Jehangir K. Tajik, Binh Q. Tran and Eric A. Hoffman
Division of Physiologic Imaging, Department of Radiology
University of Iowa College of Medicine
Iowa City, IA 52242
Microvascular red blood cell mean transit time is a crucial parameter underlying basic pulmonary physiology. Dynamic x-ray CT imaging during bolus radiopaque tracer injection offers the ability to make functional measurements throughout the lungs, but is not able to resolve individual microvascular beds. We have implemented a model-free Fast Fourier Transform deconvolution algorithm to extract the microvascular transport characteristics from the acquired time-intensity data. The deconvolved feeding arterial bolus input curves and corresponding regional pulmonary parenchymal "response" functions provide measures of regional pulmonary tracer residence times, allowing calculation of microvascular transit times for different spatial regions of the pulmonary system. The acquired feeding (main) pulmonary artery and regional pulmonary parenchyma time-intensity curves were fit to gamma variate functions which were then sampled with a temporal resolution of 0.1 seconds. Deconvolution of the feeding arterial and regional parenchymal curves consistently results in bimodal regional residue functions. The two modes consist of a relatively large, sharp, narrow peak approximating a delta function followed by a smaller more dispersed curve. The sharp, narrow peak appears to be due to small artery inclusion in the sampled parenchymal region (partial volume effects). The magnitude of the dominant arterial peak decreases as sampling locations are moved from the less expanded dependent to the more expanded non-dependent lung regions of supine dogs. Mathematical separation of the two modes allowed isolation of the arterial and microvascular components. The shape and transit times of the putative microvascular components agree well with results from similar measurements via microfocal angiography and in vivo microscopy. Reconvolving the microvascular component with the input curve results in a corrected parenchymal curve representing the regional microvascular transport characteristics, free of arterial flow signal contamination. The corrected residue curves can then be used for non-invasive in vivo quantitation of regional organ microvascular transit times, volumes and flows in relation to the existing in vivo anatomy.
Keywords: mean transit time, pulmonary imaging, computed tomography, regional perfusion, physiologic imaging, electron beam CT, lung, pulmonary physiology
The mean transit time (MTT) of red blood cells (RBC) through the pulmonary microvascular bed is a measure of the time RBC spend at the alveolar-capillary interface and thus the amount of time available for gas exchange to occur. Quantitating pulmonary microvascular MTT's and elucidating the factors influencing the spatial (re-)distribution of MTT's is, therefore, important in understanding basic pulmonary physiology in both normal and disease states.
Dynamic x-ray CT imaging of the pulmonary system when combined with a suitable radiopaque tracer agent, offers the ability to make detailed measurements of regional pulmonary function simultaneously throughout the lungs in three dimensions. Electron beam CT (EBCT) [1], with 50 msec slice acquisition times and fast scan repetition rates, is well suited for studying dynamic events in the cardiopulmonary system. With 50 msec slice acquisition times, EBCT allows stop action imaging of the heart, minimizing cardiogenic motion artifacts in the lung field of the reconstructed images. The fast scan repetition rate permits imaging of bolus radiopaque tracer passage through the lung field, so that ECG-triggered imaging during a brief breath hold (approximately 15 heart beats) can thus provide detailed time-intensity curves throughout the lung parenchyma.
The simplest method of interpreting the time-intensity curves is to assume the entire bolus is delivered to the regional microvascular bed prior to tracer washout from the region of interest (ROI). Regional flow under these circumstances is calculated as the ratio of the regional opacification (due to contrast accumulation in the ROI) to the total bolus input (integral of the feeding pulmonary artery time-intensity data) [2,3,4,5]. This model assumes negligible indicator washout from the sample prior to the peak of the regional time-intensity curve. Though this model has been validated in a glass bead phantom, the in vivo validation of the assumption remains untested.
More importantly, whole body CT scanners are not able to resolve individual capillary beds, so that even small (3 voxel x 3 voxel) samples placed in the lung field most certainly contain potentially contaminating flow signals from structures (i.e. small arteries and veins) in addition to the microvascular bed. Since we are primarily interested in the microvascular flow and transport characteristics, a method is needed to extract the microvascular signal from the acquired time-intensity curves.
The EBCT scanner operates in a high temporal resolution mode (multi-time point imaging) or in a high spatial resolution mode (volumetric imaging). In the high temporal resolution mode, the electron beam is magnetically steered sequentially along 4 tungsten target rings encompassing 210 degrees about the subject. X-rays produced from each target ring are focused onto two detector rings so that up to 8 spatial levels may be acquired at each time point. Each pair of images is gathered within 54 milliseconds followed by a 8 millisecond pause as the beam is reset for the next target ring. All 8 spatial levels are therefore acquired within 224 milliseconds. The axial resolution for the multi-time point imaging mode is 1.5-3.0 mm if only a single tomographic slice is to be acquired over multiple time points or 7 mm if the multi-slice mode (up to 8 spatial tomographic levels covering 7cm) is used in conjunction with multi-time point imaging.
The acquired time-intensity data were fit to gamma variate functions [6] and, based on our preliminary results, the gamma variate functions were sampled with a temporal resolution of 0.1 seconds.
We have obtained regional perfusion data using dynamic EBCT to follow bolus radiopaque contrast passage through the lung field in both dogs and pigs.
Preliminary results from deconvolving a feeding arterial time-intensity curve (TIC) and regional parenchymal TIC's are based on image data from a supine dog imaged at functional residual capacity. The feeding pulmonary artery and regional parenchymal time-intensity data were fit to gamma variate functions [6] which were then used in our deconvolution based assessment of regional pulmonary transit times and flow.
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We have found deconvolution via the ``straight'' FFT method to be inadequate since the reconvolving the input function with the deconvolved residue functions do not match the original output curves (figure 1). Furthermore, deconvolution by limiting the number of FFT terms to the minimum needed to accurately represent the time-intensity curves (30 terms) yields an oscillatory residue function which still does not match the original output curve upon reconvolution with the input (PA) function (figure 2).
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A filtered FFT deconvolution scheme has been found to recover satisfactory residue functions which were verified by reconvolution with the input TIC to obtain curves that matched the original output TIC (figure 3).
Where 
= Fourier Transform of feeding pulmonary artery time-intensity curve and
= Hanning Window (weighting function).
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We have found that deconvolution of the feeding pulmonary artery and regional parenchymal TIC's consistently results in bimodal regional residue functions consisting of an overlapping sharp, narrow peak and a second more dispersed peak (figure 3). The sharp, narrow peak is likely due to partial volume sampling of small arteries since regional residue functions of samples containing a visually apparent arterial vessel contain virtually only the prominent sharp, narrow peak (figure 4).
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The putative arterial and microvascular residue function components have been separated by modeling the bimodal regional residue function as the sum of two gamma variate curves and using the non-linear least squares method to identify the arterial and microvascular curve parameters (figure 5).
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After the regional arterial and microvascular curves had been isolated from the bi-modal residue function, we noted a reduction in the amplitude of the arterial component as sampling locations were moved from dependent to non-dependent lung regions (figure 6).
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Normalizing the isolated arterial component to unit area and reconvolving with the feeding PA (input) TIC yields essentially a time-delayed input time-intensity curve, supporting our belief that this peak represents partial volume sampling of small arteries. Reconvolving the unscaled microvascular component with the feeding PA TIC thus yields a corrected regional parenchymal TIC free of arterial flow signal contamination (figure 7). Notice that the peak, time to peak, peak time and curve area of the corrected parenchymal microvascular curve are all significantly different from the original contaminated curve.
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Calculation of regional arterial signal contamination (figure 8)was accomplished by comparing the area of the corrected parenchymal microvascular time-intensity curve with the original parenchymal curve.
Regional red blood cell mean transit times were calculated using the equation described above (see section 2.1.2) with a correction factor applied. The MTT result was divided by 1.4 since it has been found on average that red blood cells traverse the capillary bed 1.4 times as fast as plasma [8], and radiopaque tracer we use is a plasma tag. As can be seen in figure 9, mean transit times tend to lengthen as a function of height within the lung.
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The key finding from this study is that a portion of the measured regional parenchymal time-intensity curve represents small artery rather than microvascular flow. In samples from dependent lung regions, up to 40% of the measured signal can be attributed to small artery "contamination". The evidence for this conclusion is based on the bi-modal nature of the deconvolved residue functions. We hypothesized that the sharp, narrow mode represented partial volume averaging of small arteries within the parenchymal samples.
Supporting this notion is the data obtained deconvolving time-intensity curves taken from visually apparent small arteries in the lung field. The deconvolved residue functions from these samples are composed almost exclusively of a sharp, narrow peak. The data showing a reduction in the arterial peak as sampling locations were moved from dependent to non-dependent lung regions can be explained by: 1) due to the pulmonary vascular architecture of the dog, there are a greater number of arterial vessels in the dependent lung regions when the animal is supine. 2) due to a vertical gradient in regional lung expansion, the lung is more compressed (less expanded) in the dependent regions of a supine animal. There is, therefore, an increased chance of including arterial vessels in samples taken in dependent lung regions, and 3) lower flow in the non-dependent regions of the supine dog. The data we have obtained is, therefore, consistent with known pulmonary anatomy and physiology.
Moreover, the putative arterial component of the residue function approximates a delta function, as would be expected from a sharp bolus injection that travels unmodified (undispersed) through the pulmonary arterial system. Reconvolving the arterial component with the input function yields essentially a time-delayed version of the input curve, further reinforcing our belief that the sharp, narrow mode of the residue function represents an arterial flow signal. Moreover, the finding that the bolus signal in small arteries in the lung parenchyma is similar to the bolus signal in the main pulmonary artery suggests minimal dispersion occurs in the pulmonary arterial system, a finding consistent with data from direct measurements [9,10] (microfocal angiograms) of isolated lungs. The finding of minimal bolus dispersion through the pulmonary arterial system is consistent with the assumption of the "bolus injection, residue detection" model that the bolus must travel essentially unmodified through the arterial system. The measured input function (main PA TIC), therefore, is essentially the true input function to the microvascular bed.
Reconvolving the microvascular mode of the residue function with the input curve yields a corrected parenchymal time-intensity curve indicative of the regional microvascular transport characteristics free of arterial contamination. The peak, time-to-peak, peak time, and area of the corrected parenchymal curve are all quite different than seen in the original parenchymal curve, an important result since these curve parameters affect the calculation of regional perfusion, blood volume, meant transit time and other kinetic parameters. The corrected parechymal curve can now be used for characterization of microvascular transport/kinetic characteristics. In fact, the red blood cell mean transit times calculated from the microvascular portions of the residue functions correlate surprisingly well with direct pulmonary microvascular measurements other investigators have reported using alternative methods.
On a practical note, high-frequency information is needed to resolve the arterial and microvascular modes of the residue function. Thus, this technique requires a sharp bolus injection since a sharp bolus contains more high-frequency information than a dispersed or broadend curve. We were able to obtain sharp input functions in these studies by injecting the bolus in the right ventricular outflow tract and placing samples in a main (generations 0-2) pulmonary artery. In human studies, if a more peripheral injection is desired, the bolus will become dispersed as it passes through the right heart, so an additional bolus correction step must be made. This correction can be accomplished by deconvolving time-intensity curves from the right atrium and pulmonary artery to compute a transfer function for the right heart and then using this transfer function to provide a pulmonary artery time-intensity curve corrected for dispersion of the bolus as it passes through the right heart.
FFT based deconvolution is computationally efficient and speedy. The FFT-based algorithm we have implemented is also model free, so that the residue function is not constrained to any predefined shape or form. In fact, it is unlikely that we would have been successful had we used other deconvolution techniques which assume a shape for the residue function. Supporting the validity of the EBCT derived regional MTT measurements is the close agreement between red blood cell MTT's times (figure 9) calculated from the recovered microvascular components and direct microvascular observations [8,9,10] other investigators have reported. The close agreement between the EBCT derived data and the direct observations of others suggests that dynamic x-ray CT imaging in conjunction with a deconvolution based algorithm offers a unique method to non-invasively quantitate in vivo true regional microvascular perfusion, volumes and transit times throughout the lungs.
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