Bridging population and tissue scale tumor dynamics: a new paradigm for understanding differences in tumor growth and metastatic disease

Abstract

To provide a better understanding of the relationship between primary tumor growth rates and metastatic burden, we present a method that bridges tumor growth dynamics at the population level, extracted from the SEER database, to those at the tissue level. Specifically, with this method, we are able to relate estimates of tumor growth rates and metastatic burden derived from a population-level model to estimates of the primary tumor vascular response and the circulating tumor cell (CTC) fraction derived from a tissue-level model. Variation in the population-level model parameters produces differences in cancer-specific survival and cure fraction. Variation in the tissue-level model parameters produces different primary tumor dynamics that subsequently lead to different growth dynamics of the CTCs. Our method to bridge the population and tissue scales was applied to lung and breast cancer separately, and the results were compared. The population model suggests that lung tumors grow faster and shed a significant number of lethal metastatic cells at small sizes, whereas breast tumors grow slower and do not significantly shed lethal metastatic cells until becoming larger. Although the tissue-level model does not explicitly model the metastatic population, we are able to disengage the direct dependency of the metastatic burden on primary tumor growth by introducing the CTC population as an intermediary and assuming dependency. We calibrate the tissue-level model to produce results consistent with the population model while also revealing a more dynamic relationship between the primary tumor and the CTCs. This leads to exponential tumor growth in lung and power law tumor growth in breast. We conclude that the vascular response of the primary tumor is a major player in the dynamics of both the primary tumor and the CTCs, and is significantly different in breast and lung cancer.

Figure 1

Stochastic population-level model diagram of cancer progression from previous work of Lin and Plevritis (3). The thin gray curve represents the growth of the primary tumor and the thick black curve represents the lethal metastatic burden. This same modeling framework is applied to both IDC and NSCLC SEER data. Reproduced with kind permission from Springer Science+Business Media: Cancer Causes and Control, Comparing the benefits of screening for breast cancer and lung cancer using a novel natural history model, 23, 2012, pg. 176, Lin and Plevritis, Fig. 1.

Figure 2

Schematic representation of the tissue model showing the interactions between the tumor components and the vasculature.

Figure 3

The distribution of cell types within the two tissue types at 2.5 years post initiation. The legend details the colors for each cell type. The breast tumor (left) shows around 5% vascular content close to the edge, which is mostly occupied by normoxic cells, whereas the lung tumor (right) shows around 50% vascular content throughout and a large hypoxic fraction. The parameters for both cases are given in Table 1.

Figure 4

Tumor volume versus time for both lung (black) and breast (gray). The orange curves show power law fits (N = atⁿ) for lung with a = 4.11 × 10⁻⁵, n = 2.09, and R = 0.978 and breast with a = 6.98 × 10⁻⁶, n = 2.24, and R = 0.995. The blue dashed curves show exponential fits (N = ae^bt) for the lung with a = 1.17, b = 0.0049 d⁻¹, and R = 0.995 and the breast with a = 0.677, b = 0.0045 d⁻¹, and R = 0.994. The breast simulation fits well to a power law, but the curve becomes more exponential-like with the vascular dynamics of the lung.

Figure 5

The two metrics for correlating the models: TVDT and number of CTCs. The latter is associated with the metastatic burden. The leftmost graph shows the TVDT (via Eqn. 5) per diameter of the tumor. The horizontal lines mark the estimates from the statistical population model for the breast (light) and the lung (dark). The vertical gray box sets a window for TVDT correlation with a ~3 cm tumor. The graph to the right shows the number of CTCs over time for lung (dark) and breast (light), found by keeping count of the cells that leave the primary at each time step.

Figure 6

The left panel shows the TVDT at 3 cm diameter (via Eqn. 5) over an array of values for μ_v and α. The horizontal planes appear at the median values of 252 and 135 days for breast (light) and lung (dark), respectively. The right panel shows the primary tumor diameter upon reaching the threshold 3,300 CTCs over an array of values for μ_v and α. The horizontal planes appear at the median values of 1.9 and 0.8 cm for breast (light) and lung (dark), respectively.

Figure 7

The diameter at which CTCs reach 3,300 cells for breast (left) and lung (right) over an array of values for β_n+β_h, the total amount of cells leaving to the bloodstream, and β_n/(β_n+β_h), the fraction of this total that comes from the normoxic population.