Journal of Applied Physiology AJP: Lung Cellular and Molecular Physiology
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J Appl Physiol 88: 2279-2286, 2000;
8750-7587/00 $5.00
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Vol. 88, Issue 6, 2279-2286, June 2000

SPECIAL COMMUNICATION
Imaging obstructed ventilation with NMR using inert fluorinated gases

Dean O. Kuethe1, Arvind Caprihan2, H. Michael Gach3, Irving J. Lowe3, and Eiichi Fukushima2

1 Lovelace Respiratory Research Institute, and 2 New Mexico Resonance, Albuquerque, New Mexico 87108; and 3 Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We partially obstructed the left bronchi of rats and imaged an inert insoluble gas, SF6, in the lungs with NMR using a technique that clearly differentiates obstructed and normal ventilation. When the inhaled fraction of O2 is high, SF6 concentrates dramatically in regions of the lung with low ventilation-to-perfusion ratios (VA/Q); therefore, these regions are brighter in an image than where VA/Q values are normal or high. A second image, made when the inhaled fraction of O2 is low, serves as a reference because the SF6 fraction is nearly uniform, regardless of VA/Q. The quotient of the first and second images displays the low-VA/Q regions and is corrected for other causes of brightness variation. The technique may provide sufficient quantification of VA/Q to be a useful research tool. The noise in the quotient image is described by the probability density function for the quotient of two normal random variables. When the signal-to-noise ratio of the denominator image is >10, the signal-to-noise ratio of the quotient image is similar to that of the parent images and decreases with pixel value.

perfusion; sulfur hexafluoride; lung; quotient; magnetic resonance imaging; probability density function; nuclear magnetic resonance


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

REGIONS OF LUNGS WITH LOW alveolar ventilation-to-blood perfusion ratios (VA/Q) are of great importance to understanding pathological lung function. They are responsible for low oxygenation of arterial blood. In the absence of pneumonia or other conditions that impose a diffusion barrier between alveoli and blood capillaries, blood coming from areas with normal or high VA/Q is fully oxygenated as long as an air breather is near sea level. Although there are methods of measuring overall VA/Q heterogeneity in lungs (12, 23-25, 48, 49), there is a great desire to spatially resolve the information. Ventilation images made with gamma rays from inhaled 133Xe have low resolution, as do perfusion images made with gamma rays from 99mTc in aggregated albumin, which lodges in patent capillary beds.

The idea is to image an inert insoluble gas, such as SF6 or C2F6, taking advantage of the fact that it becomes concentrated where VA/Q values are low (8, 14). The effect can be dramatic if the inhaled fraction of O2 (FIO2) is high, because in obstructed alveoli the soluble respiratory gases can come close to equilibrium with venous blood, leaving the large partial-pressure balance to the insoluble fluorinated gas. In contrast, the gas in unobstructed alveoli is mostly O2. Figure 1 shows how the partial pressure of SF6 in alveoli (PASF6) varies with VA/Q (according to Refs. 8 and 14) with refinements (13) taking into account how the solubility of O2 and CO2 in blood is modified by the chemical environment of Hb (41). We assumed that body temperature is 37°C, venous PO2 is 40 Torr, venous PCO2 is 46 Torr, base excess is 0, barometric pressure in our laboratory at 1,636-m elevation is 630 Torr, solubility of SF6 in blood is 0.0008, and FIO2 is 75%. Figure 2 shows a comparison of VA/Q discrimination for different FIO2 values using the same calculations as in Fig. 1. For an FIO2 of 75%, PASF6 is doubled at a VA/Q of 0.06 and tripled at a VA/Q of 0.035 compared with that for a normal VA/Q of 0.84. Such two- and threefold changes can produce dramatic contrast in images.


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  		Fig. 1.   How alveolar ventilation-to-blood perfusion ratio (VA/Q) affects image brightness. Curve A shows alveolar partial pressure of SF6 (PASF6) as a function of VA/Q when inhaled mixture is 25% SF6-75% O2. Curve B shows the nearly uniform PASF6 when inhaled mixture is 80% SF6-20% O2. FIO2, inhaled fraction of O2. Curve C shows curve A divided by curve B (A/B) and displays how pixel brightness varies with VA/Q when an image made while FIO2 is 75% is divided by one made while FIO2 is 20%. Pixel values monotonically increase from 0.313 to 1.0 as a function of VA/Q, with brighter pixels representing low VA/Q values. Assumptions include a barometric pressure of 630 Torr and normal venous blood gases.



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  		Fig. 2.   How FIO2 affects discrimination of PASF6. Curves are indexed to PASF6 values that are 1.5, 2, 2.5, 3, 3.5, and 4 times the PASF6 at a normal VA/Q of 0.84. Consider curve 2: at an FIO2 of 0.8, the VA/Q at which PASF6 is twice that of alveoli with good ventilation is 0.075. Increasing FIO2 does not substantially increase sensitivity; thus at an FIO2 of 0.9, this VA/Q is 0.08, which is similar to 0.075. We might, however, gain discrimination within the range of VA/Q values. At an FIO2 of 0.9 compared with an FIO2 of 0.8, it is possible for SF6 to concentrate ~8 times above the well-ventilated PASF6, rather than ~4 times. However, this discrimination will not be beneficial if we lose the ability to image the well-ventilated part of the lung for lack of SF6. Other reasons to keep FIO2 at 80% or lower are to avoid O2 toxicity and alveolar collapse. Calculations are for a barometric pressure of 630 Torr. A sea-level pressure of 760 Torr reduces the sensitivity slightly but extends the discrimination range.

Despite the overwhelming success of nuclear magnetic resonance (NMR) at imaging most soft tissues, lungs are problematic for two primary reasons. First, there is not much water in lungs to provide hydrogen nuclei to image. Second, water is diamagnetic, and the many gas-water boundaries make the magnetic field inhomogeneous (2, 10, 17). Spins precess at different frequencies and lose phase coherence within several milliseconds. Nonetheless, lung imaging has improved greatly in the last decade, with NMR pulmonary angiography approaching clinical utility (6, 7, 19, 22, 29, 42, 50, 51).

An alternative to imaging the water in lungs is to image a gas. Although the magnetic inhomogeneities are less severe in the gas spaces (1, 9, 10), imaging gases in lungs is still difficult because of the low density of nuclei. One way this problem has been overcome is to boost the signal by polarizing 3He or 129Xe to five orders of magnitude above the thermal equilibrium polarization (3, 4, 34). Because of prepolarization, one can make NMR images of 3He or 129Xe as rapidly as one can collect data and track gas during inhalation or exhalation to get information about ventilation. Recent images of emphysema look promising (30). However, the polarization is relaxed by O2 (39), lung tissue, and the imaging sequences (18, 26, 36) on the gases' journey to and from alveoli, and obtaining quantitative information is difficult.

Our technique uses inert fluorinated gases at thermal equilibrium polarization (31). Fluorinated gases were first imaged in lungs with NMR in the early 1980s (38). The way to obtain a good signal-to-noise ratio (SNR) is to choose gases with very rapid NMR relaxation, so that the magnetization recovers fast enough to allow extensive signal averaging. The present costs of 3He and 129Xe are two orders of magnitude higher than those of SF6. The cost of polarizing noble gases is declining. SF6, C2F6, CF4, cyclo-C4F8, and other good candidates for our methods are recoverable with commercial Freon liquefiers that allow O2 and N2 to escape. To recover 3He by condensation, one must liquefy or freeze O2 and N2 with more expensive apparatus.

An advantage of SF6, C2F6, and CF4 is that the spin-rotation relaxation is so rapid that the paramagnetism of O2 has no effect (16, 35, 37, 52). Alveoli are 25 times too large to cause the lengthening of relaxation that has been observed in small pores (33). The spin-lattice relaxation time constant T1 equals the spin-spin relaxation time constant T2 and is linearly related to the density of the gas mixture (16, 35, 37, 52); therefore, it is easy to calculate spin-density images and measure equilibrium gas concentrations in lungs.

To get quantitative information about PASF6, we need to correct for other causes of brightness variation in images, such as radio frequency (RF) field inhomogeneities and gas-to-tissue ratios. We made a reference image while FIO2 was 20%; thus there was very little variation in PASF6 regardless of VA/Q (Fig. 1, curve B). By dividing an image made while FIO2 was 75% by one made while FIO2 was 20%, the pixel values of the quotient image vary with VA/Q as in Fig. 1, curve C. The quotient image is bright where VA/Q is low. The nonlinearity implies that, if there are different VA/Q values in a region represented by one image pixel, the value of the pixel may not be the average VA/Q.

Fig 1, curve C, shows that there is discrimination in the range of VA/Q that distinguishes obstructive lung diseases (5, 15, 47). How much a given reduction in ventilation affects a mammal's gas exchange depends on what fraction of the lung is obstructed. A criterion for whether the lungs are exchanging gas adequately is whether the partial pressures of O2 and CO2 in mixed arterial blood (PaO2 and PaCO2, respectively) are normal. An important regulatory mechanism is hypoxic pulmonary vasoconstriction (e.g., Refs. 5, 44, 46). It reduces blood flow to obstructed regions with low PAO2, thereby reducing the amount of hypoxic hypercapnic blood that contributes to mixed arterial blood. Low PaO2 and high PaCO2 at sea level result when shifting blood flow to the better ventilated parts of lungs fails to compensate. Thus a 40% reduction in ventilation to both lungs will disrupt arterial blood gases, but complete obstruction of one-tenth of a lung may not. Our method images low-VA/Q regions whether or not they receive enough blood flow to lower PaO2 and raise PaCO2; however, if blood gases are so altered, low-VA/Q regions are responsible, and they are what this technique is designed to image. The quantitative relationships of obstruction, VA/Q values, and blood gases are subjects of ongoing research, and this technique may be an additional noninvasive tool.

A matter that needs to be clarified is whether we can detect VA/Q values that are low, but higher than 0.1. Blood gases leaving a region with a VA/Q of 0.5 are different from normal and are of physiological relevance, but Fig. 1, curve C, indicates a VA/Q of 0.5 may be indistinguishable from a VA/Q of 1. A factor that may be in our favor is that breathing a high-FIO2 mixture will relax hypoxic vasoconstriction, thus increasing blood flow and lowering VA/Q values in obstructed regions below their values for air breathing and into our detectable range. Another possibility, yet untested, is that the high density of SF6 may reduce ventilation to obstructed regions, especially if it concentrates in them. In some cases of obstructive lung disease, blood gases improve when patients breath low-density He-O2 mixtures (20, 28, 43, 45). A possible mechanism is that VA/Q mismatch is improved by facilitating ventilation to obstructed regions. In any case, the relationship between air-breathing VA/Q values vs. those for high-FIO2 SF6 mixtures needs clarification and may serve to enhance the ability to detect obstruction.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Experimental obstructed ventilation. We attempted to obstruct the ventilation in the left lungs of seven sodium-pentobarbital-anesthetized, 350- to 450-g rats by inserting a 2.25 ± 0.03 mm outer diameter by 5.84 ± 0.003 mm length glass bead into the left bronchus. The bead lumen contains a piece of polypropylene tubing, and the combination has a resistance of 39 ± 3 Pa · s · cm-3 with a flow of air at 630-mmHg pressure and 21°C temperature. The intent was to cause a nearly uniform obstruction of the left lung while leaving the right lung unobstructed. This is difficult because the bead must be lodged in the ringed portion of the left bronchus, which, in most rats of this size, is the length of this bead. Distal to the rings, the bronchus is more compliant, and the bead may not lodge in one place or may block the openings of secondary bronchi. (The ringed portion of the right bronchus is too short to avoid blocking the secondary bronchi.) Although in prior practice procedures we could reliably place the bead in the left bronchus, we had to wait until after the imaging procedure to dissect the lungs and determine its location. If it did not fit tightly in the ringed portion of the left bronchus, it could dislodge and relocate. The bead was properly placed in two of the seven attempts.

The success of bead placement and appearance of the lungs were recorded before we saw the images. This information was recorded late in the working day, and the images were constructed on a separate computer the next day at the earliest.

Although reporting the resistance of the bead allows others to repeat the experiment, it is difficult to know how much it lowers ventilation because rat bronchi are rather small for flowmeters that can measure the flow before and after bead insertion.

NMR imaging. We imaged lungs by the methods of Kuethe et al. (31) with modifications. In short, we collected free induction decays (FIDs) in the presence of steady magnetic field gradients and varied the direction of the gradient every other breath to obtain multiple one-dimensional projections. Initial experiments to develop techniques for imaging SF6, which has faster relaxation than the C2F6 we had previously used, were performed in I. J. Lowe's laboratory in Pittsburgh, PA, taking advantage of the 10-µs dead time between the end of RF transmission and beginning of data collection. Short dead times and RF pulses are useful to minimize the loss of imaging data and to reduce the loss of a rapidly decaying signal. We then modified the NMR system in Albuquerque, NM, so that the 1.9-T magnet now has a Faraday shield that provides 30-dB attenuation to outside RF signals. The dead time, with a 400-g rat loading the 55-mm-inner-diameter quadrature bird cage coil (Morris Instruments, Gloucester, Ontario) is 8-12 µs, provided we bypass the audio stage filters in the Tecmag receiver, which requires digitizing the signal at 1 MHz to capture the full bandwidth. Ninety-degree RF pulses last 14-17 µs, depending on the size of the rat. We use a Miteq AU-1114-BNC preamplifier, which has fast response and limits overload voltage to the following Advanced Receiver Research 76-MHz narrowband preamplifier, which filters out the upper sideband frequency. The noise figure for the entire receiver chain is 1.19 F (dB), computed by comparing the noise from a 76 K (liquid N2 cooled), 50-Omega resistor and a 294 K (room temperature) 50-Omega resistor.

The gas mixture was held in a 12-liter Mylar balloon and was delivered to the rat by a Harvard ventilator (31). The gas returns to the balloon through a CO2 filter. The mixture is maintained by adding O2 to the balloon approximately every 0.5 h to bring the balloon back to the same degree of inflation. Gas fractions after 3-8 h of ventilation matched the beginning fractions within 4%. The T1 of SF6 in the lungs of a rat breathing 80% SF6-20% O2 at a barometric pressure of 630 Torr without any obstruction was 1.24 ± 0.015 ms. For an inhaled gas mixture of 20% SF6-80% O2, T1 = 0.89 ± 0.01 ms. Hahn T2 values are not measurably different, indicating that diffusion in the inhomogeneous field does not cause appreciable signal loss during the relaxation time.

We used a 15-µs RF pulse and spaced FIDs 1.727 ms apart. The pulse sequence was gated by a switch on the ventilator so that 160 FIDs were collected during the 32% of the respiratory cycle when the lungs are full. We did not gate to the cardiac cycle. It took 30.3 min to collect data for an image, averaging data over two breaths for each of 1,058 different magnetic-field gradient directions (529 positive, 529 negative) and gradient-free FIDs at the beginning and end of the sequence. From the two gradient-free FIDs, we computed the hypothetical signal at the center of the RF pulse at the beginning and end of the image acquisition. The phases of these values were used to correct the rest of the data for any linear drift in the phase of the receiver during the sequence. Their average was included in each line of data, and the matrix that was pseudoinverted to obtain the projections was modified accordingly (32).

The gyromagnetic ratio for 19F of 40.05 MHz/T and applied magnetic field gradient of 23.05 mT/m imply frequencies in the sample vary by 0.9232 MHz/m. By sampling data at 1 MHz, the bandwidth represents 1.083 m. We collected 1,024 data points in the FIDs with positive-applied gradients and 1,024 in the FIDs with negative-applied gradients. A full data set includes these and the 39 points missed during the RF pulses and dead times; thus a single point of a Fourier-transformed data set represents 1.083 m/2,087 or 0.519 mm. We know the lungs are contained within a sphere of 70-mm radius, which represents a little less than the central 136 of 2,087 transformed data points. The data were oversampled by a factor of 15.5. Combined with prior determination of the hypothetical signal at the center of the RF pulse from the gradient-free FIDs, oversampling helps determine the remaining 38 missing data points for each line of data (32).

To make projections, for each line of data we used the calculated central 39 points, the first 550 data points of FIDs from positive gradients, the first 550 data points of FIDs from negative gradients, and zero filled to obtain 2,048 data point sets. Each point of transformed data represented 1.083 m/2,048, or 0.529 mm, and the projections were contained within the central 132 frequency components. These projections were inverse transformed, interpolated onto a Cartesian grid, and three-dimensionally transformed to obtain the image. The lungs were contained in a 72 × 74 × 80-pixel portion of the image, representing a 38 × 39 × 42-mm field of view, with 0.529-mm resolution.

Noise in the quotient image. Because we are presenting a new technique for measuring relative gas concentrations, it behooves us to quantify the measurement error. The noise in typical NMR images is Gaussian for two reasons. 1) The image is a discrete Fourier transform of data that have Gaussian noise if the system is properly shielded. The Fourier transform of a Gaussian function is Gaussian. 2) Even if the noise is non-Gaussian, the Fourier transform sums large numbers of independent samples into each pixel, which will produce essentially Gaussian noise. After the magnitude of a complex image is taken, the noise associated with low-value pixels is not Gaussian because the pixels are never negative. However, masking magnitude images with a threshold value a few standard deviations above zero to isolate the object ensures that the noise is essentially Gaussian. To obtain the probability density function (PDF) for the noise in a quotient of two images, let X be a Gaussian random variable with mean µ1 and variance sigma 21 and let Y be another Gaussian random variable with mean µ2 and variance sigma 22. Then X/Y has PDF1
<IT>h</IT>(<IT>z</IT>) = exp <FENCE>− <FR><NU>1 + &agr;<SUP>2</SUP>&ggr;<SUP>2</SUP></NU><DE>2&bgr;<SUP>2</SUP></DE></FR></FENCE> <FR><NU>&ggr;</NU><DE>&pgr;(1 + &ggr;<SUP>2</SUP><IT>z</IT><SUP>2</SUP>)</DE></FR>

+ <FR><NU>&ggr;(1 + &agr;&ggr;<SUP>2</SUP><IT>z</IT>)</NU><DE><RAD><RCD>2&pgr;</RCD></RAD>&bgr;(1 + &ggr;<SUP>2</SUP><IT>z</IT><SUP>2</SUP>)<SUP>3/2</SUP></DE></FR> exp <FENCE>−<FR><NU>&ggr;<SUP>2</SUP>(<IT>z</IT> − &agr;)<SUP>2</SUP></NU><DE>2&bgr;<SUP>2</SUP>(1 + &ggr;<SUP>2</SUP><IT>z</IT><SUP>2</SUP>)</DE></FR></FENCE> erf <FENCE><FR><NU>1 + &agr;&ggr;<SUP>2</SUP><IT>z</IT></NU><DE>&bgr;<RAD><RCD>2(1 + &ggr;<SUP>2</SUP><IT>z</IT><SUP>2</SUP>)</RCD></RAD></DE></FR></FENCE> (1)
where erf (x) = <FR><NU>2</NU><DE><RAD><RCD>&pgr;</RCD></RAD></DE></FR> <LIM><OP>∫</OP><LL>0</LL><UL><IT>x</IT></UL></LIM> exp (-t2)dt, alpha  = µ1/µ2, beta  = sigma 2/µ2, and gamma  = sigma 2/sigma 1. If sigma 1 = sigma 2

<IT>h</IT>(<IT>z</IT>) = exp <FENCE>− <FR><NU>1 + &agr;<SUP>2</SUP></NU><DE>2&bgr;<SUP>2</SUP></DE></FR></FENCE> <FR><NU>1</NU><DE>&pgr;(1 + <IT>z</IT><SUP>2</SUP>)</DE></FR>

 + <FR><NU>1 + &agr;<IT>z</IT></NU><DE><RAD><RCD>2&pgr;</RCD></RAD>&bgr;(1 + <IT>z</IT><SUP>2</SUP>)<SUP>3/2</SUP></DE></FR> exp <FENCE>− <FR><NU>(<IT>z</IT> − &agr;)<SUP>2</SUP></NU><DE>2&bgr;<SUP>2</SUP>(1 + <IT>z</IT><SUP>2</SUP>)</DE></FR></FENCE> erf <FENCE><FR><NU>1 + &agr;<IT>z</IT></NU><DE>&bgr;<RAD><RCD>2(1 + <IT>z</IT><SUP>2</SUP>)</RCD></RAD></DE></FR></FENCE> (2)

The case that applies to our situation is when beta  < 0.1, i.e., the noise-to-signal ratio (NSR) of the denominator image is within reason. Then the first (Cauchy or Lorentzian) term is essentially zero. In our images, alpha  is positive [for negative alpha , reverse right and left in the rest of this paragraph]. The exponential factor of the second term has the narrowest distribution and determines the variance. It is essentially a Gaussian term with skew because of the variance being a function of position. The error function (erf) factor rises from 0 at z = -1/alpha gamma 2 to essentially 1 before z turns positive; thus it is essentially 1 over the entire range of concern. The remaining factor is positive in the same region and has a broad distribution, peaking between z = 0 and z = alpha , so that its broad tail, descending to the right, overlays the narrow exponential term, correcting some of its skew to an essentially symmetric distribution centered around alpha , with variance approximately beta 2(1 + gamma 2alpha 2)/gamma 2 [or 1/µ22 (sigma 21 + µ21/µ22 sigma 22)]. To get an accurate value, we integrate numerically to calculate the expectation of the square. The standard deviation is the measurement error for individual pixels in our quotient images and is a function of alpha . It ranges from beta /gamma to (beta 2 + beta 2/gamma 2)1/2 (from beta  to <RAD><RCD>2</RCD></RAD>beta for gamma  = 1) as our pixel values range from 0 to 1. The distribution resembles a Gaussian distribution, and the standard deviation quantifies variation like the standard deviation of a Gaussian distribution in that 68-69% of the area falls within ±1 SD and 95-96% falls within ±2 SD. In our application, we typically know gamma  and insert it to modify the distribution. It is not easy to estimate gamma  and beta  independently, because the effect of gamma  on the distribution is too similar to the inverse of beta . This paragraph's conclusions do not hold for at least two cases of this PDF with large beta .

The SNR of the quotient image is obtained from beta , the NSR of the denominator reference image. In addition to this information, the PDF provides a good procedure for estimating beta : Signal average one-half as much for the reference image to obtain two sets of data instead of one. From these two identically sampled sets of data, make two images, A and B. Use B to determine the threshold mask, and apply the mask to A. Make a histogram of the pixel values of A/B, and fit the histogram with Eq. 2 to estimate beta A/B and alpha A/B (alpha A/B will be very close to 1). The beta  of the complete denominator image, made from the combined data, is beta A/B/<RAD><RCD>2</RCD></RAD>.

This procedure can be used for SNR calculations of images in general. It has an advantage over the method of taking the mean of pixels in an object and dividing it by the root-mean-square value of a region containing no object. The object-free region of images often has different noise than the object-containing region. The above procedure estimates the noise in the region of the object.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Figure 3 is an image of obstructed ventilation that has been corrected by using a reference image. The image that detected the obstruction via PASF6 was made from 1.5 h of data collection while a rat breathed 75% O2-25% SF6. It was divided by an appropriately scaled reference image made from 1 h of data collection when the same rat breathed 20% O2-80% SF6. Before division, we used a mask to set the obstruction-detecting image to 0 in the 301,226 out of 426,240 pixels where the reference image had pixel values <330 (19.64% of the maximum pixel value 1,680.3), which eliminated the pixels outside the lung.


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  		Fig. 3.   Image of obstructed ventilation is quotient of 2 NMR images of SF6 in rat lungs. Left bronchus is partially obstructed. An obstruction-detecting image made from 1.5 h of data collection while rat breathed 25% SF6-75% O2 is divided by a reference image made from 1 h of data collection while rat breathed 80% SF6-20% O2. From top left to bottom right, 80 successive x-y planes, each with 72 × 74 pixels, are displayed from anterior (forward) to posterior (rear). First row contains anterior tips of the lungs. Lower down, the dark heart and mediastinum separate pink right lung from purple and blue left lung. Large dark area in the lowest planes is the diaphragm and liver. Pixel values range from 0 (black) to 1 (white) and are divided into 21 color bands. The width of the color bands is 1 SD for individual pixels of that color. This measurement error is greater for higher pixel values; therefore, right color bands are wider than left ones. VA/Q scale, which also appears in Fig. 4, shows which colors represent different VA/Q values. Like many lab rats, this one has a small lobe of right lung in the posterior left thorax, which accounts for pink portion on left side of the rat (right side of image).

Figure 4 shows a histogram of the pixel values in Fig. 3. We eliminated the one pixel value, 1.037, out of 125,014 that fell >1.0; thus the color scale and histogram represent values from 0 to the next highest pixel value, 0.9992. The histogram is bimodal, with a narrow peak centered around 0.34, representing the unobstructed ventilation in the right lung, and a broader peak centered around 0.52, representing the obstructed ventilation in the left lung. The dotted and dashed lines are histograms made from only the left or right lung, respectively.


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  		Fig. 4.   Histogram of pixel values for the 3-dimensional image in Fig. 3. Dashed line, histogram for right lung; dotted line, histogram for left lung. Means for right and left are 0.342 and 0.520, and SDs are 0.0487 and 0.0990, respectively. The variance in the unobstructed right lung is mostly due to measurement error, whereas that in the obstructed left lung is mostly due to variation in PASF6. Second abscissa is calculated from how VA/Q determines alveolar gas composition (Fig. 1) and how gas composition affects steady-state magnetization.

To quantify the noise in Fig. 3, we first computed beta  for the reference image and then used it to compute the standard deviation of the PDF, Eq. 1, which gave us the standard deviation for the pixels in Fig. 3. By separating the data for the reference image into two sets, thus making two images, and dividing one by the other and vice versa, we obtained two estimates of beta  (0.05075 and 0.05061; average 0.05068), the NSR of the reference image. Because we used three sets (1.5 h) of data for the obstruction-detecting image and two sets (1 h) for the reference image, gamma  in Eq. 1 is <RAD><RCD>3</RCD></RAD>/<RAD><RCD>2</RCD></RAD>. The standard deviation, from numerical integration of Eq. 1, for beta  = 0.05068, gamma  = 1.2247, and mean pixel value alpha  = 0.342 is 0.0450, and for the same beta  and gamma  and mean pixel value alpha  = 0.520 is 0.0493. The standard deviation of the right lung histogram is 0.0487, slightly higher than 0.0450, indicating that most, but not all, of its variation is measurement noise. The right lung histogram fits Eq. 1 better than a Gaussian, log normal, or Cauchy (Lorentzian) distribution. The standard deviation in the left lung histogram is 0.0990, twice as high as 0.0493, indicating much of the variation is due to variation in SF6 concentration.

One can get a quick estimate of the image noise by examining the left-hand tail of the histogram. Provided there is a substantial amount of lung with near-normal VA/Q values, it will all theoretically translate to the same low pixel value. In other words, physiology predicts a sharp left edge in the histogram. The left tail of the histogram is then an estimate of the noise in measurement.

The image in Fig. 3 has some relaxation weighting because the repetition time is ~1.7 times T1 (to maximize SNR) and T1 is a function of gas density. To obtain the correct spin-density information, we computed the dependence of T1 on gas composition by assuming that the measured T1 of SF6 for a normal rat applies to the gas composition calculated for alveoli with a normal VA/Q. Then we calculated the other T1 values from the T1 values for two different inhaled gas compositions, assuming T1 is a linear function of gas density. We obtained a revised version of Fig. 1, curve C, by using the steady-state magnetization to calculate pixel values from gas composition. Projecting the pixel values through the revised curve provides the second abscissa in Fig. 4. This VA/Q scale also appears under the color scale in Fig. 3, showing which colors represent which VA/Q. The net effect of the correction is that high VA/Q is represented by pixel value 0.353 instead of 0.313, which would be the case without relaxation weighting.

The standard deviation from Eq. 1 describes the measurement error for individual pixels. The SNR for groups of pixels increases with the square root of the number of pixels, making comparison of groups more powerful. A familiar way to compare means of two groups of pixels is Student's two-sample t statistic, t = &mgr;<SUB><IT>L</IT></SUB> − &mgr;<SUB><IT>R</IT></SUB>/<IT>s</IT><RAD><RCD>1/<IT>n</IT> + 1/<IT>m</IT></RCD></RAD>, here µL is the mean of n pixels from the left lung, µR is the mean of m pixels from the right lung, and s is a weighted average standard deviation, defined by s2 = Ns2L + Ms2R/N + M, where s2L is the sample variance of the left lung, s2R is the sample variance of the right lung, N = n - 1, and M = m - 1. If the left lung pixels and right lung pixels were both normally distributed, then under the hypothesis µL = µR, t has Student's t distribution with N + M degrees of freedom. The t-test is sufficiently robust that, if the underlying distributions resemble normal, as ours do, the operating characteristics of the test are essentially the same as if the underlying distributions were strictly normal. We have the advantage of being able to calculate s = 0.0682 using all 48,586 pixels from the left lung and all 76,428 from the right, so that t has 125,012 degrees of freedom, and t is essentially Gaussian with mean = 0 and SD = 1. Two pixels from the left lung with mean = 0.52 and two from the right with mean = 0.342 give a t of 2.6; thus µL > µR at the P < 0.005 level. Four pixels from each lung yield a t of 3.7 and P < 0.0001. Eight pixels from each lung yield a t of 5.2 and P < 10-7. When comparing both lungs, t is 451, and we cannot conveniently calculate the significance level because it is too small, but a t of merely 8.2 implies significance at the 10-16 level.

In Fig. 3, groups of pixels that are different by two color bars are statistically different. The width of the color bars shows the measurement error for individual pixels of each color. Note that they grow wider toward the right side of the color scale, reflecting how the measurement error is a function of pixel value.

The results from all seven rats support the method's ability to detect obstructed ventilation. In two rats, the bead was correctly lodged in the proximal left bronchus. One of these images is shown in Fig. 3; the other was similar with the left lung brighter than the right. On dissection, the left lungs appeared darker in color than the right, but both appeared patent. In two rats, the bead was further in the left bronchus, where it did not fit as tightly but blocked secondary bronchial openings. There was partial atelectasis of the left lung, and the image showed a wedge-shaped bright region in the left lung. In one rat, the bead was similarly situated in the right bronchus, there was a similar region of partial atelectasis in the right lung, and the image showed a similar bright wedge-shaped area in the right lung. In one rat, the bead was found loose in the distal region of the left bronchus. The left and right lungs appeared similar on dissection, and the image showed no bright regions. In two rats, the bead was found loose near the carina, the lungs were similarly undistinguished on dissection, and the images showed no bright regions.

Even though the situation in which the bead reduced the ventilation to the entire left lung was repeated only once, the other bead placement and imaging results are in one-to-one correspondence. Where there was anatomic evidence that ventilation was obstructed, there is a bright region in the image; when the anatomic evidence is lacking, there is no bright region. This correspondence and the small significance levels associated with regions of images that appear different from one another are strong indications that the images display obstructed ventilation.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We do not have an independent measurement of VA/Q; therefore, the extent to which Fig. 3 displays VA/Q values relies on the theory leading to Fig. 1. The theory is well accepted by respiratory physiologists and forms the basis of related techniques that measure VA/Q distributions (12, 23-25, 48, 49). If VA/Q of the right lung were normal, the predicted mean pixel value would be 0.364. The actual value, 0.342, is within 6%, which is good agreement considering that we were not monitoring blood gases to prevent overventilation and the gas mixtures may have each varied by 4%.

Considering the difficulties of imaging gas in lungs with NMR, we are very pleased that a quotient image has pixel values that fall within 6% of expectation and that we could quantify the noise at a reasonable level. At present, we are secure that we have imaged obstructed ventilation, and it appears that the detectable VA/Q values are in a physiologically relevant range. It is difficult to control mechanical ventilation obstructions in rats, but this would be much easier in larger mammals, which have bronchi that will accommodate bronchoscopes, flowmeters, and controllable obstruction devices. We are optimistic about the future quantitative development of this technique.

Scaling the technique from rats to human-sized mammals provides a signal-to-noise advantage. The SNR should increase by approximately the square root of the number of spins (11). Because lung volume scales with body mass (40), SNR increases by ~13 times in going from a 450-g rat to a 76-kg mammal. As a crude estimate, an image of human lungs similar to Fig. 3 with the same number of pixels would require a data collection time of 2.5 h/132 or 53 s. The resolution would be 2.92 mm instead of 0.529 mm. As with the rat, the data collection would occur during only 32% of the respiratory cycle, when the lungs are most full. People breathe 8-20 times/min at rest. Using the number of 15 breaths/min, one could acquire the obstruction-detecting image during 7 breaths and the reference image during 6 breaths. This scheme would imply collecting ~163 FIDs/breath, with each averaged over four or five acquisitions and separated by minor changes in the applied magnetic field gradient, corresponding to ~4.5° changes in direction. Alternatively, because only 53 s · 0.32/2 = 8.5 s of data are required for each image, the obstruction-detecting and reference image could each be acquired during one breath hold. However, people with obstructive lung disease often have trouble holding their breath.

Another scheme would purposely make the imaging process longer to make higher quality images by signal averaging, cardiac gating, and retrospective respiratory sorting. For example, assume that one eliminates data from one-fourth of spontaneous breaths in favor of those breaths that best match one another, collects data during only one-half of the heart cycle, and signal averages four times as much, the data collection would require 53 s · 1.33 · 2 · 4 = 10.6 min, but the image would have twice the SNR and fewer motion artifacts.

A limitation of our technique is lack of discrimination of high VA/Q values, which are useful, e.g., in detecting pulmonary embolisms. However, magnetic resonance pulmonary angiograms and lung perfusion measurements are improving rapidly. Because they may provide information sensitive to embolisms, they may be particularly useful in filling a gap in our technique. It has been common to measure VA and Q of the VA-Q-VA/Q trio when evaluating lung function, but VA/Q and Q is also a useful combination.


    ACKNOWLEDGEMENTS

Thanks go to Albert J. Olszowka, State University of New York at Buffalo, for providing computer programs of gas exchange and to Michael P. Hlastala and Thomas F. Hornbein, Univ. of Washington, Seattle, for criticism and advice in respiratory physiology. Thanks go also to Don Williams, Elena Simplaceanu, Maryann Butowicz, and Donald Bennett at Pittsburgh NMR Center for Biomedical Research (PNMRCBR) for helping D. O. Kuethe during visits to Pittsburgh. Steve Altobelli of New Mexico Resonance provided technical help in NMR, Jack Loeppky of Lovelace Respiratory Research Institute (LRRI) helped with and gave perspective in respiratory physiology, and Vicki White of LRRI helped with rats.


    FOOTNOTES

This work was supported by National Institutes of Health Grants 1R29HL57967-01 (to D. O. Kuethe) and RR-03631-04 (to the PNMRCBR).

Present address of H. M. Gach: University of Pittsburgh Medical Center, Pittsburgh, PA 15213.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

1 Algebra from expression in Ref. 27 or rederive with theorem h(z) = int infinity -infinity  |x|f(zx)g(x)dx, where f and g are PDFs of X and Y, respectively, and formula (21)
<LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>x</IT> exp (− <IT>ax</IT><SUP>2</SUP> − 2<IT>bx</IT>)d<IT>x</IT> = <FR><NU>1</NU><DE>2<IT>a</IT></DE></FR> − <FR><NU><IT>b</IT></NU><DE>2<IT>a</IT></DE></FR> <RAD><RCD><FR><NU>&pgr;</NU><DE><IT>a</IT></DE></FR></RCD></RAD> exp <FENCE><FR><NU><IT>b</IT><SUP>2</SUP></NU><DE><IT>a</IT></DE></FR></FENCE><FENCE>1 − erf <FENCE><FR><NU><IT>b</IT></NU><DE><RAD><RCD><IT>a</IT></RCD></RAD></DE></FR></FENCE></FENCE>

Address for reprint requests and other correspondence: D. O. Kuethe, NMR, 2425 Ridgecrest Dr. SE, Albuquerque, NM 87108-5127 (E-mail: dkuethe{at}NMR.org).

Received 19 April 1999; accepted in final form 20 January 2000.


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