以納維-斯托克斯方程與非侵入式光學方法連續監測平均動脈壓

Abstract

長期血壓過高容易導致心血管疾病的發生，而心血管疾病在近年皆位居十大死因之冠，因此隨時量測血壓能及早預防因高血壓而衍生的併發症。然而，目前常見的血壓計多為基於振盪法的加壓式血壓計，若要連續監測血壓，反覆地以袖帶施加壓力於手臂或手腕上會讓受試者感到不適，進而促成以光學方法估計血壓之研究。近年來，越來越多人有配戴智慧手錶或智慧手環的習慣，穿戴裝置的開發商也注意到居家個人照護的商機，因此利用穿戴裝置評估血管健康度將會是未來的趨勢。 本研究考量平均動脈壓能反映血液是否有足夠的動力推動至各大器官與末梢血管，因此將平均動脈壓作為量測目標，而本研究所使用的平均動脈壓模型由下列三個面向所構成。首先，根據納維-斯托克斯方程建立血流量與壓力間的關係式。接著，考量自律神經系統能透過人類體內的壓力受器偵測與調節平均動脈壓的狀態，且因心率變異性指標能反映自律神經系統的平衡狀態，故將心率變異性指標作為平均動脈壓模型的參數。最後，結合光體積變化描記圖法(photoplethysmography, PPG)之理論，得到平均動脈壓之迴歸模型。 本研究希望未來能將平均動脈壓的量測裝置結合智慧手錶，因此將量測位置設定在手腕處。此外，本研究希望自製的PPG量測裝置不僅能收取皮膚表層之微血管資訊，還能取得橈動脈周遭組織的資訊，故在設計量測系統時，考量近紅外光在組織中所能傳遞的距離較遠，且波段為940 nm之近紅外光受不同膚色的影響最小，因此選用該波段作為PPG量測裝置的光源。同時，本研究測試單顆發光二極體(light-emitting diode, LED)、四顆LEDs與分別搭配平凸透鏡後的光源系統，由影像式的光強度分布可知，四顆LEDs搭配平凸透鏡的系統能有效提升照明區域中的最大照度與均勻度。最後，本研究利用四顆LEDs、平凸透鏡與光電二極體建立PPG量測裝置。 在驗證實驗中，本研究以超聲波探頭取得血液流速資訊，同時以PPG量測裝置取得PPG訊號，經數學運算後，PPG訊號與平均血容量具有一致性，因此本研究利用PPG訊號取得血容量資訊，而統計結果顯示，以PPG訊號估計心率變異性指標具有可行性。根據血壓量測試驗的結果，在建立平均動脈壓之迴歸模型時，應考量群體受試者的數據並建立總體模型，因為單一受試者在無劇烈運動時，其平均動脈壓不會有大幅度的變動，導致個別模型的預測結果容易趨向同一數值，當受試者的平均動脈壓突然上升或下降時，會有誤差較大的狀況產生。本研究自製的量測系統與總體模型，在評估四位受試者的連續平均動脈壓時，實現了連續血壓監測。 綜觀而言，本研究成功提出一個得以連續監測平均動脈壓之量測系統，其同時考量了物理基礎、生理調節機制與光學原理，並將量測裝置製成探頭的型式，達到在不搭配其他儀器的條件下，以單點式PPG量測方法收取生理訊號，並使用PPG訊號取得平均血容量與心率變異性指標，進而持續估算平均動脈壓。

Long-term hypertension easily leads to cardiovascular disease, and cardiovascular disease has ranked among the top ten causes of death in recent years. Therefore, measuring blood pressure at any time can prevent complications derived from hypertension as early as possible. However, the current common devices for blood pressure measurement are oscillometric method sphygmomanometers. When continuously measuring blood pressure, the subject may feel uncomfortable due to the external force from the cuff repeatedly applied on the arm or wrist. Then, the fact contributes to the study of estimating blood pressure by optical method. Recently, more and more people have the habit of wearing smart watches or smart bracelets. Developers of wearable devices have also noticed the business opportunities of personal care at home. Therefore, using wearable devices to evaluate vascular health will be a future trend. This study considered that the mean arterial pressure (MAP) can reflect whether the blood has enough power to be transmitted to all organs and peripheral blood vessels, so the MAP was viewed as the measurement target. The three aspects of the mean arterial pressure model that was employed in this study are covered individually below. First, the relationship between blood flow and pressure drop was established according to Navier-Stokes equations. Next, considering that the autonomic nervous system (ANS) can detect and regulate the state of MAP through the baroreceptors in the human body, and the heart rate variability (HRV) indices are regarded as the parameters in MAP model because the HRV indices can reflect the balance of the ANS. Finally, the above derivation results were combined with the theory of photoplethysmography (PPG) to obtain the regression model of MAP. Since the MAP measurement device may be merged in smart watches as wearable healthy instrument, the measurement position was set in the wrist. Thus, PPG measurement device has been designed and used to receive the information including both capillaries in the skin surface and the tissue around the radial artery. Considering that the penetration depth of near infrared in the human tissue is deeper than other region spectrum, and that the absorption coefficient of 940 nm wavelength light has the least difference between different skin tone than other spectrum, the 940 nm wavelength light was selected as the light source of PPG measurement device in this study. Meanwhile, we tested four different light source system: (1) a 940 nm wavelength light-emitting diode (LED), (2) four LEDs, (3) a LED with a plano-convex lens, and (4) four LEDs with a plano-convex lens. According to the light intensity distribution by charge-coupled device, the system including four LEDs and a plano-convex lens can effectively improve the maximum illuminance and uniformity in the lighting area. Therefore, the PPG measurement device, consists of four LEDs, integrated with a convex lens and a photodiode was applied. For further validation, the blood flow information was collected by an ultrasound probe, simultaneously compared to the PPG signals. After mathematical operations, the PPG signals and mean blood volume were consistent, so that the PPG signals were viewed as blood volume in the regression model, and that the HRV indices were estimated from PPG signals were feasible. From the results of blood pressure measurement experiment, the MAP of each subject without intense exercise did not fluctuate significantly, which caused that the prediction using individual model easily tended to the same value. In other words, when the MAP of the subjects rose or fell suddenly, there was a large error in the prediction of individual models. Therefore, the regression model should consider the data from the group subjects and establish a general model to predict MAP. In the continuous blood pressure monitoring experiment, it was confirmed that the measurement system and the general model of this study can evaluate the continuous MAP of multiple subjects. In short, this study successfully proposed a measurement system for continuous monitoring of MAP, which simultaneously considered the physical basis, physiological regulation mechanism, and optical principles. At the same time, the measurement device was made into a probe type, so that the single-point PPG measurement method can be used to collect vital signals without other instruments. Finally, the mean blood volume and the HRV indices were calculated from PPG signals in order to continuously estimate the MAP.