A mathematical model of tumor volume changes during radiotherapy

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

Modeling of the metabolic energy dissipation for restricted tumor growth

Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of "the metabolic spring-pot element" is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy "structure" in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.

Optimal Placement of Irradiation Sources in the Planning of Radiotherapy: Mathematical Models and Methods of Solving

This paper proposes and analyses a mathematical model for the problem of distribution of a finite number of irradiation sources during radiotherapy in continuous environments to maximize the minimal cumulative effects. A new algorithm based on nondifferentiable optimization techniques has been developed to solve this problem.

Adaptive Mathematical Model of Tumor Response to Radiotherapy Based on CBCT Data

Mathematical modeling of tumor response to radiotherapy has the potential of enhancing the quality of the treatment plan, which can be even tailored on an individual basis. Lack of extensive in vivo validation has prevented, however, reliable clinical translation of modeling outcomes. Image-guided radiotherapy is a consolidated treatment modality based on computed tomographic (CT) imaging for tumor delineation and volumetric cone beam CT data for periodic checks during treatment. In this study, a macroscopic model of tumor growth and radiation response is proposed, being able to adapt along the treatment course as volumetric tumor data become available. Model parameter learning was based on cone beam CT images in 13 uterine cervical cancer patients, subdivided into three groups (G1, G2, G3) according to tumor type and treatment. Three group-specific parameter sets (PS1, PS2, and PS3) on one general parameter set (PSa) were applied. The corresponding average model fitting errors were 14%, 18%, 13%, and 21%, respectively. The model adaptation testing was performed using volume data of three patients, other than the ones involved in the parameter learning. The extrapolation performance of the general model was improved, while comparable prediction errors were found for the group-specific approach. This suggests that an online parameter tuning can overcome the limitations of a suboptimal patient stratification, which appeared otherwise a critical issue.