The estimation of the cardiac time-varying parameters during the ejection phase of the cardiac cycle using the Ito calculus.

Evaluation of the time-varying parameters (Compliance, Resistance, and Inertance) that describe the right and left ventricles has been of interest for some years. Analyses usually involve a particular assertion regarding energy contributions or of the nature of the parameters themselves. It is of interest to engage the issue with a more general approach by restricting prior assumptions only to that raw data measurement may be noisy and that the parameters are non negative. Here a polynomial in time model is utilized to develop each parameter. Coefficients of the polynomials are estimated from the observed data with use of the maximum likelihood method and stochastic calculus. The pump equation was finally evaluated in full from un-processed pressure and flow data and the method is provided herein.

Stress reduction by geometric compliance matching at vascular graft anastomoses.

An analysis is presented of stresses developed with different junctional configurations of end-to-end vascular graft anastomoses with severe compliance mismatch. Junctions of circular transverse sections and junctions by bias cuts (beveled ends) are compared with an anastomosis of a graft constructed with an elliptical transverse section and a bevel end cut vessel. This latter substitutes midwall inextensional deformations for extensional deformations that occur with the former, conventional configurations. Applications to end-to-side anastomoses are also discussed. A range of parameters are considered: i.e., vascular wall thickness/radius ratios between 0.1 and 0.5, locations from the anastomotic plane between 1/2 and 3/2 times the vascular wall thickness, host vessel axial stretch by external forces between 0 and 15%, maximal vascular circumferential stretch distal from the anastomosis between 0 and 25%, and perimeter locations at the anastomotic junction between 0 degree and 90 degrees. The graft constructed with an elliptic cross-section developed peak stresses that are orders of magnitude lower than those developed with conventional configurations. The introduction of matching geometric compliance that dominates at the anastomotic junction minimizes consequences of material mismatch between graft and vessel and has the potential to reduce suture line stress greatly. This analysis may suggest designs for experimental studies to confirm relationships between neointimal hyperplasia and suture line stress levels, and provide a relatively simple solution for reduction of such stresses at the anastomotic junction. Choices may be permitted of graft materials with optimal surface properties despite less favorable elastic properties.

The Korotkoff sound.

As the auscultatory method of blood pressure measurement relies fundamentally on the generation of the Korotkoff sound, identification of the responsible mechanisms has been of interest ever since the introduction of the method, around the turn of the century. In this article, a theory is proposed that identifies the cause of sound generation with the nonlinear properties of the pressure-flow relationship in, and of the volume compliance of the collapsible segment of brachial artery under the cuff. The rising portion of a normal incoming brachial pressure pulse is distorted due to these characteristics, and energy contained in the normal pulse is shifted to the audible range. The pressure transient produced is transmitted to the skin surface and stethoscope through deflection of the arterial wall. A mathematical model is formulated to represent the structures involved and to compute the Korotkoff sound. The model is able to predict quantitatively a range of features of the Korotkoff sound reported in the literature. Several earlier theories are summarized and evaluated.

Nonlinear structural and material properties and models: the pulmonary trunk.

General models are developed for static and dynamic geometric and material passive responses. The models are applied to data obtained from the main pulmonary arteries of calves and dogs. The structural model predicts distortions by simultaneous stretching and bending in a concise manner. Parameters are obtained by a five-element material model. This latter predicts static and dynamic, nonlinear, frequency-dependent, viscoelastic responses observed in biomaterials over the entire strain range irrespective of the nature of loading. Validity and baseline parameter values are investigated for the inactivated state, developed by poisoning the smooth muscle with potassium cyanide. Complexities, related to nonlinear (strain-dependent) and colloidal (thixotropic) properties of tissues, are analyzed. These properties enter into functional responses in a complex manner that can modify substantially concepts of material components and vary appreciably between physiologic circumstances and laboratory evaluations. We propose that, in general, evaluations of material responses must account for these properties.

Baroreceptor responses derived from a fundamental concept.

A model is presented that relates the change in baroreceptor firing rate to a step change in blood pressure. This relationship is nonlinear since the alteration in rate of firing depends on the current rate of firing. It is shown that this simple relationship embodies all currently established baroreceptor response modes. The model needs refinement to allow for effects arising from the properties of the tissue matrix in which the receptors are embedded. Further analysis is precluded at present owing to paucity of quantitative experimental data.

Pressure pulse transmission into vascular beds.

Observations at the microcirculatory level have revealed that (a) the pressure pulse reaches the smallest vessel, and (b) the pulse wave velocity alters from a value in the order of meters/second in large arteries to a value in the order of centimeters/second in the microvessels. We investigate, herein, whether these experimental findings are consonant with linear pulse wave transmission theory in a branching system of vessels. Our computations, utilizing available data, show that this is indeed the case. For low frequency (1 Hz), cumulative attenuation is such that about one-third of the pulse, originating at the heart, reaches the capillary. A 10-Hz pulse, however, is virtually completely attenuated by the time the capillary is reached. Transmission time for a pulse, from heart to capillary, is also frequency dependent, with higher frequencies propagating more rapidly. Vasoconstriction, at the arteriolar level in the absence of reflection, can also strongly attenuate the pulse remnant at that site.

Morphological observations of mineralizing pericardium cardiac grafts.

Pericardial patch grafts were implanted in the hearts of young sheep for periods ranging from two to 120 days. Explants seven to 21 days old revealed the formation of a "pseudoneointima" (PNI) on the blood contacting surface of the pericardium. The PNI was more heavily mineralized than the pericardium. Mineralization was most intense on the blood contacting surface of the PNI and on the chamber surface of the pericardium. After three weeks of implantation, the PNI was much thinner and was organized into a thin fibrous capsule without any signs of mineralization. In the pericardium, mineral deposits were seen in fibroblasts. Moreover, cell-related mineralization was evident prior to calcification of the surrounding collagen matrix.

Directional disparity of pulse reflection in the dog.

Local reflection coefficients were experimentally determined in the dog for the first time at the aortoiliac junction using characteristic impedances derived from phase velocity, fluid density, and the vessels' cross-sectional areas. Reflection coefficients were determined for both the normal trifurcation and with the segment of aorta between external and internal iliacs occluded. For the normal case the coefficients were as follows: antegrade, 0.7; retrograde, -0.74. For the occlusion case the coefficients were as follows: antegrade, 0.33; retrograde, -0.67. These results provide experimental support for the concept that the vascular system, at least in this region, favors antegrade and suppresses retrograde pulse transmission. In addition, global reflection coefficients were determined in the femoral artery using a three-point pressure technique. Coefficient magnitudes varied from low (1.6 Hz) to high (9.6 Hz) frequencies, i.e., control, 0.42-0.22; vasoconstriction, 0.65-0.33; vasodilation, less than 0.1 for all frequencies. Discrepancies between results appearing in the literature are evaluated and shown to be associated with the method utilized as well as with system nonlinearities enhanced by tying branches.

Mineralization of short term pericardial cardiac patch grafts.

Glutaraldehyde fixed patch grafts of bovine pericardium were implanted in myocardial windows in young (3-4 months old) sheep. The samples were retrieved after one to three weeks for study with scanning electron microscopy (SEM) and energy dispersive x-ray microanalysis (EDX). A layer of porous material (pseudoneointima, PNI), consisting mostly of a dense mesh of fibers interspersed with blood cells, was noted to form on the blood contacting surface of the graft. Four distinct sets of mineralization were noted in the retrieved grafts: (1) at the blood contacting surface of the PNI; (2) within the PNI at the junction between layers of PNI with differing densities; (3) near the junction of PNI and pericardium (but in the PNI); and (4) within the pericardium. In both the PNI and pericardium the mineral was shown by EDX analysis to contain both calcium and phosphorous indicating the mineral to be a calcium phosphate. Mineralization in the PNI differed from that in the pericardium; in the PNI it was deposited in discrete regions and apparently in association with thrombi while in the pericardium it was distributed diffusely within the collagen matrix, which may influence its formation.

Pressure gradient related to energy conversion in the aorta.

In this study, we analyzed a common form of experimental investigation of blood vessels, in which measurements are obtained with branches ligated. Utilizing representative pressure and flow pulses and the full expression for the equation of motion, we calculated the axial pressure gradient, in the time domain at a plane in the descending aorta. The time function representing the ratio between axial pressure gradient and axial flow for the resulting tapering geometry was subjected to Fourier analysis. The harmonics were utilized to obtain the real and imaginary components of the longitudinal impedance as if it were a linear system. In a linear system, the real and imaginary components represent the viscous and inertial properties of the fluid, respectively. For the system studied, however, the real part contained both viscous and substantial in-phase components arising from the inertial terms of the equation of motion. The real part, therefore, cannot be interpreted as indicative solely of dissipated energy. When measurements are obtained from an adulterated system, caution must be exercised if the interpretation is to be considered that of the real system. The analysis clarifies an anomalous issue concerning resistive features of the aorta.

Arterial tonometry: review and analysis.

A review is presented of the field of arterial tonometry and of the problems involved with its application. A second generation model is developed which interprets most of the difficulties encountered in previous experimental work. The model also identifies barriers that must be overcome to allow tonometry to become a practical technique for obtaining measurement of continuous, absolute blood pressure. Problems addressed include those of calibration, positioning sensitivity, design standardization, material properties and vascular loading characteristics. Theoretical and experimental studies provide support for the application of basic biomechanical concepts for solution of these problems and suggest required design features.

Coherence of cardiac output with rate changes.

In awake or lightly anesthetized dogs increases in heart rate (HR) induced by atrial pacing affect cardiac output (CO) and stroke volume (SV) in a predictable way that is represented by a SV-HR relationship (dSV/dHR). Under our experimental conditions where normal regulation of atrial rate was bypassed, atrial rate was the independent variable and CO and SV were dependent variables. As HR is increased, CO and SV are modified by reflex and other circulatory regulators. The dSV/dHR relation characterized the circulatory response to increasing HR. A single dSV/dHR curve consistently predicted responses under a number of different conditions (standing, recumbent, awake, various anesthetics, beta-adrenergic stimulation, or depression) and thus appeared as an expression of cardiac function. Alterations of the circulation by stellate ganglion or vagal stimulation, volume loading, aortic compression, and ventricular pacing were not represented by the same dSV/dHR function. The dSV/dHR function (including its linear version as reported by others for anesthetized dogs) showed that, when SVs were larger at low rates, maximum CO occurred at a higher HR. Recognition of this arithmetic-based feature resolves apparent contradictory findings reported in the literature.

Construction and characterization of branched, elastic, transparent vessel models.

A technique is presented for the construction of compliant branched vessel models. Properties include wall transparency and geometric reproduction to any scale. A method for characterization of vessel compliance is discussed, as is the requirement for hydrodynamic similarity.

Pulse wave propagation.

This report evaluates pulse wave propagation with respect to contributions by vascular wall elastic and geometric properties, vessel wall and blood viscosity, and nonlinearities in system parameters and in the equations of motion. Discrepancies in results obtained with different experimental methods and theory are discussed and resolved. A three-point pressure technique was used to obtain measurements from the abdominal aorta, carotid, iliac, and femoral arteries of dogs. Computations involved linear, as well as nonlinear methods. Results are presented along a continuous path of transmission (abdominal aorta, iliac, femoral), and it is shown that variations in phase velocity can be explained entirely by the geometric variation of these vessels. Phase velocities are shown to be frequency independent at approximately greater than 4 Hz whereas attenuation increases progressively for higher frequencies. Determination of propagation coefficients using maximal, compounded values of reported viscoelastic and geometric properties just manages to span the range of phase velocities, determined in different laboratories, but does not do so for attenuation. Also, differences in experimental techniques cannot explain these discrepancies. Consideration of geometric taper, nonlinear compliance, all the terms in the equation of motion, and the effect of wall and blood viscosity resolves discrepancies between theoretical and experimentally derived phenomena.