Mechanical characteristics of human skin subjected to static versus cyclic normal pressures.

Several hypotheses exist for the etiology of decubitus ulcers, with external pressures exceeding internal capillary pressures over bony prominences claimed to be the major factor. This investigation evaluated the mechanical changes that occurred in human skin as a result of its exposure to static versus cyclic normal pressures of the magnitudes earlier recorded for the heels of human subjects on various support surfaces. The skin was characterized through uniaxial tensile testing. Static pressure alone altered the tissue's mechanical properties more than dynamic pressure cycles. Tissue subjected to pressure prior to uniaxial tensile testing always was less stiff than control tissue. Damage to the initially randomly oriented tissue collagen fiber bundles in the fibrous matrix, which may occur as a result of sustained compression, may be the cause of a decrease in stiffness of tissue subjected to prior pressure loading. This is the first report of compressive-pre-load-induced strain softening (Mullins effect) of a biological material.

The coronary circulation.

Dramatic advances have been made in the last two decades in the diagnosis and treatment of coronary artery disease. The development of open heart surgical techniques for bypassing occluded arteries made quantitative diagnostic techniques more important. Computer enhanced angiographic methods, together with measurements using tomography, ultrasound and magnetic resonance imaging have greatly improved the precision of the diagnosis. A more complete understanding of coronary mechanics and control has enabled physicians to better interpret the significance of geometric information and to supplement this information with functional assessment of stenosed arteries. Finally, traditional bypass surgery is now supplemented with closed-chest techniques such as balloon angioplasty. Biomedical engineers have been involved in all of these developments. This paper will review these developments and attempt to identify remaining questions.

Models for coronary pressure-flow relationships.

We have developed a mathematical model which describes pressure-inflow relationships in the coronary circulation. Model parameters have been identified during metabolic and pharmacologic vasodilation. These two stimuli appear to affect resistance and back pressure in different ways. A possible explanation involving myogenic and metabolic effects is suggested.

Coronary input impedance is constant during systole and diastole.

Although it is well known that coronary inflow decreases substantially during systole, the mechanism responsible for this decrease remains controversial. Knowledge of how coronary input impedance is affected by contraction can differentiate between some of the proposed mechanisms. In open-chest dogs, we have measured coronary inflow in the beating heart both during constant-pressure perfusion and during 10-Hz sinusoidal pressure oscillations around the same constant pressure. By exploiting the principle of superposition, we have shown that coronary input impedance remains unchanged between systole and diastole. Using this result, we have shown that a simple lumped-parameter model with constant resistance and compliance can describe coronary inflow at heart rates of 60, 90, 120, and 150 beats/min both with vasomotor tone intact and during maximal coronary vasodilation. Coronary resistance and compliance determined using the model are comparable to those obtained in our laboratory and by others during normal diastoles and in the arrested heart. The results suggest that, despite large increases in myocardial tissue stresses during systole, coronary resistance and compliance as determined using inflow measurements are constant during systole and diastole.

Diastolic coronary resistance and capacitance are independent of the duration of diastole.

Systolic myocardial contraction may produce changes in coronary resistance and capacitance that persist throughout a normal diastole. In addition, coronary resistance and capacitance as determined in the arrested heart may not accurately describe normal diastolic behavior. To evaluate these possibilities, an identification method capable of characterizing the input impedance of the coronary circulation in as little as 150 ms was developed. Using this method, coronary dynamics were measured during early and late diastoles in the beating heart with tone intact as well as during adenosine-induced maximal vasodilation. Coronary dynamics were also measured in the arrested heart during maximal vasodilation. With vasomotor tone intact, the parameters of a lumped model of the coronary circulation showed no variation from early to late diastole. During maximal vasodilation, model parameters also showed no variation from early to late diastole. Parameters in the arrested heart were not statistically different from those of the beating heart during maximal vasodilation. However, model parameters determined during maximal vasodilation were significantly different from those determined with tone intact. These results suggest that although coronary resistance and capacitance are dependent on vasomotor tone, they remain constant throughout diastole and remain similar in the arrested heart.

Tone-dependent waterfall behavior during venous pressure elevation in isolated canine hearts.

We examined the "vascular waterfall" hypothesis, which proposes that coronary flow is unaffected by elevations in outflow pressure until the latter reaches a critical threshold level, in 29 isolated canine hearts. In fibrillating hearts vasodilated with adenosine or carbocromen, coronary flow and the coronary pressure-flow relation were not affected by changes in great cardiac vein pressure (PGCV) below a threshold value of 11 +/- 0.9 (mean +/- SEM) mm Hg. Further elevations of PGCV reduced flow and shifted the pressure-flow relation to the right, increasing its pressure-axis intercept (Pf=0). When vasomotor tone was augmented with vasopressin, threshold PGCV increased to 25 +/- 2.7 mm Hg (p less than 0.001). Once again, the pressure-flow relation was unaffected by changes in PGCV below the threshold value and shifted to the right when this value was exceeded. The amount by which spontaneous values of Pf=0 exceeded threshold values of PGCV was greater when vasomotor tone was augmented than during vasodilation. Pf=0 continued to exceed PGCV when the latter was raised above the threshold level. Both Pf=0 and threshold values of PGCV were less during a long diastole than during ventricular fibrillation. We reached the following conclusions. 1) During changes in PGCV below a threshold value, the coronary circulation exhibits traditional waterfall behavior. 2) The threshold pressure for altering waterfall behavior is affected by vascular tone and mechanical activity. 3) Pf=0 remains above PGCV when the latter is increased above the threshold value needed to alter flow.

Research directions in biomedical engineering.

The role of biomedical engineering and developments that affect it are outlined. Research areas that the authors believe will be of major importance at the beginning of the next century are discussed. They are: systems science and integrated biology; biomedical engineering in the cardiovascular system; biomaterials (metals, ceramics, and polymers); artificial organs; instrumentation and sensors; medical imaging (radiography, ultrasonic imaging, magnetic resonance imaging, and other techniques); biomedical computing; biomechanics; and rehabilitation. Some new areas for biomedical engineering research (molecular biology, minimally invasive surgery, home health care, and geriatric care) are examined.

Characterization of capacitance-free pressure-flow relations during single diastoles in dogs using an RC model with pressure-dependent parameters.

Although previous studies have proposed a variety of models to characterize diastolic pressure-flow relations, the models' ability to predict capacitance-free pressure-flow relations from dynamic information in individual studies has not been determined. This study tested the ability of a lumped RC model with pressure-dependent parameters to predict diastolic capacitance-free flow during maximum vasodilation in anesthetized dogs. Model parameters were characterized by perturbing the circumflex coronary artery with a ramp pressure waveform that caused coronary artery pressure to decline at rates varying from 30-150 mm Hg/sec. Capacitance-free relations constructed from declining and rising ramp pressure-flow data corresponded with capacitance-free pressure-flow points constructed during constant-pressure coronary artery perfusion (which are model-independent). The model parameters derived from analysis of the ramp data indicate that conductance of the coronary bed varies directly with coronary pressure and is independent of the rate of coronary pressure decay. Values of coronary capacitance vary inversely with coronary artery pressure and with the magnitude of dPLC/dt. Thus, a simple, lumped diastolic model with pressure-dependent parameters can predict capacitance-free pressure-flow behavior from dynamic pressure-flow data and characterize model parameters over a wide range of coronary pressure.

Pressure and tone dependence of coronary diastolic input impedance and capacitance.

To quantify reactive elements of the coronary circulation, we have characterized in vivo diastolic coronary input impedance by introducing sinusoidal pressure oscillations of constant amplitude and varying frequency at constant mean pressure levels during prolonged diastoles in heart-blocked dogs anesthetized with pentobarbital. The behavior of coronary input impedance is similar to that observed in other peripheral vascular beds and is a function of both mean distending pressure and vasomotor tone. The behavior of impedance modulus and phase at each pressure level could be described by a lumped resistive-capacitive (RC) parallel model over a frequency range of 1-5 Hz. At higher frequencies the phase angle response could be characterized by adding a Voigt viscoelastic element to the original RC model. Calculated coronary capacitances for both models were similar in magnitude and varied inversely with mean coronary distending pressure. Values for the RC and RC viscoelastic model in the maximally dilated coronary bed were 14.1 and 21.6 X 10(-3) ml X mmHg X 100 g-1 at 30 mmHg and 2.65 and 2.70 X 10(-3) ml X mmHg-1 X 100 g-1 at 110 mmHg. With vasomotor tone intact, calculated coronary capacitance at each pressure level was reduced by a factor of two. These results indicate that an RC parallel model with pressure- and vasomotor tone-dependent capacitance adequately describes diastolic coronary input impedance at frequencies encountered during ordinary diastoles. The addition of a viscoelastic element provides adequate fits up to frequencies of 10 Hz.

Coronary pressure-flow relationships. Controversial issues and probable implications.

On the basis of the material discussed, our current assessments of the controversial points mentioned at the beginning of this article may be summarized as follows: Pf = 0, the minimum back pressure to coronary flow associated with a measurable conductance, is indeed greater than coronary outflow pressure (and usually left ventricular diastolic pressure, as well). Pf = 0 needs to be taken into account in attempts to determine coronary driving pressure. In maximally vasodilated beds, Pf = 0 derived from diastolic pressure-flow relationships exceeds coronary outflow pressure by at least a few mm Hg. Pf = 0 varies with coronary outflow and/or diastolic ventricular cavity pressure. When left ventricular preload is elevated, Pf = 0 exceeds outflow pressure by increasing amounts. Pf = 0 appears to be systematically higher and pressure-dependent in beds in which vasomotor tone is operative. An improved understanding of the nature of, and basis for, time-dependent changes in resistance and/or Pf = 0 during long diastoles in nonvasodilated beds is needed. The contour of pressure-flow relationships which are free of reactive effects is curvilinear rather than linear. The degree of curvilinearity is substantial and can change with interventions. Curvilinearity is accentuated at lower pressures and may reflect changes in the number of perfused vascular channels as well as the caliber of individual channels. Capacitive effects need to be dealt with quantitatively in studies of pressure-flow relationships. Values of the capacitance which is involved in these effects vary with both pressure and tone. Capacitive flow also depends upon the instantaneous rate of change of pressure, which has not usually been defined in published studies. Although intramyocardial capacitance is large and plays an important role in systolic-diastolic flow interactions, a controlling role in diastolic coronary arterial pressure-flow relationships has not been established experimentally. In vasodilated beds, in-flow remains remarkably constant for several seconds after the brief transient associated with a step-change in the level of constant pressure perfusion during a long diastole. Calculations of coronary vascular resistance (by whatever method) remain of limited value, particularly when changes in response to an intervention are modest. Because of the curvilinear diastolic pressure-flow relationship, resistance is pressure-dependent and, at any given pressure, is probably best defined by establishing the slope of a diastolic pressure-flow curve which is free of reactive effects.(ABSTRACT TRUNCATED AT 400 WORDS)

Preload-induced alterations in capacitance-free diastolic pressure-flow relationship.

We have studied the influence of left ventricular diastolic pressure (LVDP) on diastolic coronary pressure-flow relationships independently of effects of capacitive flow in an open-chest heart-blocked canine preparation in which the left circumflex (LC) bed was vasodilated with adenosine and perfused with a programmable servo valve pressure source. At the onset of long diastoles produced by cessation of ventricular pacing, LVDP was adjusted to, and maintained at, a preselected level using a blood-filled reservoir. Right atrial pressure was kept constant at approximately 8 mmHg. LC pressure (PLC) was then made to decline and rise sequentially at a constant rate (2-40 mmHg/s), with LC inflow reaching zero at the nadir of the declining pressure ramp. The capacitance-free diastolic pressure-flow relationship was considered to lie midway between the instantaneous relationships derived from each down and up ramp pair. All capacitance-free relationships were curvilinear, and the degree of curvilinearity was accentuated with increasing preload. Pressure-axis intercepts (Pf = 0) increased from 14 +/- 1.1 (SE) to 23 +/- 1.4 mmHg as preload was raised from 6-10 to 31-35 mmHg. Coronary conductance, taken as the slope of the pressure-flow relationship at any given PLC, fell progressively as preload rose, with the fall being more marked at higher levels of preload and lower values of PLC. Diastolic coronary flow also decreased as a function of preload, reflecting the increases in Pf = 0 and decreases in conductance.(ABSTRACT TRUNCATED AT 250 WORDS)

A programmable pressure control system for coronary flow studies.

An electrohydraulic servo valve capable of reproducing phasic physiological pressure and flow waveforms has been designed and constructed. The device has been utilized successfully in canine coronary flow studies. By measuring coronary pressure directly it is possible to reproduce waveform frequency components as high as 50 Hz in the cannulated left circumflex coronary artery when operated in a negative feedback configuration. It may easily be adapted to operate in a pressure- or flow-controlled mode in any vascular bed. The closed-loop frequency response of the servo valve itself is flat to 100 Hz with a natural frequency of 170 Hz. When utilized in the cannulated bed the frequency response is dependent on perfusion circuit and catheter dynamics.

Zero-flow pressures and pressure-flow relationships during single long diastoles in the canine coronary bed before and during maximum vasodilation. Limited influence of capacitive effects.

The proposal that diastolic coronary flow is regulated by an intramyocardial "back-pressure" that substantially exceeds coronary venous and ventricular diastolic pressures has been examined in an open-chest canine preparation in which instantaneous left circumflex pressure and flow could be followed to cessation of inflow during prolonged diastoles. Despite correlation coefficients consistently >0.90, pressure-flow data during individual diastoles were concave to the flow axis before and during pharmacologically induced maximum coronary vasodilation. Data were better fitted (P < 0.01) by second-order equations than by linear equations in >90% of cases. Second-order pressure-axis intercepts (P(f=0))(1) averaged 29+/-7 (SD) mm Hg before vasodilation and 15+/-2 mm Hg during vasodilation; left and right atrial pressures were always substantially lower (8+/-3 and 5+/-2 mm Hg before vasodilation and 8+/-2 and 4+/-1 mm Hg during dilation). Values of P(f=0) before vasodilation varied directly with levels of coronary inflow pressure. A modification of the experimental preparation in which diastolic circumflex pressure could be kept constant was used to evaluate the suggestion that P(f=0) measured during long diastoles are misleadingly high because of capacitive effects within the coronary circulation as inflow pressure decreases. Decreases in P(f=0) attributable to capacitive effects averaged only 5.9+/-3.0 mm Hg before vasodilation and were smaller during dilation. We conclude that P(f=0) is a quantitatively important determinant of coronary driving pressure and flow, resulting from both factors related to, and independent of, vasomotor tone. Adjustments of flow during changing physiological situations may involve significant changes in P(f=0) as well as in coronary resistance.

Fluid dynamics of coronary artery stenosis.

A large-scale model of the coronary circulation, instrumented to permit detailed pressure and velocity measurements, has been used to study flow through isolated stenotic elements in large coronary arteries. Pulsatile aortic and instantaneous peripheral resistance were stimulated with servovalves. A variety of axisymmetric and asymmetric stenoses were studied and flow separation was found to occur for all but very mild stenoses. Pressure recovery downstream of the stenosis throat was limited and, in some cases, no recovery was observed. Pressure drop was primarily dependent upon the minimum area of the stenosis and relatively independent of stenosis geometry. Flow was quasi-steady at normal heart rates, and simple steady flow theory proved adequate to describe the pressure drop through the stenosis. The theory yielded results that agreed well with published data for dogs and appears promising for predicting effects of hemodynamic variables on a given stenotic lesion. Thus, principal findings of the study are that a relatively severe stenosis behaves essentially like an orifice and that a simple quasi-steady theory appears adequate to predict effects of a stenosis on coronary flow.

Estimation of systemic arterial impedance in man from cardiac catheterization data.

A five-parameter transfer function has been used to characterize the input impedance of the human systemic circulation. Aortic pressure and flow measurements obtained at cardiac catheterization are employed to evaluate the model parameters in individual patients. The appropriate parameters are chosen using a standard optimization technique to minimize the difference between pressures computed from the model and the measured values. Impedance parameters calculated for 19 patients showed considerable variation with no apparent correlation with the type of heart disease. The model is useful in describing the loading of the left ventricle produced by the systemic circulation. It may also have application to the study of vascular disease.

An efficient optimization technique for recovering ventilation-perfusion distributions from inert gas data. Effects of random experimental error.

A variable metric optimization method of numerical analysis has been used to recover known distributions of intrapulmonary ventilation-perfusion ratios from inert gas data. Hypothetical lungs were simulated and corresponding inert gas retentions calculated. By using error-free retentions for seven gases and a 50-compartment model, it was possible to recover distributions containing up to three modes accurately and with greater efficiency than with other numerical methods. When random error of a magnitude consistent with present analytical techniques was introduced into retention data, the recovered distributions differed qualitatively from the original ones. This resulted from the ill-conditioned nature of the mathematical problem, which makes a recovered distribution extremely sensitive to small errors in retention. Thus, present levels of measurement error represent an important limitation in current techniques for deriving distributions from inert gas measurements.

Influence of crossbridge compliance on the force-velocity relation of muscle.

It is shown that muscle models which describe force generation as being dependent on the extension of the individual crossbridges produce a force-velocity relation of the form: Vf= Visotonic--1/KHS dP/dt. The derivation of this equation is independent of the details of activation and the kinetics of the crossbridges. The velocity, Vf, represents the relative filament velocity, and Visontonic is the relative filament velocity which would maintain a constant muscle force. P. The quantity KHS is the net stiffness of all the force-generating crossbridges in one-half a sarcomere. Experimental methods for determining KHS are suggested . To study the force-velocity relation, computer simulations based on A. F.Huxley's 1957 kinetic model were conducted for isometric and isotonic twitch contractions. The relative filament velocity is found to depend on the contraction mode, exhibiting a sudden increase in an isometric-to-isontonic changeover and a decrease in the reverse process.