A mathematical model of pre-diagnostic glioma growth

The self-organized structure of glioma oncostreams and the disruptive role of passive cells

Oncostreams are self-organized structures formed by spindle-like, elongated, self-propelled cells recently described in glioblastomas and especially in gliosarcomas. Cells within these structures either move as large clusters in one main direction, flocks, or as linear, intermingling collections of cells advancing in opposite directions, streams. Round, passive cells are also observed, either inside or segregated from the oncostreams. Here we generalize a recently formulated particle-field approach to investigate the genesis and evolution of these structures, first showing that, in systems consisting only of identical self-propelled cells, both flocks and streams emerge as self-organized dynamic configurations. Flocks are the more stable configurations, while streams are transient and usually originate in collisions between flocks. Stream degradation is easier at low self-propulsion speeds. In systems consisting of both motile and passive cells, the latter block stream formation and accelerate their degradation and flock stabilization. Since the flock appears to be the most effective invasive structure, we thus argue that a phenotype mixture (motile and passive cells) may favor glioblastoma invasion. hlBy relating cellular properties to the observed outcome, our model shows that oncostreams are self-organized structures that result from the interplay between speed, shape, and steric repulsion.

Mathematical modeling of brain metastases growth and response to therapies: A review

Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.

Data driven modeling of pseudopalisade pattern formation

Pseudopalisading is an interesting phenomenon where cancer cells arrange themselves to form a dense garland-like pattern. Unlike the palisade structure, a similar type of pattern first observed in schwannomas by pathologist J.J. Verocay (Wippold et al. in AJNR Am J Neuroradiol 27(10):2037-2041, 2006), pseudopalisades are less organized and associated with a necrotic region at their core. These structures are mainly found in glioblastoma (GBM), a grade IV brain tumor, and provide a way to assess the aggressiveness of the tumor. Identification of the exact bio-mechanism responsible for the formation of pseudopalisades is a difficult task, mainly because pseudopalisades seem to be a consequence of complex nonlinear dynamics within the tumor. In this paper we propose a data-driven methodology to gain insight into the formation of different types of pseudopalisade structures. To this end, we start from a state of the art macroscopic model for the dynamics of GBM, that is coupled with the dynamics of extracellular pH, and formulate a terminal value optimal control problem. Thus, given a specific, observed pseudopalisade pattern, we determine the evolution of parameters (bio-mechanisms) that are responsible for its emergence. Random histological images exhibiting pseudopalisade-like structures are chosen to serve as target pattern. Having identified the optimal model parameters that generate the specified target pattern, we then formulate two different types of pattern counteracting ansatzes in order to determine possible ways to impair or obstruct the process of pseudopalisade formation. This provides the basis for designing active or live control of malignant GBM. Furthermore, we also provide a simple, yet insightful, mechanism to synthesize new pseudopalisade patterns by linearly combining the optimal model parameters responsible for generating different known target patterns. This particularly provides a hint that complex pseudopalisade patterns could be synthesized by a linear combination of parameters responsible for generating simple patterns. Going even further, we ask ourselves if complex therapy approaches can be conceived, such that some linear combination thereof is able to reverse or disrupt simple pseudopalisade patterns; this is investigated with the help of numerical simulations.

Liquid biomarkers in glioma

An ideal biomarker must meet several parameters to enable its successful adoption; however, the nature of glioma makes it challenging to discover valuable biomarkers. While biomarkers require simplicity for clinical implementation, anatomical features and the complexity of the brain make it challenging to perform histological examination. Therefore, compared to biomarkers from general histological examination, liquid biomarkers for brain disease offer many more advantages in these minimally invasive methods. Ideal biomarkers should have high sensitivity and specificity, especially in malignant tumors. The heterogeneous nature of glioma makes it challenging to determine useful common biomarkers, and no liquid biomarker has yet been adopted clinically. The low incidence of brain tumors also hinders research progress. To overcome these problems, clinical applications of new types of specimens, such as extracellular vesicles and comprehensive omics analysis, have been developed, and some candidate liquid biomarkers have been identified. As against previous reviews, we focused on and reviewed the sensitivity and specificity of each liquid biomarker for its clinical application. Perusing an ideal glioma biomarker would help uncover the common underlying mechanism of glioma and develop new therapeutic targets. Further multicenter studies based on these findings will help establish new treatment strategies in the future.

A dynamical model of combination therapy applied to glioma

Glioma is a human brain tumor that is very difficult to treat at an advanced stage. Studies of glioma biomarkers have shown that some markers are released into the bloodstream, so data from these markers indicate a decrease in the concentration of blood glucose and serum glucose in patients with glioma; these suggest an association between glucose and glioma. This decrease mechanism in glucose concentration can be described by the coupled ordinary differential equations of the early-stage glioma growth and interactions between glioma cells, immune cells, and glucose concentration. In this paper, we propose developing a new mathematical model to explain how glioma cells evolve and survive combination therapy between chemotherapy and oncolytic virotherapy, as an alternative to glioma treatment. In this study, three therapies were applied for analysis, that is, (1) chemotherapy, (2) virotherapy, and (3) a combination of chemotherapy and virotherapy. Virotherapy uses specialist viruses that only attack tumor cells. Based on the simulation results of the therapy carried out, we conclude that combination therapy can reduce the glioma cells significantly compared to the other two therapies. The simulation results of this combination therapy can be an alternative to glioma therapy.

Data Driven Mathematical Model of Colon Cancer Progression

Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.

Associations between prediagnostic blood glucose levels, diabetes, and glioma

Previous literature indicates that pre-diagnostic diabetes and blood glucose levels are inversely related to glioma risk. To replicate these findings and determine whether they could be attributed to excess glucose consumption by the preclinical tumour, we used data from the Apolipoprotein MOrtality RISk (AMORIS) (n = 528,580) and the Metabolic syndrome and Cancer project (Me-Can) cohorts (n = 269,365). We identified individuals who were followed for a maximum of 15 years after their first blood glucose test until glioma diagnosis, death, emigration or the end of follow-up. Hazard ratios (HRs), 95% confidence intervals (CIs) and their interactions with time were estimated using Cox time-dependent regression. As expected, pre-diagnostic blood glucose levels were inversely related to glioma risk (AMORIS, P_trend = 0.002; Me-Can, P_trend = 0.04) and pre-diagnostic diabetes (AMORIS, HR = 0.30, 95% CI 0.17 to 0.53). During the year before diagnosis, blood glucose was inversely associated with glioma in the AMORIS (HR = 0.78, 95% CI 0.66 to 0.93) but not the Me-Can cohort (HR = 0.99, 95% CI 0.63 to 1.56). This AMORIS result is consistent with our hypothesis that excess glucose consumption by the preclinical tumour accounts for the inverse association between blood glucose and glioma. We discuss additional hypothetical mechanisms that may explain our paradoxical findings.

Huntington's Disease: Calcium Dyshomeostasis and Pathology Models

Huntington's disease (HD) is a severe inherited neurodegenerative disorder characterized by motor dysfunction, cognitive decline, and mental impairment. At the molecular level, HD is caused by a mutation in the first exon of the gene encoding the huntingtin protein. The mutation results in an expanded polyglutamine tract at the N-terminus of the huntingtin protein, causing the neurodegenerative pathology. Calcium dyshomeostasis is believed to be one of the main causes of the disease, which underlies the great interest in the problem among experts in molecular physiology. Recent studies have focused on the development of animal and insect HD models, as well as patient-specific induced pluripotent stem cells (HD-iPSCs), to simulate the disease's progression. Despite a sesquicentennial history of HD studies, the issues of diagnosis and manifestation of the disease have remained topical. The present review addresses these issues.

Enabling personalized cancer medicine decisions: The challenging pharmacological approach of PBPK models for nanomedicine and pharmacogenomics (Review)

The existing tumor heterogeneity and the complexity of cancer cell biology critically demand powerful translational tools with which to support interdisciplinary efforts aiming to advance personalized cancer medicine decisions in drug development and clinical practice. The development of physiologically based pharmacokinetic (PBPK) models to predict the effects of drugs in the body facilitates the clinical translation of genomic knowledge and the implementation of in vivo pharmacology experience with pharmacogenomics. Such a direction unequivocally empowers our capacity to also make personalized drug dosage scheme decisions for drugs, including molecularly targeted agents and innovative nanoformulations, i.e. in establishing pharmacotyping in prescription. In this way, the applicability of PBPK models to guide individualized cancer therapeutic decisions of broad clinical utility in nanomedicine in real-time and in a cost-affordable manner will be discussed. The latter will be presented by emphasizing the need for combined efforts within the scientific borderlines of genomics with nanotechnology to ensure major benefits and productivity for nanomedicine and personalized medicine interventions.