliminating the need for labeled datasets. This approach, incorporating real-time learning and transforming 1-D CV signals into 2-D tensors, significantly improves the accuracy of LVQ measurements, achieving an error rate of less than 3.41 ± 4.84% for CO in healthy conditions and 2.83 ± 1.35% in AS cases-a 33.13% enhancement over linear diode models. These results underscore the potential of this approach for enhancing the diagnosis, prediction, and treatment of AV diseases. The key contributions of the proposed method encompass nonlinear TV-AVR estimation, investigation of transient CV responses, prediction of instantaneous CO, development of a flexible framework for noninvasive measurements integration, and the introduction of an adjustable resistance model using an extended Kalman filter (EKF) and CNN combination, all without requiring labeled data.

iCVS-Inferring Cardio-Vascular hidden States from physiological signals available at the bedside

Intensive care medicine is complex and resource-demanding. A critical and common challenge lies in inferring the underlying physiological state of a patient from partially observed data. Specifically for the cardiovascular system, clinicians use observables such as heart rate, arterial and venous blood pressures, as well as findings from the physical examination and ancillary tests to formulate a mental model and estimate hidden variables such as cardiac output, vascular resistance, filling pressures and volumes, and autonomic tone. Then, they use this mental model to derive the causes for instability and choose appropriate interventions. Not only this is a very hard problem due to the nature of the signals, but it also requires expertise and a clinician's ongoing presence at the bedside. Clinical decision support tools based on mechanistic dynamical models offer an appealing solution due to their inherent explainability, corollaries to the clinical mental process, and predictive power. With a translational motivation in mind, we developed iCVS: a simple, with high explanatory power, dynamical mechanistic model to infer hidden cardiovascular states. Full model estimation requires no prior assumptions on physiological parameters except age and weight, and the only inputs are arterial and venous pressure waveforms. iCVS also considers autonomic and non-autonomic modulations. To gain more information without increasing model complexity, both slow and fast timescales of the blood pressure traces are exploited, while the main inference and dynamic evolution are at the longer, clinically relevant, timescale of minutes. iCVS is designed to allow bedside deployment at pediatric and adult intensive care units and for retrospective investigation of cardiovascular mechanisms underlying instability. In this paper, we describe iCVS and inference system in detail, and using a dataset of critically-ill children, we provide initial indications to its ability to identify bleeding, distributive states, and cardiac dysfunction, in isolation and in combination.

Estimation of cardiac stroke volume from radial pulse waveform by artificial neural network

BACKGROUND AND OBJECTIVES

Stroke volume (SV) and cardiac output (CO) are the key indicators for the evaluation of cardiac function and hemodynamic status during the perioperative period, which are very important in the detection and treatment of cardiovascular diseases. Traditional CO and SV measurement methods have problems such as complex operation, low precision and poor generalization ability.

METHODS

In this paper, a method for estimating stroke volume based on cascade artificial neural network (ANN) and time domain features of radial pulse waveform (SV_ANN) was proposed. The simulation datasets of 4000 radial pulse waveforms and stroke volume (SV_meas) were generated by a 55 segment transmission line model of the human systemic vasculature and a recursive algorithm. The ANN was trained and tested by 10-fold cross-validation, and compared with 12 traditional models.

RESULTS

Experimental results showed that the Pearson correlation coefficients and mean difference between SV_ANN and SV_meas (R=0.95, mean standard deviation (SD) = 0.00 ± 6.45) were better than the best results of the 12 traditional models. Moreover, as increasing the number of training samples, the performance improvement of the ANN (R=0.94(Δ + 0.04), mean ± SD = 0.00 ± 6.38(Δ± 2.02)) was better than the other best model, namely, multiple linear regression model (MLR) (R=0.93(Δ + 0.03), mean ± SD = 0.00 ± 6.99(Δ± 1.50)).

CONCLUSIONS

A method is proposed to estimate cardiac stroke volume by the ANN with time domain features of radial pulse wave. It avoids the complicated modeling process based on hemodynamics within traditional models, improves the estimation accuracy of SV, and has a good generalization ability.

Ultrasound-based method for individualized estimation of central aortic blood pressure from flow velocity and diameter

Central aortic blood pressure (CABP) is a better predictor for cardiovascular events than brachial blood pressure. However, direct CABP measurement is invasive. The objective of this paper is to develop an ultrasound-based method using individualized Windkessel (WK) models for non-invasive estimation of CABP. Three WK models (with two-, three- and four-element WK, named, WK2, WK3 and WK4, respectively) were created and the model parameters were individualized based on aortic flow velocity and diameter waveforms measured by ultrasound (US). Experimental data were acquired in 42 subjects aged 21-67 years. The CABP estimated by WK models was compared with the reference CABP obtained using a commercial system. The results showed that the overall performance of the WK3 and WK4 models was similar, outperforming the WK2 model. The estimated CABP based on WK3/WK4 model showed good agreement with the reference CABP: the absolute errors of systolic blood pressure (SBP), 2.4 ± 2.1/2.4 ± 2.0 mmHg; diastolic blood pressure (DBP), 1.4 ± 1.1/1.7 ± 1.5 mmHg; mean blood pressure (MBP), 1.3 ± 0.8/1.3 ± 0.8 mmHg; pulse pressure (PP), 3.0 ± 2.3/3.2 ± 2.6 mmHg; the root mean square error (RMSE) of the waveforms, 2.5 ± 1.0/2.6 ± 1.1 mmHg. Therefore, the proposed method can provide a non-invasive CABP estimation during routine cardiac US examination.

Validation of a Non-invasive Inverse Problem-Solving Method for Stroke Volume

Stroke volume (SV) is a major biomarker of cardiac function, reflecting ventricular-vascular coupling. Despite this, hemodynamic monitoring and management seldomly includes assessments of SV and remains predominantly guided by brachial cuff blood pressure (BP). Recently, we proposed a mathematical inverse-problem solving method for acquiring non-invasive estimates of mean aortic flow and SV using age, weight, height and measurements of brachial BP and carotid-femoral pulse wave velocity (cfPWV). This approach relies on the adjustment of a validated one-dimensional model of the systemic circulation and applies an optimization process for deriving a quasi-personalized profile of an individual’s arterial hemodynamics. Following the promising results of our initial validation, our first aim was to validate our method against measurements of SV derived from magnetic resonance imaging (MRI) in healthy individuals covering a wide range of ages (n = 144; age range 18–85 years). Our second aim was to investigate whether the performance of the inverse problem-solving method for estimating SV is superior to traditional statistical approaches using multilinear regression models. We showed that the inverse method yielded higher agreement between estimated and reference data (r = 0.83, P < 0.001) in comparison to the agreement achieved using a traditional regression model (r = 0.74, P < 0.001) across a wide range of age decades. Our findings further verify the utility of the inverse method in the clinical setting and highlight the importance of physics-based mathematical modeling in improving predictive tools for hemodynamic monitoring.

A novel method for the noninvasive estimation of cardiac output with brachial oscillometric blood pressure measurements through an assessment of arterial compliance

OBJECTIVE

To propose and validate a new method for estimating cardiac output based on the total arterial compliance (Ct) formula that does not need an arterial waveform and to apply it to brachial oscillometric blood pressure measurements (OBPMs).

METHODS

One hundred subjects with normal heart anatomy and function were included. Reference values for cardiac output were measured with echocardiography, and Ct was calculated with a two-element Windkessel model. Then, a statistical model of arterial compliance (Ce) was used to estimate cardiac output. Finally, the measured and estimated cardiac output values were compared for accuracy and reproducibility.

RESULTS

The model was derived from the data of 70 subjects and prospectively tested with the data from the remaining 30 individuals. The mean age of the whole group was 43.4 ± 12.8 years, with 46% women. The average blood pressure (BP) was 107.1/65.0 ± 15.0/9.6 mmHg and the average heart rate was 67.7 ± 11.4 beats/min. The average Ct was 1.39 ± 0.27 mL/mmHg and the average cardiac output was 5.5 ± 1.0 L/min. The mean difference in the cardiac output estimated by the proposed methodology vs. that measured by Doppler echocardiography was 0.022 L/min with an SD of 0.626 L/min. The intraclass correlation coefficient was 0.93, and the percentage error was 19%.

CONCLUSION

Cardiac output could be reliably and noninvasively obtained with brachial OBPMs through a novel method for estimating Ct without the need for an arterial waveform. The new method could identify hemodynamic factors that explain BP values in an ambulatory care setting.

Blood pressure assessment with in-ear photoplethysmography

Objective. In this study, we aimed to estimate blood pressure (BP) from in-ear photoplethysmography (PPG). This novel implementation provided an unobtrusive and steady way of recording PPG, whereas previous PPG measurements were mostly performed at the wrist, finger, or earlobe.Methods. The time between forward and reflected PPG waves was very short at the ear site. To minimize errors introduced by feature extraction, a multi-Gaussian decomposition of in-ear PPG was performed. Both hand-crafted and whole-based features were extracted and the best combination of features was selected using a backward-search wrapper method and evaluated by the Akaike information criteria. Hemodynamic parameters such as compliance and inertance were estimated from a four-element Windkessel (WK4) model, which was used to pre-classify PPG signals and generate different BP estimation algorithms. Calibration was done by using previous measurements from the same class. To validate this novel approach, 53 subjects were recruited for a one-month follow-up study, and 17 subjects were recruited for a two-month follow-up study. Calibrated systolic BP estimation accuracy was significantly improved with inertance-based pre-classification, while diastolic BP showed less improvement.Results. With proper feature selection, pre-classification and calibration, we have achieved a mean absolute error of 5.35 mmHg for SBP estimation, compared to 6.16 mmHg if no pre-classification was carried out. The performance did not deteriorate in two months, showing a decent BP trend-tracking ability.Conclusion. The study demonstrated the feasibility of in-ear PPG to reliably measure BP, which represents an important technological advancement in terms of unobtrusiveness and steadiness.

Hemodynamic Patterns Before Inhospital Cardiac Arrest in Critically Ill Children: An Exploratory Study

Supplemental Digital Content is available in the text.

OBJECTIVES:

To characterize prearrest hemodynamic trajectories of children suffering inhospital cardiac arrest.

DESIGN:

Exploratory retrospective analysis of arterial blood pressure and electrocardiogram waveforms.

SETTING:

PICU and cardiac critical care unit in a tertiary-care children’s hospital.

PATIENTS:

Twenty-seven children with invasive blood pressure monitoring who suffered a total of 31 inhospital cardiac arrest events between June 2017 and June 2019.

INTERVENTIONS:

None.

MEASUREMENTS AND MAIN RESULTS:

We assessed changes in cardiac output, systemic vascular resistance, stroke volume, and heart rate derived from arterial blood pressure waveforms using three previously described estimation methods. We observed substantial prearrest drops in cardiac output (population median declines of 65–84% depending on estimation method) in all patients in the 10 minutes preceding inhospital cardiac arrest. Most patients’ mean arterial blood pressure also decreased, but this was not universal. We identified three hemodynamic patterns preceding inhospital cardiac arrest: subacute pulseless arrest (n = 18), acute pulseless arrest (n = 7), and bradycardic arrest (n = 6). Acute pulseless arrest events decompensated within seconds, whereas bradycardic and subacute pulseless arrest events deteriorated over several minutes. In the subacute and acute pulseless arrest groups, decreases in cardiac output were primarily due to declines in stroke volume, whereas in the bradycardic group, the decreases were primarily due to declines in heart rate.

CONCLUSIONS:

Critically ill children exhibit distinct physiologic behaviors prior to inhospital cardiac arrest. All events showed substantial declines in cardiac output shortly before inhospital cardiac arrest. We describe three distinct prearrest patterns with varying rates of decline and varying contributions of heart rate and stroke volume changes to the fall in cardiac output. Our findings suggest that monitoring changes in arterial blood pressure waveform-derived heart rate, pulse pressure, cardiac output, and systemic vascular resistance estimates could improve early detection of inhospital cardiac arrest by up to several minutes. Further study is necessary to verify the patterns witnessed in our cohort as a step toward patient rather than provider-centered definitions of inhospital cardiac arrest.

The Optimal Haemoglobin Target in Dialysis Patients May Be Determined by Its Contrasting Effects on Arterial Stiffness and Pressure Pulsatility

Introduction

It remains unclear why the optimal haemoglobin target is lower in patients with chronic kidney disease (CKD) than in non-CKD persons. Arteriosclerosis and consequent impaired arterial function comprise a central cardiovascular risk mechanism in CKD. We hypothesized that the optimal haemoglobin target depends on its opposing effects on arterial stiffness and pressure pulsatility in CKD.

Methods

Arterial stiffness (aortic pulse wave velocity), wave reflection (augmentation index, reflected wave pressure and reflection magnitude), and pressure pulsatility (central systolic and pulse pressure, peripheral pulse pressure, pressure amplification and forward wave pressure) were assessed in 48 dialysis patients.

Results

In established confounder and diabetes adjusted linear regression models, haemoglobin levels were directly associated with arterial stiffness (partial R=0.366, p=0.03) and inversely with central systolic pressure (partial R=−0.344, p=0.04), central pulse pressure (partial R=−0.403, p=0.01), peripheral pulse pressure (partial R=−0.521, p=0.001) and forward wave pressure (partial R=−0.544, p=0.001). The presence of heart failure and use of angiotensin converting enzyme inhibitors or angiotensin receptor blockers and erythropoietin stimulating agents did not materially alter these relationships upon further adjustment for the respective characteristics in the models, and in sensitivity analyses. In receiver operator characteristic curve analysis, the optimal haemoglobin concentration cut-off values in predicting arterial stiffness and increased central pulse pressure were remarkably similar at 10.95 g/dl and 10.85 g/dl, respectively, and with clinically useful sensitivities, specificities and positive and negative predictive values. In logistic regression models, a haemoglobin value of >10.9 mg/dl was associated with both arterial stiffness (>10 m/sec; OR (95% CI) = 10.48 (1.57–70.08), p=0.02) and normal central pulse pressure (>50 mmHg; OR (95% CI) = 7.55 (1.58–36.03), p=0.01).

Conclusion

This study suggests that the optimal haemoglobin target in dialysis patients is ~11g/dl and determined by its differential and contrasting effects on arterial stiffness and pressure pulsatility.

Noninvasive estimation of aortic hemodynamics and cardiac contractility using machine learning

Cardiac and aortic characteristics are crucial for cardiovascular disease detection. However, noninvasive estimation of aortic hemodynamics and cardiac contractility is still challenging. This paper investigated the potential of estimating aortic systolic pressure (aSBP), cardiac output (CO), and end-systolic elastance (E_es) from cuff-pressure and pulse wave velocity (PWV) using regression analysis. The importance of incorporating ejection fraction (EF) as additional input for estimating E_es was also assessed. The models, including Random Forest, Support Vector Regressor, Ridge, Gradient Boosting, were trained/validated using synthetic data (n = 4,018) from an in-silico model. When cuff-pressure and PWV were used as inputs, the normalized-RMSEs/correlations for aSBP, CO, and E_es (best-performing models) were 3.36 ± 0.74%/0.99, 7.60 ± 0.68%/0.96, and 16.96 ± 0.64%/0.37, respectively. Using EF as additional input for estimating E_es significantly improved the predictions (7.00 ± 0.78%/0.92). Results showed that the use of noninvasive pressure measurements allows estimating aSBP and CO with acceptable accuracy. In contrast, E_es cannot be predicted from pressure signals alone. Addition of the EF information greatly improves the estimated E_es. Accuracy of the model-derived aSBP compared to in-vivo aSBP (n = 783) was very satisfactory (5.26 ± 2.30%/0.97). Future in-vivo evaluation of CO and E_es estimations remains to be conducted. This novel methodology has potential to improve the noninvasive monitoring of aortic hemodynamics and cardiac contractility.

Noninvasive Cardiac Output and Central Systolic Pressure From Cuff-Pressure and Pulse Wave Velocity

GOAL

We introduce a novel approach to estimate cardiac output (CO) and central systolic blood pressure (cSBP) from noninvasive measurements of peripheral cuff-pressure and carotid-to-femoral pulse wave velocity (cf-PWV).

METHODS

The adjustment of a previously validated one-dimensional arterial tree model is achieved via an optimization process. In the optimization loop, compliance and resistance of the generic arterial tree model as well as aortic flow are adjusted so that simulated brachial systolic and diastolic pressures and cf-PWV converge towards the measured brachial systolic and diastolic pressures and cf-PWV. The process is repeated until full convergence in terms of both brachial pressures and cf-PWV is reached. To assess the accuracy of the proposed framework, we implemented the algorithm on in vivo anonymized data from 20 subjects and compared the method-derived estimates of CO and cSBP to patient-specific measurements obtained with Mobil-O-Graph apparatus (central pressure) and two-dimensional transthoracic echocardiography (aortic blood flow).

RESULTS

Both CO and cSBP estimates were found to be in good agreement with the reference values achieving an RMSE of 0.36 L/min and 2.46 mmHg, respectively. Low biases were reported, namely -0.04 ± 0.36 L/min for CO predictions and -0.27 ± 2.51 mmHg for cSBP predictions.

SIGNIFICANCE

Our one-dimensional model can be successfully "tuned" to partially patient-specific standards by using noninvasive, easily obtained peripheral measurement data. The in vivo evaluation demonstrated that this method can potentially be used to obtain central aortic hemodynamic parameters in a noninvasive and accurate way.

Unobtrusive Estimation of Cardiovascular Parameters with Limb Ballistocardiography

This study investigates the potential of the limb ballistocardiogram (BCG) for unobtrusive estimation of cardiovascular (CV) parameters. In conjunction with the reference CV parameters (including diastolic, pulse, and systolic pressures, stroke volume, cardiac output, and total peripheral resistance), an upper-limb BCG based on an accelerometer embedded in a wearable armband and a lower-limb BCG based on a strain gauge embedded in a weighing scale were instrumented simultaneously with a finger photoplethysmogram (PPG). To standardize the analysis, the more convenient yet unconventional armband BCG was transformed into the more conventional weighing scale BCG (called the synthetic weighing scale BCG) using a signal processing procedure. The characteristic features were extracted from these BCG and PPG waveforms in the form of wave-to-wave time intervals, wave amplitudes, and wave-to-wave amplitudes. Then, the relationship between the characteristic features associated with (i) the weighing scale BCG-PPG pair and (ii) the synthetic weighing scale BCG-PPG pair versus the CV parameters, was analyzed using the multivariate linear regression analysis. The results indicated that each of the CV parameters of interest may be accurately estimated by a combination of as few as two characteristic features in the upper-limb or lower-limb BCG, and also that the characteristic features recruited for the CV parameters were to a large extent relevant according to the physiological mechanism underlying the BCG.

Quantification of wave reflection using peripheral blood pressure waveforms

This paper presents a novel minimally invasive method for quantifying blood pressure (BP) wave reflection in the arterial tree. In this method, two peripheral BP waveforms are analyzed to obtain an estimate of central aortic BP waveform, which is used together with a peripheral BP waveform to compute forward and backward pressure waves. These forward and backward waves are then used to quantify the strength of wave reflection in the arterial tree. Two unique strengths of the proposed method are that 1) it replaces highly invasive central aortic BP and flow waveforms required in many existing methods by less invasive peripheral BP waveforms, and 2) it does not require estimation of characteristic impedance. The feasibility of the proposed method was examined in an experimental swine subject under a wide range of physiologic states and in 13 cardiac surgery patients. In the swine subject, the method was comparable to the reference method based on central aortic BP and flow. In cardiac surgery patients, the method was able to estimate forward and backward pressure waves in the absence of any central aortic waveforms: on the average, the root-mean-squared error between actual versus computed forward and backward pressure waves was less than 5 mmHg, and the error between actual versus computed reflection index was less than 0.03.

Estimating cardiac output from blood pressure and heart rate: the liljestrand & zander formula

Cardiac output (CO) is an important indicator of cardiovascular function. Several invasive and non-invasive methods have been developed and validated to assess CO in the clinical setting. These are often computationally complex or proprietarily-restricted, and thus, not feasible in ambulatory investigations and the laboratory research setting. Simple mathematical transforms have been proposed to estimate CO from pulse pressure (PP = mean systolic blood pressure (SBP) minus mean diastolic blood pressure (DBP)), and mean heart rate (HR). Recently we evaluated one such simple technique [CO=(PPxHR)x.002], and found moderate correlation between the CO estimate and Modelflow-derived CO. Here we aimed to evaluate a more sophisticated formula, proposed in 1940 by Liljestrand and Zander. CO was estimated (COEST) dividing PP by the sum of SBP and DBP and multiplying the product by HR. This index was correlated with the Modelflow (3 element Windkessel) -derived CO. Baseline beat-to-beat blood pressure data from 67 young (mean age = 19.94± 2.8), healthy men (n = 30) and women (n = 37) was available for analysis. Overall, the correlation of COEST and CO was moderate (r = .42, p <.0001) and stronger in men (r = .66, p < .0001) compared to women (r = .36, p < .05). These results suggest that at least in some situations the Liljestrand and Zander method may provide an adequate measure of CO when other methods are not available.

Relationship between stroke volume and pulse pressure during blood volume perturbation: a mathematical analysis

Arterial pulse pressure has been widely used as surrogate of stroke volume, for example, in the guidance of fluid therapy. However, recent experimental investigations suggest that arterial pulse pressure is not linearly proportional to stroke volume. However, mechanisms underlying the relation between the two have not been clearly understood. The goal of this study was to elucidate how arterial pulse pressure and stroke volume respond to a perturbation in the left ventricular blood volume based on a systematic mathematical analysis. Both our mathematical analysis and experimental data showed that the relative change in arterial pulse pressure due to a left ventricular blood volume perturbation was consistently smaller than the corresponding relative change in stroke volume, due to the nonlinear left ventricular pressure-volume relation during diastole that reduces the sensitivity of arterial pulse pressure to perturbations in the left ventricular blood volume. Therefore, arterial pulse pressure must be used with care when used as surrogate of stroke volume in guiding fluid therapy.