Tumor Growth Personalization

Unlike the static tumor growth models, the image-based personalization remains challenging for most forward simulators. There is little research in modeling tumor growth using patient-specific data especially those taken from medical images. The key components for Image-based tumor growth personalization are a model for tumor growth and a data resource. Cancer modeling offers a wide range of mathematical formalisms that can be classified according to their scale. Despite internal complexity, tumor growth kinetics follows relatively simple laws that can be expressed as mathematical models 70. Medical images are the most available data resources for these studies that are used in tumor diagnosis, staging, and assessment of treatments. If accurate
73. They combined the proliferation-invasion model with information on the molecular level dynamics of tumor growth referred to as the proliferation-invasion-hypoxia–necrosis–angiogenesis (PIHNA) model. Their model characterized glioblastoma tumor by partitioning the malignant tumor cells into subpopulations including normoxic and hypoxic cells, necrotic tissue, and neo-angiogenic vasculature and angiogenic factors. Using functional imaging, they evaluated the biological interaction of metabolic changes within and between cells on a patient-specific level and suggested that changes in cell kinetics are not essential to generate the imaging and histologic features of malignant progression and rather interactions of tumor cells with a constant invasion and proliferation rate alone play a key role in malignant progression. They compared survival map for different grades of glioma with the grade map and concluded that the shortest survival times are for those tumors with both high D and ρ, in contrast to WHO grading scheme which suggests that only high ρ is important. An important area of future
To bridge the gap between the model prediction and the clinical observation Liu et al.77,78 introduced two new parameters named Intracellular Volume Fraction (ICVF) measured from dual-phase CT and Standardized Uptake Value (SUV) measured from FDG-PET into the reaction-advection-diffusion model for pancreatic tumors. They also correlated proliferation rate to cell metabolic energy, via energy conservation law79 and used the logistic form of reaction term. They used two series of CT and PET images without any treatment to obtain the ICVF and SUV maps and estimating the model parameters. Second follow-ups were used for model evaluation. The patient-specific parameters of the model were estimated by minimizing the deviation between the predicted and measured ICVF maps and a reasonable agreement was beheld between model-predicted results and image-based observations. They considered isotropic diffusion with constant diffusivity in their work. Chen et al.80 modeled kidney tumor growth by coupling the reaction-diffusion model with a linear mechanical model assuming the surrounding tissue is mostly composed of fat. They used the segmented tumor volumes from contrast-enhanced CT images at multiple time points to estimate the model parameters. The estimated proliferation rates at different time points were