Berend E. 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.

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.

Nexfin noninvasive continuous blood pressure validated against Riva-Rocci/Korotkoff.

BACKGROUND The Finapres methodology offers continuous measurement of blood pressure (BP) in a noninvasive manner. The latest development using this methodology is the Nexfin monitor. The present study evaluated the accuracy of Nexfin noninvasive arterial pressure (NAP) compared with auscultatory BP measurements (Riva-Rocci/Korotkoff, RRK). METHODS In supine subjects NAP was compared to RRK, performed by two observers using an electronic stethoscope with double earpieces. Per subject, three NAP-RRK differences were determined for systolic and diastolic BP, and bias and precision of differences were expressed as median (25th, 75th percentiles). Within-subject precision was defined as the (25th, 75th percentiles) after removing the average individual difference. RESULTS A total of 312 data sets of NAP and RRK for systolic and diastolic BP from 104 subjects (aged 18-95 years, 54 males) were compared. RRK systolic BP was 129 (115, 150), and diastolic BP was 80 (72, 89), NAP-RRK differences were 5.4 (-1.7, 11.0) mm Hg and -2.5 (-7.6, 2.3) mm Hg for systolic and diastolic BP, respectively; within-subject precisions were (-2.2, 2.3) and (-1.6, 1.5) mm Hg, respectively. CONCLUSION Nexfin provides accurate measurement of BP with good within-subject precision when compared to RRK.

Noninvasive continuous arterial blood pressure monitoring with Nexfin

Background: If invasive measurement of arterial blood pressure is not warranted, finger cuff technology can provide continuous and noninvasive monitoring. Finger and radial artery pressures differ; Nexfin® (BMEYE, Amsterdam, The Netherlands) measures finger arterial pressure and uses physiologic reconstruction methodologies to obtain values comparable to invasive pressures. Methods: Intra-arterial pressure (IAP) and noninvasive Nexfin arterial pressure (NAP) were measured in cardiothoracic surgery patients, because invasive pressures are available. NAP-IAP differences were analyzed during 30 min. Tracking was quantified by within-subject precision (SD of individual NAP-IAP differences) and correlation coefficients. The ranges of pressure change were quantified by within-subject variability (SD of individual averages of NAP and IAP). Accuracy and precision were expressed as group average ± SD of the differences and considered acceptable when smaller than 5 ± 8 mmHg, the Association for the Advancement of Medical Instrumentation criteria. Results: NAP and IAP were obtained in 50 (34–83 yr, 40 men) patients. For systolic, diastolic, mean arterial, and pulse pressure, median (25–75 percentiles) correlation coefficients were 0.96 (0.91–0.98), 0.93 (0.87–0.96), 0.96 (0.90–0.97), and 0.94 (0.85–0.98), respectively. Within-subject precisions were 4 ± 2, 3 ± 1, 3 ± 2, and 3 ± 2 mmHg, and within-subject variations 13 ± 6, 6 ± 3, 9 ± 4, and 7 ± 4 mmHg, indicating precision over a wide range of pressures. Group average ± SD of the NAP-IAP differences were −1 ± 7, 3 ± 6, 2 ± 6, and −3 ± 4 mmHg, meeting criteria. Differences were not related to mean arterial pressure or heart rate. Conclusion: Arterial blood pressure can be measured noninvasively and continuously using physiologic pressure reconstruction. Changes in pressure can be followed and values are comparable to invasive monitoring.

Pulse contour cardiac output derived from non-invasive arterial pressure in cardiovascular disease

Pulse contour methods determine cardiac output semi‐invasively using standard arterial access. This study assessed whether cardiac output can be determined non‐invasively by replacing the intra‐arterial pressure input with a non‐invasive finger arterial pressure input in two methods, Nexfin CO‐trek® and Modelflow®, in 25 awake patients after coronary artery bypass surgery. Pulmonary artery thermodilution cardiac output served as a reference. In the supine position, the mean (SD) differences between thermodilution cardiac output and Nexfin CO‐trek were 0.22 (0.77) and 0.44 (0.81) l.min−1, for intra‐arterial and non‐invasive pressures, respectively. For Modelflow, these differences were 0.70 (1.08) and 1.80 (1.59) l.min−1, respectively. Similarly, in the sitting position, differences between thermodilution cardiac output and Nexfin CO‐trek were 0.16 (0.78) and 0.34 (0.83), for intra‐arterial and non‐invasive arterial pressure, respectively. For Modelflow, these differences were 0.58 (1.11) and 1.52 (1.54) l.min−1, respectively. Thus, Nexfin CO‐trek readings were not different from thermodilution cardiac output, for both invasive and non‐invasive inputs. However, Modelflow readings differed greatly from thermodilution when using non‐invasive arterial pressure input.

Arterial stiffness, cardiovagal baroreflex sensitivity and postural blood pressure changes in older adults: the Rotterdam Study

Objective Arterial stiffness may be involved in the impairment of the arterial baroreflex. In the present study the associations between arterial stiffness and cardiovagal baroreflex sensitivity (BRS) and between BRS and postural blood pressure (BP) changes were investigated within the framework of the Rotterdam Study. Methods Arterial stiffness was determined by aortic pulse wave velocity and the carotid distensibility coefficient. Continuous recording of the R–R interval and finger BP was performed with the subject resting supine, and BRS was estimated from the spontaneous changes in systolic BP and corresponding interbeat intervals. Measures of aortic stiffness or carotid distensibility and BRS were available in 2490 and 2083 subjects, respectively. The association between arterial stiffness and ln BRS was investigated by multivariate linear regression analysis and then by analysis of covariance, comparing BRS by quartiles of arterial stiffness. Results The mean age of the subjects was 71.7 ± 6.6 (41.7% men). Aortic stiffness was negatively associated [β = −0.029; 95% confidence interval (CI): −0.040, −0.019] and the carotid distensibility coefficient positively associated with BRS (β = 0.017; 95% CI: 0.010, 0.024). An orthostatic decrease in systolic BP was absent in 1609 subjects, between 1 and 10 mmHg in 502 and >10 mmHg in 269 subjects, with corresponding mean values (95% CI) of ln BRS of 1.47 (1.44–1.51), 1.43 (1.37–1.49) and 1.36 (1.28–1.44) ms/mmHg (test for trend P < 0.019). An orthostatic decrease in diastolic BP was absent in 1123 subjects, 1–10 mmHg in 1057 and >10 mmHg in 209 subjects, with corresponding mean values of ln BRS of 1.49 (1.45–1.53), 1.41 (1.37–1.45) and 1.45 (1.36–1.54) ms/mmHg (P < 0.04). Conclusion In a large population of older subjects, arterial stiffness appears to be an independent determinant of impaired BRS. Within the same population, impaired BRS was associated with orthostatic BP changes.

Different role of wave reflection magnitude and timing on left ventricular mass reduction during antihypertensive treatment.

Objective Regression of left ventricular (LV) mass during antihypertensive treatment has been associated with reduction in aortic augmentation index, a composite measure of peripheral wave reflection. The aim of this study was to clarify which of the two reflection factors, that is magnitude or timing, plays the dominant role in this regression. Methods We evaluated the reflection magnitude (RM; the reflected-to-forward pressure wave amplitude ratio), the round-trip travel time of the pressure wave (a parameter for reflection timing), and the aortic pulse wave velocity (PWV) with echocardiographic LV mass in 61 hypertensive patients before and after 1-year standard medical treatment. Results Antihypertensive therapy significantly (P < 0.01) decreased brachial and aortic blood pressures and aortic PWV, reduced LV mass, and increased travel time. Neither increase in travel time nor decrease in PWV, however, was related to the reduction in LV mass. By contrast, treatment-induced change in RM was significantly correlated with change in LV mass; the correlation was particularly close in patients with LV hypertrophy (r = 0.61, P < 0.001). Only a marginal correlation was observed between the changes in RM and travel time. The association between RM decrease and LV mass reduction was independent of age, sex, changes in travel time and blood pressure, and use of renin–angiotensin system inhibitors (β = 0.41, P = 0.001). Conclusion Decreased wave RM contributes to LV mass regression more strongly than, and independently of, delayed reflection timing. Peripheral muscular arteries (from which reflection arises) appear to be more important therapeutic targets in regressing LV mass than central elastic arteries.

Validation of brachial artery pressure reconstruction from finger arterial pressure

Objective Measurement of finger artery pressure with Finapres offers noninvasive continuous blood pressure, which, however, differs from brachial artery pressure. Generalized waveform filtering and level correction may convert the finger artery pressure waveform to a brachial waveform. An upper-arm cuff return-to-flow measurement may be used to calibrate the blood pressure on an individual basis. We tested these corrective methods as implemented in the Finometer device. Methods Intrabrachial artery pressure (BAP) and finger artery pressures were recorded simultaneously in 37 cardiac patients, aged 41–83 years, who underwent a cardiac catheterization procedure. Finger artery pressures were compared after waveform filtering and level correction and after an additional return-to-flow calibration. Measurements were performed in supine and sitting positions. Accuracy and precision were considered clinically acceptable if the mean and standard deviation of the return-to-flow intrabrachial artery pressure (reBAP)–BAP differences were smaller than 5 ± 8 mmHg (Association for the Advancement of Medical Instrumentation requirements). Results Finger artery systolic, diastolic and mean pressures for the group differed from that of intrabrachial artery pressure by −10 ± 13, −12 ± 8 and −16 ± 8 mmHg, respectively. After waveform filtering and level correction the filtered level corrected arterial pressure differed by −1 ± 11, −0 ± 7 and −2 ± 7 mmHg. After individual calibration, reBAP differed by 3 ± 8, 4 ± 6 and 3 ± 5 mmHg. Comparable results were found in the sitting position but only when the supine return-to-flow calibration was used. Conclusion Reconstruction of intrabrachial artery pressure from finger artery pressure with waveform filtering and level correction reduces the pressure differences substantially, with diastolic and mean within Association for the Advancement of Medical Instrumentation requirements. After one supine return-to-flow calibration, all pressure differences meet the requirements. Return-to-flow calibration should not be repeated in sitting position.

Location of a Reflection Site Is Elusive: Consequences for the Calculation of Aortic Pulse Wave Velocity

Aortic pulse wave velocity (PWV), a measure of aortic stiffness, is an important indicator of cardiovascular risk. Derivation of PWV from uncalibrated proximal aortic or carotid pressure alone has practical advantages. However, when the time of return of the reflected wave, &Dgr;t, is used to calculate PWV, inaccurate data are obtained. With aging PWV increases but &Dgr;t hardly decreases, suggesting that the reflection site moves toward the periphery. We hypothesized that the forward and reflected waves in the distal aorta are not in phase, leading to an undefined reflection site. We derived forward and backward waves, at the entrance and distal end of a uniform tube, with length “L.” With the tube closed at the end, forward and reflected waves are there in phase, and PWV=2L/&Dgr;t. When the tube is ended with the input impedance of the lower body, forward and backward waves at its end are not in phase, and &Dgr;t is increased, suggesting that the reflection site is further away (tube seems longer), and PWV calculated from 2L/&Dgr;t is underestimated. Using an anatomically accurate model of the human arterial system, we show that the forward and backward waves in the distal aorta are not in phase. When aortic PWV increases, &Dgr;t changes only little, and the reflection site appears to move to the periphery, similar to what is observed in humans. We conclude that to define the location of a reflection site is elusive and that PWV cannot be calculated from time of return of the reflected wave.

How to assess mean blood pressure properly at the brachial artery level

Objectives Mean arterial pressure at the upper arm is traditionally calculated by adding one-third of the pulse pressure to the diastolic pressure. We questioned the general validity of this formula. Methods We used previously recorded resting intrabrachial pressure and Riva–Rocci Korotkoff blood pressure measurements in 57 subjects (study A) and 24-h intra-arterial recordings obtained in 22 ambulant subjects (study B). Results In study A the intra-arterially measured ‘real’ mean pressure was found at 39.5 ± 2.5% of pulse pressure above diastolic pressure, namely at a level higher than the expected 33.3% of pulse pressure, in all individuals. Results were not related to age, blood pressure, pulse pressure or heart rate levels. Mean pressure calculated with the traditional one-third rule therefore underestimated ‘real’ mean pressure by 5.0 ± 2.3 mmHg (P < 0.01) when calculated from intra-arterial pressure readings, and by 4.9 ± 5.3 mmHg (P < 0.01) when calculated from Riva–Rocci Korotkoff readings. In study B we showed activity-related variations in the relative level of the ‘real’ mean pressure, which increased by 1.8 ± 1.4% (P < 0.01) during sleep, and decreased by 0.5 ± 0.9% during walking (P < 0.05) and by 0.8 ± 1.3% during cycling (P < 0.01). Conclusion The mean pressure at the upper arm is underestimated when calculated using the traditional formula of adding one-third of the pulse pressure to the diastolic pressure. This underestimation can be avoided by adding 40% of pulse pressure to the diastolic pressure. The proposed approach needs to be validated through larger scale studies.