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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The maximum amplitude algorithm (MAA) is generally utilized in the estimation of the pressure values, and it uses heuristically obtained ratios of systolic and diastolic oscillometric amplitude to the mean arterial pressure (known as systolic and diastolic ratios) in order to estimate the systolic and diastolic pressures. This paper proposes a Bayesian model to estimate the systolic and diastolic ratios. These ratios are an improvement over the single fixed systolic and diastolic ratios used in the algorithms that are available in the literature. The proposed method shows lower mean difference (MD) with standard deviation (SD) compared to the MAA for both SBP and DBP consistently in all the five measurements.

There is an increasing need to offer health care devices within the homes of senior patients. This has led to an increasing demand on home blood pressure monitors. Oscillometric measurements have recently gained popularity and are used in blood pressure (BP) monitors, which are now readily available on the market [

The organization of this paper is as follows. In Section 2, the data used in the study is described, and the Bayesian model principles and the conventional methodology used in this paper are explained. In Section 3, the experimental results and discussion obtained from the proposed method are presented. In Section 4, conclusions drawn based on the results are presented.

The proposed methodology assumes generalized Gaussian distribution [

Based on the oscillometric BP envelope, the MAA is widely used to estimate the SBP and DBP, which utilizes SBPR and DBPR to find the points which correspond to SBP and DBP. The amplitude of the maximum point is multiplied by the fixed SBPR and DBPR obtained experimentally [

_{i,j}

For any ^{th}^{th}_{i,j}_{1}, _{2},…, _{m}

Let _{s}_{d}

_{s}_{d}_{1} = 0.65 to _{k}_{1} = 0.30 to _{k}

_{s}_{d}_{s}_{(}_{i,j}_{)} = _{s}_{d}_{(}_{i,j}_{)} = _{d}_{s}_{(}_{i,j}_{)} = _{s}_{d}_{(}_{i,j}_{)} = _{d}

The _{s}_{(}_{i,j}_{)} and _{d}_{(}_{i,j}_{)}, denote the ^{th}

The likelihoods
_{s}_{(}_{i,j}_{)} that maximizes the likelihood ratio, for the available SBP reference measurements for each subject. The same idea is used for obtaining the DBPR. Since two reference auscultatory measurements are available, the average SBP and DBP measurement is used as the reference to obtain the SBPR and DBPR. We also apply the Laplacian (L) model [

The reference SBPR and DBPR are obtained for the ^{th}^{th}_{(}_{i,j}_{)} corresponds to the maximum amplitude in the OMW's envelope.

The following procedure is used for obtaining the SBP and DBP estimates using the conventional approach. The OMW is recovered using the CP and the pulse derivative waveform (PDW) [

The SBP and DBP estimates are also obtained using Bayesian inference [

The following step by step procedure is used to estimate the SBP and DBP ratios using the Bayesian approach as shown

As the first step, the ranges of the systolic and diastolic ratios used in the proposed method are initially found experimentally [

The SBP and DBP estimates are obtained using both the MA value and the fixed

The reference SBPR and DBPR are obtained using the reference auscultatory measurement, which itself is obtained using the cuff pressure, reference auscultatory measurement, and maximum amplitude for each subject.

The

The calculation of POP is performed to determine the final ratio of SBP and DBP in

The SBPR and DBPR that produced the maximum

Similarly, the ratio for the DBP,

The local research ethics committee approved the research, and all subjects provided informed consent prior to the BP measurement according to the protocol of the institutional research ethics board. The oscillometric measurements for this study were provided by Biosign Technologies Inc. (Toronto, Ontario, Canada). The experimental data set was acquired from 85 healthy subjects aged from 12 to 80, out of which thirty seven were females and forty eight were males. No recruited subject had any history of cardiovascular disease. Five sets of oscillometric BP measurements were obtained from each volunteer (5 × 85 = 425 total measurements: duration range to record a single measurement: 31–95 s, duration median: 55 s) using a wrist worn UFIT^{®} blood pressure device [

In this paper, only five measurements of each subject were assumed to be available and were used to implement was used as the true estimate. In

In order to verify the performance of BP estimation, the MD and the SD between the estimated BP and the auscultatory nurse measurements were calculated according to AAMI standard protocol recommended [

The work described in this paper is a systematic methodology with a theoretical basis using a Bayesian model for estimating the SBP and DBP. As seen from in the last row of

In addition, the SD was utilized as a tool of error variable between the auscultatory nurse measurements and the estimates obtained using the proposed MAABG. The SD obtained with the proposed methods, which are the MAABG and MAABL, was found to be 3.32 and 3.32 mmHG for the SBP, respectively, and 3.34 and 3.34 mmHG for the DBP, respectively. This performance is superior to that obtained when the conventional MAA was compared with the auscultatory nurse measurements. The difference in SD between the proposed MAABG and the conventional MAA, for SBP and DBP is 2.99 and 1.13 mmHG. Such improvements could be very significant given that the AAMI protocol recommends for the automated BP monitors [

In conclusion, the MDs and SDs of the SBP and DBP obtained through the proposed MAABG and MAABL are smaller relative to the reference nurse values when compared to the conventional MAA method. This study has established that the proposed method has outperformed the conventional MAA method in estimating the SBP and DBP. Furthermore, a systematic methodology with a theoretical basis for calculating individualized SBPR and DBPR is demonstrated that can be used with conventional MAA algorithm.

The authors thank Biosign for providing equipment and data. The authors would like to thank Hilmi Dajani, Voicu Groza, Miodrag Bolic, and Sreeraman Rajan who are with the School of Electrical and Computer Science, University of Ottawa, Canada. This research was supported by NRF(2013R1A1A2012536). This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning(2013R1A1A1010797)

The authors declare no conflict of interest.

Here, we add the basic concept of Bayes rule [

Based on _{s}_{s}_{(}_{i,j}_{)}), actually, the value that occurs and where _{s}_{(}_{i,j}_{)}) is allowed to vary over its whole range for _{1},…, _{k}

The concept of maximum amplitude algorithm (MAA). (

Systolic blood pressure (SBP) and diastolic blood pressure (DBP) ratio-points are obtained by the auscultatory nurse measured with respect to one subject (five measurements); the SBP ratios (0.91, 0.81, 0.97, 0.74, 0.75); the DBP ratios (0.41,0.48, 0.36, 0.40, 0.33).

The distribution of pseudo ratios for the SBP and DBP using the nonparametric bootstrap (NPB).

The estimation of SBP and DBP is used to estimate the SBP and DBP ratio based on the Bayesian mode.

Bland-Altman plots comparing of the performance between the proposed (MAABG) algorithm and auscultatory results, (

Bland-Altman plots comparing of the performance between thr conventional MAA and auscultatory results, (

Ratio averages of systolic blood pressure (SBP) measurements by the maximum amplitude algorithm using Bayesian with Gaussian (MAABG) and the maximum amplitude algorithm using Bayesian with Laplacian (MAABL);

MAABG | 0.79 (0.11) | 0.79 (0.12) | 0.79 (0.12) | 0.80 (0.11) | 0.80 (0.11) |

MAABL | 0.79 (0.11) | 0.79 (0.12) | 0.79 (0.12) | 0.80 (0.11) | 0.80 (0.11) |

Ratio averages of diastolic blood pressure (DBP) measurements by the maximum amplitude algorithm using Bayesian with Gaussian (MAABG) and the maximum amplitude algorithm using Bayesian with Laplacian (MAABL);

MAABG | 0.44 (0.11) | 0.43 (0.11) | 0.42 (0.11) | 0.41 (0.11) | 0.39 (0.11) |

MAABL | 0.44 (0.11) | 0.43 (0.11) | 0.42 (0.11) | 0.41 (0.11) | 0.39 (0.11) |

Summary of the averaged systolic blood pressure (SBP) estimates by the nurse, the maximum amplitude algorithm (MAA), MAA using Bayesian with Gaussian (MAABG), and the maximum amplitude algorithm (MAA), MAA using Bayesian with Laplacian (MAABL);

108.9 (13.2) | 108.9 (13.5) | 109.8 (13.8) | 110.3 (13.5) | 112.2 (14.6) | |

115.4 (14.0) | 115.5 (14.4) | 116.3 (14.5) | 118.1 (14.3) | 120.0 (15.4) | |

114.8 (13.2) | 114.6 (13.3) | 115.6 (13.1) | 116.7 (13.5) | 118.5 (14.6) | |

114.8 (13.2) | 114.6 (13.3) | 115.6 (13.1) | 116.7 (13.5) | 118.5 (14.6) |

Summary of the averaged diastolic blood pressure (DBP) estimates by the nurse, the maximum amplitude algorithm (MAA), MAA using Bayesian with Gaussian (MAABG), and the maximum amplitude algorithm (MAA), MAA using Bayesian with Laplacian (MAABL);

67.6 (9.8) | 67.1 (9.6) | 67.2 (10.0) | 67.6 (9.8) | 67.5 (10.2) | |

69.7 (10.5) | 69.8 (10.4) | 69.9 (10.3) | 72.0 (10.5) | 73.2 (10.8) | |

70.7 (10.3) | 70.4 (9.9) | 70.7 (9.9) | 72.0 (9.9) | 71.9 (9.9) | |

70.7 (10.3) | 70.4 (9.9) | 70.7 (9.9) | 72.0 (9.9) | 71.9 (9.9) |

Summary of the MD and SD obtained using the MAA and the proposed methods (MAABG and MAABL) relative to the reference auscultatory method.

1st mea. | 6.80 (6.70) | 5.39 (5.10) | 6.01 (2.99) | 4.92 (3.58) | 6.01 (2.99) | 4.92 (3.58) |

2nd mea. | 7.80 (6.22) | 5.60 (4.40) | 5.87 (3.27) | 4.56 (2.93) | 5.87 (3.27) | 4.56 (2.93) |

3rd mea. | 6.70 (5.80) | 5.70 (4.20) | 6.45 (3.73) | 4.88 (3.39) | 6.45 (3.73) | 4.88 (3.39) |

4th mea. | 6.30 (5.77) | 6.00 (4.09) | 6.14 (2.84) | 5.01 (3.32) | 6.14 (2.84) | 5.01 (3.32) |

5th mea. | 7.56 (7.07) | 7.08 (4.98) | 6.76 (3.79) | 5.63 (3.87) | 6.76 (3.79) | 5.63 (3.87) |

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avg. | 7.03 (6.31) | 5.95 (4.55) | 6.25 (3.32) | 5.00 (3.42) | 6.25 (3.32) | 5.00 (3.42) |