A comparative study of organ models and numerical techniques for the evaluation of capillary permeability from multiple-indicator data

Acute hypervolemia lengthens red cell pulmonary transit time during exercise in endurance athletes

The purpose was to determine if acute plasma volume expansion (PVE) changed red-cell pulmonary transit time (PTT) during severe exercise. Twelve endurance athletes performed 6.5 min of severe cycling exercise on different days. Pentaspan [(500 ml, infusion condition, I] or placebo [(60 ml saline), non-infusion condition, N] were infused prior to exercise. Blood gas tensions, PTT, multigated acquisition (MUGA) derived cardiac output, and oxygen uptake were measured during exercise. PTT was measured during minute 3 of exercise by radionuclide cardiography. Arterial P(O(2)) (Pa(O(2))), and alveolar-arterial oxygen pressure difference (AaD(O(2))) at minute 3 of exercise did not differ between conditions. Mean PTT at minute 3 of exercise was 0.3 sec longer in the I condition (P=0.002). However, the change in PTT between conditions was not correlated to the change in either Pa(O(2)) or AaD(O(2)). We conclude that PVE slows (lengthens) PTT without affecting pulmonary gas exchange. Therefore, rapid PTT may not be related to hypoxemia during exercise.

Microvascular hematocrit and permeability-surface area product in contracting canine skeletal muscle in situ

The dynamics of the microvasculature of the blood-perfused canine gastrocnemius-plantaris muscle in situ at rest and during contraction were determined using multiple-indicator dilution analysis. Permeability-surface area product (PS) was estimated using a bolus indicator dilution of 86Rb, with 125I-albumin serving as the reference tracer, while microvascular hematocrit (Hmv) was estimated using the relationship between plasma (125I-albumin) and erythrocyte (51Cr) tracer washout curves. The muscle was stimulated to contract, under self-perfusion, for 3-min periods with either isometric twitch (1.5, 3, or 5 Hz; 4 ms) or tetanic (20, 40, or 60 trains/min, 200 ms, 100 Hz) contractions, separated by 25 min of rest, randomized to prevent ordering effects. At all stimulation frequencies, Hmv increased significantly from rest value of 36.5 +/- 1.6% to 3 min of either isometric twitch or tetanic contractions. PS rose significantly from 0.08 +/- 0.002 ml/g min at rest to a maximum of 0. 40 +/- 0.01 ml/g min at 60 isometric tetanic contractions per minute and 0.38 +/- 0.01 at 5 Hz. Changes in PS appeared related to stimulation frequency in both twitch and tetanic contractions. The change in Hmv with muscle contraction appeared to depend on contraction frequency during twitch contractions only, but was independent of stimulus frequency during tetanic contractions.

Visualization-based analysis of multiparameter models using environment for N-dimensional model analysis

We present a methodology, based on N-dimensional computer visualization, for analyzing multiparameter models. This approach originally consisted of three steps: behavior analysis, sensitivity analysis, identifiability analysis. We have now developed a new way of calculating sensitivity based on the statistical measure of the coefficient of variation. Furthermore, we extended the methodology through the addition of an extra step, visual regression. Visual regression allows the user to visualize the process of actual parameter identification and presents a combined, empirical view of the first three steps in a single image. Next we applied this methodology to pulmonary capillary-transport models. Finally, we implemented the model analysis process as a stand-alone program. EN-DIMAN, the resulting software, allows researchers to carry out model analysis in a graphical user interface (GUI)-based environment.

Graphical lung analysis and simulation environment

The study of transport across the pulmonary vasculature is an important aspect of the study of the lung. Models have often been used in conjunction with experimental work to further the information which can be obtained from experimental work alone. GLANSE was developed as an environment to carry out such analysis on microcomputers. The main model employed is a three region, homogeneous model which includes provisions for tracer diffusion in the extravascular region, hydrophilic and lipophyilic tracers as well as physiological parameters such as blood flow. Several heterogeneous models based on simplified versions of the three region model as well as two models which are not related to the three region model are also included. Computationally efficient routines for model simulations are used so as to enable their execution on microcomputers with large data sets. In addition, several methods for models analysis, such as parameter sensitivity and curve-fitting, as well as statistical analysis of results are also included. GLANSE has been tested and has been in use for several years for routine analysis of experimental data.

Modeling blood flow heterogeneity

It has been known for some time that regional blood flows within an organ are not uniform. Useful measures of heterogeneity of regional blood flows are the standard deviation and coefficient of variation or relative dispersion of the probability density function (PDF) of regional flows obtained from the regional concentrations of tracers that are deposited in proportion to blood flow. When a mathematical model is used to analyze dilution curves after tracer solute administration, for many solutes it is important to account for flow heterogeneity and the wide range of transit times through multiple pathways in parallel. Failure to do so leads to bias in the estimates of volumes of distribution and membrane conductances. Since in practice the number of paths used should be relatively small, the analysis is sensitive to the choice of the individual elements used to approximate the distribution of flows or transit times. Presented here is a method for modeling heterogeneous flow through an organ using a scheme that covers both the high flow and long transit time extremes of the flow distribution. With this method, numerical experiments are performed to determine the errors made in estimating parameters when flow heterogeneity is ignored, in both the absence and presence of noise. The magnitude of the errors in the estimates depends upon the system parameters, the amount of flow heterogeneity present, and whether the shape of the input function is known. In some cases, some parameters may be estimated to within 10% when heterogeneity is ignored (homogeneous model), but errors of 15-20% may result, even when the level of heterogeneity is modest. In repeated trials in the presence of 5% noise, the mean of the estimates was always closer to the true value with the heterogeneous model than when heterogeneity was ignored, but the distributions of the estimates from the homogeneous and heterogeneous models overlapped for some parameters when outflow dilution curves were analyzed. The separation between the distributions was further reduced when tissue content curves were analyzed. It is concluded that multipath models accounting for flow heterogeneity are a vehicle for assessing the effects of flow heterogeneity under the conditions applicable to specific laboratory protocols, that efforts should be made to assess the actual level of flow heterogeneity in the organ being studied, and that the errors in parameter estimates are generally smaller when the input function is known rather than estimated by deconvolution.

A visualization-based analysis method for multiparameter models of capillary tissue-exchange

In order to successfully use a model for parameter identification, it must be carefully analyzed. Current analysis methods, however, are ad hoc and provide only partial information. We extended these methods through the application of stacked dimensions, a scientific visualization method. The end result of our extensions are multi-dimensional parametric model-images. These images depict a model as a function of all its parameters in a single graphic. We applied parametric model-images to model verification (behavioral analysis), sensitivity analysis, and identifiability analysis. We applied our methodology to the evaluation of pulmonary vascular capillary-transport models. Results have shown that the visualization-based method provides a more complete view of a model's behavior and its other characteristics. Furthermore, our method has also proven to be more computationally efficient than the traditional approaches.

Deduction of pulmonary microvascular hematocrit from indicator dilution curves

We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected 51Cr-labeled red cells and 125I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculated hr, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments, hr = 0.92 +/- 0.01 (mn +/- sem) at a blood flow rate of 10.7 +/- 0.3 ml s-1. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation on hr. Embolization attenuated the separation between plasma and red cells (increased hr), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreased hr), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change in hr in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measured hr. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply that hr can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.

Postischemic hypoperfusion during unilateral lung reperfusion in vivo

The incomplete restoration of blood flow during reperfusion may amplify injury by prolonging ischemia; this "no-reflow" has been studied extensively in systemic organs. Our goal was to examine lung blood flow and microvascular function, specifically to determine whether blood flow is altered during lung reperfusion injury in vivo. In a unilateral lung model of ischemia-reperfusion in awake sheep, we measured pulmonary vascular resistance in each lung by radiolabeled microspheres. Measurements were made before 14 h of ischemia and again 4 h after reperfusion. Vascular resistance in the reperfused lung increased 3-fold (9.64 +/- 0.85 to 27.04 +/- 4.73 cm H2O/L/min) during reperfusion. The increase in vascular resistance in the reperfused lung fully accounted for the small increase in overall pulmonary vascular resistance (4.04 +/- 0.26 to 5.52 +/- 0.70 cm H2O/L/min). Microvascular permeability in the reperfused lung increased 52% more than in the contralateral lung, measured by an improved indicator dilution method with additional markers sensitive to surface area (butanediol). We conclude that changes in vascular resistance and microvascular function occur during lung reperfusion injury in vivo. The demonstration that postischemic hypoperfusion occurs during lung reperfusion in vivo suggests possible new avenues of approach to related clinical disorders.

Assessment of pulmonary vascular injury

The assessment of pulmonary injury in experimental and clinical situations remains a challenge. A method of quantifying pulmonary vascular aberrations in animal models and human clinical situations is described. A multiple-indicator dilution technique is employed to assess changes in lung capillary permeability--surface area product, extravascular lung water, and cardiac output. A mixture of 51Cr-RBC, 125I-albumin, tritiated water, and [14C]urea is injected into a central vein. Samples of the subject's blood are collected at timed intervals and counted for beta and gamma activity. Time concentration curves for each isotope are constructed. The capillary permeability--surface area product is calculated from the extraction pattern for [14C]urea. Extravascular lung water is calculated from the extraction pattern of tritiated water and cardiac output is calculated from the inverse of the area under the 51Cr curve. Normal reference curves are constructed for all subject groups. Significant changes occurred in capillary-permeability surface area product and extravascular lung water in various experimental models producing injury, in the patient population manifesting adult respiratory distress syndrome, and in those patients who have received cardiopulmonary transplants. The multiple-indicator dilution technique represents a sensitive tool for evaluating pulmonary vascular changes.

Xenon handling in the liver: red cell capacity effect

Xenon, despite its lack of chemical reactivity, associates preferentially with red cells in blood. To characterize the effect of this and the nature of xenon-tissue interaction in the liver, multiple indicator dilution studies were performed in the anesthetized normal dog through portal vein injection and hepatic vein collection of anaerobic blood samples. Two experimental runs were carried out in each animal, one at the prevailing hematocrit and the other at reduced hematocrit after bleeding and replacement with dextran. For comparison, the injection mixtures contained labeled red blood cells (a vascular reference), sucrose (an interstitial space reference), and labeled water (which freely enters liver cells), as well as labeled xenon. At the higher hematocrit, the labeled xenon curves generally rose earlier, peaked higher, and decayed more quickly than the labeled water curve; at the lower hematocrit, the xenon curve was delayed and diminished in magnitude in relation to the labeled water curves. Analysis of the curve shapes indicated that xenon, like labeled sucrose and water, underwent delayed wave flow-limited distribution. With knowledge of the red cell plasma partition coefficient (2.89 ml/ml), it was possible to both account for the change in form of the xenon curves with hematocrit and to use the data to estimate the liver cell tissue plasma xenon partition coefficient. Values averaged 1.93 ml/ml liver space, or 1.79 ml/g, and did not change significantly from first to second runs. Theoretical analysis indicated that flow cannot be estimated from xenon downslopes.

Lung water and vascular permeability-surface area in premature newborn lambs with hyaline membrane disease

Extravascular lung water and vascular permeability-surface area products were measured with a multiple indicator dilution method in 6 premature lambs with hyaline membrane disease 1-5 hours following delivery by cesarean section. The indicators used were 51Cr-labelled erythrocytes, 125I-albumin, 3H-water, and 14C-urea. Results were compared with previously obtained data in newborn lambs without hyaline membrane disease also delivered by cesarean section. Extravascular lung water was significantly higher in lambs with hyaline membrane disease [23.2 +/- 1.0 (SEM) vs. 10.7 +/- 1.4 ml/kg body wt]. Vascular permeability-surface area products for 14C-urea were significantly lower in lambs with hyaline membrane disease (0.30 +/- 0.10 vs 0.78 +/- 0.11 ml/s per kg). It is concluded that extravascular lung water is high in lambs with hyaline membrane disease. Permeability-surface area products for 14C-urea is low in lambs with hyaline membrane disease, which probably indicates a decrease in detectable surface area for exchange due to derecruitment or hypoperfusion of pulmonary exchange vessels in edematous and hypoxic areas of the lungs.

Through the microcirculatory maze with machete, molecule, and minicomputer (1986 Alza lecture)

This is a personal historical essay on meanderings through the jungle of the microcirculatory swamp. Because one pretends that the wandering was purposefully exploratory, a few guideposts are placed at positions where one could discern blaze-marks from earlier wanderers, and the path cut a little wider along some of the routes that may be enjoyed by investigators wanting to put their blazes along more distant paths. Naturally, one starts by coming up the broad rivers, then branching into the little streams. Each of us chooses to seek a different "mother lode," up a different stream.

Model identification and estimation of organ-function parameters using radioactive tracers and the impulse-response function

Examination of the input-output events in functioning organs by the use of the impulse-response function (IRF) for a radioactive tracer is gaining more and more ground in nuclear medicine. This study summarizes the development of deconvolution analysis, laying special stress on the 'model-free' approach. System linearity and time invariance are discussed, and means of eliminating noise in IRFs originating from the input and organ-time-activity curves are outlined. Typical IRFs are illustrated by flow diagrams, time-domain curves, and their representation by Laplace transforms. The cases of nondiffusible and diffusible tracers as well as parenchymally extracted and transported substances are discussed. Methods for the derivation of models and for the calculation of physiologically important parameters from the IRFs are suggested.

Characterisation of the unsteady transport of labelled species in permeable capillaries: role of convective dispersion

A mathematical model of transcapillary exchange has been developed which considers in detail the contribution of Taylor dispersion (i.e., non-uniform velocity and inequalities in radial concentration) to the uptake and wash-out of multiple tracers from single capillaries. A numerical solution to the two-dimensional unsteady-state species continuity equation for a single capillary is obtained (by the use of an array processor) which simulates the convective dispersion of labelled indicators in permeable capillaries. Particular attention is directed toward an analysis of the roles of capillary permeability, transport regime as characterised by the Peclet number, velocity profile and the length of the exchange region on the development of time-concentration profiles and on the importance of convective dispersion. For the physiologic range of parameters consistent with pulmonary capillary transport of multiple indicators (e.g., labelled urea, albumin, etc.), we find that the magnitude of convective dispersion is insufficient to markedly affect the shapes of simulated tracer concentration profiles. The implication in these circumstances is that the use of one-dimensional models, which do not account for Taylor dispersion, does not lead to significant errors in parameter estimates derived from data of multiple indicator dilution.

Model-free deconvolution techniques for estimating vascular transport functions

In this paper we present two methods which can be used to numerically deconvolve indicator dilution curves to obtain vascular transport functions. In the first method, direct algebraic deconvolution is made stable and practical by the damped least squares method. The second method involves a time-shift of the output curve which is based on the first and second moments of the input and output curves. This method is stable, computationally simple and can provide reasonable estimates of the transport function.

Changes in lung function after routine exposure manipulations during thoracotomy

The effect of manual retraction and bronchial occlusion upon right lung function during a 2-hr thoracotomy was evaluated in sheep. Group 1 (seven sheep) underwent manual lung retraction. Group 2 (seven sheep) underwent right bronchial occlusion. Group 3 (seven sheep) served as controls. Radioisotopic indicators (51Cr-RBC, 125I-albumin, [14C]urea, 3H2O) were used to assess changes in capillary permeability-surface area product (PS-urea), extravascular lung water (VE), and intravascular blood volume (Vv). Lung water was further quantified by gravimetric technique. Pulmonary vascular resistance increased following thoracotomy in both groups (34% Group 1, 66% Group 2) and compliance decreased (16% Group 1, 33% Group 2). Mean right lung shunt increased in Group 1 from 17 to 37% (P less than 0.05) and for Group 2 from 18 to 36% (P less than 0.02). A reduction (greater than 25%) in both groups for PS-urea and VE occurred (P less than 0.05). The fall in PS-urea and VE and the increase in PVR indicate a reduction in the right lung perfusion for both groups. It is concluded that a similar marked reduction in ventilation, perfusion, and V/Q occurred after reexpansion whether the lung was retracted or the bronchus occluded.

Comparison of sodium and urea as indicators of pulmonary vascular permeability

The objective of this work was to compare the blood-tissue transport properties of 14C-urea and 24Na in the lung circulation. The extraction of both substances was measured relative to intravascular reference tracers (125I-albumin for 24Na, 51Cr red cells and 125I-albumin for 14C-urea) in single-pass transpulmonary multiple indicator curves measured in awake sheep. Sheep were studied in baseline condition, after infusion of histamine solution (4 micrograms/kg-min for 4 hr), and after microvascular pressure was elevated. Permeability-surface area was computed for both sodium (PSn) and urea (PSu) by the Crone extraction model and by a mathematical model. In spite of the fact that the free diffusion coefficients of sodium and urea are approximately equal, the mean ratio of Crone PSn/PSu for baseline studies was 0.76. PSu was significantly increased by histamine infusion but PSn was not. The variation in PSn with histamine and increased pressure was marked. Thus, neither manipulation altered the ratio PSn/PSu in a consistent fashion. Correction of PS for extravascular distribution volumes of urea and Na did not change the PS ratio significantly. We concluded that the diffusional resistance to sodium is higher than expected from its diffusivity, possibly because of charge, and that PS for urea is more sensitive to changes in lung vascular permeability.

Role of longitudinal diffusion in the extravascular pulmonary space on parameter estimates derived from data of multiple indicator dilution

A mathematical model of transcapillary exchange has been developed that considers in detail the role of axial diffusion in the extravascular tissue region on estimates of such physiological parameters as lung water (VE) and pulmonary capillary permeability-surface area products (PS), obtained from multiple indicator dilution studies. The experimental cases considered correspond to two animal models of pulmonary oedema in which the integrity of the pulmonary capillary membrane is disrupted and the effects of extravascular axial diffusion may be important. A novel feature of the computational scheme is the use of an Array Processor in the solution of the governing equations, initial and boundary conditions. Computer time is reduced to 2-3 min for parameter identification, thereby allowing a wide range of values for extravascular axial diffusion coefficients (D'/L2) to be studied at little computational expense. The results indicate that diffusion in the extravascular region does not influence parameter estimates for PS to urea. A statistical correlation is suggested between values for VE, PS to water, and D'/L2.

The exchange of small molecules as a measure of normal and abnormal lung microvascular function

Evidence exists for the utility of measures of small-molecule exchange in assessing the normal and abnormal transport status of the lung vasculature. The evidence for the usefulness of PS for 14C-urea is: 1. PSu compares to other small molecules as would be expected from free-diffusion coefficients. 2. The extraction of 14C-urea decreases with increase flow as would be expected of a diffusion-limited indicator. 3. PSu is unaffected by moderate pressure increase, it increases when lymph protein flow indicated permeability increase, and it decreases when surface area is reduced. 4. Lung injuries such as E. coli endotoxemia in sheep and ARDS in patients can both reduce PSu, presumably through surface area reduction, and increase PSu, through increased permeability. Two events that accompany clinically important vascular injury complicate the interpretation of lung MT curves. These events are surface area loss and heterogeneity of flow and transport properties in the lung. Additional work is needed to precisely measure these variables and assess their importance.