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Published online before print April 19, 2002, 10.1148/radiol.2233011026
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(Radiology 2002;223:798-805.)
© RSNA, 2002


Thoracic Imaging

Volumetric Growth Rate of Stage I Lung Cancer prior to Treatment: Serial CT Scanning1

Helen T. Winer-Muram, MD, S. Gregory Jennings, MD, Robert D. Tarver, MD, Alex M. Aisen, MD, Mark Tann, MD, Dewey J. Conces, MD and Cristopher A. Meyer, MD

1 From the Department of Radiology, Indiana University School of Medicine, Indianapolis (H.T.W.M., S.G.J., R.D.T., A.M.A., M.T., D.J.C., C.A.M.); and the Department of Radiology, Richard L. Roudebush Veterans Administration Medical Center, 1481 W 10th St, Rm C-2172, Indianapolis, IN 46202 (H.T.W.M., A.M.A.). Received June 12, 2001; revision requested July 10; final revision received December 14; accepted December 20. Address correspondence to H.T.W.M. (e-mail: hwinermu@iupui.edu).


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
PURPOSE: To determine the range of growth rates of stage I lung cancers prior to treatment by using volumetric measurement at serial chest computed tomographic (CT) examinations.

MATERIALS AND METHODS: The study population comprised 50 patients who underwent two CT examinations at 25-day or greater intervals. Tumor craniocaudal length and cross-sectional diameters and perimeters were used to volumetrically model each tumor in three ways (spherical, elliptical, perimeter). Volumes were compared by determining Pearson correlation coefficients. By using these volumes, tumor doubling time was determined for each patient.

RESULTS: Volumes measured with all three methods were highly correlated. With the perimeter method, median doubling time was 181 days, with a very wide range. Eleven (22%) of 50 tumors had doubling times of 465 days or more. There was considerable overlap in doubling time between histologic subtypes. Assuming constant growth, only three (6%) of the 50 tumors would have been the size of a stage IA tumor for less than 1 year.

CONCLUSION: Comparison of tumor volumes at serial CT examinations reveals a very wide range of growth rates. Some tumors grow so slowly that biopsy is required to prove they are malignant.

© RSNA, 2002

Index terms: Lung neoplasms, 60.32 • Lung neoplasms, CT, 60.12115


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Although only 15% of patients who receive a diagnosis of lung cancer survive, up to 60%–70% survive when the cancer is diagnosed at stage I (13). Because screening chest radiography enables detection of only 15% of lung cancers at stage I, several investigators (47) have initiated protocols to determine whether screening with spiral computed tomography (CT) can reduce lung cancer mortality by increasing the percentage of tumors detected before metastasis. Furthermore, patients receiving a diagnosis at stage IA (tumor <3 cm in diameter) have a better 5-year survival rate (61%) than do patients receiving a diagnosis at stage IB (tumor >=3 cm) (38%) (1). However, the optimal frequency of screening to detect stage IA disease is dependent not only on the time at which tumors metastasize but also on the range of growth rates of lung cancers.

Almost all data on the growth rate of lung cancers are derived from chest radiographic studies (812). These studies have limitations because the authors assumed the lesions were spherical and used the mean diameter to calculate the doubling time (DT) of lesions on serial chest radiographs. To our knowledge, few data have been published in which CT was used to measure serial volumes of lung cancers prior to treatment. The only large (61 patients) series to date (13) used the maximum cross-sectional area of the tumor and not its volume to calculate growth rate; moreover, not all tumors were stage I at diagnosis. Yankelevitz et al (14) showed that growth rates derived from maximum tumor cross-sectional areas could not be used to distinguish benign (n = 8) from malignant (n = 5) nodules but that growth rates derived from CT volumetric measurements of CT images could be used. The authors concluded that volumetric measurement is necessary to evaluate tumor growth, since growth may be asymmetrical in not just two dimensions, but in all three.

Software that allows one to quickly measure the dimensions of irregular nonspherical lesions on each CT section and automatically compute cross-sectional area is becoming widely available. These areas can easily be integrated to calculate volume. If serial CT scans are available, the rate at which the tumor is growing can then be estimated. For a variety of reasons, patients may undergo serial CT examinations prior to treatment (Figure).



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Reasons for multiple chest CT examinations prior to lung cancer therapy.

 
The purpose of this study was to determine the range of growth rates of stage I lung cancers prior to treatment, by using volumetric measurement at serial chest CT examinations.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The study was performed at the Richard L. Roudebush Veterans Administration, or VA, Medical Center in Indianapolis, Ind, and was approved by the university institutional review board, with waiver of patient informed consent.

From the VA Medical Center tumor registry we obtained a list of patients who had received a diagnosis of stage I lung cancer and were being followed up at the VA Medical Center between February 1996 and May 2001. This list included patient age at diagnosis, cancer stage at diagnosis, cancerous histologic findings, and treatment type (surgery, chemotherapy, radiation therapy, or none). The medical records of each patient were reviewed by one of the authors (S.G.J.), and any patient with a previous diagnosis of primary lung cancer or cancer metastasis to the lung in the preceding 5 years was excluded. Records also were reviewed for other pertinent data, including method of lung cancer diagnosis (eg, fine-needle aspiration biopsy, sputum cytology, bronchoscopy), comorbidities, smoking history, and other malignancy. Rationales for treatment (or no treatment) were documented.

For each remaining patient, all chest CT examinations performed prior to initiation of treatment and available on the departmental picture archiving and communication system (archiving had begun in February 1996) were identified. The examination date, nominal section width, and section increment (in millimeters) were noted. A CT examination was excluded from the study if it had been performed with the patient in the prone position only, since prone positioning might have influenced the measured volume of the tumor, introducing error into serial measurements. CT examinations were also excluded if the entire tumor was not depicted or if the entire tumor margin could not be visualized.

The minimum interval allowed between successive CT examinations used in the current study was based on the estimate of Yankelevitz et al (15) that an automated detection algorithm can be used to reliably detect a 12% increase in cross-sectional area. We thus determined the time that a spherical tumor growing at a constant rate with the mean DT of 102 days, reported by Geddes (16) in his summary of the radiography literature, would require to increase its cross-sectional area by 12%. If this initial area is {pi}R2, where R is radius (in millimeters), Rf is final radius, and Ri is initial radius, {pi}Rf2 = 1.12 {pi}Ri2, and Rf2/Ri2 = 1.12.

If we assume Ri = 1, then Rf = 1.0583. Initial volume (Vi) is then (4/3){Pi}Ri3 = 4.1889, and final volume (Vf) is (4/3){pi}Rf3 = 4.9651.

By using Geddes’ (16) estimate of DT, we can calculate the interval necessary for the minimally perceptible 12% increase in cross-sectional area suggested by Yankelevitz et al (15), by using the following standard volumetric DT formula: DT = (t · ln 2)/ln (Vf/Vi), where t is time in days and DT is measured in days, DT = (t · .6931)/ln (4.9651/4.1889), and t = DT/4.077. If DT = 102 days, then t = 102/4.077 = 25.02 days. Therefore, we used 25 days as the minimum interval between CT examinations.

For each patient, the first and last CT examinations that met the preceding entry criteria and were separated by at least 25 days were used. All examinations were performed with a Picker PQ 2000 scanner (Marconi Medical Systems, Cleveland, Ohio). For examinations that included multiple section increments, only images from the smallest increment that displayed the full craniocaudal extent of the tumor and were obtained with a spiral technique during a single breath hold were used. Each CT examination was downloaded from the archive to a video display system (MGD 521; BarcoView, Duluth, Ga) with 2,500 x 2,000-pixel monitors. All scans were displayed at standard lung settings (window width, 2,000 HU; window level, -700 HU). Image viewing and manipulation were controlled with Radworks 5.1 software (Applicare Medical Imaging, Zeist, the Netherlands), which allows the reader to draw lines through and perimeters around regions of interest. The software then automatically calculates the line and perimeter length and the area enclosed by a perimeter.

To reduce bias, the following procedure was used to display the scans: Each CT scan was displayed twice, in random order, to a board-certified chest radiologist (H.T.W.M.) who was experienced in using the image viewing and manipulation software. On each section containing a tumor, the radiologist was initially directed either to measure the major axis of the tumor and its in-plane perpendicular (minor axis) or to draw a line around the perimeter of the tumor. After all scans had been viewed, the radiologist viewed them again, and the measurement method not used in the first viewing was used.

The volume of each tumor was calculated by using three methods:

Spherical.—The tumor was modeled as a sphere with a diameter equal to the average of the length in the z axis and the largest major axis measured (Dmax). This volume, or V1, was calculated by using the corresponding radius (Rmax): V1 = (4/3){pi}Rmax3.

Elliptical.—The tumor was modeled as an ellipsoid with cross-sectional area (AE) determined by using the pair of major and minor axes measured by the radiologist on each section. For a particular section x, AEx = {pi}(major axisx)(minor axisx)/4. Volume, or V2, was calculated by summing the cross-sectional areas and multiplying by the section increment (I): V2 = I(AE1 + AE2 + . . . AEn), where n = the number of sections containing tumor (length of z axis = I · n).

Perimeter.—The tumor was modeled as an irregularly shaped object. On each section, a cross-sectional area (AP) was calculated by using the Radworks 5.1 software and by using the perimeter drawn by the radiologist. Volume (V3) was then calculated as with the second method: V3 = I(AP1 + AP2 + ... APn).

By using the volumes obtained for each tumor on each CT scan, the time needed for the tumor to double in volume was calculated for each patient by using each of the volume measurement methods and the DT formula. We also measured the time needed to measure cross sections and calculate tumor volume, including data entry into the volume calculation program, by using each of the three methods.

For each volume calculation method, the interval during which the tumor volume would have filled a sphere 0.5–3.0 cm in diameter was estimated. Knowledge of this interval is necessary to predict the percentage of patients whose cancers will progress from "too small to characterize" to greater than 3 cm in diameter in the interval between screening examinations. This interval was found by first determining the volume ratio of a sphere with a diameter of 0.5 cm (5.0 mm) to one with a diameter of 3.0 cm (30.0 mm) by using the following formula: Volume (0.5 cm) = 4/3 · {pi} · (2.5)3 = 65.45 mm3, volume (3.0 cm) = 4/3 · {pi} · (15.0)3 = 14,137 mm3, then the volume ratio = 14,137/65.45 = 216.00. The number of DTs needed to increase the volume by a factor of 216 is given as follows: 2x = 216, then ln 2x = ln 216, x · ln 2 = ln 216, x = ln 216/ln 2, x = 7.755. Therefore, the interval during which lesion volume would have filled a sphere 0.5–3.0 cm in diameter is given by multiplying DT by 7.755. This interval was estimated for each patient.

Intraobserver variability may have major effects on serial measurement of cross-sectional area, particularly for small tumors and/or short intervals between examinations. As the reader did not obtain repeat measurements of each lung cancer by using the same method, we estimated whether intraobserver variability affected our measurements, by using two methods. First, we determined the mean difference between elliptical and perimeter-derived volumes and noted whether this mean differed for small (<5,000 mm3 with the perimeter method) and large lesions (>=5,000 mm3 with the perimeter method). Second, we divided the patients into two groups of equal size on the basis of perimeter DT: the patients with the longest and shortest DTs, or the "longest-shortest" group, and those with medium-length DTs, or the "medium" group. We then compared mean intervals between the two CT examinations between groups.

In a similar way, we also assessed whether differing section increments for the two CT examinations influenced volume measurements by dividing the patient population into longest-shortest and medium groups and comparing mean differences in section increment between the two groups.

To determine how well tumor volumes calculated with the three methods agreed, the following Pearson correlation coefficients were calculated: (a) spherical method volume and elliptical method volume (first CT examination), (b) spherical method volume and perimeter method volume (first CT examination), (c) elliptical method volume and perimeter method volume (first CT examination), (d) spherical method volume and elliptical method volume (second CT examination), (e) spherical method volume and perimeter method volume (second CT examination), and (f) elliptical method volume and perimeter method volume (second CT examination).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Two hundred sixteen patients with lung cancer diagnosed at stage I were followed up at the VA Medical Center in Indianapolis, Ind, during the study period. Of these patients, 104 underwent fewer than two chest CT examinations prior to treatment. Thirty-eight patients underwent at least two pretreatment CT examinations, but these were performed less than 25 days apart. In 13 patients, one of the two pretreatment CT examinations was performed with the patient in the prone position. In two patients, one of the two pretreatment CT examinations did not depict the entire tumor (in both patients, this examination was performed during fine-needle aspiration biopsy). Two patients developed a new primary cancer. In seven patients, the tumor margins could not be visualized entirely at subsequent CT examinations due to effusion (n = 2), lobar collapse (n = 2), chest wall invasion (n = 2), or extension to hilar structures (n = 1). The remaining 50 patients constituted the study group. Measurements were obtained for 701 CT sections in these patients.

Median patient age at diagnosis was 72 years (range, 43–85 years). Comorbidities are listed in Table 1. All but one patient had a documented smoking history, with a median of 60 pack-years; 27 were continuing to smoke at the time of diagnosis. A diagnosis was made by using fine-needle aspiration (n = 47), protected specimen brushing (n = 2), or sputum cytology (n = 1). Most cancers (n = 38) were in the upper lobes; histologic diagnoses were squamous cell carcinoma (n = 16), adenocarcinoma (n = 15), bronchioloalveolar carcinoma (n = 9), and other cell types (n = 10) (Table 2). Thirty-four patients were classified as having stage IA (diameter <3.0 cm) cancer at diagnosis and 16 as having stage IB (diameter >=3.0 cm) cancer. For each patient, histologic findings, cancer stage at diagnosis, interval between first and last CT examination prior to treatment, and DT as measured by using the three methods are listed in Table 3. The interval between the first and last pretreatment CT examinations ranged from 25–1,212 days, with a median of 128 days.


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TABLE 1. Comorbidities

 

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TABLE 2. Histologic Type and Site of Lung Cancer

 

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TABLE 3. DT by Stage, Type, and Measurement Technique

 
For each of the measurement methods, DTs ranged widely in the study population (Table 3). The median DT was 147 days (range, -95 to 30 days) for the spherical method, 174 days (range, -468 to 30 days) for the elliptical method, and 181 days (range, -26,711 [stable] to 32 days) for the perimeter method. "Negative" growth (indicating that the tumor appeared smaller at the later CT examination) was measured in seven patients by using the spherical method, in three patients by using the elliptical method, and in one patient by using the perimeter method.

Pearson correlation coefficients for volume measurement with the first CT examination were 0.938 (spherical vs elliptical), 0.936 (spherical vs perimeter), and 0.995 (elliptical vs perimeter); for the second CT examination, they were 0.982 (spherical vs elliptical), 0.976 (spherical vs perimeter), and 0.999 (elliptical vs perimeter). All were significant at the .01 level (two-tailed test). In the calculation of DT, the elliptical-perimeter methods were in closest agreement in 25 (50%) patients; the spherical-elliptical methods, in 13 (26%) patients; and the spherical-perimeter methods, in 11 patients (22%). (In one patient, spherical-perimeter and elliptical-perimeter measurements were equally close.) Mean volumes were similar with elliptical-perimeter methods, and SDs were lower than those obtained with the spherical method (Table 4).


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TABLE 4. Means and SDs of Tumor Volume for Each Measurement Method

 
Averages were obtained from five CT examinations at which the tumor appeared on 6–8 sections (mean for all examinations, 7.01 sections). For each examination, the time needed to display the examination, measure all cross-sectional axes and perimeters, and enter data into the volume calculation program was 310 seconds for the spherical method, 355 seconds for the elliptical method, and 315 seconds for the perimeter method.

By using the perimeter method, in patients with squamous cell carcinoma (n = 16), the median DT was 119 days (range, 1,004 to 33 days); with adenocarcinoma (n = 15), 157 days (range, -26,711 to 64 days); and with bronchioloalveolar carcinoma (n = 9), 370 days (range, 6,960 to 40 days). In patients with tumors diagnosed at stage IA (n = 34), the median DT was 129 days (-26,711 to 32 days) and in patients with tumors diagnosed at stage IB, 218 days (2,359 to 66 days).

By using growth rates based on the perimeter method, the tumor would have had a diameter of 0.5–3.0 cm for less than 1 year in three (6%) patients, for 1–2 years in eight (16%) patients, and for more than 2 years in 39 (78%) patients (Table 5).


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TABLE 5. Theoretical Interval during which Nodule Was 0.5-3.0 cm Diameter, Based on Perimeter Method

 
In tests for intraobserver variability, the mean difference between elliptical- and perimeter-derived volumes was 16.5%; the mean difference was 20.8% for small lesions (<5,000 mm3) and 13.3% for large lesions (>5,000 mm3). With the perimeter method, the mean DT was 129 days both in patients with short DTs and in those with medium DTs. The mean difference in section increment between CT examinations was 3.3 mm for patients with long-short DTs and 3.5 mm for patients with medium DTs.

Table 6 lists the types and rationales for the therapy chosen. Only 13 patients underwent surgery; curative radiation therapy and/or chemotherapy were administered in 24 patients. In 13 patients, no definitive treatment was administered.


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TABLE 6. Patient Treatment and Rationale

 

    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
By using the perimeter method of measurement, the median DT for all cancers in our study was 181 days, with a range of -26,711 (ie, stable) to 32 days. We report median rather than mean values for DT because a small number of very slowly growing tumors strongly affected the arithmetic mean (-56 days). The true mean of the data can be better approximated by averaging the sum of the reciprocals of DT (ie, 1/DT1 + 1/DT2 + ...1/DT50) and taking the reciprocal of this average. This yields a mean of 129 days ± 138 for the study population. This value is slightly larger than the mean DT found by Geddes (102 days) (16) in a summary of growth rate studies with the use of chest radiography. In addition, tumors in 11 of the 50 patients in our study were growing so slowly that by one frequently quoted measure of benignity versus malignancy (DT >= 465 days), they would have been considered benign (17).

Many investigators (812) have estimated the growth rates of various types of lung cancer by using chest radiography. In one series of 67 patients, DT ranged from 30 to 490 days (8); in another review (18) of 52 patients, DT varied from 1 to 14 months. Radiographically, it has been estimated that a tumor requires 27 DTs to reach a diameter of 5 mm and 35 DTs to reach 3 cm (16). At 40 DTs, the tumor is 10 cm in diameter; however, most patients die before this occurs (16). Tumor DT has been shown to be an independent predictor of mortality (19).

To our knowledge, there are few data regarding the use of CT to measure serial volumes of lung cancers prior to treatment. Aoki et al (20) measured tumor growth at serial CT examinations in 10 patients with adenocarcinoma prior to treatment but used only mean tumor diameters, not volume, and did not separate the CT-derived results from radiographic measurements. Combined CT and radiographic results yielded DTs ranging from 42 to 1,486 days. As part of a screening program, Hasagawa et al (13) measured the DT of nodules on successive CT images in 61 patients whose nodules were later proven to be cancerous and found that DT ranged from 52 to 1,733 days (mean, 452 days; median not reported). In their study, however, the largest nodular cross-sectional area, not volume, was used in DT calculations, not all tumors were stage I at diagnosis, and 80% of tumors were adenocarcinomas. Yankelevitz et al (14) used automated three-dimensional reconstruction of CT images to measure the growth of small nodules in 13 patients; in their study, all benign tumors had a DT greater than 395 days, and all malignant tumors had a DT less than 178 days; use of maximum cross-sectional area did not separate benign and malignant tumors.

We measured the volume of the tumor by using three methods because each method is used in different clinical situations. The spherical method recreates that used with posteroanterior and lateral chest radiography, in which the craniocaudal extent and largest transverse diameter are used to estimate tumor size. The elliptical method is similar to measurement on hard-copy CT images, on which tumor axes are measured on the section showing the largest tumor cross-sectional area. Radiation oncologists, including those at our facility, frequently use the perimeter method to measure tumor cross-sectional area on each CT section. These areas are integrated to compute the tumor volume and subsequent total radiation dose to be delivered.

In the absence of a reference standard and because the results with all three methods were highly correlated, to determine the best method we compared the growth rates determined with each method for each patient and counted the number of patients for whom the closest agreement was between spherical-elliptical, spherical-perimeter, and elliptical-perimeter measurement methods. Elliptical-perimeter methods agreed most closely in 25 (50%) patients. In addition, the mean volumes obtained with the elliptical-perimeter methods were more similar to each other than to those obtained with the spherical method and had lower SDs. Use of the spherical method consistently resulted in overestimation of nodule volume by 50%–60%, as compared with either the elliptical or perimeter methods; yet, because of this consistency, spherical results were highly correlated with the elliptical-perimeter results. We thus concluded that the spherical method was the outlier among the three methods. On the basis of our results, there is no way to choose the "best" between the two remaining methods, elliptical and perimeter. As the perimeter method is commonly used by radiation oncologists, for much of the following discussion we decided to use volumes measured with the perimeter method to calculate tumor growth. Moreover, we expect that increasing use of video rather than hard-copy display will make use of automated measurement tools such as the RadWorks software more commonplace.

Even with measurement of volume by using these tools, estimations of growth rate based on these measurements are fraught with potential sources of error. Intraobserver variability may represent a substantial percentage of the total cross-sectional area, especially when measuring small tumors. Staron and Ford (21) demonstrated that repeated measurements of cross-sectional area by a single observer varied by about ±5% for an object of cross-sectional area of 705 mm2 (similar to the mean tumor cross-sectional area measured on the 701 CT sections used in the current study) and as much as ±20% for very small areas (75 mm2). Whereas our reader did not perform repeated measurements, an estimation of the change in variability with changing lesion size can be computed by comparing percentage difference between elliptical- and perimeter-derived volumes for small (<5,000 mm3 with perimeter method) and larger lesions. One would expect this difference to be larger for small lesions if intraobserver variability increased. In the current study, the mean difference between elliptical- and perimeter-derived volumes was 20.8% for small lesions and 13.3% for large lesions. While this difference was not large, it was evidence for increased intraobserver variability with measurement of small tumors.

Intraobserver variability may also be observed when the delay between the initial and final CT examinations is brief. We chose a cutoff of 25 days between examinations as the minimum interval necessary to reliably detect growth on the basis of both radiographic (16) and preliminary CT volumetric (15) data, but in slow-growing tumors, intraobserver variability may cloud measurement of growth even with substantially longer intervals between examinations. To determine whether this occurred, we observed whether the time between examinations was shorter for the 12 patients with the fastest DTs and the 12 patients with the slowest DTs, or "fast-slow" group, as compared with the remaining patients with medium-speed DTs, or the "medium" group. If short intervals between CT examinations imparted error to growth rate measurements, we would expect that unusually fast or slow DTs would be associated with short intervals. In the study population, this did not occur; the mean interval between examinations was 229 days for both the fast-slow and medium groups. This result is evidence that serial CT examinations as close as 25 days apart can be used to estimate growth rate.

Another source of variability that was unavoidable in the current series was differing section widths and increments at the initial and final chest CT examinations. Over the period of the study, standard chest CT examinations were performed with either 10- or 6-mm section increments, as were "thin-section" examinations with either 2- or 3-mm increments. Biopsy- and radiation-planning CT examinations involved 5-mm section increments. We considered measuring only CT scans obtained with the same section increment (even if it required combining images), but if we had done so, a majority of studies would have had a 10-mm section increment. Measurement of tumor cross-sectional area, and particularly craniocaudal extent, is obviously less precise with wider section increments, and we reasoned that the loss of precision would have been larger than the error introduced by comparing studies with different section increments. Whether this error is substantial can be estimated by comparing the mean difference in increments between the first and last CT examinations, between the fast-slow group and medium group, as was done before. This mean difference was 3.3 mm for the fast-slow group and 3.5 mm for the medium group; these similar values are evidence that varying section increments imparted negligible error into the growth calculations.

Tumor shape may change when a patient is turned to the prone position, as is necessary for some biopsies. As this introduces a source of error that we were uncertain how to correct, we decided not to include CT studies obtained with the patient in a prone position.

Finally, since our calculations were based on only two data points for each patient, the times of the initial and the final CT examinations, for the purpose of this study we assumed that each tumor grew at a constant rate. The possibility of nonlinear growth or growth that slows as an asymptotic value is approached (eg, Gompertzian model) has been advanced (22,23). However, to ascertain whether growth is nonlinear rather than linear would require at least three temporally separated CT volume measurements. Doing so would have reduced the number of qualifying patients in the current study by more than half. Furthermore, to use a Gompertzian growth model, one must determine what upper bound the growth curve asymptotically approaches. Several studies (2426) have been published in which Gompertzian growth of lung cancer metastases was investigated, but none to our knowledge involve primary lung tumors. If one uses the most commonly quoted estimation of an upper bound, that of Geddes (death occurs at 10-cm diameter) (16), then the Gompertzian asymptote is approximately 500,000 mm3. The largest tumor in our study measured approximately 200,000 mm3, and the median volume was approximately 6,000 mm3. Even a spherical tumor of 3.0-cm diameter (the largest stage IA tumor possible) has a volume of only 14,000 mm3. We believe that a majority of tumors in the current study were so small relative to the asymptotic value that even if a Gompertzian model were assumed, they would be on the "linear" portion of the growth curve.

While stage I, II, and IIIA tumors are considered resectable, patient comorbidities often make surgery unfeasible, particularly with increasing stage. Even in stage I there is substantial difference in survival rates between patients who have stage IA versus stage IB tumors and undergo surgery (27). In stage IA, however, tumor size and survival may not be correlated (28). While screening CT studies in at-risk patients should be designed to maximize the probability of detection while the tumor is at stage IA (0.5–3.0 cm diameter), this desire must be balanced against the cost and inconvenience of the study. In the study population, we calculated the duration that each tumor would have been detectable but no larger than a stage IA tumor (ie, T1), assuming spherical shape and constant growth. Only three of these tumors would have been this size for less than 1 year, and another eight would have been this size for less than 2 years. Therefore, in the population of the current study, annual screening would have resulted in detection of 47 (94%) of the 50 tumors while they were less than 3 cm in diameter, and biennial screening would still have revealed 39 (78%) of the 50 tumors at this size.

While lung cancer was at stage I at diagnosis in all patients in the current study population, surgical resection was performed in only 13 patients. Some patients refused therapy, but in most patients surgery was not performed because of risk factors such as chronic obstructive pulmonary disease or coronary arterial disease. Significant comorbidity is not unexpected in the patients in this study, who are served by a VA medical center and are older (median age, 72 years) than other patient populations with stage I lung cancer (28).

In summary, volumes measured with all three methods were highly correlated, and the elliptical and perimeter DTs showed best agreement. By using the perimeter method, comparison of lung tumor volumes at serial chest CT examinations revealed a median DT of 181 days, with a very wide range (32 days to essentially infinite). Eleven tumors had such slow growth that they might have been considered benign if biopsy had not been performed. Because we have a relatively elderly population, indolent tumors may be overrepresented. In 94% of the patient population of the current study, annual CT screening would have enabled detection of the tumor while it was less than 3 cm in diameter.


    FOOTNOTES
 
Abbreviation: DT = doubling time

Author contributions: Guarantor of integrity of entire study, H.T.W.M.; study concepts, H.T.W.M., S.G.J.; study design, H.T.W.M., S.G.J., A.M.A.; literature research, S.G.J., H.T.W.M.; clinical studies, S.G.J., H.T.W.M.; data acquisition and analysis/interpretation, S.G.J., H.T.W.M.; statistical analysis, S.G.J., C.A.M.; manuscript preparation, H.T.W.M., S.G.J.; manuscript definition of intellectual content, H.T.W.M., S.G.J., A.M.A.; manuscript editing, H.T.W.M., S.G.J., A.M.A., C.A.M.; manuscript revision/review, R.D.T., D.J.C., M.T.; manuscript final version approval, H.T.W.M., S.G.J.


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

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