This work describes the methods for the non-invasive estimation of BP in a healthy volunteer study in which BP changes were induced by the infusion of phenylephrine. Phenylephrine is an alpha-1 adrenergic receptor agonist which causes venous and arterial vasoconstriction, increasing cardiac preload (initial stretching of cardiac muscles) and afterload (pressure against which the heart has to work to pump blood around the body)35. The dosing regimen was guided by the pharmacist in the Medical Sciences Division Ethics Committee (University of Oxford) who balanced the desired clinical effect against safety concerns surrounding bradycardia and a potentially rapid increase in blood pressure. Among our participants, we observed heart rate of around 40 beats per minute at peak infusion using this regimen. These decisions are outlined in the study protocol38. Our aim was to induce vasoconstriction using weight-based dosing protocol, rather than be BP-target driven. On average, we achieved an increase of approximately 20 mmHg in systolic blood pressure, with maximum increase of 40 mmHg in a subset of participants. One of the key advantages of this study was that, in a relatively short period of time, and without causing large movement, the volunteers experienced a wide range of BP values (see Fig. 6). This helped to validate algorithms for non-invasive estimation of BP.
Figure 2 shows the typical vital-sign response to the phenylephrine infusion for a 28-year-old female. As the dose increased, heart rate (HR), PAT and PTT decreased, whereas BP and PEP typically increased. and RR had no significant correlations to the dose of phenylephrine. In this work, the data from the BP cuff was processed using a cubic smoothing spline. To the authors’ knowledge, the only method for processing the BP cuff time series that has been used in the literature is a simple low-pass filter29. However, this assumes an evenly-sampled time series and requires a defined frequency range of interest.
PAT is inversely correlated with BP and the majority of volunteers had their own unique and strong relationship between changes in PAT and BP (see Fig. 3). As shown in Table 2, the absolute correlation between PAT and BP was high, with the correlation coefficients consistently higher than the values reported in the literature (see Mukkamala et al.9). This suggests that the complex pathways that link changes in BP to changes in PAT are likely to be associated with the pathways affected by phenylephrine. The correlation coefficients between PAT and BP were relatively consistent for SBP, MAP and DBP whereas in the literature, PAT is shown to have a much stronger relationship with either DBP21,39 or SBP40,41. All individuals had their own unique gradient defining the relationship between BP and PAT. The gradients varied from − 2946 to − 470.64 mmHg/s in our dataset. The gradient of the PAT to BP relationship is thought to reflect arterial properties such as compliance and resistance9. Shallow gradients are thought to be associated with young, healthy individuals. Conversely, steeper gradients are thought to be associated with more elderly individuals42.
There are several caveats to interpreting the relationship between BP and PAT. At points along the arterial tree where there are significant changes in impedance (such as at points of arterial branching), the difference in impedance to flow results in back propagation of part of the pressure wave. Thus, at any point in the arterial tree, the pressure wave can be considered a summation of forwards and backwards travelling waves. As a result, the proximal and distal waveforms used to compute PAT do not differ by simply a time delay but also by shape and amplitude9. This is a significant source of errors in PAT estimation43. To tackle this problem, fiducial points close to the onset of the PPG are typically used as they are thought to be the least impacted by reflected waves44. In this work, the intersecting tangents method was used to define the fiducial point of the PPG9.
Due to the impact of phenylephrine, smooth muscle activation was the dominant component regulating changes in the arterial stiffness. As the distal measurement site was located in the peripheral arteries, this effect cannot be considered negligible. This might explain why such large variations in gradients were found in this study, due to individual responses to the medication. The precise clinical effect of the weight-based dosing of phenylephrine (see “Methods” section) in an individual would depend on the balance between their sensitivity to the increase in afterload, the effect of bradycardia on cardiac filling (therefore contractility, the Frank–Starling law45), and the proportion of venous/arterial action of phenylephrine causing the increase in preload and afterload.
Additionally, we hypothesise that, in some volunteers, the dominant smooth muscle component may have given rise to a hysteresis effect, where the response is different between the period of dose escalation to the period of washout. This effect has been highlighted previously during an exercise test46, where the level of hysteresis was proportional to higher levels of ANS activity and smooth muscle tone. As a result, there are different baroreflex responses when blood pressure is rising or falling. We quantified the effect of hysteresis as differences in the PAT or PTT calibration gradients during the periods of dose increase and washout. Due to the small sample size, the significance of the hysteresis effect was examined using a Wilcoxon rank sum test on the magnitudes of the dose increase and washout gradients. Despite being clearly evident in a number of individuals, there was no statistically significant difference in gradient values found across the whole cohort or in gender and age subgroups. Equally, there was no evidence of differences in hysteresis effects present between PAT and PTT, suggesting that PEP does not play a significant contributing factor to PAT hysteresis. It should be noted, however, that the presented study was a healthy volunteer study and an examination of hysteresis was not a primary objective. Therefore, more work should be performed to examine this effect. For example, the hysteresis effect during multiple perturbations of BP should be examined over a longer duration.
It has also been suggested that changes in PAT can often be significantly driven by changes in PEP14, making PAT an unreliable surrogate measure of blood pressure. As Wong et al.22 found, high correlations between PAT and BP do not necessarily suggest lack of influence of PEP, as this relationship could be driven primarily through changes in PEP. We found that PEP had a moderately strong, positive correlation () with SBP, MAP and DBP. Phenylephrine is known to increase both preload and afterload (by vasoconstriction) which have opposing effects on PEP magnitudes. The positive correlation found in our dataset suggests that the afterload effect played a more dominant role. However, the large interquartile range (IQR > 0.6) indicates that the relationship between BP and PEP was multifactorial. The gradients of SBP-PEP relationship varied from − 22,320 to 63,162 mmHg/s in our dataset. PTT had a marginal increase in median correlation coefficient and a marginal decrease in IQR compared to PAT (as shown in Table 2), suggesting that PEP was not a significant contribution to PAT in our dataset.
The maximum deviation from baseline of PEP in our study had a mean value of 5.5 ms with a standard deviation of 4.5 ms (see Fig. 6f). This is comparable to the range seen in Payne et al.14 of 7.6 (10.1) ms in volunteers under norepinephrine, which acts in a similar manner to phenylephrine. Payne et al.14, concluded that the changes in PEP were too significant to allow for BP estimation using PAT. In our study, while we experienced relatively similar magnitude of changes in PEP, both PAT and PTT had a very strong correlation with BP. This was because the changes in PTT, mean − 16.8 (± 6.1) ms, were considerably larger than the changes in PEP. Furthermore, Payne et al.14 claimed that PEP could could vary between 12 and 35% of PAT. In our study, we found that PEP contributed between 28.8 and 35.2% of PAT (see Fig. 6g), a much lower range of values. Therefore, while the changes in PEP cannot be neglected, its relative contribution to PAT was nearly constant and so changes in PTT accounted for most of the changes in PAT during the 30 min of the study.
However, it is important to note that there are reported experiments, such as changes in posture24 or exercise47, where PEP is a non-negligible component of PAT. These effects suggest that a simple constant coefficient fit on PAT/PTT, may not be the best approach. Using this dataset, we found promising results suggesting that adding terms for PEP as well as the interaction between PEP and PAT/PTT may help to normalise the model coefficients leading to a more generalised model. However, as this was deemed outside the scope of this paper it should be considered further in future work.
We implemented both a posteriori models and population-based models to estimate BP from PAT and PTT (see Table 3). A posteriori models assume a unique relationship between BP and PAT/PTT. The model parameters (slope and intercept) are estimated by least squares using all data points available for that individual (see Supplementary material C for an assessment on the number of data points required for accurate BP estimation using a posteriori models). All a posteriori models reported comparable RMSE, MAE and MAD values for SBP and DBP estimation via PAT or PTT. The inverse squared model reported slightly lower RMSE, MAE and MAD values, although the difference is small.
Population-based models approximate model parameters using averaged physiological constants (such as the density of blood), global averages and calibration. Three different population-based models were tested: Poon16, Gesche18 and Fung37, three of the most highly cited population-based models for BP estimation using PAT or PTT. In each case, the models were validated using PAT estimates rather than PTT estimates.
The Gesche model had the worst performance for both PAT and PTT. This model used population-based averages derived using PAT on a study with 13 volunteers. In our dataset, the model errors using PAT were too large (RMSE > 40 mmHg) for accurate BP estimation. In addition, its performance was significantly worsened when implemented using PTT estimates. The Fung model, which is derived from a model of laminar blood flow through a rigid pipe, performed well on PAT estimates. The model approximated the gradient of an inverse squared model based on the subject’s height. However, the results on BP estimation using PTT were significantly worse, with RMSE values greater than 30 mmHg.
Overall the Poon model performed the best of the population-based models. The Poon model is derived from a combination of the Moens–Korteweg equation10 and a model relating the elastic modulus of a vessel to the mean pressure of the fluid inside it12. Even though the model was initially validated on PAT estimates, its accuracy was improved when PTT estimates were used as the input instead. This is to be expected as PEP is not included in the modelling by Poon. However, even in this best case, the error values for the Poon model were still approximately twice the error values from the inverse square a posteriori model. The Poon model approximates a physiological parameter, , for all individuals. relates the distending pressure in an artery to the elasticity of the arterial wall. This relationship varies from person to person and can change as individuals age. Shao et al.48 highlighted that the Poon model errors are particularly sensitive to variations in .
The relationship between changes in PAT or PTT and changes in BP is unique to each individual, and so population averages are not sufficient to describe the complex underlying relationship on an individual level. All three models do not account for the effect of smooth muscle contraction which in our intervention was the dominant factor affecting changes in elasticity. This may go some way to explain why these models performed so poorly in our dataset. We would therefore suggest that individualised profiles are needed for accurate tracking of BP.
The findings presented in this paper have important clinical implications for ambulatory non-invasive monitoring of BP. Firstly, we present an experiment where the changes in PAT are dominated by changes in PTT as opposed to the PEP component, making PAT an accurate surrogate of BP. For effective ambulatory non-invasive monitoring of BP, the relationship between PEP and PTT needs to be further explored and documented so that modes of failure can be highlighted and addressed. Secondly, a posteriori models naturally outperform population-based models for BP estimation, but they are not without their limitations. In this study, estimation of the calibration curve required monitoring during a drug-induced increase in vascular tone. This set-up would not be viable to be developed for non-invasive blood pressure monitoring for the general population. Additionally, the calibration curve will likely depend on basal cardiovascular factors which cannot be assumed constant in ambulatory monitoring such as intravascular fluid volume, cardiac contractility, and caffeine intake. More work should investigate the long-term stability of the calibration parameters and their relationship to these basal factors42,49.
There are several limitations to the methodology used in this study that should be noted. PEP was estimated using the Lozano method50. This method avoids detecting the B-point (point of aortic valve opening) by detecting the C-point (maximum of ICG pulse) of the ICG and a derived relationship between the ECG R-peak and the ICG B and C points. However, van Lien et al.51 reported considerable errors between PEP estimation using the Lozano method and hand annotated PEP values, especially for extreme values. Other techniques for detecting the B-point exist52,53, however, in our study, the Lozano method produced considerably less noisy estimates than these techniques.
The ICG signal was sampled at 200 Hz, resulting in a time resolution of 5ṁs for the detection of the C-point. This could potentially lead to errors in the estimation of PEP. Supplementary material F provides a comparison of PEP estimates from the original 200 Hz signal against PEP estimates from an upsampled ICG waveform at 1 kHz using cubic splines. Although we found that this limitation did not significantly impact the results and conclusions of this paper, further studies should aim to record the ICG waveform at a high sampling rate, such as 1 kHz, especially to estimate a wide range of PEP values.
Measurements of BP using a sphygmomanometer cuff are susceptible to various forms of noise that can distort the readings. The oscillometric device used as a BP reference in this study was compliant with the IEC 60601-2-30/EN60601-2-30 and with the American National Standard for Electronic or Automated Sphygmomanometers (ANSI/AAMI SP 10/92)54 with a maximum mean error of ± 5 mmHg (± 0.7 kPa) and a maximum standard deviation of 8 mmHg (1.1 kPa). As these tolerances are of similar magnitude to the errors seen in this work, we suggest that some of the errors in our BP estimates are not only due to problems in the PAT or PTT time series, but also due to errors in the reference BP values.
Finally, our results were reported across a small number of homogenous healthy volunteers. Volunteers were screened to ensure that they did not have a history of cardiovascular disease or hypertension. Meaningful estimation of BP must be evaluated on large heterogenous datasets involving both free-living individuals and those diagnosed with cardiovascular disease.
To conclude, PAT can be considered an approximation of PTT if the contribution of PEP is neglected. Previous studies14 have suggested that the contribution of PEP provides a significant limitation to BP estimation using PAT. We have shown that under an infusion of phenylephrine, changes in PTT were significantly larger than changes in PEP and so the use of PAT instead of PTT is justifiable. Blood pressure estimation using PAT is best used in settings for which changes in PTT are significantly larger than changes in PEP. One such area could be sleep, where typically a decrease in night-time BP is experienced55. Forouzanfar et al.53 reported similar changes in PEP during a sleep study compared to those we found in our study.
Finally, we have confirmed that population-based models do not adequately reflect the unique and individualised relationship between changes in BP and changes in PAT, and so the use of these models to estimate BP in a given individual is not justified.
