Synthetic Lung Tumor Data Sets for Comparison of

Volumetric Algorithms1

Adele P. Peskin,

(a)(d) Karen Kafadar,(b) Alden Dima,(c) Javier Bernal,(c) and David Gilsinn(c)

(a)

National Institute of Standards and Technology, Boulder, Colorado 80305 USA

(b)

Department of Statistics and Physics, Indiana University, Bloomington, Indiana 47408 USA

(c) National Institute of Standards and Technology, Gaithersburg, Maryland 20899 USA

(d)

Corresponding author: peskin@boulder.nist.gov

Abstract - We present a set of synthetic lung tumor data

in which synthetic tumors of known volume are 

embedded in clinical lung computerized tomographic 

(CT) data in different background settings in the lung.

Because the change in pulmonary nodules over time is

an important indicator of lung tumor malignancy, it is

important to be able to accurately measure changes in

tumor size from measurements made at different times

and possibly with different equipment. Standardized

lung tumor data sets can be used to calibrate the 

differences between sets of scans as well as accurately 

compare volumetric measurement techniques. Our

standard data sets combine the usefulness of phantom

data with the clinical challenges of realistic CT scans.

Keywords: image processing, segmentation, synthetic data,

reference data.

1

1 Introduction

The change in pulmonary nodules over time is an extremely

important indicator of tumor malignancy and rate of growth.

Physicians base both diagnoses and treatment on perceived

changes in size, so accurate and precise measurement of such

changes can have significant implications for the patient. With

current technology, tumor sizes, from which changes in size

over time are calculated, are measured via computed

tomography (CT), though often on different CT machines,

with different operators, at different times of the day, and with

patients in different physical positions relative to the CT

equipment. Thus, a particular tumor is unlikely to be divided

into slices at exactly the same places on two different sets of

scans. The pixel distributions, intensity of grayscale, and

average background values also may not be the same between

two different sets of data.

 1 This contribution of NIST, an agency of the U.S.

Government, is not subject to copyright.

Many articles have described a variety of techniques for

calculating tumor volumes and/or the change in tumor size

between two sets of data on the same tumor [1–6]. To

compare these techniques, we need standardized data with

known tumor volumes of various sizes within different levels

of background noise. Although phantom tumor data are

currently available and published studies [7,8] have compared

volumetric methods on these phantom data sets, the phantom

data settings are often not realistic, because the synthetic

phantoms are placed in a synthetic background. A realistic

and valid assessment of these volumetric methods needs

realistic calibrated data sets, in which phantom ``tumors'' of

constructed size, shape, and volume are placed within data

collected from clinical CT scans of background (non-tumor)

tissue. These data sets should contain data that represent the

different types of tumors seen in more realistic data. In this

study we present a method for generating phantom lung

tumors in various settings: centrally located in the lung and

free of blood vessels, centrally located in the lung in a region

where blood vessels also are located, and attached to the

pleural surface of the lung by a tail. We present a set of

synthetic lung tumor data in which synthetic tumors of known

volume are embedded in clinical lung CT data for each of

these situations. We show the resulting pixel distributions

from many sets of clinical lung tumor data, and how we use

these distributions to develop algorithms to create these data

sets.

2 Objective

Our goal is to create sets of artificial tumors of known

volumes embedded in real lung data, for use in comparing

techniques that measure tumor size and growth. The data

should include a wide variety of tumor sizes and shapes.

Analyzing the artificial data should involve the same

complications associated with making volume measurements

of clinical tumors, such as those that arise due to connectivity

to blood vessels and the pleural lining. The end result of our

work is the creation of techniques to produce diverse types of
embedded tumors that cover the range of tumor types seen in

real life, in terms of sizes, shapes, and confounding features,

as needed to perform robust tests of volumetric software.

3 Data Description

To develop a method for creating standardized synthetic

tumors, we studied the pixel distributions of many sets of

images obtained from the Public Lung Database to Address

Drug Response, which is funded by the Cancer Research and

Prevention Foundation (www.via.cornell.edu/crpf.html). This

database contains many examples of each of the types of

tumors listed above. Figure 1a shows an example from this

database of a single slice of data containing a tumor relatively

free of blood vessels, and Figure 1b shows a region of the

pixels in and around the tumor in this slice of data. To

visualize the pixel distributions of the lung data sets, we

discretize each individual pixel in each slice of data in the

region of the tumor and color-code the categories accordingly.

In this way, the clear differences in pixel intensities between

pixels inside of lung tumors, pixels on or near the surfaces of

lung tumors, and pixels in the surrounding lungs are apparent.

4 Data Creation

To create synthetic tumors embedded in CT data, we begin

with a large, centrally located tumor, which is relatively free

of blood vessels. The tumor is located in slices 110-150 of this

data set, and for each slice we collect pixels in the region of

the tumor. We are interested both in the pixel intensity

distribution in this region as a whole, and in the subdistributions at the tumor center and along the tumor edges.

Figure 1c shows a histogram of all of the pixel intensities

within the larger bounding box of Figure 1b, and are

representative of the data sets in general. Figure 1d shows a

histogram of all of the pixel intensities within the smaller

bounding box shown in Figure 1b, which correspond to the

interior of the tumor.

The actual edge of the tumors in CT data will not necessarily

lie exactly along grid points, but it will lie within one pixel

length of a grid point. Each pixel has a nominal location, but

the intensity value at that pixel represents a volume in the

original sample; we refer to this volume as a "voxel". The

intensity of a pixel that is representing the edge of the tumor

will vary with the distance between the closest pixel location

and the actual edge. So the edge itself will not appear as a

clear edge in the data, but rather as a blurred pixel-length

region that represents the edge, and hence this region will

have a distribution of pixel intensities much wider than that

for the lung pixels. We attempt to define this distribution here.

We isolated the pixels in regions of many lung tumors from

the Public Lung Database, and compared the pixel intensity

distributions. We found that the mean and standard deviation

of these distributions vary slightly across data sets and hence

cannot be used as standard metrics. A more consistent metric

across data sets comes from an empirical estimate of the

magnitude of the gradient of the pixel intensities. The mean

and standard deviation of the gradient magnitude at the tumor

edges are consistent across a wide range of data sets [9]. This

makes sense, because the lung tissue is a fairly consistent

density, the tumor is a fairly consistent density, and the

change between tumor and lung tissue covers a consistent

range. The distribution of pixel intensities at the edge reflects

this overall difference. The spread of intensities at the edge is

in part a function of the physical spacing between adjacent

pixels. If the locations are closer to one another, the edge will

be more clearly defined. The pixel intensity associated with

the highest point in the gradient of the intensity field,

however, should not depend upon the pixel spacing.

Figure 1: a.) Section of a slice of lung CT data containing a

lung tumor; b.) Pixel intensities in Hounsfield units for data

in 1a: white: -150 to 100, orange:-250 to -150, pink:-350 to

-250, red :-450 t0 -350, yellow: -550 to -450, green: -650 to

-550, blue: -750 to -650, purple: -850 to -750, teal: less than

-850; c.) Histogram of the intensities inside the larger box of

1b; d.) Histogram of intensities inside smaller box of 1b.

We step back from the clinical data and use synthetic data to

perform calibrations to determine exactly how to create our

blurred boundary regions. Separately from the lung data, sets

of synthetic images are created, containing spheres of sizes
ranging from 4 to 20 pixel lengths. The pixel intensities at

grid points in each of these grids represent the distance from

the grid point to a central specified point in the grid. An

isosurface within this grid at a particular value, therefore,

represents an exact sphere with the radius of that isovalue.

The goal is to represent a sphere of known volume with

simulated data that has blurring at its boundary that is

equivalent (or similar to) the blurring at edges of tumors in

real CT scans. We compare the known analytical volumes of

these spheres with volumes calculated from our technique to

measure tumor volumes, described in [9], since we will use

this measurement technique to analyze our new data. These

results are shown in Table 1.

Table 1. Volumes of spheres measured with our marching

cubes algorithm

radius Calculated

volume*

Analytical

volume*

Percent

error**

4 258.267 268.082 3.66

5 511.185 523.598 2.37

6 890.219 904.778 1.61

7 1420.494 1436.754 1.13

8 2124.761 2144.659 0.93

9 3031.675 3053.625 0.72

10 4164.123 4188.787 0.59

11 5547.871 5575.275 0.49

12 7208.727 7238.223 0.41

13 9170.843 9202.765 0.35

14 11460.105 11494.030 0.30

15 14099.811 14137.155 0.26

16 17118.117 17157.270 0.23

17 20537.883 20579.510 0.20

18 24385.213 24429.004 0.18

19 28684.250 28730.889 0.16

20 33460.980 33510.293 0.15

(*cubic pixel length)(**100(analytical-caculated)/analytical))

Now we create similar spheres of each size, but the edges of

these spheres will represent the blurred edges of the clinical

images. Instead of using distances from a central point for the

pixel intensities in our synthetic data sets, we now use clinical

intensities sampled from lung tumor data. All pixel intensities

are taken from the tumor of the data set shown in Figure 1.

Pixel intensities for pixel locations that are entirely inside of

the sphere are chosen at random from a collection of

intensities representing the clinical tumor data, shown in

Figure 1d. Pixel intensities for all pixels on or near the edge

are calculated differently.

Each pixel location is defined as the center point of a unit

sized voxel. The intensity of that pixel depends on the density

not just at the pixel location, but the density throughout that

voxel. We compute a weighted average of subsamples where

the weight is dependent on the distance to the center of the

voxel and the subsample points are evenly distributed through

the voxel. We divide the voxel into 100 x 100 x 100 pieces. If

a piece is outside of the sphere, it contributes nothing. If it is

inside the sphere, it contributes a term that is proportional to

the inverse of its distance from the central pixel location. In

the case of a voxel entirely within the sphere, this sum is equal

to 1.0. For a voxel at the edge, this sum is a fraction, f,

between 0.0 and 1.0. The actual value of the pixel intensity for

the center point of the voxel is then:

Intensity = f * (tumor mean value) +

(1.0-f) * (maximum background value) (1)

The maximum background value of pixel intensity in the

region of the tumor is defined as a constant, k2, for a

particular data set, as described in [9]. The images of spheres

with blurred edges are then embedded into the slices of the

data set. Figure 2a is a section of a slice of the resulting data.

We then calculate the magnitude of the new gradient of the

pixel intensity field and compare it to the gradient of the pixel

intensity field in the region of the clinical tumor in that data

set. For each tumor, the clinical tumor and the synthetic

sphere, we find the average magnitude of the gradient at each

intensity value between -800 Hounsfield units (HU) and -100

HU. These curves are smoothed using a locally weighted

linear smoother (using R software; see www.r-project.org),

and presented in Figure 2b, along with a graph of the

normalized differences in the square roots of the gradient

magnitudes from the two tumors, Figure 2c. These figures

Figure 2: a.) Section of a slice of lung data with

embedded sphere; b.) Smoothed curves of the average 

gradient magnitude of the pixel intensity in the region of 

the clinical tumor (in black) and the synthetic sphere (in

blue); c.) Normalized differences in the square roots of 

the curves in 2b.
show the similarity between the gradients of the pixel

intensity fields of the clinical tumor and the synthetic tumors.

5 TYPES OF LUNG DATA

Sets of synthetic spheres with blurred edges were then

embedded into a section of the lung data where clusters of

blood vessels reside. Where the blood vessels and sphere

edges overlap, the edge of the sphere blends with the pixels

representing the blood vessels. Figure 3a shows a spherical

synthetic tumor embedded into a section of the lung

surrounded by blood vessels. This is an example of a data set

that could be used to evaluate methods that eliminate attached

blood vessels from tumor volume measurements. By situating

geometric objects of known volume into regions of lung tissue

in areas that lead to difficult volumetric measurements, we

can study and compare methods that deal with removing

vascular attachments from tumor volume measurements. The

edges of these objects will be realistic blurred edges,

constructed to maintain the volumes associated with objects

with precise edges.

Attaching synthetic tumors to the pleural lining of lung tumor

data can be done in many different ways. Most of the tumor

data we have investigated so far has shown that the extent of

attachment of the tumors varies over the slices containing the

tumor. In each we have found, by looking at 3D pictures of

these tumors and their attachments, slices in which the tumor

pixels blend into the pixels of the lining, and neighboring

slices in which the attachment gradually disappears. In many

of these examples, networks of blood vessels also complicate

the distribution of middle range edge pixel values.

An example of a synthetic sphere that is attached to the

pleural lining is given in Figure 3b. A geometric attachment is

created, whose pixels are selected at random from the tumor

in this data set, and the pixel intensities at the edges of the

attachment are calculated according to our integration method.

The extent of attachment of the sphere to the pleural lining

varies in different slices containing the sphere, and tapers off

as in seen in each example of the clinical data.

We investigated one last example of this type of synthetic

data, shown in Figure 3c. Micro CT data of a phantom tumor

from the FDA, pictured in Figure 3d, is embedded into the

lung data. As in the synthetic spherical tumors, the edges of

the phantom tumor cover a one pixel length edge, in which the

pixel intensities vary with the distance from the edge of the

tumor. Table 2 gives the embedded geometries and

placements of the various synthetic data sets we have created

so far.

5 Volumetric Comparisons

Clinical lung CT data of lung tumors do not have well-defined

edges, and the strength of a method for determining lung

tumor volumes from these data depends on how well it

defines those edges. We use the synthetic lung tumor data to

begin to evaluate a variety of methods for lung tumor volume

measurement. Estimates of the embedded sphere volumes for

the case of a radius of 20 pixel lengths show clearly that the

volume is highly dependent on the method of determining the

sphere boundary. The pixel spacing within a slice is 0.57 mm,

and 1.25 mm between slices, i.e., the sphere has a radius of

11.4 mm and a volume of 6205.87 cubic mm. The volume

estimate by the method described in [9] was 6196.74 cubic

mm or approximately a 0.15 % error. The radius estimate in

this case would be 11.39 mm. Thus a 0.09 % radius error

produced a 0.15 % volume error. A second method based on a

Canny edge detection algorithm produced a volume of

6596.88 cubic mm with a radius of 11.63 mm. In this case a

2 % error in radius estimate produced a 6.3 % volume error. A

third method involving approximately the edge produced by a

Canny edge algorithm with B-splines gave a volume of

6626.57 cubic mm was based on a radius estimate of 11.65

mm. In this case a 2.2 % error estimate for the radius

produced a 6.8 % volumetric error. We also computed a

volume using a commercial software package using several

accurate but very interactive methods of region selection and

refinement. Depending upon the specific set of steps selected

Figure 3: a.) Section of a slice of lung data with a sphere

embedded in the location of a large blood vessel; b.)

Section of a slice of lung data with a sphere attached to

the pleural lining of the lung; c.) Section of a slice of 

lung data with a phantom tumor embedded; d.)

Isosurface at 30 HU of the phantom tumor.
for the measurement, the volumetric accuracy varied between

1.13 % and 2.95 % error. Clearly the method to approximate a

tumor boundary requires a great deal of accuracy to lead to

good volume measurements. These data sets now provide a

tool to compare different types of measurement strategies.

Table 2. Sets of available synthetic tumor data

geometry Sphere

radius*

Ellipsoid

dimensions

type**

sphere 10 free

sphere 15 free

sphere 20 free

sphere 15 embedded

sphere 15 attached

ellipsoid 20-10-10 free

ellipsoid 10-20-10 free

ellipsoid 10-10-20 free

ellipsoid 10-20-10

rotated 45

degrees about

slice direction

free

ellipsoid 10-10-20

rotated 45

degrees

perpendicular

to slice

free

FDA phantom

*in pixel lengths, system variant

**free = free of blood vessels, embedded = embedded in vessels,

attached = attached to pleural lining

6 Conclusions and Future Work

We have created an initial group of synthetic lung tumor data

sets, in which both known geometric shapes and well defined

phantom tumors have been embedded into clinical lung tumor

data. We have developed methods for the insertion of these

synthetic tumors in different regions of the lung data, so that

the synthetic tumors can be used as standardized data to test

methods for measuring lung tumors whose edges are either

clearly defined or partially hidden by local blood vessels in

the lung. The methods proposed here will allow researchers to

create their own synthetic sets, enabling a systematic

comparison of the volumetric methods currently available to

measure tumor size and growth. Lung tumors often grow in

non-symmetric directions, in the shapes of spines and knobs

growing from an original sphere-like region. Future work in

the creation of these synthetic data sets includes plans to

create a variety of characteristic synthetic shapes in the lung

tumor data, and to greatly expand the sets of data we currently

have available.

ACKNOWLEDGEMENTS

Support for Dr. Kafadar from the Army Research Office,

Grant Number W911NF-05-1-0490 awarded to the University

of Colorado-Denver, and from the National Science

Foundation, Grant Number DMS0802295 awarded to Indiana

University, is gratefully acknowledged.

7 References

[1]Kostis, W.J., Reeves, A.P., Yankelevitz, D.F., Henschke,

C.I. Three-Dimensional Segmentation and Growth-Rate

Estimation of Small Pulmonary Nodules in Helical CT

Images. IEEE Trans. on Medical Imaging 22, No. 10,

October 2003.

[2]Reeves, A.P., Chan, A. B., Yankelevitz, D.F., Henschke,

Kressler, C.I.B., Kostis, W.J. On measuring the change in size

of pulmonary nodules. IEEE Trans. on Medical Imaging IEEE

25(4):435-450 (2006).

[3]Mendonca., P., Bhotika, R., Sirohey, S., Turner, W.,

Miller, J., Avila, R.S. Model-based Analysis of Local Shape

for Lesion Detection in CT Lung Images. Proceedings of the

International Conference on Medical Image Computing and

Computer-Assisted Intervention (MICCAI 2005). October

2005.

[4]McCulloch,C.C., Kaucic, R.A., Mendonca, P.R., Walter,

D.J., Avila, R.S. Model-based Detection of Lung Nodules in

Computed Tomography Exams. Academic Radiology. March

2004.

[5]Preim, B., Bartz, D. Image Analysis for Medical

Visualization. Visualization in Medicine 83-131, 2007.

[6]Preim,B., Bartz, D. Exploration of Dynamic Medical

Volume Data. Visualization in Medicine 83-131, 2007.

[7]Das, M., Ley-Zaporozhan, J., Gietema, H.A., Czech, A.,

Nuhlenbruch, G., Mahnken, A.H., Katoh, M., Bakai, A.,

Salganicoff, M., Diederich, S., Prokop, M., Kauczor, H.,

Gunther, R.W., Wildberger, J.E. Accuracy of automated

volumetry of pulmonary nodules across different multislice

CT scanners. Eur Radiol 17:1979-1984 (2007).

[8]Ko, J.P., Rusinek, H.,Jacobs, E.L., Babb, J.S., Betke, M.,

McGuinness, G., Naidich, D.P.: Small Pulmonary Nodules:

Volume Measurement at Chest CT-Phantom Study. Radiology

228:864-70 (2003).

[9]Peskin, A.P., Kafadar, K.,Santos, A.M., Haemer, G.G.

Robust Volume Calculations of Tumors of Various Sizes.

2009 International Conference on Image Processing,

Computer Vision, and Pattern Recognition.