Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology—defined here simply as the use of mathematics in cancer research—complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Radiomic features are potential imaging biomarkers for therapy response assessment in oncology. However, the robustness of features with respect to imaging parameters is not well established. Previously identified potential imaging biomarkers were found to be intrinsically dependent on voxel size and number of gray levels (GLs) in a recent texture phantom investigation. Here, we validate the voxel size and GL in-phantom normalizations in lung tumors. Eighteen patients with non-small cell lung cancer of varying tumor volumes were analyzed. To compare with patient data, phantom scans were acquired on eight different scanners. Twenty four previously identified features were extracted from lung tumors. The Spearman rank (r_s) and interclass correlation coefficient (ICC) were used as metrics. Eight out of 10 features showed high (r_s > 0.9) and low (r_s < 0.5) correlations with number of voxels before and after normalizations, respectively. Likewise, texture features were unstable (ICC < 0.6) and highly stable (ICC > 0.8) before and after GL normalizations, respectively. We conclude that voxel size and GL normalizations derived from a texture phantom study also apply to lung tumors. This study highlights the importance and utility of investigating the robustness of radiomic features with respect to CT imaging parameters in radiomic phantoms.

Ultrasound is an attractive modality for temperature monitoring because it is non-ionizing, convenient, inexpensive and has relatively simple signal processing requirements. This modality may be useful for temperature estimation if a temperature-dependent ultrasonic parameter can be identified, measured and calibrated. The most prominent methods for using ultrasound as a non-invasive thermometer exploit either (1) echo shifts due to changes in tissue thermal expansion and speed of sound (SOS), (2) variation in the attenuation coefficient or (3) change in backscattered energy from tissue inhomogeneities. The use of echo shifts has received the most attention in the last decade. By tracking scattering volumes and measuring the time shift of received echoes, investigators have been able to predict the temperature from a region of interest both theoretically and experimentally in phantoms, in isolated tissue regions in vitro and preliminary in vivo studies. A limitation of this method for general temperature monitoring is that prior knowledge of both SOS and thermal-expansion coefficients is necessary. Acoustic attenuation is dependent on temperature, but with significant changes occurring only at temperatures above 50°C, which may lead to its use in thermal ablation therapies. Minimal change in attenuation, however, below this temperature range reduces its attractiveness for use in clinical hyperthermia. Models and measurements of the change in backscattered energy suggest that, over the clinical hyperthermia temperature range, changes in backscattered energy are dependent on the properties of individual scatterers or scattering regions. Calibration of the backscattered energy from different tissue regions is an important goal of this approach. All methods must be able to cope with motion of the image features on which temperature estimates are based. A crucial step in identifying a viable ultrasonic approach to temperature estimation is its performance during in vivo tests.