Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy

Personalized in silico model for radiation-induced pulmonary fibrosis

Radiation-induced pulmonary fibrosis (RIPF) is a severe late-stage complication of radiotherapy (RT) to the chest area, typically used in lung cancer treatment. This condition is characterized by the gradual and irreversible replacement of healthy lung tissue with fibrous scar tissue, leading to decreased lung function, reduced oxygen exchange and critical respiratory deficiencies. Currently, predicting and managing lung fibrosis post-RT remains challenging, with limited preventive and treatment options. Accurate prediction of fibrosis onset and progression is therefore clinically crucial. We present a personalized in silico model for pulmonary fibrosis that encompasses tumour regression, fibrosis development and lung tissue remodelling post-radiation. Our continuum-based model was developed using data from 12 RT-treated lung cancer patients and integrates computed tomography (CT) and dosimetry data to simulate the spatio-temporal evolution of fibrosis. We demonstrate the ability of the in silico model to capture the extent of fibrosis in the entire cohort with a less than 1% deviation from clinical observations, in addition to providing quantitative metrics of spatial similarity. These findings underscore the potential of the model to improve treatment planning and risk assessment, paving the way for more personalized and effective management of RIPF.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Recent Advancements on Self-Immolative System Based on Dynamic Covalent Bonds for Delivering Heterogeneous Payloads

The precisely spatial-temporal delivery of heterogeneous payloads from a single system with the same pulse is in great demand in realizing versatile and synergistic functions. Very few molecular architectures can satisfy the strict requirements of dual-release translated from single triggers, while the self-immolative systems based on dynamic covalent bonds represent the "state-of-art" of ultimate solution strategy. Embedding heterogeneous payloads symmetrically onto the self-immolative backbone with dynamic covalent bonds as the trigger, can respond to the quasi-bio-orthogonal hallmarks which are higher at the disease's microenvironment to simultaneously yield the heterogeneous payloads (drug A/drug B or drug/reporter). In this review, the modular design principles are concentrated to illustrate the rules in tailoring useful structures, then the rational applications are enumerated on the aspects of drug codelivery and visualized drug-delivery. This review, hopefully, can give the general readers a comprehensive understanding of the self-immolative systems based on dynamic covalent bonds for delivering heterogeneous payloads.

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.

Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model

Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.

IDH-wild-type glioblastoma cell density and infiltration distribution influence on supramarginal resection and its impact on overall survival: a mathematical model

OBJECTIVE

Recent studies have proposed resection of the T2 FLAIR hyperintensity beyond the T1 contrast enhancement (supramarginal resection [SMR]) for IDH-wild-type glioblastoma (GBM) to further improve patients' overall survival (OS). GBMs have significant variability in tumor cell density, distribution, and infiltration. Advanced mathematical models based on patient-specific radiographic features have provided new insights into GBM growth kinetics on two important parameters of tumor aggressiveness: proliferation rate (ρ) and diffusion rate (D). The aim of this study was to investigate OS of patients with IDH-wild-type GBM who underwent SMR based on a mathematical model of cell distribution and infiltration profile (tumor invasiveness profile).

METHODS

Volumetric measurements were obtained from the selected regions of interest from pre- and postoperative MRI studies of included patients. The tumor invasiveness profile (proliferation/diffusion [ρ/D] ratio) was calculated using the following formula: ρ/D ratio = (4π/3)2/3 × (6.106/[VT21/1 - VT11/1])2, where VT2 and VT1 are the preoperative FLAIR and contrast-enhancing volumes, respectively. Patients were split into subgroups based on their tumor invasiveness profiles. In this analysis, tumors were classified as nodular, moderately diffuse, or highly diffuse.

RESULTS

A total of 101 patients were included. Tumors were classified as nodular (n = 34), moderately diffuse (n = 34), and highly diffuse (n = 33). On multivariate analysis, increasing SMR had a significant positive correlation with OS for moderately and highly diffuse tumors (HR 0.99, 95% CI 0.98-0.99; p = 0.02; and HR 0.98, 95% CI 0.96-0.99; p = 0.04, respectively). On threshold analysis, OS benefit was seen with SMR from 10% to 29%, 10% to 59%, and 30% to 90%, for nodular, moderately diffuse, and highly diffuse, respectively.

CONCLUSIONS

The impact of SMR on OS for patients with IDH-wild-type GBM is influenced by the degree of tumor invasiveness. The authors' results show that increasing SMR is associated with increased OS in patients with moderate and highly diffuse IDH-wild-type GBMs. When grouping SMR into 10% intervals, this benefit was seen for all tumor subgroups, although for nodular tumors, the maximum beneficial SMR percentage was considerably lower than in moderate and highly diffuse tumors.

Nonlocal Reaction-Diffusion Equations in Biomedical Applications

Nonlocal reaction-diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications. This review will present the state of the art in the investigation of nonlocal reaction-diffusion models in biomedical applications. We will consider various models arising in mathematical immunology, neuroscience, cancer modelling, and we will discuss their mathematical properties, nonlinear dynamics, resulting spatiotemporal patterns and biological significance.

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.

Improving cancer treatments via dynamical biophysical models

Despite significant advances in oncological research, cancer nowadays remains one of the main causes of mortality and morbidity worldwide. New treatment techniques, as a rule, have limited efficacy, target only a narrow range of oncological diseases, and have limited availability to the general public due their high cost. An important goal in oncology is thus the modification of the types of antitumor therapy and their combinations, that are already introduced into clinical practice, with the goal of increasing the overall treatment efficacy. One option to achieve this goal is optimization of the schedules of drugs administration or performing other medical actions. Several factors complicate such tasks: the adverse effects of treatments on healthy cell populations, which must be kept tolerable; the emergence of drug resistance due to the intrinsic plasticity of heterogeneous cancer cell populations; the interplay between different types of therapies administered simultaneously. Mathematical modeling, in which a tumor and its microenvironment are considered as a single complex system, can address this complexity and can indicate potentially effective protocols, that would require experimental verification. In this review, we consider classical methods, current trends and future prospects in the field of mathematical modeling of tumor growth and treatment. In particular, methods of treatment optimization are discussed with several examples of specific problems related to different types of treatment.

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.

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.

A neuro evolutionary algorithm for patient calibrated prediction of survival in Glioblastoma patients

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is the most common and malignant type of primary brain tumors. Radiation therapy (RT) plus concomitant and adjuvant Temozolomide (TMZ) constitute standard treatment of GBM. Existing models for GBM growth do not consider the effect of different schedules on tumor growth and patient survival. However, clinical trials show that treatment schedule and drug dosage significantly affect patient survival. The goal is to provide a patient calibrated model for predicting survival according to the treatment schedule.

METHODS

We propose a top-down method based on artificial neural networks (ANN) and genetic algorithm (GA) to predict survival of GBM patients. A feed forward undercomplete Autoencoder network is integrated with the neuro-evolutionary (NE) algorithm in order to extract a compressed representation of input clinical data. The proposed NE algorithm uses GA to obtain optimal architecture of a multi-layer perceptron (MLP). Taguchi L₁₆ orthogonal design of experiments is used to tune parameters of the proposed NE algorithm. Finally, the optimal MLP is used to predict survival of GBM patients.

RESULTS

Data from 8 related clinical trials have been collected and integrated to train the model. From 847 evaluable cases, 719 were used for train and validation and the remaining 128 cases were used to test the model. Mean absolute error of the predictions on the test data is 0.087 months which shows excellent performance of the proposed model in predicting survival of the patients. Also, the results show that the proposed NE algorithm is superior to other existing models in both the mean and variability of the prediction error.

No prognostic differences between GBM-patients presenting with postoperative SMA-syndrome and GBM-patients involving cortico-spinal tract and primary motor cortex

BACKGROUND

The supplementary motor area (SMA) is involved in several aspects of motor control and its can be associated to a contralateral motor deficit and speech disorders. After the resection of low-grade gliomas, this syndrome is diffusely reported but it is rarely investigated in high-grade gliomas. SMA deficits may resolve completely or with minor sequelae within weeks. Whether this condition of transient deficit affects survival, was not previously investigated, and is not currently understood.

OBJECTIVE

The study aimed to perform an accurate investigation concerning the real clinical and prognostic impact of the postoperative SMA syndrome in order to shed light over its relationship to survival parameters and postoperative functional status of the patients.

METHODS

We performed a retrospective review of a series of 176 surgically treated patients suffering from Glioblastomas. Tumors classified as Group A: Involving the SMA and Group B: Lesion located outside and distal to the SMA but in anatomical relationship to primary motor cortices (PM1) or corticospinal tract (CST), in order to investigate differences concerning immunohistochemical and molecular profiles in regard to the survival parameters.

RESULTS

Although lesions involving SMA demonstrated a significantly higher volume in respect to their general counterparts they did not significantly differ in concerns to the molecular patterns, pre and postoperative KPS scores and in PFS and OS findings.

CONCLUSIONS

In our cohort SMA-syndrome is reversible and therefore guarantees a satisfactory functional status at follow-up, apparently not compromising survival when compared to other lesions affecting the primary or cortical motor area -spinal tract.

Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect

We present a 3D fully-automatic method for the calibration of partial differential equation (PDE) models of glioblastoma (GBM) growth with "mass effect", the deformation of brain tissue due to the tumor. We quantify the mass effect, tumor proliferation, tumor migration, and the localized tumor initial condition from a single multiparameteric Magnetic Resonance Imaging (mpMRI) patient scan. The PDE is a reaction-advection-diffusion partial differential equation coupled with linear elasticity equations to capture mass effect. The single-scan calibration model is notoriously difficult because the precancerous (healthy) brain anatomy is unknown. To solve this inherently ill-posed and illconditioned optimization problem, we introduce a novel inversion scheme that uses multiple brain atlases as proxies for the healthy precancer patient brain resulting in robust and reliable parameter estimation. We apply our method on both synthetic and clinical datasets representative of the heterogeneous spatial landscape typically observed in glioblastomas to demonstrate the validity and performance of our methods. In the synthetic data, we report calibration errors (due to the ill-posedness and our solution scheme) in the 10%-20% range. In the clinical data, we report good quantitative agreement with the observed tumor and qualitative agreement with the mass effect (for which we do not have a ground truth). Our method uses a minimal set of parameters and provides both global and local quantitative measures of tumor infiltration and mass effect.

Reinforcement learning for optimal scheduling of Glioblastoma treatment with Temozolomide

BACKGROUND

Glioblastoma multiforme (GBM) is the most frequent primary brain tumor in adults and Temozolomide (TMZ) is an effective chemotherapeutic agent for its treatment. In Silico models of GBM growth provide an appropriate foundation for analysis and comparison of different regimens. We propose a mathematical frame for patient specific design of optimal chemotherapy regimens for GBM patients.

METHODS

The proposed frame includes online interaction of a virtual GBM with an optimizing agent. Spatiotemporal dynamics of GBM growth and its response to TMZ are simulated with a three dimensional hybrid cellular automaton. Q learning is tailored to the virtual GBM for treatment optimization aimed at minimizing tumor size at the end of treatment course. Q learning consists of a learning agent that interacts with the virtual GBM. System state is affected by the agent decisions and the obtained rewards guide Q learning to the optimal schedule.

RESULTS

Computational results confirm that the optimal chemotherapy schedule depends on some patient specific parameters including body weight, tumor size and its position in the brain. Furthermore, the algorithm is used for scheduling 2100 mg of TMZ on a virtual GBM and the obtained schedule is to administer150 mg of TMZ every other day. The obtained schedule is compared to the standard 7/14 regimen and the results show that it is superior to the 7/14 regimen in minimizing tumor size.

CONCLUSION

The proposed frame is an appropriate decision support system for patient specific design of TMZ administration regimens on GBM patients. Also, since the obtained optimal schedule outperforms the standard 7/14 regimen, it is worthy of further clinical testing.

Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations

Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute to disappointing clinical trial results. Image-localized biopsy techniques allow multiple biopsies to be taken during surgery and provide information that identifies regions where particular sub-populations occur within an individual GBM, thus providing insight into their regional genetic variability. These sub-populations may also interact with one another in a competitive or cooperative manner; it is important to ascertain the nature of these interactions, as they may have implications for responses to targeted therapies. We combine genetic information from biopsies with a mechanistic model of interacting GBM sub-populations to characterise the nature of interactions between two commonly occurring GBM sub-populations, those with EGFR and PDGFRA genes amplified. We study population levels found across image-localized biopsy data from a cohort of 25 patients and compare this to model outputs under competitive, cooperative and neutral interaction assumptions. We explore other factors affecting the observed simulated sub-populations, such as selection advantages and phylogenetic ordering of mutations, which may also contribute to the levels of EGFR and PDGFRA amplified populations observed in biopsy data.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

IMAGE-DRIVEN BIOPHYSICAL TUMOR GROWTH MODEL CALIBRATION

We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, multiparametric magnetic resonance imaging (MRI) scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations (PDEs). Thus, we have to generate a second snapshot to be able to extract significant information from a single patient snapshot. We create this two-snapshot scenario as follows. We use an atlas (an average of several scans of healthy individuals) as a substitute for an earlier, pretumor, MRI scan of the patient. Then, using the patient scan and the atlas, we combine image-registration algorithms and parameter estimation algorithms to achieve a better estimate of the healthy patient scan and the tumor growth parameters that are consistent with the data. Our scheme is based on our recent work (Scheufele et al., Comput. Methods Appl. Mech. Engrg., to appear), but we apply a different and novel scheme where the tumor growth simulation in contrast to the previous work is executed in the patient brain domain and not in the atlas domain yielding more meaningful patient-specific results. As a basis, we use a PDE-constrained optimization framework. We derive a modified Picard-iteration-type solution strategy in which we alternate between registration and tumor parameter estimation in a new way. In addition, we consider an ℓ ₁ sparsity constraint on the initial condition for the tumor and integrate it with the new joint inversion scheme. We solve the sub-problems with a reduced space, inexact Gauss-Newton-Krylov/quasi-Newton method. We present results using real brain data with synthetic tumor data that show that the new scheme reconstructs the tumor parameters in a more accurate and reliable way compared to our earlier scheme.

WHERE DID THE TUMOR START? AN INVERSE SOLVER WITH SPARSE LOCALIZATION FOR TUMOR GROWTH MODELS

We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

Image-based metric of invasiveness predicts response to adjuvant temozolomide for primary glioblastoma

Background

Temozolomide (TMZ) has been the standard-of-care chemotherapy for glioblastoma (GBM) patients for more than a decade. Despite this long time in use, significant questions remain regarding how best to optimize TMZ therapy for individual patients. Understanding the relationship between TMZ response and factors such as number of adjuvant TMZ cycles, patient age, patient sex, and image–based tumor features, might help predict which GBM patients would benefit most from TMZ, particularly for those whose tumors lack O⁶–methylguanine–DNA methyltransferase (MGMT) promoter methylation.

Methods and findings

Using a cohort of 90 newly–diagnosed GBM patients treated according to the standard of care, we examined the relationships between several patient and tumor characteristics and volumetric and survival outcomes during adjuvant chemotherapy. Volumetric changes in MR imaging abnormalities during adjuvant therapy were used to assess TMZ response. T1Gd volumetric response is associated with younger patient age, increased number of TMZ cycles, longer time to nadir volume, and decreased tumor invasiveness. Moreover, increased adjuvant TMZ cycles corresponded with improved volumetric response only among more nodular tumors, and this volumetric response was associated with improved survival outcomes. Finally, in a subcohort of patients with known MGMT methylation status, methylated tumors were more diffusely invasive than unmethylated tumors, suggesting the improved response in nodular tumors is not driven by a preponderance of MGMT methylated tumors.

Conclusions

Our finding that less diffusely invasive tumors are associated with greater volumetric response to TMZ suggests patients with these tumors may benefit from additional adjuvant TMZ cycles, even for those without MGMT methylation.

Personalized image-based tumor growth prediction in a convection-diffusion-reaction model

Inter-individual heterogeneity of tumors leads to non-effectiveness of unique therapy plans. This issue has caused a growing interest in the field of personalized medicine and its application in tumor growth evaluation. Accordingly, in this paper, a framework of personalized medicine is presented for growth prediction of brain glioma tumors. A convection-diffusion-reaction model is used as the patient-specific tumor growth model which is associated with multimodal magnetic resonance images (MRIs). Two parameters of intracellular area fraction (ICAF) and metabolic rate have been used to incorporate the physiological data obtained from medical images into the model. The framework is tested on the data of two cases of glioma tumors to document the approach; parameter estimation is made using particle swarm optimization (PSO) and genetic algorithm (GA) and the model is evaluated by comparing the predicted tumors with the observed tumors in terms of root mean square error of the ICAF maps (IRMSE), relative area difference (RAD) and Dice's coefficient (DC). Results show the differences of IRMSE, RAD and DC in 4.1 ∓ 1.15%, 0.099 ∓ 0.041 and 85.5 ∓ 7.5%, respectively. Survival times are estimated by assuming the tumor radius of 35 mm as the fatal burden. Results confirm that less-diffusive tumors lead to higher survival times. The represented framework makes it possible to personally predict the growth behavior of glioma tumors only based on patients' routine MRIs and provides a basis for modeling the personalized therapy and walking in the path of personalized medicine.

Function Based Brain Modeling and Simulation of an Ischemic Region in Post-Stroke Patients using the Bidomain

BACKGROUND

Several studies have shown that post-stroke patients develop divergent activity in the sensorimotor areas of the affected hemisphere of the brain compared to healthy people during motor tasks. Proper mathematical models will help us understand this activity and clarify the associated underlying mechanisms. New Method. This research describes an anatomically based brain computer model in post-stroke patients. We simulate an ischemic region for arm motion using the bidomain approach. Two scenarios are considered: a healthy subject and a post-stroke patient with motion impairment. Next, we limit the volume of propagation considering only the sensorimotor area of the brain. Comparison with existing methods. In comparison to existing methods, we combine the use of the bidomain for modeling the propagation of the electrical activity across the brain volume with functional information to limit the volume of propagation and the position of the expected stimuli, given a specific task. Whereas just using the bidomain without limiting the functional volume, propagates the electrical activity into non-expected areas.

RESULTS

To validate the simulation, we compare the activity with patient measurements using functional near-infrared spectroscopy during arm motion (n=5) against controls (n=3). The results are consistent with empirical measurements and previous research and show that there is a disparity between position and number of spikes in post-stroke patients in contrast to healthy subjects.

CONCLUSIONS

These results hold promise in improving the understanding of brain deterioration in stroke patients and the re-arrangement of brain networks. Furthermore, shows the use of functionality based brain modeling.

Thalamic Glioblastoma: Clinical Presentation, Management Strategies, and Outcomes

BACKGROUND

Thalamic glioblastomas (GBMs) represent a significant neurosurgical challenge. In view of the low incidence of these tumors, outcome data and management strategies are not well defined.

OBJECTIVE

To identify the natural history and factors associated with survival in patients with thalamic glioblastoma.

METHODS

A retrospective review of all patients with thalamic glioblastoma over a 10-yr period was performed. Presenting clinical, radiological, and outcome data were collected. Chi-squared and Fisher's exact tests were used to compare clinical characteristics across tumor groups. Cox proportional hazard models were utilized to investigate variables of interest with regard to overall survival.

RESULTS

Fifty-seven patients met inclusion criteria, with a median age of 53 and median Karnofsky Performance Scale (KPS) score of 80. The most common presenting symptoms were weakness, confusion, and headache. Hydrocephalus was present in 47% of patients preoperatively. Stereotactic biopsy was performed in 47 cases, and 10 patients underwent craniotomy. The median overall survival was 12.2 mo. Higher KPS, younger age, and cerebrospinal fluid (CSF) diversion were correlated with better overall survival univariately, respectively, while the presence of language deficits at initial presentation was associated with poorer survival. In multivariate analysis, the only significant predictor of survival was presenting KPS.

CONCLUSION

The overall survival of patients with thalamic glioblastoma is comparable to unresectable lobar supratentorial GBMs. Younger patients and those with good presenting functional status had improved survival. Midbrain involvement by the tumor is not a negative prognostic factor. Improved therapies are needed, and patients should be considered for early trial involvement and aggressive upfront therapy.

Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

In this article, we present a multispecies reaction-advection-diffusion partial differential equation coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so-called "mass effect", a term-of-art that refers to the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and a semi-Lagrangian method for advection. We also present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.

Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay

We formulate a mathematical model of functional partial differential equations for oncolytic virotherapy which incorporates virus diffusivity, tumor cell diffusion, and the viral lytic cycle based on a basic oncolytic virus dynamics model. We conduct a detailed analysis for the dynamics of the model and carry out numerical simulations to demonstrate our analytic results. Particularly, we establish the positive invariant domain for the [Formula: see text] limit set of the system and show that the model has three spatially homogenous equilibriums solutions. We prove that the spatially uniform virus-free steady state is globally asymptotically stable for any viral lytic period delay and diffusion coefficients of tumor cells and viruses when the viral burst size is smaller than a critical value. We obtain the conditions, for example the ratio of virus diffusion coefficient to that of tumor cells is greater than a value and the viral lytic cycle, is greater than a critical value, under which the spatially uniform positive steady state is locally asymptotically stable. We also obtain conditions under which the system undergoes Hopf bifurcations, and stable periodic solutions occur. We point out medical implications of our results which are difficult to obtain from models without combining diffusive properties of viruses and tumor cells with viral lytic cycles.

Coupling brain-tumor biophysical models and diffeomorphic image registration

We present SIBIA (Scalable Integrated Biophysics-based Image Analysis), a framework for joint image registration and biophysical inversion and we apply it to analyze MR images of glioblastomas (primary brain tumors). We have two applications in mind. The first one is normal-to-abnormal image registration in the presence of tumor-induced topology differences. The second one is biophysical inversion based on single-time patient data. The underlying optimization problem is highly non-linear and non-convex and has not been solved before with a gradient-based approach. Given the segmentation of a normal brain MRI and the segmentation of a cancer patient MRI, we determine tumor growth parameters and a registration map so that if we "grow a tumor" (using our tumor model) in the normal brain and then register it to the patient image, then the registration mismatch is as small as possible. This "coupled problem" two-way couples the biophysical inversion and the registration problem. In the image registration step we solve a large-deformation diffeomorphic registration problem parameterized by an Eulerian velocity field. In the biophysical inversion step we estimate parameters in a reaction-diffusion tumor growth model that is formulated as a partial differential equation (PDE). In SIBIA, we couple these two sub-components in an iterative manner. We first presented the components of SIBIA in "Gholami et al., Framework for Scalable Biophysics-based Image Analysis, IEEE/ACM Proceedings of the SC2017", in which we derived parallel distributed memory algorithms and software modules for the decoupled registration and biophysical inverse problems. In this paper, our contributions are the introduction of a PDE-constrained optimization formulation of the coupled problem, and the derivation of a Picard iterative solution scheme. We perform extensive tests to experimentally assess the performance of our method on synthetic and clinical datasets. We demonstrate the convergence of the SIBIA optimization solver in different usage scenarios. We demonstrate that using SIBIA, we can accurately solve the coupled problem in three dimensions (256³ resolution) in a few minutes using 11 dual-x86 nodes.

BioVR: a platform for virtual reality assisted biological data integration and visualization

Background

Functional characterization of single nucleotide variants (SNVs) involves two steps, the first step is to convert DNA to protein and the second step is to visualize protein sequences with their structures. As massively parallel sequencing has emerged as a leading technology in genomics, resulting in a significant increase in data volume, direct visualization of SNVs together with associated protein sequences/structures in a new user interface (UI) would be a more effective way to assess their potential effects on protein function.

Results

We have developed BioVR, an easy-to-use interactive, virtual reality (VR)-assisted platform for integrated visual analysis of DNA/RNA/protein sequences and protein structures using Unity3D and the C# programming language. It utilizes the cutting-edge Oculus Rift, and Leap Motion hand detection, resulting in intuitive navigation and exploration of various types of biological data. Using Gria2 and its associated gene product as an example, we present this proof-of-concept software to integrate protein and nucleic acid data. For any amino acid or nucleotide of interest in the Gria2 sequence, it can be quickly linked to its corresponding location on Gria2 protein structure and visualized within VR.

Conclusions

Using innovative 3D techniques, we provide a VR-based platform for visualization of DNA/RNA sequences and protein structures in aggregate, which can be extended to view omics data.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2666-z) contains supplementary material, which is available to authorized users.

A radiopharmaceutical [89Zr]Zr-DFO-nimotuzumab for immunoPET with epidermal growth factor receptor expression in vivo

INTRODUCTION

The potential of the positron-emitting zirconium-89 (⁸⁹Zr) (t_1/2 = 78.4 h) has been recently reported for immune positron emission tomography (immunoPET) radioimmunoconjugates design. In our work, we explored the optimized preparation of [⁸⁹Zr]Zr-DFO-nimotuzumab, and evaluated ⁸⁹Zr-labeled monoclonal antibody (mAb) construct for targeted imaging of epidermal growth factor receptor (EGFR) overexpressed in glioma.

METHODS

To optimize the radiolabeling efficiency of ⁸⁹Zr with DFO-nimotuzumab, multiple immunoconjugates and radiolabeling were performed. Radiolabeling yield, radiochemical purity, stability, and activity assay were investigated to characterize [⁸⁹Zr]Zr-DFO-nimotuzumab for chemical and biological integrity. The in vivo behavior of this tracer was studied in mice bearing subcutaneous U87MG (EGFR-positive) tumors received a 3.5 ± 0.2 MBq/dose using PET/CT imaging. One group mice bearing subcutaneous U87MG (EGFR-positive) tumors received [⁸⁹Zr]Zr-DFO-nimotuzumab (3.5 ± 0.2 MBq, ~3 μg) (nonblocking) for immunoPET; the other group had 30 μg predose (blocking) of cold nimotuzumab 24 h prior to [⁸⁹Zr]Zr-DFO-nimotuzumab.

RESULTS

[⁸⁹Zr]Zr-DFO-nimotuzumab was prepared with high radiochemical yield (>90%), radiochemical purity (>99%), and specific activity (115 ± 0.8 MBq/mg). In vitro validation showed that [⁸⁹Zr]Zr-DFO-nimotuzumab had an initial immunoreactive fraction of 0.99 ± 0.05 and remained active for up to 5 days. A biodistribution study revealed excellent stability of [⁸⁹Zr]Zr-DFO-nimotuzumab in vivo compared with ⁸⁹Zr as a bone seeker. High uptake in the liver and heart and modest penetration in the brain were observed, with no significant accumulation of activity in other organs. ImmunoPET studies also indicated prominent image contrast that remarkably high uptake up to ~20%ID/g for nonblocking and ~2%ID/g for blocking in tumor between 12 and 120 h after administration.

CONCLUSION

These studies developed a radiopharmaceutical [⁸⁹Zr]Zr-DFO-nimotuzumab with optimized synthesis. The potential utility of [⁸⁹Zr]Zr-DFO-nimotuzumab in assessing EGFR status in glioma was demonstrated in this study.

A novel radiological classification system for cerebral gliomas: The Brain-Grid

Purpose

Standard radiological/topographical classifications of gliomas often do not reflect the real extension of the tumor within the lobar-cortical anatomy. Furthermore, these systems do not provide information on the relationship between tumor growth and the subcortical white matter architecture. We propose the use of an anatomically standardized grid system (the Brain-Grid) to merge serial morphological magnetic resonance imaging (MRI) scans with a representative tractographic atlas. Two illustrative cases are presented to show the potential advantages of this classification system.

Methods

MRI scans of 39 patients (WHO grade II and III gliomas) were analyzed with a standardized grid created by intersecting longitudinal lines on the axial, sagittal, and coronal planes. The anatomical landmarks were chosen from an average brain, spatially normalized to the Montreal Neurological Institute (MNI) space and the Talairach space. Major white matter pathways were reconstructed with a deterministic tracking algorithm on a reference atlas and analyzed using the Brain-Grid system.

Results

In all, 48 brain grid voxels (areas defined by 3 coordinates, axial (A), coronal (C), sagittal (S) and numbers from 1 to 4) were delineated in each MRI sequence and on the tractographic atlas. The number of grid voxels infiltrated was consistent, also in the MNI space. The sub-cortical insula/basal ganglia (A3-C2-S2) and the fronto-insular region (A3-C2-S1) were most frequently involved. The inferior fronto-occipital fasciculus, anterior thalamic radiation, uncinate fasciculus, and external capsule were the most frequently associated pathways in both hemispheres.

Conclusions

The Brain-Grid based classification system provides an accurate observational tool in all patients with suspected gliomas, based on the comparison of grid voxels on a morphological MRI and segmented white matter atlas. Important biological information on tumor kinetics including extension, speed, and preferential direction of progression can be observed and even predicted with this system. This novel classification can easily be applied to both prospective and retrospective cohorts of patients and increase our comprehension of glioma behavior.

Virtual reality and augmented reality in the management of intracranial tumors: A review

Neurosurgeons are faced with the challenge of planning, performing, and learning complex surgical procedures. With improvements in computational power and advances in visual and haptic display technologies, augmented and virtual surgical environments can offer potential benefits for tests in a safe and simulated setting, as well as improve management of real-life procedures. This systematic literature review is conducted in order to investigate the roles of such advanced computing technology in neurosurgery subspecialization of intracranial tumor removal. The study would focus on an in-depth discussion on the role of virtual reality and augmented reality in the management of intracranial tumors: the current status, foreseeable challenges, and future developments.

Integrated mapping of pharmacokinetics and pharmacodynamics in a patient-derived xenograft model of glioblastoma

Therapeutic options for the treatment of glioblastoma remain inadequate despite concerted research efforts in drug development. Therapeutic failure can result from poor permeability of the blood-brain barrier, heterogeneous drug distribution, and development of resistance. Elucidation of relationships among such parameters could enable the development of predictive models of drug response in patients and inform drug development. Complementary analyses were applied to a glioblastoma patient-derived xenograft model in order to quantitatively map distribution and resulting cellular response to the EGFR inhibitor erlotinib. Mass spectrometry images of erlotinib were registered to histology and magnetic resonance images in order to correlate drug distribution with tumor characteristics. Phosphoproteomics and immunohistochemistry were used to assess protein signaling in response to drug, and integrated with transcriptional response using mRNA sequencing. This comprehensive dataset provides simultaneous insight into pharmacokinetics and pharmacodynamics and indicates that erlotinib delivery to intracranial tumors is insufficient to inhibit EGFR tyrosine kinase signaling.

Dynamics of 3D carcinoma cell invasion into aligned collagen

Carcinoma cells frequently expand and invade from a confined lesion, or multicellular clusters, into and through the stroma on the path to metastasis, often with an efficiency dictated by the architecture and composition of the microenvironment. Specifically, in desmoplastic carcinomas such as those of the breast, aligned collagen tracks provide contact guidance cues for directed cancer cell invasion. Yet, the evolving dynamics of this process of invasion remains poorly understood, in part due to difficulties in continuously capturing both spatial and temporal heterogeneity and progression to invasion in experimental systems. Therefore, to study the local invasion process from cell dense clusters into aligned collagen architectures found in solid tumors, we developed a novel engineered 3D invasion platform that integrates an aligned collagen matrix with a cell dense tumor-like plug. Using multiphoton microscopy and quantitative analysis of cell motility, we track the invasion of cancer cells from cell-dense bulk clusters into the pre-aligned 3D matrix, and define the temporal evolution of the advancing invasion fronts over several days. This enables us to identify and probe cell dynamics in key regions of interest: behind, at, and beyond the edge of the invading lesion at distinct time points. Analysis of single cell migration identifies significant spatial heterogeneity in migration behavior between cells in the highly cell-dense region behind the leading edge of the invasion front and cells at and beyond the leading edge. Moreover, temporal variations in motility and directionality are also observed between cells within the cell-dense tumor-like plug and the leading invasive edge as its boundary extends into the anisotropic collagen over time. Furthermore, experimental results combined with mathematical modeling demonstrate that in addition to contact guidance, physical crowding of cells is a key regulating factor orchestrating variability in single cell migration during invasion into anisotropic ECM. Thus, our novel platform enables us to capture spatio-temporal dynamics of cell behavior behind, at, and beyond the invasive front and reveals heterogeneous, local interactions that lead to the emergence and maintenance of the advancing front.

Treatment of glioblastoma with herbal medicines

BACKGROUND

In the latest years, a lot of research studies regarding the usage of active agents from plants in the treatment of tumors have been published, but there is no data about successful usage of herbal remedies in the treatment of glioblastoma in humans.

METHODS

The phytotherapy involved five types of herbal medicine which the subjects took in the form of tea, each type once a day at regular intervals. Three patients took herbal medicine along with standard oncological treatment, while two patients applied for phytotherapy after completing medical treatment. The composition of herbal medicine was modified when necessary, which depended on the results of the control scans using the nuclear magnetic resonance technique and/or computed tomography.

RESULTS

Forty-eight months after the introduction of phytotherapy, there were no clinical or radiological signs of the disease, in three patients; in one patient, the tumor was reduced and his condition was stable, and one patient lived for 48 months in spite of a large primary tumor and a massive recurrence, which developed after the treatment had been completed.

CONCLUSIONS

The results achieved in patients in whom tumor regression occurred exclusively through the use of phytotherapy deserve special attention. In order to treat glioblastoma more effectively, it is necessary to develop innovative therapeutic strategies and medicines that should not be limited only to the field of conventional medicine. The results presented in this research paper are encouraging and serve as a good basis for further research on the possibilities of phytotherapy in the treatment of glioblastoma.

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain

Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors-the "recruitment" of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells-in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of "white matter disease," where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.

Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging: a preclinical study

BACKGROUND

Over the last decade, several theoretical tumor-models have been developed to describe tumor growth. Oncology imaging is performed using various modalities including computed tomography (CT), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT) and fluorodeoxyglucose-positron emission tomography (FDG-PET). Our goal is to extract useful, otherwise hidden, quantitative biophysical parameters (such as growth-rate, tumor-necrotic-factor, etc.) from these serial images of tumors by fitting mathematical models to images. These biophysical features are intrinsic to the tumor types and specific to the study-subject, and expected to add valuable information on the tumor containment or spread and help treatment plans. Thus, fitting realistic but practical models and assessing parameter-errors and degree of fit is important.

METHODS

We implemented an existing theoretical ode-compartment model and variants and applied them for the first time, in vivo. We developed an inversion algorithm to fit the models for tumor growth for simulated as well as in vivo experimental data. Serial SPECT/CT scans of mice breast-tumors were acquired, and SPECT data was used to segment the proliferating-layers of tumors.

RESULTS

Results of noisy data simulation and inversion show that 5 out of 7 parameters were recovered to within 4.3% error. In particular, tumor "growth-rate" parameter was recovered to 0.07% error. For model fitting to in vivo mice-tumors, regression analysis on the P-layer volume showed R² of 0.99 for logistic and Gompertzian while surface area model yielded R²=0.96. For the necrotic layer the R² values were 0.95, 0.93 and 0.94 respectively for surface-area, logistic and Gompertzian. The Akaike Information Criterion (AIC) weights of the models (giving their relative probability of being the best Kullback-Leibler (K-L) model among the set of candidate models) were ~0, 0.43 and 0.57 for surface-area, logistic and Gompertzian models.

CONCLUSIONS

Model-fitting to mice tumor studies demonstrates feasibility of applying the models to in vivo imaging data to extract features. Akaike information criterion (AIC) evaluations show Gompertzian or logistic growth model fits in vivo breast-tumors better than surface-area based growth model.

Mathematical Analysis of Glioma Growth in a Murine Model

Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm³ to 62 mm³, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.

A Feasibility Study of Personalized Prescription Schemes for Glioblastoma Patients Using a Proliferation and Invasion Glioma Model

Purpose: This study investigates the feasibility of personalizing radiotherapy prescription schemes (treatment margins and fractional doses) for glioblastoma (GBM) patients and their potential benefits using a proliferation and invasion (PI) glioma model on phantoms. Methods and Materials: We propose a strategy to personalize radiotherapy prescription schemes by simulating the proliferation and invasion of the tumor in 2D according to the PI glioma model. We demonstrate the strategy and its potential benefits by presenting virtual cases, where the standard and personalized prescriptions were applied to the tumor. Standard prescription was assumed to deliver 46 Gy in 23 fractions to the initial, gross tumor volume (GTV₁) plus a 2 cm margin and an additional 14 Gy in 7 fractions to the boost GTV₂ plus a 2 cm margin. The virtual cases include the tumors with a moving velocity of 0.029 (slow-move), 0.079 (average-move), and 0.13 (fast-move) mm/day for the gross tumor volume (GTV) with a radius of 1 (small) and 2 (large) cm. For each tumor size and velocity, the margin around GTV₁ and GTV₂ was varied between 0–6 cm and 1–3 cm, respectively. Equivalent uniform dose (EUD) to normal brain was constrained to the EUD value obtained by using the standard prescription. Various linear dose policies, where the fractional dose is linearly decreasing, constant, or increasing, were investigated to estimate the temporal effect of the radiation dose on tumor cell-kills. The goal was to find the combination of margins for GTV₁ and GTV₂ and a linear dose policy, which minimize the tumor cell-surviving fraction (SF) under a normal tissue constraint. The efficacy of a personalized prescription was evaluated by tumor EUD and the estimated survival time. Results: The personalized prescription for the slow-move tumors was to use 3.0–3.5 cm margins for GTV₁, and a 1.5 cm margin for GTV₂. For the average- and fast-move tumors, it was optimal to use a 6.0 cm margin for GTV₁ and then 1.5–3.0 cm margins for GTV₂, suggesting a course of whole brain therapy followed by a boost to a smaller volume. It was more effective to deliver the boost sequentially using a linearly decreasing fractional dose for all tumors. Personalized prescriptions led to surviving fractions of 0.001–0.465% compared to the standard prescription, and increased the tumor EUDs by 25.3–49.3% and estimated survival times by 7.6–22.2 months. Conclusions: Personalizing treatment margins based on the measured proliferative capacity of GBM tumor cells can potentially lead to significant improvements in tumor cell kill and related clinical outcomes.

A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient's multiscale data and experimenting in silico (ie, on the computer).

The diagnostic performance of perfusion MRI for differentiating glioma recurrence from pseudoprogression: A meta-analysis

BACKGROUND

The purpose of this meta-analysis was to evaluate the diagnostic accuracy of perfusion magnetic resonance imaging (MRI) as a method for differentiating glioma recurrence from pseudoprogression.

METHODS

The PubMed, Embase, Cochrane Library, and Chinese Biomedical databases were searched comprehensively for relevant studies up to August 3, 2016 according to specific inclusion and exclusion criteria. The quality of the included studies was assessed according to the quality assessment of diagnostic accuracy studies (QUADAS-2). After performing heterogeneity and threshold effect tests, pooled sensitivity, specificity, positive likelihood ratio, negative likelihood ratio, and diagnostic odds ratio were calculated. Publication bias was evaluated visually by a funnel plot and quantitatively using Deek funnel plot asymmetry test. The area under the summary receiver operating characteristic curve was calculated to demonstrate the diagnostic performance of perfusion MRI.

RESULTS

Eleven studies covering 416 patients and 418 lesions were included in this meta-analysis. The pooled sensitivity, specificity, positive likelihood ratio, negative likelihood ratio, and diagnostic odds ratio were 0.88 (95% confidence interval [CI] 0.84-0.92), 0.77 (95% CI 0.69-0.84), 3.93 (95% CI 2.83-5.46), 0.16 (95% CI 0.11-0.22), and 27.17 (95% CI 14.96-49.35), respectively. The area under the summary receiver operating characteristic curve was 0.8899. There was no notable publication bias. Sensitivity analysis showed that the meta-analysis results were stable and credible.

CONCLUSION

While perfusion MRI is not the ideal diagnostic method for differentiating glioma recurrence from pseudoprogression, it could improve diagnostic accuracy. Therefore, further research on combining perfusion MRI with other imaging modalities is warranted.

Ferritin heavy chain as a molecular imaging reporter gene in glioma xenografts

PURPOSE

The development of glioma therapy in clinical practice (e.g., gene therapy) calls for efficiently visualizing and tracking glioma cells in vivo. Human ferritin heavy chain is a novel gene reporter in magnetic resonance imaging. This study proposes hFTH as a reporter gene for MR molecular imaging in glioma xenografts.

METHODS

Rat C6 glioma cells were infected by packaged lentivirus carrying hFTH and EGFP genes and obtained by fluorescence-activated cell sorting. The iron-loaded ability was analyzed by the total iron reagent kit. Glioma nude mouse models were established subcutaneously and intracranially. Then, in vivo tumor bioluminescence was performed via the IVIS spectrum imaging system. The MR imaging analysis was analyzed on a 7T animal MRI scanner. Finally, the expression of hFTH was analyzed by western blotting and histological analysis.

RESULTS

Stable glioma cells carrying hFTH and EGFP reporter genes were successfully obtained. The intracellular iron concentration was increased without impairing the cell proliferation rate. Glioma cells overexpressing hFTH showed significantly decreased signal intensity on T₂-weighted MRI both in vitro and in vivo. EGFP fluorescent imaging could also be detected in the subcutaneous and intracranial glioma xenografts. Moreover, the expression of the transferritin receptor was significantly increased in glioma cells carrying the hFTH reporter gene.

CONCLUSION

Our study illustrated that hFTH generated cellular MR imaging contrast efficiently in glioma via regulating the expression of transferritin receptor. This might be a useful reporter gene in cell tracking and MR molecular imaging for glioma diagnosis, gene therapy and tumor metastasis.

Mechanistic mathematical models: An underused platform for HPV research

Health economic modeling has become an invaluable methodology for the design and evaluation of clinical and public health interventions against the human papillomavirus (HPV) and associated diseases. At the same time, relatively little attention has been paid to a different yet complementary class of models, namely that of mechanistic mathematical models. The primary focus of mechanistic mathematical models is to better understand the intricate biologic mechanisms and dynamics of disease. Inspired by a long and successful history of mechanistic modeling in other biomedical fields, we highlight several areas of HPV research where mechanistic models have the potential to advance the field. We argue that by building quantitative bridges between biologic mechanism and population level data, mechanistic mathematical models provide a unique platform to enable collaborations between experimentalists who collect data at different physical scales of the HPV infection process. Through such collaborations, mechanistic mathematical models can accelerate and enhance the investigation of HPV and related diseases.