Frontiers in MathOnco, Part 2

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Heiko Enderling, Alexander R.A. Anderson


The mathematical oncology subgroup of the Society for Mathematical Biology is growing, reflecting the increasing number of scientific publications on the mathematical modeling of cancer. Cancer models are being developed to answer a diversity of questions, that cover almost every cancer type and stage, including how we might better understand or treat this deadly disease. The specific modelling approach used varies widely, while some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. This two-part minisymposium showcases the breadth of mathematical oncology research from scientists at both Universities and Hospitals at different career stages form around the world to spur discussions and collaborations in the field of mathematical modeling of cancer.

Mohit Kumar Jolly

Indian Institute of Science, India
"Integrating mechanism-based and data-based approaches to identify hybrid epithelial/mesenchymal phenotypes"
Epithelial–mesenchymal transition (EMT) is a key driver of metastasis and therapy resistance. During EMT, cells lose their epithelial traits and acquire mesenchymal ones to varying degrees. Recent evidence has suggested that cells need not necessarily display 'pure' epithelial or mesenchymal states, but can stably acquire one or more hybrid epithelial/mesenchymal (E/M) ones. In silico, in vitro and in vivo analysis indicates that these hybrid E/M states can be more aggressive and perhaps the 'fittest' for metastasis, thus identifying mechanisms enabling these hybrid E/M states is crucial for decoding tumor aggressiveness. Using an integrative approach involving mechanism-based models to identify master regulators of such hybrid E/M phenotypes, data-based models to decipher transcriptomics signatures specific to the hybrid E/M phenotypes, and experiments to test our predictions, we have identified how these hybrid E/M cell states may be maintained via cell-autonomous and non-cell autonomous mechanisms. Our work also highlights that the hybrid E/M specific signatures associate with worse clinicopathological traits, thus offering a mechanistic basis for its aggressiveness and pinpointing novel putative targets.

Pamela Jackson

Mayo Clinic, Phoenix, USA
"Parameterizing a Brain Tumor Growth Model Using Noisy Simulated MRIs"
Mathematical models of brain tumor growth are commonly parameterized using volumes of abnormal regions segmented from magnetic resonance imaging (MRI). For imaging-level brain tumor growth modeling, such as the Proliferation-Invasion (PI) model and its more complex variants, the abnormality region requires an assumption for the tumor cell density. This assumption is necessary to make estimates regarding the shape of the leading edge, however the use of an assumption can be limiting. Searching across MRI images that have been simulated across the model parameter space could eliminate the need for a cell density assumption, however noisy MRIs will reduce the reliability of such a technique. Our objective is to determine if matching the noise between simulations and MRIs can increase our ability to predict model parameters based on an image's characteristics. We generated phantom brain tumors using the Proliferation-Invasion-Hypoxia-Necrosis-Angiogenesis- Edema (PIHNA-E) model. One hundred unique phantoms were created assuming 10 different rates of migration (D [mm2/year]) and 10 different rates of proliferation ( [1/year])]. PIHNA-E simulations were then passed into a MRI signal model for generating simulated T2-weighted MRIs. We created two independent runs of six sets of 100 simulated MRIs, with each set incorporating a different level noise. The first run represented simulated images with known D and or 'ground truth', while the second run represented candidate 'real-world' noisy images for which we would have not normally known D and . We then compared each noise level from the second 'real-world' run to each noise level from the first 'ground truth' run. Within each set comparison, we calculated the L2-norm of twelve statistical features for each image in the second 'real-world' set relative to the 'ground truth' set of images. The D and of the 'ground truth' image with the lowest L2-norm relative to the 'real-world' image were selected as the predicted parameters. For each noise level, a prediction rate is calculated by assessing the percentage rate that the L2-norm-based selection was correct. As expected, the prediction rates decreased overall as the image noise level increased. For 'real- world' images with limited noise, creating a similar noise level in the 'ground truth' images did enable higher prediction rates of D and . Future directions of this work include repeating these methods across additional replicates and exploring processing steps for reducing MRI noise, which could increase our prediction rate of D.

Jeffrey West

Moffitt Cancer Center, Tampa, USA
"Anti-fragile Cancer Therapy"
Herein we present a novel paradigm of evolutionary cancer therapy based on the 'anti-fragility' of the drug dose-response function. Anti-fragility is a situation where the curvature of the dose-response function is convex, mathematically defined as a positive second derivative. This positive curvature is associated with benefits from increased variance or unevenness of a treatment schedule. For example, if the curvature is positive near a dose of ‘x’, continuous administration of x may have a less efficacious response compared to a regimen that switches equally between 120% of x and 80% of x, even though both regimens use the same total drug. Although dose-response data is readily available, such second-order effects are typically ignored. Nonlinear sigmoidal dose-response curves are ubiquitous in medicine and have both convex and concave regions. Selection pressure due to treatment selects for resistant phenotypes over time. In response, the magnitude of dose response curvature and the  convex-concave inflection point both decrease in value. The key insight is that dose-response convexity ('anti-fragility') decreases in proportion to the amount of resistance in the tumor population. This provides a time-dependent metric which 1) predicts the emergence of resistance and 2) determines the optimal subsequent dosing strategy. We demonstrate this paradigm using a Hill function model parameterized by in vitro experimental data of H3122 non-small cell lung cancer cell lines confronted to 10 different drugs. Through this dataset, we present antifragility applied to 1) treatment resistance, 2) collateral sensitivity, and 3) combination therapy.

Anna Marciniak-Czochra

University of Heidelberg, Germany
"Stem cell niche dynamics in acute leukemia: Insights from mathematical modeling"
Acute myeloid leukemia (AML) is one of the most aggressive blood cancers. The cancer originates from a small population of so called leukemia stem cells (LSC) that survive treatment and trigger re- lapse. During the course of the disease leukemic cells accumulate in the bone marrow and impair healthy blood cell formation. The impact of this interaction on the clinical course of the disease remains not well understood. We develop and validate a mathematical model of stem cell competition in the human hematopoietic stem cell niche. Model simulations predict how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantify the selective pressure LSC exert on HSC and demonstrate model's prognostic significance. We develop a novel model-based risk-stratification approach. This approach allows extracting prognostic information from counts of healthy and malignant cells at the time of diagnosis. We demonstrate its feasibility based on a cohort of ALDH-rare AML patients and show that the model-based risk strati- fication is an independent predictor of disease free and overall survival. This proof of concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalization of treatment. The talk is based on joint works with Thomas Stiehl (Institute of Applied Mathematics, Heidelberg University), Wenwen Wang and Christoph Lutz (Heidelberg Medical Clinic).

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