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Simple Summary  Systemic therapy in advanced hepatocellular-carcinomas (HCC) has limited benefits, but some patients show partial responses (PR) and a few even a complete response (CR). Understanding the biological mechanisms could help clinicians in decision-making. Aim of this study was to develop a physic-mathematical model to investigate tumor dynamics using α-fetoprotein (AFP) and protein induced by vitamin K absence-II (PIVKA-II) measures combined with digital imaging. The model was set-up in three prototype patients with CR/PR to sorafenib and PR to regorafenib, and then applied in seven patients with different types of response. Overall, the rate constant of cancer cells production ranged between 0.250–0.372 C × day −1 . During therapy, neo-angiogenesis reduction was higher in four CR than in four PR or stable disease (SD) and in two non-responders (median: 83.2% vs. 29.4% vs. 2.0%). Tumor vasculature decay appeared accelerated in CR. We conclude that modeling serological and imaging biomarkers could help personalization of systemic therapy.    Abstract  In advanced HCC, tyrosine-kinase inhibitors obtain partial responses (PR) in some patients and complete responses (CR) in a few. Better understanding of the mechanism of response could be achieved by the radiomic approach combining digital imaging and serological biomarkers (α-fetoprotein, AFP and protein induced by vitamin K absence-II, PIVKA-II) kinetics. A physic-mathematical model was developed to investigate cancer cells and vasculature dynamics in three prototype patients receiving sorafenib and/or regorafenib and applied in seven others for validation. Overall four patients showed CR, two PR, two stable-disease (SD) and two progressive-disease (PD). The rate constant of cancer cells production was higher in PD than in PR-SD and CR (median: 0.398 vs. 0.325 vs. 0.316 C × day −1 ). Therapy induced reduction of neo-angiogenesis was greater in CR than in PR-SD and PD (median: 83.2% vs. 29.4% and 2.0%), as the reduction of cell-proliferation (55.2% vs. 7.6% and 0.7%). An additional dose-dependent acceleration of tumor vasculature decay was also observed in CR. AFP and cancer cells followed the same kinetics, whereas PIVKA-II time/dose dependent fluctuations were influenced also by tissue ischemia. In conclusion, pending confirmation in a larger HCC cohort, modeling serological and imaging biomarkers could be a new tool for systemic therapy personalization.

Modeling Hepatocellular Carcinoma Cells Dynamics by Serological and Imaging Biomarkers to Explain the Different Responses to Sorafenib and Regorafenib