A mathematical model of umbilical venous pulsation.

Pulsations in the fetal heart propagate through the precordial vein and the ductus venosus but are normally not transmitted into the umbilical vein. Pulsations in the umbilical vein do occur, however, in early pregnancy and in pathological conditions. Such transmission into the umbilical vein is poorly understood. In this paper we hypothesize that the mechanical properties and the dimensions of the vessels do influence the umbilical venous pulsations, in addition to the magnitude of the pressure and flow waves generated in the fetal atria. To support this hypothesis we established a mathematical model of the umbilical vein/ductus venosus bifurcation. The umbilical vein was modeled as a compliant reservoir and the umbilical vein pressure was assumed to be equal to the stagnation pressure at the ductus venosus inlet. We calculated the index of pulsation of the umbilical vein pressure ((max-min)/mean), the reflection and transmission factors at the ductus venosus inlet, numerically and with estimates. Typical dimensions in the physiological range for the human fetus were used, while stiffness parameters were taken from fetal sheep. We found that wave transmission and reflection in the umbilical vein ductus venosus bifurcation depend on the impedance ratio between the umbilical vein and the ductus venosus, as well as the ratio of the mean velocity and the pulse wave velocity in the ductus venosus. Accordingly, the pulsations initiated by the fetal heart are transmitted upstream and may arrive in the umbilical vein with amplitudes depending on the impedance ratio and the ratio between the mean velocity and the pulse wave velocity in the ductus venosus.

Semiautomatic contour detection in ultrasound M-mode images.

We have developed a method for semiautomatic contour detection in M-mode images. The method combines tissue Doppler and grey-scale data. It was used to detect: 1. the left endocardium of the septum, the endocardium and epicardium of the posterior wall in 16 left ventricular short-axis M-modes, and 2. the mitral ring in 38 anatomical M-modes extracted pair-wise in 19 apical four-chamber cine-loops (healthy subjects). We validated the results by comparing the computer-generated contours with contours manually outlined by four echocardiographers. For all boundaries, the average distance between the computer-generated contours and the manual outlines was smaller than the average distance between the manual outlines. We also calculated left ventricular wall thickness and diameter at end-diastole and end-systole and lateral and septal mitral ring excursions, and found, on average, clinically negligible differences between the computer-generated indices and the same indices based on manual outlines (0.8-1.8 mm). The results were also within published normal values. In conclusion, this initial study showed that it was feasible in a robust and efficient manner to detect continuous wall boundaries in M-mode images so that tracings of left ventricular wall thickness, diameter and long axis could be derived.

Aortic reflection coefficients and their association with global indexes of wave reflection in healthy controls and patients with Marfan's syndrome.

Early return of reflected pressure waves increases the load on central arteries and may increase the risk of aortic rupture in patients with Marfan's syndrome (MFS). To assess whether wave reflection is elevated in MFS, we used ultrasound and MRI to measure central pressure and flow waveforms in 26 patients (13-54 yr of age) and 26 age- and gender-matched controls. Aortic systolic and diastolic cross-sectional areas were measured at the ascending and descending aorta (AA and DA), diaphragm (DIA), and lower abdominal aorta (AB). From these measurements, local characteristic impedance (Z(0-xx)) and local reflection coefficients (Gamma(xx-yy)) were calculated. Calculated global wave reflection indexes were the augmentation index (AIx) and the ratio of backward to forward pressure wave (P(b)/P(f)). The aorta was wider in MFS patients at AA (P < 0.01) and DA (P < 0.01). Aortic pulse wave velocity was 42 cm/s higher in MFS patients (P < 0.05). Z(0-xx) was not different between groups, except at DA, where it was lower in MFS patients. In controls, Gamma(AA-DA) was 0.31 +/- 0.08, Gamma(DA-DIA) was 0.00 +/- 0.11, and Gamma(DIA-AB) was 0.31 +/- 0.16. Mean values of Gamma(xx-yy) were not different between MFS patients and controls. In controls, aging diminished Gamma(AA-DA) but increased Gamma(DIA-AB). Clear age-related patterns were absent in MFS patients. AIx or P(b)/P(f) was not higher in MFS patients than in controls. There were indications for enhanced wave reflection in young MFS patients. Our data demonstrated that the major determinants of AIx were pulse wave velocity and the effective length of the arterial system and, to a lesser degree, HR and P(b)/P(f).

Equations for estimating muscle fiber stress in the left ventricular wall.

Left ventricular muscle fiber stress is an important parameter in cardiac energetics. Hence, we developed equations for estimating regional fiber stresses in rotationally symmetric chambers, and equatorial and apical fiber stresses in prolate spheroidal chambers. The myocardium was modeled as a soft incompressible material embedding muscle fibers that support forces only in their longitudinal direction. A thin layer of muscle fibers then contributes with a pressure increment determined by the fiber stress and curvature. The fiber curvature depends on the orientation of the fibers, which varies continuously across the wall. However, by assuming rotational symmetry about the long axis of the ventricle and including a longitudinal force balance, we obtained equations where fiber stress is completely determined by the principal curvatures of the middle wall surface, wall thickness, and cavity pressure. The equations were validated against idealized prolate spheroidal chambers, whose wall thicknesses are such that the fiber stress is uniform from the equator to the apex. Because the apex is free to rotate, the resultant moment about the long axis of the LV must be zero. By using this constraint together with our fiber-stress equations, we were able to estimate a muscle fiber orientation distribution across the wall that was in qualitative agreement with published measurements.

Model-based estimation of vascular parameters: evaluation of robustness and suitability of models.

Left ventricular performance depends not only on myocardial state, but also on the properties of the systemic arterial tree. These properties can be assessed from recordings of aortic root pressure and flow by the use of appropriate vascular models. Noninvasive estimates of aortic root pressure and flow can be obtained by the combined use of calibrated external subclavian artery pulse tracing and Doppler echocardiography. With recent advances in computer technology, estimation of model parameters are thus accessible in the clinical setting. We discuss the suitability of different parametric vascular models together with methods for adapting these models to the measured aortic root pressure. We compared the results obtained with simple vascular models (three-component modified Windkessel models) with those of five-component models. The simpler models gave less accurate approximation of the measured pressure waveform, but for a representative set of aortic root pressure and flow data, the simpler models provided adequate estimates of the peripheral arterial resistance, the total arterial compliance, and the proximal aortic area compliance. Furthermore, the simpler models are robust for measurement noise with simple estimation algorithms. Distal arterial pressure and flow waveforms are more oscillatory, and for these the five-component model has more robust estimation schemes with more accurate estimated parameters. Hence, we conclude that for clinical noninvasive assessment of aortic vascular properties, the simpler three-component models provide adequate information. For assessment of the peripheral arteries with large oscillations in the flow, the three-component models can give more than 10% error in the compliance estimate and more complex models can be appropriate.

High frame rate strain rate imaging of the interventricular septum in healthy subjects.

OBJECTIVE: In the present study the feasibility was assessed of a new strain rate imaging method with a very high frame rate of around 300 frames per second. METHODS: Digital radio-frequency (RF) data were obtained in nine healthy subjects using a sector of 20-30 degrees in an apical four chamber view. The RF data were analysed using a dedicated software package that displays strain rate images and profiles and calculates strain rate values. With the new method, it is possible to study events and spatial-temporal differences in the heart cycle with duration down to 3.5-3 ms, including the pre-ejection period and the isovolumic relaxation period. Since the interventricular septum (IVS) is of crucial importance for the left and right ventricular function, we assessed changes through the heart cycle of the strain rate in the IVS. RESULTS: Mean peak systolic strain rate in the healthy subjects was -1.65+/-0.13 s(-1). Mean peak diastolic strain rate during early filling was 3.14+/-0.50 s(-1) and during atrial systole 0.99+/-0.09 s(-1). We found individual differences in the strain rate patterns, but in all subjects, the ventricular contraction started simultaneously in all parts of the septum. After the ejection period, the elongation started before aortic valve closure, in the midinferior septum and propagated towards the apex. CONCLUSION: High frame rate strain rate imaging makes it possible to study rapid deformation patterns in the heart walls.

Individualizing the aorto-radial pressure transfer function: feasibility of a model-based approach.

We fitted a three-segment transmission line model for the radial-carotid/aorta pressure transfer function (TFF) in 31 controls and 30 patients with coronary artery disease using noninvasively measured (tonometry) radial and carotid artery pressures (P(car)). Except for the distal reflection coefficient (0.85 +/- 0.21 in patients vs. 0.71 +/- 0.25 in controls; P < 0.05), model parameters were not different between patients or controls. Parameters were not related to blood pressure, age, or heart rate. We further assessed a point-to-point averaged TFF (TFF(avg)) as well as upper (TFF(max)) and lower (TFF(min)) enveloping TFF. Pulse pressure (PP) and augmentation index (AIx) were derived on original and reconstructed P(car) (P(car,r)). TFF(avg) yielded closest morphological agreement between P(car) and P(car,r) (root mean square = 4.3 +/- 2.3 mmHg), and TTF(avg) best predicted PP (41.5 +/- 11.8 vs. 41.1 +/- 10.0 mmHg measured) and AIx (-0.02 +/- 0.19 vs. 0.01 +/- 0.19). PP and AIx, calculated from P(car) or P(car,r), were higher in patients than in controls, irrespectively of the TFF used. We conclude that 1) averaged TFF yield significant discrepancies between reconstructed and measured pressure waveforms and subsequent derived AIx; and 2) different TFFs seem to preserve the information in the pressure wave that discriminates between controls and patients.