INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

REGIONAL PULMONARY PERFUSION and ventilation are often measured noninvasively by means of nuclear imaging techniques and analyzed by using models of tracer kinetics to represent tracer fate. Spatial distribution of pulmonary perfusion has been measured with positron emission tomography (PET) after deposition in lung during first transit of intravenously (IV) injected tracer-labeled particles (⁶⁸Ga), water (H₂¹⁵O), and molecular nitrogen (¹³NN) dissolved in saline (6-8). Ventilation has been measured from alveolar clearance (washout) of ¹³NN previously equilibrated in a closed (rebreathing) circuit (6, 8). Of these three isotopes, only the tracer ¹³NN lends itself to measurement of both perfusion and ventilation. The validity of the perfusion measurement after an IV injection of ¹³NN gas dissolved in saline rests on the assumption that at first pass all tracer diffuses from pulmonary capillaries into aerated alveoli. Because of the low solubility of nitrogen in water and tissues, in normal aerated lungs, the ¹³NN tracer remains in the alveoli during a breath hold and its intrapulmonary distribution measured by PET is directly proportional to local perfusion (6). During the breathing period after apnea, the dominant mechanism of tracer removal is alveolar ventilation, resulting in exponential clearance of the tracer. Regional specific ventilation is then derived from the clearance rate constant and represents ventilation per unit of perfused lung volume. The process is complicated in lungs with pulmonary pathology involving atelectatic or edematous lung units because the injected ¹³NN tracer is not retained in these units during breath hold and, instead, is reabsorbed by shunting blood. Therefore, in the presence of shunt, raw PET images of ¹³NN content collected during apnea cannot be directly used to quantify perfusion. Also, simple clearance analysis of ¹³NN during a washout period of ventilation cannot separate tracer removal by shunting blood from that by ventilation in regions including aerated and nonaerated alveolar units. In this paper, we present a three-compartment tracer kinetic model that was used to assess regional perfusion, shunt blood flow fraction, and specific alveolar ventilation of perfused and aerated alveoli. The model accounts for tracer transit from injection site to alveoli and alveolar removal of tracer by shunted blood flow and ventilation. The model was applied to PET images obtained from normal dog lungs and from dog and sheep lungs experimentally injured with IV oleic acid, smoke inhalation (14), and bilateral surfactant depletion simulating conditions in acute respiratory distress syndrome. The model, its relevant assumptions, and methods of parameter identification are described, and the sensitivity of derived parameters to expected and exaggerated levels of experimental noise is examined.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

Experimental Data

We used two PET cameras to collect experimental data analyzed in this paper: a single-slice prototype camera PCR1, described previously (12, 13), and a PC-4096 PET scanner (Scanditronix) that imaged 15 contiguous slices of 6.5-mm separation. Collected sinograms were reconstructed into tomographic images by using a convolution-back-projection algorithm yielding an effective spatial resolution of 7.0 mm for multiring PET camera images and 10 mm for single-ring PET camera images. Image reconstruction included corrections for nonuniform crystal sensitivity and gamma-ray energy attenuation in body tissue and PET camera supporting structures. Reconstructed images, in units of radioactivity per cubic centimeter of imaged volume, were used to calculate tracer-averaged kinetics data from regions of interest (ROI) defined as follows. First, a unity mask was defined manually over the imaged lung field with all pixels in extra-pulmonary regions set equal to zero. Three ROI of equal height [nondependent (ND), middle (M), and dependent (D)] were defined by horizontal lines. The volume of each ROI was calculated from the corresponding number of voxels and were typically 25, 50, and 25% of the volume of the mask for the ND, M, and D regions, respectively.

Average specific activity in each ROI was then calculated from each sequential image. The resulting tracer kinetics data were decay corrected (¹³NN half-life = 9.96 min) to a reference time taken as the onset of intravenous injection. Infusate-specific activities were measured in a radiation counter previously cross-calibrated with the PET camera. This activity was also corrected to the same reference time as the tracer kinetics data. Tracer kinetics data were then plotted vs. time, with each data point plotted in the middle of its image-collection time interval.

Tracer Kinetic Model and General Assumptions

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Model schematic showing an initial compartment with effective mixing volume VH. The model represents mixing and dilution of intravenously injected 13N-labeled molecular nitrogen (13NN)-labeled saline in pulmonary arterial blood. Tracer output concentration Cpa(t), time-shifted by tTD, is the input to the imaged section of the lung, which consists of 3 regions of interest (ROI): nondependent (ND), middle (M), and dependent (D). Each ROI is comprised of 2 compartments: aerated (A) and shunt (S). Time-dependent tracer content after injection is associated with each compartment in an ROI and described by its differential equation. Dashed lines emanating from the middle ROI point to representative tracer content curves. Regional tracer is the sum of the aerated and shunt compartment tracer contents and represents the signal continuously integrated and then averaged by the positron emission tomography (PET) camera yielding average tracer content (i) per ROI. See APPENDIX A for definitions of other abbreviations.

The function Cpa(t + t_TD) is then used as input to the D, M, and ND ROI, each with a net regional perfusion flow rate _R. Alveolar units of each ROI are lumped into two independent parallel compartments. One compartment represents aerated units with regional tracer concentration CA(t) and volume of distribution VA. This compartment is continuously perfused with a blood flow A and is ventilated with specific alveolar ventilation sA starting at the time at which mechanical ventilation is restarted after apnea (t_v). The second compartment represents airless (fluid-filled or collapsed) alveolar units with regional tracer concentration CS(t) and volume of distribution VS. This compartment is perfused with a shunt flow S and is never ventilated. Regional perfusion _R is the sum of perfusion to these two compartments: _R = A + S. Total tracer content of each region VACA(t) + VSCS(t) is used as an input function to a PET camera module that calculates for each image, i, the regional average tracer content _i. This model makes four general assumptions: 1) Tracer is distributed uniformly in each compartment. 2) Tracer is distributed in aerated alveoli in amount proportional to local perfusion. 3) Tracer transport between compartments or ROI caused by diffusion, cardiogenic motion, or rebreathing is negligible. 4) Perfusion and ventilation are invariant during the apneic and washout imaging periods.

Model Equations and Specific Assumptions

Mixing and transport of infused bolus. Tracer entering the right heart (and pulmonary blood) compartment has two sources: 1) tracer in saline solution infused, from t = 0 to length of time during which ¹³NN-labeled saline is infused (t_inf), as a bolus at rate _I and specific activity C_I, and 2) recirculating tracer with specific activity C_R returning to the heart at flow rate equal to the cardiac output T. The net rate of change of tracer concentration in the right heart compartment is approximated by

(1)

if we assume that cardiac output is much greater than tracer infusion rate.

Regional tracer kinetics. Tracer, at a concentration Cpa(t), enters the aerated alveoli compartment at perfusion rate A and is removed simultaneously by the pulmonary venous blood flow at concentration Cv and by alveolar ventilation A at concentration CA(t). To account for intraregional heterogeneity in ventilation, when appropriate, the aerated compartment is subdivided into two compartments (i = 1 for a "fast" compartment and i = 2 for a "slow" compartment), each with its respective perfusion and ventilation rates. The rate of change of tracer content in each aerated subcompartment is therefore

(2)

To further simplify Eq. 2, we assume full equilibration of the tracer between end-capillary blood and alveolar gas with Cv determined by the product of C_Ai times the nitrogen gas-water partition coefficient (_A = 0.018). In that condition, removal of tracer by pulmonary blood may be assumed to be negligible. We also assume that the volumes of tracer distribution, VA_i, of each aerated compartment is equal to the regional volume of gas. [Regarding this latter assumption, as pointed out by Schuster (9), the volume of distribution of tracer depends on the number of perfused alveoli. Because some aerated alveoli may not be perfused by tracer-labeled blood, gas volume in a region may be larger than VA.] With these assumptions, and taking the total regional perfusion as the sum of perfusion rates to aerated and to shunted compartments, Eq. 2 may be rewritten for each subcompartment i as

(3)

where total regional perfusion to the aerated region is ₁ + ₂ = A. It is understood that for conditions in which a single compartment is appropriate, one of the regional perfusions rates, ₁ or ₂, is zero, whereas the other is equal to A.

Regional index of specific ventilation. To provide an index of ventilation for the aerated compartment in the presence of a two-compartment model of ventilation, we defined sA as a perfusion-weighted average of the specific ventilation of each subcompartment, i.e.,

(4)

Regional shunt compartment. Intrapulmonary shunt refers to deoxygenated blood that enters the pulmonary venous circulation without passing through aerated alveolar units. In these nonaerated units, tracer removal occurs only by back-diffusion into pulmonary blood at a tracer concentration CS(t). By analogy to Eq. 3, the rate of change of regional tracer content of a shunt region is

(5)

where the model parameter _S = V_S/S is a transport time constant. An implicit assumption in Eq. 5 is that the nitrogen partition coefficient between blood and atelectatic, edematous, and/or interstitial fluid is 1.0.

PET camera module. Total regional tracer content VA₁CA₁(t) + VA₂CA₂(t) + VSCS(t), the input function to the PET camera module, is normalized by the image collection time t_img and by regional organ volume to be expressed in terms of instantaneous tracer radioactivity per voxel. Given that the PET camera effectively averages the radioactivity originating from each voxel, a tracer kinetics data point S_i for a given ROI from an image collected between times t_i and t_i + t_img is equivalent to

(6)

Tracer recirculation. From our studies, we have observed that, even in severely injured lungs, tracer content from nondependent regions does not decrease during the postinfusion apneic period. This observation suggests the absence of shunt in these nondependent regions even when substantial shunt is evident in the rest of the lung. Also, in lungs with high levels of shunt in dependent and middle regions, we observed a slow but progressive increase in tracer concentration in nondependent ROI starting after the first 20-30 s of apnea (see Fig. 5). Given that during that time no tracer was infused into the animal, we attributed this increase in activity to recirculating tracer that had bypassed nonaerated alveoli. In cases in which such tracer content increase was observed in the nondependent ROI, the specific activity of recirculating blood, C_R, was defined as a step function starting at time t_r with height equal to C_R and ending t_r seconds after the initiation of the washout period. Such a tracer concentration was assumed to be the same for all ROI, and tracer leaving the lung after the initiation of ventilation was neglected.

Nonlinear Parameter Identification

PET imaging data for each ROI was normalized by total injected activity. This normalization allowed us to use a unit area pulse of height equal to the reciprocal of the injection time as input to the model. Because the time required for the algorithm to converge roughly increases exponentially with the number of model parameters, to shorten computation time each ROI was analyzed individually and its parameters were identified in two phases. First, parameters related to pulmonary perfusion, shunt fraction, and shunt compartment transport rate constant were identified by analyzing exclusively the PET data obtained during the apneic period. Then, parameters related to ventilation were identified by running the NLID model with perfusion-related parameters kept constant at the previously identified values. Details of the parameter identification scheme and the selection of initial parameter guesses are presented in APPENDIX B.

Parameter Sensitivity Analysis

Each data set was analyzed with the NLID model in the manner described above, for which values of the parameters t_TD, _R/T, S/_R, and sA were obtained. Identified parameters were recorded, and the model ran with these parameters to define noise-free data sets. These noise-free data sets were perturbed in proportion to expected and exaggerated noise levels in the following way. The coefficient of variation (cov) of expected noise corresponding to each ROI in each image was assumed to be inversely proportional to the number of radioactive decay events detected in that ROI and directly proportional to a constant reported previously for this camera (13). A pseudorandom number generator was used to define a series of 10 elements from a normal distribution with a unity variance and mean value equal to zero. The expected cov array was multiplied element by element to this random series and unity was added before multiplying element by element this resulting array to the noise-free data set. This method produced noise-perturbed tracer kinetics data with a cov in each ROI and image equal to that of the expected corresponding noise. Each of the two noise-free data sets (corresponding to a normal and an injured lung) was perturbed 10 times by use of this method, and the process was repeated for 8 and 16 times the expected noise levels. Each of the perturbed data sets was reidentified with the NLID method described above to estimate the variability of the parameters caused by the three levels of noise. Mean deviations from the noiseless parameters and the corresponding standard deviations (SD) of the reidentified parameters were calculated.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

The model had excellent fit to experimental data from normal and acute respiratory distress syndrome (ARDS) lungs, allowing quantification of t_TD, _R/T, S/_R, _S, and sA. Examples of model simulations fitted to experimental data under different physiological conditions are presented in Figs. 2-4. In those examples, and in all the data reported in the accompanying paper (14), the model fitted the data with regression coefficients R² > 0.99. Thus the model accounted for more than 99% of the total variance in the experimental PET data.

View larger version (24K): [in this window] [in a new window]   Fig. 2.   A: model-simulated tracer content functions VACA(t) and VSCS(t) for the dependent ROI of a normal dog lung. B: model-simulated tracer content function created by adding the 2 curves in A to give VACA(t) + VSCS(t). Image data () represent average tracer content over the imaging period and are plotted at the middle of the corresponding image-collection time interval.

View larger version (20K): [in this window] [in a new window]   Fig. 3.   A: model-simulated tracer content functions VACA(t) and VSCS(t) for the dependent ROI of an acute respiratory distress syndrome (ARDS) dog lung induced by oleic acid. B: model-simulated tracer content function created by adding the 2 curves in A to give VACA(t) + VSCS(t). Image data () represent average tracer content over the imaging period and are plotted at the middle of the corresponding image-collection time interval.

View larger version (22K): [in this window] [in a new window]   Fig. 4.   A: model-simulated tracer content functions VACA(t) and VSCS(t) for the middle ROI of ARDS sheep lungs bilaterally depleted of their surfactant. B: model-simulated tracer content function created by adding the 2 curves in A to give VACA(t) + VSCS(t). Image data () represent average tracer content over the imaging period and are plotted at the middle of the corresponding image-collection time interval.

Figure 5 shows tracer kinetics data from a surfactant-depleted sheep lung.

View larger version (14K): [in this window] [in a new window]   Fig. 5.   ND, M, and D ROI tracer kinetics data from a bilaterally surfactant-depleted sheep lung. High levels of shunt flow are evident in the M and D ROI from the drop of activity occurring during the apneic period. Note in contrast the slow but progressive increase in tracer content in the nondependent ROI (from the third data point onward), suggesting that recirculating tracer shunted through nonaerated alveoli.

Parameter Sensitivity Analysis

View larger version (8K): [in this window] [in a new window]   Fig. 6.   Effect of expected and exaggerated levels of experimental noise on the estimates of regional perfusion parameter, R/T, for control and ARDS data. Noise-free parameter value corresponds to the dashed lines in the plot, and data points represent the average of the 10 model-identified values from noise-perturbed data. Error bars are ±SD.

View larger version (8K): [in this window] [in a new window]   Fig. 7.   Effect of expected and exaggerated levels of experimental noise on the estimates of shunt-fraction parameter, S/R, for control and ARDS data. Noise-free parameter value corresponds to the dashed lines in the plot, and data points represent the average of the 10 model-identified values from noise-perturbed data. Error bars are ±SD.

View larger version (9K): [in this window] [in a new window]   Fig. 8.   Effect of expected and exaggerated levels of experimental noise on the estimates of the shunt-compartment time-constant parameter, S, for control and ARDS data. Noise-free parameter value corresponds to the dashed lines in the plot, and data points represent the average of the 10 model-identified values from noise-perturbed data. Error bars are ±SD.

View larger version (8K): [in this window] [in a new window]   Fig. 9.   Effect of expected and exaggerated levels of experimental noise on the estimates of the ventilation parameter, sA, for control and ARDS data. Noise-free parameter value corresponds to the dashed lines in the plot, and data points represent the average of the 10 model-identified values from noise-perturbed data. Error bars are ±2 SD from average.

The shunt transport time constant, _S, for a normal lung ROI deviated from a noiseless value of 6.3 s by 0.52, 0.93, and 1.16 s in average with cov (=SD/mean) of 0.094, 0.018, and 0.19 for noise levels of 1, 8, and 16 times the expected experimental levels, respectively. For the ARDS lung data, average deviations of _S from a noiseless value of 6.8 s were 0.09, 0.35, and 1.05 s with respective cov of 0.001, 0.07, and 0.16. The parameter S/_R had average deviations from normal data of 0.4, 1.8, and 2.9% for the respective increasing levels of noise and of 0.02, 1.1, and 2.3% in the ARDS data for the respective levels of noise.

For the normal lung data, the parameter _R/T deviated from the noise-free value by only 0.14, 0.43, and 0.52% for 1-, 8-, and 16-fold levels of noise above expected values. For the ARDS data, the mean deviations were 0.06, 2.17, and 5.6% for the corresponding levels of noise.

Finally, for the same increasing levels of noise, the parameter estimates of sA in the normal lung data deviated in average by 0.85, 2.98, and 2.97% from the noiseless value, and in the ARDS lung data the parameter estimates deviated by 0.19, 4.81, and 9.96%, respectively.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

We developed a multicompartmental model for analysis of ¹³NN tracer kinetics data from PET images collected after intravenous bolus injection of ¹³NN-labeled saline solution during a transient period of breath hold (apnea) and during subsequent ventilatory clearance of tracer (washout). The model was successfully used to analyze PET data obtained from animals with experimentally altered pulmonary physiology including sheep lungs imaged 1, 2, and 4 h after exposure to cotton smoke inhalation, as presented in the accompanying paper (14). Using a nonlinear parameter identification routine, we fitted the model predictions to experimental data to yield regional parameters of perfusion fraction _R/T, shunt fraction S/_R, and specific alveolar ventilation sA. Model-simulated data with these parameters accounted for more than 99% of the variance in the experimental data. The most significant improvements of this model over existing methodologies using radiolabeled microspheres or ¹⁵O-labeled water are 1) the ability to separate regional perfusion into shunt and gas-exchanging fractions and 2) the ability to account for two competing mechanisms of tracer removal during the washout: transport by shunt flow from nonaerated spaces and by ventilation from aerated spaces.

Pulmonary blood flow determined from distribution of tracer-labeled microspheres has the advantage that measured tracer content is linearly related to regional blood flow over a wide physiological range. However, the typically long half-life of tracer-labeled microspheres restricts the ability to conduct multiple studies in the same subject. Also, microspheres may be subject to artifacts that include clustering and streaming in the pulmonary vasculature. Furthermore, microspheres lodge in small precapillary arterioles of the lung, irrespective of whether those pulmonary blood vessels feed aerated or nonaerated shunting alveolar units. Regional perfusion data evaluated from the distribution of microspheres therefore cannot distinguish between flow to gas-exchanging or shunting regions. More importantly, ventilation cannot be assessed from microsphere data.

Measurements of pulmonary blood flow using water labeled with H₂¹⁵O water (half-life ~2 min) are repeatable, and the data have been shown to correlate with data obtained from microspheres over a wide range (7). That method has the additional advantage that measured tissue activity reflects local tissue water content because H₂¹⁵O diffuses freely into and out of vascular and extravascular spaces. However, the short residence time of this tracer in the lung (<20 s) necessitates the collection of short-duration images, limiting the signal-to-noise ratio and/or the spatial resolution of the resulting PET images. Furthermore, the single-compartment model used to analyze H₂¹⁵O data requires the assumptions that tracer is fully extracted during a single pass through the lung and that the partition coefficient for the tracer describes the equilibrium ¹⁵O distribution volume in the tissue divided by its distribution volume in blood (7). Because the density of lung tissue varies throughout the thorax depending on local transpulmonary pressures, the partition coefficient for H₂¹⁵O is expected to vary within the lung, thereby requiring its independent measurement, before assessment of the regional distribution of blood flow. Finally, the measurement of blood flow with H₂¹⁵O cannot quantify regional shunt fraction or regional ventilation.

Use of ¹³NN gas as a tracer is nearly ideal for the assessment of lung function. Nitrogen gas is biologically inert, and ¹³NN-labeled molecular nitrogen can be dissolved in aqueous saline to obtain sufficiently practical specific activity for imaging during intravenous infusion. Rhodes et al. (8) pioneered tomographic measurements of regional ventilation-perfusion ratio during constant infusion of ¹³NN-labeled saline solution. Mijailovich et al. (6) added to that technique the measurement of regional perfusion after injecting a single bolus injection of the labeled saline during apnea. However, the primary assumption of these techniques, namely that ¹³NN gas resides only in aerated spaces, breaks down in lungs with atelectatic or edematous alveolar units.

Our analysis of ¹³NN tracer kinetic imaging expands the previous techniques for use in pathological lungs and makes it possible to identify the fractions of blood flow reaching gas-filled and fluid-filled or collapsed alveolar units. Because of the low solubility of nitrogen in water and blood, as the bolus of ¹³NN reaches aerated alveolar units most of the tracer (98%) diffuses from the capillary bed into alveolar airspace during the first pass and remains there for the duration of a short apneic period of imaging (6). Although interregional mixing, by diffusion or cardiogenic oscillations, may alter the local distribution of ¹³NN during apnea, this effect has not been found to be important at spatial length scales equal to or greater than the resolution of our PET images (7.0 mm for images collected with the multiring PET camera and 1.0 cm for images collected with the single-ring PET camera). Thus, in healthy and fully aerated lung units, local tracer content is directly proportional to local perfusion, and PET images collected during the postinfusion apneic period yield a direct measurement of regional perfusion distribution. Subsequent ventilatory clearance rate of ¹³NN (washout) is then representative of regional ventilation of perfused and aerated lung units.

The need for the more sophisticated model presented in this paper arises when aerated and nonaerated alveolar units coexist within an ROI. In contrast to what happens when ¹³NN reaches aerated units, when it reaches atelectatic or edematous alveolar units, tracer content rises to a peak value and then decreases exponentially toward an asymptote. This drop in tracer content is caused by reabsorption of the ¹³NN gas into the pulmonary circulation because there is no preferential solubility between blood and collapsed, or fluid-filled, alveolar spaces. If peak tracer content value is taken as an index of total regional perfusion, the asymptotic value would represent the fraction of blood flow reaching aerated alveolar units, and the relative drop in activity provides direct assessment of regional shunt fraction. Unfortunately, the peak and asymptote values are difficult to measure or extrapolate from PET data, plus there are two different mechanisms removing regional tracer during the ventilation-washout period: shunt in atelectatic or edematous units and ventilation in aerated units.

As a first approximation, we described a method to quantify regional perfusion and shunt flow by back-extrapolating regional tracer concentration to the time of arrival and then estimating the shunt fraction by curve fitting the tracer kinetics data (10). Application of that method to unilaterally surfactant-depleted dog lungs after lavage with Tween-80 yielded values of S/_R ranging from 80 to 95% in dependent lung regions with a tissue-to-water content ratio of 70-95%. A shortcoming of that method became evident when long infusion times were used. In those cases, tracer reaching nonaerated units clearly shunted away before the end of the injection, leading to an underestimation of total perfusion and shunt. For example, data for a dependent ROI in a bilaterally lavaged lung analyzed with that method yielded a regional perfusion of 16.5% of the total cardiac output and a regional shunt fraction of 68%. This result underestimates the regional perfusion of 23.79% and the regional shunt fraction of 81.07% obtained by using our new method.

The general approach that we adopted to formulate the model was to use the minimum number of compartments capable of simulating the injected ¹³NN tracer kinetics yielding a good fit (R  0.99) to our experimental data. To accomplish this, we lumped regional blood flow into nonaerated and aerated subcompartments and assumed that regional washout from aerated units in a compartment followed a single or double exponential model. These are oversimplifications of a system that has been shown to have regional heterogeneity at length scales much smaller that those of the ROI used in this study (12). The model, however, is able to estimate an average regional behavior and with greater computing power may be used to analyze data from substantially smaller ROI, as discussed below. We also made simplifying assumptions to model the effect of tracer recirculation by assuming a constant tracer concentration in the venous return during a period equal to the duration of the breath hold. To qualify these assumptions, we stipulated that unless extremely high levels of shunt and low levels of ventilation are present, the amount of recirculation should rapidly decrease as the tracer is washed out from the lungs. Although tracer recirculation is minimal in normal lungs, it is not insignificant in injured lungs and can have a measurable effect on the measured tracer kinetics of lungs with substantial amounts of shunt. We observed that effect on nondependent ROI of ARDS lungs with large shunt levels by noting that, after 20-30 s, regional tracer content began to monotonically increase in that region. Given that no tracer was being injected during that time, we concluded that such an increase had to be caused by recirculation of tracer bypassing the lungs via shunting regions. We acknowledge that tracer recirculation could have been modeled with lumped compartments to represent the tracer kinetics along the systemic circulation. However, adding these compartments would have enlarged the model with new parameters that are difficult to assess independently. In future studies, we plan to refine the model to include the systemic circulation and extend our experimental measurements to assess the tracer concentration of the mixed venous blood during the PET imaging period. Finally, we acknowledge that mechanisms other than tracer recirculation (a second-order effect) could have been responsible for the slow increase in tracer content during apnea in the nondependent ROI of injured lungs. One could, for example, theorize that, owing to the interregional gradients in blood flow, regional gradients in tracer content could have been responsible for diffusive intraregional transport during the apneic period. This mechanism, however, is unlikely to be responsible for the increase in ND activity seen in shunting lungs because in normal supine lungs no increase in tracer content was observed in ND ROI despite the large ventro-dorsal gradients in tracer concentration.

A parameter-identification scheme was designed to minimize the computation time of the identification algorithm. The scheme consisted of analyzing the tracer kinetics data in two parts: first the data collected during apnea to identify _R/T, S/_R, and _S, and second the data collected during the washout period to obtain regional sA. By identifying the perfusion-related parameters independently, the number of identified parameters was reduced from four to three for the single-compartment model or from six to three for the dual-compartment washout model. In addition, we used objective methods to define initial parameter guesses and realistic boundaries to further reduce the computation time.

Studying the sensitivity of the model parameters to different levels of imaging noise was important to test the robustness of the modeling approach and to extrapolate the usefulness of the model to analyze experimental data with higher levels of noise. High noise levels can occur when the injected activity of the ¹³NN-labeled saline is low, the sizes of the ROI are small, or short-duration images are required. We evaluated parameter sensitivity to experimental noise by use of the standard Monte Carlo approach. As discussed by Eidelman et al. (3), the Monte Carlo approach can be used to determine confidence on any model parameter regardless of its relation to the dependent variable of the model. This was the only viable approach to test the sensitivity to noise of our model, given the complexity of its structure and the iterative process of the parameter identification procedure. To conduct the Monte Carlo simulations with data from realistic distributions of these parameters, we started by fitting experimental data, collected with a single-ring PET camera whose noise characteristics had been well documented (13), in two representative conditions (normal and ARDS lung). These data were then used to recreate noise-free data sets that were perturbed 10 times each for 1, 8, and 16 times the expected noise level. For each noise-perturbed data set, all four parameters were reidentified and then compared with their respective original values. As expected, variability of the identified parameters systematically increased as noise levels were increased. For example, as the level of imaging noise was increased by 16 times from the expected value, the identified values of _R/T had an increased deviation around the noiseless values from 0.14 to 0.5% for the normal lung data and from 0.06 to 5.6% for the ARDS lung data. Likewise, the 16-fold increase in noise increased the mean deviation of identified S/T around the noiseless values from 0.4 to 2.9% and from 0.02 to 2.3% in the normal and surfactant-depleted lung data, respectively. The shunt compartment time constant, _S, was relatively the most sensitive parameter to noise, with a cov that changed from 0.094 to 0.19 and from 0.001 to 0.16 for the normal and ARDS lung data sets, respectively. All together, the low deviations of these parameters demonstrate the robustness of the model and the parameter-identification scheme against exaggerated levels of experimental noise. We conclude that these parameters could be calculated to within 10% accuracy in ROI that would be reduced in volume by a factor of 256. For _S, accuracy under the same conditions is within 20%.

In summary, we have developed a model to analyze regional tracer kinetics obtained with PET after an apneic IV bolus infusion of ¹³NN-labeled saline and a subsequent washout period. The model quantifies regional perfusion, shunt fraction, and specific ventilation and overcomes two important limitations of previous methods of analysis: 1) it can separate intraregional perfusion into gas-exchanging and shunt flow and 2) it can account for parallel mechanisms of regional tracer removal by ventilation from aerated spaces and by shunting blood flow in nonaerated spaces. Model-fitted data accounted for >99% of experimental ROI data for both normal and injured lungs presented in the accompanying paper (14).