SYSTEM AND METHODS FOR REAL TIME NONINVASIVE ESTIMATION OF CARDIOVASCULAR PARAMETERS USING MACHINE LEARNING

Abstract

Systems and methods are provided for that use noninvasively measured physiologic parameters to predict in real time noninvasively unobservable cardiovascular parameters by employing a one-dimensional arterial tree numerical model calibrated with representative patient data. The numerical model further may be trained and calibrated on a larger database that includes synthetic data using machine-learning algorithms to provide a robust generalized estimator for multiple cardiovascular and hemodynamic parameters.

Claims

1. A system configured to use non-invasively measurable physiologic data to estimate cardiovascular parameters of a patient that are non-invasively unobservable, the system comprising: a plurality of pulse sensors configured to be applied to a patient, the outputs of which enable computation of pulse wave velocities; a cuff for measuring values of systolic and diastolic blood pressures and heart rate; a console including a processor and non-volatile storage, wherein the non-volatile storage stores instructions that, when executed by the processor: receive the values of measured systolic and diastolic blood pressure and heart rate; compute actual pulse wave velocities using the outputs of the plurality of pulse sensors; iteratively compute values of estimated systolic and diastolic blood pressure using an arterial tree model, until a difference between the values of estimated systolic and diastolic blood pressure and the measured values of systolic and diastolic blood pressure are less than a first threshold; determine an estimator by iteratively computing estimated pulse wave velocities, until the difference between the estimated values of systolic and diastolic blood pressure and the measured values of systolic and diastolic blood pressure are less than the first threshold, and a difference between the estimated pulse wave velocities and the actual pulse wave velocities is less than a second threshold; and compute estimated values of cardiac output or aortic (central) systolic blood pressure using the estimator and as input additional measured values of systolic and diastolic blood pressure and additional actual pulse wave velocities.

2. The system of claim 1, wherein the instructions that iteratively compute values of estimated systolic and diastolic blood pressure also adjust at least one parameter corresponding to vascular distensibility or vascular resistance.

3. The system of claim 1, wherein the instructions that determine an estimator by iteratively computing estimated pulse wave velocities also adjust at a stroke volume.

4. The system of claim 1, wherein the non-invasively measurable physiologic data comprises data collected from a single patient.

5. The system of claim 1, wherein the non-invasively measurable physiologic data comprises in-vivo clinical data collected from a representative patient population.

6. The system of claim 5, wherein the non-invasively measurable physiologic data further comprises a database of synthetically generated data.

7. The system of claim 5, wherein the system is configured to accept as inputs ECG waveform timing data and an output from a heart sound detector for use in computing left ventricular end-systolic elastance.

8. The system of claim 7, wherein the instructions further include machine learning generated algorithms that train the estimator on the database of synthetically generated data, and wherein estimator further computes in real time an estimated value of at least one of central systolic blood pressure, left ventricular end-systolic elastance, total arterial compliance and aortic impedance.

9. The system of claim 1, wherein the cuff is configured to measure brachial systolic and diastolic blood pressures.

10. The system of claim 1, wherein a first one of the plurality of sensors is disposed on a patch configured to be disposed on skin of the patient in a vicinity of a proximal arterial site and a second one of the plurality of sensors is disposed on a patch configured to be disposed on skin of the patient in a vicinity of a distal arterial site.

11. The system of claim 1, wherein the instructions compute actual pulse wave velocities by determining a propagation time of an arterial pulse from a carotid artery of the patient to a femoral artery of the patient.

12. The system of claim 8, wherein machine learning generated algorithms are trained and tested using cross-validation.

13. A method for estimating in real time a noninvasively unobservable cardiovascular parameter for a patient, the method comprising: noninvasively obtaining for the patient a measured blood pressure value and a measured pulse wave velocity; non-invasively determining a time interval between the onset of aortic valve closure and the dicrotic notch in an ECG waveform for the patient; and using machine learning generated algorithms trained on a synthetically generated database, computing in real time an estimated value of at least one of cardiac output, central systolic blood pressure, left ventricular end-systolic elastance, total arterial compliance and aortic impedance.

14. The method of claim 13, wherein the measured blood pressure value corresponds to at least a diastolic blood pressure value.

15. The method of claim 13, wherein the measured blood pressure value corresponds to at least a systolic brachial pressure value.

16. The method of claim 13, wherein the measured blood pressure value is obtained using a blood pressure cuff.

17. The method of claim 13, wherein the measured pulse wave velocity value is obtained using at least one pulse sensor configured to be disposed on a skin of the patient adjacent a proximal arterial site of the patient, the measured pulse velocity value obtained by measuring propagation time of an arterial pulse from the proximal site of the patient to a distal site of the patient.

18. The method of claim 13, wherein the synthetically generated database is generated using a mathematical arterial tree model.

19. The method of claim 13, wherein the one-dimensional arterial tree model is calibrated with representative patient data.

20. The method of claim 13, wherein machine learning generated algorithms are trained and tested using cross-validation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1 illustrates an exemplary system for noninvasively estimating cardiovascular and hemodynamic parameters of a patient in accordance with the principles of the present invention.

[0026] FIG. 2 is a schematic view of exemplary hardware and software components of a console of the present invention.

[0027] FIG. 3 is a flowchart of an exemplary inverse problem-solving model having two layers of optimization for estimating vascular parameters using noninvasive measurements in accordance with the principles of the present invention.

[0028] FIGS. 4A and 4B are graphs comparing results for CO predicted by an exemplary estimator of the present invention computed using noninvasive measurements against reference values of CO.

[0029] FIGS. 5A and 5B are graphs comparing results for cSBP predicted by an exemplary estimator of the present invention computed using noninvasive measurements against reference values of cSBP.

[0030] FIGS. 6A, 6B and 6C are, respectively, a graph depicting aortic blood pressure, ventricular blood pressure and atrial blood pressure fluctuations as a function of cardiac valvular events, a graph illustrating variation of left ventricular elastance as a function of time and the corresponding cardiac events, and a graph depicting the derivation of the time period between the beginning of a patient's Q-wave and closure of the aortic valve.

[0031] FIG. 7 is a schematic depicting how segregated data may be used train a regression model for predicting unobserved vascular parameters.

[0032] FIGS. 8A and 8B are comparisons showing performance of the inventive estimator in predicting Ees and the corresponding Bland-Altman plot.

[0033] FIGS. 9A and 9B are comparisons showing performance of the inventive estimator in predicting CT and the corresponding Bland-Altman plot.

[0034] FIGS. 10A and 10B are comparisons showing performance of the inventive estimator in predicting Zao and the corresponding Bland-Altman plot.

DETAILED DESCRIPTION OF THE INVENTION

[0035] The present invention is directed to systems and methods for providing real time estimates of selected vascular hemodynamic parameters using patient-specific values of noninvasively measured physiologic parameters.

[0036] In accordance with one aspect of the invention, a personalized numerical model of an arterial tree may be created to provide a patient-specific estimator of cardiac output for a patient based on noninvasively measured physiologic parameters. The patient-specific estimator, once calibrated, may be used continuously or intermittently to provide CO estimates using physiologic data obtained with inexpensive and readily available monitoring components, such as automatic blood pressure cuffs and pulse sensors.

[0037] More specifically, in one embodiment CO may be accurately estimated using noninvasively obtained patient-specific information, such as blood pressure and pulse wave velocity measurements, to first personalize a numerical arterial tree model, and following such calibration, may be used with subsequently obtained noninvasive measurements to provide updated CO and cSBP values. A generalized one-dimensional (1-D) arterial tree model is personalized using measurements of blood pressure, e.g., brachial systolic and diastolic blood pressure, heart rate (HR), and pulse wave velocity, e.g., carotid-to-femoral pulse wave velocity (cf-PWV) of a patient. A two-layer optimization process is employed calibrate the numerical model with the measured patient data, during which calibration process arterial model parameters are adjusted so that model predictions converge, to within a specified threshold, of the noninvasive patient data. Once the numerical model is calibrated to an initial set of patient data, the patient-specific model may thereafter be used to predict CO and CSBP for subsequent set of noninvasively measured patient physiologic values.

[0038] In accordance with a further aspect of the invention, the above systems and methods may be generalized, in which a one-dimensional cardiovascular model may be trained and calibrated using non-invasively measured and invasively measured physiologic parameter values from a representative patient population. Thereafter, additional values for the non-invasively measurable parameters are synthetically generated for clinically useful physiologic ranges and input to the model to generate additional synthetic values of the unmeasured cardiovascular parameters of interest. Machine learning algorithms then are applied to the synthetic dataset to generate algorithms that correlate the noninvasively measurable patient physiologic parameters to desired vascular hemodynamic parameters heretofore obtainable only via invasive measurements. Once the database and algorithms are created, the system and methods of the present invention may be used to generate real time estimates for key cardiovascular parameters, previously measurable only by invasive techniques, using physiologic data obtained with inexpensive and readily available monitoring components, such as automatic blood pressure cuffs, pulse sensors and conventional ECG systems.

[0039] In accordance with this further aspect of the present invention, methods are provided for accurately estimating selected cardiovascular parameters, including CO, cSBP, Ees, CT, and Zao using noninvasively obtained patient-specific information, such as blood pressure and pulse wave velocity measurements, together with a synthetic database and machine learning algorithms trained on that database. The synthetic database also is generated using the generalized one-dimensional (1-D) arterial tree model calibrated with actual measurements of blood pressure, e.g., brachial systolic and diastolic blood pressure, heart rate (HR), and pulse wave velocity, e.g., carotid-to-femoral pulse wave velocity (cf-PWV) of a patient. In an exemplary embodiment, a two-layer optimization process is employed calibrate the numerical model with the measured patient data, wherein arterial model parameters are iteratively adjusted so that model predictions converge, to within a specified threshold, of the noninvasively measure patient data. Once the numerical model is calibrated, additional values of noninvasively measurable patient physiologic parameters are input to the model to generate additional synthetic estimates to complete the dataset. Machine learning algorithms, including regression and classification are used to analyze the resulting dataset, together with noninvasively measured physiologic values, to generate a model that provides real time estimates for the non-invasively unobservable hemodynamic parameters.

[0040] In a preferred embodiment, four easily obtainable inputs are employed: noninvasive brachial systolic blood pressure (SBP); brachial diastolic blood pressure (DBP); heart rate; and pulse wave velocity (PWV). A measured set of these data may be used to adjust a one dimensional arterial tree model, such as that described in P. Reymond et al. “Validation of a patient specific one-dimensional model of the systemic arterial tree,” Am. J. Physiol. Heart Circ. Physiol., 301(3):H1173-1182 (September 2011), to accurately predict mean flow (i.e., cardiac output) at the aortic root.

[0041] Training and calibration of a generic arterial tree model with clinically relevant noninvasive data is expected to enable generation of clinically accurate absolute values of CO and trends without the cost and complexity of previously-known used CO measurement techniques. PWV is routinely measured in clinical practice and has been identified as an independent predictor of cardiovascular disease, especially when it used in conjunction with pressure measurements. Low cost, readily available sensors, such as a blood pressure cuff and pulse sensors, may be employed to obtain noninvasive physiologic measurements, thereby providing a reduced-cost system, compared to previously known systems such as, e.g., esophageal Doppler, partial carbon dioxide rebreathing, and volume clamping. Additional vascular hemodynamic parameters may be derived from those non-invasive physiologic parameters values, as described herein, thus enabling real time prediction for clinical application of CO and other key cardiovascular parameters.

[0042] Referring now to FIG. 1, exemplary system 100 is described for noninvasively estimating CO of a patient, and optionally, additional parameters including cSBP, Ees, CT and Zao. System 100 includes one or more sensors, e.g., pulse sensors 102 and 104, blood pressure cuff 106, optional ECG system 108 and heart sound detector 110, e.g., a stethoscope, and console 200. Console 200 receives the output from sensors 102, 104, cuff 106, and optionally, ECG system 108 and from a clinician who inputs certain data determined using stethoscope 110. Console 200 is programmed with software that analyzes the input data and executes the inventive estimator algorithms. The one or more sensors are operatively coupled to console 200 via cables or alternatively, via wireless transmission.

[0043] In one preferred embodiment, pulse sensor 102 is an accelerometer configured to be located on the patient's skin in the vicinity of a carotid artery, while pulse sensor 104 is an accelerometer configured to be located in the vicinity of a femoral artery. Each of pulse sensors 102 and 104 may be disposed on a patch that includes a biocompatible adhesive for securing the patch to the patient's skin in. Blood flow pulse detected by pulse sensors 102 and 104 during the cardiac cycle are transmitted to console 200, where that information is used to determine the time for an arterial pulse to propagate from the carotid to the femoral artery, referred to herein as the “carotid to femoral pressure wave velocity” or “cf-PWV”. Pulse sensors 102 and 104 may be connected to console 200 via electrical leads, or alternatively may be coupled to a transmitter that sends the measured outputs of the accelerometers to console 200 wirelessly, e.g., via transmitters that comply with Bluetooth or IEEE 802.11 standards. In alternative embodiments, pulse sensors 102 and 104 may comprise vibrometers, optical sensors, or tonometer or Doppler-based sensors.

[0044] Blood pressure cuff 106 may comprise an automated blood pressure cuff configured to be disposed on a patient's arm, e.g., a commercial oscillometric cuff, and measures brachial systolic blood pressure (SBP) and brachial diastolic blood pressure (DBP). Data output by cuff 106 are transmitted to console 200 for processing via electrical leads or wirelessly. As will be understood, cuff 106 does not provide continuous pressure readings, but only at periodic intervals set using the cuff controller (not shown) or console 200.

[0045] As further discussed below, for prediction of certain cardiovascular parameters, the output of heart sound detector 110 and EKG system 108 may be required. Heart sound detector 110 may be a conventional acoustic or electronic stethoscope, by which a clinician determines certain heart sounds corresponding to cardiac valve events, as described below, the occurrence of which the clinician inputs to console 200 via an input device. Alternatively, as will be understood by one of skill in the art, an automated system may be employed for electronically detecting heart, the output of which is provided directly to console 200 without clinician intervention. ECG system 110 may be a conventional ECG multi-lead system, preferably 5 to 12 leads, and generates an electrocardiograph waveform that is input to console 200.

[0046] Console 200 may be programmed to output values of estimated real time cardiovascular parameters to a video display or to graphical plotter, to transmit such estimated values to a central monitoring system or nursing station, to generate a report, and/or to monitor trends in estimated values and to generate alarms or notifications if one or more estimated values falls below clinically acceptable levels.

[0047] Exemplary hardware and software components of console 200 are now described with respect to FIG. 2. Console 200 includes a computer, e.g., laptop, desktop, or tablet that is programmed with the inventive estimator software as described herein, and includes at least one processor 202, memory 204, non-volatile storage 214, transceiver 206, power source 208, and one or more input devices 210 and output devices 212.

[0048] Processor 202 may be a conventional multi-core processor, such as an Intel CORE i5 or i7 processor. Memory 204 may comprises volatile (e.g. random-access memory (RAM)), non-volatile (e.g. read-only memory (ROM)), flash memory, or any combination thereof. Transceiver 206 may receive and/or transmit information to and from other components in system 100 including pulse sensors 102 and 104, cuff 106, and optional heart sound detector 108 and ECG system 110, using any well-known communication infrastructure facilitating communication over wired or wireless connection, such as any IEEE 802 standard. Power source 208 preferably connects to a standard wall outlet and/or may include a battery. Non-volatile storage 214 preferably includes removable and/or non-removable storage, such as, solid-state disk memory of magnetic hard drive.

[0049] Input device 210 may be one or more devices coupled to, or integrated into, console 200 for inputting data to the console, and may include, for example, a keyboard or touchscreen, a mouse and/or a pen. Input device 210 may be used to input patient specific information into the estimator, e.g., height, age, weight, gender, and identity, and/or to modify the sampling rate of pulse sensors 102 and 104, the frequency with which pressure measurements are taken with cuff 106, or the sampling of the outputs of ECG system 108 or heart sound detector 110. Output device 212 may be any suitable device coupled to or integrated into console 200 for outputting or otherwise displaying data, such as video screen, printer or plotter. Output device 212, further may include a speaker or alarm bell that may be activated if one or more of the monitored estimated parameter values falls below a clinically significant threshold indicating patient distress.

[0050] Still referring to FIG. 2, operating system 216 and estimator module 218 are stored in non-volatile storage 214. Operating system 216 includes the operating system for console, e.g., Microsoft Windows or Linux, as well as the necessary drivers for the input and output devices. Estimator module 218 may be personalized for a specific patient, or in an alternative embodiment may include machine learning and search algorithms for analyzing the input patient-specific values and optional composite dataset or database 220 to generate real-time values for CO, cSBP, Ees, CT and Zao. Estimator module 218 also may include programming for communicating with and adjusting the input sampling rates for inputs received from pulse sensors 102 and 104, cuff 106, ECG system 108 and heart sound detector 110, and further for generating output to be displayed on output device 212.

[0051] Estimator module 218 includes programmed instructions that enable generation of a patient-specific estimator by personalizing a generic arterial tree model using noninvasively physiologic patient data measurements. Specifically, the estimator module may employ a two-layer optimization algorithm for personalizing a generic 1-D arterial tree model using noninvasively-measured patient physiologic data, which thereafter may be used to estimate CO and other parameters for a range of measured data values for that specific patient.

[0052] Referring to FIG. 3, an exemplary, generic one dimensional arterial tree model, such as that described in P. Reymond, et al., “Validation of a one-dimensional model of the systemic arterial tree,” Am. J. Physiol. Heart Circ. Physiol., 297(1):H208-222 (July 2009), is trained and calibrated with data from a single patient to generate a patient-specific estimator. Alternatively, the estimator may be trained on patient data for a representative patient population, and the model then used to generate synthetic data that is analyzed with machine learning algorithms. That arterial tree model describes the fluid dynamic characteristics of the main arteries of systemic circulation, and includes a detailed representation of the cerebral circulation and the coronary circulation networks. The governing equations of the model are obtained by integration of longitudinal momentum and continuity of the Navier-Stokes equations over the arterial cross sections.

[0053] Propagations of pressure and flow waves throughout the vasculature are obtained by solving the governing equations using an implicit finite-difference scheme, in which the arterial segments are modeled as long tapered tubes having compliances defined by a nonlinear function of pressure and location. In the model, arterial wall behavior is considered nonlinear and viscoelastic, and local arterial compliance is calculated after approximating pulse wave velocity (PWV) as an inverse power function of arterial lumen diameter, using the measured physiologic values. Distal vessels of the model are terminated with three-element Windkessel models, and resistance of the peripheral vasculature is accounted for by coupling distant vessels with three-element Windkessel models. As input, the arterial tree receives either a prescribed input aortic flow waveform or is coupled with a time-varying elastance model to simulate contractility of the left ventricle.

[0054] For a given set of values of peripheral SBP and DBP, HR, and cf-PWV, solving the arterial tree model generates a single corresponding value of CO and cSBP, assuming other model parameters are constrained within the range of physiologically possible values. Thus, by simultaneously adjusting such properties/variables of the model and specifying input aortic blood flow to capture a given peripheral (brachial) pressure and cf-PWV, an estimator may be generated that is specifically calibrated for an individual patient. Once that initial calibration of the estimator is completed, the estimator may be used to generate additional values of CO over a range of clinically useful values of the measured physiologic values for that specific patient. Alternatively, in accordance with another aspect of the present invention, the estimator may be trained and calibrated over measure data from a representative patient population. In this case, machine learning may be employed to correlate datasets output by the model with additional non-invasively measurable patient physiologic data to derive estimated values for other cardiovascular parameters, including Ees, CT and Zao.

[0055] The inter-subject variability of arterial trees with respect to arterial compliance, total peripheral resistance, and geometry requires fine-tuning of the generic 1-D arterial model. For example, distensibility of each arterial segment may be modified in a uniform way for young individuals whereas, for older or hypertensive subjects, distensibility may be modeled as non-uniform, with more pronounced stiffening in the proximal aortic path. Data for age-related local non-uniform aortic stiffening and its effects on central circulatory hemodynamics and wave reflections are available from the scientific literature, and such data preferably are used in the arterial model to provide physiologic constraints on potential parameter ranges. Similarly, resistance may be altered in a uniform way for all terminal vessels in the model, and the geometry of the arterial vessels, i.e., diameter and length, may be assumed to be unchanged for the different individuals. Depending upon the specific implementation, such parameters may be adjusted within physiologic ranges in an iterative process to obtain a CO and cSBP solution consistent with the input measured patient values.

[0056] Still referring to FIG. 3, exemplary two-layer optimization algorithm 300 is described for calibrating the generic arterial tree model to provide a patient-specific CO and cSBP estimator. As noted above, potential ranges for physiologic parameters are adjusted while iteratively to solve the model with measured patient-specific physiologic data. To initialize the model with appropriate ranges, for example, for distensibility and resistance of peripheral vessels, the clinician may input, using input devices 210, certain static patient data, such as gender, age, body mass index or weight, and/or whether the patient has any known illnesses that affect cardiovascular health, such as diabetes, hypertension or atherosclerosis. In one embodiment, the estimator may include empirically derived equations that use such static input data to compute an initial aortic flow, indicated at 301 in FIG. 3. Alternatively, an arbitrary value of initial aortic flow may be used, which obviates the need for static input data but may require additional iterations to reach convergence.

[0057] In a first optimization loop, diastolic and systolic blood pressure values are computed using the initial aortic flow value 301 using the arterial tree model at block 302, and the computed values are compared to the values of DBP and SBP measured using cuff 106 at decision block 303. If the difference between the computed and measured values exceed a first predetermined threshold value, the distensibility and resistance characteristics of the arterial tree model are adjusted at block 304, and new values for DBP and SBP are computed along pathway 305 and block 302 until the difference between computed and measured values of DBP and SBP are less than the first predetermined threshold. Once the difference is less than the first threshold value, the first optimization loop is adjudged to have converged.

[0058] Once the computed values of DBP and SBP are judged to converge at block 303, a computed cf-PWV value is calculated analytically based on the compliance of each arterial segment in the carotid-femoral pathway. The Estimator then compares the computed cf-PWV value, at decision block 306, to the value of the carotid to femoral pressure wave determined by processing the outputs transmitted to console 200 by pulse sensors 102 and 104. If the difference between computed cf-PWV and the measured cf-PWV exceeds a second predetermined threshold, the stroke volume, i.e., the volume of blood ejected from each ventricle due to contraction of the ventricles, is adjusted at block 307 and the arterial tree model is again solved along path 308. At step 302, arterial model 302 again recalculates all pressures and flows throughout the arterial tree by repeating the first optimization loop, along path 305, to confirm that the difference between the computed to values of SBP and DBP are less than the first predetermined threshold from the measured values. Next, the computed value of cf-PWV is computed to the measured value generated from the outputs of pulse sensors 102 and 104, and the process repeats with further adjustment to the stroke volume at block 307, until the difference between the computed and measured values of cf-PWV are less than the second predetermined threshold. Once that difference is less than the second predetermined threshold, the second optimization loop is adjudged to be converged, thereby establishing a patient-specific estimator, block 309. Patient-specific estimates of the stroke volume and cSBP are provided by the patient-specific estimator. The estimated CO is determined by multiplying the stroke volume by the patient's measured heart rate (HR), as may be provided by cuff 106.

[0059] In a preferred embodiment, the first and second optimization loops may use a gradient descent approach for scaling the values of vascular compliance and resistance of the generic arterial tree model at block 304 and for adjusting the stroke volume at block 307. For example, scaling factors may be chosen so that a range of 0.1 to 3.8 mL/mmHg and 0.4 to 0.2 mmHg s/mL is covered for compliance and resistance, respectively. These limits are chosen so that the pressure values generated by the arterial tree model correspond to physiologically acceptable hemodynamic conditions. The SV scaling factors may be chosen so as the corresponding cardiac output is within the physiological range of 2 to 8 L/min. Different gradient algorithms may be used for the first and second optimization loops. And as will be understood by those familiar with finite-difference programming, alternative approaches also may be used to scale parameters, including non-gradient approaches, so long as the resulting adjustments remain within the range of physiologically acceptable hemodynamic conditions.

[0060] The two optimization loops run continuously until convergence is attained for both computed brachial SBP and DBP and computed cf-PWV. The first and second predetermined thresholds may tolerate different degrees of error, for example, the threshold for converging on brachial SBP and DBP values may be set to 0.001%, while the threshold for converging on cf-PWV may be set to 0.01%. The estimator also may include a maximum number of iterations for each optimization loop, e.g., 25, which maximum number of iterations may be different for the first and second optimization loops. If convergence on the measured parameters is not obtained when the maximum number of iterations is reached, a new value of aortic flow input may be selected at block 301, and the entire process repeated. Once the convergence is achieved for both optimization loops, the values of the distensibility and resistance are stored in memory 204, and used as the initial values for computing subsequent values of CO and cSBP responsive to changes in further measured values of DBP, SBP, cf-PWV and HR. At this point, the converged estimator may be used as a patient-specific CO and cSBP estimator for measured values of the non-invasively measured parameters.

[0061] In one embodiment, console 200 may be programmed to output patient-specific values of estimated CO and estimated cSBP to a video display or to graphical plotter, to transmit such estimated values of CO and cSBP to a central monitoring system or nursing station, to generate a report, and/or to monitor trends in estimated CO and estimated cSBP and to generate alarms or notifications if the estimated CO and estimated cSBP falls below clinically acceptable levels.

[0062] FIGS. 4A and 4B are graphs showing the results achieved by the estimator of the present invention compared to previously known CO measurements obtained with a standard reference method, two-dimensional (2-D) echocardiography, for a population of 80 adults. The study population included subjects with risk factors including, e.g., smoking, diabetes, hypertension, dyslipidemia, renal disease, cardiovascular disease, stroke, or those receiving medication.

[0063] In particular, FIG. 4A is a scatter-plot of computed CO estimates compared to in vivo measurements using the reference method, wherein the solid and dashed lines, respectively, represent equality and linear regression. FIG. 4B is the corresponding Bland-Altman plot for the same data presented in FIG. 4A, and indicates that most of CO estimates fall within +/− two standard deviations. Limits of agreement are defined by the two horizontal dotted lines.

[0064] The root mean square error (RMSE) for the estimated CO was about 0.48 L/min. In 70% of the cases, the difference between estimated CO and measured (reference) CO was below 0.5 L/min, and for 48% of the cases, the difference was below 0.35 L/min A low bias of −0.09 L/min was observed and variability of difference was found to be ±0.47 L/min, p<0.0001. Parameters of accuracy, correlation, and agreement of CO estimation by the method in comparison to the reference method are summarized in the Table 1 below.

TABLE-US-00001 TABLE 1 Parameter Value Mean difference (L/min) −0.09 Standard deviation of difference (L/min) 0.47 Limits of Agreement (L/min) [−1.02, 0.83] Normalized root mean square error (%) 12.01 Pearson's correlation coefficient 0.82 Interclass correlation coefficient 0.81

[0065] As discussed above, the foregoing 1-dimensional model also may be used to determine cSBP. More specifically, central systolic pressure (cSBP) may be derived for the cardiovascular model discussed above when tuned to patient-specific standards. Successful tuning of the generic one-dimensional tree using brachial systolic blood pressure (brSBP), diastolic blood pressure (brDBP), heart rate (HR), and carotid-to-femoral pulse wave velocity (cfPWV) provides patient specific cardiac output (CO) and cSBP. Results of the preclinical evaluation of the cSBP estimation compared to reference values of cSBP determined by previously known methods are provided in FIGS. 5A and 5B.

[0066] FIG. 5A is a scatterplot showing correspondence between noninvasive cSBP predictions determined using a tuned 1-Dimensional model versus in vivo measurements. The model yielded an accurate estimation of cSBP, with a root-mean-square error of 2.46 mm Hg and a Pearson's correlation coefficient of 0.98. FIG. 5B is depicts the Bland-Altman analysis, showing good agreement between the model and the reference cSBP values. In particular, the difference between estimated-cSBP and reference cSBP was less than 1.5 mmHg in 30% of the cases, ranged between 1.5 and 3.5 mm Hg for 60% of the cases, and exceeded the 3.5 mm Hg for only 10% of cases. Parameters of precision, correlation and agreement between the estimates and the actual values are shown in Table 2.

TABLE-US-00002 TABLE 2 Parameter Value Mean difference (mmHg) −0.27 Standard deviation of difference (mmHg) 2.51 Root mean square error (mmHg) 2.46 Pearson's correlation coefficient 0.98

[0067] Further in accordance with the principles of the invention, methods of providing estimates ventricular end-systolic elastance (Ees), arterial compliance (CT) and aortic impedance (Zao) are provided. This aspect of the invention does not make use of the inverse problem-solving approach discussed above, but instead relies on the machine learning models. In particular, Ees, CT, and Zao may be derived from noninvasive clinical measurements that are readily available in clinical practice using regression analysis, based on a training/testing scheme using synthetic data generated from the tuned cardiovascular model discussed above.

[0068] Using reported values of key hemodynamic values available in the literature, synthetically generated datasets were created for a generalized study population. Synthetic datasets provide a reliable and cost-effective way to correct for gaps in reference data and provide a well-balanced dataset. In one embodiment, a database of 6000 synthetic hemodynamics cases was created. In one embodiment, the 1-Dimensional cardiovascular model was run using an arbitrary but physiological set of input model parameters. Thus, instead of input data for the model coming from a patient, the model is run with an arbitrary, but clinically relevant, parameter set. For one embodiment, the input parameters of the 1-D cardiovascular model were altered by multiplying input values with different scaling factors.

[0069] For example, end-systolic and end-diastolic elastance varied in the range of 1.00-3.50 and 0.05-0.20 mmHg/mL, respectively, based on reported values for these parameters as reported, for example, in C. H. Chen, M. Nakayama, E. Nevo, B. J. Fetics, W. L. Maughan, and D. A. Kass, “Coupled systolic-ventricular and vascular stiffening with age,” Journal of the American College of Cardiology, vol. 32, no. 5, pp. 1221-1227, November 1998, M. D. Feldman et al., “Acute Cardiovascular Effects of OPC-18790 in Patients With Congestive Heart Failure: Time- and Dose-Dependence Analysis Based on Pressure-Volume Relations,” Circulation, vol. 93, no. 3, pp. 474-483, Feb. 1996 and P. H. Pak, W. L. Maughan, K. L. Baughman, R. S. Kieval, and D. A. Kass, “Mechanism of Acute Mechanical Benefit From VDD Pacing in Hypertrophied Heart: Similarity of Responses in Hypertrophic Cardiomyopathy and Hypertensive Heart Disease,” Circulation, vol. 98, no. 3, pp. 242-248, July 1998.

[0070] In addition, filling pressures in a range of 7.00 — 23.00 mmHg were used, as reported in C. H. Chen et al., “Noninvasive single-beat determination of left ventricular end-systolic elastance in humans,” J. Am. Coll. Cardiol., vol. 38, no. 7, pp. 2028-2034, December 2001. The dead volume (V.sub.d) and the time of maximal elastance were kept unchanged and equal to the average values of V.sub.d=15.00 mL and t.sub.max=340.00 ms, as reported in P. Reymond, F. Merenda, F. Perren, D. Rüfenacht, and N. Stergiopulos, “Validation of a one-dimensional model of the systemic arterial tree,” Am. J. Physiol. Heart Circ. Physiol., vol. 297, no. 1, pp. H208-222, July 2009 and M. R. Starling, R. A. Walsh, L. J. Dell'Italia, G. B. Mancini, J. C. Lasher, and J. L. Lancaster, “The relationship of various measures of end-systole to left ventricular maximum time-varying elastance in man.,” Circulation, vol. 76, no. 1, pp. 32-43, July 1987. The value of heart rate (HR) was varied between 60 and 100 bpm.

[0071] Arterial geometry was varied by adapting the height of the arterial tree, while the diameter of each arterial segment was modified uniformly to simulate different body types. The heights covered a range of 150 to 200 cm, while limits for aortic diameter of 1.90 to 4.00 cm were employed. Total peripheral resistance varied from 0.50 to 2.00 mm Hg.s/mL Total arterial compliance was chosen so that a range of 0.10 to 3.80 mL/mmHg was covered. The foregoing values correspond to an extensive range of arterial tree stiffness values, as reported in G. J. Langewouters, Visco-elasticity of the Human Aorta in Vitro in Relation to Pressure and Age. 1982 and P. Segers et al., “Three- and four-element Windkessel models: assessment of their fitting performance in a large cohort of healthy middle-aged individuals,” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine.

[0072] Synthetic values for noninvasively measurable parameters, such brachial systolic blood pressure (brSBP), brachial diastolic blood pressure (brDBP) and heart rate (HR) data were generated as inputs. brSBP and brDBP correspond to pressures measured at the left brachial artery using a conventional blood pressure cuff.

[0073] The carotid to femoral pressure wave velocity (CfPWV) was derived using the tangential method described in O. Vardoulis, T. G. Papaioannou, and N. Stergiopulos, “Validation of a novel and existing algorithms for the estimation of pulse transit time: advancing the accuracy in pulse wave velocity measurement,” American Journal of Physiology-Heart and Circulatory Physiology, vol. 304, no. 11, pp. H1558—H1567, June 2013. That method uses the intersection point of two tangents on the arterial pressure wave as a characteristic marker. The first tangent is defined as the line that passes tangentially through the initial systolic upstroke, i.e., the maximum of the first derivative. The second tangent line is the horizontal line passing through the minimum pressure point.

[0074] In the context of the analysis performed to generate the synthetic dataset, the method was applied to estimate the pulse transit time (PTT) between the synthetic “measured” carotid artery pressure and the synthetic “measured” femoral artery pressure, and between the synthetic “measured” carotid artery pressure and the synthetic “measured” radial artery pressure. Total aortic length was determined by summing the lengths of the arterial segments within the transmission paths. Consequently, the values of cfPWV and crPWV were calculated by dividing the respective total length by the respective PTT. In clinical practice, the same method is used to estimate cfPWV and crPWV, however, with the total arterial length of the transmission paths being approximated as, e.g., 80% of the measured distance between the two arterial sites.

[0075] In addition, the time of the aortic valve closure was derived as the dicrotic notch point of the aortic blood pressure wave, as depicted in FIG. 6A. The pre-ejection time (PEP) is defined as the period between onset of ventricular contraction and when the aortic valve opens, which includes excitation-contraction coupling (or electromechanical dissociation EMD) and isovolumic contractions (ICT). FIG. 6B, reproduced from T. Shishido, K. Hayashi, K. Shigemi, T. Sato, M. Sugimachi, and K. Sunagawa, “Single-beat estimation of end-systolic elastance using bilinearly approximated time-varying elastance curve.,” Circulation, vol. 102, no. 16, pp. 1983-1989, October 2000, illustrates that for known left ventricular elastance, PEP can be derived by subtracting the time of end-diastolic elastance, t.sub.ed, from the time at the end of the isovolumic contraction phase, t.sub.ad. Left-ventricular Ejection time (LVET) then may be obtained by subtracting t.sub.ad from the time of end-systolic elastance, t.sub.es. As illustrated in FIG. 6C, the sum of PEP and LVET, also referred to as the Q-Ac period, also may be derived using clinically observable data, as the time duration between the beginning of the Q-wave appearing on a patient's ECG, and the time point when the aortic valve closes, as may be determined from a heart sound detector or stethoscope.

[0076] All simulated information generated using the tuned 1-dimensional model then was discarded, except the synthetically generated values of the measurable input parameters: brSBP, brDBP, HR, cfPWV, crPWV, and Q-Ac period and the corresponding output values for cSBP, CO, Ees, CT, and Zao. The total dataset, organized in pairs of inputs and outputs, was divided into a training set and a testing set and 10-fold cross-validation was performed. In 10-fold cross validation, all subjects were randomly divided into 10 equal sets. One set was retained as a validation group to validate the methods, and the other nine sets were used as a training group to tune the parameters of the machine-learning model. This process was iterated 10 times, so that all synthetic patient groups appeared once in all validation groups. The outputs of the testing set were blinded and reserved as de facto accurate for later comparison. The synthetic data then were corrupted with random Gaussian noise in order to represent a more realistic data collection, as suggested in J. Liu, H.-M. Cheng, C. H. Chen, S. H. Sung, J. O. Hahn, and R. Mukkamala, “Patient-Specific Oscillometric Blood Pressure Measurement: Validation for Accuracy and Repeatability,” IEEE J Transl Eng Health Med, vol. 5, p. 1900110, 2017.

[0077] After generation of the synthetic dataset, a regression model was trained and tested to estimate the corresponding targets for the subject under consideration. By definition, the regressor (namely, the machine learning model) involved the following components: (i) the unknown parameters, β, (ii) the independent variables, Xi, and (iii) the dependent variable, Yi. In one preferred embodiment, the aim of the analysis was to investigate if the regressors f.sub.i can estimate the values of Ees, CT, and Zao for each subject from the input predictors (brSBP, brDBP, HR, cfPWV, crPWV, PEP, LVET), i.e.,

Y.sub.i≈f.sub.i(X;β), i∈{E.sub.es, CT, Zao}

[0078] FIG. 7 schematically depicts the method in which the regression analysis was performed in an exemplary embodiment, which 9 of the 10 groups of data were used to train the regression model and the input values for the remaining tenth group was used to test the accuracy of the regression model in predicting the output values for the tenth group. Results obtained from the machine learning analysis of the data is described herein below.

[0079] End Systolic Elastance (Ees) was predicted from input values of brSBP, brDBP, HR, and the sum of PEP and LVET. As noted above, the sum of PEP and LVET may be derived clinically as the time duration between the beginning of the Q-wave (as observed on the ECG) and the time point when the aortic valve closes (as determined by the heart sound detector or stethoscope). The sum was used, as opposed to separate estimations for PEP and LVET, because the separate time periods cannot be easily derived in a real clinical setting. Regression analysis as described in J. H. Friedman, “Greedy Function Approximation: A Gradient Boosting Machine,” IMS Reitz Lecture (1999), available online at: https://statweb.stanford.edu/˜jhf/ftp/trebst.pdf was employed.

[0080] FIGS. 8A and 8B present, respectively, a comparison of the model Ees estimates to the reference Ees values and the corresponding Bland-Altman plot. Parameters of accuracy, correlation and agreement between the estimates and the actual values are shown in Table 3.

TABLE-US-00003 TABLE 3 Parameter Value Mean difference (mmHg/mL) −0.003 Standard deviation of difference (mmHg/mL) 0.052 Normalized root mean square error (%) 5.84 Pearson's correlation coefficient 0.95

[0081] Total arterial compliance (CT) and aortic input impedance (Zao) were predicted from input values for brSBP, brDBP, cfPWV, crPWV, HR, and Q-Ac period by employing regression analysis. In one embodiment, the CART machine learning algorithm described in A. Liaw and M.E.A. Wiener, “Classification and regression by randomForest,” RNews 2:18-22 (2002), available online at: http://cogns.northwestern.ed/cbmg/LiawAndWiener2002.pdf was employed.

[0082] FIGS. 9A and 9B present, respectively, a comparison of the model CT estimates to the reference CT and the corresponding Bland-Altman plot. Parameters of accuracy, correlation and agreement between the estimates and the actual values are shown in Table 4.

TABLE-US-00004 TABLE 4 Parameter Value Mean difference (mL/mmHg) −0.0004 Standard deviation of difference (mL/mmHg) 0.076 Normalized root mean square error (%) 5.14 Pearson's correlation coefficient 0.99

[0083] FIGS. 10A and 10B present, respectively, a comparison of the model Zao estimates to the reference Zao and the corresponding Bland-Altman plot. Parameters of accuracy, correlation and agreement between the estimates and the actual values are shown in Table 5.

TABLE-US-00005 TABLE 5 Parameter Value Mean difference (mmHg .Math. sec/mL) −0.000 Standard deviation of difference (mmHg .Math. sec/mL) 0.003 Normalized root mean square error (%) 6.49 Pearson's correlation coefficient 0.93

[0084] In an exemplary embodiment of the system of the present invention, the algorithm for adjusting the cardiovascular model and the machine learning models is embedded in Estimator Module 218 of console 200. The inputs required for predicting CO, cSBP, Ees, CT, and Zao, as described above, include brSBP, brDBP, HR, cfPWV, crPWV, and Q-Ac period. A conventional cuff may be used to acquire brachial pressure and HR.

[0085] CfPWV is determined from the time taken for the arterial pulse to propagate from the carotid to the femoral artery, whereas crPWV is determined from the time taken for the arterial pulse to propagate from the carotid to the radial artery. Values for cfPWV and crPWV may be computed using the outputs of three pulse sensors placed at the carotid, radial, and femoral arteries, which measure the respective arterial pulsation signals at each location. As depicted in FIG. 1, these pulse sensors may be embodied in three patches that are placed at the three arterial sites to capture signals simultaneously; the propagation times and PWVs are derived from the measured arterial pulsation signals.

[0086] Finally, the Q-AC period may be extracted using the electrocardiogram (ECG)) and an automated heart sound detector, or alternatively, a clinician using a conventional stethoscope. The heart sound detector provided the time when aortic valve closes (the second acoustic beat) with respect to the initiation of the Q-wave (observed from the ECG waveform). This data is then transmitted to console 200 running Estimator Module 218, which in turn computes CO, cSBP, Ees, CT, and Zao.

[0087] Advantageously, the system of the present invention enables the use of low-cost, readily available sensors and computer hardware with an arterial tree model of systemic circulation yields accurate estimates of CO when personalized with patient-specific noninvasive measurements of peripheral blood pressure and cf-PWV. In vivo validation of the inventive system and method demonstrates that is provides clinically acceptable estimates for CO and other key cardiovascular parameters using only patient-specific noninvasive measurements for a variety of patient conditions and age groups. As further described above, the inventive system and methods further may be augmented to provide a complete system for estimating central aortic and cardiac parameters, i.e., CO, cSBP, Ees, CT, and Zao, using inverse problem-solving techniques and machine learning models, with good accuracy and specificity for all parameters of interest.

[0088] It should be understood that the embodiments described herein are illustrative, and components may be arranged, substituted, combined, and designed in a wide variety of different configurations, all of which are contemplated and fall within the scope of this disclosure. Accordingly, the foregoing description of illustrative embodiments has been presented for purposes of illustration and of description. It is not intended to be exhaustive or limiting with respect to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the disclosed embodiments. It is intended that the scope of the invention be defined by the claims.