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FOREWORD

J Biomech Eng. 1992;114(1):1. doi:10.1115/1.2895442.
FREE TO VIEW
Abstract
Topics: Vessels , Blood flow
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J Biomech Eng. 1992;114(1):2-9. doi:10.1115/1.2895445.

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, flowrate and diameter.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):10-14. doi:10.1115/1.2895433.
Abstract
Topics: Waves
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):15-19. doi:10.1115/1.2895441.

Although slightly affected by alterations in preload, the maximum first derivative of left ventricular pressure with respect to time, Max(dP/dt), is widely regarded as a simple and convenient index of cardiac contractility for clinical use. The feasibility of noninvasive, hence repeatable, measurement of Max (dP/dt) will certainly lead to re-evaluation of its usefulness. Max(dP/dt) is given by the following equation: Max(dP/dt)=ρc Max(du/dt), where ρ is the blood density, c the pulse wave velocity, and u the flow velocity in the aorta. This equation has been previously validated in animal experiments and has now been applied to the clinical setting for the first time. In 20 patients without aortic stenosis, left ventricular pressure was measured with a catheter-tip micromanometer, aortic ejection flow velocity was measured by Doppler echocardiography, and pulse wave velocity by mechanocardiography or Doppler echocardiography. Then, δc Max (du/dt was calculated from the measured data and compared with measured Max (dP/dt). A significant positive correlation was found between them (ρc Max (du/dt) = 0.96 x Max (dP/dt) + 6.52, r=0.83, p<0.001.) In 11 patients with hypertension, ρc Max (du/dt) was obtained before and after long-term (average 13.1 months) treatment with antihypertensive drugs. In spite of the expected reduction in blood pressure and the regression of left ventricular mass, ρc Max (du/dt) remaioned unchanged. In 9 patients with dilated cardiomyopathy, the effects of β1 -agonist were tested at the beginning of therapy (30 mg/day denopamine) and 6 months later. The increase in ρc Max (du/dt) observed 1 hour after oral administration of he drug had not changed significantly 6 months later. We conclude that the index ρc Max (du/dt), is useful in assessing the contractile state of the left ventricle noninvasively.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):20-25. doi:10.1115/1.2895443.

Arterial post-stenotic dilatation (PSD) is a fusiform swelling immediately downstream to a stenosis. It is characterized by the presence of turbulent blood flow and wall vibration which has been claimed by others to be causal by producing structural weakening. We tested the hypothesis that vibration causes PSD in vivo by attaching electromagnetic and pneumatic vibrators to the aortic wall in chronic rabbits. We also observed whether mechanical vibration of the aorta in vivo influenced the distribution of oil-red-O lesions during one percent dietary cholesterol feeding. Low mass vibration gauges were developed to measure the vibration. Electromechanical vibrators having a ceramic magnet slug within a coil supplied with 50 Hz were glued to the aorta of chronic rabbits and the vibration maintained for an average of 8 weeks. Despite greater amounts of energy imparted to the wall there was no dilatation or difference in oil-red-O staining from the controls. Five weeks vibration at 100 Hz and an amplitude equal to the normal diameter pulse also produced no dilatation. We conclude that vibration does not cause PSD in vivo and suggest that its cause is likely to involve the vascular muscle stimulated by the effect of turbulent flow on the endothelium.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):26-33. doi:10.1115/1.2895444.

Oscillatory and pulsatile flows of Newtonian fluids in straight elastic tubes are simulated numerically with the aid of Ling and Atabek’s “local flow” assumption for the nonlinear convective acceleration terms. For the first time, a theoretical assessment of the local flow assumption is presented, and the range of validity of the assumption is estimated by comparison with perturbation solutions of the complete flow problem. Subsequent simulations with the local flow model indicate that the flow field and associated wall shear stress are extremely sensitive to the phase angle between oscillatory pressure and flow waves (impedance phase angle). This phase angle, which is a measure of the wave reflection present in the system, is known to be altered by arterial disease (e.g., hypertension) and vasoactive drugs. Thus, the paper elucidates a mechanism by which subtle changes in systemic hemodynamics (i.e., phase angles) can markedly influence local wall shear stress values.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):34-39. doi:10.1115/1.2895446.

Recent publications have emphasized the relationship between the spectrum of the backscattered acoustic signal, beam geometry, and flow patterns in the measurement of blood flow by Doppler ultrasound. On this basis, we believe that in the future more importance will be placed on analyzing various characteristics of the spectral shape rather than absolute parameters of measurement, such as the mean frequency. The potential of this approach for extracting more information from the raw Doppler signal is introduced by considering the Spectral Broadening Index (SBI). We explain the use of the SBI parameter for measuring flow angle under restricted flow conditions. This is done by using an analytic/computational model for prediction of the spectral broadening effect. By simulation study, the performance of various spectral estimators for determining the SBI from finite Doppler signal segments is evaluated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):40-49. doi:10.1115/1.2895448.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200≤Re≤1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):50-54. doi:10.1115/1.2895449.

A nonuniform channel is used as a simple model of a constricted arterial vessel. Flow patterns have been calculated for pulsatile flow with both sinusoidal and nonsinusoidal flow rates for a range of Reynolds number, Re , and Strouhal number, St. The results show that even for relatively low frequency flows a strong vortex wave will be generated with a complex wall shear stress distribution and peak values much greater than those found in steady or unsteady parallel flow. The vortex wave increases in strength with increasing Re and St , with its total length and wavelength independent of Re but inversely proportional to St. The form of the imposed flow rate is found to have an important effect on the flow and the shear stress distribution.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):55-59. doi:10.1115/1.2895450.

A steady flow through a segment of externally pressurized, collapsible tube can become unstable to a wide variety of self-excited oscillations of the internal flow and tube walls. A simple, one-dimensional model of the conventional laboratory apparatus, which has been shown previously to predict steady flows and multiple modes of oscillation, is investigated numerically here. Large amplitude oscillations are shown to have a relaxation structure, and the nonlinear interaction between different modes is shown to give rise to quasiperiodic and apparently aperiodic behavior. These predictions are shown to compare favorably with experimental observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):60-67. doi:10.1115/1.2895451.

There are several mechanisms potentially involved in the breakdown of steady fluid flow in a collapsible tube under external pressure. Here we investigate one that has received little attention in the past: the fact that the longitudinal tension in the tube wall, T , decreases with distance downstream as a consequence of the viscous shear stress exerted by the fluid. If the tube is long enough, or the initial tension small enough, T may fall to zero before the end of the collapsible tube, and unsteady motion would presumably then ensue; this is what we mean by “breakdown.” We study the phenomenon theoretically, when the flow Reynolds number is of order one, using lubrication theory in a symmetric two-dimensional channel in which the collapsible tube is replaced by membranes occupying a segment of each wall. The resulting nonlinear ordinary differential equations are solved numerically for values of the dimensionless parameters that cover all the qualitatively different types of solution (e.g., in which the channel is distended over all its length, collapsed over all its length, or distended in the upstream part and collapsed downstream). Reducing the longitudinal tension has a marked effect on the shape of the collapsible segment, causing it to become much more deformed for the same flow rate and external pressure. Indeed, the wall slope is predicted to become very large when the downstream tension is very small, so the model is not self-consistent then. Nevertheless, the parameter values for which T becomes zero are mapped out and are expected to be qualitatively useful. The relationships between the values of T during flow and its value before the flow begins is also considered.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):68-77. doi:10.1115/1.2895452.

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.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):78-83. doi:10.1115/1.2895453.

Blood flow in human brachial arteries, compressed by a pneumatic cuff for blood pressure measurement, is examined using several different noninvasive techniques. From the experimental results it is shown that, when arterial pressure distal to the cuff is always lower than cuff pressure, flow in the artery under the cuff becomes supercritical near the cuff downstream margin and no reflection occurs there and the reflected wave from the peripheral vascular system of the arm does not propagate beyond the cuff downstream margin. Therefore an unsteady transition from supercritical to subcritical flow occurs near the cuff downstream margin. When the peak value of distal arterial pressure exceeds cuff pressure, a reflection occurs near the cuff downstream margin. The reflection becomes stronger corresponding to decrement of the cuff pressure and the whole artery segment under the cuff inflates fully at systole. At diastole, however, the artery segment under the cuff does not collapse completely and, hence, the phenomenon becomes that of pressure wave propagation in a partially collapsed artery segment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):84-91. doi:10.1115/1.2895454.

Compliant tubes attain a complex three-dimensional geometry when the external pressure exceeds the internal pressure and the tube is partially collapsed. A new technique for remote measurement of dynamic surfaces was applied to classical experiments with collapsible tubes. This work presents measurements of the threedimensional structure of the tube as well as pressure and flow measurements during static loading and during steady-state fluid flow. Results are shown for two tubes of the same material and internal diameter but with different wall thicknesses. The measured tube laws compare well with previously published data and suggest the possible existence of a similarity tube law. The steady flow measurements did not compare well with the one-dimensional theoretical predictions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):92-100. doi:10.1115/1.2895455.

Six-revolute-joint instrumented spatial linkages (6R ISLs) have become often-used devices to measure the complete six-degree-of-freedom motion of anatomical joints. Accuracy of motion measurement depends on ISL design and calibration technique. In this paper, a design process is outlined that uses computer graphics and numerical methods as aids in developing 6R ISLs that (i) physically assemble within the desired range of motion of the joint; (ii) do not collide with either the experimental apparatus or the subject joint; (iii) avoid singular linkage configurations that can cause forces to be applied to the joint; and (iv) measure selected anatomical motions most accurately. It is found that a certain subgroup of 6R linkages are suitable for accurate measurement of specific motions, and can be the basis for new ISL designs. General guidelines are developed that can assist in the generation of unique linkage designs for different anatomical joints. The design process is demonstrated in the creation of an ISL to measure knee motion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):101-110. doi:10.1115/1.2895432.

The six-revolute-joint instrumented spatial linkage (6R ISL) is often the measurement system of choice for monitoring motion of anatomical joints. However, due to tolerances of the linkage parameters, the system may not be as accurate as desired. A calibration algorithm and associated calibration device have been developed to refine the initial measurements of the ISL’s mechanical and electrical parameters so that the measurement of six-degree-of-freedom motion will be most accurate within the workspace of the anatomical joint. The algorithm adjusts the magnitudes of selected linkage parameters to reduce the squared differences between the six known and calculated anatomical position parameters at all the calibration positions. Weighting is permitted so as to obtain a linkage parameter set that is specialized for measuring certain anatomical position parameters. Output of the algorithm includes estimates of the measuring system accuracy. For a particular knee-motion-measuring ISL and calibration device, several interdependent design parameter relationships have been identified. These interdependent relationships are due to the configuration of the ISL and calibration device, the number of calibration positions, and the limited resolution of the devices that monitor the position of the linkage joints. It is shown that if interdependence is not eliminated, then the resulting ISL parameter set will not be accurate in measuring motion outside of the calibration positions, even though these positions are within the ISL workspace.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):111-118. doi:10.1115/1.2895434.

In this first part of a two-part paper, interelement stress compatible finite elements are developed and used to perform the stress analysis of a push-out test with a fixed interface. In the formulation, the required continuity of some of the stresses along either a specific interface or all interelement interfaces is enforced by a penalty procedure. The model is axisymmetric and consists of two cylinders attached to each other through the interface. Various relative material properties and boundary conditions are simulated in order to examine their effects on the interface stresses. Both loadings of axial compression force and axial torque are considered. The predicted results exhibit identical interelement stresses and displacements even when highly dissimilar materials are used. They also exhibit a complex state of interface stresses which depend on the geometry, material arrangement, boundary conditions, and loading. The variation of the shear stress is often highly nonuniform and the radial normal stresses are likely to be large. The present results, therefore, disagree with the common assumptions made in the pull-out tests in the orthopaedic applications. Finally, stress analysis of a number of possible testing configurations could lead to the design of an optimal pull-out test which maximizes the usefulness of the measured results in terms of the interface bond strength and factors affecting it.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):119-128. doi:10.1115/1.2895435.

For a cantilever beam-column with one end built-in and the free end subjected to an oblique-eccentric arbitrary concentrated force, general formulas to produce failure were derived. The original generalized uniform solution to the oblique-eccentric buckling problem was obtained. The Secant formula and Euler’s formula were proved to be specific cases in this general solution. The load ratio, F/aE, was derived as functions of the force acting direction, α, the slenderness ratio, L/r, as well as the eccentricity ratio, ec/r2 . Material and buckling failures aspects were combined in a uniform structural failure analysis. Safe regions for the load ratio, F/aE, were visualized in the three-dimensional (F/aE)-α-(L/r) space with the eccentricity ratios, ec/r2 , as a parameter. The column failure factor, kL, was shown to be a key index controlling both aspects of failure as well as the orientation of the second stiff est region. The angle αE = tan−1 (2L/πe) for kL = π/2 is the singular point for both strength and buckling failure, and αII = tan−1 (2L/3e) for kL = 0 is the upper bound of the second stiffest region. The feasible domain of the second stiffest region is bounded by αE and αII both of which are only functions of geometrical properties. The implications of these analyses for the experimental validation of cervical spine trauma are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):129-136. doi:10.1115/1.2895436.

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of this model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):137-141. doi:10.1115/1.2895437.

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):142-146. doi:10.1115/1.2895438.

A micromechanical model of fibrous soft tissue has been developed which predicts upper and lower bounds on mechanical properties based on the structure and properties of tissue components by Ault and Hoffman [3, 4]. In this paper, two types of biological tissue are modeled and the results compared to experimental test data. The highly organized structure of rat tail tendon is modeled using the upper bound aggregation rule which predicts uniform strain behavior in the composite material. This model fits the experimental data and results in a correlation coefficient of 0.98. Applied to cat knee joint capsule, the lower bound aggregation rule of the model correlates with the data and predicts uniform stress within this more loosely organized tissue structure. These studies show that the nature of the interactions between the components in tissue differs depending upon its structure and that the biomechanical model is capable of analyzing such differences in structure.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1992;114(1):147-149. doi:10.1115/1.2895439.

The blood flow in arteries affects both the biology of the vessels and the development of atherosclerosis. The flow is three dimensional, unsteady, and difficult to measure or to model computationally. We have used phase-shift-based magnetic resonance angiography to image and measure the flow in the common carotid arteries of a healthy human subject. There was curvature of the vessels and thin-slice dynamic flow imaging showed evidence of the presence of secondary motions. Flexing the cervical spine straightened the vessels and reduced the asymmetry of the flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1992;114(1):149-153. doi:10.1115/1.2895440.

The transplantation of stored shell osteochondral allografts is a potentially useful alternative to total joint replacements for the treatment of joint ailments. The maintenance of normal cartilage properties of the osteochondral allografts during storage is important for the allograft to function properly and survive in the host joint. Since articular cartilage is normally under large physiological stresses, this study was conducted to investigate the biomechanical behavior under large strain conditions of cartilage tissue stored for various time periods (i.e., 3, 7, 28, and 60 days) in tissue culture media. A biphasic large strain theory developed for soft hydrated connective tissues was used to describe and determine the biomechanical properties of the stored cartilage. It was found that articular cartilage stored for up to 60 days maintained the ability to sustain large compressive strains of up to 40 percent or more, like normal articular cartilage. Moreover, the equilibrium stress-strain behavior and compressive modulus of the stored articular cartilage were unchanged after up to 60 days of storage.

Commentary by Dr. Valentin Fuster

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