Inert gas diffusion in heterogeneous tissue II: With perfusion

In this paper, a tractable mathematical model is proposed to describe transient inert gas diffusion in heterogeneous tissue with perfusion controlling gas input to the cellular region. The corresponding solution of overall mass uptake of the inert gas is derived exactly and should be useful in interpreting washout curves from particular tissue zones, whether there is any interaction with cellular diffusion or not. It is shown that the solution contains effectively nearly all models hitherto proposed to describe gas uptake in tissue. However some indication is given of a possible situation where perfusion, extra-cellular and cellular diffusion will need to be treated separately.     

Estimation of blood flow distribution in skeletal muscle from inert gas washout

A new method is evaluated for the estimation of blood flow-to-volume distribution in skeletal muscle from inert gas washout kinetics. Acetylene washout from the isolated, blood-perfused canine gracilis muscle was measured continuously with a blood gas catheter in combination with a mass spectrometer. The washout curves were transformed to flow-to-volume ratio distributions by means of a 50-compartment model. The algorithm fits the expression for the washout curve derived from the model by a least-squares method with enforced smoothing. The algorithm was evaluated using computer simulations in which artificial washout curves were generated by a multicompartment model with a known flow distribution. A wide range of given flow distributions could be recovered from the simulated data. The data were also analyzed using a linear programming technique. Analysis of the experimental data with the least-squares method showed that there is considerable heterogeneity in the distribution of perfusion in resting gracilis muscle. The distribution is characterized by at least two modes and a single compartment with a very low perfusion-to-volume ratio. Experimental noise made it impossible to obtain feasible flow distributions by means of linear programming.     

The interaction of diffusion and perfusion in homogeneous tissue

A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.     

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

Nuclear cardiac imaging for the assessment of myocardial viability

An important aspect of the diagnostic and prognostic work-up of patients with ischaemic cardiomyopathy is the assessment of myocardial viability. Patients with left ventricular dysfunction who have viable myocardium are the patients at highest risk because of the potential for ischaemia but at the same time benefit most from revascularisation. It is important to identify viable myocardium in these patients, and radionuclide myocardial scintigraphy is an excellent tool for this. Single-photon emission computed tomography perfusion scintigraphy (SPECT), whether using ²⁰¹thallium, ^99mTc-sestamibi, or ^99mTc- tetrofosmin, in stress and/or rest protocols, has consistently been shown to be an effective modality for identifying myocardial viability and guiding appropriate management.Metabolic and perfusion imaging with positron emission tomography radiotracers frequently adds additional information and is a powerful tool for predicting which patients will have an improved outcome from revascularisation. New techniques in the nuclear cardiology field, such as attenuation corrected SPECT, dual isotope simultaneous acquisition (DISA) SPECT and gated FDG PET are promising and will further improve the detection of myocardial viability. Also the combination of multislice computed tomography scanners with PET opens possibilities of adding coronary calcium scoring and noninvasive coronary angiography to myocardial perfusion imaging and quantification.     

Correction of inert gas washin or washout for gas solubility in blood

We show that when an inert gas is washed into the lungs its retention in the blood during any one breath is approximately proportional to its solubility. This relationship makes possible the correction of washin or washout data for blood uptake or release, provided that two gases of different solubility are used simultaneously. The method automatically allows for the characteristics of an individual washin or washout and for the occurrence of recirculation within a fairly short washin or washout period. It has been tested in models with nonuniform ventilation and perfusion and closely approximates the behavior of a truly insoluble gas. In the derived ventilation distribution, gas solubility appears as ventilation to units of low turnover. In the case of N2 this effect is small but causes appreciable overestimation of lung volume. The recovered dead space and main alveolar distribution are insignificantly affected.     

Inert gas clearance from tissue by co-currently and counter-currently arranged microvessels

To elucidate the clearance of dissolved inert gas from tissues, we have developed numerical models of gas transport in a cylindrical block of tissue supplied by one or two capillaries. With two capillaries, attention is given to the effects of co-current and counter-current flow on tissue gas clearance. Clearance by counter-current flow is compared with clearance by a single capillary or by two co-currently arranged capillaries. Effects of the blood velocity, solubility, and diffusivity of the gas in the tissue are investigated using parameters with physiological values. It is found that under the conditions investigated, almost identical clearances are achieved by a single capillary as by a co-current pair when the total flow per tissue volume in each unit is the same (i.e., flow velocity in the single capillary is twice that in each co-current vessel). For both co-current and counter-current arrangements, approximate linear relations exist between the tissue gas clearance rate and tissue blood perfusion rate. However, the counter-current arrangement of capillaries results in less-efficient clearance of the inert gas from tissues. Furthermore, this difference in efficiency increases at higher blood flow rates. At a given blood flow, the simple conduction-capacitance model, which has been used to estimate tissue blood perfusion rate from inert gas clearance, underestimates gas clearance rates predicted by the numerical models for single vessel or for two vessels with co-current flow. This difference is accounted for in discussion, which also considers the choice of parameters and possible effects of microvascular architecture on the interpretation of tissue inert gas clearance.     

A new class of biophysical models for predicting the probability of decompression sickness in scuba diving.

Interconnected compartmental models have been used for decades in physiology and medicine to account for the observed multi-exponential washout kinetics of a variety of solutes (including inert gases) both from single tissues and from the body as a whole. They are used here as the basis for a new class of biophysical probabilistic decompression models. These models are characterized by a relatively well-perfused, risk-bearing, central compartment and one or two non-risk-bearing, relatively poorly perfused, peripheral compartment(s). The peripheral compartments affect risk indirectly by diffusive exchange of dissolved inert gas with the central compartment. On the basis of the accuracy of their respective predictions beyond the calibration regime, the three-compartment interconnected models were found to be significantly better than the two-compartment interconnected models. The former, on the basis of a number of criteria, was also better than a two-compartment parallel model used for comparative purposes. In these latter comparisons, the models all had the same number of fitted parameters (four), were based on linear kinetics, had the same risk function, and were calibrated against the same dataset. The interconnected models predict that inert gas washout during decompression is relatively fast, initially, but slows rapidly with time compared with the more uniform washout rate predicted by an independent parallel compartment model. If empirically verified, this may have important implications for diving practice.     

A rapid technique for the isolation and purification of adult cardiac muscle cells having respiratory control and a tolerance to calcium

A rapid technique is described for the isolation of muscle cells from adult rat myocardium using in vitro perfusion with calcium-free bicarbonate buffer containing crude collagenase. Under optimum conditions, 5 × 10⁶ cells per g tissue are obtained and the suspension may be purified to contain 70% intact cells. The complete procedure is rapid and isolated myocytes beat, exclude vital stains, have conventional sub-cellular morphology, show tight respiratory coupling and also have a tolerance to external calcium not found in cells isolated by other perfusion techniques. This represents a significant advance in the development of an isolated cell model for the study of myocardial mechanisms.     

Nitrogen gas exchange in the human knee

Human decompression sickness is presumed to result from excess inert gas in the body when ambient pressure is reduced. Although the most common symptom is pain in the skeletal joints, no direct study of nitrogen exchange in this region has been undertaken. For this study, nitrogen tagged with radioactive 13N was prepared in a linear accelerator. Nine human subjects rebreathed this gas from a closed circuit for 30 min, then completed a 40- to 100-min washout period breathing room air. The isotope 13N was monitored continuously in the subject's knee during the entire period using positron detectors. After correction for isotope decay (half-life = 9.96 min), the concentration in most knees continued to rise for at least 30 min into the washout period. Various causes of this unexpected result are discussed, the most likely of which is an extensive redistribution of gas within avascular knee tissues.     

Homogenization modeling for the mechanics of perfused myocardium

Altered coronary perfusion can change the apparent diastolic stiffness of ventricular myocardium--the ‘garden hose’ effect. Our recent findings showed that myocardial strains are reduced during ventricular filling, primarily along the directions transverse to the coronary microvessels. In this article, we review hypotheses and theoretical models regarding the role that regional wall stress plays in the mechanical interaction between myocardium and coronary circulation. Various mechanisms have been used to explain the effects of the tissue stress on coronary flow, as well as the effect of coronary dynamics on myocardial mechanics. Many models of coronary pressure-flow relations using lumped parameter circuit analogs. Poroelasticity and swelling theories have been used to model the mechanics of perfused muscle. Here, we describe a new mathematical model of the mechanics of perfused myocardium derived using homogenization theory. In this model, perfused myocardium is treated as a nonlinear anisotropic elastic solid embedded with cylindrical vessels of known distensibility. The solid compartment is incompressible but the vascular compartment may change volume according to a simple relation between vessel diameter and perfusion pressure. The work done by the perfusion pressure in changing vascular volume contributes to the macroscopic strain energy and hence affects the stress and stiffness of the composite. Conversely, the stress in the tissue affects microvessel diameter and volume, since tractions transverse to the vessel axis oppose the internal blood pressure. Finite element simulations of passive filling show good agreement of model with experimental results.     

Myocardial blood perfusion and transport modeling using inert-tracer techniques: a review and recent investigations

The inert-gas clearance method for measuring blood perfusion in the heart may be useful in detecting and assessing coronary disease and myocardial infarctions. Estimating perfusion from clearance data requires a model of tracer transport. The tracer transport models in use are the compartmental model, the kinetic model, and more complex models which yield estimates by optimal estimation techniques. The implementation of one such complex model in which tissue need not be assumed homogeneous, and the resulting myocardial perfusion and diffusibility estimates, are discussed. Methods are reviewed which may be used to detect and assess coronary disease by average and regional myocardial-perfusion measurements. Possible explanations for the observed multicompartment myocardial clearance curve are discussed.     

Myocardial uptake of thiopental enantiomers by the isolated perfused rat heart

Myocardial uptake of thiopental enantiomers by an isolated perfused rat heart preparation was examined after perfusion with protein-free perfusate. Outflow perfusate samples were collected at frequent intervals for 20 min during single-pass perfusion with 10 μg/ml racemic thiopental (washin phase) and for another 45 min during perfusion with drug-free perfusate (washout phase). (+)- and (−)-thiopental concentrations were assayed by chiral high-performance liquid chromatography. Heart rate, perfusion pressure, and electrocardiogram were also monitored. During the washin phase, there was no significant difference between the mean values of the equilibration rate constants of (+)- and (−)-thiopental enantiomers (0.44 ± 0.07 min⁻¹ and 0.43 ± 0.09 min⁻¹, respectively, P > 0.05). Mean volumes of distribution of (+)- and (−)-thiopental enantiomers were similar (6.34 ± 1.20 and 6.45 ± 1.29 ml/g for the washin phase and 7.22 ± 0.71 and 7.47 ± 0.81 ml/g for the washout phase, respectively, P > 0.05). This indicates that tissue accumulation of thiopental enantiomers in the isolated perfused rat heart was not stereoselective. Uptake of thiopental by the heart was perfusion flow rate-limited and independent of capillary permeability. These findings suggest that myocardial tissue concentration of racemic thiopental should be an accurate predictor of myocardial drug effect. © 1996 Wiley-Liss, Inc.     

Impaired resting perfusion in viable myocardium distal to chronic coronary stenosis in rats

Chronic coronary artery stenosis results in patchy necrosis in the dependent myocardium and impairs global and regional left ventricular (LV) function in rats in vivo. The aim of the present study was to compare regional myocardial blood flow (RMBF) and function (F) in poststenotic myocardium by using magnetic resonance imaging (MRI) and to compare MRI blood flow changes to histological alterations to assess whether RMBF in the viable poststenotic tissue remains normal. MRI was performed in 11 anesthetized Wistar rats with 2-wk stenosis of the left coronary artery. Postmortem, the extent of fibrotic tissue was quantified. Poststenotic RMBF was significantly reduced to 2.21 +/- 0.30 ml.g(-1).min(-1) compared with RMBF in the remote myocardium (4.05 +/- 0.50 ml.g(-1).min(-1)). A significant relationship between the poststenotic RMBF (%remote area) and the poststenotic F (%remote myocardium) was calculated (r = 0.61, P < 0.05). Assuming perfusion in scar tissue to be 32 +/- 5% of perfusion of remote myocardium, as measured in five additional rats, and that in remote myocardium to be 114 +/- 25% of that in normal myocardium, as assessed in five sham rats, the calculated perfusion in partially fibrotic tissue samples (35.7 +/- 5.2% of analyzed area) was 2.88 +/- 0.18 ml.g(-1).min(-1), whereas measured MRI perfusion was only 1.86 +/- 0.24 ml.g(-1).min(-1) (P < 0.05). These results indicate that resting perfusion in viable poststenotic myocardium is moderately reduced. Alterations in global and regional LV function are therefore secondary to both patchy fibrosis and reduced resting perfusion.     

Coronary microcirculatory vasoconstriction is heterogeneously distributed in acutely ischemic myocardium

The classical model of coronary physiology implies the presence of maximal microcirculatory vasodilation during myocardial ischemia. However, Doppler monitoring of coronary blood flow (CBF) documented severe microcirculatory vasoconstriction during pacing-induced ischemia in patients with coronary artery disease. This study investigates the mechanisms that underlie this paradoxical behavior in nine patients with stable angina and single-vessel coronary disease who were candidates for stenting. While transstenotic pressures were continuously monitored, input CBF (in ml/min) to the poststenotic myocardium was measured by Doppler catheter and angiographic cross-sectional area. Simultaneously, specific myocardial blood flow (MBF, in ml.min(-1).g(-1)) was measured by 133Xe washout. Perfused tissue mass was calculated as CBF/MBF. Measurements were obtained at baseline, during pacing-induced ischemia, and after stenting. CBF and distal coronary pressure values were also measured during pacing with intracoronary adenosine administration. During pacing, CBF decreased to 64 +/- 24% of baseline and increased to 265 +/- 100% of ischemic flow after adenosine administration. In contrast, pacing increased MBF to 184 +/- 66% of baseline, measured as a function of the increased rate-pressure product (r = 0.69; P < 0.05). Thus, during pacing, perfused myocardial mass drastically decreased from 30 +/- 23 to 12 +/- 11 g (P < 0.01). Distal coronary pressure remained stable during pacing but decreased after adenosine administration. Stenting increased perfused myocardial mass to 39 +/- 23 g (P < 0.05 vs. baseline) as a function of the increase in distal coronary pressure (r = 0.71; P < 0.02). In conclusion, the vasoconstrictor response to pacing-induced ischemia is heterogeneously distributed and excludes a tissue fraction from perfusion. Within perfused tissue, the metabolic demand still controls the vasomotor tone.     

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.     

Stable labeled microspheres to measure perfusion: validation of a neutron activation assay technique

Neutron activation is an accurate analytic method in which trace quantities of isotopes of interest in a sample are activated and the emitted radiation is measured with high-resolution detection equipment. This study demonstrates the application of neutron activation for the measurement of myocardial perfusion using stable isotopically labeled microspheres. Stable labeled and standard radiolabeled microspheres (15 microm) were coinjected in an in vivo rabbit model of myocardial ischemia and reperfusion. Radiolabeled microspheres were detected with a standard gamma-well counter, and stable labeled microspheres were detected with a high-resolution Ge detection after neutron activation of the myocardial and reference blood samples. Regional myocardial blood flow was calculated from the deposition of radiolabeled and stable labeled microspheres. Both sets of microspheres gave similar measurements of regional myocardial blood flow over a wide range of flow with a high linear correlation (r = 0.95-0.99). Neutron activation is capable of detecting a single microsphere in an intact myocardial sample while providing simultaneous quantitative measurements of multiple isotope labels. This high sensitivity and capability for measuring perfusion in intact tissue are advantages over other techniques, such as optical detection of microspheres. Neutron activation also can provide an effective method for reducing the production of low-level radioactive waste generated from biomedical research. Further applications of neutron activation offer the potential for measuring other stable labeled compounds, such as fatty acids and growth factors, in conjunction with microsphere measured flow, providing the capability for simultaneous measurement of regional metabolism and perfusion.     

A METHOD OF CORONARY RETROPERFUSION FOR THE TREATMENT OF ACUTE MYOCARDIAL ISCHEMIA

A method of retrograde perfusion of the myocardium has been developed in dogs. It consists of a double lumen balloon-tipped catheter inserted transvenously into the coronary sinus, with one lumen connected to a roller pump, the other to a helium counterpulsing pump. Oxygenated heparinized blood is obtained from the femoral artery and pumped continuously into the coronary sinus at a pressure of 50-75 mm Hg. The balloon is inflated during diastole, sealing the coronary sinus and promoting retrograde flow, and is deflated during systole, allowing blood drainage into the right atrium and preventing venous congestion. Thirteen anesthetized open-chest dogs were subjected to 15 minutes of proximal LAD artery occlusion and 30 minutes of diastolic coronary sinus perfusion (DCSP). The area of ischemia was mapped by means of platinum electrodes capable of simultaneously measuring myocardial tissue oxygen tension M(p)O(2)) and electrograms. Reduction of M(p)O(2) with simultaneous elevation of the ST segment on the corresponding electrogram was considered an indication of ischemia. Diastolic coronary sinus perfusion improved myocardial oxygen tension in the ischemic myocardium, reduced ST segment elevation, and tended to restore arterial blood pressure. Histologically, there was no intramyocardial hemorrhage.     

Kinetics of isobaric counterdiffusion

Isobaric inert gas counterdiffusion has been demonstrated to produce gas lesions in man (Lambertsen and Idicula, 1975) and lethal gas embolism in animals (Lambertsen, Cunnington and Cowley, 1975). Equations have been derived for the stable-state supersaturation pressures developing at interfaces during inert gas counterdiffusion (Graveset al., 1973). The present analysis is a mathematical treatment of the kinetics of the isobaric counterdiffusion of a pair of gases through a membrane consisting of two layers composed of substances with different diffusion coefficients and solubilities for each of the gases involved. The time to reach the stable supersaturation state due to isobaric counterdiffusion, even when circulatory transport and pulmonary washout times are included, is found to be at least an order of magnitude smaller than the time required for visible bubble formation and tissue distortion.     

Treatment of chronical myocardial ischemia by adenovirus-mediated hepatocyte growth factor gene transfer in minipigs

Growth factor gene transfer-induced therapeutic angiogenesis has become a novel approach for the treatment of myocardial ischemia. In order to provide a basis for the clinical application of an adeno- virus with hepatocyte growth factor gene (Ad-HGF) in the treatment of myocardial ischemia, we estab- lished a minipig model of chronically ischemic myocardium in which an Ameroid constrictor was placed around the left circumflex branch of the coronary artery (LCX). A total of 18 minipigs were ran- domly divided into 3 groups: a surgery control group, a model group and an Ad-HGF treatment group implanted with Ameroid constrictor. Ad-HGF or the control agent was injected directly into the ischemic myocardium, and an improvement in heart function and blood supply were evaluated. The results showed that myocardial perfusion remarkably improved in the Ad-HGF group compared with that in both the control and model groups. Four weeks after the treatment, the density of newly formed blood vessels was higher and the number of collateral blood vessels was greater in the Ad-HGF group than in the model group. The area of myocardial ischemia reduced evidently and the left ventricular ejection fraction improved significantly in the Ad-HGF group. These results suggest that HGF gene therapy may become a novel approach in the treatment of chronically ischemic myocardium.