Discussion
The most effective therapy to treat breast cancer is to surgically remove the primary tumor before it has formed a distant metastasis (DM). Unfortunately the technology available to detect the presence of DM at the time of diagnosis cannot accurately make this determination and a large portion of patients receiving adjuvant therapy do not benefit from this therapy whereas others could have benefitted from adjuvant therapy they did not receive. To identify those patients at risk for DM the traditional TNM-classification has been complemented with differentiation grade, peri-tumor vascular invasion, estrogen, progesterone, Her2neu receptor expression and more recently through molecular characterization of the tumor [
46‐
51]. Although improvement in the risk assessment helps to identify the patients that need additional therapy after surgical removal of the primary tumor, detection of the actual presence of tumor cells beyond the primary tumor is preferred. Indeed the presence of micrometastases in bone marrow [
52,
53] and tumor cells in blood [
12‐
14,
54] of breast cancer patients have been associated with an increased risk for disease recurrence, but have not become part of clinical practice partly because the current technology lacks sufficient sensitivity and specificity. The observations that CTC have been detected in patients years after a diagnosis and treatment of breast cancer with curative intent further challenges the technology to identify those CTC characteristics that predict imminent relapse [
55,
56].
To identify the basic requirements for detection of DM we have modeled the probability that a DM has been formed prior to surgery. Three key components of this probability are the tumor doubling time (
DT), the rate of tumor cell dissemination (
R
diss
), and the probability of successful completion of the metastatic cascade (
γ
metastatic
). Rate of dissemination can be determined from the CTC concentration values reported in literature [
8‐
15]. Here we combined literature values with clinical data from the NCR to obtain estimates for
DT, and (
γ
metastatic
) for patients. Using this model, we predicted the sensitivity needed for radiographic imaging and CTC enumeration for the detection of a primary tumor before DM formation has occurred.
The major assumptions in the model are:
1)
Metastatic efficiency and dissemination rate are not dependent on doubling time. Considering the high incidence of recurrence within the first 5 years compared to years 6–15, metastatic efficiency or dissemination rate are probably smaller for slower growing tumors. If, for example, 75% of recurrences are found in the first five years (doubling time < 3 months), 20% of recurrences in years 5–15 (doubling time 3–9 months), and 5% of recurrences in years 15–25 (doubling time 9–15 months), the metastatic efficiency for 0–3 month doubling time would be approximately 6-fold higher than for 3–9 months, and approximately 24-fold higher than for 9–15 months. A shorter doubling time reduces the probability of DM; the tumor has a shorter time to form a metastasis before it is large enough to be discovered. However, a reduction of probability of DM by an x-fold shorter doubling time is negated by a x½-fold higher metastatic efficiency. A 6 fold increase in metastatic efficiency and/or dissemination rate for a fourfold shorter doubling time would mean that the faster growing tumor has a higher probability of DM.
2)
The rate of dissemination and metastatic efficiency are independent of cancer type. We need to make this assumption because 1.) We lack data on CTC concentrations versus cancer type, and 2.) We lack data on cancer types for the patients in our data set. In another study, the five year risk of recurrence for patients with triple negative breast cancer (11% of total) was estimated to be 2.6 fold higher than for patients with other breast cancers (89% of total) [
37]. To assess the impact of a subtype with high risk of recurrence, we implemented a subgroup of 11% of patients with 2.6 fold higher product of metastatic efficiency and dissemination rate than the other 89%, while the average metastatic efficiency was held constant. The estimated detection limits did not change due to a higher metastatic efficiency nor to a higher dissemination rate.
3)
The metastatic efficiency does not evolve over time. While we expect that metastatic efficiency actually increases over time [
16], we lack data describing such evolution. The high relative probability of distant metastasis formation just before tumor discovery implies that the estimated metastatic efficiency also applies to the period just before tumor discovery. To obtain a fit between the CTC data in early stage patients and in metastatic patients, we applied a single increase in the dissemination rate of 25-fold, or an increase in the metastatic efficiency of 10,000-fold. Our rationale was that the metastatic cell has become efficient at disseminating and/or metastasizing due to natural selection by the metastatic cascade and has thus become genetically more prone to formation of new metastases [
57,
58]. We recognize that it is equally feasible that such evolution occurs more gradually.
4)
The transit from primary tumor to metastatic site is instant. Temporary storage of cells in the bone marrow, or temporary dormancy at the metastatic site, would result in a delay in the start of growth, and thus in an underestimation of the doubling time. For long delays the recurrence would likely be pushed outside the 5-year window, and for small delays the doubling time is marginally affected. For example, if we assume a typical delay of four months, the previous doubling time estimate of 1.7 months would become 1.5 months.
5)
The probability of DM is defined as the probability that at least one metastasis was present at the time of surgery, continues to grow and is discovered once it has reached a size of 8 mm. Changing the size at which a tumor is discovered affects the estimated growth rate. For example, if the typical tumor is discovered at a size of 15 mm, the estimated doubling time is 1.5 months instead of 1.7 months.
Data from the NCR was used to determine the probability for breast cancer DM by T-stage and the time between surgical intervention and DM. To obtain a patient group with minimal risk of DM, we included only patients with complete removal of the tumor after surgical resection, relatively small tumors (T
1,2) and no detectable metastasis (N
XM
0). The NCR recorded data for DM five years after surgical intervention. From the time to DM of 32 ± 18 months, we determined a
DT of 1.7 ± 0.9 months for DM; threefold faster than the
DT of 5.7 months (range 2.0-11.2) determined from primary tumor imaging data. A DM with a
DT of 5.7 months would lead to discovery of a DM 9.5 years after initiation of the DM. Our 5-year (60 month) observation window is too short to observe tumors with a
DT of 5.7 months. It is likely that our estimate of 1.7 months represents tumors with aggressive growth rates. Concurrent, the 5-year observation window may select for specific organs, because aggressive growth rates are more likely in organs that provide high levels of nutrients and tumor specific growth factors. Approximately three quarters of recurrences take place in the first five years [
59]. With a 15-year observation window we expect to find a doubling time of 2.7 months. In addition, the literature value for
DT of 5.7 months is determined on primary tumors, while the model fit
DT of 1.7 months is determined on the DM. The DM may have a different
DT than the primary lesion in the same patient due to natural selection in the metastatic cascade, differences in the tumor microenvironment or accumulation of growth enhancing mutations.
From murine studies, we conclude that dissemination rate is linearly dependent on the diameter of a lesion. For a diameter of 8 mm (typical T
1B) we find a dissemination rate of 280 CTC/h · g tumor (range 90–470) when we fit the clinical data to our model. This is on the low end of the range of dissemination rates determined from the tumor efferent vein in human studies of 90–78,000 CTC/h · g tumor (Additional file
1: Table S3). Dissemination rates determined in murine models span a very wide range of 7 orders of magnitude (0.15-8,700,000 CTC/h · g tumor, Additional file
1: Table S2). While this variation may be caused by differences in the detection methods used or differences between cell lines, the variation between murine estimates makes comparison with our model futile.
Metastatic efficiency in our model is estimated at 1 metastasis per 60 million disseminated tumor cells. This is substantially less efficient than the murine model median estimate of 1 metastasis in 14,000 disseminated cells (range 1 in 170 to 1 in 1 million). The large difference of metastatic efficiency between murine model and human model may be attributed to many factors, including use of cell lines with high metastatic efficiency, the 2,000-fold difference in size between human and mouse and the immunodeficiency of most mouse models. A host specific (immune) response to tumor cells most likely reduces metastatic efficiency, and may reduce tumor growth of small lesions. Studies quantifying the impact of the host response on tumor growth are needed before inclusion in any model. Murine models suggest that disseminated cells have high survival in circulation and are efficient at extravasation, Additional file
1: Table S4. Survival of extravasated cells beyond 2 weeks is estimated between 4% and 50%, if these tumor cells continue to survive this would leave a substantial number of dormant cells scattered throughout the body, up to a million cells in our model, Additional file
1: Supplemental S4. These cells may constitute a malignant time-bomb, since dormant cells may be reactivated at a later time [
60]. In the shorter term, metastatic efficiency is limited primarily by the ability of a disseminated cell to grow in a new site Table
4.
Table 4
Blood flow to different organ systems[
61]
and % of breast cancer patients (N = 432) with distant metastases in these organs at time of death[
62]
Adrenal gl. | < 1 | 9 | >9 |
Pleura | < 1 | 9 | >9 |
Bone | 5 | 12 | 2.40 |
Skin | 9 | 7 | 0.78 |
Liver | 27 a
| 13 | 0.48 |
Brain | 13 | 2 | 0.15 |
Lung | 100 | 13 | 0.13 |
Kidney | 20 | 2 | 0.10 |
Muscle | 15 | 0 | 0 |
Other | 10 | < 3 | < 0.3 |
Based on murine studies in different organs (see Additional file
1) we expect the model to be applicable to other cancers. It should be noted that tumors with high metastatic efficiency, such as melanoma [
63] or non-small cell lung cancer [
64] will have substantially lower numbers of CTC. Similarly, colorectal CTC are captured in the hepatic microcirculation and are lower when detected in the peripheral circulation [
9,
45]. Determination of tumor size is more difficult for some tumor types such as prostate cancer, which will result in higher error margins in the model parameters.
To determine the probability of metastases in a patient, three parameters are relevant, the dissemination rate, the growth rate and the metastatic efficiency. The dissemination rate can be determined from the CTC concentration, the growth rate and metastatic efficiency can be estimated from the primary tumor or, alternatively, by genotyping captured CTC. This is supported by the observation that both CTC concentration and hormone receptor status from primary tissue information are independent prognostic data in multivariate analyses [
65,
66].
The model can be applied to estimate the probability of metastases as a function of primary tumor size. Figure
3 illustrates that the model reasonably predicts the probability of DM for stages T
1B to T
2. The probability of DM grows slightly faster in the data than in the model, which may be caused by a slow increase in dissemination rate or metastatic efficiency over time. With current imaging technology, 94% of detected lesions have a size of 6 mm or more, with a specificity of 40% [
67]. From the data of the NCR, we conclude that current clinical practice in the Netherlands has similar detection characteristics, with 95% of the tumors detected when the tumor is 5 mm or larger, with a median size of 17 mm. The larger probability of DM for T
1A than T
1B in the NCR data is unexpected and raises the question whether these small tumors are truly more aggressive, or whether the difficulty to detect tumors smaller than 5 mm has caused a sampling bias in the T
1A sample.
To implement CTC as a screening tool, the improved CTC detection will need to have a minimal impact on the screened patient and to have similar specificity to radiological imaging. We note that by definition, CTC enumeration will not detect benign lesions. On the other hand, CTC detection could have excellent sensitivity and specificity for malignant lesions if the malignancy of detected CTC is confirmed with for example whole genome comparative genome hybridization [
68,
69].
Competing interests
This work was supported by Veridex LLC. Prof. Leon WMM Terstappen is an inventor of several patents related to the CTC technology that have been assigned to Veridex LLC, he is presently a consultant for Veridex and receives research funding from Veridex LLC. All remaining authors have declared no competing interest.
Authors’ contributions
FC and LT designed the study and drafted the manuscript. FC and SB performed the statistical analysis. FC, SB and LT performed the data analysis and data interpretation. All authors read and approved the final manuscript.