R. Busse

Separate determination of the pulsatile elastic and viscous forces developed in the arterial wall in vivo.

The viscoelastic behaviour of arteries in vivo is analyzed by separate representation of the purely elastic and the purely viscous properties, using natural pressure and diameter pulses of various dog arteries recorded under steady-state conditions. The circumferential wall stress (σ) and the radius (r) of the mean wall layer are calculated as functions of time and the hysteresis of the σ-r diagram is represented. The stress is regarded as the sum of an elastic stress (σel) which is a function ofr, and a viscous stress (σvis) which is a function ofdr/dt. Thus σel=σ−σvis. Since the σel-r diagram must be free from hysteresis, the disappearance of the loop is the criterion that indicates that σel has been found.σvis is formulated as a second degree polynomial ofdr/dt whose coefficients are determined using that criterion.The σel-r curve is always nonlinear and the elastic modulus increases with increasing radius. The σvis-dr/dt curve, too, is nonlinear. Its slope decreases with increasingdr/dt. The same applies to the wall viscosity (pseudoplastic behaviour). The nonlinear properties can be represented adequately by processing the experimental data in the time domain. Problems inherent in investigations based on the frequency domain, as reported in the literature, are pointed out.

The mechanical properties of exposed human common carotid arteries in vivo

SummaryIn exposed common carotid arteries of 15 patients (36–74 years) undergoing neck surgery, the intra-arterial pressure (P) was recorded by means of a catheter-tip manometer and, at the same site, the external diameter (D) by means of a contactfree photoelectric device. On the average, the pulsatile diameter changes were 5.6% of the end-diastolic diameter at pulse pressures of about 50 mm Hg. Due to viscoelasticity, the P-D diagrams exhibited hysteresis loops. Using the criterion of loop elimination, an iterative procedure was applied which permitted, by the use of an appropriate computer program, the separation of the purely elastic and the purely viscous components of the P-D relationships. In all cases, the purely elastic P-D curves markedly deviated from linearity. The tangential elastic modulus (Et) and the pulse wave velocity (c) calculated from these curves were normalized by dividing these quantities by the respective end-diastolic values and plotted against the normalized external diameters. During each pulse cycle, Et increased, with increasing diameter, by a factor between 1.2 and 3.5, while c increased by a factor between 1.1 and 1.9 with reference to the respective end-diastolic values.ZusammenfassungAn 15 Patienten im Alter zwischen 36 und 74 Jahren, bei denen während einer Halsoperation die A.carotis communis freigelegt war, wurden simultan der intraarterielle Karotisdruck (P) mit einem Katheterspitzenmanometer und an derselben Stelle der arterielle Außendurchmesser (D) mit einem berührungsfreien photoelektrischen Verfahren registriert. Die relativen Durchmesseränderungen, bezogen auf den enddiastolischen Außendurchmesser, betrugen im Mittel 5,6% bei Druckamplituden von etwa 50 mm Hg. Die durch die Viskoelastizität der Arterienwand bedingten Hystereseschleifen der pulsatorischen P-D-Beziehungen wurden mit Hilfe eines iterativen Verfahrens unter Verwendung eines Digitalrechners eliminiert, wodurch eine Trennung der rein elastischen und der rein viskösen Komponenten der P-D-Beziehung ermöglicht wurde. Aus den rein elastischen P-D-Beziehungen wurden der tangentiale Elastizitätsmodul und die Pulswellengeschwindigkeit als Funktionen des Außendurchmessers berechnet und in normierter Form, d. h. bezogen auf den jeweiligen enddiastolischen Wert, dargestellt. Mit wachsendem Durchmesser stieg der Elastizitätsmodul während jedes Pulszyklus auf das 1,2- bis 3,5fache des enddiastolischen Wertes an. Entsprechend nahm die Pulswellengeschwindigkeit auf das 1,1- bis 1,9fache des enddiastolischen Wertes zu.

Photoelectric device for the recording of diameter changes of opaque and transparent blood vessels in vitro

A new photoelectric device for measuring blood vessel diameters is described. The principle of this device consists in locating the vessel within a beam of parallel light at right angles to the beam direction, and eliminating all light striking the vessel. Thus only the light passing by the side of the vessel determines the signal strength of a photocell. The elimination of the light by the vessel due to reflection, refraction, diffraction, or scattering, is achieved with the aid of a lens and pinhole representing a spatial filter. This arrangement is effective irrespective of whether the vessel is opaque or transparent. The resolving power of the device in measuring changes of outside diameter is better than 0.5 μm for vessels up to 3 mm in diameter. The upper frequency limit is 300 Hz (−3 dB). The application of the method is demonstrated by two examples of measurements obtained on a small muscular artery.

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.

Dependence of elastic and viscous properties of elastic arteries on circumferential wall stress at two different smooth muscle tones

AbstractUsing isolated segments of the abdominal aorta of normotensive rats, the dependence of the dynamic circumferential elastic modulus (Ed), the loss modulus (ωηw), and and the coefficient of wall viscosity (ωηw) on the mean circumferential wall stress (σt) and the frequency of radius changes were studied under conditions of strong smooth muscle activation, induced by norepinephrine (NE), and during relaxation, induced by papaverine (PAP). The arterial segments were subjected to quasistatic and to small sinusoidal volume changes of 0.1–20 Hz at mean pressure levels of 1–23 kPa. The diameter changes were recorded by means of a photoelectric device with high spatial and temporal resolution.Ed, ωηw, and ηw were calculated from the mean external and internal radii and from the dynamic pressure-radius changes determined at each pressure level. Results and Conclusions1.The relative decrease in mean radius produced by NE-activation of the resting smooth muscle, is only of the order of 10–15%. The maximum active decrease in radius occurs at a pressure level of about 10 kPa.2.The quotient of the dynamic to the quasistatic elastic modulus increases from 1.5–2.1 under NE, and from 1.2–1.5 under PAP when σt is increased from 1·102 to 15·102 kPa.3.Ed and ηw increase with increasing σt. At a given σt,Ed is virtually independent of frequency, while ωηw slightly increases with increasing frequency. The values ofEd and ηw obtained under NE and PAP are virtually identical. From these findings it is concluded that the elastic behaviour of the vessel wall is determined chiefly by the stiffness of the passive elements.4.At a given frequency, ηw increases with increasing σt, while ηw decreases markedly with increasing frequency when σt remains unchanged. This behaviour is called, in the terms of polymer rheology, thixotropy or pseudoplasticity. The values of ηw obtained under NE and under PAP are virtually identical. This leads to the conclusion that the viscous properties of the arterial wall, under pulsatile conditions, reflect the viscosity of the passive elements rather than the viscosity of the contractile element.

Photoelectric device for contact-free recording of the diameters of exposed arteries in situ.

SummaryA photoelectric device is described which permits contact-free recording of the diameter of an in situ exposed artery. The light emitted by the filament of a bulb (6 W) is collimated by a projection lens (1∶2.8, 50 mm) and directed onto the surface of a silicone photocell (12.6×6.2 mm) covered by a neutral light filter. The voltage drop caused by the photocell current flowing through an adjustable load resistor represents the signal voltage which is fed into the input of an instrumentation amplifier. The artery under investigation is positioned above the photocell parallel to its short axis. The signal voltage decreases linearly with increasing area of the shadow cats by the artery on the photocell and thus the output voltage of the amplifier is linearly proportional to the diameter of the artery.The combined frequency response of photocell and amplifier was examined by sinusoidally modulated light emitted by a luminescent diode. The amplitude ratio was constant up to 200 Hz and the time lag was about 0.2 ms.The device was used on the canine carotid and femoral arteries. An example is shown.

New Ways of Determining the Propagation Coefficient and the Visco-Elastic Behaviour of Arteries in situ

In the theoretic treatment of the pulse waves generated by the left ventricle in the arterial system, two basic equations are important, the equation of motion and that of continuity. The first equation contains the longitudinal impedance (z1) as the relation between the longitudinal pressure gradient and the local flow, while in the second, the transverse impedance (zt) represents the relation between the local pressure and the longitudinal flow gradient. Each of the two impedances is related to the unit of vessel length. Pressure (p) and flow (i) are functions of the point (x) on the longitudinal axis of the vessel and of the time (t) [for literature, see 2, 9, 12, 13, 18, 20].

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.

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.

Frequenzspektren direkt und unblutig registrierter Arterienpulse - Frequency spectra of directly and noninvasively recorded arterial pulses

Unsere Untersuchungen und Berechnungen widerlegen die immer wieder geäußerte Ansicht, daß aus Meßräumen die Drosseln von Leuchtstoffröhren herauszuziehen seien. Ihr Anteil am Magnetfeld ist nicht größer als der, der von Meßgeräten selbst erzeugt wird. Es entzieht sich unserer Kenntnis, warum man besagte Empfehlung ausgesprochen hat. Vielleicht waren die Drosseln in den Anfangs jähren so schlecht, daß das von ihnen erzeugte Streufeld erheblich höher lag als das der heutigen Drosseln. Es ist auch möglich, daß eine nichtvergossene Drossel, bei der sich das geschichtete Kernpaket lockert, zu höherem Streuflüssen führen kann. Aus diesem Grunde aber den großen Aufwand der Drosselverlegung treiben zu wollen, halten wir für unangebracht, da es bei der heutigen Technik doch möglich sein muß, derartige Erscheinungen zu verhindern. In jeden Falle sollte man Leuchtstoffdrosseln, wenn sie einen hörbaren Brummton erzeugen, auf ihre Funktionstüchtigkeit hin überprüfen. Eine derartige Maßnahme ist auch schon deswegen angebracht, weil dadurch Mikrophonmessungen beeinträchtigt werden könnten. Aus Meßgründen sollten flackernde Leuchtstoffröhren und defekte Starter ausgewechselt werden, sie erzeugen sehr schwer beherrschbare Störimpulse. In der Nähe von Leuchtstoffröhren muß man im Bereich oberhalb von 2 KHz mit hochfrequenten Störungen rechnen, die durch den Entlademechanismus innerhalb der Leuchtstoffröhre erzeugt werden. 290 Anschrift der Verfasser: Priv.-Doz. Dr.-Ing. W. Irnich A. Johnen Abteilung Innere Medizin I der RWTH Aachen Goethestraße 27/29 5100 Aachen