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Frank's Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload.

Abstract Rationale Exercise tolerance is decreased in patients with pulmonary hypertension (PH). It is unknown whether exercise intolerance in PH coincides with an impaired rest-to-exercise response in right ventricular (RV) contractility. Objectives To investigate in patients with PH the RV exertional contractile reserve, defined as the rest-to-exercise response in end-systolic elastance (ΔEes), and the effects of exercise on the matching of Ees and RV afterload (Ea) (i.e., RV–arterial coupling; Ees/Ea). In addition, we compared ΔEes with a recently proposed surrogate, the rest-to-exercise change in pulmonary artery pressure (ΔPAP). Methods We prospectively included 17 patients with precapillary PH and 7 control subjects without PH who performed a submaximal invasive cardiopulmonary exercise test between January 2013 and July 2014. Ees and Ees/Ea were assessed using single-beat pressure–volume loop analysis. Measurements and Main Results Exercise data in 16 patients with PH and 5 control subjects were of sufficient quality for analysis. Ees significantly increased from rest to exercise in control subjects but not in patients with PH. Ea significantly increased in both groups. As a result, exercise led to a decrease in Ees/Ea in patients with PH, whereas Ees/Ea was unaffected in control subjects (Pinteraction = 0.009). In patients with PH, ΔPAP was not related to ΔEes but significantly correlated to the rest-to-exercise change in heart rate. Conclusions In contrast to control subjects, patients with PH were unable to increase Ees during submaximal exercise. Failure to compensate for the further increase in Ea during exercise led to deterioration in Ees/Ea. Furthermore, ΔPAP did not reflect ΔEes but rather the change in heart rate.

During aging, systolic blood pressure continuously increases over time, whereas diastolic pressure first increases and then slightly decreases after middle age. These pressure changes are usually explained by changes of the arterial system alone (increase in arterial stiffness and vascular resistance). However, we hypothesise that the heart contributes to the age-related blood pressure progression as well. In the present study we quantified the blood pressure changes in normal aging by using a Windkessel model for the arterial system and the time-varying elastance model for the heart, and compared the simulation results with data from the Framingham Heart Study. Parameters representing arterial changes (resistance and stiffness) during aging were based on literature values, whereas parameters representing cardiac changes were computed through physiological rules (compensated hypertrophy and preservation of end-diastolic volume). When taking into account arterial changes only, the systolic and diastolic pressure did not agree well with the population data. Between 20 and 80 years, systolic pressure increased from 100 to 122 mmHg, and diastolic pressure decreased from 76 to 55 mmHg. When taking cardiac adaptations into account as well, systolic and diastolic pressure increased from 100 to 151 mmHg and decreased from 76 to 69 mmHg, respectively. Our results show that not only the arterial system, but also the heart, contributes to the changes in blood pressure during aging. The changes in arterial properties initiate a systolic pressure increase, which in turn initiates a cardiac remodelling process that further augments systolic pressure and mitigates the decrease in diastolic pressure.

Background Longitudinal wall motion of the right ventricle (RV), generally quantified as tricuspid annular systolic excursion (TAPSE), has been well studied in pulmonary hypertension (PH). In contrast, transverse wall motion has been examined less. Therefore, the aim of this study was to evaluate regional RV transverse wall motion in PH, and its relation to global RV pump function, quantified as RV ejection fraction (RVEF). Methods In 101 PH patients and 29 control subjects cardiovascular magnetic resonance was performed. From four-chamber cine imaging, RV transverse motion was quantified as the change of the septum-free-wall (SF) distance between end-diastole and end-systole at seven levels along an apex-to-base axis. For each level, regional absolute and fractional transverse distance change (SFD and fractional- SFD) were computed and related to RVEF. Longitudinal measures, including TAPSE and fractional tricuspid-annulus-apex distance change ( fractional -TAAD) were evaluated for comparison. Results Transverse wall motion was significantly reduced at all levels compared to control subjects (p < 0.001). For all levels, fractional -SFD and SFD were related to RVEF, with the strongest relation at mid RV (R 2 = 0.70, p < 0.001 and R 2 = 0.62, p < 0.001). For TAPSE and fractional -TAAD, weaker relations with RVEF were found (R 2 = 0.21, p < 0.001 and R 2 = 0.27, p < 0.001). Conclusions Regional transverse wall movements provide important information of RV function in PH. Compared to longitudinal motion, transverse motion at mid RV reveals a significantly stronger relationship with RVEF and thereby might be a better predictor for RV function.

Introduction: Pressure waveshape derived parameters such as the augmentation index are related to unfavourable cardiovascular events [1]. Wave reflections determine wave shape [2], however, several findings seem to contradict the current views. Current view. The arterial system can be modelled by a tube with a reflection site at the end: the heart sets up waves propagating down the system, reflecting at the end and returning to the heart after twice the travel time, i.e. aortic length over Pulse Wave Velocity (PWV).Data. Return time of the reflected wave is not inversely proportional to PWV [3]. Also, reflected waves appear to run downstream rather than to the heart [4]. These findings conflict with the current concepts. Interpretation: At all locations in the arterial system, wave reflection is determined by the characteristic impedance of the supplying vessel and the input impedance of the downstream system. The input impedance results from a system of many arteries with multiple reflection sites [5]. Time delay between forward and reflected wave is mainly determined by the phase angle of the downstream impedance, and does not systematically increase or decrease with distance. This implies that the time difference between reflected and forward wave is not increasing towards the heart as assumed by the single-tube model. As a consequence, the return time of the reflected wave is not inversely proportional to PWV. Conclusion: The single tube model should be abandoned as conceptual model as is does not explain the measured data. A frequency domain (impedance) model is required.

Introduction Pressure waveshape derived parameters such as the augmentation index are related to unfavourable cardiovascular events [ 1 ]. Wave reflections determine wave shape [ 2 ], however, several findings seem to contradict the current views. Current view. The arterial system can be modelled by a tube with a reflection site at the end: the heart sets up waves propagating down the system, reflecting at the end and returning to the heart after twice the travel time, i.e. aortic length over Pulse Wave Velocity (PWV).Data. Return time of the reflected wave is not inversely proportional to PWV [ 3 ]. Also, reflected waves appear to run downstream rather than to the heart [ 4 ]. These findings conflict with the current concepts. Interpretation At all locations in the arterial system, wave reflection is determined by the characteristic impedance of the supplying vessel and the input impedance of the downstream system. The input impedance results from a system of many arteries with multiple reflection sites [ 5 ]. Time delay between forward and reflected wave is mainly determined by the phase angle of the downstream impedance, and does not systematically increase or decrease with distance. This implies that the time difference between reflected and forward wave is not increasing towards the heart as assumed by the single-tube model. As a consequence, the return time of the reflected wave is not inversely proportional to PWV. Conclusion The single tube model should be abandoned as conceptual model as is does not explain the measured data. A frequency domain (impedance) model is required.

Decrease in arterial compliance leads to an increased pulse pressure, as explained by the Windkessel effect. Pressure waveform is the sum of a forward running and a backward running or reflected pressure wave. When the arterial system stiffens, as a result of aging or disease, both the forward and reflected waves are altered and contribute to a greater or lesser degree to the increase in aortic pulse pressure. Two mechanisms have been proposed in the literature to explain systolic hypertension upon arterial stiffening. The most popular one is based on the augmentation and earlier arrival of reflected waves. The second mechanism is based on the augmentation of the forward wave, as a result of an increase of the characteristic impedance of the proximal aorta. The aim of this study is to analyze the two aforementioned mechanisms using a 1-D model of the entire systemic arterial tree. A validated 1-D model of the systemic circulation, representative of a young healthy adult was used to simulate arterial pressure and flow under control conditions and in presence of arterial stiffening. To help elucidate the differences in the two mechanisms contributing to systolic hypertension, the arterial tree was stiffened either locally with compliance being reduced only in the region of the aortic arch, or globally, with a uniform decrease in compliance in all arterial segments. The pulse pressure increased by 58% when proximal aorta was stiffened and the compliance decreased by 43%. Same pulse pressure increase was achieved when compliance of the globally stiffened arterial tree decreased by 47%. In presence of local stiffening in the aortic arch, characteristic impedance increased to 0.10 mmHg s/mL vs. 0.034 mmHg s/mL in control and this led to a substantial increase (91%) in the amplitude of the forward wave, which attained 42 mmHg vs. 22 mmHg in control. Under global stiffening, the pulse pressure of the forward wave increased by 41% and the amplitude of the reflected wave by 83%. Reflected waves arrived earlier in systole, enhancing their contribution to systolic pressure. The effects of local vs. global loss of compliance of the arterial tree have been studied with the use of a 1-D model. Local stiffening in the proximal aorta increases systolic pressure mainly through the augmentation of the forward pressure wave, whereas global stiffening augments systolic pressure principally though the increase in wave reflections. The relative contribution of the two mechanisms depends on the topology of arterial stiffening and geometrical alterations taking place in aging or in disease.

Abstract Rationale Pulmonary hypertension (PH) is characterized by increased arterial load requiring more right ventricular (RV) hydraulic power to sustain adequate forward blood flow. Power can be separated into a mean and oscillatory part. The former is associated with mean and the latter with pulsatile blood flow and pressure. Because mean power provides for net blood flow, the ratio of oscillatory to total power (oscillatory power fraction) preferably should be small. It is unknown whether this is the case in pulmonary arterial hypertension (PAH). Objectives To derive components of power generated by the right ventricle in PAH. Measurements and Main Results Thirty-five patients with idiopathic PAH (IPAH) and 14 subjects without PH were included. The patients were divided in two groups, “moderate” and “high,” based on pulmonary artery (PA) pressure. PA pressures were obtained by right heart catheterization and PA flows by magnetic resonance imaging. Total hydraulic power (Powertotal) was calculated as the integral product of pressure and flow. Mean hydraulic power (Powermean) was calculated as mean pulmonary artery pressure times mean flow. Their difference is oscillatory power (Poweroscill). Total hydraulic power in subjects without PH compared with moderate and high IPAH was 0.29 ± 0.10 W (n = 14), 0.52 ± 0.14 W (n = 17), and 0.73 ± 0.24 W (n = 18), respectively. The oscillatory power fraction is approximately 23% and not different between groups. Conclusions In this study, oscillatory power fraction is constant at 23% in non-PH and IPAH, implying that a considerable amount of power is not used for forward flow, making the RV less efficient with respect to its arterial load. Our findings emphasize the need to develop new therapy strategies to optimize RV power output in PAH.

Exercise variables determined in patients with pulmonary arterial hypertension (PAH) at the time of diagnosis, predict survival. It is unknown whether upon treatment, subsequent changes in these exercise variables reflect improvements in survival. The aim of this study was to determine changes in exercise variables in PAH patients and to relate these changes to survival. Baseline cardiopulmonary exercise test (CPET) variables and six-minute-walk-distance (6MWD) were available from 65 idiopathic PAH patients (50 females; mean age 45±2yrs). The same variables were determined after treatment (13months) in a sub group of 43 patients. To estimate the association between changes in exercise variables and changes in cardiac function, right-ventricle ejection fraction (RVEF) was measured by cardiac MRI at baseline and after treatment in 34 patients. Mean follow-up time after the second CPET was 53 (range: 4-111) months. Kaplan-Meier analysis was used to relate survival to baseline and treatment-associated changes in exercise variables. Survivors showed a significantly greater change in maximal oxygen uptake than non-survivors and this change in aerobic capacity was significantly related to changes in RVEF. From baseline until the end of the study period, two patients underwent a lung transplantation and 19 patients died. Survival analysis showed that baseline 6MWD (p<0.0001), maximal heart rate (p<0.0001) and the slope relating ventilation with carbon dioxide production (p≤0.05) were significant predictors of survival, whereas baseline oxygen uptake and oxygen pulse held no predictive value. Treatment associated changes in 6MWD (p<0.01), maximal heart rate (p<0.05), oxygen uptake (p<0.001) and oxygen pulse predicted survival (p<0.05), whereas changes in the slope relating ventilation with carbon dioxide production did not. Exercise variables with prognostic significance when determined at baseline, retain their prognostic relevance after treatment. However, when changes in exercise variables upon treatment are considered, a different set of variables provides prognostic information.