The evolution of mathematical modeling of glioma proliferation and invasion

Hybrid of glioma growth model and deformable image registration for longitudinal brain MRIs synthesis

Modeling and visualization of glioma growth could assist in cancer diagnosis, tumor progression prediction, and clinical treatment outcome improvement. However, most studies either failed to make patient-specific predictions or could only display information about tumor size and shape, lacking the capability to characterize the impact of tumor growth on surrounding tissues. In this study, a method (HybrSyn) combining tumor growth model and deformable image registration technique for synthesizing MRIs at arbitrary time point after the detection time has been proposed. Through the tumor growth model, tumor growth process for consecutive time point has been predicted according to the characteristics of tumor cell diffusion and proliferation within the brain. The glioma deformable image registration model was employed to obtain the deformation fields between the tumors at detection time and simulations at subsequent time points. These fields were then mapped to the patient's initial MRI scans to generate the synthetic MRIs corresponding to that time points. To validate the HybrSyn, various experiments were conducted on the BraTS19 and the internal dataset collected from Zigong First People's Hospital. The quantitative results demonstrated a structural similarity of 80.93% between the synthesized MRIs and the patients' MRI scans. The qualitative results indicated that the HybrSyn could effectively capture changes during tumor progression and provide a global view. From the clinical point of view, synthesized longitudinal brain MRIs could potentially aid in presenting the impact of glioma growth on surrounding functional areas, and identifying target regions for personalized treatment planning.

Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans. Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion partial differential equation (PDE) model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse-domain method is employed to handle the complex brain geometry within the PINN framework. The method is validated on both synthetic and patient datasets, showing promise for personalized GBM treatment through parametric inference within clinically relevant timeframes.

Role of modeled high-grade glioma cell invasion and survival on the prediction of tumor progression after radiotherapy

Objective.Glioblastoma (GBM) prognosis remains poor despite progress in radiotherapy and imaging techniques. Tumor recurrence has been attributed to the widespread tumor invasion of normal tissue. Since the complete extension of invasion is undetectable on imaging, it is not deliberately treated. To improve the treatment outcome, models have been developed to predict tumor invasion based standard imaging data. This study aimed to investigate whether a tumor invasion model, together with the predicted number of surviving cells after radiotherapy, could predict tumor progression post-treatment.Approach.A tumor invasion model was applied to 56 cases of GBMs treated with radiotherapy. The invasion was quantified as the volume encompassed by the 100 cells mm-3isocontour (V100). A new metric, cell-volume-product, was defined as the product of the volume with cell density greater than a threshold value (in cells mm-3), and the number of surviving cells within that volume, post-treatment. Tumor progression was assessed at 20 ± 10 d and 90 ± 20 d after treatment. Correlations between the disease progression and the gross tumor volume (GTV),V100, and cell-volume-product, were determined using receiver operating characteristic curves.Main results.For the early follow-up time, the correlation between GTV and tumor progression was not statistically significant (p= 0.684). However, statistically significant correlations with progression were found betweenV100and cell-volume-product with a cell threshold of 10-6cells mm-3with areas-under-the-curve of 0.69 (p= 0.023) and 0.66 (p= 0.045), respectively. No significant correlations were found for the late follow-up time.Significance.Modeling tumor spread otherwise undetectable on conventional imaging, as well as radiobiological model predictions of cell survival after treatment, may provide useful information regarding the likelihood of tumor progression at an early follow-up time point, which could potentially lead to improved treatment decisions for patients with GBMs.

A Learnable Prior Improves Inverse Tumor Growth Modeling

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%.

Biopsy location and tumor-associated macrophages in predicting malignant glioma recurrence using an in-silico model

Predicting the biological behavior and time to recurrence (TTR) of high-grade diffuse gliomas (HGG) after maximum safe neurosurgical resection and combined radiation and chemotherapy plays a pivotal role in planning clinical follow-up, selecting potentially necessary second-line treatment and improving the quality of life for patients diagnosed with a malignant brain tumor. The current standard-of-care (SoC) for HGG includes follow-up neuroradiological imaging to detect recurrence as early as possible and relies on several clinical, neuropathological, and radiological prognostic factors, which have limited accuracy in predicting TTR. In this study, using an in-silico analysis, we aim to improve predictive power for TTR by considering the role of (i) prognostically relevant information available through diagnostics used in the current SoC, (ii) advanced image-based information not currently part of the standard diagnostic workup, such as tumor-normal tissue interface (edge) features and quantitative data specific to biopsy positions within the tumor, and (iii) information on tumor-associated macrophages. In particular, we introduced a state-of-the-art spatio-temporal model of tumor-immune interactions, emphasizing the interplay between macrophages and glioma cells. This model serves as a synthetic reality for assessing the predictive value of various features. We generated a cohort of virtual patients based on our mathematical model. Each patient's dataset includes simulated T1Gd and Fluid-attenuated inversion recovery (FLAIR) MRI volumes. T1-weighted imaging highlights anatomical structures with high contrast, providing clear detail on brain morphology, whereas FLAIR suppresses fluid signals, improving the visualization of lesions near fluid-filled spaces, which is particularly helpful for identifying peritumoral edema. Additionally, we simulated results on macrophage density and proliferative activity, either in a specified part of the tumor, namely the tumor core or edge ("localized"), or unspecified ("non-localized"). To enhance the realism of our synthetic data, we imposed different levels of noise. Our findings reveal that macrophage density at the tumor edge contributed to a high predictive value of feature importance for the selected regression model. Moreover, there are lower MSE values for the "localized" biopsy in prediction accuracy toward recurrence post-resection compared with "non-localized" specimens in the noisy data. In conclusion, the results show that localized biopsies provided more information about tumor behavior, especially at the interface of tumor and normal tissue (Edge).

Heterogeneous biomechanical/mathematical modeling of spatial prediction of glioblastoma progression using magnetic resonance imaging-based finite element method

BACKGROUND AND OBJECTIVE

Brain tumors are one of the most common diseases and causes of death in humans. Since the growth of brain tumors has irreparable risks for the patient, predicting the growth of the tumor and knowing its effect on the brain tissue will increase the efficiency of treatment strategies.

METHODS

This study examines brain tumor growth using mathematical modeling based on the Reaction-Diffusion equation and the biomechanical model based on continuum mechanics principles. With the help of the image threshold technique of magnetic resonance images, a heterogeneous and close-to-reality environment of the brain has been modeled and experimental data validated the results to achieve maximum accuracy in predicting growth.

RESULTS

The obtained results have been compared with the reported conventional models to evaluate the presented model. In addition to incorporating the chemotherapy effects in governing equations, the real-time finite element analysis of the stress tensors of the surrounding tissue of tumor cells and considering its role in changing the shape and growth of the tumor has added to the importance and accuracy of the current model.

CONCLUSIONS

The comparison of the obtained results with conventional models shows that the heterogeneous model has higher reliability due to the consideration of the appropriate properties for the different regions of the brain. The presented model can contribute to personalized medicine, aid in understanding the dynamics of tumor growth, optimize treatment regimens, and develop adaptive therapy strategies.

Insights from a multiscale framework on metabolic rate variation driving glioblastoma multiforme growth and invasion

Non-physiological levels of oxygen and nutrients within the tumors result in heterogeneous cell populations that exhibit distinct necrotic, hypoxic, and proliferative zones. Among these zonal cellular properties, metabolic rates strongly affect the overall growth and invasion of tumors. Here, we report on a hybrid discrete-continuum (HDC) mathematical framework that uses metabolic data from a biomimetic two-dimensional (2D) in-vitro cancer model to predict three-dimensional (3D) behaviour of in-vitro human glioblastoma (hGB). The mathematical model integrates modules of continuum, discrete, and neurons. Results indicated that the HDC model is capable of quantitatively predicting growth, invasion length, and the asymmetric finger-type invasion pattern in in-vitro hGB tumors. Additionally, the model could predict the reduction in invasion length of hGB tumoroids in response to temozolomide (TMZ). This model has the potential to incorporate additional modules, including immune cells and signaling pathways governing cancer/immune cell interactions, and can be used to investigate targeted therapies.

Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time.

Beyond conventional imaging: Advancements in MRI for glioma malignancy prediction and molecular profiling

This review examines the advancements in magnetic resonance imaging (MRI) techniques and their pivotal role in diagnosing and managing gliomas, the most prevalent primary brain tumors. The paper underscores the importance of integrating modern MRI modalities, such as diffusion-weighted imaging and perfusion MRI, which are essential for assessing glioma malignancy and predicting tumor behavior. Special attention is given to the 2021 WHO Classification of Tumors of the Central Nervous System, emphasizing the integration of molecular diagnostics in glioma classification, significantly impacting treatment decisions. The review also explores radiogenomics, which correlates imaging features with molecular markers to tailor personalized treatment strategies. Despite technological progress, MRI protocol standardization and result interpretation challenges persist, affecting diagnostic consistency across different settings. Furthermore, the review addresses MRI's capacity to distinguish between tumor recurrence and pseudoprogression, which is vital for patient management. The necessity for greater standardization and collaborative research to harness MRI's full potential in glioma diagnosis and personalized therapy is highlighted, advocating for an enhanced understanding of glioma biology and more effective treatment approaches.

Optimization of SOX2 Expression for Enhanced Glioblastoma Stem Cell Virotherapy

The Zika virus has been shown to infect glioblastoma stem cells via the membrane receptorα v β 5 , which is activated by the stem-specific transcription factor SOX2. Since the expression level of SOX2 is an important predictive marker for successful virotherapy, it is important to understand the fundamental mechanisms of the role of SOX2 in the dynamics of cancer stem cells and Zika viruses. In this paper, we develop a mathematical ODE model to investigate the effects of SOX2 expression levels on Zika virotherapy against glioblastoma stem cells. Our study aimed to identify the conditions under which SOX2 expression level, viral infection, and replication can reduce or eradicate the glioblastoma stem cells. Analytic work on the existence and stability conditions of equilibrium points with respect to the basic reproduction number are provided. Numerical results were in good agreement with analytic solutions. Our results show that critical threshold levels of both SOX2 and viral replication, which change the stability of equilibrium points through population dynamics such as transcritical and Hopf bifurcations, were observed. These critical thresholds provide the optimal conditions for SOX2 expression levels and viral bursting sizes to enhance therapeutic efficacy of Zika virotherapy against glioblastoma stem cells. This study provides critical insights into optimizing Zika virus-based treatment for glioblastoma by highlighting the essential role of SOX2 in viral infection and replication.

Impact of glioma peritumoral edema, tumor size, and tumor location on alternating electric fields (AEF) therapy in realistic 3D rat glioma models: a computational study

Objective.Alternating electric fields (AEF) therapy is a treatment modality for patients with glioblastoma. Tumor characteristics such as size, location, and extent of peritumoral edema may affect the AEF strength and distribution. We evaluated the sensitivity of the AEFs in a realistic 3D rat glioma model with respect to these properties.Approach.The electric properties of the peritumoral edema were varied based on calculated and literature-reported values. Models with different tumor composition, size, and location were created. The resulting AEFs were evaluated in 3D rat glioma models.Main results.In all cases, a pair of 5 mm diameter electrodes induced an average field strength >1 V cm-1. The simulation results showed that a negative relationship between edema conductivity and field strength was found. As the tumor core size was increased, the average field strength increased while the fraction of the shell achieving >1.5 V cm-1decreased. Increasing peritumoral edema thickness decreased the shell's mean field strength. Compared to rostrally/caudally, shifting the tumor location laterally/medially and ventrally (with respect to the electrodes) caused higher deviation in field strength.Significance.This study identifies tumor properties that are key drivers influencing AEF strength and distribution. The findings might be potential preclinical implications.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Preoperative growth dynamics of untreated glioblastoma: Description of an exponential growth type, correlating factors, and association with postoperative survival

Background

Little is known about the growth dynamics of untreated glioblastoma and its possible influence on postoperative survival. Our aim was to analyze a possible association of preoperative growth dynamics with postoperative survival.

Methods

We performed a retrospective analysis of all adult patients surgically treated for newly diagnosed glioblastoma at our center between 2010 and 2020. By volumetric analysis of data of patients with availability of ≥3 preoperative sequential MRI, a growth pattern was aimed to be identified. Main inclusion criterion for further analysis was the availability of two preoperative MRI scans with a slice thickness of 1 mm, at least 7 days apart. Individual growth rates were calculated. Association with overall survival (OS) was examined by multivariable.

Results

Out of 749 patients screened, 13 had ≥3 preoperative MRI, 70 had 2 MRI and met the inclusion criteria. A curve estimation regression model showed the best fit for exponential tumor growth. Median tumor volume doubling time (VDT) was 31 days, median specific growth rate (SGR) was 2.2% growth per day. SGR showed negative correlation with tumor size (rho = -0.59, P < .001). Growth rates were dichotomized according to the median SGR.OS was significantly longer in the group with slow growth (log-rank: P = .010). Slower preoperative growth was independently associated with longer overall survival in a multivariable Cox regression model for patients after tumor resection.

Conclusions

Especially small lesions suggestive of glioblastoma showed exponential tumor growth with variable growth rates and a median VDT of 31 days. SGR was significantly associated with OS in patients with tumor resection in our sample.

An image-based modeling framework for predicting spatiotemporal brain cancer biology within individual patients

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 image-localized 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.

Agent-Based Modelling Reveals the Role of the Tumor Microenvironment on the Short-Term Success of Combination Temozolomide/Immune Checkpoint Blockade to Treat Glioblastoma

Glioblastoma is the most common and deadly primary brain tumor in adults. All glioblastoma patients receiving standard-of-care surgery-radiotherapy-chemotherapy (i.e., temozolomide (TMZ)) recur, with an average survival time of only 15 months. New approaches to the treatment of glioblastoma, including immune checkpoint blockade and oncolytic viruses, offer the possibility of improving glioblastoma outcomes and have as such been under intense study. Unfortunately, these treatment modalities have thus far failed to achieve approval. Recently, in an attempt to bolster efficacy and improve patient outcomes, regimens combining chemotherapy and immune checkpoint inhibitors have been tested in trials. Unfortunately, these efforts have not resulted in significant increases to patient survival. To better understand the various factors impacting treatment outcomes of combined TMZ and immune checkpoint blockade, we developed a systems-level, computational model that describes the interplay between glioblastoma, immune, and stromal cells with this combination treatment. Initializing our model to spatial resection patient samples labeled using imaging mass cytometry, our model's predictions show how the localization of glioblastoma cells, influence therapeutic success. We further validated these predictions in samples of brain metastases from patients given they generally respond better to checkpoint blockade compared with primary glioblastoma. Ultimately, our model provides novel insights into the mechanisms of therapeutic success of immune checkpoint inhibitors in brain tumors and delineates strategies to translate combination immunotherapy regimens more effectively into the clinic. SIGNIFICANCE STATEMENT: Extending survival times for glioblastoma patients remains a critical challenge. Although immunotherapies in combination with chemotherapy hold promise, clinical trials have not shown much success. Here, systems models calibrated to and validated against patient samples can improve preclinical and clinical studies by shedding light on the factors distinguishing responses/failures. By initializing our model with imaging mass cytometry visualization of patient samples, we elucidate how factors such as localization of glioblastoma cells and CD8+ T cell infiltration impact treatment outcomes.

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

3D-Printed Tumor-on-a-Chip Model for Investigating the Effect of Matrix Stiffness on Glioblastoma Tumor Invasion

Glioblastoma multiform (GBM) tumor progression has been recognized to be correlated with extracellular matrix (ECM) stiffness. Dynamic variation of tumor ECM is primarily regulated by a family of enzymes which induce remodeling and degradation. In this paper, we investigated the effect of matrix stiffness on the invasion pattern of human glioblastoma tumoroids. A 3D-printed tumor-on-a-chip platform was utilized to culture human glioblastoma tumoroids with the capability of evaluating the effect of stiffness on tumor progression. To induce variations in the stiffness of the collagen matrix, different concentrations of collagenase were added, thereby creating an inhomogeneous collagen concentration. To better understand the mechanisms involved in GBM invasion, an in silico hybrid mathematical model was used to predict the evolution of a tumor in an inhomogeneous environment, providing the ability to study multiple dynamic interacting variables. The model consists of a continuum reaction-diffusion model for the growth of tumoroids and a discrete model to capture the migration of single cells into the surrounding tissue. Results revealed that tumoroids exhibit two distinct patterns of invasion in response to the concentration of collagenase, namely ring-type and finger-type patterns. Moreover, higher concentrations of collagenase resulted in greater invasion lengths, confirming the strong dependency of tumor behavior on the stiffness of the surrounding matrix. The agreement between the experimental results and the model's predictions demonstrates the advantages of this approach in investigating the impact of various extracellular matrix characteristics on tumor growth and invasion.

Overall survival prediction for high-grade glioma patients using mathematical modeling of tumor cell infiltration

PURPOSE

This study aimed at applying a mathematical framework for the prediction of high-grade gliomas (HGGs) cell invasion into normal tissues for guiding the clinical target delineation, and at investigating the possibility of using tumor infiltration maps for patient overall survival (OS) prediction.

MATERIAL & METHODS

A model describing tumor infiltration into normal tissue was applied to 93 HGG cases. Tumor infiltration maps and corresponding isocontours with different cell densities were produced. ROC curves were used to seek correlations between the patient OS and the volume encompassed by a particular isocontour. Area-Under-the-Curve (AUC) values were used to determine the isocontour having the highest predictive ability. The optimal cut-off volume, having the highest sensitivity and specificity, for each isocontour was used to divide the patients in two groups for a Kaplan-Meier survival analysis.

RESULTS

The highest AUC value was obtained for the isocontour of cell densities 1000 cells/mm3 and 2000 cells/mm3, equal to 0.77 (p < 0.05). Correlation with the GTV yielded an AUC of 0.73 (p < 0.05). The Kaplan-Meier survival analysis using the 1000 cells/mm3 isocontour and the ROC optimal cut-off volume for patient group selection rendered a hazard ratio (HR) of 2.7 (p < 0.05), while the GTV rendered a HR = 1.6 (p < 0.05).

CONCLUSION

The simulated tumor cell invasion is a stronger predictor of overall survival than the segmented GTV, indicating the importance of using mathematical models for cell invasion to assist in the definition of the target for HGG patients.

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.

A stochastic hierarchical model for low grade glioma evolution

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise diffusion Markov process (PDifMP) at the cellular level, we derive an equation for the density of the transition probability of this Markov process based on the generalised Fokker-Planck equation. Then, a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.

Remote neuronal activity drives glioma infiltration via Sema4f

The tumor microenvironment (TME) plays an essential role in malignancy and neurons have emerged as a key component of the TME that promotes tumorigenesis across a host of cancers. Recent studies on glioblastoma (GBM) highlight bi-directional signaling between tumors and neurons that propagates a vicious cycle of proliferation, synaptic integration, and brain hyperactivity; however, the identity of neuronal subtypes and tumor subpopulations driving this phenomenon are incompletely understood. Here we show that callosal projection neurons located in the hemisphere contralateral to primary GBM tumors promote progression and widespread infiltration. Using this platform to examine GBM infiltration, we identified an activity dependent infiltrating population present at the leading edge of mouse and human tumors that is enriched for axon guidance genes. High-throughput, in vivo screening of these genes identified Sema4F as a key regulator of tumorigenesis and activity-dependent infiltration. Furthermore, Sema4F promotes the activity-dependent infiltrating population and propagates bi-directional signaling with neurons by remodeling tumor adjacent synapses towards brain network hyperactivity. Collectively, our studies demonstrate that subsets of neurons in locations remote to primary GBM promote malignant progression, while revealing new mechanisms of tumor infiltration that are regulated by neuronal activity.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Deep learning characterization of brain tumours with diffusion weighted imaging

Glioblastoma multiforme (GBM) is one of the most deadly forms of cancer. Methods of characterizing these tumours are valuable for improving predictions of their progression and response to treatment. A mathematical model called the proliferation-invasion (PI) model has been used extensively in the literature to model the growth of these tumours, though it relies on known values of two key parameters: the tumour cell diffusivity and proliferation rate. Unfortunately, these parameters are difficult to estimate in a patient-specific manner, making personalized tumour forecasting challenging. In this paper, we develop and apply a deep learning model capable of making accurate estimates of these key GBM-characterizing parameters while simultaneously producing a full prediction of the tumour progression curve. Our method uses two sets of multi sequence MRI in order to produce estimations and relies on a preprocessing pipeline which includes brain tumour segmentation and conversion to tumour cellularity. We first apply our deep learning model to synthetic tumours to showcase the model's capabilities and identify situations where prediction errors are likely to occur. We then apply our model to a clinical dataset consisting of five patients diagnosed with GBM. For all patients, we derive evidence-based estimates for each of the PI model parameters and predictions for the future progression of the tumour, along with estimates of the parameter uncertainties. Our work provides a new, easily generalizable method for the estimation of patient-specific tumour parameters, which can be built upon to aid physicians in designing personalized treatments.

Learn-Morph-Infer: A new way of solving the inverse problem for brain tumor modeling

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer, the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.

Liquid biopsies for early diagnosis of brain tumours: in silico mathematical biomarker modelling

Brain tumours are the biggest cancer killer in those under 40 and reduce life expectancy more than any other cancer. Blood-based liquid biopsies may aid early diagnosis, prediction and prognosis for brain tumours. It remains unclear whether known blood-based biomarkers, such as glial fibrillary acidic protein (GFAP), have the required sensitivity and selectivity. We have developed a novel in silico model which can be used to assess and compare blood-based liquid biopsies. We focused on GFAP, a putative biomarker for astrocytic tumours and glioblastoma multi-formes (GBMs). In silico modelling was paired with experimental measurement of cell GFAP concentrations and used to predict the tumour volumes and identify key parameters which limit detection. The average GBM volumes of 449 patients at Leeds Teaching Hospitals NHS Trust were also measured and used as a benchmark. Our model predicts that the currently proposed GFAP threshold of 0.12 ng ml-1 may not be suitable for early detection of GBMs, but that lower thresholds may be used. We found that the levels of GFAP in the blood are related to tumour characteristics, such as vasculature damage and rate of necrosis, which are biological markers of tumour aggressiveness. We also demonstrate how these models could be used to provide clinical insight.

The use of fibroblasts as a valuable strategy for studying mitochondrial impairment in neurological disorders

Neurological disorders (NDs) are characterized by progressive neuronal dysfunction leading to synaptic failure, cognitive impairment, and motor injury. Among these diseases, Alzheimer's disease (AD), Parkinson's disease (PD), Huntington's disease (HD), and amyotrophic lateral sclerosis (ALS) have raised a significant research interest. These disorders present common neuropathological signs, including neuronal dysfunction, protein accumulation, oxidative damage, and mitochondrial abnormalities. In this context, mitochondrial impairment is characterized by a deficiency in ATP production, excessive production of reactive oxygen species, calcium dysregulation, mitochondrial transport failure, and mitochondrial dynamics deficiencies. These defects in mitochondrial health could compromise the synaptic process, leading to early cognitive dysfunction observed in these NDs. Interestingly, skin fibroblasts from AD, PD, HD, and ALS patients have been suggested as a useful strategy to investigate and detect early mitochondrial abnormalities in these NDs. In this context, fibroblasts are considered a viable model for studying neurodegenerative changes due to their metabolic and biochemical relationships with neurons. Also, studies of our group and others have shown impairment of mitochondrial bioenergetics in fibroblasts from patients diagnosed with sporadic and genetic forms of AD, PD, HD, and ALS. Interestingly, these mitochondrial abnormalities have been observed in the brain tissues of patients suffering from the same pathologies. Therefore, fibroblasts represent a novel strategy to study the genesis and progression of mitochondrial dysfunction in AD, PD, HD, and ALS. This review discusses recent evidence that proposes fibroblasts as a potential target to study mitochondrial bioenergetics impairment in neurological disorders and consequently to search for new biomarkers of neurodegeneration.

Knowledge-infused Global-Local Data Fusion for Spatial Predictive Modeling in Precision Medicine

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 paper proposes a novel machine learning framework to fuse the three sources of data/information to generate spatial prediction, namely the knowledge-infused global-local data fusion (KGL) 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 6 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.

Radiomic Deformation and Textural Heterogeneity (R-DepTH) Descriptor to Characterize Tumor Field Effect: Application to Survival Prediction in Glioblastoma

The concept of tumor field effect implies that cancer is a systemic disease with its impact way beyond the visible tumor confines. For instance, in Glioblastoma (GBM), an aggressive brain tumor, the increase in intracranial pressure due to tumor burden often leads to brain herniation and poor outcomes. Our work is based on the rationale that highly aggressive tumors tend to grow uncontrollably, leading to pronounced biomechanical tissue deformations in the normal parenchyma, which when combined with local morphological differences in the tumor confines on MRI scans, will comprehensively capture tumor field effect. Specifically, we present an integrated MRI-based descriptor, radiomic-Deformation and Textural Heterogeneity (r-DepTH). This descriptor comprises measurements of the subtle perturbations in tissue deformations throughout the surrounding normal parenchyma due to mass effect. This involves non-rigidly aligning the patients' MRI scans to a healthy atlas via diffeomorphic registration. The resulting inverse mapping is used to obtain the deformation field magnitudes in the normal parenchyma. These measurements are then combined with a 3D texture descriptor, Co-occurrence of Local Anisotropic Gradient Orientations (COLLAGE), which captures the morphological heterogeneity and infiltration within the tumor confines, on MRI scans. In this work, we extensively evaluated r-DepTH for survival risk-stratification on a total of 207 GBM cases from 3 different cohorts (Cohort 1 ( n1 = 53 ), Cohort 2 ( n2 = 75 ), and Cohort 3 ( n3 = 79 )), where each of these three cohorts was used as a training set for our model separately, and the other two cohorts were used for testing, independently, for each training experiment. When employing Cohort 1 for training, r-DepTH yielded Concordance indices (C-indices) of 0.7 and 0.65, hazard ratios (HR) and Confidence Intervals (CI) of 10 (6 - 19) and 5 (3 - 8) on Cohorts 2 and 3, respectively. Similarly, training on Cohort 2 yielded C-indices of 0.6 and 0.7, HR and CI of 1 (0.7 - 2) and 3 (2 - 5) on Cohorts 1 and 3, respectively. Finally, training on Cohort 3 yielded C-indices of 0.75 and 0.63, HR and CI of 24 (10 - 57) and 12 (6 - 21) on Cohorts 1 and 2, respectively. Our results show that r-DepTH descriptor may serve as a comprehensive and a robust MRI-based prognostic marker of disease aggressiveness and survival in solid tumors.

Modelling glioma progression, mass effect and intracranial pressure in patient anatomy

Increased intracranial pressure is the source of most critical symptoms in patients with glioma, and often the main cause of death. Clinical interventions could benefit from non-invasive estimates of the pressure distribution in the patient's parenchyma provided by computational models. However, existing glioma models do not simulate the pressure distribution and they rely on a large number of model parameters, which complicates their calibration from available patient data. Here we present a novel model for glioma growth, pressure distribution and corresponding brain deformation. The distinct feature of our approach is that the pressure is directly derived from tumour dynamics and patient-specific anatomy, providing non-invasive insights into the patient's state. The model predictions allow estimation of critical conditions such as intracranial hypertension, brain midline shift or neurological and cognitive impairments. A diffuse-domain formalism is employed to allow for efficient numerical implementation of the model in the patient-specific brain anatomy. The model is tested on synthetic and clinical cases. To facilitate clinical deployment, a high-performance computing implementation of the model has been publicly released.

Advanced Imaging Techniques for Newly Diagnosed and Recurrent Gliomas

Management of gliomas following initial diagnosis requires thoughtful presurgical planning followed by regular imaging to monitor treatment response and survey for new tumor growth. Traditional MR imaging modalities such as T1 post-contrast and T2-weighted sequences have long been a staple of tumor diagnosis, surgical planning, and post-treatment surveillance. While these sequences remain integral in the management of gliomas, advances in imaging techniques have allowed for a more detailed characterization of tumor characteristics. Advanced MR sequences such as perfusion, diffusion, and susceptibility weighted imaging, as well as PET scans have emerged as valuable tools to inform clinical decision making and provide a non-invasive way to help distinguish between tumor recurrence and pseudoprogression. Furthermore, these advances in imaging have extended to the operating room and assist in making surgical resections safer. Nevertheless, surgery, chemotherapy, and radiation treatment continue to make the interpretation of MR changes difficult for glioma patients. As analytics and machine learning techniques improve, radiomics offers the potential to be more quantitative and personalized in the interpretation of imaging data for gliomas. In this review, we describe the role of these newer imaging modalities during the different stages of management for patients with gliomas, focusing on the pre-operative, post-operative, and surveillance periods. Finally, we discuss radiomics as a means of promoting personalized patient care in the future.

Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics

Simple Summary

Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Abstract

The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.

Silencing of AKIP1 Suppresses the Proliferation, Migration, and Epithelial-Mesenchymal Transition Process of Glioma Cells by Upregulating DLG2

Gliomas, the most prevalent brain tumors, account for nearly one-third of the all brain and central nervous system (CNS) tumors diagnosed in the USA. The purpose of this study was to discuss the important role of A kinase-interacting protein 1 (AKIP1) in glioma and reveal the potential mechanism. After prediction by CCLE, the expression of AKIP1 was determined by qRT-PCR and western blot. The impacts of AKIP1 knockdown on the proliferation, migration, and invasion were then measured by MTT, colony formation assay, wound healing, and transwell assays. Western blot was used to assess the protein levels of migration and epithelial-mesenchymal transition- (EMT-) related factors. Subsequently, the expression of Disks Large Homolog 2 (DLG2) was predicted by bioinformatics analyses, and the interaction between AKIP1 and DLG2 was confirmed by IP assay, qRT-PCR, and western blot. Finally, DLG2 was further downregulated in glioma cells to detect the association between AKIP1 and DLG2 in the cellular functions of glioma. It was demonstrated that AKIP1 exhibited a high level in glioma cells, and interference of AKIP1 led to reductions in the proliferation, migration, invasion, and EMT of glioma cells. DLG2, which was lowly expressed in glioma cells, demonstrated a negative link to AKIP2. Inhibition of both AKIP2 and DLG2 counteracted the inhibited cellular behaviors on account of AKIP1 interference. To be concluded, this study presented evidence that AKIP1 silencing suppressed the progression of glioma via targeting DLG2, which could provide novel insights to impede the development of glioma.

A method to remove the influence of fixative concentration on postmortem T2 maps using a kinetic tensor model

Formalin fixation has been shown to substantially reduce T₂ estimates, primarily driven by the presence of fixative in tissue. Prior to scanning, post‐mortem samples are often placed into a fluid that has more favourable imaging properties. This study investigates whether there is evidence for a change in T₂ in regions close to the tissue surface due to fixative outflux into this surrounding fluid. Furthermore, we investigate whether a simulated spatial map of fixative concentration can be used as a confound regressor to reduce T₂ inhomogeneity. To achieve this, T₂ maps and diffusion tensor estimates were obtained in 14 whole, formalin‐fixed post‐mortem brains placed in Fluorinert approximately 48 hr prior to scanning. Seven brains were fixed with 10% formalin and seven brains were fixed with 10% neutral buffered formalin (NBF). Fixative outflux was modelled using a proposed kinetic tensor (KT) model, which incorporates voxelwise diffusion tensor estimates to account for diffusion anisotropy and tissue‐specific diffusion coefficients. Brains fixed with 10% NBF revealed a spatial T₂ pattern consistent with modelled fixative outflux. Confound regression of fixative concentration reduced T₂ inhomogeneity across both white and grey matter, with the greatest reduction attributed to the KT model versus simpler models of fixative outflux. No such effect was observed in brains fixed with 10% formalin. Correlations between the transverse relaxation rate R₂ and ferritin/myelin proteolipid protein (PLP) histology lead to an increased similarity for the relationship between R₂ and PLP for the two fixative types after KT correction.

Spatiotemporal dynamics of a glioma immune interaction model

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.

The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.

The Effect of Radiotherapy on Diffuse Low-Grade Gliomas Evolution: Confronting Theory with Clinical Data

Diffuse low-grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the evolution of the tumor radius before and after the radiotherapy process and propose a novel model that is simple yet biologically motivated and that remedies some shortcomings of previously proposed ones. We confront this with clinical data consisting of time series of tumor radii from 43 patient records by using a stochastic optimization technique and obtain very good fits in all cases. Since our model describes the evolution of a tumor from the very first glioma cell, it gives access to the possible age of the tumor. Using the technique of profile likelihood to extract all of the information from the data, we build confidence intervals for the tumor birth age and confirm the fact that low-grade gliomas seem to appear in the late teenage years. Moreover, an approximate analytical expression of the temporal evolution of the tumor radius allows us to explain the correlations observed in the data.

Improving personalized tumor growth predictions using a Bayesian combination of mechanistic modeling and machine learning

BACKGROUND

In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient's pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient's clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics.

METHODS

Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges.

RESULTS

We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The method results in improved predictions in almost all simulated patients, especially for those with a late clinical presentation (>95% patients show improvements compared to standard mathematical modeling). In addition, we test the methodology in two additional settings dealing with real patient cohorts. In both cases, namely cancer growth in chronic lymphocytic leukemia and ovarian cancer, predictions show excellent agreement with reported clinical outcomes (around 60% reduction of mean squared error).

CONCLUSIONS

We show that the combination of machine learning and mathematical modeling approaches can lead to accurate predictions of clinical outputs in the context of data sparsity and limited knowledge of disease mechanisms.

Differential Effects of a Left Frontal Glioma on the Cortical Thickness and Complexity of Both Hemispheres

Glioma is a type of brain tumor that infiltrates and compresses the brain as it grows. Focal gliomas affect functional connectivity both in the local region of the lesion and the global network of the brain. Any anatomical changes associated with a glioma should thus be clarified. We examined the cortical structures of 15 patients with a glioma in the left lateral frontal cortex and compared them with those of 15 healthy controls by surface-based morphometry. Two regional parameters were measured with 3D-MRI: the cortical thickness (CT) and cortical fractal dimension (FD). The FD serves as an index of the topological complexity of a local cortical surface. Our comparative analyses of these parameters revealed that the left frontal gliomas had global effects on the cortical structures of both hemispheres. The structural changes in the right hemisphere were mainly characterized by a decrease in CT and mild concomitant decrease in FD, whereas those in the peripheral regions of the glioma (left hemisphere) were mainly characterized by a decrease in FD with relative preservation of CT. These differences were found irrespective of tumor volume, location, or grade. These results elucidate the structural effects of gliomas, which extend to the distant contralateral regions.

In-Silico Modeling of Tumor Spheroid Formation and Growth

Mathematical modeling has significant potential for understanding of biological models of cancer and to accelerate the progress in cross-disciplinary approaches of cancer treatment. In mathematical biology, solid tumor spheroids are often studied as preliminary in vitro models of avascular tumors. The size of spheroids and their cell number are easy to track, making them a simple in vitro model to investigate tumor behavior, quantitatively. The growth of solid tumors is comprised of three main stages: transient formation, monotonic growth and a plateau phase. The last two stages are extensively studied. However, the initial transient formation phase is typically missing from the literature. This stage is important in the early dynamics of growth, formation of clonal sub-populations, etc. In the current work, this transient formation is modeled by a reaction–diffusion partial differential equation (PDE) for cell concentration, coupled with an ordinary differential equation (ODE) for the spheroid radius. Analytical and numerical solutions of the coupled equations were obtained for the change in the radius of tumor spheroids over time. Human glioblastoma (hGB) cancer cells (U251 and U87) were spheroid cultured to validate the model prediction. Results of this study provide insight into the mechanism of development of solid tumors at their early stage of formation.

Modeling of Glioma Growth with Mass Effect by Longitudinal Magnetic Resonance Imaging

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called ?mass effect?). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained T₂-weighted and contrast-enhanced T₁-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and tumor concentration, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 ? 10^-3 mm²d^-1) is significantly less than those for the RD and RDM models (17.46 ? 10^-3 mm²d^-1 and 19.38 ? 10^-3 mm²d^-1, respectively). The tumor concentrations for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case

Glioblastoma extensively infiltrates the brain; despite surgery and aggressive therapies, the prognosis is poor. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of glioblastoma evolution in every single patient, with the aim of tailoring therapeutic weapons. In particular, the ultimate goal of biomathematics for cancer is the identification of the most suitable theoretical models and simulation tools, both to describe the biological complexity of carcinogenesis and to predict tumor evolution. In this report, we describe the results of a critical review about different mathematical models in neuro-oncology with their clinical implications. A comprehensive literature search and review for English-language articles concerning mathematical modelling in glioblastoma has been conducted. The review explored the different proposed models, classifying them and indicating the significative advances of each one. Furthermore, we present a specific case of a glioblastoma patient in which our recently proposed innovative mechanical model has been applied. The results of the mathematical models have the potential to provide a relevant benefit for clinicians and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. Further prospective comparative trials, however, are still necessary to prove the impact of mathematical neuro-oncology in clinical practice.

Superlinear growth reveals the Allee effect in tumors

Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies emphasize the role of competition among tumor cells, they fail to explain recently observed superlinear growth dynamics across human tumors. Here we study tumor growth dynamics by developing a model that incorporates evolutionary dynamics inside tumors with tumor-microenvironment interactions. Our results reveal that tumor cells' ability to manipulate the environment and induce angiogenesis drives superlinear growth-a process compatible with the Allee effect. In light of this understanding, our model suggests that, for high-risk tumors that have a higher growth rate, suppressing angiogenesis can be the appropriate therapeutic intervention.

WAM to SeeSaw model for cancer therapy - overcoming LQM difficulties

PURPOSE

The assessment of biological effects caused by radiation exposure has been currently carried out with the linear-quadratic (LQ) model as an extension of the linear non-threshold (LNT) model. In this study, we suggest a new mathematical model named as SeaSaw (SS) model, which describes proliferation and cell death effects by taking account of Bergonie-Tribondeau's law in terms of a differential equation in time. We show how this model overcomes the long-standing difficulties of the LQ model.

MATERIALS AND METHODS

We construct the SS model as an extended Wack-A-Mole (WAM) model by using a differential equation with respect to time in order to express the dynamics of the proliferation effect. A large number of accumulated data of such parameters as α and β in the LQ based models provide us with valuable pieces of information on the corresponding parameter b 1 and the maximum volume V m of the SS model. The dose rate b 1 and the notion of active cell can explain the present data without introduction of β, which is obtained by comparing the SS model with not only the cancer therapy data but also with in vitro experimental data. Numerical calculations are presented to grasp the global features of the SS model.

RESULTS

The SS model predicts the time dependence of the number of active- and inactive-cells. The SS model clarifies how the effect of radiation depends on the cancer stage at the starting time in the treatment. Further, the time dependence of the tumor volume is calculated by changing individual dose strength, which results in the change of the irradiation duration for the same effect. We can consider continuous irradiation in the SS model with interesting outcome on the time dependence of the tumor volume for various dose rates. Especially by choosing the value of the dose rate to be balanced with the total growth rate, the tumor volume is kept constant.

CONCLUSIONS

The SS model gives a simple equation to study the situation of clinical radiation therapy and risk estimation of radiation. The radiation parameter extracted from the cancer therapy is close to the value obtained from animal experiment in vitro and in vivo. We expect the SS model leads us to a unified description of radiation therapy and protection and provides a great development in cancer-therapy clinical-planning.

Radiological evaluation of ex novo high grade glioma: velocity of diametric expansion and acceleration time study

Background

One of the greatest neuro-oncological concern remains the lack of knowledge about the etiopathogenesis and physiopathology of gliomas. Several studies reported a strict correlation between radiological features and biological behaviour of gliomas; in this way the velocity of diametric expansion (VDE) correlate with lower grade glioma aggressiveness. However, there are no the same strong evidences for high grade gliomas (HGG) because of the lack of several preoperative MRI.

Patients and methods

We describe a series of 4 patients affected by HGG followed from 2014 to January 2019. Two patients are male and two female; two had a pathological diagnosis of glioblastoma (GBM), one of anaplastic astrocytoma (AA) and one had a neuroradiological diagnosis of GBM. The VDE and the acceleration time (AT) was calculated for fluid attenuated inversion recovery (FLAIR) volume and for the enhancing nodule (EN). Every patients underwent sequential MRI study along a mean period of 413 days.

Results

Mean VDE evaluated on FLAIR volume was 39.91 mm/year. Mean percentage ratio between peak values and mean value of acceleration was 282.7%. Median appearance time of EN after first MRI scan was 432 days. Mean VDE was 45.02 mm/year. Mean percentage ratio between peak values and mean value of acceleration was 257.52%.

Conclusions

To our knowledge, this is the first report on VDE and acceleration growth in HGG confirming their strong aggressiveness. In a case in which we need to repeat an MRI, time between consecutive scans should be reduced to a maximum of 15–20 days and surgery should be executed as soon as possible.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.

The role of computational methods for automating and improving clinical target volume definition

Treatment planning in radiotherapy distinguishes three target volume concepts: the gross tumor volume (GTV), the clinical target volume (CTV), and the planning target volume (PTV). Over time, GTV definition and PTV margins have improved through the development of novel imaging techniques and better image guidance, respectively. CTV definition is sometimes considered the weakest element in the planning process. CTV definition is particularly complex since the extension of microscopic disease cannot be seen using currently available in-vivo imaging techniques. Instead, CTV definition has to incorporate knowledge of the patterns of tumor progression. While CTV delineation has largely been considered the domain of radiation oncologists, this paper, arising from a 2019 ESTRO Physics research workshop, discusses the contributions that medical physics and computer science can make by developing computational methods to support CTV definition. First, we overview the role of image segmentation algorithms, which may in part automate CTV delineation through segmentation of lymph node stations or normal tissues representing anatomical boundaries of microscopic tumor progression. The recent success of deep convolutional neural networks has also enabled learning entire CTV delineations from examples. Second, we discuss the use of mathematical models of tumor progression for CTV definition, using as example the application of glioma growth models to facilitate GTV-to-CTV expansion for glioblastoma that is consistent with neuroanatomy. We further consider statistical machine learning models to quantify lymphatic metastatic progression of tumors, which may eventually improve elective CTV definition. Lastly, we discuss approaches to incorporate uncertainty in CTV definition into treatment plan optimization as well as general limitations of the CTV concept in the case of infiltrating tumors without natural boundaries.