Zijian Huang

Year of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics

Principal Supervisor

Peng, Heng


Hypertension ; Blood pressure




Blood pressure is one of the most important indicators of human health. The symptoms of many cardiovascular diseases like stroke, atrial fibrillation, and acute myocardial infarction are usually indicated by the abnormal variation of blood pressure. Severe symptoms of diseases like coronary syndrome, rheumatic heart disease, arterial aneurysm, and endocarditis also usually appear along with the variation of blood pressure. Most of the current blood pressure measurements rely on the Korotkoff sounds method that focuses on one-time blood pressure measuring but cannot supervise blood pressure continuously, which cannot effectively detect diseases or alert patients. Previous researches indicating the relationship between photoplethysmogram (PPG) signal and blood pressure brought up the new research direction of blood pressure measurement method. Ideally, with the continuous supervision of the PPG signal, the blood pressure of the subject could be measured longitudinally, which matches the current requirements of blood pressure measurement better as an indicator of human health. However, the relationship between blood pressure and PPG signal is very comprehensive that is related to personal and environmental status, which leads to the research challenge for many previous works that tried to find the mapping from PPG signal to blood pressure without considering other factors. In this thesis, we propose two statistical methods modeling the comprehensive relationships among blood pressure, PPG signals, and other factors for blood pressure prediction. We also express the modeling and predicting process for the real data set and provide accurate prediction results that achieve the international blood pressure measurement standard. In the first part, we propose the Independent Variance Components Mixed- model (IVCM) that introduces the variance components to describe the relationship among observations. The relationship indicators are collected as information to divide observations into different groups. The latent impacts from the properties of groups are estimated and used for predicting the multiple responses. The Stochastic Approximation Minorization-maximization (SAM) algorithm is used for IVCM model parameter estimation. As the expansion of Minorization-maximization (MM) algorithm, the SAM algorithm could provide comparable-level estimations as MM algorithm but with faster computing speed and less computational cost. We also provide the subsampling prediction method for IVCM model prediction that could predict multiple responses variables with the conditional expectation of the model random effects. The prediction speed of the subsampling method is as fast as the SAM algorithm for parameter estimation with very small accuracy loss. Because the SAM algorithm and subsampling prediction method requires assigning tuning parameters, a great amount of simulation results are provided for the tuning parameter selection. In the second part, we propose the Groupwise Reweighted Mixed-model (GRM) to describe the variation of random effects as well as the potential components of mixture distributions. In the model, we combine the properties of mixed-model and mixture model for modeling the comprehensive relationship among observations as well as between the predictive variables and the response variables. We bring up the Groupwise Expectation Minorization-maximization (GEM) algorithm for the model parameter estimation. Developed from MM algorithm and Expectation Maximization (EM) algorithm, the algorithm estimates parameters fast and accurate with adopting the properties of the diagonal blocked matrix. The corresponding prediction method for GRM model is provided as well as the simulations for the number of components selection. In the third part, we apply the IVCM model and the GRM model in modeling real data and predicting blood pressure. We establish the database for modeling blood pressure with PPG signals and personal characteristics, extract PPG features from PPG signal waves, and analyze the comprehensive relationship between PPG signal and blood pressure with the IVCM model and the GRM model. The blood pressure prediction results from different models are provided and compared. The best prediction results not only achieve the international blood pressure measurement standard but also show great performance in high blood pressure prediction


Principal supervisor: Dr. Peng Heng ; Thesis submitted to the Department of Mathematics


Includes bibliographical references (pages 135-140)

Available for download on Wednesday, November 09, 2022

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