Pulse transit time estimation of aortic pulse wave velocity and blood pressure using machine learning and simulated training data
[['This paper considers continuous monitoring of cardiac health using computational modelling .', 'Stiffening of the arterial wall , such as aorta , causes reduction in the pulsatile properties in the vascular tree , accelerates the vascular premature ageing and predisposes to the dysfunction of the heart , brain and other organs [1 , 2] .', 'Aortic stiffness can be measured by using invasive methods or medical imaging such as ultrasound [3] and MRI [2] .', 'Another indicator reflecting the cardiac performance is stroke volume ( SV ) , which is typically measured using Doppler ultrasound [4] .', 'However , these imaging modalities typically require special expertise and are only carried out clinically .', 'On the other hand , aortic stiffness is associated with the unfavourable changes in the diastolic and systolic blood pressures ( DBP/SBP ) , which can have several negative consequences in cardiac function and structure [1] .', 'Ambulatory home measurements of DBP and SBP use the techniques based on inflated cuffs , but continuous recording is still cumbersome .', 'It would be helpful to find unobtrusive methods for the long-term monitoring of these cardiac indices during the daily activities and sleep .', 'Arterial stiffness is often assessed by measuring pulse wave velocity ( PWV ) , which is increased in stiffer arteries .', 'The PWV can be estimated by measuring arrivals of pulse waves at two arterial sites:', 'PWV = distancebetweenthesites traveltimebetweenthesites .', 'The travel time is commonly referred as pulse transit time ( PTT ) .', 'Arrival of the pulse wave to distal arterial sites can be easily measured by using a photoplethysmogram ( PPG ) , which is an optical non-invasive sensor that can be placed , for example , in a wearable device [5] .', 'On the other hand , in order to predict aortic stiffness reliably , the first arterial site should be located at the beginning of aorta ( for measurement of aortic valve opening ) .', 'However , a measurement of valve opening can require a device such as phonocardiograph , ultrasound or MRI .', 'To overcome this difficulty , PTT is often approximated using pulse arrival time ( PAT ) which uses the R- wave of electrocardiogram ( ECG ) as a reference timing [6] .', 'However , there exists controversy in the clinical accuracy of using PAT in the predictions due to variations in pre-ejection period ( PEP ) from the R-wave to aortic valve opening [7 , 8] .', 'An alternative approach is to approximate the reference with a measurement from another distal site near aorta .', 'For example , the gold standard for aortic PWV measurement is to measure differences of pulse arrivals to carotid and femoral arteries .', 'The estimation of blood pressure from arrival of pulse waves has also been largely studied; see e . g . [6 , 9 , 10] .', 'Although promising results have been reported , clinical use of these techniques is still limited .', 'Haemodynamic alterations can have significant effects on the accuracy [11] .', 'A common problem with the clinical use of the above methodologies is that the development and validation of the methods typically require a large set of measurements from real human subjects with sufficient variety .', 'Such data collection can be a very difficult and expensive task .', 'A preliminary assessment of the methods without extensive data collection can be carried out using simulators .', 'For example , Willemet et al [12 , 13] proposed approach to use cardiovascular simulator for generation of a database of “virtual subjects” with sizes limited only by computational resources .', 'In their study , the databases were generated using one-dimensional ( 1D ) model of wave propagation in a artery network comprising of largest human arteries [14] .', 'Such 1D models provide computationally efficient way to simulate blood circulation and are also used in several other applications [15] .', 'There are also studies validating 1D simulations against real measurement [16–18] .', 'The virtual database approach was used to assess accuracy of pulse wave velocity measurements for estimation of aortic stiffness [12] and the accuracy of pulse wave analysis algorithms [13] .', 'The aim of our study is to assess theoretical limitations for the prediction of aortic pulse wave velocity ( aPWV ) , blood pressures ( DBP/SBP ) and SV from PTT/PAT measurements .', 'We apply a similar virtual database approach to find correlations between these cardiac indices and PTT/PAT timings measured from different locations .', 'In particular , we train Gaussian process regressor to predict the cardiac indices using different combinations of PTT and PAT measurements .', 'The regressor model is trained using a large set of virtual subjects generated using 1D cardiovascular simulator , and the results are validated using another set of virtual subjects .', 'The result of study can give preliminary implications for the accuracy of such predictions in rather ideal circumstances .', 'Our study is based on the 1D haemodynamic model of entire adult circulations introduced by Mynard and Smolich [19] .', 'It includes heart functions and all larger arteries and veins for both systemic and pulmonary circulation .', 'As heart is included to the model , it can also simulate variations in PEP that are essential in the comparison of PTT and PAT timings .', 'This paper is organized as follows .', 'Cardiovascular model , generation of virtual subjects and prediction methods are described in Methods and Models section .', 'Results section contains numerical experiments .', 'We will finish with Discussion .'], ['The blood circulation model is based on the 1D haemodynamic model described in [19] , which basically extends commonly used 1D wave dynamics model ( see e . g . [14] ) with heart functions and realistic arteria and venous networks including pulmonary and coronary circulations .', 'The components of the model are shortly summarized below , see [19] for more details .', 'The database is created by running the cardiovascular model repeatedly .', 'The model parameters are varied to reflect variations between individual ( virtual ) subjects .', 'In [12 , 13] , the seven parameters were varied: elastic artery PWV , muscular artery PWV , the diameter of elastic arteries , the diameter of muscular arteries , heart rate ( HR ) , SV and peripheral vascular resistance .', 'In their study , the parameters were varied by specifying a few possible values for each parameter and the cardiovascular model was run for all of the resulting 7776 combinations .', 'However , in our study , the cardiovascular model has significantly more model parameters ( e . g . parameters related to heart model and valves , vascular beds , … ) .', 'Such systematic variation of all essential parameters would lead to excessively large number of combinations .', 'In this study , we choose “sampling” approach in which the model parameters are varied randomly .', 'Our aim is to choose random variations that would represent healthy subject and , where applicable , the range of the parameters is of similar range as in [12] .', 'Some choices can be rather subjective due to the limited amount of ( probabilistic ) information from related physiological quantities .', 'Our goal is to choose variations to be wide enough so that “real world” can be considered as a subset of the population covered by the variations .', 'However , if more sufficient information about parameters becomes available , it should be rather straightforward to carry out the analysis with the adjusted distributions .', 'In the following , the superscript ( s ) refers to a virtual subject for which the parameters are specified .', 'The overbar notation ( e . g . L ¯ ) refers to the values used in [19] ( the baseline ) .', 'Unless otherwise mentioned , the variations are chosen to be normally distributed .', 'Furthermore , the statements such as 10% relative variation should be understood in terms of standard deviations instead explicit ranges of the parameter .', 'We use slightly unconventional notation N ( μ , X % ) to denote the Gaussian distribution with mean μ and the standard deviation σ = X/100μ ( i . e . X% variation relative to the mean/baseline ) .', 'The uniform distribution is denoted as U ( a , b ) .', 'We apply Gaussian process regression for the computation of predictors .', 'GPs are widely used , for example , in machine learning , hydrogeology and analysis of computer experiments ( e . g . see [25–27] ) .', 'GPs also provide flexible predictors that can handle non-linear relationship between input data and the response variable as well as uncertainties in the data .', 'However , we note that any other class of regressions capable of nonlinear relationships can also be used for the analysis .', 'For example , similar results can be achieved with multivariate adaptive regression splines [28] .', 'A GP is a stochastic process f ( z ) ( z ∈ R d ) such that f ( z1 ) , … , f ( zn ) is a multivariate Gaussian random variable for all combinations of z1 , … , zn .', 'It can be described by the specifying mean function μ ( z ) = E ( f ( z ) ) and the covariance function k ( z , z′ ) = cov ( f ( z ) , f ( z′ ) ) .', 'For more details , see e . g . [25] .', 'Consider a case in which the inputs z are a vector of PTT or PATs and possibly HR and y is the response variable ( aPWV , DBP , SBP or SV ) .', 'We model the response variables as', 'y ( z ) = h ( z ) T β + f ( z ) + ϵ , ( 34 )', 'where h ( z ) is a vector of ( deterministic ) basis functions , β is a vector of basis function coefficients , f ( z ) is a GP with zero mean and covariance function k ( z , z′ ) , and ϵ is an Gaussian white noise .', 'The first term represents mean behavior of the GP model .', 'The GP term models non-linear relationship between input data and the response variable as well as correlated uncertainties in the data .', 'Training data comprises of input-output pairs { ( zi , yi ) ; i = 1 , … , N } .', 'We assume that yi’s are output of the above model i . e . yi = y ( z1 ) .', 'Furthermore , let Z ′ = ( z 1 ′ , … , z p ′ ) be inputs for which we want to calculate predictions .', 'Then Y = ( y1 , … , yN ) and Y ′ = ( y ( z 1 ′ ) , … , y ( z p ′ ) ) are both Gaussian and the conditional distribution of Y′ given Y is ( see e . g . [25] , Appendix A . 2] ) ,', 'p ( Y ′ | Y ) = N ( μ Y ′ + Σ Y ′ Y Σ Y - 1 ( Y - μ Y ) , Σ Y ′ + Σ Y ′ Y Σ Y - 1 Σ Y Y ′ ) ( 35 )', 'where μY and ΣY denotes the mean and covariance of Y and ΣYY′ is the cross-covariance of Y and Y′ .', 'The means and covariances can be calculated by pluggin in the model ( 34 ) , which gives', 'μ Y ′ | Y = h ( Z ′ ) T β + k ( Z ′ , Z ) ( k ( Z , Z ) + σ ϵ 2 I ) − 1 ( Y − h ( Z ) T β ) ( 36 ) Σ Y ′ | Y = k ( Z ′ , Z ′ ) − k ( Z ′ , Z ) ( k ( Z , Z ) + σ ϵ 2 I ) − 1 k ( Z , Z ′ ) ( 37 )', 'where h ( Z′ ) and k ( Z′ , Z ) are shorthand notations for the vector and matrix with the components h ( z i ′ ) and k ( z i ′ , z j ) , respectively .', 'The above conditional mean gives us an prediction of Y′ with a confidence estimate given by the conditional covariance .', 'In this study , the covariance function are chosen to be Matern kernel function with ν = 3/2 with a separate length scales for each input parameter .', 'This kernel function can be written as', 'k ( z , z′ ) =σ2 ( 1+3r ) exp ( −3r ) , r= ( ∑md ( zi−zj ) 2ℓm2 ) 1/2 ( 38 )', 'where σ2 is the variance and ℓm are the length scales for each input .', 'We note that the choice of the kernel function does not have a large effect to the results as our sample size is large .', 'For example , our experiments show that use of the squared exponential covariance function gives very similar results with differences of the same scale as the prediction uncertainty .', 'The predictors are computed using fitrgp function in MATLAB Machine Learning Toolbox which provides numerically efficient implementation for the GP regression .', 'The basis functions h ( z ) are chosen to be linear .', 'The fitrgp function also estimates hyperparameters θ ( β , σϵ2 , σ2 , ℓ1 , … , ℓd ) by minimizing the negative loglikelihood ,', 'L ( θ ) = - log p ( y | Z , θ ) = 1 2 y T Σ θ - 1 y + 1 2 log det Σ θ + n 2 log 2 π ( 39 )', 'where Σ θ = k ( Z , Z ; θ ) + σ ϵ 2 I .', 'The optimization is carried out using a subset of observations to avoid high computational load .', 'The parameters of fitrgp related to this hyperparameter optimization are chosen to be the default values .'], ['Fig 6 shows predictions of aPWV for a selected set of combinations when the measurement location is LCA .', 'Table A in S1 Appendix summarizes the results for the complete set of combinations .', 'The results show that using PTTff or PTTD as a single input gives moderate accuracy and predictions using either HR , PTTp , or DAT are insufficient .', 'Performance can be improved by combining multiple different timings .', 'For example , the accuracy is significantly improved if both PTTff and PTTp are used for predictions ( r = 0 . 90 ) .', 'Furthermore , including also DAT provides the accuracy of r = 0 . 94 , and adding other timings does not significantly improve accuracy any further .', 'Measurements from RCA provide less accurate predictions ( Table B in S1 Appendix ) : for example , the combination of PTTff , PTTp , PTTD and DAT provides one of highest accuracies for RCA ( r = 0 . 79 ) , but is still only moderate .', 'Such results can be expected as pulse waves travel shorter distance in aorta and also travel through brachiocephalic artery ( see Fig 1 ) inducing additional variations to the ( average ) wave speeds .', 'Performance of wrist measurements ( LRad / RRad ) are even worse ( see Table C in S1 Appendix for LRad; results for RRad are similar ) .', 'For example , the highest accuracy ( r = 0 . 73 ) can be achieved with the combination of PTTff , PTTp , PTTD and DAT .', 'This is also expected as relative large part of the arterial tree to these measurement locations are comprised of brachial and radialis arteries with their own variations to PWV .', 'On the other hand , measurements from lower limb could provide better performance: for right femoral artery , we can achieve r = 0 . 75 using PTTff and r = 0 . 84 using PTTff , PTTp , PTTD and DAT ( Table D in S1 Appendix ) .', 'In this case , pulse travels though the whole aorta to reach these measurement locations .', 'As mentioned above , in practice , the R-peak location in ECG signal is often used as a surrogate to aortic valve opening due to simpler measurement .', 'However , using PATs gives only mediocre accuracy compared to PTT due to the physiological variations in PEP [7 , 8] .', 'Our finding are similar , see for example , Fig A and Table E in S1 Appendix for LCA .', 'The highest accuracy is r = 0 . 79 ( e . g . PATff , PATp , PATD and HR ) which is significantly worse compared to using PTTs .', 'Another approach to avoid measurement of aortic valve opening is to consider differences of pulse arrival times to two distal locations .', 'Such setup also allows us to avoid the influence of PEP variations .', 'Results for measurement between LCA and Fem can be seen in Fig B and Table F in S1 Appendix: difference of PTTff gives r = 0 . 76 which is slightly better than using normal PTTff measurement from Fem , but not as good as normal PTTff measurement from LCA .', 'The highest accuracy ( r = 0 . 87 ) can be obtained , for example , with PTTff , PTTp , PTTD and HR .', 'The predictions of PWV that use the difference between LCA and RCA or the difference between LRad and RRad are less accurate ( r ≈ 0 . 75 − 0 . 78 at best ) ; see Tables G and H in S1 Appendix .', 'Figs 7 and 8 show predictions for DBP and SBP for selected PTT time combinations when measurements are taken from LCA; see also Table A in S1 Appendix for all combinations .', 'For DBP , predictions using PTTff as a single input achieves very low accuracy ( r = 0 . 33 ) .', 'Significantly more accurate predictions can be achieved using HR ( r = 0 . 85 ) or DAT ( r = 0 . 86 ) .', 'For SBP , the performance of PTT based predictions is better but still quite low ( r = 0 . 58 for PTTff and r = 0 . 60 for PTTp ) .', 'Predictions can be improved by adding additional input timings .', 'For DBP , combining PTTff with HR or DAT gives r = 0 . 92 and the highest accuracy r = 0 . 94 is obtained with PTTff , PTTp , PTTD and DAT .', 'Additional input timings also improves performance of SDB predictions: PTTff and HR/DAT results in r = 0 . 735 and the highest accuracy is r = 0 . 75 ( PTTff , PTTp , PTTD and DAT ) .', 'Findings the other measurements locations are similar; see Tables B , C and D in S1 Appendix .', 'We also consider predictions from pulse arrival times ( i . e . using R-peak as a reference timing ) .', 'Compared to PTT times , the results are of mixed accuracy; see Table E for PAT measurements from LCA .', 'For DBP , using PATff as single input yields insufficient predictions ( r = 0 . 19 ) , but PATp gives moderate accuracy ( r = 0 . 67 ) .', 'Combinations of different PAT timings can even achieve higher accuracy than using PTTs: for example , r = 0 . 95 with PATff and DAT and r = 0 . 96 for PATff , PATp , PATD and DAT .', 'For SBP , PATff provides slightly better accuracy compared to PTTff ( r = 0 . 62 ) , but otherwise results are similar .', 'As with aPWV , we consider differences of pulse transit/arrival times measured with two sensor .', 'Measuring between LCA and Fem gives very similar performance to PTT measurements from LCA ( Table F in S1 Appendix ) .', 'However , other considered setups provide less accurate results: see Table G in S1 Appendix for differences between LCA and RCA measurements and Table H for differences between measurements from radialis arteries .', 'Results show that HR has largest contribution to the predictions of SV , meanwhile performance with pulse transit or arrival timings ( without HR information ) can only provide moderate accuracy at best .', 'For example , Fig G and Table A in S1 Appendix show the predictions using measurements from LCA .', 'Predictions with HR as a single input reaches r = 0 . 81 , but predictions using PTTff or PTTD are insufficient estimates ( r < 0 . 25 ) and predictions with PTTp are of moderate accuracy ( r = 0 . 60 ) .', 'SV can be predicted with good accuracy with DAT , but this is due to the strong correlation between HR and DAT as mentioned above .', 'Furthermore , significant improvements will not be achieved by combining several inputs .', 'For example , highest accuracy is r = 0 . 83 which can be obtained , for example , with PTTff , PTTD and HR .', 'Results are similar for all other measurement setups; see Tables B-H in S1 Appendix .'], ['This paper assessed theoretical limitations for the prediction of aortic pulse wave velocity ( aPWV ) , DBP/SBP and SV from pulse transit and arrival time measurements .', 'We applied a virtual database approach proposed by Willemet et al [12 , 13] in which a cardiovascular simulator is used to generate a database of virtual subjects .', 'In this work , we applied one-dimensional haemodynamic model by Mynard and Smolich [19] to construct a simulator for entire adult circulation .', 'This simulator was used to generate a large database of synthetic blood circulations with varied physiological model parameters .', 'The generated database was then used as training data for Gaussian process regressors .', 'Finally , these trained regressors were applied to another synthetic database ( test set ) to assess capability of regressors to predict aPWV , SDB , DBP and SV using different combinations pulse transit/arrival time and HR measurements .', 'The results indicate that aPWV and DBP can be estimated from PPG signal with a high accuracy ( Pearson correlation r > 0 . 9 between true and predicted values for measurement from left carotid artery ) when , in addition to foot-to-foot PTT time , information about the peak and dicrotic notch location is also given as input to the predictor .', 'The predictions of SDB were less accurate ( r = 0 . 75 at best ) .', 'For SV , accurate predictions were mostly based on heart rate , with only a very minor improvement in accuracy when PTT timings were also included as inputs .', 'As this was entirely in silico study , it is not guaranteed that the result can be applicable to the real world as is .', 'However , the aim of the study was to give preliminary results about correlations between the cardiac indices and PTT/PAT timings and the applicability of such predictions .', 'The hope is that the results could to be extended to real clinical applications in future research .', 'The limitations to be addressed in future are the following .', 'First , the cardiovascular model has its limitations .', 'Although previous studies have shown that similar cardiovascular models can be used to simulate human physiology relatively well [16–18] , not all physiological phenomena are fully covered in the Mynard’s model .', 'One example of such phenomenon is respiration .', 'The effect of respiration can be important as the breathing and cardiac cycles are in a close interaction .', 'Several physiological factors , such as the changes in the intrathoracic pressure and the variation in the interbeat intervals modulate the cardiac mechanics and blood outflow from the heart .', 'Even the timing of the shorter cardiac cycles coupled with the longer respiratory cycles has effects on the central circulation .', 'When we considering a healthy heart , the effects of respiration can perhaps be managed by interpreting different virtual subjects to represent inspiratory and expiratory phases of the breathing .', 'Other phenomena that are not covered by the model are , for example , gravity and baroreceptors .', 'Furthermore , lumped parameter models that are used for heart and vascular beds were relatively simple approximations .', 'However , new analytical methods allow us to bridge the models and human bodily functions [30] .', 'The chosen baselines and variations of the model parameters were chosen to represent healthy subject .', 'The choices , however , can be subjective due to the limited amount of ( probabilistic ) information .', 'Our attempt were to produce variations such that the virtual population covered by the chosen parameter variations includes real physiological variations .', 'We , however , emphasize that the presented approach is not limited to the chosen parameters variations and it can be adjusted if more precise information becomes available .', 'Due to the limited phenomena covered by the model , the results may not be reliable when considering subjects with medical conditions .', 'For example , the simplified heart model and variations of related model parameter may not present subjects with heart diseases .', 'In this study , we only considered pulse transit and arrival type of time information as the input to the predictor .', 'Predictions could potentially be improved with other kinds of additional information .', 'For example , aortic PWV predictions could be improved by using information about the distances between aorta and/or measurement points .', 'Information about arterial path lengths could have been easily used in our simulation analysis , but in practice such information would require clinical measurements such as MRI [21 , 22] .', 'On the other hand , the arterial path length are often estimated using the body lengths or measuring distances of certain points in the body [21 , 22] .', 'Such information was not used in this simulation study as precise statistical knowledge of connection between such body measurement and arterial length was not available .', 'Instead , Gaussian process regressors implicitly marginalize predictions over different arterial lengths that are present in the virtual database .', 'Ultimately it would be beneficial to develop approaches that do not need reference measurement ( aortic valve opening/R-peak ) .', 'For example , Choudhury et al [31] presented a machine learning algorithm which uses raise times and pulse widths derived from PPG signal to predict DBP and SBP .', 'Furthermore , deep learning approaches could perhaps be used to infer optimal information from PPG waveform .', 'These are subject of our future research .']]
['Introduction', 'Methods and models', 'Results', 'Discussion']
['Recent developments in cardiovascular modelling allow us to simulate blood flow in an entire human body .', 'Such model can also be used to create databases of virtual subjects , with sizes limited only by computational resources .', 'In this work , we study if it is possible to estimate cardiovascular health indices using machine learning approaches .', 'In particular , we carry out theoretical assessment of estimating aortic pulse wave velocity , diastolic and systolic blood pressure and stroke volume using pulse transit/arrival timings derived from photopletyshmography signals .', 'For predictions , we train Gaussian process regression using a database of virtual subjects generated with a cardiovascular simulator .', 'Simulated results provides theoretical assessment of accuracy for predictions of the health indices .', 'For instance , aortic pulse wave velocity can be estimated with a high accuracy ( r > 0 . 9 ) when photopletyshmography is measured from left carotid artery using a combination of foot-to-foot pulse transmit time and peak location derived for the predictions .', 'Similar accuracy can be reached for diastolic blood pressure , but predictions of systolic blood pressure are less accurate ( r > 0 . 75 ) and the stroke volume predictions are mostly contributed by heart rate .']
['Recently there has been a strong trend for self-monitoring of your cardiovascular health and new wearable sport trackers and mobile applications are coming to the market everyday .', 'However , such solutions are mostly taking advantage of heart rate measurement .', 'Other health indices such as blood pressure and pulse wave velocity reflecting to the condition of cardiovascular system would also be of great interest , but such solutions for continuous monitoring are barely existing or are at least unreliable .', 'In this paper , we use computational modelling to assess theoretical capabilities of such measurements .', 'We concentrate on predicting health indices using on pulse transmit time type of measurements .', 'Such measurements could be carried out , for example , with photopletyshmography sensor or an optical sensor already found from several wearable sport trackers .', 'We use cardiovascular modelling to create a database of “virtual subjects” , which is applied with machine learning to construct predictors for health indices .', 'Our findings suggest that aortic pulse wave velocity and diastolic blood pressured could be predicted with a high accuracy , but predictions of systolic blood pressure are less accurate .']
['medicine and health sciences', 'cardiovascular anatomy', 'notch signaling', 'arteries', 'cardiology', 'blood vessels', 'aortic valve', 'blood pressure', 'heart rate', 'signal transduction', 'anatomy', 'cell biology', 'aorta', 'biology and life sciences', 'coronary arteries', 'vascular medicine', 'cell signaling', 'heart']