With a demonstartion from the popular ¡°Where¡¯s Waldo¡± book series, the authors vividly illustrate the difficulty of detecting small breast lesions on standard mammograms. To overcome these obstacles, the authors promote the potential of 3D screening technology and review four 3D imaging modalities.
n this article, we postulate that research in breast imaging should
be focussed toward routine three-dimensional (3D) screening of
In the "Where's Waldo?"
series of children's books, a small figure of Waldo is sought in a
complex image. Using overlapping scenes containing Waldo, we aim to
show how the detection of a small lesion in a projection image
(i.e., in a standard mammogram) becomes an exceptionally difficult
and unnecessary task, given the option of 3D imaging. This handicap
is present in both film and digital mammography. With appropriate
registration of longitudinal 3D images, Waldo, and perhaps small
breast lesions, could be made to almost "jump out" of the picture.
We briefly evaluate the future potential of four different 3D
imaging modalities to detect small breast tumors: MRI, ultrasound,
x-ray CT, and EIT. Any 3D modality that replaces mammography for
standard screening would also, in the process, significantly reduce
describes the frustrations of two opposing camps, both deeply
concerned with the epidemic of breast cancer. The U.S. National
Institutes of Health
was disposed to bring these parties to a consensus. There is now a
consensus that for women over the age of 50 years, mammographic
screening is of significant benefit, reducing mortality by about
30%. The remaining frustration and controversy lies in whether or
not to regularly screen women 40 to 49 years old with mammography.
Though the two camps take the opposing endpoints of "all or
nothing," the underlying fact remains that traditional mammography
has serious limitations, despite recent declines in mortality rates
for breast cancer.
The technique still misses about 5% to 15% of all tumors.
Also, the overall yield of breast cancers per number of breast
biopsies recommended on the basis of screening mammograms ranges
between roughly 10% and 50%.
X-ray mammography is especially ineffective in detecting cancers in
radiographically dense breasts.
Additionally, there is a deeper and usually unspoken
frustration, stemming from the fact that we have no useful
screening technique for women younger than 40, except breast
self-examination and clinical breast examination. Younger women are
simply on their own,
though 21% of breast cancer cases are in women under 50 years of
age. Spratt et al
suggest, "No subset of adult women has a risk so low as to permit
their exclusion from an effective breast cancer control
While it is important to detect breast tumors early to reduce
the likelihood of metastatic spread,
it is clear that we need to look beyond mammography in order to
The problems with mammography stem from its two-dimensional (2D)
nature. A tumor is missed most probably because tissue present
above and below it is superimposed together on a 2D projection in
We would like to demonstrate this using "Waldograms," and thus make
a case for 3D longitudinal breast imaging. Perhaps, in the future,
better diets, environmental cleanup, drug treatment, and genetic
screening will eventually make medical imaging irrelevant. For now,
we argue that aggressive research toward 3D breast imaging and 3D
registration, to permit 3D longitudinal digital subtraction, is the
best path to detecting tumors small enough to reduce the likelihood
of metastasis and to cure this disease.
For example, it was demonstrated that reliable detection and
removal of tumors by the time they reach 4 mm in diameter
corresponds to a 25-year metastasis rate of only 0.6%.
We would like to interpret this extrapolation of a French study
to mean a 99.4% cure rate, if we had an imaging tool that
successful. Due to the cautions needed in interpreting
epidemiological data, we have embarked on a further epidemiological
Because many of the normal structures found within the breast
will likely be of the same size as the small tumors we are looking
for, the most reliable way to detect small tumors is by their
growth relative to local tissue. In order to do this, we need two
longitudinal images of the breast which could be aligned with each
other. Subtracting one from the other would reveal a tumor which
has grown in the time interval between the two images. However, the
loose and non-rigid nature of breast tissue almost guarantees that
two images of the breast taken at different times will be not be
exactly aligned. Hence, along with a good 3D imaging technique, a
good 3D registration algorithm
also will be necessary to succeed in detecting small breast
We will demonstrate, using the popular cartoon character Waldo,
that 3D longitudinal imaging with 3D registration and subtraction
provides a pathway towards detection of small tumors in the
Waldo is a cartoon character appearing in a series of children's
books by the English cartoonist Martin Handford.
The idea is to find Waldo amongst myriads of other small-scale
Figure 1 is a typical example of the problem of detecting Waldo,
but already we encounter one handicap for radiologists: the
original is in color, but we must deal in shades of gray. Let us
call this "Waldogram" A. Figures 2 and 3 are two more Waldograms, B
and C, and Figure 4 is the superposition of figures 1, 2, and 3,
represented by D = A + B + C. Start by trying to find Waldo in D
(figure 4), and you'll be confronting the problem of tumor
detection in mammograms head on.
A "Waldogram" (A) representing a plane through a woman's breast.
Reprinted with permission from Walker Books Ltd.
A "Waldogram" (B) representing another plane through a woman's
breast. Reprinted with permission from Walker Books Ltd.
A "Waldogram" (B) representing third plane through a woman's
breast. Reprinted with permission from Walker Books Ltd.
This image (D) represents the superposition of A, B, and C.
A, B, and C can be considered analogous to three planes through
a woman's breast. While A may have a clear (albeit hard to find)
picture of Waldo, that character is nearly indiscernible when
covered up by the uncorrelated structure added to the image by B
and C in D (figure 4).
One approach to the problem of finding Waldo is by digital
subtraction. We created another picture from A by eliminating
Waldo; let us call it A − W. We then superimposed A − W, B, and C
to yield a picture A + B + C − W. The negative of this was made
[i.e., W − (A + B + C)]. Now, when we superimpose D and this
negative, we should get:
E = A + B + C + W − (A + B + C) = W
E is shown in figure 5. But where is Waldo? If you are a
practiced Waldo finder, you can probably see him. However, there
are many Waldo-sized artifacts in the difference image E.
This (E) was obtained by the equation E=A+B+C+W-(A+B+C)=W
representing a digital subtraction mammogram which, if perfect
should show Waldo (W). it is peppered with "registration noise"
of comparable magnitude and texture.
We took care to align A + B + C − XW and A + B + C as accurately
as possible before superimposition. The small registration errors
lead to many artifactual errors in E ("false positives"). If we
were dealing with a woman's breast imaged at two different times,
our inability to align it the same way twice would produce small
registration errors. Any attempt to locate a small tumor that grew
in the time interval between the two mammograms, by subtraction
imaging, is then also likely to fail.
Suppose we were working in three dimensions and therefore could
isolate corresponding planes. If we add the negative of A − W to A
F = A + (W − A) = W
Again, A − W and A were aligned as accurately as possible before
This time Waldo jumps out at us in F (figure 6). Certainly,
there is still much background registration error, but it does not
overlap Waldo and it is quite distinguishable from him.
This image (F) was obtained by the equation F=A+(W-A)=W
representing digital subtraction between corresponding planes
isolated by a 3D imaging modality. While some registration noise
persist, Waldo stands out clearly.
The Waldogram demonstration suggests that breast tumors are
missed by mammography because of its two-dimensional nature and
that if we were to routinely image the breast in 3D we might detect
small, growing tumors reliably, by registration of 3D longitudinal
images and their digital subtraction.
Toward this end, we present below brief evaluations of four
potential technologies for 3D breast screening with respect to the
detection of 4 mm tumors.
The four modalities are MRI (magnetic resonance imaging), 3D
ultrasound, EIT (electrical impedance tomography), and CT
mammography. We are not evaluating optical tomography, positron
emission tomography (PET), thermography, or nuclear medicine
imaging of the breast,
because it is not clear that these modalities can attain sufficient
resolution to screen for and detect small breast tumors.
It must be stated here that in proposing modalities for 3D
longitudinal imaging, there are two considerations from an imaging
point of view. First, the method must have sufficient spatial
resolution to detect 4 mm tumors. Second, although it would be
helpful to have adequate contrast resolution (i.e., density or gray
level contrast relative to surrounding tissue) this is not
absolutely essential, as the local architectural distortion caused
by a small growing tumor may be sufficient to locate it by 3D
longitudinal registration and subtraction.
Our evaluations on MRI, 3D ultrasound, and EIT will be short for
the following reasons: the role of MRI in breast cancer screening
has already been discussed adequately in the literature, and we
shall merely indicate relevant articles in the literature; 3D
ultrasound is just taking off and has a long way to go before it
could routinely achieve 4 mm detection capability; and EIT of the
breast is still in its infancy. However, CT of the breast is the
natural extension of mammography to 3D. Thus, the desirable x-ray
characteristics of breast tissue can still be retained with this
modality. However, it has never been seriously considered as a
screening technique due to the large x-ray doses involved. Recent
literature in relation to CT mammography has only described it as a
useful diagnostic tool and not as a primary screening tool. We
therefore discuss CT of the breast in greater detail to see what
techniques could be used to reduce the dose to acceptable levels
while still aiming for 4 mm lesion detection.
It might be argued that even if an imaging modality is able to
detect all 4 mm lesions, it may not be able to detect
microcalcifications, which are heavily used by mammographers for
diagnosis. Since microcalcifications are typically in the range of
0.1 mm, it would seem that this would place a big demand in terms
of resolution on any imaging technique which attempts to replace
mammography. Even if the contrast were available, all current
commercially available 3D imaging techniques like MRI, ultrasound,
and CT of the breast do not approach 0.1 mm spatial resolution,
though micro-CT units which have spatial resolutions ranging from
25 to 100 ¦Ìm have been reported.
It must be pointed out that microcalcifications mostly occur
with accompanying lesions or inside a "bed" of dysplastic/
hyperplastic cells and actually represent the calcium secretions of
Let us call this entire "bed" of cells a "lesion" for simplicity.
In mammography, because the visibility of a lesion is occluded by
overlapping tissue above and below a lesion, often only the calcium
deposits inside a lesion are visible, due to their high contrast,
and the lesion itself is not seen directly. The shapes and other
attributes of microcalcifications are used diagnostically to
evaluate whether the accompanying lesion is benign or malignant.
However, an important question would be: If one had an imaging
technique which could delineate all lesions and indicate their
presence reliably, would we still need to image
microcalcifications? This is a controversial issue and needs
further investigation and evaluation.
Detection and diagnosis are two separate issues. The first is to
be able to detect every lesion which develops inside a woman's
breast. The next step would be to decide how to diagnose each of
these lesions. Needle biopsy can provide the true histologic nature
of a lesion, with a failure rate of less than 1%.
Future developments in imaging may even reach the point where
malignant and benign lesions may be distinguished with a similar
failure rate. For now, we address the issue of detection of all 4
mm tumors and put aside the issue of how they will be diagnosed;
without detection, there can be no diagnosis.
Brief evaluations of 3D imaging modalities
Magnetic resonance imaging (MRI)¡ª
Increasingly, MRI has been used as a diagnostic tool to resolve
mammographically ambiguous lesions, as well as for cancer staging.
The development of dedicated surface coils resulted in the ability
to image smaller lesions than was traditionally possible with
The use of dedicated surface coils, under homogeneous magnetic
fields, has allowed spatial resolutions close to 5 mm, with slice
thicknesses in the same range.
However, with current 3D imaging techniques,
the entire breast can be imaged without gaps at a 1 to 2 mm slice
thickness. Also, 3D imaging techniques allow nearly cubic voxels.
While the tomographic quality of these images has an obvious
advantage (because the exact location of a lesion can be known in
three dimensions), the question as to whether MRI can be used for
breast cancer screening has been addressed by several researchers
and the general consensus appears to be that the high cost for
imaging and long examination time prevent it from becoming a
screening modality. The nearly standard use of gadolinium contrast
agents, which are mildly neurotoxic,
also makes MRI of the breast an invasive procedure.
The issue of examination time has been solved with current fast
3D imaging techniques, which allow complete signal acquisition in a
fast 3D gradient echo (GE) sequence images of the entire breast can
be acquired in about a minute.
Even if, as explained earlier, we set aside the fact that MRI
cannot image microcalcifications, cost continues to remain a
stumbling block. Quoting Harms and Flamig,
"The cost of the contrast medium alone for breast MR imaging is
about double the current cost of screening mammography." To reduce
these costs, the use of contrast agents could be avoided by using
coils coaxial to the breast and shielding the chest from the
It remains to be seen, however, whether future development of
technology and development of superior imaging sequences will
obviate the need for the use of contrast agents, as well as bring
down the cost for an examination. Until such time, MR screening
will not be able to replace mammography.
¡ªOrdinary B-mode ultrasound is not reliable for breast cancer
However, Moskalik et al,
suggest that 3D compound ultrasound images obtained from multiple
views can be registered to correct for refraction artifacts, as
well as motion during image acquisition. They also propose image
registration of 3D longitudinal ultrasound compound images "to
display growth of abnormalities." Further studies need to be
performed to determine the limiting resolution of this
Ultrasound computed tomography (UCT), introduced at least 20
uses standard CT algorithms to obtain 3D images of the breast,
where changes in gray level between voxels indicate changes in
acoustical properties of the tissue. In reflection-mode UCT, the
transducer is used both to transmit pulses and receive the echoes.
In transmission-mode UCT, two transducers are used, one to transmit
pulses and the other on the opposite side of the breast to receive
echoes. Another possibility is to measure the time taken for the
pulses to travel between the transmitter and receiver and construct
a speed-of-sound image based on these measurements.
However, due to artifacts introduced as a result of attenuation and
refraction along the path of the pulses, the resolution with
transmission-mode UCT is much lower than with reflection-mode UCT.
Another major problem with transmission UCT is the time needed to
gather the projections and reconstruct the image.
Problems due to long imaging times with UCT have been tackled by
a hybrid technique which fuses information from a compound B-scan
image and a limited speed-of-sound CT image
to produce an image which depicts both tissue morphology and
acoustic properties. The algorithm uses the Fourier back-projection
(FBP) algorithm, although given the limited number of views (4 to
64), an iterative algorithm may have done better.
A voxel size of 1 mm
was used, although no studies have been performed to quantitate the
achievable resolution. It is clear that further research is
warranted to evaluate 3D ultrasound as a screening modality to
detect small breast tumors.
Electrical impedance tomography (EIT)
¡ªEIT works by surrounding the breast with many electrodes either
by direct skin contact or by immersing the breast in a conducting
fluid. One pair of electrodes is chosen to drive a weak, harmless
current through the breast. This current is below the threshold of
sensation and does not cause tissue damage. Voltage measurements
are taken simultaneously from all the other electrodes. Then,
another pair of electrodes is chosen for current injection, to
yield another "view." An image of the electrical resistance or
impedance by varying the frequency of the current can be
reconstructed using an appropriate algorithm.
To date, EIT has been a low-resolution imaging method, probably due
to the small number of electrodes used (16 to 32)
and imprecise reconstruction algorithms, which presume that the
electric current follows straight line paths.
The ultimate physical resolution may be limited by thermal
fluctuations in the electric currents (Hoult D, personal
Breast tumors have high impedance contrast.
Currently, computer simulations are being developed of many more
electrodes, to predict if EIT spatial resolution could be
competitive with CT, MRI, and 3D ultrasound.
Guardo et al
experimented with the back-projection reconstruction algorithm and
were able to detect a 3 mL plastic sphere at the center of a
torsosized cylinder of saline. Shahidi et al
reported that simulation results with a 3D finite element method
show that a 10-mL edema region with a conductivity equal to that of
blood can be detected at a 40 dB signal-to-noise ratio (SNR).
Furthermore, detection of a smaller volume, in the order of 2 mL,
should be possible by improving either the instrumentation to
achieve a 60 dB SNR or the performance of the reconstruction
These results, scaled to the size of the breast, indicate that even
small breast tumors (less than 4 mm in diameter) should detectably
alter surface potentials. However, future research into this
imaging modality is needed to determine if this is practicable and
will lead to images of sufficient resolution.
X-ray computed tomography (CT)
CT mammography, while the obvious extension of mammography to 3D,
has remained controversial because of the supposedly high doses
required for full breast imaging. There was considerable enthusiasm
for CT mammography in the late 1970s. Initial clinical trials using
dedicated and conventional CT scanners suggested that several
benign lesions could be distinguished from malignant lesions by
imaging the breast twice: once before and once after intravenous
Radiological contrast agents created a 5% increase in CT numbers
for breast cancers compared to benign lesions.
But, enthusiasm for CT mammography was not sustained because of
concerns regarding radiation exposure, as well as the need for the
use of contrast agents. The earlier experiments, however, used a
low spatial resolution (1 voxel = 1 mm ¡Á 1 mm ¡Á 1 cm).
With the introduction of spiral or helical scanning, which allow
the imaging of the whole breast in less than a minute, recent
studies have begun focusing once again on CT breast imaging.
Raptopoulos et al
assessed the performance of high-resolution CT (slice thickness of
1 to 2 mm) on breast biopsy specimens following conventional x-ray
specimen mammography. They conclude that, with fatty breasts, CT
and mammography performed equally well. However, for masses in
radiographically dense tissue, CT performed much better. This is
because the masses are not occluded by the presence of overlapping
tissue. Raptopoulos and coworkers thus concluded that CT could be
used selectively for patients with dense, difficult to evaluate
breasts where mammography has proved ineffective. They also stated
that because of the averaging effect of the large voxels used in
CT, microcalcifications would be poorly detected or missed.
Nevertheless, if the lesion itself is visible in the image, do the
microcalcifications really need to be imaged? Also it may be
possible to image microcalcifications in the following way: Let us
say we use 50 ¦Ìm voxels and 50 ¦Ìm wide detectors over a 30-cm
cube volume. We would need a reconstruction volume of 6000
(large, but attainable). The readings along a line of detectors
could be run length encoded,
and the runs used to create variable ray widths for an iterative CT
algorithm. This should allow preservation of microcalcifications,
while retaining full SNR for each ray sum. Again, this warrants
The dose constraint for standard screening mammography (average
glandular dose/view) given by the 1995 draft protocol of the
Commision of the European Communitie,
is 2 mGy with grid. Thus, it is about 4 mGy for 2 views. Teifke et
estimated that the average glandular dose for helical CT scanning
using slices which are 6 mm in thickness is about 10 mGy, with
in-slice resolution of 1 to 2 mm. Thus, it is seen that resolutions
close to our 4 mm target are already available at only about 3
times the dose of standard mammography. This also agrees with the
calculations of Muller,
who determined the dose of CT mammography to be three to six times
that of diagnostic x-ray mammography. Niklason et al,
using digital tomosynthesis with data collected by a fullfield
digital mammography camera, obtained images with 1.5 to 3 mm pixels
with "a total radiation dose of 0.89 to 1.74 times that in
conventional mammography in the same specimen." Tomosynthesis uses
simple back-projection, and can be improved upon by the use of CT
In order for CT to be used on a regular basis for screening of
asymptomatic women, the dose will have to be reduced even further.
The dose problem can be tackled in several ways
: In commercial x-ray CT machines, 180 or more views are taken in
order to "overdetermine" the equations; most commercial CT scanners
use variants of the FBP algorithm. The curve of image quality
versus number of views peaks earlier for iterative algorithms than
for FBP, at least under most conditions. Thus, a switch to
iterative algorithms might reduce the number of views required. The
original objection of increased computer time has been alleviated
by much faster computers, and a new approach to algebraic
reconstruction technique algorithms in particular produces
converged images in one or two iterations.
Reconstruction of images from limited data has been studied
extensively in the literature.
Dhawan et al
obtained significantly improved images, compared to standard
algorithms, using as few as 3 views, with Weiner deconvolution of
the point spread function (PSF) of a CT algorithm. It should be
possible to extend this to allow for a spatially varying PSF, which
occurs in nonlinear CT algorithms such as ART.
Because the total dose is proportional to the number of views
multiplied by the number of photons per view, another new approach
is to use a large number of views with relatively few photons per
view, at the level where one can do photon counting at each
detector. A CT algorithm based on single photon data, such as has
been devised for PET,
also is under development.
Substantial dose reduction by a factor of 10 also may be
possible by performance of CT mammography with monochromatic
Dose reduction should be attainable using steered x-ray microbeams.
It is thus entirely possible that, with these approaches, CT
dose could be reducible to levels at or below that of mammography.
A voxel width of 0.5 mm is already available in commercial CT
though the x-ray peak energy is not optimized for mammography.
Whether this voxel size is adequate to reliably detect 4 mm tumors
remains to be seen. A new kind of CT scanner could potentially be
built with substantially smaller voxel widths using detectors
currently used in fullfield digital mammography units.
Thus, future research of 3D CT mammography as a standard tool for
breast imaging can be anticipated, of course operating at the
appropriate energy range. If we combine all the tricks we know, can
we squeeze out sufficient image quality at an acceptable x-ray dose
to detect tumors at a small enough size to make a significant
impact on mortality? Our guess is "yes," but much work lies
It can be argued that high resolution breast imaging will result
in many small "lesions" and "false positives." Is it better to
ignore them all until some show up as larger tumors? If our
of empirical data
to small tumor sizes is correct, then all small tumors should be
removed. Leaving them in with a "wait-and-watch" policy only
increases their size and thus their probability of metastasis.
If we succeed in imaging small tumors reliably, control studies
could then be undertaken to determine whether "wait-and-watch" or
"excise when found" is best.
It could also be argued that the image registration procedure
will uncover normal changes in the breast occurring during the time
interval between the two images, due to pregnancy and lactation,
aging, menstruation, surgery, etc., which could be confused with a
growing tumor. Once the image registration procedure detects all
changes (normal and abnormal) in the breast, deciding which are
abnormal becomes a classification and diagnosis issue. By
conducting well-designed studies using healthy volunteers, it may
be possible to evaluate how normal changes in the breast over time
appear on an image.
It may then be possible to develop classification criteria to
separate these normal changes from those that occur due to a
growing tumor. This should be the focus of future research.
Standardization of breast position (most likely pendant) may be
necessary to avoid the internal slippage of tissue that appears to
occur on breast compression.
This is, again, a topic for future research.
Another reason for detecting and possibly removing tumors early
is the bimodal nature of recurrence of breast cancer.
According to this new model, many large tumors produce angiostatin,
an anti-angiogenic factor, which keeps distant micrometastases in
an avascular state. However, surgical removal of the tumor removes
the source of angio-statin, causing micrometastases to grow. Since
smaller tumors will probably not produce enough angiostatin to
suppress distant micrometastases, removing them should not cause an
early recurrence. In fact, removing them may prevent the formation
of distant micrometastases in the first place.
On the other hand, an argument could be made that: 1) there are
many benign "lesions" that never get large but could be confused
with small tumors; and 2) there are many small tumors that never
grow and are therefore not harmful to the patient. It could be the
latter that show up in autopsies of women who died of causes other
than breast cancer.
Let us grant these two possibilities. Small tumors that grow
slowly, do not grow, or regress can be distinguished from faster
growing tumors by rate of growth (low, zero, or negative,
respectively). Thus two 3D longitudinal registered breast images
could be used to estimate rate of growth.
A recent article described the normal appearance of "lesions" in
contrast-enhanced breast images which appear and disappear
throughout the menstrual cycle and across consecutive cycles.
Kuhl et al
noted that contrast-enhancing foci are normal in healthy
premenopausal breasts. These foci may even fall within formal
malignancy criteria with regard to "enhancement velocity" (the rate
at which the "lesion" uptakes the contrast agent), but may
disappear in the next menstrual cycle, indicating the benign,
transient nature of most of these "lesions."Exact localization of
the "lesions" in 3D will allow us to track the size and location of
each lesion versus time to determine whether it is a transient or a
persistent lesion requiring further diagnosis. The latter would, we
presume, be indicative of a tumor, shifting a study (in a clinical
setting) from screening to diagnosis. Small lesions that appear
transiently could require at least three registered 3D breast
images taken at consecutive times to distinguish them from faster
growing tumors that keep on growing. On the other hand, gating to
the menstrual cycle might take care of this problem.
Recent literature suggests that prostate specific antigen (PSA),
used to signal the presence of prostate cancer in men, is also
present in fluid extracted from the nipple of a woman's breast, as
well as in the serum.
However, like other chemical markers, this is present in only 30%
to 40% of tumors. Hence, even if the presence of cancer were
inferred through monitoring the changes in the antigen level, 3D
breast imaging would have to be performed subsequently to find the
location of the lesion. Whether 4 mm tumors can be reliably
detected (but not located) by chemical tests is not yet known.
We have ignored all methods which attempt to visualize the
vascular bundle around a breast tumor. With our goal of detecting 4
mm tumors, it is possible that many of these have little or no
vascularization. Kallinowski and colleague's
model using implantation of human breast cancer in nude mice showed
a 10-fold variation in tumor perfusion, thus indicating the
existence of a large variation in the degree of angiogenesis in
small cancers. Recent studies have also suggested that vascularity
is not a reliable indicator of malignancy, as several benign
lesions also display vascularity.
In a study performed by Nakata et al,
8% of malignant tumors larger than our 4 mm goal did not display
vascularity. We anticipate that thisfigure would increase as tumor
size decreases and, hence, the role of vascularity in breast
screening is questionable.
Throughout our discussion of different imaging modalities, we
have indicated minimum pixel and voxel sizes used by different
researchers. However, in most of these studies, quantitative
measurements of resolution, as well as studies to estimate the
minimum detectable size of a lesion, have not been performed. As
Williams and Fajardo
point out, "The pixel-to-pixel spacing merely puts an upper limit
on the achievable resolution. For this reason, the common (and
incorrect) equating of pixel size with spatial resolution usually
leads to an overly optimistic prediction of imaging performance for
a digital system." Hence, it is clear that for all the imaging
modalities discussed above, quantitative studies will have to be
undertaken to obtain estimates of the actual spatial resolution
achievable in each case.
We thus conclude that rigorous pursuit of small tumors via 3D
screening, and subsequent registration and subtraction of
longitudinal images, should be a top priority in breast cancer
research. As we learn to handle such 3D images, we will likely gain
the experience to distinguish potentially malignant tumors from
benign small tumors and/or transient "lesions," as well as possible
normal changes in the breast.
Reliable detection of all breast cancers before they reach 4 mm
in diameter could potentially reduce the likelihood of metastasis
to less than 1%, which we tentatively take to mean a potential cure
rate of greater than 99%. We have presented an argument, using the
popular cartoon character Waldo, that mammography misses tumors
primarily because of its two-dimensional nature. We have also
presented a brief evaluation of four different 3D imaging
modalities which can potentially be used for 3D longitudinal breast
screening. Small tumors could then be detected by registration and
subtraction of these longitudinal images.
While none of these modalities have yet reached reliable
detection of 4 mm tumors, we believe that future research in breast
imaging should be directed toward this goal. The criteria to select
an appropriate imaging modality would include safety, ability to
detect small tumors, and cost.
This work was supported in part by fellowships to the first
author from the Cancer Research Society, Montreal and the
University of Manitoba, Winnipeg, by Nicholas Anthonisen, Dean of
Medicine, University of Manitoba and by contributions to the Nancy
Taylor Breast Cancer Fund by Donald and Ruth Gordon and Caroline
and Marvin Ben-ari. We would also like to thank Jerry Hlady for his
help in preparing the Waldograms.