Comparison of rat aortic, carotid & femoral artery viscoelastic properties using harmonic analysis.

Viscoelastic properties of rat (Wistar Kyota) large (6 aorta), medium (12 carotid) and small (8 femoral) in vitro artery segments, were contrasted over a wide range of static and dynamic pressures. Relationship of change in static pressure (delta dyne/mm2) to diameter (delta mm) was used to estimate a segment's incremental elasticity (KD) at each pressure level. Dynamic intravascular pressure response (Po) was recorded during swept frequency pressure (2-200 Hz; +/- 10 mm Hg) inputs as superimposed on mean pressure steps of 40, 80, 120, 160 and 200 mm Hg (P(i)). Analysis of dynamic data included Fast Fouier Transform of Po/P(i) with FANSIM (TUTSIM Products) curve fit to Bode plots. Curve fit coefficients were used to estimate properties of natural frequency (omega n) damping, viscosity and inertia. Statistical analysis employed ANOVA and SNK multiple comparison procedures. Results indicated that as step-pressure was increased diameter, KD and omega n increased proportionately in all segments. Values of KD and omega n were always highest in femoral and lowest in aortic segments. In all segments damping decreased inversely with increasing pressure while, viscosity and inertia were lowest between 80 and 160 mm Hg. These results documented distinct viscoelastic properties for the three arteries as well as, differences in their response characteristics.

Transfer function comparisons of rat aortic wall image and intravascular pressure harmonic responses.

This study examined the relationship between rat (mature Sprague-Dawley males) thoracic aortic wall and intraluminal pressure responses to a dynamic pressure input. High speed video image (Do) of outer wall area and intravascular pressure (Po) responses of the in vitro aorta were digitized and computer recorded during swept frequency pressure input (2-200 Hz; +/- 10 mm Hg) that was superimposed on static pressures from 20 to 200 mm Hg (Pi). Analysis included Fast Fourier transform (FFT) for Do/Pi and Po/Pi transfer functions and focused on comparison of coefficients from FANSIM (TUTSIM Products) polynomial equation fit to Bode plots for mean data of multiple aortas. The working hypothesis was that Do/Pi = Po/Pi. In FANSIM division by B0 of the general transfer function equality (A1s + A0)/(B2s2 + B1s + B0) yields (a1s + a0)/(b2s2 + b1s + 1); which was the form analyzed. Graphic and statistical comparisons indicated no difference for coefficients a1, a0, b2, and b1 between Do/Pi and Po/Pi. Coefficients b2, and b1 varied with change in level of static pressure. Values for a1 for both Do/Pi and Pi/Po remained relatively constant and appeared independent of static pressure. These results indicated appropriateness of the transfer function form and suggested that: b2, represented inertia of wall and intraluminal fluid mass; b1, represented wall and fluid viscosity influence; a1, represented influence of fluid viscosity and a0, represented influence of wall elasticity.

Harmonic analysis of intravascular pressure response as an index of arterial wall mechanical properties.

The ability to routinely assess mechanical properties of large blood vessels, like the aorta, before an aneurysm or rupture occurs, could benefit diagnostic and therapeutic procedures and save lives. In this study, images of the wall area and intravascular pressure (IP) responses of in vitro rat aorta were recorded during swept frequency pressure input (2-200 Hz; +/- 10 mm Hg) superimposed on mean pressures from 20 to 160 mm Hg. Data analysis included Fast Fourier transform (FFT) of input and responses. Wall and IP responses were underdamped with respective resonance frequencies (Wn) that varied as a function of mean input pressure and the nonlinear nature of wall elasticity. Results indicated closely coupled wall and IP responses and suggested that the IP response may be an adequate index of wall elasticity without need of a direct measure of wall displacement. We considered results to be a key step towards development of a clinical tool which would facilitate analysis of mechanical properties of in vivo conducting vessels.

Virtual instrumentation for frequency analysis of carotid sinus responses.

An advanced microcomputer based process control and instrumentation system was developed for real time frequency analysis of the viscoelastic relationships between the carotid sinus wall and indwelling baroreceptors. A 486 based AT bus microprocessor running data acquisition and visualization software was customized providing a virtual instrument for data collection, display, and recording. A full complement of signal processing algorithms was developed for the collection of large time sampled data sets and their conversion to the frequency domain for analysis. Polynomial curve fitting procedures were used for transfer function estimation of wall viscoelastic properties. Simulated in situ sinus data was collected and analysis was used to test the methodology.

Endothelial vasoactive influence simulated by exponential feedback.

We hypothesized that results from rabbit carotid sinus wall and baroreceptors could be simulated using exponential feedback in a viscoelastic model. Wall and baroreceptor were each modeled by second order differential equations. Coefficients for viscosity, elasticity and feedback were estimated from experimental data. Feedback of model wall distension (y1) on viscosity (C) was expressed by the transfer function: C/y1 = RW/(s tau W + 1). With gain (RW) = 52.5E6 N(s)/m2 and tau W = 34 sec, this feedback resulted in simulation of wall response for sinuses with intact endothelium. Model receptor required no (or negative gain) feedback to simulate baroreceptors.

Model inferences on baroreceptor & sinus wall responses.

Mechanical associations between sinus wall elements and those between wall and baroreceptor were modeled with differential equations. Viscoelastic relationships were tested using frequency domain analysis (TUTSIM, FANSIM). Two wall models were examined. The first had a single degree of freedom (df) and the second was a cascade system with two df. Component of the cascade model represented adventitia and media layers of the wall. This wall model had little deviation in gain between 0.1 and 10 Hz; regardless of a 100 fold difference in component damping. Properties of a wall-receptor model were in part estimated from myelinated baroreceptor responses (Brown et al., Circ. Res. 42:694-702, 1978). The wall-receptor model was designed with a natural frequency (omega b) of 12.7 Hz and damping ratio (zeta b) of 0.2 for the receptor and omega w of 50 Hz and zeta w of 1.2 for the wall component. Analysis of receptor responses, with respect to input forcing function, resulted in a omega b of 12.6 Hz. Analysis of responses with respect to those of the wall, resulted in a omega b of 16.0 Hz. These results are indicative of the complexity involved with interactive systems. If frequency analysis is used to estimate mechanical associations between sinus wall elements and baroreceptors, modeling can provide comparative data for interpretation of experimental responses.

Frequency analysis instrumentation for sinus wall and baroreceptor responses.

Blood pressure regulation involves feedback signals from baroreceptors detecting wall strain of arterial sinuses. A research goal is identification of wall viscoelastic properties and associations between elements and baroreceptors. This report presents development of computer-based procedures for control of pressure inputs and recording responses of an in situ carotid sinus. Features include a hydraulic system to generate swept-frequency sinusoidal pressure inputs (0.2 to 200 Hz); measurements of: (i) sinus wall area and vectors of strain using a fiber optic sensor system, (ii) intrasinus pressure using solid state probes, (iii) baroreceptor fiber activity using a unipolar electrode and (iv) algorithms for data archival, frequency domain analysis and transfer function determinations. Data analysis will focus on estimates of wall properties of elasticity (K), viscosity (C), natural frequency (omega w), damping ratio (zeta w), reactive mass (Mw) and relationships to similar properties at tissue-baroreceptor junctions. Computer-based procedures are exemplified with data detailing mechanical properties of the hydraulic system; which is an important prerequisite to analysis of sinus viscoelastic properties.