Abstract Background The prediction of response is one of the major challenges in radiation-based therapies. Although the selection of accurate linear–quadratic model parameters is essential for the estimation of radiation response and treatment outcome, there is a limited knowledge about these radiobiological parameters for liver tumours using radionuclide treatments. Methods The “clinical radiobiological” parameters ($T_{{\text{p}}}$ T p , $T_{{\text{k}}}$ T k , $α$ α , $α {/}β$ α / β ) for twenty-five patients were derived using the generalised linear–quadratic model, the diagnostic ([¹⁸F] FDG PET/CT) and therapeutic ([⁹⁰Y]-SIR-Spheres PET/CT) images to compute the biological effective dose and tumour control probability (TCP) for each patient. Results It was estimated that the values for $α$ α and $α {/}β$ α / β parameters range in ≈ 0.001–1 Gy⁻¹ and ≈ 1–49 Gy, respectively. We have demonstrated that the time factors, $T_{{\text{p}}}$ T p , $T_{{\text{k}}}$ T k and $T_{{{\text{critic}}}}$ T critic are the key parameters when evaluating liver malignancy lesional response to [⁹⁰Y]SIR-Spheres treatment. Patients with cholangiocarcinoma have been shown to have the longest average $T_{{\text{p}}}$ T p (≈ 236 ± 67 d), highest TCP (≈ 53 ± 17%) and total liver lesion glycolysis response ($Δ {\text{TLG}}_{{{\text{liver}}}}$ Δ TLG liver ≈ 64%), while patients with metastatic colorectal cancer tumours have the shortest average $T_{{\text{p}}}$ T p (≈ 129 ± 19 d), lowest TCP (≈ 28 ± 13%) and $Δ {\text{TLG}}_{{{\text{liver}}}}$ Δ TLG liver ≈ 8%, respectively. Conclusions Tumours with shorter $T_{{\text{k}}}$ T k have shown a shorter $T_{{{\text{critic}}}}$ T critic and thus poorer TCP and $Δ {\text{TLG}}_{{{\text{liver}}}}$ Δ TLG liver . Therefore, these results suggest for such tumours the [⁹⁰Y]SIR-Spheres will be only effective at higher initial dose rate (e.g. > 50 Gy/day).