Buckling of elastic tubes: study of highly compliant device.
Explore the source record for details and available documents.
Biomechanical Phenomena↗
Biomedical subjects
C D Bertram
Publications and source records attributed to C D Bertram.
The dynamics of collapsible tubes.
The importance of collapsible-tube phenomena derives primarily from blood, air and urine flows in mammals, although similar principles underlie invertebrate jetting and the avian syrinx. Biological fluid conduits have flexible walls and many experience higher external than internal pressures during physiological manoeuvres. The tube typically becomes noncircular, and large shape and cross-sectional area changes occur for small transmural pressure change. Two consequences ensue: a highly nonlinear constitutive relationship, and strong coupling between the fluid and solid mechanics. Depending on how flow is controlled, the tube can exhibit flow-rate-independent pressure-drop, or pressure-drop-independent flow-rate, or a locally negative slope to the pressure-drop to flow-rate relationship. At sufficiently large Reynolds number, these behaviours are accompanied by self-excited oscillation in a surprising variety of modes, including aperiodic ones. Chaotic behaviour has been predicted numerically, but not unequivocally demonstrated. Intrinsic chaotic oscillation must be distinguished from sensitivity to turbulent through-flow. To this end, the response to periodic upstream forcing is currently being investigated.
Animals↗
Analysis of the effects of measurement errors on the evaluation of propagation coefficients, in rubber tubes and canine aorta in vivo.
Published measurements of canine arterial propagation coefficients show large disparities in pulse wave attenuation and considerable variation with frequency, suggesting both random and systematic error. Here we devise methods of assessing the likely magnitude of each measurement error source, and calculate the individual and cumulative effects on the propagation coefficients derived using three different schemes to compensate for reflections: the three-point method (3PT), the total occlusion method (OCC) and the general iterative method applied to Cox's arrangement of four transducers (GEN). Results from measurements using impulse excitation in a latex tube show that each method accumulates error in a characteristic frequency pattern. The predicted error bands for OCC are very small except at the fundamental, and clearly exclude a significant further error component. The predicted 3PT error is large at low and at high frequency, and the error bands are better predictors of actual error than in the OCC case. Transducer position error is less than any one of the three pressure measurement errors. The predicted GEN error increases with frequency and when averaged across frequency is of magnitude intermediate between those for OCC and 3PT. Results for the OCC and GEN methods from the canine aorta in vivo generally confirm these trends, but the concentration of natural pulse wave energy at low frequencies acts to reduce low-frequency error and increase high-frequency error.
Algorithms↗
Analysis of all possible combinations of four measurements determining true propagation in arteries.
All possible combinations of four measurements of blood pressure, blood flow and vascular diameter are examined by transmission-line theory. It is found that only nine measurement combinations can give the attenuation coefficient gamma, reflection coefficient R and characteristic impedance Z0 simultaneously. At least one pressure measurement must be included. Their general expressions with arbitrary measuring locations are presented, together with some simplified forms which cover all the previous methods. A greater choice of method is thereby made available for use in practice. The results show that, regardless of the measurement locations, all combinations can be solved in the order gamma first, R second and Z0 last.
Arteries↗
Detecting right ventricular volume changes using the conductance catheter.
The purpose of this study was to assess the role of conductance catheter position within the right ventricle in obtaining adequate indications of phasic changes in ventricular volume. Possible applications of this technology are in rate responsive pacemakers and implantable defibrilators. The conductance catheter was placed in the right ventricle by cannulation of a jugular or femoral vein or a branch of the pulmonary artery. Position within the ventricle was documented from biplane fluoroscopy. Stroke volume was perturbed by: bolus injection of blood, vagal stimulation, venous infusion of methylcholine chloride, or isoprenaline. Four criteria were used to assess the quality of volume signals: (1) volume signal phase relative to the electrocardiogram; (2) magnitude parity of volume change from each electrode pair; (3) freedom from artifact; and (4) indication of stroke volume change during interventions. Greyhound dogs of either sex (n = 33), weight 20-32 kg. A total of 236 recordings from 14 distinct catheter positions were analyzed. Catheter positions originating from a femoral cannulation and one position from the pulmonary artery gave markedly superior volume transduction compared to those from the jugular route. Although right ventricular volume transduction was possible from all catheter trajectories, those resulting from the femoral approach were clearly superior. In the right ventricle, the inability to transduce a sufficient proportion of ventricular volume, in concert with the potential sensitivity of the catheter to atrial volume changes, may seriously limit the potential of the conductance technique in the applications envisaged.
Animals↗
A general method of determining the frequency-dependent propagation coefficient and characteristic impedance of an artery in the presence of reflections.
An iterative method of calculating propagation parameters at harmonics of heart rate for a uniform vascular segment from a combination of four arterial waveform measurements is presented. Measurements of blood pressure, vascular diameter, and blood flow-rate may be combined arbitrarily provided only that at least one measurement of pressure and one of flow-rate be included; the requirement of four measurements implies at least two measurement sites along the vessel. The analysis is thus a generalization of those associated with previous methods of determining propagation parameters, allowing for instance relaxation of the requirement of equal spacing in the three-point method. Results are presented for the propagation of an impulse along a rubber tube when the measurements are pressure at two sites, flow-rate and diameter.
Arteries↗
Possible sources of discrepancy between sphygmomanometer cuff pressure and blood pressure quantified in a collapsible-tube analogue.
This paper examines the assumption that the audible events detected as Korotkov sounds in sphygmomanometry occur when blood pressure equals arm-cuff pressure. Several effects that contribute to discrepancy between these pressures are quantified using an idealised arm-and-cuff system consisting of a thick-walled collapsible tube subject to external compression along a central part of its length. The effects studied are (1) transverse pressure difference, resulting from tissues sustaining a part of the external compression through (a) circumferential bending stiffness and (b) longitudinal curvature of the tensed localised neck at the site of initial collapse, (2) longitudinal pressure difference between upstream pressure and pressure at the collapse point due to both (a) viscous and (b) inertial pressure drop. These effects are found to compensate partially for each other; the pressure within the vessel at the collapse point is less than the cuff pressure, but is also less than the blood pressure at the upstream end of the cuff. All four of the contributing terms increase proportionally to the flow-rate raised to a power greater than one, except the viscous pressure drop. Owing to a progressive shortening of the collapsed neck as flow-rate increases, the viscous term is almost independent of the flow-rate. The overall discrepancy displays less flow-rate dependency and is smaller than some of the terms which contribute to it. This means that considerable accuracy is needed if measurements of the effects are to be used to correct the raw data on cuff pressure at the time of Korotkov sound emission so as to obtain an improved estimate of the blood pressure.
Auscultation↗
Measurements of wave speed and compliance in a collapsible tube during self-excited oscillations: a test of the choking hypothesis.
Indirect evidence links self-excited oscillation of flow through collapsed tubes with choking, defined by the cross-sectionally averaged fluid speed u reaching the local speed of small pressure waves c. This was tested by measuring both c-u and c as functions of tube cross-sectional area during self-excited oscillation, using small superimposed high-frequency wave packets. The wavespeed c was derived from the local slope of the pressure/area relationship, measured at both high and low frequency, while c-u was taken as the upstream propagation rate of the pressure disturbances. When u = 0, these were shown to agree with each other. The propagation results showed that choking did not occur at high frequency. At the low frequency of the self-excited oscillation the results were less conclusive, because of dispersion and indirect methodology, but choking appeared not to happen at the modest flow rate of the oscillation investigated. Results on the attenuation of the wave packets were successfully explained using a model of the tube throat consisting of two equal and opposite reflection sites.
Hemodynamics↗
Cross-sectional area measurement in collapsed tubes using the transformer principle.
To avoid the necessity for intraluminal catheters as used with the axial impedance method of measuring the cross-sectional area of flexible tubes independently of their shape, while retaining the advantage of an immediate electrical output, an electromagnetic method was tested. The method uses a single-turn sensing coil attached to or embedded in the tube wall at the site of interest as the secondary winding of a transformer. One or more primary coils coaxial with the tube provide an alternating magnetic field parallel to the tube axis, and the resulting secondary voltage, after amplification and demodulation, is directly proportional to tube cross-sectional area. Tube pressure/area relationships measured thus were compared with those measured using both an ultrasonic imaging technique and liquid volume displacement. The method was shown to provide an accurate and relatively simple alternative to the impedance method. Various ways to fabricate tubes with or otherwise introduce the necessary sensing coil are discussed.
Biomechanical Phenomena↗
Effect of radial position on volume measurements using the conductance catheter.
A finite-difference computer model has been used to determine the potential distributions arising from a dipole current source aligned parallel to the axis of bounding cylinders. The radial position of this source had large and nonlinear influence on the potentials along the dipole axis. The accuracy of the computer simulation was established from comparison with an analytic solution of a simple geometry. Measurements using a conductance catheter in saline-filled cylinders also demonstrated the dependence of the conductance on the radial position. The dependence of the potential distribution on the radial position of the dipole places limits on the ultimate accuracy of the conductance catheter technique when used for the measurement of ventricular volume. Radial movement of the catheter within the ventricular cavity, resulting in changes in the potential distribution, could explain some artefacts that appear on volume recordings from the conductance catheter.
Animals↗
Oscillations in a collapsed-tube analog of the brachial artery under a sphygmomanometer cuff.
To determine whether self-excited oscillations in a Starling resistor are relevant to physiological situations, a collapsible tube conveying an aqueous flow was externally pressurized along only a central segment of its unsupported length. This was achieved by passing the tube through a shorter and wider collapsible sleeve which was mounted in Starling resistor fashion in a pressure chamber. The tube size and material, and all other experimental parameters, were as used in our previous Starling resistor studies. Both low- and high-frequency self-excited oscillations were observed, but the low-frequency oscillations were sensitive to the sleeve type and length relative to unsupported distance. Pressure-flow characteristics showed multiple oscillatory modes, which differed quantitatively from those observed in comparable Starling resistors. Slow variation of driving pressure gave differing behavior according to whether the pressure was rising or falling, in accord with the hysteresis noted on the characteristics and in the tube law. The results are discussed in terms of the various possible mechanisms of collapsible tube instability, and reasons are presented for the absence of the low-frequency mode under most physiological circumstances.
Blood Pressure Determination↗
The effects of wall thickness, axial strain and end proximity on the pressure-area relation of collapsible tubes.
Segments of silicone rubber tube were suspended between rigid pipes and subjected to slowly varying transmural pressure covering a range from slight distension to collapse with osculation. The local inside cross-sectional area at a chosen axial site was simultaneously measured via catheter by an electrical impedance method. Pressure-area relations were recorded thus at various axial sites, under varying conditions of axial tube wall tension, in tubes of two different wall thickness (0.3 and 0.4 of mean radius). Unsupported tube segment length was also varied by means of an insert device. The relations were used to calculate the variation of wave velocity with area according to Young's equation. First opposite wall contact during collapse was shown to occur at a smaller fraction of undistended circular cross-sectional area than in the thin-walled tubes investigated previously by others.
Blood Pressure↗
Right ventricular volumetry by catheter measurement of conductance.
The electrical conductivity of blood is sufficiently higher than that of myocardium to make feasible the detection of cardiac volume changes by measurement of intraventricular fluid conductance. An eight-electrode catheter was used to inject an alternating current (100 microA or less, at 1500 Hz) via the two electrodes nearest the ventricular base and apex, then the resulting five voltage differences between adjacent pairs of the six intervening electrodes were measured. When current amplitude was held constant, the cross-sectional area of the ventricular cavity slice defined by planes perpendicular to the catheter through the relevant pair of electrodes was inversely proportional (to the first order) to the voltage difference. Measurement of multiple segments compensated for isovolumic cavity shape changes. The technique had previously been shown to measure left ventricular volume successfully, but the geometry of the right ventricle made this measurement more problematical. Using open-chested, anesthetized greyhounds, we compared the catheter-measured right ventricular volume change with stroke volume as measured by a pulmonary arterial electromagnetic blood flowmeter. With optimal catheter placement, good correlation between stroke volume and catheter-measured volume changes was achieved when stroke volume was perturbed on a beat-to-beat basis. In six data records from three dogs, involving two different means of varying stroke volume (rapid injection of blood and sinus node irritation), the correlations yielded r2 values between 0.82 and 0.98.(ABSTRACT TRUNCATED AT 250 WORDS)
Animals↗
Unstable equilibrium behaviour in collapsible tubes.
Thick-walled silicone rubber tube connected to rigid pipes upstream and downstream was externally pressurised (pe) to cause collapse while aqueous fluid flowed through propelled by a constant upstream head. Three types of equilibrium were found: stable equilibria (steady flow) at high downstream flow resistance R2, self-excited oscillations at low R2, and 'unattainable' (by varying external pressure) or exponentially unstable equilibria at intermediate R2. The self-excited oscillations were highly non-linear and appeared in four, apparently discrete, frequency bands: 2.7 Hz, 3.8-5.0 Hz, 12-16 Hz and 60-63 Hz, suggesting that the possible oscillation modes may be harmonically related. Stable, intermediate 'two-in-every-three-beats' oscillation was also observed, with a repetition frequency in the 3.8-5.0 Hz band. As pe was increased, self-excited oscillations were eventually suppressed, leaving internal fluid pressure varying with no single dominant frequency as a result of turbulent jet dissipation at the downstream rigid pipe connection. Comparison of pressure-wave velocity calculated from the local pressure-area relation for the tube with fluid velocity indicated that supercritical velocities were attained in the course of the self-excited oscillations.
Biomechanical Phenomena↗
Real time detection of significant blood pressure events in ambulant subjects.
A typical twenty-four hour continuous ambulatory blood pressure (BP) record demonstrates many marked, apparently spontaneous blood pressure spikes. Awareness of such BP fluctuations may help determine their causative mechanisms and lead to improved applications of conscious learned control of BP (Biofeedback). A microprocessor device has been constructed to monitor direct arterial blood pressure in real time and to compile a profile history of the BP and heart rate (HR). When the BP level exceeds a threshold based on the BP history, an audio signal prompts the subject, who is then able to record the current physical and emotional status. Alternatively, a combination of the parameters (SBP,DBP,HR) may be used to determine the threshold criteria. A decision table determines whether each parameter should lie above, below or within the threshold region. Triggering will occur only if a predefined relationship has occurred. The device will aid in the detection and interpretation of significant BP events occurring during a 24 hour recording as well as in the application and assessment of biofeedback control of blood pressure.
Biofeedback, Psychology↗
Optical endpoint sensing in an automatic whole blood clotting timer.
Explore the source record for details and available documents.
Biomedical Engineering↗
A mathematical model of unsteady collapsible tube behaviour.
A simple, third-order lumped parameter model is presented to describe unsteady flow in a short segment of collapsible tube held between two rigid segments and contained in a pressurised chamber. Equilibrium states and their stability are analysed in detail, as is fully non-linear time dependent behaviour, including in particular the excitation and sustenance of limit--cycle oscillations. The model explicitly neglects both wave propagation (and hence the possibility of choking) and the influence on the elastic properties of the tube of longitudinal tension, but it is otherwise firmly based on fluid mechanical principles. The results emphasise the profound importance of (a) the unsteady head loss (but with some pressure recovery) in the separated flow at the oscillating throat, and (b) the mechanical properties of the parts of the system both downstream and upstream of the collapsible segment. The nature of the upstream segment in particular determines whether it is an upstream pressure head or the inflow to the collapsible segment that is held constant during oscillations. The results are discussed in the context both of other models and of experiment.
Biomechanical Phenomena↗
Two models of instability in a thick-walled collapsible tube conveying a flow.
Explore the source record for details and available documents.
Movement↗