Annals of Biomedical Engineering, Vol. 42, No. 6, June 2014 (Ó 2014) pp. 1145–1147 DOI: 10.1007/s10439-014-1007-7
Validation of Algorithms for the Estimation of Pulse Transit Time: Where do We Stand Today? Response to Commentaries by Papaioannou et al. NICHOLAS R. GADDUM,1 JORDI ALASTRUEY,2 PHIL CHOWIENCZYK,1 and TOBIAS SCHAEFFTER2 1 King’s College London, British Heart Foundation Centre, St. Thomas’ Hospital, 4th Floor Lambeth Wing, Westminster Bridge Road, London SE1 7EH, UK; and 2Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK
(Received 21 March 2014; accepted 28 March 2014; published online 12 April 2014) Associate Editor Dan Elson oversaw the review of this article.
traditional foot-to-foot method, a least squares fit of the systolic rise, and cross correlation of the entire waveform. The software developed for this study containing all algorithms tested was made available to the public3 in the interest of continued discussion upon this topic. We agree with the Papainnou et al.’s6 assertion that pressure and velocity waveforms may need to be addressed differently. Certainly the results we presented in our article (Fig. 4) explicitly show differences between algorithm accuracies when applied to pairs of pressure or velocity waveforms. Furthermore, these differences were outlined as a warning in Point 4 of the algorithm selection recommendations. We found wave shape mismatch between the proximal and distal wave pairs to be a crucial factor in determining which algorithm to use. For example, cross correlation is by definition a comparison of wave shapes weighted by local magnitude. In our article we measured waveshape similarity using a normalised cross-correlation coefficient (CCCoefficient) where a value of 1.0 would indicate identical shapes. Papainnou et al.6 were interested to know the CCCoefficient for the carotid and femoral arterial waveforms as these are the standard measurements made by clinical devices such as the SphygmoCor system. The CCCoefficient of the carotid-and-femoral-artery pressure waves was 0.78 for the numerical data and 0.84 ± 0.10 for our patient cohort (n = 20).4 These results indicate substantial wave shape mismatch in clinical assessment. Measuring beat-to-beat variation in carotid femoral PWV in our patient cohort was done retrospectively using 10 s tonometric signals measured sequentially at the carotid, and then the femoral artery. As each signal was measured concurrently with the ECG, individual waveforms could be dissected from the 10 s signal and aligned in time with reference to the R-wave of the ECG. Beat-to-beat variation was therefore assessed as the variation in measured PWV from as many wave-
Pulse wave velocity (PWV) has been shown to be a good predictor of cardiovascular risk.9 Measuring PWV normally constitutes quantifying the transit time (TT) between proximally and distally measured blood pressure or velocity waveforms. However various factors affect our ability to measure PWV accurately making it a topic of continued attention. Primarily, the selection of the algorithm used to measure TT has been shown to have a remarkable effect upon accuracy.4,8 Other factors pertain to the quality and nature of the waveform data. The quality of the data (assuming good sensor function) worsens with increasing signal noise and decreasing sampling frequency, and the nature of the waveform data refers to waveform shape (e.g. pressure vs. velocity) or shape mismatch between the distal and proximal waveforms.4 Papaioannou et al.’s6 letter reflects upon an article our group published in the Annals of Biomedical Engineering (2013 Dec; 41(12):2617-29)4 which assessed current algorithms’ accuracies and variabilities due to waveform signal noise, temporal resolution, shape and shape mismatch. We used waveform data generated by a one-dimensional (1-D) arterial model2 for which the theoretical TT was known a priori, thus algorithm accuracy could be explicitly measured. Furthermore, the same algorithms were applied to beat-to-beat clinical data to investigate beat-to-beat variability in PWV measurement. Based on this study we proposed a set of recommendations for choosing the most accurate algorithm for a given waveform set.4 The algorithms tested included two variations of the
Address correspondence to Nicholas R. Gaddum, King’s College London, British Heart Foundation Centre, St. Thomas’ Hospital, 4th Floor Lambeth Wing, Westminster Bridge Road, London SE1 7EH, UK. Electronic mail:
[email protected]
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Ó 2014 Biomedical Engineering Society
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form pairs as could be assembled within the 10 s measurement window. Papainnou et al.6 are correct in noting that this is not truly beat-to-beat analysis. However as such ECG-referencing is used by clinical devices we feel that the method is sufficient to indicate the variability in standard clinical PWV measurements. The requirements of a numerical simulation to be suitable for PWV algorithm analysis is an interesting debate. Assessing a model’s efficacy to represent human physiology requires firstly that both the physics, and the implementation of the physics are assessed. Then, estimation of model parameters from clinical measurement should be done in order to simulate an individual’s or group of individuals’ haemodynamics. In our model both the physics and its implementation have been rigorously assessed against a comprehensive in vitro arterial model in which detailed haemodynamic measurements could be obtained directly.5 Following this, model parameters were chosen according to clinical validation work by a group, of which Papainnou et al.7 are part. These model parameters were varied in our article in order to simulate a hypertensive subject. Certainly this renders our simulation haemodynamics to be less similar to the individuals from the validation study. However, we believe it is representative of human physiology and reasonable for our assessment of PWV algorithms. More importantly, we used the linearised 1-D formulation without wall visco-elasticity to have a constant PWV in time in each arterial segment with which to calculate the exact theoretical TT. If the 1-D model is nonlinear then the PWV is time-dependent and if the arterial wall is visco-elastic then the PWV is frequencydependent. When employing this complexity in a numerical arterial model to assess TT algorithm accuracy Vardoulis et al.8 approximated the theoretical TT based on PWV during diastolic pressure thus possibly confounding their measured errors. Papainnou et al.6 inquire as to the kind of least squares algorithm was used in our analysis. We used a standard sum-of-the-squared-differences algorithm where the discrete transient data of the waveforms were subtracted, then squared to give a vector of absolute differences, and finally the sum of the squared differences vector provided a single quantity of the shape mismatch within the window selection. The window of least squares comparison is taken from the foot to the systolic peak. This algorithm is detailed within the methods as well as graphically depicted in Fig. 3.4 The software is also available3 for scrutiny if further confusion exists. Vardoulis et al.’s8 numerical assessment of waveform accuracies was published as our article4 was in press, and so we could not incorporate their ‘diastolic patching’ method in our analysis. Papainnou et al.6 suggest
this method instead of our least squares algorithm, as it centres the window for least squares comparison about the foot, (incorporation late diastole and early systole), as opposed to extending the window to the systolic peak. They are correct in their assertion that our approach is influenced by wave reflections that may compromise performance. However, wave reflections from previous cardiac cycles are also present in late diastole and early systole which lead to an erroneous indication of a reflection-free period in early systole and additional error in the estimates of PWV given by the PU–loop method1 and may also affect the PWV estimate provided by the ‘diastolic patching’ method. From a practical point of view, our numerical simulations indicated issues with the window size and section of the waveform for comparison for TT assessment. Initial designs of the least-squares algorithm employed a window from diastolic minimum to maximum systolic gradient, however with such a small segment of waveform we found high variability in TT, particularly when augmented with random noise. By extending the window up to the systolic maximum, greater stability between measurements was observed. Furthermore, considering the section of the waveform to use in the window we found that regions with high rates of change, (high gradient), provided greater stability as they lend greater differentiation as the algorithm makes sliding least squares subtractions. This meant that a window incorporating the systolic upstroke (steep) provides greater stability than a window incorporating end-diastole of a velocity waveform for example (flat). We commend Papainnou et al. in continuing what is a critical discussion if PWV analysis is to realise its potential in clinical practice. Algorithm selection and implementation is as crucial as the sensitivity of the non-invasive devices which provide the clinical data. Offering these algorithms for the wider research community to test and offer feedback3 has already led to substantial refinement of their implementation.
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