G. Drzewiecki

Theory of the oscillometric maximum and the systolic and diastolic detection ratios

It is proposed that the maximum in cuff pressure oscillations during oscillometry is due to the buckling of the brachial artery under a cuff. This theory is investigated by means of a mathematical model of oscillometry that includes the mechanics of the occlusive arm cuff, the arterial pressure pulse waveform, and the mechanics of the brachial artery. A numerical solution is provided for the oscillations in cuff pressure for one cycle of cuff inflation and deflation. The buckling pressure is determined from actual arterial data and the von Mises buckling criteria. The buckling of an artery under a cuff occurs near — 2 to 0 mm Hg transmural pressure. This effect corresponds with a maximum arterial compliance and maximum cuff pressure oscillations when cuff pressure is nearly equal to mean arterial pressure (MAP), in support of the suggested theory. The model was also found to demonstrate the basic characteristics of experimental oscillometry, such as an increasing and decreasing amplitude in oscillations as cuff pressure decreases, the oscillations that occur when cuff pressure is above systolic pressure, maximum oscillation amplitudes in the range of 1 to 4 mm Hg, and an oscillatory maximum at cuff pressure equal to MAP. These findings support the case that the model is representative of oscillometry. Finally, the model predicted values for the systolic and diastolic detection ratios of 0.593 and 0.717, respectively, similar to those found empirically. These ratios alter with blood pressure, but the tightness of the cuff wrap did not change their value.

A nonlinear model of the arterial system incorporating a pressure-dependent compliance

An examination is made of the consequences of incorporating a pressure dependent compliance in a modified arterial system model. This nonlinear model is evaluated under control and acute pressure-loading conditions. Results show that the nonlinear compliance model in general can more accurately predict the measured pressure waveforms during control and during acute pressure loading. The difference between the predicted waveforms is more pronounced when blood pressure is high and when the pulse pressure is large.<<ETX>>

Vessel growth and collapsible pressure-area relationship

The role that the pattern of vessel wall growth plays in determining pressure-lumen area (P-A) and pressure-compliance curves was examined. A P-A vessel model was developed that encompasses the complete range of pressure, including negative values, and accounts for size given the fixed length, nonlinear elastic wall properties, constant wall area, and collapse. Data were obtained from excised canine carotid and femoral arteries, jugular veins, and elastic tubing. The mean error of estimate was 8 mmHg for all vessels studied and 2 mmHg for blood vessels. The P-A model was employed to examine two patterns of arterial wall thickening, outward growth and remodeling (constant wall area), under the assumption of constant wall properties. The model predicted that only outward wall growth resets compliance such that it increases at a given arterial pressure, explaining previously contradictory data. In addition, it was found that outward wall growth increases the lumen area between normal and high pressures. Remodeling resulted in lumen narrowing and a decrease in compliance for positive pressures.

The Korotkoff sound

As the auscultatory method of blood pressure measurement relies fundamentally on the generation of the Korotkoff sound, identification of the responsible mechanisms has been of interest ever since the introduction of the method, around the turn of the century. In this article, a theory is proposed that identifies the cause of sound generation with the nonlinear properties of the pressure-flow relationship in, and of the volume compliance of the collapsible segment of brachial artery under the cuff. The rising portion of a normal incoming brachial pressure pulse is distorted due to these characteristics, and energy contained in the normal pulse is shifted to the audible range. The pressure transient produced is transmitted to the skin surface and stethoscope through deflection of the arterial wall. A mathematical model is formulated to represent the structures involved and to computer the Korotkoff sound. The model is able to predict quantitatively a range of features of the Korotkoff sound reported in the literature. Several earlier theories are summarized and evaluated.

Noninvasive Measurement of the Human Brachial Artery Pressure–Area Relation in Collapse and Hypertension

AbstractA noninvasive method to obtain pressure–lumen area (P-A) measurements of the human brachial artery is introduced. The data obtained from this method are analyzed using a mathematical model of the relationship between vessel pressure and lumen area including vessel collapse and hypertension. An occlusive arm cuff is applied to the brachial artery of ten normal subjects. The cuff compliance is determined continuously by means of a known external volume calibration pump. This permits the computation of the P-A curve of the brachial artery under the cuff. A model is applied to analyze the P-A relation of each subject. The results show that the lumen area varies considerably between subjects. The in vivo resting P-A curve of the brachial artery possesses features similar to that of in vitro measurements. A primary difference is that the buckling pressure is higher in vivo, presumably due to axial tension, as opposed to in vitro where it is near zero or negative. It is found that hypertension causes a shift in the P-A curve towards larger lumen areas. Also, the compliance–pressure curve is shown to shift towards higher transmural pressures. Increased lumen area provides an adaptive mechanism by which compliance can be maintained constant in the face of elevated blood pressure, in spite of diminished distensibility.

Mechanics of the occlusive arm cuff and its application as a volume sensor

The occlusive arm cuff is examined using a mathematical mechanics model and experimental measurements. Cuff stretch was modeled by a nonlinear pressure-volume function. Air compression was represented by Boyles law. An apparatus was developed to measure pressure due to the air volume pumped into the cuff for fixed arm volume. Data were obtained for two different cuff designs, and reveal a nonlinear cuff pressure-volume relationship that could be represented accurately by the mathematical model. Calibration constants are provided for the two types of occlusive cuff. The cuff pressure was found to consist of a balance between that produced by stretch of the elastic cuff bladder and that of the compression of the air contained within the bladder. The use of the gas law alone was found to be inadequate to represent the cuff mechanics. It is found that when applying the cuff to measure change in arm volume, such as during plethysmography or oscillometry, it cannot be assumed that the cuff sensitivity is constant.<<ETX>>

Analysis and Assessment of Cardiovascular Function

1. Cardiovascular Function.- 1. Cardiovascular Concepts in Antiquity.- 2. A New Approach to the Analysis of Cardiovascular Function: Allometry.- 2. Cardiac Muscle.- 3. Muscle Contraction Mechanics from Ultrastructural Dynamics.- 4. Crossbridge Cycling and Cooperative Recruitment Can Account for Oscillatory Dynamics of Constantly Activated Heart.- 5. Modeling Reversible Mechanical Dysfunction in the Stunned Myocardium.- 6. Computer-Based Myocardial Tissue Characterization Using Quantitative Description of Texture.- 3. Coronary Circulation.- 7. Interpretation of Coronary Vascular Perfusion.- 8. New-Age Rapid Diagnosis of Acute Myocardial Injury.- 4. Ventricular Dynamics.- 9. Modeling of the Effects of Aortic Valve Stenosis and Arterial System Afterload on Left Ventricular Hypertrophy.- 10. Ventricular Shape: Spherical or Cylindrical?.- 11. Pathophysiology of Diastole and Left Ventricular Filling in Humans: Noninvasive Evaluation.- 12. Echocardiographic Evaluation of Thrombolytic Intervention After Acute Myocardial Infarction.- 5. Arterial/Ventricular Circulation.- 13. Modeling of Noninvasive Arterial Blood Pressure Methods.- 14. Measurement and Applications of Arterial and Ventricular Pressure-Dimension Relationships in Animals and Humans.- 6. Microcirculation.- 15. Quantitative Analysis of the Lee Method for Determination of the Capillary Filtration Coefficient.- 16. Assessment of Human Microvascular Function.- 7. Venous System.- 17. Dynamic Response of the Collapsible Blood Vessel.- 8. Electrophysiology.- 18. Microvolt-Level T Wave Alternans as a Marker of Vulnerability to Cardiac Arrhythmias: Principles and Detection Methods.- 19. Quantification of Heart Rate Variability Using Methods Derived from Nonlinear Dynamics.- 20. Transesophageal Electrophysiology.- 21. Occurrence and Diagnostic Importance of Postural ST-Segment Depression in Ambulatory Holter Monitoring in Male Patients After Myocardial Infarction.

Modeling of mechanical dysfunction in regional stunned myocardium of the left ventricle

Reversible mechanical dysfunction of the myocardium after a single or multiple episode(s) of coronary artery occlusion has been observed in previous studies and is termed myocardial stunning. The hypothesis that stunning could be represented by a decrease in maximum available muscle force in the stunned region was examined by means of a mathematical model that incorporates series viscoelastic elements. A canine experimental model was also employed to demonstrate depressed contractility and a consistent delay of shortening in the stunned region. The mechanical model of the left ventricle was designed to include a normal and stunned region, for which the stunned region was allowed to have variable size. Each region consisted of a volume and time dependent force generator in parallel with a passive elastic force element. The passive elastic element was placed in series with a constant viscosity component and a series elastic component. The model was solved by means of a computer. Passive and active properties of each region could be altered independently. The typical regional measures of muscle performance such as percent shortening, percent bulge, percent thickening, delay of shortening, percent increase in end-diastolic length and other hemodynamic measures were computed. These results were similar to those observed in animal models of stunning. In addition, a nearly linear relationship with end-diastolic length and delay of shortening was predicted by the model. It was concluded that a decrease in the peak isovolumic elastance and augmentation of viscosity effect of creep during stunning can explain mechanical abnormalities of stunned myocardium.

Tonometric Arterial Pulse Sensor With Noise Cancellation

Arterial tonometry provides for the continuous and noninvasive recording of the arterial pressure waveform. However, tonometers are affected by motion artifact that degrades the signal. An arterial tonometer was constructed using two piezoelectric transducers centered within a solid base. In two subjects, one transducer was positioned over the radial pulse (p) and the other was positioned on the wrist not overlying the pulse (n). The presence of induced motion artifact and any noise was removed after signal digitization by noise cancellation. Besides fixed weighting, two adaptive algorithms were used for cancellation-LMS and differential steepest descent (DSD). Criteria were developed for comparison of the adaptive techniques. The best fixed weighting for noise cancellation was w = 0.6. For fixed-weighting, LMS, and DSD, the mean peak-to-peak errors were 1.22 plusmn 0.54, 1.18 plusmn 0.30, and 1.16 plusmn 0.23 V, respectively, and the mean point-to-point errors were 15.86 plusmn 3.15, 11.40 plusmn 1.96, and 10.13 plusmn 1.25 V, respectively. Noise cancellation using a common-mode reference input substantially reduces motion artifact and other noise from the acquired tonometric arterial pulse signal. Adaptive weighting provides better cancellation than fixed weighting, likely because the mechanical gain at the transducer-skin interface is time-varying.

Physiological basis for mechanical time-variance in the heart: Special consideration of non-linear function

A relationship between ventricular pressure and volume is developed starting from basic cardiac muscle mechanics. The known and measurable properties of myocardium, such as the Hill law, the periodic excitation-contraction mechanism, and non-linear elasticity of the surrounding elastin and collagen structure, are formulated into a myofibril unit. A cylindrical geometry is chosen to represent the structure of the ventricle, using the myofibril unit as the basic building block. Pressure-volume isochrones computed from this model illustrate non-linear function in the heart which arises from both geometric effects and muscle effects. The above theory and model is linearized to provide a special study case. The behavior that resulted is that of a time-varying elastance, E(t), and, hence, can help in the interpretation of its meaning. It is found that the minimum in E(t) is the consequence of the stiffness of the myocardial fibrous network, adjusted by a geometric factor. In addition, the magnitude of E(t) is governed by myocardial contractility, a geometric factor, and the excitation-contraction mechanism, where time-dependency is imparted by periodic excitation. Since the elastic fibers are the only true elastic elements, the quantity of elastance is determined by controlled volume feedback. A circuit model is provided to illustrate this concept. The non-linear active and passive heart function curves are specified independently. These curves are required to intersect below the resting volume and result in a negative pressure at the intersection. This is found to explain the phenomenon of ventricular suction. In addition, they lead to a time-varying dead volume by virtue of time-dependent isochronal slope. Non-linear function is introduced to the model and is found to explain the variation in curvature of the ventricular isochrones.