A review of mechanistic learning in mathematical oncology.

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent.

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.

Using birth-death processes to infer tumor subpopulation structure from live-cell imaging drug screening data.

Tumor heterogeneity is a complex and widely recognized trait that poses significant challenges in developing effective cancer therapies. In particular, many tumors harbor a variety of subpopulations with distinct therapeutic response characteristics. Characterizing this heterogeneity by determining the subpopulation structure within a tumor enables more precise and successful treatment strategies. In our prior work, we developed PhenoPop, a computational framework for unravelling the drug-response subpopulation structure within a tumor from bulk high-throughput drug screening data. However, the deterministic nature of the underlying models driving PhenoPop restricts the model fit and the information it can extract from the data. As an advancement, we propose a stochastic model based on the linear birth-death process to address this limitation. Our model can formulate a dynamic variance along the horizon of the experiment so that the model uses more information from the data to provide a more robust estimation. In addition, the newly proposed model can be readily adapted to situations where the experimental data exhibits a positive time correlation. We test our model on simulated data (in silico) and experimental data (in vitro), which supports our argument about its advantages.

Phenotypic deconvolution in heterogeneous cancer cell populations using drug-screening data.

Tumor heterogeneity is an important driver of treatment failure in cancer since therapies often select for drug-tolerant or drug-resistant cellular subpopulations that drive tumor growth and recurrence. Profiling the drug-response heterogeneity of tumor samples using traditional genomic deconvolution methods has yielded limited results, due in part to the imperfect mapping between genomic variation and functional characteristics. Here, we leverage mechanistic population modeling to develop a statistical framework for profiling phenotypic heterogeneity from standard drug-screen data on bulk tumor samples. This method, called PhenoPop, reliably identifies tumor subpopulations exhibiting differential drug responses and estimates their drug sensitivities and frequencies within the bulk population. We apply PhenoPop to synthetically generated cell populations, mixed cell-line experiments, and multiple myeloma patient samples and demonstrate how it can provide individualized predictions of tumor growth under candidate therapies. This methodology can also be applied to deconvolution problems in a variety of biological settings beyond cancer drug response.

A combined experimental-computational approach uncovers a role for the Golgi matrix protein Giantin in breast cancer progression.

Our understanding of how speed and persistence of cell migration affects the growth rate and size of tumors remains incomplete. To address this, we developed a mathematical model wherein cells migrate in two-dimensional space, divide, die or intravasate into the vasculature. Exploring a wide range of speed and persistence combinations, we find that tumor growth positively correlates with increasing speed and higher persistence. As a biologically relevant example, we focused on Golgi fragmentation, a phenomenon often linked to alterations of cell migration. Golgi fragmentation was induced by depletion of Giantin, a Golgi matrix protein, the downregulation of which correlates with poor patient survival. Applying the experimentally obtained migration and invasion traits of Giantin depleted breast cancer cells to our mathematical model, we predict that loss of Giantin increases the number of intravasating cells. This prediction was validated, by showing that circulating tumor cells express significantly less Giantin than primary tumor cells. Altogether, our computational model identifies cell migration traits that regulate tumor progression and uncovers a role of Giantin in breast cancer progression.

Quantification of Tumor Hypoxia through Unsupervised Modelling of Consumption and Supply Hypoxia MR Imaging in Breast Cancer.

The purpose of the present study is to investigate if consumption and supply hypoxia (CSH) MR-imaging can depict breast cancer hypoxia, using the CSH-method initially developed for prostate cancer. Furthermore, to develop a generalized pan-cancer application of the CSH-method that doesn't require a hypoxia reference standard for training the CSH-parameters. In a cohort of 69 breast cancer patients, we generated, based on the principles of intravoxel incoherent motion modelling, images reflecting cellular density (apparent diffusion coefficient; ADC) and vascular density (perfusion fraction; fp). Combinations of the information in these images were compared to a molecular hypoxia score made from gene expression data, aiming to identify a way to apply the CSH-methodology in breast cancer. Attempts to adapt previously proposed models for prostate cancer included direct transfers and model parameter rescaling. A novel approach, based on rescaling ADC and fp data to give more nuanced response in the relevant physiologic range, was also introduced. The new CSH-method was validated in a prostate cancer cohort with known hypoxia status. The proposed CSH-method gave estimates of hypoxia that was strongly correlated to the molecular hypoxia score in breast cancer, and hypoxia as measured in pathology slices stained with pimonidazole in prostate cancer. The generalized approach to CSH-imaging depicted hypoxia in both breast and prostate cancers and requires no model training. It is easy to implement using readily available technology and encourages further investigation of CSH-imaging in other cancer entities and in other settings, with the goal being to overcome hypoxia-induced resistance to treatment.

Circulatory Response to Rapid Volume Expansion and Cardiorespiratory Fitness in Fontan Circulation.

The role of dysfunction of the single ventricle in Fontan failure is incompletely understood. We aimed to evaluate hemodynamic responses to preload increase in Fontan circulation, to determine whether circulatory limitations in different locations identified by experimental preload increase are associated with cardiorespiratory fitness (CRF), and to assess the impact of left versus right ventricular morphology. In 38 consecutive patients (median age = 16.6 years, 16 females), heart catheterization was supplemented with a rapid 5-mL/kg body weight volume expansion. Central venous pressure (CVP), ventricular end-diastolic pressure (VEDP), and peak systolic pressure were averaged for 15‒30 s, 45‒120 s, and 4‒6 min (steady state), respectively. CRF was assessed by peak oxygen consumption (VO2peak) and ventilatory threshold (VT). Median CVP increased from 13 mmHg at baseline to 14.5 mmHg (p < 0.001) at steady state. CVP increased by more than 20% in eight patients. Median VEDP increased from 10 mmHg at baseline to 11.5 mmHg (p < 0.001). Ten patients had elevated VEDP at steady state, and in 21, VEDP increased more than 20%. The transpulmonary pressure difference (CVP‒VEDP) and CVP were consistently higher in patients with right ventricular morphology across repeated measurements. CVP at any stage was associated with VO2peak and VT. VEDP after volume expansion was associated with VT. Preload challenge demonstrates the limitations beyond baseline measurements. Elevation of both CVP and VEDP are associated with impaired CRF. Transpulmonary flow limitation was more pronounced in right ventricular morphology. Ventricular dysfunction may contribute to functional impairment after Fontan operation in young adulthood.ClinicalTrials.gov identifier NCT02378857.

A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy.

Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models with continuous models using hybrid cellular automata (CA) is a powerful approach for mimicking biological complexity and describing the dynamical exchange of information across different scales. However, when clinically relevant cancer portions are taken into account, such models become computationally very expensive. While efficient parallelization techniques for continuous models exist, their coupling with discrete models, particularly CA, necessitates more elaborate solutions. Building upon FEniCS, a popular and powerful scientific computing platform for solving partial differential equations, we developed parallel algorithms to link stochastic CA with differential equations (https://bitbucket.org/HTasken/cansim). The algorithms minimize the communication between processes that share CA neighborhood values while also allowing for reproducibility during stochastic updates. We demonstrated the potential of our solution on a complex hybrid cellular automaton model of breast cancer treated with combination chemotherapy. On a single-core processor, we obtained nearly linear scaling with an increasing problem size, whereas weak parallel scaling showed moderate growth in solving time relative to increase in problem size. Finally, we applied the algorithm to a problem that is 500 times larger than previous work, allowing us to run personalized therapy simulations based on heterogeneous cell density and tumor perfusion conditions estimated from magnetic resonance imaging data on an unprecedented scale.

Regional performance variation in external validation of four prediction models for severity of COVID-19 at hospital admission: An observational multi-centre cohort study.

BACKGROUND: Prediction models should be externally validated to assess their performance before implementation. Several prediction models for coronavirus disease-19 (COVID-19) have been published. This observational cohort study aimed to validate published models of severity for hospitalized patients with COVID-19 using clinical and laboratory predictors. METHODS: Prediction models fitting relevant inclusion criteria were chosen for validation. The outcome was either mortality or a composite outcome of mortality and ICU admission (severe disease). 1295 patients admitted with symptoms of COVID-19 at Kings Cross Hospital (KCH) in London, United Kingdom, and 307 patients at Oslo University Hospital (OUH) in Oslo, Norway were included. The performance of the models was assessed in terms of discrimination and calibration. RESULTS: We identified two models for prediction of mortality (referred to as Xie and Zhang1) and two models for prediction of severe disease (Allenbach and Zhang2). The performance of the models was variable. For prediction of mortality Xie had good discrimination at OUH with an area under the receiver-operating characteristic (AUROC) 0.87 [95% confidence interval (CI) 0.79-0.95] and acceptable discrimination at KCH, AUROC 0.79 [0.76-0.82]. In prediction of severe disease, Allenbach had acceptable discrimination (OUH AUROC 0.81 [0.74-0.88] and KCH AUROC 0.72 [0.68-0.75]). The Zhang models had moderate to poor discrimination. Initial calibration was poor for all models but improved with recalibration. CONCLUSIONS: The performance of the four prediction models was variable. The Xie model had the best discrimination for mortality, while the Allenbach model had acceptable results for prediction of severe disease.

CellMAPtracer: A User-Friendly Tracking Tool for Long-Term Migratory and Proliferating Cells Associated with FUCCI Systems.

Cell migration is a fundamental biological process of key importance in health and disease. Advances in imaging techniques have paved the way to monitor cell motility. An ever-growing collection of computational tools to track cells has improved our ability to analyze moving cells. One renowned goal in the field is to provide tools that track cell movement as comprehensively and automatically as possible. However, fully automated tracking over long intervals of time is challenged by dividing cells, thus calling for a combination of automated and supervised tracking. Furthermore, after the emergence of various experimental tools to monitor cell-cycle phases, it is of relevance to integrate the monitoring of cell-cycle phases and motility. We developed CellMAPtracer, a multiplatform tracking system that achieves that goal. It can be operated as a conventional, automated tracking tool of single cells in numerous imaging applications. However, CellMAPtracer also allows adjusting tracked cells in a semiautomated supervised fashion, thereby improving the accuracy and facilitating the long-term tracking of migratory and dividing cells. CellMAPtracer is available with a user-friendly graphical interface and does not require any coding or programming skills. CellMAPtracer is compatible with two- and three-color fluorescent ubiquitination-based cell-cycle indicator (FUCCI) systems and allows the user to accurately monitor various migration parameters throughout the cell cycle, thus having great potential to facilitate new discoveries in cell biology.

DIscBIO: A User-Friendly Pipeline for Biomarker Discovery in Single-Cell Transcriptomics.

The growing attention toward the benefits of single-cell RNA sequencing (scRNA-seq) is leading to a myriad of computational packages for the analysis of different aspects of scRNA-seq data. For researchers without advanced programing skills, it is very challenging to combine several packages in order to perform the desired analysis in a simple and reproducible way. Here we present DIscBIO, an open-source, multi-algorithmic pipeline for easy, efficient and reproducible analysis of cellular sub-populations at the transcriptomic level. The pipeline integrates multiple scRNA-seq packages and allows biomarker discovery with decision trees and gene enrichment analysis in a network context using single-cell sequencing read counts through clustering and differential analysis. DIscBIO is freely available as an R package. It can be run either in command-line mode or through a user-friendly computational pipeline using Jupyter notebooks. We showcase all pipeline features using two scRNA-seq datasets. The first dataset consists of circulating tumor cells from patients with breast cancer. The second one is a cell cycle regulation dataset in myxoid liposarcoma. All analyses are available as notebooks that integrate in a sequential narrative R code with explanatory text and output data and images. R users can use the notebooks to understand the different steps of the pipeline and will guide them to explore their scRNA-seq data. We also provide a cloud version using Binder that allows the execution of the pipeline without the need of downloading R, Jupyter or any of the packages used by the pipeline. The cloud version can serve as a tutorial for training purposes, especially for those that are not R users or have limited programing skills. However, in order to do meaningful scRNA-seq analyses, all users will need to understand the implemented methods and their possible options and limitations.

Evaluation and improvement of the National Early Warning Score (NEWS2) for COVID-19: a multi-hospital study.

BACKGROUND: The National Early Warning Score (NEWS2) is currently recommended in the UK for the risk stratification of COVID-19 patients, but little is known about its ability to detect severe cases. We aimed to evaluate NEWS2 for the prediction of severe COVID-19 outcome and identify and validate a set of blood and physiological parameters routinely collected at hospital admission to improve upon the use of NEWS2 alone for medium-term risk stratification. METHODS: Training cohorts comprised 1276 patients admitted to King's College Hospital National Health Service (NHS) Foundation Trust with COVID-19 disease from 1 March to 30 April 2020. External validation cohorts included 6237 patients from five UK NHS Trusts (Guy's and St Thomas' Hospitals, University Hospitals Southampton, University Hospitals Bristol and Weston NHS Foundation Trust, University College London Hospitals, University Hospitals Birmingham), one hospital in Norway (Oslo University Hospital), and two hospitals in Wuhan, China (Wuhan Sixth Hospital and Taikang Tongji Hospital). The outcome was severe COVID-19 disease (transfer to intensive care unit (ICU) or death) at 14 days after hospital admission. Age, physiological measures, blood biomarkers, sex, ethnicity, and comorbidities (hypertension, diabetes, cardiovascular, respiratory and kidney diseases) measured at hospital admission were considered in the models. RESULTS: A baseline model of 'NEWS2 + age' had poor-to-moderate discrimination for severe COVID-19 infection at 14 days (area under receiver operating characteristic curve (AUC) in training cohort = 0.700, 95% confidence interval (CI) 0.680, 0.722; Brier score = 0.192, 95% CI 0.186, 0.197). A supplemented model adding eight routinely collected blood and physiological parameters (supplemental oxygen flow rate, urea, age, oxygen saturation, C-reactive protein, estimated glomerular filtration rate, neutrophil count, neutrophil/lymphocyte ratio) improved discrimination (AUC = 0.735; 95% CI 0.715, 0.757), and these improvements were replicated across seven UK and non-UK sites. However, there was evidence of miscalibration with the model tending to underestimate risks in most sites. CONCLUSIONS: NEWS2 score had poor-to-moderate discrimination for medium-term COVID-19 outcome which raises questions about its use as a screening tool at hospital admission. Risk stratification was improved by including readily available blood and physiological parameters measured at hospital admission, but there was evidence of miscalibration in external sites. This highlights the need for a better understanding of the use of early warning scores for COVID.

Toward Personalized Computer Simulation of Breast Cancer Treatment: A Multiscale Pharmacokinetic and Pharmacodynamic Model Informed by Multitype Patient Data.

The usefulness of mechanistic models to disentangle complex multiscale cancer processes, such as treatment response, has been widely acknowledged. However, a major barrier for multiscale models to predict treatment outcomes in individual patients lies in their initialization and parametrization, which needs to reflect individual cancer characteristics accurately. In this study, we use multitype measurements acquired routinely on a single breast tumor, including histopathology, MRI, and molecular profiling, to personalize parts of a complex multiscale model of breast cancer treated with chemotherapeutic and antiangiogenic agents. The model accounts for drug pharmacokinetics and pharmacodynamics. We developed an open-source computer program that simulates cross-sections of tumors under 12-week therapy regimens and used it to individually reproduce and elucidate treatment outcomes of 4 patients. Two of the tumors did not respond to therapy, and model simulations were used to suggest alternative regimens with improved outcomes dependent on the tumor's individual characteristics. It was determined that more frequent and lower doses of chemotherapy reduce tumor burden in a low proliferative tumor while lower doses of antiangiogenic agents improve drug penetration in a poorly perfused tumor. Furthermore, using this model, we were able to correctly predict the outcome in another patient after 12 weeks of treatment. In summary, our model bridges multitype clinical data to shed light on individual treatment outcomes. SIGNIFICANCE: Mathematical modeling is used to validate possible mechanisms of tumor growth, resistance, and treatment outcome.

Arginine Deprivation Therapy: Putative Strategy to Eradicate Glioblastoma Cells by Radiosensitization.

Tumor cells-even if nonauxotrophic-are often highly sensitive to arginine deficiency. We hypothesized that arginine deprivation therapy (ADT) if combined with irradiation could be a new treatment strategy for glioblastoma (GBM) patients because systemic ADT is independent of local penetration and diffusion limitations. A proof-of-principle in vitro study was performed with ADT being mimicked by application of recombinant human arginase or arginine-free diets. ADT inhibited two-dimensional (2-D) growth and cell-cycle progression, and reduced growth recovery after completion of treatment in four different GBM cell line models. Cells were less susceptible to ADT alone in the presence of citrulline and in a three-dimensional (3-D) environment. Migration and 3-D invasion were not unfavorably affected. However, ADT caused a significant radiosensitization that was more pronounced in a GBM cell model with p53 loss of function as compared with its p53-wildtype counterpart. The synergistic effect was independent of basic and induced argininosuccinate synthase or argininosuccinate lyase protein expression and not abrogated by the presence of citrulline. The radiosensitizing potential was maintained or even more distinguishable in a 3-D environment as verified in p53-knockdown and p53-wildtype U87-MG cells via a 60-day spheroid control probability assay. Although the underlying mechanism is still ambiguous, the observation of ADT-induced radiosensitization is of great clinical interest, in particular for patients with GBM showing high radioresistance and/or p53 loss of function. Mol Cancer Ther; 17(2); 393-406. ©2017 AACRSee all articles in this MCT Focus section, "Developmental Therapeutics in Radiation Oncology."

Autonomy and Non-autonomy of Angiogenic Cell Movements Revealed by Experiment-Driven Mathematical Modeling.

Angiogenesis is a multicellular phenomenon driven by morphogenetic cell movements. We recently reported morphogenetic vascular endothelial cell (EC) behaviors to be dynamic and complex. However, the principal mechanisms orchestrating individual EC movements in angiogenic morphogenesis remain largely unknown. Here we present an experiment-driven mathematical model that enables us to systematically dissect cellular mechanisms in branch elongation. We found that cell-autonomous and coordinated actions governed these multicellular behaviors, and a cell-autonomous process sufficiently illustrated essential features of the morphogenetic EC dynamics at both the single-cell and cell-population levels. Through refining our model and experimental verification, we further identified a coordinated mode of tip EC behaviors regulated via a spatial relationship between tip and follower ECs, which facilitates the forward motility of tip ECs. These findings provide insights that enhance our mechanistic understanding of not only angiogenic morphogenesis, but also other types of multicellular phenomenon.

Early embryonic vascular patterning by matrix-mediated paracrine signalling: a mathematical model study.

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling.