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Life sciences · Journal article
Open Research Europe · October 6, 2026
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Reliable quantitative assessment of tumor treatment response remains a major challenge in preclinical oncology because longitudinal tumor volume measurements are inherently noisy and conventional end-point metrics fail to capture the full temporal evolution of disease. To address these limitations, we present a medical engineering framework for quantitative assessment of tumor treatment response based on cumulative tumor dynamics. The proposed approach transforms longitudinal tumor volume measurements into a cumulative descriptor of tumor burden by integrating the tumor growth trajectory over time, thereby providing a robust representation of the overall therapeutic response while reducing the influence of experimental variability. A variational formulation is introduced to describe cumulative treatment dynamics, leading to a scale-invariant Euler–Cauchy differential equation that models the temporal evolution of the difference between treated and untreated tumors through quantities directly related to the area under the tumor growth curve (AUC). The resulting second-order model represents treatment response as the superposition of two independent dynamical modes, enabling the characterization of both transient therapeutic effects and sustained tumor suppression within a unified mathematical framework. The proposed methodology was validated using experimental breast cancer datasets involving photodynamic therapy (PDT), the tumor microenvironment-modulating agent tranilast, and combination therapy with tranilast and doxorubicin. Across all treatment protocols, the framework accurately reproduced the observed cumulative treatment dynamics, generated smooth and stable representations of tumor evolution, and demonstrated excellent agreement with experimental data. By integrating concepts from medical engineering, mathematical modeling, and experimental oncology, the proposed framework provides a general methodology for quantitative treatment-response assessment from longitudinal tumor trajectories. Beyond the analyzed datasets, the approach has the potential to support comparative evaluation of anticancer therapies, longitudinal monitoring of therapeutic efficacy, and the development of predictive tools for preclinical and translational oncology.