Julius Melbin

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.

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 noniinearities 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 54 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 betweeen theoretical models and experimentally derived phenomena.

Reduced Models of Arterial Systems

Simple models that manifest input impedances of arterial systems are compared. An improvement upon documented two-, three-, and five-element models is presented. The classical two-element model (the windkessel) accounts for the lowest frequency components, and the three-element model (the modified windkessel) accounts for both low-and high-frequency components of the spectrum of interest. Five-element models, however, by allowing for reflection, can account for principal features over the entire frequency range of interest.

Hereditary defects of the conotruncal septum in keeshond dogs: Pathologic and genetic studies☆

Abstract Pathologic studies of a hereditary cardiovascular defect in Keeshond dogs demonstrated a spectrum of malformations, primarily involving the ventricular outflow tracts. Lesions ranged from subclinicai defects of the crista supraventricularis to end-stage tetralogy of Fallot and included isolated ventricular septal defects and pulmonic stenosis. The spectrum can be explained by assuming that the anatomic variations represent different thresholds along a continuum of maldevelopment producing hypoplasia and malpositioning of the conotruncal septum. The results of breeding experiments conducted in a colony of Keeshond dogs with conotruncal septal defects confirmed the hereditary nature of the abnormality but were not consistent with any simple genetic hypothesis. Both the incidence and the severity of the conotruncal lesions increased with the severity of the parental defect. The results are shown to fit a polygenic model with three developmental thresholds, in which multiple genes act additively to produce a continuous distribution of maldevelopment involving the conotruncal septum. Lesions of increasing severity occur with an increasing “dose” of genes predisposing to conotruncal septal defects.

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 computer 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.

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.

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.

Constriction of the Fetal Ductus Arteriosus Induced by Oxygen, Acteylcholine, and Norepinephrine in Normal Dogs and those Genetically Predisposed to Persistent Patency

Functional closure of the isolated perfused ductus arteriosus was studied in normal dog fetuses and in fetuses receiving various known proportions of their genes from dogs with patent ductus arteriosus (PDA). Constriction of the ductus in response to O2, acetylcholine (ACh), and norepinephrine (NE) was evaluated by plotting changes in input conductance against time. Ductuses from the control (normal dog) fetuses constricted in response to high PO2, ACh, and NE, indicating that in the dog the response of the ductus arteriosus to these agents is qualitatively similar to that in other mammals. Hypoxia relaxed the O2 constricted ductus. After two to three cycles of oxygenation and hypoxia, the ductus became refractory to O2 but remained responsive to ACh and NE. Ductuses from PDA-related fetuses tended to be more widely patent when hypoxic and did not respond to O2, ACh, and NE to a degree comparable to the control fetuses. Both the proportion of subnormal ductal responses and degree of abnormality in the PDA-related group increased as the degree of relationship to dogs with PDA increased. These experimental results are consistent with the polygenic mode of inheritance previously demonstrated for canine PDA. It is suggested that the liability to defective ductal closure in the dog results from a quantitatively inherited inability of the ductus to constrict.

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 0° and 90°. 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 domimates 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.

Elastic Deformation in Orthotropic Vessels: Theoretical and Experimental Results

Excursions of the semiaxes were used to define the distortion and shape of the vessel cross section considered for conic and almost conic models. Some describing functions and mensuration expressions closely approximate, yet greatly simplify, calculations of perimeter and cross sections. Theory and experiments with models were in good agreement, but preliminary experiments showed the real case to be more complicated. Physical properties of the pulmonary trunk varied along its axis, growing stiffer toward the periphery. Furthermore, the dimension variations with transmural loading alter concepts of properties derived from measurements of a single diameter. The influence of the pericardium on the deformation of the main pulmonary artery under transmural stress was also explored. It was seen that the pericardium exerts significant restraint on the distortion and volume variations of this vessel. Over normal pressure ranges, removal of the pericardium can result in trunk volumes up to 100% greater than realized with the pericardium intact.