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1Department of Anesthesia and Critical Care, and 2Pulmonary and Critical Care Unit, Department of Medicine, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114; and 3Clinic of Anesthesiology and Intensive Care Medicine, University Clinic Carl Gustav Carus, Dresden University of Technology, Dresden 01307, Germany
Submitted 22 April 2003 ; accepted in final form 24 July 2003
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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right-to-left shunt; pulmonary gas exchange; mathematical model; positron emission tomography; functional imaging
Assessment of shunt from intravenously injected low-solubility tracers is not without complication. Reabsorption of tracer from alveolar gas spaces and recirculation have been long recognized as sources of significant inaccuracy in these methods (6, 8, 21, 22, 25). This is particularly critical in conditions of lung injury, because imaging techniques report reduced alveolar volumes and areas of reduced volume-to-perfusion ratios (10, 18, 19), both of which cause increased tracer reabsorption. Thus we expect that, during ALI, the tracer volume of distribution into aerated lung regions is important for accurate estimation of right-to-left shunt. In addition, this volume is physiologically significant, because it represents the effective volume available for distribution of gas eliminated by the pulmonary capillaries. To our knowledge, no estimates of this volume have been made. Although a reduction in alveolar volume during ALI has been demonstrated, the fraction of the remaining alveolar volume that is available for gas exchange has not been established.
The main objective of this study was to develop a method to estimate overall right-to-left shunt and the volumes of distribution of 13NN in alveolar gas and shunt tissue on the basis of the arterial kinetics of 13NN. The method is conceived to be complementary to, and performed simultaneously with, functional imaging of the lung with PET. In addition, we tested the following hypotheses: 1) estimates of total shunt on the basis of the arterial kinetics of 13NN correlate with estimates derived from O2 blood concentrations and from PET images, and 2) the alveolar gas volume of 13NN distribution estimated from the peripheral kinetics of 13NN is equivalent to the alveolar gas volume estimated with PET imaging techniques.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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The study was approved by the Massachusetts General Hospital Subcommittee on Research Animal Care. Eleven sheep were anesthetized, intubated, and mechanically ventilated. General anesthesia was induced with an intravenous bolus of thiopental sodium (30–35 mg/kg) and fentanyl (12.5–25 µg/kg) and maintained with a continuous infusion of thiopental sodium (15–25 mg · kg-1 · h-1) and fentanyl (10–30 µg · kg-1 · h-1). Pancuronium (0.2 mg · kg-1 · h-1) was used for muscle paralysis. Five normal (23 ± 5 kg) and six lung-injured sheep (22 ± 3 kg) were studied. Lung injury was produced with bilateral warmed isotonic saline lung lavage (30 ml/kg) to remove lung surfactant. The solution was flushed into and out of the lungs, and the process was repeated after 5 min until an arterial O2 partial pressure (PaO2)-to-inspired O2 fraction (FIO2) ratio of <100 Torr was achieved. The ventilator (Harvard Apparatus, Millis, MA) was set at FIO2 = 0.26 ± 0.04, positive end-expiratory pressure (PEEP) = 5 cmH2O, and tidal volume (VT) = 11 ± 2 ml/kg (262 ± 61 ml) for normal sheep and FIO2 = 1.0, PEEP = 5 cmH2O, and VT = 8 ml/kg (176 ± 25 ml) for injured sheep. Inspiratory time was 30% of the breathing period, and respiratory rate (17 ± 4 breaths/min) was set to maintain normocapnic arterial blood gases at the beginning of the experiment and fixed at that value for the rest of the experiment. The right femoral artery was cannulated for systemic arterial pressure monitoring and blood sampling and the right femoral vein for administration of drugs. A heparinized Swan-Ganz catheter (model 93A-131H-7F, Edwards Laboratory, Santa Ana, CA) was inserted into the left femoral vein and advanced into the pulmonary artery. Its distal port was used for monitoring of pulmonary arterial pressure and sampling of mixed venous blood. A central line was introduced in a jugular vein and positioned into the superior vena cava for delivery of the 13NN-saline solution. The animal received an initial dose of 200 U/kg heparin, followed by 50 U · kg-1 · h-1, to prevent thromboembolism. Airway, arterial, and pulmonary arterial pressures were continuously monitored with a strip chart recorder (Hewlett-Packard, Palo Alto, CA). Total cardiac output (
T) was measured with thermodilution (model COM-1, Edwards Laboratory).
Imaging Protocol
Sheep were initially placed in the PET camera in the supine or prone position (3 surfactant-depleted supine, 3 surfactant-depleted prone, and 5 normal prone). Surfactant-depleted sheep in the prone position were studied with un-compressed abdomen. A 5-min transmission scan was collected before each set of emission scans to correct for absorption of annihilation photons by body tissues. Emission scans were performed in the following manner. Starting with a tracer-free lung, ventilation was stopped, and the lungs were kept at a pressure equal to the mean airway pressure previously measured during tidal breathing. Simultaneously, a bolus of 13NN-saline (with volume VI and specific activity CI) was injected into the central venous catheter, and the PET camera began collecting a series of sequential images. Eight images of 2.5-s duration and four images of 10-s duration were acquired during 60 s of apnea. Ventilation was then resumed, and the camera continued to acquire images for 3 min. The time trend of the total activity in each of these images, normalized by the total injected activity (CI · VI), provided a kinetics description of 13NN transit through the imaged lung (i.e., lung kinetics). Continuous measurement of arterial tracer activity (sampling frequency = 1 Hz) was started 
20 s before tracer injection to attain a steady-state withdrawal rate during and after the injection. The measured arterial kinetics data were then normalized by CI. For the saline lung lavage studies, the sheep were rotated to the opposite position after this imaging sequence, and an identical sequence was repeated. In total, six surfactant-depleted sheep were studied in the supine and prone positions, and five normal sheep were studied in the prone position.
Arterial Tracer Kinetics Model
Overview. The arterial kinetics model consisted of four compartments describing the central blood volume, right-to-left shunt, gas-exchanging lung, and systemic recirculation (Fig. 1). 13NN dissolved in saline was injected into the superior vena cava at an infusion flow rate I. The injectant was diluted in the central volume compartment, assumed to be well mixed, with a volume Vcv, and to be perfused by a continuous and uniform blood flow T. This compartment represented tracer mixing between the injection site and the lungs (i.e., superior vena cava, right heart, and major pulmonary arteries) and between the lungs and the sampling site (i.e., major pulmonary veins, left heart, and aorta). Vasculature on both sides of the lung was lumped into a single compartment, because their time constants (volume/blood flow) are similar and, thus, indistinguishable on the basis of the effluent arterial tracer kinetics. The uniform concentration inside this compartment [ccv(t)] was used as the input for two independent, well-mixed compartments. One compartment corresponded to right-to-left shunt, including completely nonaerated atelectatic and flooded alveolar units and extrapulmonary shunt. This compartment had a volume Vs and a uniform concentration cs(t) and was perfused by the shunting blood flow s = Fs · T, where Fs is the shunt fraction. The other compartment represented gas-exchanging regions, consisting of perfused and aerated alveolar units with a volume VA, uniform concentration cA(t), and blood flow A = (1 - Fs) · T. The tracer concentrations in blood leaving the shunting and gas-exchanging compartments were cs(t) and 
· cA(t), respectively, where = 0.0145 is the 13NN blood-gas partition coefficient at 37°C (20). The perfusion-weighted average of these concentrations represented the tracer concentration in arterial blood [ca(t)] after a time delay 
ta. This time delay accounted for all convective delays between the injection site and the measurement site. The concentration ca(t), after a time delay tr, was also used as an input to a recirculation compartment with a volume Vr, uniform concentration cr,tot(t), and blood flow T. The time delay tr represented the recirculation time relative to ta. A fraction Fr of cr,tot(t) was used to represent the recirculated concentration cr(t), which was input into the central volume compartment.
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Injection and central volume compartment. The simulated injected 13NN (I · CI) was normalized by CI and modeled as a step function with an amplitude of 1 and a width of VI/I. Thus all described concentrations are normalized by CI. The step function (I) was input into the central volume compartment. With the use of the law of mass conservation and the assumption of a well-mixed uniform concentration ccv(t) and constant T, this compartment is described by the first-order differential equation
 | (1) |
 | (2) |
T is independently measured.
Gas-exchanging lung and shunt compartments. The tracer concentration ccv(t) was input to a shunting tissue and gas-exchanging lung compartment. The shunt compartment is described by
 | (3) |
s is the partition coefficient between the blood and shunting units. If we divide by Vs and assume s = 1, this becomes
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s = Vs/s and, implicitly, Fs are unknowns. The gas-exchanging compartment is described by
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· cA(t). When solved for the normalized activity leaving the compartment, this equation becomes
 | (6) |
A = VA/( · A) and, implicitly, Fs are unknowns.
Arterial sample. The arterial tracer concentration [ca,t(t)] is calculated as the perfusion-weighted average of cs(t) and · cA(t) according to
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ta according to
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Recirculation. The arterial concentration entering the recirculation compartment [ca,r(t)] is calculated by shifting ca(t) in time by a delay tr according to
 | (9) |
 | (10) |
 | (11) |
r = Vr/T is unknown. This compartment describes tracer interactions in the systemic circulation with time constants short enough to significantly influence the measured arterial kinetics. The remainder of the activity is assumed to be absorbed by tissues throughout the circulation or to have delay times greater than the time of measurement. A fraction Fr of the activity behaved with such short time constants. Thus the recirculated concentration that reached the pulmonary circulation is calculated according to
 | (12) |
Simulations
The effect of Fs, s, and A on the arterial tracer kinetics was evaluated by using the developed mathematical model. The corresponding effect on the lung tracer kinetics was studied by using the model developed by Galletti and Venegas (9). Curves from both models were generated by using starting values of Fs = 0.25, s = 10 s, and A = 1,000 s. Changes in the curves were studied by using ranges of 0 < Fs < 0.75, 5 s < s < 20 s, and 250 s < A < 2,000 s. Each parameter was varied in that range, while the remaining two parameters were fixed at the starting values.
Experimental Apparatus
The experimental setup consisted of an automated 13NN tracer preparation system, PET camera, gamma counter, and in-line blood pump (Fig. 2). 13NN gas (half-life = 9.97 min) was dissolved in normal saline and injected as a rapid bolus (VI = 23–34 ml and CI = 0.16–0.49 mCi/ml) into a central vein at a rate I of 10 ml/s. The PET camera was a multi-ring full-body camera that imaged a 10-cm cross section of the lung (Scanditronix PC4096, General Electric, Milwaukee, WI). Arterial 13NN concentration was measured with a peripheral dual-channel gamma counter (Scanditronix, General Electric). Arterial blood was drawn from the right femoral artery at a rate of 10 ml/min (Harvard Apparatus), passed through the gamma counter, and collected in two 60-ml syringes. Flexible polymer tubing (Tygon R-3603) was used throughout the system, except for an 8-inch section of glass tubing for the path through the counter.
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Model Parameter Identification
Equations 2, 4, 6–9, 11, and 12 define a system of eight unknowns: Vcv, Fs, s, A, ta, r, Fr, and tr. To minimize the number of parameters estimated simultaneously by the optimization routine for each experimental set of arterial kinetics data, a stepwise identification strategy was used and simplifying assumptions were made, as described below. This reduced the number of parameters identified to three (Fs, s, and A).
Fixed parameters. Vcv was assumed to be 200 ml on the basis of preliminary optimizations. Because of the low shunt in the lavage prone and normal prone conditions, the amount of recirculated tracer activity was considered negligible and cr(t) was set to zero. Surfactant-depleted supine sheep exhibited much greater shunt fractions, so the kinetics of recirculated activity were approximated by setting tr = -4 s, Fr = 0.493, and r = 38 s on the basis of the measurements and calculations described in APPENDIX A.
Optimization algorithm. The arterial kinetics defined by Eqs.4, 6, 7, and 8 were simulated using Simulink and Matlab (MathWorks, Natick, MA). Fs, s, and A were identified by minimizing a weighted square difference (WSD) between the normalized kinetics simulated by the model (ca) and the kinetics measured by the gamma counter (cm). The WSD was defined by
 | (13) |
ta), including a value visually estimated from the arterial curve and four values defined as 1 and 2 s shorter and longer than the visual estimate. The parameter set that resulted in the lowest WSD was chosen as the final solution.
Initial conditions and parameter bounds. Parameter bounds of 0 
Fs 1, 1 s s 20 s, and 20 s A 2,000 s were used. Initial values of s and A were set to 10 and 500 s, respectively. To estimate an initial value for Fs, linear regression was used to find the empirical relation between the shunt measured by the O2 method (FsO2, see Shunt Calculations) and the maximum normalized measured arterial concentration (Cm,max) from the experiments. The relation (FsO2 = 29.6 · Cm,max + 0.01) was then used along with Cm,max to make the initial Fs estimate.
Optimization Accuracy
Accuracy of parameter identification was evaluated with a Monte Carlo analysis. The mean identified Fs, s, and A in the lavage supine, lavage prone, and normal prone conditions were used to simulate noise-free kinetics curves. Noise was assumed to be normally distributed with a zero mean and a standard deviation that, for each experimental group, was estimated by the standard deviation (
noise) of the point-by-point difference cm - ca from all experiments within the group. Noise was added to each simulated data point by selecting a random number first from this distribution and then from a distribution with a standard deviation equal to 3 · noise. The mean and standard deviation of identified parameters, correlation coefficients between the original noise-free and simulated data, and residuals were calculated for 100 simulations at both noise levels. Recirculation parameter values were fixed to the values identified in APPENDIX A for the analysis with the mean parameters from the lavage supine condition, whereas recirculation was excluded for the analysis with the mean parameters from the lavage prone and normal prone conditions. Initial values were set as described in Initial conditions and parameter bounds.
Sensitivity to the fixed values of Vcv, r, and Fr was evaluated by performing the parameter identification when each of the values was changed by ±12.5%. Because recirculation was not considered in the analysis of the lavage prone and normal prone conditions, only the experiments from the lavage supine condition were used to evaluate r and Fr. Mean identified values of Fs, s, and A were then compared with those found using the assumed values of Vcv = 200 ml, r = 38 s, and Fr = 0.493.
Shunt Calculations
Arterial and mixed venous blood gases taken before each emission imaging sequence were used to calculate the O2 shunt fraction for the surfactant-depleted sheep and the venous admixture for the normal sheep, both of which will be noted as FsO2 (4). Samples were taken from the pulmonary artery and right femoral artery. PO2, PCO2, and pH were measured with a rapid blood-gas analyzer (model ABL5/BPH5, Radiometer Medical, Copenhagen, Denmark). These values were used to calculate the arterial and venous O2 saturation fractions on the basis of an O2 dissociation curve for sheep (33). Total hemoglobin content was measured with a hemoximeter (model OSM3, Radiometer Medical). The lung model developed by Galletti and Venegas (9) was used to estimate the shunt fraction (Fs,PET) on the basis of the 13NN pulmonary kinetics.
Aerated Lung Volume of Distribution
Fractional gas content (Fgas), representing the fraction of the volume of a voxel (Vvox) occupied by gas, was calculated from the transmission scan, as previously described (5, 12, 35). The total imaged gas volume of the lung was then calculated as 
, where n is the number of voxels within the imaged lung field. The volume of gas participating in exchange with pulmonary blood was estimated from the modeling results as VA = A · · A. This volume was scaled by the estimated fraction of imaged lung gas volume (FL) to compare it with Vgas. To estimate FL, it was assumed that the volume-to-perfusion ratio (VG/) was the same in the imaged and nonimaged lung. FL was then calculated as the ratio of the peak activity in the lung kinetics measured by the PET camera, assumed to be proportional to the blood flow to the imaged region, to the total injected activity, assumed to be proportional to T.
Shunt Volume of Distribution
The volume of distribution of 13NN in shunting blood and tissue was calculated from the modeling results as Vs = s · s. This volume was scaled by FL for comparison with the total imaged tissue volume, calculated as 
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Statistical Analysis
Least-squares linear regression was used to estimate all regression relations. Student's t-test for paired data was used to assess differences between the lavage supine and lavage prone conditions, and an unpaired Student's t-test was used to assess differences between the surfactant-depleted (lavage supine and lavage prone conditions) and normal sheep. Values are means ± SD.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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In the absence of shunt, simulated arterial and lung tracer kinetics during apnea showed increasing activity converging to a plateau (Fig. 3, A and D). The presence of shunt produced marked changes in tracer kinetics. As shunt increased, a prominent early peak was followed by a monotonic decrease toward a plateau. In the lung kinetics, this peak was primarily caused by decreasing plateau activities with increasing shunt; in the arterial kinetics, the peak was caused by rising peak activities with increasing shunt. Changes in s affected the arterial kinetics more markedly than the lung kinetics (Fig. 3, B and E). Increases in s slightly raised the peak of the lung kinetics and caused a slower decrease from the peak toward the plateau. In contrast, increasing s caused a marked decrease in the height and an increase in the width of the arterial kinetics peak. Changes in A had the least effect on the lung and arterial kinetics (Fig. 3, C and F), inasmuch as decreases in A caused a slightly greater decline in the lung kinetics plateau and a small rise in the arterial kinetics curve.
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Experimental Studies
Saline lung lavage caused deterioration of gas exchange, particularly in the supine position (Table 1). FsO2 was markedly higher for this condition than for normal and surfactant-depleted prone sheep (P < 0.01). Consequently, PaO2 was significantly lower in the surfactant-depleted supine than in the surfactant-depleted prone sheep (P < 0.01). Furthermore, although venous admixture, rather than shunt, was measured in the normal prone sheep, FsO2 values for this group were clearly lower than those in the surfactant-depleted groups. No change in cardiac output was observed for the different conditions. Consistent with these physiological observations, the transmission scans showed less aeration in the surfactant-depleted supine sheep than in the normal and surfactant-depleted prone sheep (Fig. 4).
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Tracer kinetics. During apnea, the lung and arterial tracer kinetics in the normal prone sheep showed convergence toward a plateau (Fig. 5), consistent with results of the simulations. In contrast, the kinetics from the surfactant-depleted sheep showed an early peak followed by convergence to a plateau. Measured peaks were more prominent in the lavage supine than lavage prone condition and in the arterial than lung kinetics. The peak for the arterial tracer kinetics was >10 times larger in the lavage supine condition (Fig. 5F) than in the lavage prone condition (Fig. 5E).
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In all cases, the model of arterial kinetics was able to accurately describe the measured data, as evidenced by high correlation coefficients (r2) and low residuals (R; Table 2). Identified Fs values were significantly higher for the lavage supine than lavage prone and normal prone conditions (P < 0.01). Also, Fs was higher for the surfactant-depleted prone than normal prone sheep (P < 0.05). Identified A values were significantly lower for the lavage supine than lavage prone and normal prone conditions (P < 0.01).
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The Monte Carlo analysis demonstrated that the identification algorithm was able to accurately estimate Fs, s, and A. The mean values of these parameters from the 100 simulations were within 3% of the true values at the observed noise level (noise) for the experimental data (Table 3). Furthermore, the parameters were identified within 17% of the true values at the exaggerated noise level (3 · noise).
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Sensitivity analyses using data from the lavage supine condition revealed that A was the most sensitive parameter to changes in the assumed values for Vcv,Fr, and r (Fig. 6). Estimates of Fs, A, and s for normal and surfactant-depleted prone sheep were less sensitive to changes in Vcv, with the mean Fs remaining unchanged, the mean s being identified within 14%, and the mean A being identified within 4% of the true value for changes in Vcv of ±12.5%.
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Estimates of Fs were correlated with FsO2 (r2 = 0.85, n = 11, P < 0.01) and with Fs,PET (r2 = 0.82, n = 11, P < 0.01; Fig. 7). The bias in Fs was 0.01 ± 0.11 relative to FsO2 and 0.01 ± 0.12 relative to Fs,PET. The relations between these parameters were described by Fs = 1.11 · FsO2 - 0.01 and Fs = 0.69 · Fs,PET + 0.06.
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(VA · FL)/Vgas, representing the fraction of the available gas volume participating in gas exchange, was significantly lower in the lavage supine condition (0.18 ± 0.09) than in the lavage prone (0.96 ± 0.28) and normal prone (1.28 ± 0.30) conditions (P < 0.01). In addition, (Vs · FL)/Vtis, representing the volume of 13NN distribution as a fraction of blood and tissue in the lung, was significantly higher in the lavage supine condition (0.46 ± 0.26) than in the lavage prone (0.05 ± 0.08) and normal prone (0.02 ± 0.03) conditions (P < 0.01).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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Simulations
In the presence of shunt, lung and arterial kinetics curves during apnea were characterized by two distinct portions (Fig. 3): an early peak and a subsequent plateau. A peak in lung kinetics is a manifestation of intrapulmonary shunt, whereas a peak in arterial kinetics is a manifestation of overall right-to-left shunt, including extrapulmonary shunt. The lung kinetics plateau corresponds to tracer that diffuses into and remains in alveolar gas spaces. The plateau in arterial kinetics corresponds to tracer that is reabsorbed by the pulmonary circulation.
Our numerical simulations showed that the model parameters (Fs, s, and A) had markedly different effects on lung and arterial tracer kinetics. Increased Fs leads to decreased plateau values in the lung kinetics and increased peak values in the arterial kinetics. The peak in relation to the plateau was larger in the arterial kinetics because of the low blood-gas partition coefficient of 13NN, which reduced the relative influence of the gas-exchanging compartment on the arterial kinetics. Thus arterial kinetics were more sensitive than lung kinetics to changes in Fs.
The shunt time constant s reflects the amount of blood and tissue in the shunting compartment per unit of shunting blood flow. Consequently, as s increased, the arterial kinetics showed lower peaks with prolonged time to reach a plateau, and the lung kinetics showed a slower decrease in activity from peak to plateau. Because of the greater relative influence of shunted activity on the arterial kinetics, s affected the arterial kinetics more than the lung kinetics.
A had the least effect on lung and arterial kinetics. Decreases in A reflect decreases in VG/ of aerated lung units. As VG/ decreases, more tracer will be reabsorbed from alveolar gas spaces and measured arterially (6, 21). The relative decrease in activity near the end of apnea in the lung kinetics due to such reabsorption was small. Changes in A were less marked on the arterial kinetics because of the relatively smaller influence of the aerated regions.
Method and Model Critique
Because of the large number of parameters and the nonlinear nature of the model, a global search for an optimum solution using all eight unknowns leads to multiple local solutions and consequent nonuniqueness in parameter identification. For this reason, we used a stepwise identification strategy and made the following simplifying assumptions to minimize the number of parameters and allow for a single, robust solution. 1) We used a compartmental approach with lumped parameters to model arterial 13NN kinetics and to estimate the model parameters. Compartmental models, despite their limitations (40), have been traditionally used to describe arterial tracer kinetics and to estimate right-to-left shunt and cardiac output (9, 11, 31, 37). The small residuals of the parameter estimation obtained in all cases with our model and the results of the Monte Carlo simulation showing robustness of identification corroborate the use of the compartmental model. Models with distributed parameters could be conceptually applied to this study. However, the complexity of the pulmonary and systemic circulation and the impracticality of describing their geometry and other physical properties in individual animals would increase the number of variables and involve additional assumptions, thus limiting the application of the model for parameter identification, an essential component of this study. 2) The mean convective transit time delays through shunting and gas-exchanging regions were assumed to be equal (ta). This is a reasonable assumption, provided that large fistulas between major pulmonary vessels or direct right-to-left shunts in the heart were not present (8). 3) Transit time heterogeneity due to distributions in capillary geometry and flow (1, 2) and axial diffusion were not included in the model. The overall effect on the identified parameters would correspond to an increase in the volumes of distribution. 4) A single mixing compartment with a fixed volume (Vcv) was used to represent tracer dispersion between the injection site and the lungs and between the lungs and the gamma counter. Although a more anatomically realistic representation would include separate compartments to account for mixing before and after passage through the lungs, the time constants of each portion would be of the same order of magnitude and, thus, difficult to discriminate on the basis of the arterial kinetics. 5) For the surfactant-depleted supine sheep, recirculated tracer was modeled by using a single mixing compartment and convective delay to represent the systemic circulation (see APPENDIX A). The single compartment and delay were shown to accurately describe the measured venous kinetics. In cases with substantial right-to-left shunt, modeling recirculation is necessary for accurate description of arterial tracer kinetics and parameter identification. In the study of a general case, the significance of shunt can be determined from a variety of sources, such as visual inspection of the arterial or pulmonary tracer kinetics, pulse oximetry, and arterial and mixed venous blood gas measurements.
The Monte Carlo analysis indicated that all parameters were identified exactly for the noise-free simulation. Parameter identification remained accurate at the observed levels of experimental noise. Even in the presence of exaggerated noise, parameters were identified within 20% of their true values. The largest residuals corresponded to the portion of the curve immediately before the peak region (Fig. 5), where the simulated kinetics rose sharply while the measured kinetics initially rose slowly. This slow rise was due to dispersion mechanisms not accounted for in the model, such as transit time heterogeneity, axial mixing, and multicompartment behavior.
The model was able to accurately describe measured arterial 13NN kinetics by including the effects of tracer reabsorption and, in surfactant-depleted supine sheep, recirculation. Previous attempts to estimate physiological parameters on the basis of arterial tracer sampling presented significant variability in humans (16, 25) and animals (6, 16, 25) in conditions with less lung injury than in our study. As discussed below, variability in shunt estimates is expected to be highest for measurements made in an ALI model because of the greater contribution of factors such as tracer reabsorption and recirculation. Nevertheless, the variability in Fs derived from the arterial tracer kinetics model was of the same order of magnitude as that reported in the literature. This suggests that accounting for tracer reabsorption and recirculation in our modeling allowed for the recovery of reasonable estimates of physiological parameters under the most unfavorable conditions.
Estimation of Physiological Parameters
Shunt fraction. Previous measurements of shunt using arterial samples of low-solubility tracers (krypton, tritium, xenon, and nitrogen) reported significant limitations because of tracer reabsorption ("backpressure") and recirculation (8, 16, 21, 22, 25). ALI is a condition associated with low VG/, which causes greater reabsorption, and increased shunt, which causes greater recirculation. Various methods, such as tracer rebreathing to estimate the amount of reabsorption (25) or diversion of recirculated blood (6), proved to be inaccurate or impractical. For the steady-state situation, the use of SF6, a gas with one-third the solubility of nitrogen, has been shown to yield the best estimates of shunt (13, 14). However, use of SF6 as a tracer does not allow for simultaneous PET imaging, and because SF6 is so insoluble, the time necessary to reach steady-state conditions (>20 min) (39) is much longer than the 60 s of apnea during which the PET and arterial 13NN kinetics measurements were made. Measurement of O2 shunt is not affected by backpressure or recirculation, but breathing 100% O2 may alter the physiological state by changing ventilation and perfusion distributions and causing O2 absorption atelectasis (6, 13, 16). Our method of measuring shunt by modeling arterial 13NN kinetics has the advantages that recirculation and reabsorption are accounted for, that 13NN does not affect pulmonary physiology in the concentrations used here, and that it can be performed simultaneously with PET imaging of the lung.
Differences are expected between Fs and FsO2, because they assess different anatomic pathways and are based on different physiological maneuvers (13). FsO2 assesses the contribution of unsaturated blood to the arterial blood. It is affected by extra- and postpulmonary shunts through bronchial veins, thebesian veins, anterior cardiac veins, and portal-pulmonary venous anastomoses. In contrast, Fs measures the fraction of the pulmonary blood flow that does not encounter aerated alveoli. Another important potential source of differences is the recently described oscillation in PaO2 throughout the respiratory cycle (3). Baumgardner et al. (3) presented evidence of cyclic recruitment of atelectasis in a rabbit model of ALI. With prolonged sampling of blood gases, such oscillations should not affect FsO2, because blood is sampled over several breathing cycles. In contrast, the described Fs measurement is performed during apnea at mean airway pressure and, thus, could be biased, particularly if apneic airway pressure does not result in a shunt equivalent to the mean shunt during the breathing cycle. Variations in the lung volume during apnea could add further bias to Fs. There are no data at this time on the dynamic relation between airway pressures and right-to-left shunt. A possible source of overestimation of Fs is that regions of very low VG/ were identified as shunt. The amount of measured arterial tracer concentration is inversely related to VG/ (6, 21). In this study, shunting and gas-exchanging regions were arbitrarily defined on the basis of their time constants. The lower limit for A and upper limit for s were set at 20 s, corresponding to VG/ = 0.3 s (e.g., a unit with VG = 3 ml and = 10 ml/s = 600 ml/min). Regions with VG/ < 0.3 s were identified as shunt. Other potential sources of error are the relative instability of physiological condition for severe lung injury and PO2 electrode-based errors (13, 32). Despite these differences, our estimates of Fs were significantly correlated with FsO2 with a mean bias of 1%. This confirms that Fs provides an estimate of right-to-left shunt.
Fs, an estimate of the overall right-to-left shunt, approximated Fs,PET, the intrapulmonary shunt assessed from PET, in most cases (Fig. 7). This supports the previous theoretical assumption that the initial fast drop in tracer activity during the apneic phase measured by PET corresponded to intrapulmonary shunt (9). Differences between Fs and Fs,PET may be attributed to extrapulmonary shunt or intrapulmonary shunt in regions outside the limited imaging field of our camera, in addition to experimental error and/or noise. Given that the imaging field does not include the entire lung, intrapulmonary shunt is only partially quantified with Fs,PET. The fact that Fs and Fs,PET were well correlated and did not show any bias indicates that the imaged lung was a reasonable representation of the total lung. Future studies using full-body cameras, which are currently available, will provide a complete assessment of intrapulmonary shunt and, thus, allow, in theory, for estimates of extrapulmonary shunt. Availability of these cameras will also permit the development of more robust mathematical models describing the lung and arterial kinetics simultaneously.
Shunt volume of distribution. In the absence of extrapulmonary shunt, Vs corresponds to the volume of tissue, intra- and perialveolar fluids, and capillary blood into which 13NN carried by shunting blood distributes during the pulmonary transit. Although this study was not designed to assess the factors contributing to changes in the magnitude of Vs, we can speculate that the parameter should increase, not only with the number of shunting alveolar units, as in "dry" reabsorption atelectasis, but also with the degree of alveolar flooding and/or lung edema of those units. If one assumes that the volume of tissue per unit of lung in the imaged region is representative of the whole lung, then Vs multiplied by the imaged lung fraction (FL) should scale with the imaged intrapulmonary tissue volume (Vtis). In an attempt to account for the variability of Vs due to the extent of the lung injury, we calculated (Vs · FL)/Vtis. (Vs · FL)/Vtis was significantly higher in our surfactant-depleted supine sheep than in surfactant-depleted prone sheep or normal sheep. This means that, in the supine position, a greater fraction of the intrapulmonary tissue was involved in shunt. We take this speculation with caution, because the sensitivity of the model to s, and thus Vs, varies proportionally to Fs. Thus, in situations when Fs is high and the estimation of tissue shunting volume is relevant, the model has its highest sensitivity to s. On the other hand, in the limiting case of Fs approaching zero, the simulated kinetics become totally insensitive to s. This probably explains the much greater variability of (Vs · FL)/Vtis in the normal and surfactant-depleted sheep in the prone position that had substantially less shunt.
Aerated lung volume of distribution. VA corresponds to the volume of alveolar gas in which the 13NN distributes during its transit through the lung. The volume of gas in unperfused units (alveolar dead space) or in conducting airways should not contribute to VA. If alveolar gas volume and blood flow were homogeneously distributed within the lung, ignoring the small contribution of the conducting airways, VA · FL would scale with the imaged intrapulmonary gas volume (Vgas). Consistent with this theory, the average (VA · FL)/Vgas was around unity in normal and surfactant-depleted prone sheep. In contrast, in surfactant-depleted supine sheep, this ratio was <0.2. This means that, in the supine position, only 20% of the available intrapulmonary gas participated in gas exchange. Thus our findings suggest that, in addition to the reported reduction in total gas volume and functional residual capacity during lung injury (10, 18, 19), there is also a reduction in the fraction of that volume effective in gas exchange. A corollary to this observation is that the volume of intrapulmonary gas, assessed with imaging techniques, may overestimate the true volume of gas participating in gas exchange during ALI.
Although A was sensitive to measurement error, the Monte Carlo simulations indicated that experimental error would not explain the fivefold discrepancy between VA · FL and Vgas in the supine position compared with the prone position. One possible explanation for that discrepancy could be that because of the use of 100% O2 inspired gas, mean alveolar volume was reduced as a result of rapid formation of reabsorption atelectasis during apnea. In APPENDIX B, evidence is presented that this is not the case. Another explanation could be that the mean alveolar volume could have been higher during breathing than during apnea because of the nonlinear shape of the pulmonary system pressure-volume curve. However, this is unlikely, because apnea occurred at a pressure equal to the mean airway pressure during breathing, resulting in a reduced number of collapsed units compared with the number of units that collapsed at the end of exhalation. Alternatively, fluid menisci could have formed intermittently, reducing the gas volume available for diffusion of 13NN. Further study of the dynamic relation between airway pressure and lung volume is necessary to substantiate these proposed explanations. Another potential explanation for the discrepancy could be the presence of substantial heterogeneity in local VG/. Mismatch of local VG/ would result in a lower global VG/ than that computed from the ratio of imaged gas to pulmonary perfusion. However, estimates of blood flow-weighted Vgas from our images minimally reduced the discrepancy between VA · FL and Vgas for the supine position. This suggests that, if responsible for the discrepancy, the heterogeneity in local VG/ must have occurred at a finer length scale than the imaging resolution of PET.
Other experimental and methodological considerations are expected to be less likely: 1) Fs was overestimated; because VA = A · (1 - Fs) · · T, an overestimation of Fs results in an underestimation of VA. 2) VCV was overestimated; overestimation of VCV causes an underestimation in A (Fig. 6) and, consequently, VA. 3) The larger percentage of conducting airways contributed to the total estimated aerated volume in the supine compared with the prone position. 4)FL was underestimated; calculation of FL was based on the assumption that VG/ of the imaged lung represented that of the whole lung. If the imaged perfusion fraction were less than the imaged aerated volume, FL would be underestimated.
Summary
A method was developed to estimate the overall right-to-left shunt and the volume of distribution of 13NN tracer in alveolar gas and shunt tissue on the basis of measured arterial kinetics of 13NN after an intravenous bolus injection. A mathematical model describing arterial tracer kinetics was developed that accounted for tracer reabsorption and recirculation. The model accurately fit experimental data from normal and surfactant-depleted sheep studied in prone and supine positions. The main conclusions of this study are as follows: 1) estimates of shunt derived from the model correlated well with estimates obtained from blood gas sampling and with estimates obtained by PET imaging, and 2) the volume of distribution of 13NN in perfused and aerated alveolar units was equivalent to PET-measured total lung gas volume in normal and surfactant-depleted prone sheep. However, in surfactant-depleted supine sheep, that volume of distribution was substantially smaller than the available intrapulmonary gas volume.
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APPENDIX A |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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tr, Fr, and r were identified by finding the set of values that minimized the squared difference between the simulated and measured venous tracer kinetics. This was done by first incrementally setting tr (relative to ta) from -5 and +5 s and then using the multilevel coordinate search optimization program (15) to find the best Fr and r for each value of tr. The parameter set that yielded the least overall squared difference among the four sets of data was then used to describe the venous kinetics of all surfactant-depleted sheep in the supine position. That parameter set of tr, Fr, and r was -4 s, 0.493, and 38 s, respectively. With the use of these values, the model was able to simulate the measured venous kinetics (Fig. 8). The parameters tr, Fr, and r are descriptive of the animal's peripheral circulation and tissues. Thus they are expected to change in different species, sizes, and disease conditions.
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APPENDIX B |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BDISCLOSURESREFERENCES |
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DISCLOSURES |
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TOPABSTRACT |
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) and model fits (ca, solid lines) for normal prone, surfactant-depleted prone, and surfactant-depleted supine sheep during the apneic period, along with residuals (R = cm - ca) from each experiment in the group. A–C: results from PET images and lung model. D–F: results from arterial kinetics and model. Contribution from recirculated activity (dashed line) is also shown in F. Lung tracer activity was normalized by total injected activity, and arterial tracer activity was normalized by injected tracer concentration. Shunt fractions estimated from each respective model are shown (Fs,PET and Fs). Correlation coefficients (r2) for arterial fits were 0.926 for D, 0.931 for E, and 0.992 for F. Note different scale used for y-axis to illustrate arterial kinetics in F compared with D and E.
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) values from surfactant-depleted supine sheep as a result of changes in assumed values of Vcv = 200 ml (A), Fr = 0.493 (B), and 
