Estimation of distributions of ventilation/perfusion ratios

For many years physiologists have sought to estimate the distribution of ventilation/perfusion ratios ( ) in the lung. While many different procedures have been described, most share two features that limit their usefulness. First, while the lung consists of some 10⁵ separate gas exchange units, mismatch is usually analyzed in terms of just two or three hypothetical units sufficient to explain the measured data. Second, no attempts are made to explore alternate distributions which could account for the measured data, nor the degree to which these alternate cases differ from each other. The second problem arises from (a) the fact that the lung is numerically complex, while only few data are obtained, and (b) experimental errors. We summarize here our approach to these problems. Methods involving both linear and quadratic programming algorithms are applied to obtain the most reliable and complete information from a set of data. While we focus on the intravenous infusion of several foreign gases as the tool for obtaining data pertinent to maldistribution, the proposed scheme is equally applicable to other linear systems in the lung, such as the multibreath N₂ washout and the forced expiratory spirogram.     

Noninvasive estimation of cardiac output with nonprescribed breathing

A noninvasive method to estimate cardiac output without special patient cooperation was developed by modifying a previous acetylene-helium (C₂H₂−He) rebreathing technique (ART). Estimation of using ART is based on a single-compartment model that is valid only under prescribed breathing; e.g., fast, deep breathing, and emptying of the rebreathing bag on each breath. To make the ART less dependent on subject cooperation, a more sophisticated mathematical model and estimation method are needed. For this purpose, we modeled the C₂H₂ and He concentration dynamics at the mouth over successive breaths using a multi-compartment model. This model takes into account the effects of breathing pattern, compartmental volumes, and gas solubility. From computer simulations and sensitivity analysis, we found that could be estimated from the available data with adequate precision. Our model and estimation method were tested on a group of six normal adult subjects, at rest and during submaximal exercise (75 watts). Estimates of from our new method (6.5±0.4 L/min at rest, 12.5±0.4 L/min at 75 watts) were in agreement with those obtained using a previous ART (7.0±0.3 L/min at rest, 12.6±0.5 L/min at 75 watts). We conclude that this approach promises to provide reliable estimates of in patients (e.g., children and elderly), at rest and during exercise, without the need of prescribed breathing patterns or changes in rebreathing bag volume. Supported in part by a Grant from the Board of Trustees of Rainbow Babies and Childrens Hospital.     

Arterial pressure-flow relationships in the anesthetized dog

Arterial pressure-flow (P _a - ) and closing arterial pressure-flow (P _c - ) relationships of the systemic vascular bed were determined in anesthetized dogs with the aid of a right heart bypass preparation.P _c was estimated from plateau values of arterial pressure obtained during stop-flow procedures and plotted against the flow which existed immediately prior to the procedure. Two types of arterial pressure-flow relationships were observed. With type I, theP _a - curve was steep and extrapolated to a positive arterial pressure at zero flow which was equal to the meanP _c occurring over the experimental flow range. With type II, the slope of theP _a - curve was relatively shallow and extrapolated to right atrial pressure (0 mm Hg). TheP _c - relationships were identical for all dogs. These data suggest the existence of a pressure regulatory function in the downstream arterial vasculature in type-I animals which established an effective back pressure to arterial perfusion and decouples the arterial pressure-flow characteristics from the remainder of the systemic circulation. This work was supported by National Institutes of Health Grant HL 20371.     

Computer simulation of equations for indicator-concentration curves in parabolic flow model

Two indicator-concentration parabolic mathematical flow models were simulated on a digital computer for the purpose of comparing the relationship between computed and correct values for flow , mean transit time and volume (Q), in a model tube system. Both parabolic flow model systems were based on pulse input and flow tagging of the indicator substance at the injection site. One flow model (Gonzalez-Fernandez) assumes mean flow concentration at the detection site; the other flow model (Rossiet al.) assumes mean cross-sectional concentration at the detection site. It is concluded from these model and simulation studies that (a) mean flow concentration at the detection site is more appropriate for the determination of ,- andQ; (b) either flow model will give correct values for- at infinite time; however, substantially less time is required for reasonable values of flow with the Gonzalez-Fernandez model; (c) assuming mean flow concentration, 99% accuracy for- requires 10 appearance times (t _a); 99% accuracy for- requires 100×t _a, and (d) for an indicator-concentration system in which mean cross-sectional concentration is assumed at the detection site, correct values for- andQ can never be obtained. At the moment, there appears to be no practical way of achieving flow tagging at the injection site or mean flow concentration at the detection site without the use of mixers. Presented at the 55th Annual FASEB Meeting, Biomedical Engineering Society Session, Chicago, Illinois, April 14, 1971. This research has been supported in part by grants from the National Institutes of Health (HE-00487, HE-05392, HE-00344 and FR-00147) and the North Carolina Heart Association.     

Die Verteilungsanalyse von Ventilation,Perfusion und O2-Diffusionskapazität in der Lunge durch Konzentrationswechsel dreier Inspirationsgase

Zusammenfassung Es wird die theoretische Begründung für ein Untersuchungsverfahren gegeben, das gleichzeitig die Inhomogenitäten des Ventilations-Perfusions-Verhältnisses sowie des Diffusionskapazitäts-Perfusions-Verhältnisses in der menschlichen Lunge zu bestimmen erlaubt. Dazu müssen drei inspiratorisch angebotene Gase, die sich in ihren Diffusionseigenschaften unterscheiden, z.B. CO₂, O₂ und He, plötzlich in ihren Konzentrationen verändert und die nachfolgenden alveolären Einmischvorgänge fortlaufend verfolgt werden.Die Lösungen der Differentialgleichungen für die drei Einmischprozesse zeigen, daß deren Zeitkonstanten in unterschiedlicher Weise von der alveolären Ventilation , der Lungendurchblutung und der DiffusionskapazitätD _L abhängen. Aus den Zeitkonstanten lassen sich daher die funktionellen Verteilungen von undD _L berechnen. Diese Verteilungskurven bilden dann die Grundlage für die Bestimmung der diagnostisch wichtigen Anteile der alveolär-arteriellen DruckdifferenzAD für Sauerstoff und Kohlendioxyd. Auf diese Weise findet man dieAD _{Distr. 1}, die auf Verteilungsungleichmäßigkeiten von zurückzuführen ist, ferner dieAD _{Distr. 2}, die von der Größe und Verteilung von abhängt, und schließlich die durch das Ausmaß der extrapulmonalen Kurzschlußdurchblutung bestimmteAD _sh .Mit Unterstützung durch die Landesversicherungsanstalt Rheinland-Pflaz, Speyer.     

Patient-ventilator partitioning of the work of breathing during weaning

The work of breathing and its division between the patient and the mechanical ventilator were studied during weaning of 5 post-operative surgical patients from Synchronized Intermittent Mandatory Ventilation. Work by the patient was estimated by integrating the product of flow and pressure over time during intervals when waveforms indicated patient effort; ventilator work was similarly estimated during positive pressure inspirations. The ratio of to the rate of work on the lungs increased progressively during weaning from 0.14±0.04 to 1.2±0.15 while dropped from 1.31±0.08 to 0.13±0.11. Work on the lungs decreased during weaning. This was due in part to significant improvements in lung mechanics: resistance decreased from 9.9±0.9 to 6.1±1.6 cmH₂O/1/s and compliance increased from 58±17 to 102±30 ml/cmH₂O. The patient and ventilator work ratios, and the work of breathing quantify factors which may be directly useful to the clinician and to future systems to automate weaning. This work was supported by a grant from the National Institute of General Medical Sciences, National Institutes of Health, P50-GM-15426. It was part of a thesis submitted to Rensselaer Polytechnic Institute by F.W. Chapman in partial fulfillment of the requirements for the degree of Doctor of Philosophy.     

Arterial wave propagation phenomena,ventricular work,and power dissipation

The effects of wave propagation phenomena, namely global reflection coefficient (Γ_G[ω]) and pulse wave velocity (c _ph), are studied in a model of the coupled left ventricle/arterial system. The left ventricle consists of a time-varying elastance, while the arterial system is modeled as a single, uniform, elastic tube terminating in a complex load. Manipulation of model parameters allowed for the precise control of (Γ_G[ω]) andc _phindependent of each other, peripheral resistance, and characteristic impedance. Reduction of Γ_G(ω) andc _ph were achieved through increases in load compliance and tube compliance, respectively. The equations describing the system were solved for left ventricular and aortic pressures and aortic flow. From these, stroke volume (SV), left ventricular stroke work (SW), and steady , oscillatory , and total power dissipation in the arterial system were calculated. An index of arterial system efficiency was the ratio , with lower values indicating higher efficiency. Reduction of Γ_G(ω) yielded initial increases in , while increased for the entire range of Γ_G(ω), resulting in increased . This reduced efficiency is imposed on the ventricle, resulting in increasedSW without increasedSV. On the other hand, decreasedc _ph yielded in a steady increase in and a biphasic response in , resulting in reduced for most of the range of reducedc _ph. These results suggest that differential effects on arterial system efficiency can result from reductions of Γ_G(ω) andc _ph. In terms of compliance, changes in arterial compliance can have different effects on efficiency, depending on where the compliance change takes place. Reasons for these results are suggested, and the role of distributed compliances is raised as a new problem.     

Regional transit time estimation from image residue curves

Methods for estimating regional flow from digital angiography or dynamic computed tomography images require determination of indicator mean transit time ( ) through a region-of-interest (ROI). We examine how the ROI kinematics and input dispersion influence the recovery of using a computer-simulated vessel network representing that which might occur in a real organ. The network simulates flow through a large artery branching into two small arteries, each feeding a system of smaller vessels intended to represent capillaries and small vessels below the resolution of the imaging system. The capillaries are drained by a similar system of veins. Concentration curves measured over the inlet to the network and microvascular ROI residue curves are simulated. When the area-height ratio of the microvascular ROI curve is used and all of the indicator is contained within the ROI for at least one time point, is recovered exactly. As the size of the ROI is reduced or the inlet concentration curve becomes more dispresed, the error in the recovery of grows. By first deconvolving the inlet concentration curve from the microvascular ROI curve, and then calculating the area-height ratio, is recovered accurately. If the inlet concentration curve becomes more dispersed between its measured site and the actual inlet to the ROI, or if the flow distribution within the ROI is changed, the estimation of can be degraded. To put the simulations in perspective relative to an example of image data, the methods were applied to microfocal x-ray angiography data obtained from a ⊃700 μm canine pulmonary artery and vein, the surrounding microvasculature and the inlet lobar arterial cannula.     

Cardiorespiratory response to absolute and relative work intensity in untrained men

Summary Twenty young, untrained men performed two tests on cycle ergometer in order to verify whether the kinetics of the cardiorespiratory reactions exhibit any relation to maximal oxygen uptake ( ) in the untrained state. On the 1st day, the subjects exercised at work intensities of 50 and 100 W, the increase as a step function, for periods of 10 min each. The next day, they performed exercise at a relative intensity of 50% for 10 min. Respiratory frequency, tidal volume, minute ventilation ( ), heart rate (HR), stroke volume (SV), and cardiac output ( ) were measured continuously. The SV was measured by impedance plethysmography. All the cardiorespiratory variables increased rapidly at the onset of both absolute and relative intensity of work, with a faster response for than for . The increase in absolute intensity of work from 50 to 100 W caused a significantly slower cardiorespiratory reaction than at the beginning of exercise. The SV increased by 20 ml during first 20 s of both absolute and relative intensities of work and then began to decrease after 6 and 4 min of the exercise, respectively. The decrease in SV was associated with an increase in HR and a stable value of . Acceleration at the beginning of, and deceleration during recovery from, the relative intensity of work for , HR, and were well correlated with individual levels of in the tested men. It is concluded that the kinetics of cardiorespiratory reaction to a constant, relative intensity of work is related to in untrained men, and that the kinetics probably constitute a physiological feature of an individual.     

Relationship between chamber mechanical properties and mean pressure-mean flow diagram of the left ventricle

We undertook a theoretical analysis of the source resistance of the left ventricle represented in a mean pressure-mean flow diagram, using the chamber properties established in terms of the pressure-volume relationship. This analysis showed that pairs of points should lie above the linear function proposed by Elzinga and Westerhof. A third-order polynomial function would theoretically explain better than a linear relation or a parabolic fit the curved shape of experimentally obtained relationships. The analysis resolves the discrepancy between Elzinga and Westerhof's theoretical concept of linear source resistance and the actual nonlinear relationship.     

A nonlinear model of respiratory mechanics in emphysematous lungs

Existing mechanical models of chronic obstructive lung disease have failed to explain a number of experimental findings of airway obstruction, e.g., the varying manners of frequency dependence of resistance (FDR). Departing from the parallelunit concept and attempting to account for the “check-valve” mechanism in the emphysematous lung, we proposed a single-compartment lung model with a nonlinear pressure-flow relationship: , where is a constant. The plus and minus signs in the cubic term indicate the expiratory and inspiratory check valves, respectively. The choice of an asymmetric relation reflects several properties of emphysematous lungs such as airflow limitation and higher expiratory resistance. Implementation of the above equation using sine wave, white noise, and step inputs resulted in various forms of FDR at frequencies between 0 and 40 Hz depending on the type of input used. Resistance was most sensitive to changes in input pressure amplitude. The model's results suggest that the nonlinearity can have a significant influence on the impedance construct in obstructed lung disease.     

Bymixer provides on-line calibration of measurement of CO2 volume exhaled per breath

The measurement of CO₂ volume exhaled per breath can be determined during anesthesia by the multiplication and integration of tidal flow and . During side-stream capnometry, must be advanced in time by transport delay (TD), the time to suction gas through the sampling tube. During ventilation, TD can vary due to sample line connection internal volume or flow rate changes. To determine correct TD and measure accurate during actual ventilation, TD can be iteratively adjusted (TD_ADJ) until /tidal volume equals measured in a mixed expired gas collection (J. Appl. Physiol. 72:2029–2035, 1992). However, is difficult to measure during anesthesia because CO₂ is absorbed in the circle circuit. Accordingly, we implemented a bypass flow-mixing chamber device (bymixer) that was interposed in the expiration limb of the circle circuit and accurately measured over a wide range of conditions of ventilation of a test lung-metabolic chamber (regression slope=1.01;R ²=0.99). The bymixer response (time constant) varied from 18.1±0.03 sec (12.5 l/min ventilation) to 66.7±0.9 sec (2.5 l/min). Bymixer was used to correctly determine TD_ADJ (without interrupting respiration) to enable accurate measurement of over widely changing expiratory flow patterns.     

Breath-by-breath measurement of alveolar gas exchange with a slow-response gas analyser

The O₂-paramagnetic or polarographic and CO₂-infra-red expired gas analyser have a response delay which results in an underestimation in breath-by-breath and calculations. In this study, correction for this delay has been made. After measuring the step response of the O₂-polarographic and CO₂-infra-red analyser, the damping factor and the natural angular frequency were determined as well as the time constant, assuming the response was a first-order one. and were calculated when the response of the analyser was corrected for the first- and second-order responses using the inverse Laplace transform. For the uncorrected and , values from the breath-by-breath method were 27·5 and 18·1 per cent systematically underestimated (p<0·001) compared with those of the Douglas bag method. When correction for the first-order response was made, values of the breath-by-breath method became equivalent to those of the Douglas bag method for whereas there was still a 17·5 per cent systematic underestimation (p<0·001) for . The correction for the second-order response gave equivalence and significant correlation (p<0·001) between the values of both methods for and . These results might indicate that breath-by-breath measurement of alveolar gas exchange with a slow-response gas analyser is valid when a second-order response delay correction is used.     

Influence of the viscoelastic properties of the respiratory system on the energetically optimum breathing frequency

We hypothesized that the viscoelastic properties of the respiratory system should have significant implications for the energetically optimal frequency of breathing, in view of the fact that these properties cause marked dependencies of overall system resistance and elastance on frequency. To test our hypothesis we simulated two models of canine and human respiratory system mechanics during sinusoidal breathing and calculated the inspiratory work ( ) and pressure-time integral (PTI) per minute under both resting and exercise conditions. The two models were a two-compartment viscoelastic model and a single-compartment model. Requiring minute alveolar ventilation to be fixed, we found that both models predicted almost identical optimum breathing frequencies. The calculated PTI was very insensitive to increases in breathing frequency above the optimal frequencies, while was found to increase slowly with frequency above its optimum. In contrast, both and PTI increased sharply as frequency decreased below their respective optima. A sensitivity analysis showed that the model predictions were very insensitive to the elastance and resistance values chosen to characterize tissue viscoelasticity. We conclude that the criterion for choosing the frequency of breathing is compatible with observations in nature, whereas the optimal frequency predictions of the PTI are rather too high. Both criteria allow for a fairly wide margin of choice in frequency above the optimum values without incurring excessive additional energy expenditure. Furthermore, contrary to our expectations, the viscoelastic properties of the respiratory system tissues do not pose a noticeable problem to the respiratory controller in terms of energy expenditure.     

Ventilation-perfusion ratios and the pulmonary shunt

Tests were carried out on 63 healthy persons aged 17–29 years, in the sitting position. The following parameters of lung ventilation were determined: Vd, phys/ Vt=30±0.6%,AaDO₂=10±0.9 mm Hg, aADCO₂/p_aCO₂ was equal to the end-expiratory pCO₂, i.e., to Pet,CO₂=5.0±0.4 mm Hg, (air)=2.3±0.3%, (O₂)=1.8±0.2%. For the lungs as a whole was normal (0.86±0.30). No difference in could be found between men and women. The main contribution to the development of in healthy subjects belongs to the anatomical shunt and perfusion of unventilated alveoli.Department of Internal Medicine, Smolensk Medical Institute. (Presented by Academician of the Academy of Medical Sciences of the USSR A. D. Ado.) Translated from Byulleten' Éksperimental'noi Biologii i Meditsiny, Vol. 89, No. 3, pp. 267–269, March, 1980.     

A model of transient oscillatory pressure-flow relationships of canine airways

In a previous paper (27) we developed a lumped parameter model of canine pulmonary airway mechanics featuring airway wall elasticity, gas inertance, and laminar and turbulent gas flow. The model accurately accounted for the steadystate pressure-flow data we obtained during sinusoidal cycling of the lung following a period of apnea. In the present paper, we extend the model to account for the transient decrease in the amplitude of the trans-airway pressure swings that we observed immediately following the apnea, which we have shown to be due to a vagally mediated bronchodilatation reflex. The extended model accounts for this transient in terms of a sudden change in airway smooth muscle tone acting on the viscoelastic properties of the airway wall and tissues mechanically coupled to it. Consequently, this model is able to temporarily store a volume of gas in the conducting airway tree as its volume changes cyclically with that of the whole lung. This means that the flow entering the airway tree from the trachea at any instant ( ) is not precisely equal to that entering the alveoli ( ) even when the gas is considered incompressible. We found that assuming to be equal to can lead to errors in estimating respiratory tissue impedance of as much as 10%. However, tissue hysteresivity remained almost unaffected, suggesting that the hysteretic properties of respiratory system tissues and airway wall are well matched.     

Rheology of rat basophilic leukemia cells

Rat basophilic leukemia (RBL) cells, decorated with IgE, have been shown to bind irreversibly to antigen-coated sub-strates. In this paper we measured RBL cell deformability and demonstrated that this irreversible binding is not due to a compliant cellular rheology of these cells. The rheological properties of RBL cells were assessed with single-cell micropipette aspiration. Small-sized (G₁/G₀ phase) cells were found to be more deformable than medium-sized (S phase) cells. No changes in cellular rheology were observed after binding of anti-dinitrophenol IgE to Fc_e receptors. Furthermore, cytoplasmic viscosity μ showed power-law dependence on mean shear rate , where μc is a characteristic viscosity at characteristic shear rate , andb is a material coefficient. All the cells exhibited similar dependence on shear rate (b≈0.5). When was set to 1 s⁻¹, μ_c, 560±40 and 490±10 Pa·s for G₁/G₀, S cells, and G₁/G₀ cells treated with the antibody, respectively. In general, RBL cells were much more rigid than normal neutrophils (μ_c = 130 ± 20 Pa · s,b ≈ 0.05). Thus the biochemistry of the adhesion molecules,not the cellular deformability of the cell, is the cause of the irreversibility of RBL cell adhesion under flow.     

Central and peripheral hemodynamics during maximal leg extension exercise

Summary The purpose of this study was to examine the central and peripheral hemodynamic adaptations to maximal leg extension exercise. Seventeen men (¯X=25 years, 84 kg) performed leg extension exercise (Universal equipment) for 12 repetitions (90s) to fatigue. Each repetition consisted of a 3s lifting motion, 1s pause, and 3s lowering motion. Impedance cardiography was used to measure stroke volume (SV), cardiac output ( ), systolic time intervals, and impedance contractility indices on a beat-by-beat basis. There were significant increases in systolic, diastolic, mean arterial pressure, total peripheral resistance, and HR during exercise. The mean remained similar throughout the protocol. SV decreased even though indices of myocardial performance indicated an enhancement of contractility. The magnitude of and SV were dependent upon the phase of leg extension. SV and during the lifting portions of the exercise were smaller than the lowering portions. The differences in SV and during the concentric and eccentric phases of the exercise most likely reflect the large static forces in exercising muscle which impeded venous return and increased afterload.     

A model for studying the distortion of muscle oxygen uptake patterns by circulation parameters

Summary The transmission of muscle oxygen uptake patterns to the pulmonary site is a basically nonlinear process during unsteady state exercise. We were mainly interested in three questions concerning the dynamic relationship between power input and pulmonary output: 1. To what extent can linear system analysis be applied? 2. What is the relative influence of muscle on pulmonary as compared to other parameters such as muscle perfusion kinetics? 3. To what extent does pulmonary reflect muscle ? Investigations were performed by means of a mathematical model including a muscle compartment and two serial, flow-varying time delays. The non-exercising parts of the body were. incorporated as one term for perfusion and one for . Parameters were adjusted so as to represent a reference state of aerobic exercise while monofrequent sinusoidal changes in aerobic metabolism were used as forcing signals. The following answers were derived from the simulations: 1. Non-linear distortions of the signals are negligible provided that analyses are not driven too far into the higher frequency range (periods shorter than about 1 min). 2. Variations of muscle kinetics have greater effects on pulmonary than changes of perfusion kinetics or venous volume. This finding applies irrespective of whether or not pulmonary closely reflects muscle 3. Small differences in the time constants for muscle perfusion and muscle are a major prerequisite if pulmonary , kinetics are to be taken as correct estimates of muscle kinetics. High basal muscle perfusion, small perfusion changes and small venous volumes between muscle and lungs are further factors reducing dynamic distortions of the muscle signal.     

Estimation of turbulent shear stress in free jets: Application to valvular regurgitation

In an attempt to better assess the severity of valvular regurgitation, anin-vitro experiment has been conducted to estimate turbulent shear stress levels within free jets issuing from different orifice shapes and sizes by means of hot-wire anemometry. On the basis of the measured mean velocities and the jet profiles, the distributions of the normalized kinematic turbulent shear stress were estimated for different jets by using an equation available for self-preserving circular jet. The results indicate that the equation can estimate the distributions of independent of the orifice shape and Reynolds number of the jet. For the range of Reynolds numbers considered, the estimation of maximum turbulent shear stress inferred from these distributions suggests that the critical shear stress level of approximately 200 N/m², corresponding to destruction of blood cells, is exceeded for typical blood flow velocity of 5 m/s at the valvular lesion.