R. D. Bauer

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.

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.

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.

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.

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].