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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.

Imaging is central to the clinical surveillance of brain tumors yet it provides limited insight into a tumor’s underlying biology. Machine learning and other mathematical modeling approaches can leverage paired magnetic resonance images and image-localized tissue samples to predict almost any characteristic of a tumor. Image-based modeling takes advantage of the spatial resolution of routine clinical scans and can be applied to measure biological differences within a tumor, changes over time, as well as the variance between patients. This approach is non-invasive and circumvents the intrinsic challenges of inter- and intratumoral heterogeneity that have historically hindered the complete assessment of tumor biology and treatment responsiveness. It can also reveal tumor characteristics that may guide both surgical and medical decision-making in real-time. Here we describe a general framework for the acquisition of imagelocalized biopsies and the construction of spatiotemporal radiomics models, as well as case examples of how this approach may be used to address clinically relevant questions. [ABSTRACT FROM AUTHOR]

BACKGROUND. Temozolomide (TMZ) is one of the most potent chemotherapy agents for the treatment of glioblastoma. Unfortunately, almost half of glioblastoma tumors are TMZ resistant due to overexpression of methylguanine methyltransferase ([MGMT.sup.hi]). Coadministration of [O.sup.6]-benzylguanine ([O.sup.6]BG) can restore TMZ sensitivity, but causes off-target myelosuppression. Here, we conducted a prospective clinical trial to test whether gene therapy to confer [O.sup.6]BG resistance in hematopoietic stem cells (HSCs) improves chemotherapy tolerance and outcome. METHODS. We enrolled 7 newly diagnosed glioblastoma patients with [MGMT.sup.hi] tumors. Patients received autologous gene-modified HSCs following single-agent carmustine administration. After hematopoietic recovery, patients underwent [O.sup.6]BG/TMZ chemotherapy in 28-day cycles. Serial blood samples and tumor images were collected throughout the study. Chemotherapy tolerance was determined by the observed myelosuppression and recovery following each cycle. Patient specific biomathematical modeling of tumor growth was performed. Progression-free survival (PFS) and overall survival (OS) were also evaluated. RESULTS. Gene therapy permitted a significant increase in the mean number of tolerated [O.sup.6]BG/TMZ cycles (4.4 cycles per patient, P < 0.05) compared with historical controls without gene therapy (n = 7 patients, 1.7 cycles per patient). One patient tolerated an unprecedented 9 cycles and demonstrated long-term PFS without additional therapy. Overall, we observed a median PFS of 9 (range 3.5-[57.sup.+]) months and OS of 20 (range 13-[57.sup.+]) months. Furthermore, biomathematical modeling revealed markedly delayed tumor growth at lower cumulative TMZ doses in study patients compared with patients that received standard TMZ regimens without [O.sup.6]BG. CONCLUSION. These data support further development of chemoprotective gene therapy in combination with [O.sup.6]BG and TMZ for the treatment of glioblastoma and potentially other tumors with overexpression of MGMT. TRIAL REGISTRATION. Clinicaltrials.gov NCT00669669. FUNDING. R01CA114218, R01AI080326, R01HL098489, P30DK056465, K01DK076973, R01HL074162, R01CA164371, R01NS060752, U54CA143970., Introduction Glioblastoma multiforme (GBM), the most common and aggressive primary brain tumor in adults, is almost uniformly fatal, carrying a 47% chance of survival at one year from diagnosis and [...]

The automated capability of generating spatial prediction for a variable of interest is desirable in various science and engineering domains. Take precision medicine of cancer as an example, in which the goal is to match patients with treatments based on molecular markers identified in each patient’s tumor. A substantial challenge, however, is that the molecular markers can vary significantly at different spatial locations of a tumor. If this spatial distribution could be predicted, the precision of cancer treatment could be greatly improved by adapting treatment to the spatial molecular heterogeneity. This is a challenging task because no technology is available to measure the molecular markers at each spatial location within a tumor. Biopsy samples provide direct measurement, but they are scarce/local. Imaging, such as MRI, is global, but it only provides proxy/indirect measurement. Also available are mechanistic models or domain knowledge, which are often approximate or incomplete. This article proposes a novel machine learning framework to fuse the three sources of data/information to generate a spatial prediction, namely, the knowledge-infused global-local (KGL) data fusion model. A novel mathematical formulation is proposed and solved with theoretical study. We present a real-data application of predicting the spatial distribution of tumor cell density (TCD)—an important molecular marker for brain cancer. A total of 82 biopsy samples were acquired from 18 patients with glioblastoma, together with six MRI contrast images from each patient and biological knowledge encoded by a PDE simulator-based mechanistic model called proliferation-invasion (PI). KGL achieved the highest prediction accuracy and minimum prediction uncertainty compared with a variety of competing methods. The result has important implications for providing individualized, spatially optimized treatment for each patient. Note to Practitioners—This article proposes a machine learning framework to fuse local data, global imaging, and domain knowledge to generate a spatial prediction for a variable of interest. This methodology is relevant to multiple application domains. In precision medicine, it will allow for mapping the spatial distribution of important, treatment-informing molecular markers across each tumor by integrating biopsy data, MRI, and biological knowledge. This capability can help resolve the spatial heterogeneity of molecular characteristics and greatly improve the precision of cancer treatment. Other applications include early detection of regional fire risk across a forest by integrating ground/aerial survey data, satellite imagery, and fire simulator output, as well as regional poverty estimation for resource allocation. [ABSTRACT FROM AUTHOR]

Glioblastoma (GBM) is the most aggressive primary brain tumor and can have cystic components, identifiable through magnetic resonance imaging (MRI). Previous studies suggest that cysts occur in 7–23% of GBMs and report mixed results regarding their prognostic impact. Using our retrospective cohort of 493 patients with first-diagnosis GBM, we carried out an exploratory analysis on this potential link between cystic GBM and survival. Using pretreatment MRIs, we manually identified 88 patients with GBM that had a significant cystic component at presentation and 405 patients that did not. Patients with cystic GBM had significantly longer overall survival and were significantly younger at presentation. Within patients who received the current standard of care (SOC) (N = 184, 40 cystic), we did not observe a survival benefit of cystic GBM. Unexpectedly, we did not observe a significant survival benefit between this SOC cystic cohort and patients with cystic GBM diagnosed before the standard was established (N = 40 with SOC, N = 19 without SOC); this significant SOC benefit was clearly observed in patients with noncystic GBM (N = 144 with SOC, N = 111 without SOC). When stratified by sex, the survival benefit of cystic GBM was only preserved in male patients (N = 303, 47 cystic). We report differences in the absolute and relative sizes of imaging abnormalities on MRI and the prognostic implication of cysts based on sex. We discuss hypotheses for these differences, including the possibility that the presence of a cyst could indicate a less aggressive tumor. [ABSTRACT FROM AUTHOR]

Many drugs investigated for the treatment of glioblastoma (GBM) have had disappointing clinical trial results. Efficacy of these agents is dependent on adequate delivery to sensitive tumor cell populations, which is limited by the blood-brain barrier (BBB). Additionally, tumor heterogeneity can lead to subpopulations of cells with different sensitivities to anti-cancer drugs, further impacting therapeutic efficacy. Thus, it may be important to evaluate the extent to which BBB limitations and heterogeneous sensitivity each contribute to a drug's failure. To address this challenge, we developed a minimal mathematical model to characterize these elements of overall drug response, informed by time-series bioluminescence imaging data from a treated patient-derived xenograft (PDX) experimental model. By fitting this mathematical model to a preliminary dataset in a series of nonlinear regression steps, we estimated parameter values for individual PDX subjects that correspond to the dynamics seen in experimental data. Using these estimates as a guide for parameter ranges, we ran model simulations and performed a parameter sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients. Results from this analysis combined with simulations suggest that BBB permeability may play a slightly greater role in therapeutic efficacy than relative drug sensitivity. Additionally, we discuss recommendations for future experiments based on insights gained from this model. Further research in this area will be vital for improving the development of effective new therapies for glioblastoma patients. [ABSTRACT FROM AUTHOR]

Background: Temozolomide (TMZ) has been the standard-of-care chemotherapy for glioblastoma (GBM) patients for more than a decade. Despite this long time in use, significant questions remain regarding how best to optimize TMZ therapy for individual patients. Understanding the relationship between TMZ response and factors such as number of adjuvant TMZ cycles, patient age, patient sex, and image–based tumor features, might help predict which GBM patients would benefit most from TMZ, particularly for those whose tumors lack O6–methylguanine–DNA methyltransferase (MGMT) promoter methylation. Methods and findings: Using a cohort of 90 newly–diagnosed GBM patients treated according to the standard of care, we examined the relationships between several patient and tumor characteristics and volumetric and survival outcomes during adjuvant chemotherapy. Volumetric changes in MR imaging abnormalities during adjuvant therapy were used to assess TMZ response. T1Gd volumetric response is associated with younger patient age, increased number of TMZ cycles, longer time to nadir volume, and decreased tumor invasiveness. Moreover, increased adjuvant TMZ cycles corresponded with improved volumetric response only among more nodular tumors, and this volumetric response was associated with improved survival outcomes. Finally, in a subcohort of patients with known MGMT methylation status, methylated tumors were more diffusely invasive than unmethylated tumors, suggesting the improved response in nodular tumors is not driven by a preponderance of MGMT methylated tumors. Conclusions: Our finding that less diffusely invasive tumors are associated with greater volumetric response to TMZ suggests patients with these tumors may benefit from additional adjuvant TMZ cycles, even for those without MGMT methylation. [ABSTRACT FROM AUTHOR]

Purpose: Physical and digital phantoms play a key role in the development and testing of nuclear medicine instrumentation and processing algorithms for clinical and research applications, including neuroimaging using positron emission tomography (PET). We have developed and tested a digital reference object (DRO) version of the original segmented magnetic resonance imaging (MRI) data used for the three‐dimensional (3D) PET brain phantom developed by Hoffman et al., which is used as the basis of a commercially available physical test phantom. Methods: The DRO was constructed by subdividing the MRI image planes the original phantom was based on to create equal‐thickness slices and re‐labeling voxels. The digital data was then embedded in a PET Digital Imaging and Communications in Medicine format and tested for compliance. Results: We then tested the DRO by comparing it to computed tomography (CT) images of the physical phantom summed to form composite slices with axial extent similar to the DRO, but with a factor of two better in‐slice resolution. For composite slices, 91% of voxels were labeled in full agreement, 5% of the voxels were 50–75% accurate, and the remaining 4% of voxels had 25% or less agreement. Conclusions: This DRO can be used as an input for PET scanner simulation studies or for comparing simulations to measured Hoffman phantom images. [ABSTRACT FROM AUTHOR]