Mathematical Modeling of Oscillometric Blood Pressure Measurement: A Complete, Reduced Oscillogram Model
Vishaal Dhamotharan, Anand Chandrasekhar, Hao‐Min Cheng, Chen‐Huan Chen, Shih‐Hsien Sung, Cederick Landry, Jin‐Oh Hahn, Aman Mahajan, Sanjeev G. Shroff, Ramakrishna Mukkamala
Abstract
<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Objective:</i> Oscillogram modeling is a powerful tool for understanding and advancing popular oscillometric blood pressure (BP) measurement. A reduced oscillogram model relating cuff pressure oscillation amplitude ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta O$</tex-math></inline-formula> ) to external cuff pressure of the artery ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${P}_e$</tex-math></inline-formula> ) is: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta O\ ({{P}_e}) = k\mathop \int \nolimits_{{P}_d - {P}_e}^{{P}_s - {P}_e} g(P)dP$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$g(P)$</tex-math></inline-formula> is the arterial compliance versus transmural pressure ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> ) curve, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${P}_s$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${P}_d$</tex-math></inline-formula> are systolic and diastolic BP, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is the reciprocal of the cuff compliance. The objective was to determine an optimal functional form for the arterial compliance curve. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> Eight prospective, three-parameter functions of the brachial artery compliance curve were compared. The study data included oscillometric arm cuff pressure waveforms and invasive brachial BP from 122 patients covering a 20-120 mmHg pulse pressure range. The oscillogram measurements were constructed from the cuff pressure waveforms. Reduced oscillogram models, inputted with measured systolic and diastolic BP and each parametric brachial artery compliance curve function, were optimally fitted to the oscillogram measurements in the least squares sense. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> An exponential-linear function yielded as good or better model fits compared to the other functions, with errors of 7.9±0.3 and 5.1±0.2% for tail-trimmed and lower half-trimmed oscillogram measurements. Importantly, this function was also the most tractable mathematically. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusion:</i> A three-parameter exponential-linear function is an optimal form for the arterial compliance curve in the reduced oscillogram model and may thus serve as the standard function for this model henceforth. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Significance:</i> The complete, reduced oscillogram model determined herein can potentially improve oscillometric BP measurement accuracy while advancing foundational knowledge.