Improved pulse wave velocity estimation using an arterial tube-load model

Physics-Informed Neural Networks for Modeling Physiological Time Series: A Case Study with Continuous Blood Pressure

The bold vision of AI-driven pervasive physiological monitoring, through the proliferation of off-the-shelf wearables that began a decade ago, has created immense opportunities to extract actionable information for precision medicine. These AI algorithms model the input-output relationships of a system that, in many cases, exhibits complex nature and personalization requirements. A particular example is cuffless blood pressure estimation using wearable bioimpedance. However, these algorithms need to be trained with a significant amount of ground truth data. In the context of biomedical applications, collecting ground truth data, particularly at the personalized level is challenging, burdensome, and in some cases infeasible. Our objective is to establish physics-informed neural network (PINN) models for physiological time series data that would reduce reliance on ground truth information. We achieve this by building Taylor's approximation for the gradually changing known cardiovascular relationships between input and output (e.g., sensor measurements to blood pressure) and incorporating this approximation into our proposed neural network training. The effectiveness of the framework is demonstrated through a case study: continuous cuffless BP estimation from time series bioimpedance data. We show that by using PINNs over the state-of-the-art time series regression models tested on the same datasets, we retain a high correlation (systolic: 0.90, diastolic: 0.89) and low error (systolic: 1.3 ± 7.6 mmHg, diastolic: 0.6 ± 6.4 mmHg) while reducing the amount of ground truth training data on average by a factor of 15. This could be helpful in developing future AI algorithms to help interpret pervasive physiologic data using minimal amount of training data.

Improving the accuracy and robustness of carotid-femoral pulse wave velocity measurement using a simplified tube-load model

Arterial stiffness, as measured by pulse wave velocity, for the early non-invasive screening of cardiovascular disease is becoming ever more widely used and is an independent prognostic indicator for a variety of pathologies including arteriosclerosis. Carotid-femoral pulse wave velocity (cfPWV) is regarded as the gold standard for aortic stiffness. Existing algorithms for cfPWV estimation have been shown to have good repeatability and accuracy, however, further assessment is needed, especially when signal quality is compromised. We propose a method for calculating cfPWV based on a simplified tube-load model, which allows for the propagation and reflection of the pulse wave. In-vivo cfPWV measurements from 57 subjects and numerical cfPWV data based on a one-dimensional model were used to assess the method and its performance was compared to three other existing approaches (waveform matching, intersecting tangent, and cross-correlation). The cfPWV calculated using the simplified tube-load model had better repeatability than the other methods (Intra-group Correlation Coefficient, ICC = 0.985). The model was also more accurate than other methods (deviation, 0.13 ms⁻¹) and was more robust when dealing with noisy signals. We conclude that the determination of cfPWV based on the proposed model can accurately and robustly evaluate arterial stiffness.

Tapered vs. Uniform Tube-Load Modeling of Blood Pressure Wave Propagation in Human Aorta

In this paper, tapered vs. uniform tube-load models are comparatively investigated as mathematical representation for blood pressure (BP) wave propagation in human aorta. The relationship between the aortic inlet and outlet BP waves was formulated based on the exponentially tapered and uniform tube-load models. Then, the validity of the two tube-load models was comparatively investigated by fitting them to the experimental aortic and femoral BP waveform signals collected from 13 coronary artery bypass graft surgery patients. The two tube-load models showed comparable goodness of fit: (i) the root-mean-squared error (RMSE) was 3.3+/−1.1 mmHg in the tapered tube-load model and 3.4+/−1.1 mmHg in the uniform tube-load model; and (ii) the correlation was r = 0.98+/−0.02 in the tapered tube-load model and r = 0.98+/−0.01 mmHg in the uniform tube-load model. They also exhibited frequency responses comparable to the non-parametric frequency response derived from the aortic and femoral BP waveforms in most patients. Hence, the uniform tube-load model was superior to its tapered counterpart in terms of the Akaike Information Criterion (AIC). In general, the tapered tube-load model yielded the degree of tapering smaller than what is physiologically relevant: the aortic inlet-outlet radius ratio was estimated as 1.5 on the average, which was smaller than the anatomically plausible typical radius ratio of 3.5 between the ascending aorta and femoral artery. When the tapering ratio was restricted to the vicinity of the anatomically plausible typical value, the exponentially tapered tube-load model tended to underperform the uniform tube-load model (RMSE: 3.9+/−1.1 mmHg; r = 0.97+/−0.02). It was concluded that the uniform tube-load model may be more robust and thus preferred as the representation for BP wave propagation in human aorta; compared to the uniform tube-load model, the exponentially tapered tube-load model may not provide valid physiological insight on the aortic tapering, and its efficacy on the goodness of fit may be only marginal.

Estimation of echocardiogram parameters with the aid of impedance cardiography and artificial neural networks

The advent of cardiovascular diseases as a disease of mass catastrophy, in recent years is alarming. It is expected to spread as an epidemic by 2030. Present methods of determining the health of one's heart include doppler based echocardiogram, MDCT (Multi Detector Computed Tomography), among various other invasive and non-invasive hemodynamic monitoring techniques. These methods require expert supervision and costly clinical set-ups, and cannot be employed by a common individual to perform a self diagnosis of one's cardiac health, unassisted. In this work, the authors propose a novel methodology using impedance cardiography (ICG), for the determination of a person's cardio-vascular health. The recorded ICG signal helps in extraction of features which are used for estimating parameters for cardiac health monitoring. The proposed methodology with the aid of artificial neural network is able to determine Stroke Volume (SV), Left Ventricular End Systolic Volume (LVESV), Left Ventricular End Diastolic Volume (LVEDV), Left Ventricular Ejection Fraction (LVEF), Iso Volumetric Contraction Time (IVCT), Iso Volumetric Relaxation Time (IVRT), Left Ventricular Ejection Time (LVET), Total Systolic Time (TST), Total Diastolic Time (TDT), and Myocardial Performance Index (MPI), with error margins of ±8.9%, ±3.8%, ±1.4%, ±7.8%, ±16.0%, ±9.0%, ±9.7%, ±6.9%, ±6.2%, and ±0.9%, respectively. The proposed methodology could be used in screening of precursors to cardiac ailments, and to keep a check on the cardio-vascular health.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

Estimation of Pulse Transit Time From Radial Pressure Waveform Alone by Artificial Neural Network

OBJECTIVE

To validate the feasibility of the estimation of pulse transit time (PTT) by artificial neural network (ANN) from radial pressure waveform alone.

METHODS

A cascade ANN with ten-fold cross validation was applied to invasively and simultaneously recorded aortic and radial pressure waveforms during rest and nitroglycerin infusion () for the estimation of mean and beat-to-beat PTT. The results of the ANN models were compared to a multiple linear regression (LR) model when the features of radial arterial pressure waveform in time and frequency domains were used as the predictors of the models.

RESULTS

For the estimation of mean PTT and beat-to-beat PTT by ANN ( ), the correlation coefficient between the and the measured PTT () (mean: ; beat-to-beat: ) is higher than that between the PTT estimated by LR ( ) and (mean: ; beat-to-beat: ). The standard deviation (SD) of the difference between the and ( ; beat-to-beat: ) is significantly less than that between the and (; beat-to-beat: 10 ms), but no significant difference exists between their mean ( ). The lack of frequency features of radial pressure waveform caused obvious reduction in the correlation coefficient and SD of the difference between the and . The performance of the ANN was improved by increasing the sample number but not by increasing the neuron number.

CONCLUSION

ANN is a potential method of PTT estimation from a single pressure measurement at radial artery.

Comparison of noninvasive pulse transit time estimates as markers of blood pressure using invasive pulse transit time measurements as a reference

Pulse transit time (PTT) measured as the time delay between invasive proximal and distal blood pressure (BP) or flow waveforms (invasive PTT [I-PTT]) tightly correlates with BP PTT estimated as the time delay between noninvasive proximal and distal arterial waveforms could therefore permit cuff-less BP monitoring. A popular noninvasive PTT estimate for this application is the time delay between ECG and photoplethysmography (PPG) waveforms (pulse arrival time [PAT]). Another estimate is the time delay between proximal and distal PPG waveforms (PPG-PTT). PAT and PPG-PTT were assessed as markers of BP over a wide physiologic range using I-PTT as a reference. Waveforms for determining I-PTT, PAT, and PPG-PTT through central arteries were measured from swine during baseline conditions and infusions of various hemodynamic drugs. Diastolic, mean, and systolic BP varied widely in each subject (group average (mean ± SE) standard deviation between 25 ± 2 and 36 ± 2 mmHg). I-PTT correlated well with all BP levels (group average R(2) values between 0.86 ± 0.03 and 0.91 ± 0.03). PPG-PTT also correlated well with all BP levels (group average R(2) values between 0.81 ± 0.03 and 0.85 ± 0.02), and its R(2) values were not significantly different from those of I-PTT PAT correlated best with systolic BP (group average R(2) value of 0.70 ± 0.04), but its R(2) values for all BP levels were significantly lower than those of I-PTT (P < 0.005) and PPG-PTT (P < 0.02). The pre-ejection period component of PAT was responsible for its inferior correlation with BP In sum, PPG-PTT was not different from I-PTT and superior to the popular PAT as a marker of BP.

Estimation of Pulse Transit Time as a Function of Blood Pressure Using a Nonlinear Arterial Tube-Load Model

OBJECTIVE

pulse transit time (PTT) varies with blood pressure (BP) throughout the cardiac cycle, yet, because of wave reflection, only one PTT value at the diastolic BP level is conventionally estimated from proximal and distal BP waveforms. The objective was to establish a technique to estimate multiple PTT values at different BP levels in the cardiac cycle.

METHODS

a technique was developed for estimating PTT as a function of BP (to indicate the PTT value for every BP level) from proximal and distal BP waveforms. First, a mathematical transformation from one waveform to the other is defined in terms of the parameters of a nonlinear arterial tube-load model accounting for BP-dependent arterial compliance and wave reflection. Then, the parameters are estimated by optimally fitting the waveforms to each other via the model-based transformation. Finally, PTT as a function of BP is specified by the parameters. The technique was assessed in animals and patients in several ways including the ability of its estimated PTT-BP function to serve as a subject-specific curve for calibrating PTT to BP.

RESULTS

the calibration curve derived by the technique during a baseline period yielded bias and precision errors in mean BP of 5.1 ± 0.9 and 6.6 ± 1.0 mmHg, respectively, during hemodynamic interventions that varied mean BP widely.

CONCLUSION

the new technique may permit, for the first time, estimation of PTT values throughout the cardiac cycle from proximal and distal waveforms.

SIGNIFICANCE

the technique could potentially be applied to improve arterial stiffness monitoring and help realize cuff-less BP monitoring.

Toward Ubiquitous Blood Pressure Monitoring via Pulse Transit Time: Theory and Practice

Ubiquitous blood pressure (BP) monitoring is needed to improve hypertension detection and control and is becoming feasible due to recent technological advances such as in wearable sensing. Pulse transit time (PTT) represents a well-known potential approach for ubiquitous BP monitoring. The goal of this review is to facilitate the achievement of reliable ubiquitous BP monitoring via PTT. We explain the conventional BP measurement methods and their limitations; present models to summarize the theory of the PTT-BP relationship; outline the approach while pinpointing the key challenges; overview the previous work toward putting the theory to practice; make suggestions for best practice and future research; and discuss realistic expectations for the approach.

Ballistocardiogram as Proximal Timing Reference for Pulse Transit Time Measurement: Potential for Cuffless Blood Pressure Monitoring

GOAL

We tested the hypothesis that the ballistocardiogram (BCG) waveform could yield a viable proximal timing reference for measuring pulse transit time (PTT).

METHODS

From 15 healthy volunteers, we measured PTT as the time interval between BCG and a noninvasively measured finger blood pressure (BP) waveform. To evaluate the efficacy of the BCG-based PTT in estimating BP, we likewise measured pulse arrival time (PAT) using the electrocardiogram (ECG) as proximal timing reference and compared their correlations to BP.

RESULTS

BCG-based PTT was correlated with BP reasonably well: the mean correlation coefficient (r ) was 0.62 for diastolic (DP), 0.65 for mean (MP), and 0.66 for systolic (SP) pressures when the intersecting tangent method was used as distal timing reference. Comparing four distal timing references (intersecting tangent, maximum second derivative, diastolic minimum, and systolic maximum), PTT exhibited the best correlation with BP when the systolic maximum method was used (mean r value was 0.66 for DP, 0.67 for MP, and 0.70 for SP). PTT was more strongly correlated with DP than PAT regardless of the distal timing reference: mean r value was 0.62 versus 0.51 (p = 0.07) for intersecting tangent, 0.54 versus 0.49 (p = 0.17) for maximum second derivative, 0.58 versus 0.52 (p = 0.37) for diastolic minimum, and 0.66 versus 0.60 (p = 0.10) for systolic maximum methods. The difference between PTT and PAT in estimating DP was significant (p = 0.01) when the r values associated with all the distal timing references were compared altogether. However, PAT appeared to outperform PTT in estimating SP ( p = 0.31 when the r values associated with all the distal timing references were compared altogether).

CONCLUSION

We conclude that BCG is an adequate proximal timing reference in deriving PTT, and that BCG-based PTT may be superior to ECG-based PAT in estimating DP.

SIGNIFICANCE

PTT with BCG as proximal timing reference has potential to enable convenient and ubiquitous cuffless BP monitoring.

A region-matching method for pulse transit time estimation: potential for improving the accuracy in determining carotid femoral pulse wave velocity

Carotid femoral pulse wave velocity (cfPWV) is the 'gold standard' for assessment of arterial stiffness. The reliability of cfPWV measurement depends on the estimation of pulse transit time (PTT). This study aimed to validate a region-matching method for determining PTT and cfPWV against the existing 'foot-to-foot' methods. A cohort of 81 subjects (33 males and 48 females) aged 25-80 (45.1±15.7 years) were studied. PTTs were estimated by the region matching and 'foot-to-foot' methods ('diastole minimum', 'maximum first derivative', 'maximum second derivative' and 'tangent intersection' methods) with manual identification as the reference method and were subsequently used to calculate cfPWV. In a subgroup of 30 individuals, the measurements were repeated after 1 h. There were excellent correlations between cfPWV obtained by the reference method and all the estimated methods (r>0.9, P<0.001 for all), except the diastole minimum method (r=0.793, P<0.001). The region-matching method yielded cfPWV with a better accuracy (mean difference=-0.161 m s(-1), limits of agreement: -0.79 to 0.46 m s(-1)) and repeatability (mean difference=-0.228 m s(-1), intraclass correlation coefficient=0.957) comparing with the 'foot-to-foot' methods. These results demonstrate that the proposed region-matching method is more accurate and suitable for PTT estimation and cfPWV measurement.