Chair for Mathematical Modeling at the Center of Mathematics, Technical University of Munich, Germany
"How Mathematical Modeling Could Contribute to the Quantification of Metastatic Tumor Burden Under Therapy"
Cancer is one of the leading death causes globally with about 8.2 million deaths per year with rising numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but to metastases, of which most are not clinically identifiable due to their relatively small size at primary diagnosis and limited technical possibilities. However, as therapeutic decisions are formed depending on the existence of metastases and their properties - non-identified metastases might have huge influence in the treatment outcome. It is therefore of clinical interest to give an estimation of the metastatic burden to assist in planning optimal treatments accordingly for individual cancer patients. A mathematical model addressing this problem has been developed based on a transport equation introduced by (Iwata et. al.) and extended by currently available systemic treatment options such as chemo- and immunotherapy. The model is defined in a continuous setting which allows it to also model the transition of a single primary tumor towards a metastatic disease, therefore indicating the metastatic cascade necessary to develop multiple metastatic tumors. Numerical implementation of the model framework allows for parameter estimation from clinical data, in our case we gathered parameter values from systemically treated lung cancer patients. We successfully quantified the total metastatic burden retrospectively for those patients over time given systemic treatment. In silico experiments allow for insights in differing therapeutic schedules, different medications and the further development of the metastatic burden. A sensitivity analysis on the model framework gave valuable insights in the behavior of model parameters and the clinical outcome.
Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center Tampa, USA
"Personalising adaptive cancer therapy in theory and in practice: the role of resistance costs and cellular competition"
Control and conquer - this is the philosophy behind adaptive therapy, which seeks to exploit intra- tumoral competition to avoid, or at least, delay the emergence of therapy resistance in cancer. Motivated by promising results from theoretical, experimental and, most recently, clinical studies, there is an in- creasing interest in extending this approach to other cancers. As such, it is urgent to understand the characteristics of a cancer which determine whether it will respond well to adaptive therapy, or not. One plausible such candidate is the “cost of resistance” in which acquisition of the resistance mechanism decreases a cell’s fitness in the absence of drug. To investigate the role of fitness costs, we initially study a simple 2-population ODE model in which we assume tumour cells are either drug-sensitive or resistant and compete in a Lotka-Volterra fashion. We identify the initial fraction of resistance, the proximity of the tumour to carrying capacity, resistance costs and turnover as important determinants of the benefit of adaptive therapy over standard-of-care continuous therapy. Moreover, we show that a resistance cost is neither a necessary nor a sufficient criterion for the success of adaptive therapy, but that the effect of a cost is dependent on the tumour’s proximity to carrying capacity and the rate of cellular turnover. Subsequently, we test whether our conclusions extend into space by considering a 2-D on-lattice cellular automaton model. While all the aforementioned factors remain important, we show that they interact in a non-linear fashion with the spatial architecture of the tumour. To conclude, we will show applications of our insights to the development of an adaptive therapy trial for the treatment of ovarian cancer with PARP inhibitors. This illustrates some of our theoretical predictions and raises new questions about when to adapt therapy and when not to. Overall, our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role.
Stanford University School of Medicine, Stanford, USA
"A mathematical model of ctDNA shedding predicts tumor detection size"
Early cancer detection aims to find tumors before they progress to an uncurable stage. Prospective studies with tens of thousands of healthy participants are ongoing to determine whether asymptomatic cancers can be accurately detected by analyzing circulating tumor DNA (ctDNA) from blood samples. We developed a stochastic mathematical model of tumor evolution and ctDNA shedding to investigate the potential and the limitations of ctDNA-based cancer early detection tests. We inferred ctDNA shedding rates of early stage lung cancers and calculated that a 15 mL blood sample contains on average only 1.5 genome equivalents of ctDNA for lung tumors with 1 billion cells (size of 1 cm3). We considered two clinically different scenarios: cancer screening and cancer relapse detection. For monthly relapse testing with a sequencing panel covering 20tumor-specific mutations, we found a median detection size of 0.24 cm3 corresponding to a lead time of 160 days compared to imaging-based relapse detection. For annual screening, we found a median detection size of 2.8-4.8 cm3 depending on the sequencing panel size and on the mutation frequency. The expected detection sizes correspond to lead times of 390-520 days compared to current median lung tumor sizes at diagnosis. This quantitative framework provides a mechanistic interpretation of ctDNA-based cancer detection approaches and helps to optimize cancer early detection strategies.