Th. Pasch

The quasistatic and dynamic circumferential elastic modulus of the rat tail artery studied at various wall stresses and tones of the vascular smooth muscle

SummaryIn vitro the pressure-volume curves of small segments of the rat tail artery containing 75% smooth muscle were determined in the frequency range 0.018–25 Hz. The segments were held at in-situ lengths of about 6 mm. The vascular smooth tone muscle was influenced by treatment with norepinephrine and papaverine. The circumferential stressσt was changed by varying the mean transmural pressure. The circumferential elastic modulusEt was calculated from values obtained by the static and dynamic pressure-diameter relations. The formula used is valid for thick-walled, longitudinally constrained vessels and is derived in a theoretical paragraph.Results and conclusions:1.The quasistatic circumferential elastic modulus is 105 dynes/cm2 for the smallest stresses considered and increases to 2×106 dynes/cm2, occuring at maximum stress. These values are smaller by a factor of ten than those measured by other authors on large arteries.2.There is a linear relationship betweenEt andσt at each frequency range investigated. The moduli observed after treatment with papaverine aregreater than those observed after excitation of the smooth muscle with norepinephrine, the same stress applying in each case.3.The dynamic elastic modulusEd (real part ofEt) and the loss modulusωηw (imaginary part ofEt) are related toσt and plotted against frequency.Ed/σt increases slightly with frequency; this quotient is far smaller after treatment with norepinephrine than after the application of papaverine. The expressionωηw/σt shows the well-known frequency dependence and proves to be independent of the smooth muscle tone. Therefore, when the smooth muscle is activated, the relative contribution of the loss modulus to the circumferential elastic modulus is greater than under conditions of relaxation.

The genesis of the pulse contours of the distal leg arteries in man.

SummaryIn order to clarify the genesis of the human pressure and flow pulse contours of the distal leg arteries, in particular the posterior tibial artery, pulse recordings were performed with transcutaneous techniques under normal conditions and in the state of strong vasodilatation (reactive hyperaemia) in the distal parts of the lower legs. From the experimental results it is concluded that the contour of the incident pressure wave arriving in the leg arteries is very similar to the pressure pulse contour of the abdominal aorta, while the resulting contour in the leg arteries is determined by this incident wave and superimposed reflected waves. The latter arise from positive reflection in the periphery of the lower legs. They travel in retrograde direction, are reflected negatively in proximal regions, particularly in the abdomimal aorta, and appear again, with opposite sign, in the leg arteries. In addition, retrograde waves reflected positively at the aortic valve and then traveling in antegrade direction also influence the pulse contours. By considering this wave travel, the genesis of the characteristic contours of the pressure and flow pulses of the lower leg arteries is explained in a satisfactory way. This is demonstrated by a simplified graphical pulse construction as well as by the calculation of pulse contours on the basis of a theoretical tube model of the arterial system with the aid of a digital computer. The results of these calculations are discussed with respect to the findings of previous investigators who used analog and digital models of the arterial system.

Theoretical studies on the human arterial pressure and flow pulse by means of a non-uniform tube model

Abstract A theoretical model of the arterial system is described. It consists of three unbranched uniform tubes arranged in series. Using a digital computer (CD 3300), both pressure and flow pulses are computed at certain sites of the model on the basis of a primary pulse wave resembling the flow pulse in the ascending aorta. The calculations are performed assuming both undamped wave propagation and frequency-dependent damping. In each of these assumptions, real reflection coefficients are used. In a theoretical section the conditions, under which the use of real reflection coefficients is justified in frequency-dependent damping, are examined. Computed and natural pulses correspond well, in particular with respect to the profiles of the pressure pulses. Therefore, the model permits us to clarify the genesis of the main characteristics of the contours of human arterial pulses. The influence of frequency-dependent damping on the pulse contours, as well as on the input impedance is demonstrated.

[Method for improving the accuracy of blood flow-rate registration measured transcutaneous by using the ultrasonic Doppler principle].

SummaryA number of difficulties inherent in ultrasound Doppler blood flowmetry are discussed. The method is improved by electronic averaging of a series of flow pulses recorded in steady state circulation. This procedure permits to raise the upper frequency limit of the low-pass filter to such an extent that the recordings are suitable for hemodynamic studies.ZusammenfassungVerschiedene Schwierigkeiten, die der Blutströmungsmessung mittels des Ultraschall-Doppler-Verfahrens anhaften, werden besprochen. Eine Verbesserung wird dadurch erzielt, daß bei stationärem Kreislaufzustand eine große Zahl von Einzelpulsen registriert und diese elektronisch gemittelt werden (averaging). Hierdurch ergibt sich die Möglichkeit, die obere Frequenzgrenze der Registrierung auf einen für hämodynamische Untersuchungen erforderlichen Wert zu erhöhen.

Comparison of the visco-elastic properties of the tail artery in spontaneously hypertensive and normotensive rats.

AbstractSummaryThe quasistatic and dynamic elastic behaviour of the tail artery of male normotensive (NCR) and spontaneously hypertensive (SHR) rats was determined in vitro. The tone of the smooth muscle was enhanced by norepinephrine and diminished by papaverine. The circumferential wall stress was changed by varying the transmural pressure level. The experimental procedure was the same as that used in a previous investigation (Bauer and Pasch, 1971). The circumferential (tangential) elastic wall modulusEt was calculated from the mean internal and external radii determined at each pressure level and from dynamic pressure-volume recordings in the frequency range between 0.03 and 20 Hz. The calculation was based on a formula valid for thick-walled, longitudinally constrained vessels.Results1.The cross-sectional wall area is only slightly increased in SHR as compared with NCR. While under norepinephrine the quasistatic pressure-radius loops are virtually identical in NCR and SHR, the loops obtained under papaverine are shifted towards significantly greater radii in NCR than in SHR. It is concluded that in SHR there is a change in the structure of the non-muscular wall elements, but no essential alteration of the smooth muscle.2.The dynamic elastic modulusEd (real part ofEt) increases with increasing wall stress σt. In NCR, theEd − σt regression line for papaverine is significantly shifted towards higher moduli as compared with that for norepinephrine. This shift is only small in SHR.At a given wall stress,Ed is virtually independent of frequency within the range investigated in both NCR and SHR.3.The loss modulus ωηw (imaginary part ofEt) shows virtually the same dependence on the wall stress asEd. It increases markedly with frequency in NCR and SHR. There is a clear difference between the effects of spontaneous hypertension on the tail artery and on the peripheral resistance vessels.

A simple method of obtaining quasi-continuous frequency spectra of the input impedance of arterial systems

SummaryA simple method is described which permits a complete determination of the input impedance of the arterial system from a single flow and its accompanying pressure pulse. The method is based on the assumption that the pulse under consideration is a non-periodic function and not a periodic one. Thus, an approximation to the Fourier integral permits us to obtain a quasi-continuous frequency spectrum instead of the non-continuous spectrum provided by the usual Fourier analysis of natural pulses.

The resolution of arterial pulses into forward and backward waves as an approach to the determination of the characteristic impedance

SummaryPressure and flow recordings from a given site in an artery can be used for the resolution of the pulse wave into its forward and backward components if the characteristic impedance (Z) is known. The principle of this method was reported by von Kries in 1892.In the present work, the procedure is first applied to a theoretical, non-uniform tube model. The characteristic impedances of the model are assumed to be real magnitudes. From the results it is seen that the calculated backward wave provides a criterion which indicates whether the true value ofZ actually has been used for the resolving procedure. If, as in the case of natural pulses,Z is not known, its value can be obtained by repeatedly performing the resolving procedure using various values ofZ, and choosing the value ofZ employed to calculate the backward wave which best fits the criterion.The method is demonstrated on pulses of the abdominal aorta and carotid artery of the dog. The results are compared with the average values of the input impedance in the higher frequency range.

Neuere Untersuchungen zur Entstehung der Pulsformen in großen Arterien des Menschen

Die Versuche zur Erklarung des Zustandekommens der arteriellen Pulsformen mit Hilfe der Wellenlehre, der Windkessellehre oder einer Kombination dieser beiden haben eine lange Vorgeschichte [(2, 3, 13,), ausfuhrliche Darstellung (21)]. Diesen Versuchen liegt jeweils ein Modell zugrunde, das entweder als theoretisches Modell zu Berechnungen oder als physisches Modell zu Experimenten dient. Das theoretische Modell gestattet sowohl die Analyse naturlicher Pulse als auch die Gewinnung berechneter Pulse, wahrend das physische Modell selbst Pulse liefert. Ein Vergleich der berechneten bzw. der durch das physische Modell erzeugten Pulse mit den naturlichen Pulsen ermoglicht ein Urteil uber den Wert des Modells. Von den wesentlichen Arbeiten dieser Art aus neuerer Zeit seien Pulsformanalysen (10), die Synthese arterieller Pulse des Hundes (18, 19), die Schaffung eines elektrischen Analogmodells des menschlichen Arteriensystems (15), die Experimente und Berechnungen an inhomogenen zweiteiligen bzw. mit kontinuierlicher Anderung des Wellenwiderstandes ausgestatteten Schlauchmodellen (11, 12, 20) sowie die von uns vorgenommene Synthese des menschlichen Femoralispulses (1) genannt. Diese Arbeiten aus neuerer Zeit stutzen sich ausschlieslich auf die Wellenlehre.

Determination of arterial input impedance spectra from non-invasively recorded pulses.

SummaryThe frequency spectra of modulus and phase of the input impedance (Zin) of large human arteries (abdominal aorta, femoral and subclavian arteries) were computed from transcutaneousky recorded, uncalibrated pressure and flow pulses picked up as sphygmograms and Doppler flow velocity pulses, respectively. Since these pulses cannot be calibrated, the modulus (|Zin|) of the input impedance is calculated in relative units; its spectrum, however, is not influenced by this fact. A modification of the computing procedure makes it possible to natural pressure and flow pulses which may be regarded as periodic functions. This is the prerequisite for a detailed analysis of the wave transmission properties of the arterial bed which manifest themselves in the input impedance. For this purpose the peripheral reflection site was moved in a proximal direction by bilateral occlusion of limb arteries. This was done by inflating cuffs placed symmetrically on both sides around the upper or lower parts of the respective limbs. When the occluding cuffs were placed around both lower legs or both thighs, the shortening of the arterial wave transmission line resulted in a marked shift of the first maximum of |Zin| to higher frequencies in the spectrum of |Zin| of the abdominal aorta and femoral artery. Bilateral occlusion of the arteries of the forearms or upper arms, however, did not have any measurable influence on |Zin| of the subclavian artery. Theoretical considerations show that this difference in behaviour of the several parts of the arterial system may be attributed to the varying extent of their inhomogeneity.ZusammenfassungDie Frequenzspektren von Betrag und Phase des Eingangswiderstandes (Zin) großer Arterien des Menschen (Aorta abdominalis, A. fermoralis und subclavia) wurden aus transkutan registrierten, ungeeichten Druck- und Strompulsen berechnet. Die Pulse wurden in Form von Sphygmogrammen und Doppler-Strömungsgeschwindigkeitspulsen gewonnen. Da solche Pulse nicht eichbar sind, wird der Betrag (|Zin|) des Einganswiederstandes in relativen Einheiten berechnet; der Verlauf des Spektrums von Zin wird hierdurch aber nicht beeinflußt. Eine Modifikation des Berechnungsverfahrens ermöglicht die näherungsweise Bestimmung eines quasi-kontinuierlichen Frequenzspektrums von Zin aus den als periodische Funktionen aufzufassenden natürlichen Druck- und Strompulsen. Diese Möglichkeit bildet die Voraussetzung für eine eingehende Analyse der sich im Eingangswiderstand widerspiegelnden Wellenleitungseigenschaften des Arteriensystems. Zu diesem Zwecke wurde der periphere Reflektionsort durch beiderseitigen Verschluß der Extremitätenarterien nach proximal verschoben, indem Manschetten um die jeweiligen Extremitäten gelegt und aufgeblasen wurden. Lagen die Manschetten an beiden Unter- oder Oberschenkeln, so führte die Verkürzung der arteriellen Wellenleitung im Falle der Aorta abdominalis und der A. femoralis zu einer deutlichen Verschiebung des ersten Maximums von |Zin| zu höheren Frequenzen. |Zin| der A. subclavia wurde jedoch durch bilaterale Arterienabsperrung im Bereich der Unter- oder Oberarme nicht wesentlich beeinflußt. Theoretische Überlegungen ergeben, daß sich diese Unterschiede im Verhalten verschiedener teile des Arteriensystems auf das Ausmaß ihrer Inhomogenität zurüchführen lassen.

Einfluß der kontrollierten Hypotension auf arterielle Oxygenierung und Plasma-Katecholamine während koronarer Bypass-Operationen

Hauptziel der Herabsetzung erhohter Blutdruckwerte wahrend der Koronarchir-urgie ist die Reduzierung des myokardialen Sauerstoffbedarfs und in manchen Fallen die Verbesserung der linksventrikularen Funktion. Peripher wirkende Vasodi-latatoren vom Typ des Natrium-Nitroprussid (NNP) oder des Nitroglycerin (NTG) werden hierzu bevorzugt. Ihr Effekt ist durch einen schnellen Abfall des Blutdrucks, der nach Infusionsende sehr schnell wieder ansteigt, gekennzeichnet. Auf diese Weise konnen die bei Patienten mit koronarer Herzkrankheit (KHK) wahrend der Operation haufig vorkommenden Hochdruck-Episoden gefahrlos bekampft werden [4, 6]. Die durch die kontrollierte Hypotension verursachten Veranderungen der Kreislauf-Homoostase werden durch einen reflektorischen Anstieg der Herzfrequenz kompensiert, und es treten auserdem Veranderungen der Atemfunktion auf. Letztere bestehen in einem Abfall des arteriellen Sauerstoffdrucks (PaO2) und einer erhohten Beimischung von venosem Blut [1, 3, 5, 7, 8].