Relationship between Stroke Volume and Pulse Pressure during Blood Volume Perturbation: A Mathematical Analysis

Abstract

Arterial pulse pressure has been widely used as surrogate of stroke volume, for example, in the guidance of fluid therapy. However, recent experimental investigations suggest that arterial pulse pressure is not linearly proportional to stroke volume. However, mechanisms underlying the relation between the two have not been clearly understood. The goal of this study was to elucidate how arterial pulse pressure and stroke volume respond to a perturbation in the left ventricular blood volume based on a systematic mathematical analysis. Both our mathematical analysis and experimental data showed that the relative change in arterial pulse pressure due to a left ventricular blood volume perturbation was consistently smaller than the corresponding relative change in stroke volume, due to the nonlinear left ventricular pressure-volume relation during diastole that reduces the sensitivity of arterial pulse pressure to perturbations in the left ventricular blood volume. Therefore, arterial pulse pressure must be used with care when used as surrogate of stroke volume in guiding fluid therapy.

Modeling Arterial Pulse Pressure From Heart Rate During Sympathetic Activation by Progressive Central Hypovolemia

“…However, none of these represent biomarkers highly sensitive to the detection of a blood volume deficit since during the initial phase of hypovolemic shock mean BP is maintained by a baroreflex mediated increment in HR and total peripheral resistance (Grant and Reeve, 1941 ; Barcroft et al, 1944 ; McMichael, 1944 ; Ryan et al, 2012 ; Secher and Van Lieshout, 2016 ). In contrast, PP decreases progressively during hypovolemic shock and rather than mean BP reflects central blood volume due to its relation to SV (Convertino et al, 2006 ; Bighamian and Hahn, 2014 ). Since PP is an important biomarker for changing volume state, application of the reported model could assist in the monitoring of patients at risk for blood loss or development of hypovolemia.…”

Robust computation of pulse pressure variations

“…The left ventricular stroke volume (SV) is related to arterial pulse pressure (PP), being the difference between systolic and diastolic pressure, through Laplace law. While SV and PP cannot be assumed to be linearly proportional [3], they exhibit a strong correlation. Consequently, stroke volume variations (∆SV) cause pulse pressure variations (∆PP 3 ) over the respiratory cycle [4].…”

Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

“…For (3), it presents the mathematical model for productivity rate with average stations failure rate. By applying the data in Table 3 into (3), the result is shown in (8). Equation (4) presents the mathematical model for productivity rate with different stations failure and (9) is the result after substituting the data above into (4).…”

“…From the productivity rate result in (8) and (9), (7) which is the actual productivity rate is used as guideline to check which mathematical model can provide more accurate result to actual result and the percentage error is calculated in (10) and (11). Regarding result of (10) and (11), it presents the percentage error when compared to actual productivity rate result.…”

“…In engineering field, mathematic theory and application become a basic tool for design and analysis work such as network, biomedical, and manufacturing engineering as well as with mathematical model or mathematical analysis [7,8]. Mathematical method generally combines with statistical method in analysis stage which is graphical presented with support of mathematical calculation.…”