Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

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Immune checkpoint inhibitors (ICIs) are revolutionary cancer treatments. However, the mechanisms behind their effectiveness are not yet fully understood. Here, we aimed to investigate the role of the pH-regulatory enzyme carbonic anhydrase IX (CAIX) in ICI success. Consequently, we developed an in silico model of the tumour microenvironment. The hybrid model consists of an agent-based model of tumour–immune cell interactions, coupled with a set of diffusion-reaction equations describing substances in the environment. It is calibrated with data from the literature, enabling the study of its qualitative behaviour. In our model, CAIX-expressing tumours acidified their neighbourhood, thereby reducing immune infiltration by 90% ( p < 0.001) and resulting in a 25% increase in tumour burden ( p < 0.001). Moreover, suppression of CAIX improved the response to anti-PD-1 (23% tumour reduction in CAIX knockouts and 6% in CAIX-expressing tumours, p < 0.001), independently of initial PD-L1 expression. Our simulations suggest that patients with CAIX-expressing tumours could respond favourably to combining ICIs with CAIX suppression, even in the absence of pre-treatment PD-L1 expression. Furthermore, when calibrated with tumour-type-specific data, our model could serve as a high-throughput tool for testing the effectiveness of such a combinatorial approach.

Immune checkpoint inhibitors (ICIs) have revolutionized the treatment of solid malignancies, including non-small-cell lung cancer. However, immunotherapy resistance constitutes a significant challenge. To investigate carbonic anhydrase IX (CAIX) as a driver of resistance, we built a differential equation model of tumor–immune interactions. The model considers treatment with the small molecule CAIX inhibitor SLC-0111 in combination with ICIs. Numerical simulations showed that, given an efficient immune response, CAIX KO tumors tended toward tumor elimination in contrast to their CAIX-expressing counterparts, which stabilized close to the positive equilibrium. Importantly, we demonstrated that short-term combination therapy with a CAIX inhibitor and immunotherapy could shift the asymptotic behavior of the original model from stable disease to tumor eradication. Finally, we calibrated the model with data from murine experiments on CAIX suppression and combination therapy with anti-PD-1 and anti-CTLA-4. Concluding, we have developed a model that reproduces experimental findings and enables the investigation of combination therapies. Our model suggests that transient CAIX inhibition may induce tumor regression, given a sufficient immune infiltrate in the tumor, which can be boosted with ICIs.

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