Linking radiomic PET features with metabolic tissue parameters using a hybrid mathematical model of tumor growth

Objectives: The genetic diversity in tumor cells and the varying microenvironments lead to phenotypic heterogeneity within and between tumors (Marusyk et al., 2010), which can be assessed using PET imaging. More heterogeneous tumors may be more resilient to treatment and result in complications that are harder to treat (Hirata et al., 2017). Thus, understanding how tissue and tumor microparameters are linked to observable PET imaging features is of great interest, motivating the development of novel radiomics-based biomarkers. The objective of this work is to develop a multiscale mathematical model of tumor growth in vascularized tissue that can generate synthetic PET images of glucose metabolism. Using the model, we aim to establish a link between radiomic features and tissue microparameters.

Methods: We simulate tumor growth using a hybrid mathematical model, which combines 1) grids of agents, namely autonomous decision-making entities representing blood vessels and different cell types (normal cells, tumor cells, hypoxic cells, necrotic cells), and 2) partial differential equation grids to simulate the tumor microenvironment (Robertson-Tessi, 2015). Blood is the source of oxygen and glucose (drugs or radionuclides can also be incorporated), which diffuse through tissue and are consumed by cells. In each simulation step, the state of each agent and the next action is determined based on the local microenvironment. The model uses realistic biological parameters, such as oxygen diffusion coefficient in tissue (1.62x10^-5 cm²/s), consumption rates (2.5x10^-18 to 2.0x10^-15 mol/min/cell), and average cell size (20um). The oxygen consumption rate follows the Michaelis-Menten kinetics and is simplified to a constant for each cell type (Grimes et al, 2014). The simulated grid size was 1000x1000 cells (2x2 cm). The time-sequences of agent maps were converted to pseudo-standardized uptake value (pSUV) maps, assuming the relative glucose consumption rates 1, 8, 12, and 0 for normal, cancer, cancer hypoxic, and necrotic cells, respectively. pSUV maps were downsampled to a resolution of 3 mm (mid-point between pre-clinical and clinical PET resolution). The assumed PET tracer is a glucose analog, applicable to 18F-fluorodeoxyglucose (FDG).

Results: To demonstrate the utility of our method, we used different combinations of microparameters to simulate 3 distinct tumor types (Fig. 1). Altered parameters included blood vessel density (types A,C: 20/mm², B: 100/mm²), spatial arrangement (types A,C: random placement, B: uniform-density placement), and vascular network alteration by tumor cells such as vessel removal probability (types A,B: 1, C: 0.05). The resulting tumors of different types had very distinct phenotypes, which were visually distinguishable in the corresponding pSUV PET images (Fig. 2). The model produced diverse and realistic tumor growth rates, ranging from ~80 to ~310 days to reach a 1-cm tumor diameter (Fig. 3). Likewise, 4 radiomic features computed from the synthetic PET images of tumors (pSUV mean uptake, shape compactness, Haralick texture contrast and homogeneity), were significantly different between the tumor types. Specifically, the values for 1-cm tumors were: mean pSUV - 4.58 ± 0.03 (type A), 7.63 ± 0.72 (type B), 4.71 ± 0.04 (type C); Compactness - 0.91 ± 0.01 (A), 0.95 ± 0.01 (B), 0.94 ± 0.005 (C); Contrast - 1.67 ± 0.08 (A), 1.58 ± 0.04 (B), 1.36 ± 0.1 (C); Homogeneity - 0.71 ± 0.01 (A), 0.80 ± 0.006 (B), 0.79 ± 0.01 (C). From a combination of all 4 features, each tumor phenotype and set of tissue parameters can be uniquely identified.

Conclusions: Realistic tumor growth can be achieved through modeling tissue and tumor microparameters. By changing the parameter values, distinctly different tumor phenotypes were obtained measurable through PET image radiomics. Hence, the model can help establish a link between tissue metabolic parameters and PET radiomics, and identify optimal radiomic features for tumor assessment.

• Download figure
• Open in new tab
• Download powerpoint