Noninvasive and convenient measurement of vascular stiffness is of considerable importance for early detection and treatment of arteriosclerosis. Volume elastic modulus (\({E}_{{v}}\)) is one of representative measures reflecting effective vascular elasticity that is strongly dependent upon blood pressure (BP) or transmural pressure (\({P}_{{t}{r}}\) = mean BP – (externally applied pressure)). However, its nonlinear nature in terms of functional form has not been fully investigated in human vasculature. This paper therefore seeks to clarify the functional form of \({E}_{{v}}({P}_{{t}{r}})\) in the human finger and radial arteries based on photoplethysmographic volume-oscillometry developed for novel indirect BP measurement. Using a smartphone-based instrument specially designed for this study, \({E}_{{v}}\) values at various \({P}_{{t}{r}}\) levels were obtained in 11 male and female volunteers with various ages. It was demonstrated that \({E}_{{v}}({P}_{{t}{r}})\) showed an exponential behavior with respect to \({P}_{tr}\) changes, expressed as \({E}_{{v}}({P}_{{t}{r}})={E}_{{v}0}\bullet {e}{x}{p}(\alpha \bullet {P}_{{t}{r}})\) (\({E}_{{v}0}\), α; constant) with a high coefficient of determination, the validity of which was also supported through theoretical derivation. Conclusively, the \({E}_{{v}}({P}_{{t}{r}})\) is found to increase exponentially with arterial distending pressure, and the independent measures \({E}_{{v}0}\) and α would be useful parameters to conveniently evaluate progressive changes of vascular stiffness among and/or within individuals, indicating that this measurement has potential for arteriosclerosis screening (200/200).

Graphical abstract

Schematic diagram of overall configuration of the measurement system of arterial elasticity in the finger and the wrist, consisting of a measuring, signal processing and control (MSC) unit (surrounded by the dashed line) and a smartphone for data display and storage. An occlusive cuff and a photoplethysmographic placement of LED and PD for the finger and the wrist are shown in the upper middle part. Measurement scenes of the finger and the wrist are also inset in the upper left and in the upper right part, respectively.

中文翻译：

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具有透壁压力指数函数的体积弹性模量作为通过光电容积描记容积示波法在人手指和桡动脉中得出的有效刚度测量：动脉硬化筛查的潜力

血管硬度的无创且方便的测量对于动脉硬化的早期检测和治疗具有相当重要的意义。体积弹性模量 ( \({E}_{{v}}\) ) 是反映有效血管弹性的代表性指标之一，它强烈依赖于血压 ( BP ) 或透壁压 ( \({P}_{{t }{r}}\) = 平均血压–（外加压力））。然而，其在功能形式方面的非线性性质尚未在人类脉管系统中得到充分研究。因此，本文试图阐明\({E}_{{v}}({P}_{{t}{r}})\)的函数形式在人类手指和桡动脉中，基于为新型间接血压测量而开发的光电容积脉搏波体积示波法。使用专为本研究设计的基于智能手机的仪器，在 11 名男性中获得了不同\({P}_{{t}{r}}\)水平的\({E}_{{v}}\)值和不同年龄的女性志愿者。证明\({E}_{{v}}({P}_{{t}{r}})\)表现出关于\({P}_{tr}\)变化的指数行为，表示为\({E}_{{v}}({P}_{{t}{r}})={E}_{{v}0}\bullet {e}{x}{p} (\alpha \bullet {P}_{{t}{r}})\) ( \({E}_{{v}0}\) , α; 常数）具有较高的决定系数，其有效性也得到了理论推导的支持。最后，发现\({E}_{{v}}({P}_{{t}{r}})\)随动脉扩张压力呈指数增加，独立测量值\({E}_ {{v}0}\)和α将是有用的参数，可以方便地评估个体之间和/或内部血管硬度的渐进性变化，表明该测量具有用于动脉硬化筛查的潜力 (200/200)。

图形概要

手指和手腕动脉弹性测量系统整体配置示意图，由测量、信号处理和控制（MSC）单元（虚线包围）和用于数据显示和存储的智能手机组成。手指和手腕的闭塞袖带和 LED 和 PD 的光电容积描记图放置显示在中上部。手指和手腕的测量场景也分别嵌入在左上角和右上角。