人體動脈硬化程度，直接關係著許多與心血管有關的慢性病的發生，脈波傳導速率是目前用以評估動脈硬化的重要指標之ㄧ，然而現今量測脈波傳導速率需在醫院量測，醫院所採用的非侵入式動脈硬化檢測，大都是以壓脈帶方式量測脈波傳導速率，其計算方式是以量測之間的距離與時間差下去評估，如果在家就能隨時量測，可增加便利性並且有助於病情的診斷。目前光容積波訊號的形態已得到廣泛研究，可以由光容積波訊號獲取與血液動力學狀態高度相關的各種特徵，加上最近穿戴式設備的快速發展，透過泛用性的生理訊號量測來得知血管變化的方式逐漸引起了人們的廣泛關注。
本論文使用心電訊號和光容積波訊號來估測脈波傳導速率。從穿戴式裝置量測手腕和手指心電訊號和光容積波訊號，對手腕和手指做同步和前處理，將量測產生的干擾或不良訊號移除。對光容積波訊號取特徵，針對特徵丟失和歧義性的問題，提出了解決方法來處理，利用三階微分和二階微分光容積脈衝波的極值來識別二階微分和一階微分的光容積脈衝波波形中缺失或模糊的特徵，可使特徵萃取達98.6%以上的比率。另外，針對光體積描記信號的加權脈衝分解分析，採用五個高斯波解析，並以加權最小平方法準則進行優化，我們將權重施加於被認為可提供血管年齡和血管僵硬度的脈搏段，另外適當設定高斯參數的邊界約束，從結果可以看出加權使分解穩定，高斯參數的平均方差減小。最後使用手腕特徵估測脈波傳導速率，採用極限梯度提升(XGBoost)的演算法，女性均方根誤差最好的結果可以達到177.70(cm/s)，男性均方根誤差最好的結果約為144.39(cm/s)。

The degree of arteriosclerosis is directly related to the occurrence of many chronic diseases. Currently, pulse wave velocity is one essential metricused to evaluate arteriosclerosis. However, the pulse wave velocity is usually measured in the hospital nowadays. The non-invasive method is mostly based on the pressure belt, and calculates their distance divided by the time difference. At present, morphology of the photoplethysmography signals has been widely studied so as to acquire various features that are highly related with hemodynamic states. Recently, the rapid development of wearable devices makes it possible to realize vascular conditions. This change has gradually aroused widespread concern.
In this thesis, we use wrist electrocardiogram (ECG) signals and photoplethysmography (PPG) signals to estimate pulse wave velocity. The ECG and PPG of wrist and finger are measured from wearable devices. These signals are first synchronized and pre-processed to remove interference and bad-quality signals generated during the measurement. Considering the problems of missing and ambiguous features, we propose imputation and resolution techniques. The extrema of the third-order derivative and second-order derivative PPG waveforms are employed to identify the missing or ambiguous features of the second-order derivative and first-order derivative PPG waveforms. We propose weighted pulse decomposition analysis that emphasize the PPG pulse portion corresponding to point a to point f of the second-order derivative PPG. Five Gaussian waves are used for decomposition In addition, the boundary constraints for Gaussian wave parameters are properly set. From the results, we can see that weighting makes the decomposition stable and the variances of Gaussian parameters reduced. Finally, the wrist PPG and ECG features are employed to estimate the brachial ankle pulse wave velocity. The root mean square errors (RMSE) of female estimation results is 177.70(cm/s), and of male estimation results is about 144.39(cm/s), which outperform the result from the conventional multiple linear regression.

[1] S. R. Alty, N. Angarita-Jaimes, S. C. Millasseau and P. J. Chowienczyk, "Predicting arterial stiffness from the digital volume pulse waveform," IEEE Transactions on Biomedical Engineering, vol. 54, no. 12, pp. 2268-2275, 2007.
[2] T. Otsuka, T. Kawada, M. Katsumata, et al., "Independent Determinants of Second Derivative of the Finger Photoplethysmogram among Various Cardiovascular Risk Factors in Middle-Aged Men.," Hypertens Res, vol. 30, pp. 1211-1218, 2008.
[3] Junichiro Hashimoto, Daisuke Watabe, Atsushi Kimura, Hisaki Takahashi, Takayoshi Ohkubo, Kazuhito Totsune, Yutaka Imai, "Determinants of the second derivative of the finger photoplethysmogram and brachial-ankle pulse-wave velocity: The Ohasama study," American Journal of Hypertension, vol. 18, no. 4, pp. 477-485, 2005.
[4] L. A. Bortolotto, J. Blacher, T. Kondo, K. Takazawa, M. E. Safar,, "Assessment of vascular aging and atherosclerosis in hypertensive subjects: second derivative of photoplethysmogram versus pulse wave velocity," American Journal of Hypertension, vol. 13, no. 2, pp. 165-171, 2000.
[5] K. Takazawa, N. Tanaka, M. Fujita, O. Matsuoka, T. Saiki, M. Aikawa, S. Tamura, C. Ibukiyama, "Assessment of vasoactive agents and vascular aging by the second derivative of photoplethysmogram waveform," Hypertension, vol. 32, no. 2, pp. 365-370, 1998.
[6] "https://en.wikipedia.org/wiki/Electrocardiography," [Online].
[7] C.-H. Chen, "The Study of the Variation Trend Diastolic Pressure of the Surhical Patients utilizing Non-Invasive Plethysmohraphy Signal," National Sun Yat-sen University, 2004.
[8] J. Cho, H. J. Baek, "A Comparative Study of Brachial–Ankle Pulse Wave Velocity and Heart–Finger Pulse Wave Velocity in Korean Adults," Sensors, vol. 7, no. 20, 7 Apr 2020.
[9] A. Vehkaoja et al., "System for ECG and heart rate monitoring during group training,," 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC,, pp. 4832-4835, 2008.
[10] P. M. Mohan, A. A. Nisha, V. Nagarajan and E. S. J. Jothi, "Measurement of arterial oxygen saturation (SpO2) using PPG optical sensor,," 2016 International Conference on Communication and Signal Processing (ICCSP), Melmaruvathur,, pp. 1136-1140, 2016.
[11] R. Wang, W. Jia, Z. Mao, R. J. Sclabassi and M. Sun, "Cuff-free blood pressure estimation using pulse transit time and heart rate,," 2014 12th International Conference on Signal Processing (ICSP),Hangzhou, pp. 115-118, 2014.
[12] S. Puke, T. Suzuki, K. Nakayama, H. Tanaka, S. Minami, "Blood pressure estimation from pulse wave velocity measured on the chest," Conf Proc IEEE Eng Med Biol Soc. 2013, pp. 6107-6110, 2013.
[13] J. Pan and W. J. Tompkins, "A Real-Time QRS Detection Algorithm," in IEEE Transactions on Biomedical Engineering, Vols. BME-32, no. 3, pp. 230-236, 1985.
[14] G. Wang, M. Atef, and Y. Lian, "Towards a continuous noninvasive cuffless blood pressure monitoring system using PPG: systems and circuits review," IEEE Circuits and systems magazine, vol. 18, no. 3, pp. 6-26, 2018.
[15] Junichiro Hashimoto, Daisuke Watabe, Atsushi Kimura, Hisaki Takahashi, Takayoshi Ohkubo, Kazuhito Totsune, Yutaka Imai,, "Determinants of the second derivative of the finger photoplethysmogram and brachial-ankle pulse-wave velocity: The Ohasama study," American Journal of Hypertension, vol. 18, no. 4, pp. 477-485, 2005.
[16] C. H. Huang, et al., "Weighted pulse decomposition analysis of fingertip photoplethysmogram signals for blood pressure assessment," in Proc. of International Symposium on Circuits and Systems (ISCAS), 2020.
[17] H. Shin and S. D. Min,, "Feasibility study for the non-invasive blood pressure estimation based on ppg morphology: normotensive subject study," Biomed Eng Online, vol. 16, 2017.
[18] I. Khurana and A. Khurana, Medical Physiology for Undergraduate Students-E-book, Second Edition, Elsevier, 2018.
[19] M. Elgendi, "On the analysis of fingertip photoplethysmogram signals," Current Cardiology Reviews, vol. 8, pp. 14-25, 2012.
[20] M. Elgendi, "Optimal signal quality index for photoplethysmogram signals," Bioengineering, vol. 3, no. 4, p. 21, 2016.
[21] "https://en.wikipedia.org/wiki/Skewness," [Online].
[22] M.C. Baruch, D.ER Warburton, S.SD Bredin, et al., "Pulse decomposition analysis of the digital arterial pulse during hemorrhage simulation," Nonlinear Biomedicine Physics, vol. 5, pp. 1-1, 2011.
[23] R. Couceiro, et al., "Assessment of cardiovascular function from multi-Gaussian fitting of a finger photoplethysmogram," Physiological measurement, vol. 36, pp. 1801-1825, 2015.
[24] U. Rubins, "Finger and ear photoplethysmogram waveform analysis by fitting with Gaussians," Medical and Biological, vol. 46, no. 12, pp. 1271-1276, 2008.
[25] T. Tigges, et al., "Model selection for the pulse decomposition analysis of fingertip photoplethysmograms," in International conference of the IEEE engineering in medicine and biology society (EMBC), 2017.
[26] L. Wang, L. Xu, S. Feng, M. Q. H. Meng and K. Wang, "Multi-Gaussian fitting for pulse waveform using weighted least squares and multi-criteria decision making method," Computers in Biology and Medicine, vol. 43, pp. 1661-1672, 2013.
[27] Y. Liang et al., "Hypertension assessment via ECG and PPG signals: an evaluation using MIMIC database.," Diagnostics (Base), vol. 8, p. 65, 2018.
[28] T.R.Dawber,H.E.Thomas,P.M.McNamara,et al., "Characteristics of the dicrotic notch of the arterial pulse wave in coronary heart disease," Angiology, vol. 24, no. 4, pp. 244-255, 1973.
[29] P. Salvi, E. Magnani, F. Valbusa et al., "Comparative study of methodologies for pulse wave velocity estimation," J Hum Hypertens 22, vol. 22, pp. 669-677, 2008.
[30] D. Jang, U. Farooq, S. Park, C. Goh and M. Hahn, "A Knowledge-Based Approach to Arterial Stiffness Estimation Using the Digital Volume Pulse," in IEEE Transactions on Biomedical Circuits and Systems, vol. 6, no. 4, pp. 366-374, 2012.
[31] L Breiman, "Random Forests," Machine Learning, vol. 45, pp. 5-32, 2001.
[32] T. Hastie, R. Tibshirani, and J. Friedman., The Elements of Statistical Learning, second edition, New York: Springer, 2008.
[33] H. Tomiyama et al., "Influences of age and gender on results of noninvasive brachial/ankle pulse wave velocity measurement- a survey of 12 517 subjects," Atherosclerosis, vol. 166, no. 2, pp. 303-309, 2003.
[34] "Python API Reference -xgboost 1.2.0," [Online]. Available: https://xgboost.readthedocs.io/en/latest/index.html.