Nico Westerhof

The arterial Windkessel

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.

Progressive right ventricular dysfunction in patients with pulmonary arterial hypertension responding to therapy.

OBJECTIVES The purpose of this study was to examine the relationship between changes in pulmonary vascular resistance (PVR) and right ventricular ejection fraction (RVEF) and survival in patients with pulmonary arterial hypertension (PAH) under PAH-targeted therapies. BACKGROUND Despite the fact that medical therapies reduce PVR, the prognosis of patients with PAH is still poor. The primary cause of death is right ventricular (RV) failure. One possible explanation for this apparent paradox is the fact that a reduction in PVR is not automatically followed by an improvement in RV function. METHODS A cohort of 110 patients with incident PAH underwent baseline right heart catheterization, cardiac magnetic resonance imaging, and 6-min walk testing. These measurements were repeated in 76 patients after 12 months of therapy. RESULTS Two patients underwent lung transplantation, 13 patients died during the first year, and 17 patients died in the subsequent follow-up of 47 months. Baseline RVEF (hazard ratio [HR]: 0.938; p = 0.001) and PVR (HR: 1.001; p = 0.031) were predictors of mortality. During the first 12 months, changes in PVR were moderately correlated with changes in RVEF (R = 0.330; p = 0.005). Changes in RVEF (HR: 0.929; p = 0.014) were associated with survival, but changes in PVR (HR: 1.000; p = 0.820) were not. In 68% of patients, PVR decreased after medical therapy. Twenty-five percent of those patients with decreased PVR showed a deterioration of RV function and had a poor prognosis. CONCLUSIONS After PAH-targeted therapy, RV function can deteriorate despite a reduction in PVR. Loss of RV function is associated with a poor outcome, irrespective of any changes in PVR.

Arterial Stiffness Increases With Deteriorating Glucose Tolerance Status The Hoorn Study

Background—Type 2 diabetes (DM-2) and impaired glucose metabolism (IGM) are associated with an increased cardiovascular disease risk. In nondiabetic individuals, increased arterial stiffness is an important cause of cardiovascular disease. Associations between DM-2 and IGM and arterial stiffness have not been systematically investigated. Methods and Results—In a population-based cohort (n=747; 278 with normal glucose metabolism, 168 with IGM, and 301 with DM-2; mean age, 68.5 years), arterial stiffness was ultrasonically estimated by distensibility and compliance of the carotid, femoral, and brachial arteries and by the carotid elastic modulus. After adjustment for age, sex, and mean arterial pressure, DM-2 was associated with increased carotid, femoral, and brachial stiffness, whereas IGM was associated only with increased femoral and brachial stiffness. Carotid but not femoral or brachial stiffness increased from IGM to DM-2. Standardized &bgr;s (95% CI) for IGM and DM-2, compared with normal glucose metabolism, were −0.06 (−0.23 to 0.10) and −0.37 (−0.51 to −0.23) for carotid distensibility; −0.02 (−0.18 to 0.18) and −0.25 (−0.40 to −0.09) for carotid compliance; −0.05 (−0.23 to 0.13) and 0.25 (0.10 to 0.40) for carotid elastic modulus; −0.70 (−0.89 to −0.51) and −0.67 (−0.83 to −0.52) for femoral distensibility; and −0.62 (−0.80 to −0.44) and −0.79 (−0.94 to −0.63) for femoral compliance. The brachial artery followed a pattern similar to that of the femoral artery. Increases in stiffness indices were explained by decreases in distension, increases in pulse pressure, an increase in carotid intima-media thickness, and, for the femoral artery, a decrease in diameter. Hyperglycemia or hyperinsulinemia explained only 30% of the arterial changes associated with glucose tolerance. Adjustment for conventional cardiovascular risk factors did not affect these findings. Conclusions—IGM and DM-2 are associated with increased arterial stiffness. An important part of the increased stiffness occurs before the onset of DM-2 and is explained neither by conventional cardiovascular risk factors nor by hyperglycemia or hyperinsulinemia.

Increased Central Artery Stiffness in Impaired Glucose Metabolism and Type 2 Diabetes. The Hoorn Study

Abstract—Impaired glucose metabolism (IGM) and type 2 diabetes (DM-2) are associated with high cardiovascular disease risk. Increases in peripheral and central artery stiffness may represent pathophysiologic pathways through which glucose tolerance status leads to cardiovascular disease. Peripheral artery stiffness increases with deteriorating glucose tolerance status, whereas this trend remains unclear for central artery stiffness. Therefore, we investigated the associations between glucose tolerance status and estimates of central arterial stiffness. We performed a population-based study of 619 individuals (normal glucose metabolism, n=261; IGM, n=170; and DM-2, n=188) and assessed central artery stiffness by measuring total systemic arterial compliance, aortic pressure augmentation index, and carotid-femoral transit time. After adjustment for sex, age, heart rate, height, body mass index, and mean arterial pressure, DM-2 was associated with decreased total systemic arterial compliance, increased aortic augmentation index, and decreased carotid-femoral transit time. IGM was borderline significantly associated with decreased total systemic arterial compliance. Respective regression coefficients (95% confidence intervals) for IGM and DM-2 compared with normal glucose metabolism were −0.05 (−0.11 to 0.01) and −0.13 (−0.19 to −0.07) mL/mm Hg for total systemic arterial compliance; 1.1 (−0.2 to 2.5) and 1.6 (0.2 to 3.0) percentage points for aortic augmentation index; and −0.85 (−5.20 to 3.49) and −4.95 (−9.41 to −0.48) ms for carotid-femoral transit time. IGM and DM-2 are associated with increased central artery stiffness, which is more pronounced in DM-2. Deteriorating glucose tolerance is associated with increased central and peripheral arterial stiffness, which may partly explain why both DM-2 and IGM are associated with increased cardiovascular risk.

Total arterial inertance as the fourth element of the windkessel model

In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method ( P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different ( P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies ( P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate estimates of total arterial compliance. To overcome this problem, we introduce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better from aortic flow by using the four-element windkessel than by using the three-element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkessel. The three-element windkessel overestimated total arterial compliance compared with the values derived from the area and the pulse pressure method (P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different (P = 0.81). The characteristic impedance was underestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modulus at high frequencies (P = 0.0017 and 0.031, respectively). When applied to the human, the four-element windkessel also was more accurate in these same aspects. Using a distributed model of the systemic arterial tree, we found that the inertial term results from the proper summation of all local inertial terms, and we call it total arterial inertance. We conclude that the fourelement windkessel, with all its elements having a hemodynamic meaning, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascular properties.

Pulmonary vascular resistance and compliance stay inversely related during treatment of pulmonary hypertension

AIMS Pulmonary arterial compliance (C) is increasingly being recognized as an important contributor to right ventricular afterload, but for monitoring of treatment of pulmonary hypertension (PH) most often still only pulmonary vascular resistance (R) is used. We aimed at testing the hypothesis that R and C are coupled during treatment of PH and that substantial changes in both R and C would result in more haemodynamic improvement than changes in R alone. METHODS AND RESULTS Data were analysed of two right-heart catheterizations of 52 patients with pulmonary arterial hypertension and 10 with chronic-thromboembolic PH. The product of R and C (= stroke volume over pulse pressure) did not change during therapy (P = 0.320), implying an inverse relationship. Changes in cardiac index correlated significantly (P < 0.001) with changes in R (R(2) = 0.37), better with changes in C (R(2) = 0.66), and best with changes in both (R(2) = 0.74). CONCLUSION During therapy for PH, R and C remain inversely related. Therefore, changes in both R and C better explain changes in cardiac index than either of them alone. Not only resistance but also compliance plays a prominent role in PH especially in an early stage of the disease.

Quantification of Wave Reflection in the Human Aorta From Pressure Alone: A Proof of Principle

Wave reflections affect the proximal aortic pressure and flow waves and play a role in systolic hypertension. A measure of wave reflection, receiving much attention, is the augmentation index (AI), the ratio of the secondary rise in pressure and pulse pressure. AI can be limiting, because it depends not only on the magnitude of wave reflection but also on wave shapes and timing of incident and reflected waves. More accurate measures are obtainable after separation of pressure in its forward (Pf) and reflected (Pb) components. However, this calculation requires measurement of aortic flow. We explore the possibility of replacing the unknown flow by a triangular wave, with duration equal to ejection time, and peak flow at the inflection point of pressure (FtIP) and, for a second analysis, at 30% of ejection time (Ft30). Wave form analysis gave forward and backward pressure waves. Reflection magnitude (RM) and reflection index (RI) were defined as RM=Pb/Pf and RI=Pb/(Pf+Pb), respectively. Healthy subjects, including interventions such as exercise and Valsalva maneuvers, and patients with ischemic heart disease and failure were analyzed. RMs and RIs using FtIP and Ft30 were compared with those using measured flow (Fm). Pressure and flow were recorded with high fidelity pressure and velocity sensors. Relations are: RMtIP=0.82RMmf+0.06 (R2=0.79; n=24), RMt30=0.79RMmf+0.08 (R2=0.85; n=29) and RItIP=0.89RImf+0.02 (R2=0.81; n=24), RIt30=0.83RImf+0.05 (R2=0.88; n=29). We suggest that wave reflection can be derived from uncalibrated aortic pressure alone, even when no clear inflection point is distinguishable and AI cannot be obtained. Epidemiological studies should establish its clinical value.

Opposite Effects of Training in Rats With Stable and Progressive Pulmonary Hypertension

Background— Exercise training in pulmonary arterial hypertension (PH) is a promising adjunct to medical treatment. However, it is still unclear whether training is beneficial for all PH patients. We hypothesized that right ventricular adaptation plays a pivotal role in the response to training. Methods and Results— Two different dosages of monocrotaline were used in rats to model stable PH with preserved cardiac output and progressive PH developing right heart failure. Two weeks after injection, PH was confirmed by echocardiography, and treadmill training was initiated. Rats were trained for 4 weeks unless manifest right heart failure developed earlier. At the end of the study protocol, all rats were functionally assessed by endurance testing, echocardiography, and invasive pressure measurements. Lungs and hearts were further analyzed in quantitative histomorphologic analyses. In stable PH, exercise training was well tolerated and markedly increased exercise endurance (from 25±3.9 to 62±3.9 minutes; P<0.001). Moreover, capillary density increased significantly (from 1.21±0.12 to 1.51±0.07 capillaries per cardiomyocyte; P<0.05). However, in progressive PH, exercise training worsened survival (hazard ratio, 2.7; 95% confidence interval, 1.1 to 14.2) and increased pulmonary vascular remodeling. In addition, training induced widespread leukocyte infiltration into the right ventricle (from 135±14 to 276±18 leukocytes per 1 mm2; P<0.001). Conclusions— In our rat model, exercise training was found to be beneficial in stable PH but detrimental in progressive PH. Future studies are necessary to address the clinical implications of our findings.

Right Ventricular Diastolic Impairment in Patients With Pulmonary Arterial Hypertension

Background— The role of right ventricular (RV) diastolic stiffness in pulmonary arterial hypertension (PAH) is not well established. Therefore, we investigated the presence and possible underlying mechanisms of RV diastolic stiffness in PAH patients. Methods and Results— Single-beat RV pressure-volume analyses were performed in 21 PAH patients and 7 control subjects to study RV diastolic stiffness. Data are presented as mean±SEM. RV diastolic stiffness (&bgr;) was significantly increased in PAH patients (PAH, 0.050±0.005 versus control, 0.029±0.003; P<0.05) and was closely associated with disease severity. Subsequently, we searched for possible underlying mechanisms using RV tissue of PAH patients undergoing heart/lung transplantation and nonfailing donors. Histological analyses revealed increased cardiomyocyte cross-sectional areas (PAH, 453±31 &mgr;m2 versus control, 218±21 &mgr;m2; P<0.001), indicating RV hypertrophy. In addition, the amount of RV fibrosis was enhanced in PAH tissue (PAH, 9.6±0.7% versus control, 7.2±0.6%; P<0.01). To investigate the contribution of stiffening of the sarcomere (the contractile apparatus of RV cardiomyocytes) to RV diastolic stiffness, we isolated and membrane-permeabilized single RV cardiomyocytes. Passive tension at different sarcomere lengths was significantly higher in PAH patients compared with control subjects (>200%; Pinteraction<0.001), indicating stiffening of RV sarcomeres. An important regulator of sarcomeric stiffening is the sarcomeric protein titin. Therefore, we investigated titin isoform composition and phosphorylation. No alterations were observed in titin isoform composition (N2BA/N2B ratio: PAH, 0.78±0.07 versus control, 0.91±0.08), but titin phosphorylation in RV tissue of PAH patients was significantly reduced (PAH, 0.16±0.01 arbitrary units versus control, 0.20±0.01 arbitrary units; P<0.05). Conclusions— RV diastolic stiffness is significantly increased in PAH patients, with important contributions from increased collagen and intrinsic stiffening of the RV cardiomyocyte sarcomeres.

Manipulation of ascending aortic pressure and flow wave reflections with the Valsalva maneuver: relationship to input impedance.

SUMMARY Dramatic changes in the shape of pulsatile ascending aortic pressure and flow wave forms occur during the Valsalva maneuver in man. To study these changes, aortic pressure and flow signals were recorded in eight patients using a multisensor catheter. Aortic input impedance was derived during the control, strain and postrelease phases of the Valsalva maneuver. During control, well-defined minima and maxima occurred in the spectral plots of impedance moduli. This pattern was accentuated during the postrelease phase. In contrast, input impedance during strain was almost equal to the characteristic impedance for all harmonics. These results imply that during the control and postrelease phases, strong reflections return to the ascending aorta, but during the strain phase, reflections are minimal, absent or more diffuse. From wave transmission theory, it also follows that pulsatile pressure and flow wave forms should be similar in shape in the absence of reflections and dissimilar in the presence of reflections. This was observed in all eight patients. By provoking changes in the arterial tree during the Valsalva maneuver, the magnitude and timing of wave reflections were significantly altered, resulting in marked changes in the shape of pulsatile aortic pressure and flow wave forms. This study demonstrates the importance of reflections in determining the shape of the arterial pulse.