Spatially quantifying microscopic tumor invasion and proliferation using a voxel-wise solution to a glioma growth model and serial diffusion MRI

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.

Opportunities for improving brain cancer treatment outcomes through imaging-based mathematical modeling of the delivery of radiotherapy and immunotherapy

Immunotherapy has become a fourth pillar in the treatment of brain tumors and, when combined with radiation therapy, may improve patient outcomes and reduce the neurotoxicity. As with other combination therapies, the identification of a treatment schedule that maximizes the synergistic effect of radiation- and immune-therapy is a fundamental challenge. Mechanism-based mathematical modeling is one promising approach to systematically investigate therapeutic combinations to maximize positive outcomes within a rigorous framework. However, successful clinical translation of model-generated combinations of treatment requires patient-specific data to allow the models to be meaningfully initialized and parameterized. Quantitative imaging techniques have emerged as a promising source of high quality, spatially and temporally resolved data for the development and validation of mathematical models. In this review, we will present approaches to personalize mechanism-based modeling frameworks with patient data, and then discuss how these techniques could be leveraged to improve brain cancer outcomes through patient-specific modeling and optimization of treatment strategies.

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.

Integration of machine learning and mechanistic models accurately predicts variation in cell density of glioblastoma using multiparametric MRI

Glioblastoma (GBM) is a heterogeneous and lethal brain cancer. These tumors are followed using magnetic resonance imaging (MRI), which is unable to precisely identify tumor cell invasion, impairing effective surgery and radiation planning. We present a novel hybrid model, based on multiparametric intensities, which combines machine learning (ML) with a mechanistic model of tumor growth to provide spatially resolved tumor cell density predictions. The ML component is an imaging data-driven graph-based semi-supervised learning model and we use the Proliferation-Invasion (PI) mechanistic tumor growth model. We thus refer to the hybrid model as the ML-PI model. The hybrid model was trained using 82 image-localized biopsies from 18 primary GBM patients with pre-operative MRI using a leave-one-patient-out cross validation framework. A Relief algorithm was developed to quantify relative contributions from the data sources. The ML-PI model statistically significantly outperformed (p < 0.001) both individual models, ML and PI, achieving a mean absolute predicted error (MAPE) of 0.106 ± 0.125 versus 0.199 ± 0.186 (ML) and 0.227 ± 0.215 (PI), respectively. Associated Pearson correlation coefficients for ML-PI, ML, and PI were 0.838, 0.518, and 0.437, respectively. The Relief algorithm showed the PI model had the greatest contribution to the result, emphasizing the importance of the hybrid model in achieving the high accuracy.

Surgical Decision Making From Image-Based Biophysical Modeling of Glioblastoma: Not Ready for Primetime

BACKGROUND

Biophysical modeling of glioma is gaining more interest for clinical practice. The most popular model describes aggressivity of tumor cells by two parameters: net proliferation rate (ρ) and propensity to migrate (D). The ratio ρ/D, which can be estimated from a single preoperative magnetic resonance imaging (MRI), characterizes tumor invasiveness profile (high ρ/D: nodular; low ρ/D: diffuse). A recent study reported, from a large series of glioblastoma multiforme (GBM) patients, that gross total resection (GTR) would improve survival only in patients with nodular tumors.

OBJECTIVE

To replicate these results, that is to verify that benefit of GTR would be only observed for nodular tumors.

METHODS

Between 2005 and 2012, we considered 234 GBM patients with pre- and postoperative MRI. Stereotactic biopsy (BST) was performed in 109 patients. Extent of resection was assessed on postoperative MRI and classified as GTR or partial resection (PR). Invasiveness ρ/D was estimated from the preoperative tumor volumes on T1-Gadolinium-enhanced and fluid-attenuated inversion recovery sequences.

RESULTS

We demonstrate that patients with diffuse GBM (low ρ/D), as well as more nodular (mid and high ρ/D) GBM, presented significant survival benefit from GTR over PR/BST ( P < .001).

CONCLUSION

Whatever the degree of tumor invasiveness, as estimated from MRI-driven biophysical modeling, GTR improves survival of GBM patients, compared to PR or BST. This conflicting result should motivate further studies.

An Update on the Approach to the Imaging of Brain Tumors

PURPOSE OF REVIEW

Neuroimaging plays a critical role in diagnosis of brain tumors and in assessment of response to therapy. However, challenges remain, including accurately and reproducibly assessing response to therapy, defining endpoints for neuro-oncology trials, providing prognostic information, and differentiating progressive disease from post-therapeutic changes particularly in the setting of antiangiogenic and other novel therapies.

RECENT FINDINGS

Recent advances in the imaging of brain tumors include application of advanced MRI imaging techniques to assess tumor response to therapy and analysis of imaging features correlating to molecular markers, grade, and prognosis. This review aims to summarize recent advances in imaging as applied to current diagnostic and therapeutic neuro-oncologic challenges.

Posttreatment Evaluation of Brain Gliomas

The imaging of treated gliomas is complicated by a variety of treatment related effects, which can falsely simulate disease improvement or progression. Distinguishing between disease progression and treatment effects is difficult with standard MR imaging pulse sequences and added specificity can be gained by the addition of advanced imaging techniques.

Imaging of the Posttherapeutic Brain

This review covers important topics relating to the imaging evaluation of glioblastoma multiforme after therapy. An overview of the Macdonald and Response Assessment in Neuro-Oncology criteria as well as important questions and limitations regarding their use are provided. Pseudoprogression and pseudoresponse as well as the use of advanced magnetic resonance imaging techniques such as perfusion, diffusion, and spectroscopy in the evaluation of the posttherapeutic brain are also reviewed.

Response Assessment and Magnetic Resonance Imaging Issues for Clinical Trials Involving High-Grade Gliomas

There exist multiple challenges associated with the current response assessment criteria for high-grade gliomas, including the uncertain role of changes in nonenhancing T2 hyperintensity, and the phenomena of pseudoresponse and pseudoprogression in the setting of antiangiogenic and chemoradiation therapies, respectively. Advanced physiological magnetic resonance imaging (MRI), including diffusion and perfusion (dynamic susceptibility contrast MRI and dynamic contrast-enhanced MRI) sensitive techniques for overcoming response assessment challenges, has been proposed, with their own potential advantages and inherent shortcomings. Measurement variability exists for conventional and advanced MRI techniques, necessitating the standardization of image acquisition parameters in order to establish the utility of these imaging methods in multicenter trials for high-grade gliomas. This review chapter highlights the important features of MRI in clinical brain tumor trials, focusing on the current state of response assessment in brain tumors, advanced imaging techniques that may provide additional value for determining response, and imaging issues to be considered for multicenter trials.

Comparison of diffusion tensor imaging and 11C-methionine positron emission tomography for reliable prediction of tumor cell density in gliomas

OBJECTIVE Diffusion MRI is attracting increasing interest for tissue characterization of gliomas, especially after the introduction of antiangiogenic therapy to treat malignant gliomas. The goal of the current study is to elucidate the actual magnitude of the correlation between diffusion MRI and cell density within the tissue. The obtained results were further extended and compared with metabolic imaging with ¹¹C-methionine (MET) PET. METHODS Ninety-eight tissue samples from 37 patients were stereotactically obtained via an intraoperative neuronavigation system. Diffusion tensor imaging (DTI) and MET PET were performed as routine presurgical imaging studies for these patients. DTI was converted into fractional anisotropy (FA) and apparent diffusion coefficient (ADC) maps, and MET PET images were registered to Gd-administered T1-weighted images that were used for navigation. Metrics of FA, ADC, and tumor-to-normal tissue ratio of MET PET along with relative values of FA (rFA) and ADC (rADC) compared with normal-appearing white matter were correlated with cell density of the stereotactically obtained tissues. RESULTS rADC was significantly lower in lesions obtained from Gd-enhancing lesions than from nonenhancing lesions. Although rADC showed a moderate but statistically significant negative correlation with cell density (p = 0.010), MET PET showed a superb positive correlation with cell density (p < 0.0001). On the other hand, rFA showed little correlation with cell density. CONCLUSIONS The presented data validated the use of rADC for estimating the treatment response of gliomas but also caution against overestimating its limited accuracy compared with MET PET.

Location of brain tumor intersecting white matter tracts predicts patient prognosis

Brain tumor cells invade adjacent normal brain along white matter (WM) bundles of axons. We therefore hypothesized that the location of tumor intersecting WM tracts would be associated with differing survival. This study introduces a method, voxel-wise survival analysis (VSA), to determine the relationship between the location of brain tumor intersecting WM tracts and patient prognosis. 113 primary glioblastoma (GBM) patients were retrospectively analyzed for this study. Patient specific tumor location, defined by contrast-enhancement, was combined with diffusion tensor imaging derived tractography to determine the location of axons intersecting tumor enhancement (AXITEs). VSA was then used to determine the relationship between the AXITE location and patient survival. Tumors intersecting the right anterior thalamic radiation (ATR), right inferior fronto-occipital fasciculus (IFOF), right and left cortico-spinal tract (CST), and corpus callosum (CC) were associated with decreased overall survival. Tumors intersecting the CST, body of the CC, right ATR, posterior IFOF, and inferior longitudinal fasciculus are associated with decreased progression-free survival (PFS), while tumors intersecting the right genu of the CC and anterior IFOF are associated with increased PFS. Patients with tumors intersecting the ATR, IFOF, CST, or CC had significantly improved survival prognosis if they were additionally treated with bevacizumab. This study demonstrates the usefulness of VSA by locating AXITEs associated with poor prognosis in GBM patients. This information should be included in patient-physician conversations, therapeutic strategy, and clinical trial design.

A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18F-FMISO-PET

Glioblastoma multiforme (GBM) is a highly invasive primary brain tumour that has poor prognosis despite aggressive treatment. A hallmark of these tumours is diffuse invasion into the surrounding brain, necessitating a multi-modal treatment approach, including surgery, radiation and chemotherapy. We have previously demonstrated the ability of our model to predict radiographic response immediately following radiation therapy in individual GBM patients using a simplified geometry of the brain and theoretical radiation dose. Using only two pre-treatment magnetic resonance imaging scans, we calculate net rates of proliferation and invasion as well as radiation sensitivity for a patient's disease. Here, we present the application of our clinically targeted modelling approach to a single glioblastoma patient as a demonstration of our method. We apply our model in the full three-dimensional architecture of the brain to quantify the effects of regional resistance to radiation owing to hypoxia in vivo determined by [(18)F]-fluoromisonidazole positron emission tomography (FMISO-PET) and the patient-specific three-dimensional radiation treatment plan. Incorporation of hypoxia into our model with FMISO-PET increases the model-data agreement by an order of magnitude. This improvement was robust to our definition of hypoxia or the degree of radiation resistance quantified with the FMISO-PET image and our computational model, respectively. This work demonstrates a useful application of patient-specific modelling in personalized medicine and how mathematical modelling has the potential to unify multi-modality imaging and radiation treatment planning.

A Proposed Paradigm Shift in Initializing Cancer Predictive Models with DCE-MRI Based PK Parameters: A Feasibility Study

Glioblastoma multiforme is the most aggressive type of glioma and the most common malignant primary intra-axial brain tumor. In an effort to predict the evolution of the disease and optimize therapeutical decisions, several models have been proposed for simulating the growth pattern of glioma. One of the latest models incorporates cell proliferation and invasion, angiogenic net rates, oxygen consumption, and vasculature. These factors, particularly oxygenation levels, are considered fundamental factors of tumor heterogeneity and compartmentalization. This paper focuses on the initialization of the cancer cell populations and vasculature based on imaging examinations of the patient and presents a feasibility study on vasculature prediction over time. To this end, pharmacokinetic parameters derived from dynamic contrast-enhanced magnetic resonance imaging using Toft’s model are used in order to feed the model. K^trans is used as a metric of the density of endothelial cells (vasculature); at the same time, it also helps to discriminate distinct image areas of interest, under a set of assumptions. Feasibility results of applying the model to a real clinical case are presented, including a study on the effect of certain parameters on the pattern of the simulated tumor.

Predicting in vivo glioma growth with the reaction diffusion equation constrained by quantitative magnetic resonance imaging data

Reaction-diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction-diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor 'grown' for ten days as dictated by the reaction-diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model's accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction-diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions.

Multi-site clinical evaluation of DW-MRI as a treatment response metric for breast cancer patients undergoing neoadjuvant chemotherapy

PURPOSE

To evaluate diffusion weighted MRI (DW-MR) as a response metric for assessment of neoadjuvant chemotherapy (NAC) in patients with primary breast cancer using prospective multi-center trials which provided MR scans along with clinical outcome information.

MATERIALS AND METHODS

A total of 39 patients with locally advanced breast cancer accrued from three different prospective clinical trials underwent DW-MR examination prior to and at 3-7 days (Hull University), 8-11 days (University of Michigan) and 35 days (NeoCOMICE) post-treatment initiation. Thirteen patients, 12 of which participated in treatment response study, from UM underwent short interval (<1hr) MRI examinations, referred to as "test-retest" for examination of repeatability. To further evaluate stability in ADC measurements, a thermally controlled diffusion phantom was used to assess repeatability of diffusion measurements. MRI sequences included contrast-enhanced T1-weighted, when appropriate, and DW images acquired at b-values of 0 and 800 s/mm2. Histogram analysis and a voxel-based analytical technique, the Parametric Response Map (PRM), were used to derive diffusion response metrics for assessment of treatment response prediction.

RESULTS

Mean tumor apparent diffusion coefficient (ADC) values generated from patient test-retest examinations were found to be very reproducible (|ΔADC|<0.1x10-3mm2/s). This data was used to calculate the 95% CI from the linear fit of tumor voxel ADC pairs of co-registered examinations (±0.45x10-3mm2/s) for PRM analysis of treatment response. Receiver operating characteristic analysis identified the PRM metric to be predictive of outcome at the 8-11 (AUC = 0.964, p = 0.01) and 35 day (AUC = 0.770, p = 0.05) time points (p<.05) while whole-tumor ADC changes where significant at the later 35 day time interval (AUC = 0.825, p = 0.02).

CONCLUSION

This study demonstrates the feasibility of performing a prospective analysis of DW-MRI as a predictive biomarker of NAC in breast cancer patients. In addition, we provide experimental evidence supporting the use of sensitive analytical tools, such as PRM, for evaluating ADC measurements.

Imaging biomarkers for antiangiogenic therapy in malignant gliomas

The discovery that malignant gliomas produce an excessive amount of VEGF, a key mediator of angiogenesis, has heightened interest in developing drugs that block angiogenic pathways. These antiangiogenic drugs tend to decrease vascular permeability, thereby diminishing tumor contrast enhancement independent of anti-tumor effects. This has made the determination of tumor response difficult, since contrast enhancement on post-contrast T1-weighted images is standard for assessing therapy effectiveness. In light of these unique challenges in assessing antiangiogenic therapy, new biomarkers have been proposed, based on advanced magnetic resonance techniques and PET. This article outlines the challenges associated with the evaluation of antiangiogenic therapy in malignant gliomas and describes how new imaging biomarkers can be used to better predict response.

Pitfalls in the neuroimaging of glioblastoma in the era of antiangiogenic and immuno/targeted therapy - detecting illusive disease, defining response

Glioblastoma, the most common malignant primary brain tumor in adults is a devastating diagnosis with an average survival of 14–16 months using the current standard of care treatment. The determination of treatment response and clinical decision making is based on the accuracy of radiographic assessment. Notwithstanding, challenges exist in the neuroimaging evaluation of patients undergoing treatment for malignant glioma. Differentiating treatment response from tumor progression is problematic and currently combines long-term follow-up using standard magnetic resonance imaging (MRI), with clinical status and corticosteroid-dependency assessments. In the clinical trial setting, treatment with gene therapy, vaccines, immunotherapy, and targeted biologicals similarly produces MRI changes mimicking disease progression. A neuroimaging method to clearly distinguish between pseudoprogression and tumor progression has unfortunately not been found to date. With the incorporation of antiangiogenic therapies, a further pitfall in imaging interpretation is pseudoresponse. The Macdonald criteria that correlate tumor burden with contrast-enhanced imaging proved insufficient and misleading in the context of rapid blood–brain barrier normalization following antiangiogenic treatment that is not accompanied by expected survival benefit. Even improved criteria, such as the RANO criteria, which incorporate non-enhancing disease, clinical status, and need for corticosteroid use, fall short of definitively distinguishing tumor progression, pseudoresponse, and pseudoprogression. This review focuses on advanced imaging techniques including perfusion MRI, diffusion MRI, MR spectroscopy, and new positron emission tomography imaging tracers. The relevant image analysis algorithms and interpretation methods of these promising techniques are discussed in the context of determining response and progression during treatment of glioblastoma both in the standard of care and in clinical trial context.

Short-interval estimation of proliferation rate using serial diffusion MRI predicts progression-free survival in newly diagnosed glioblastoma treated with radiochemotherapy

Cell invasion, motility, and proliferation level estimate (CIMPLE) mapping is a new imaging technique that provides parametric maps of microscopic invasion and proliferation rate estimates using serial diffusion MRI data. However, a few practical constraints have limited the use of CIMPLE maps as a tool for estimating these dynamic parameters, particularly during short-interval follow-up times. The purpose of the current study was to develop an approximation for the CIMPLE map solution for short-interval scanning involving the assumption that net intervoxel tumor invasion does not occur within sufficiently short time frames. Proliferation rate maps created using the "no invasion" approximation were found to be increasingly similar to maps created from full solution during increasingly longer follow-up intervals (3D cross correlation, R (2) = 0.5298, P = 0.0001). Results also indicate proliferation rate maps from the "no invasion" approximation had significantly higher sensitivity (82 vs. 64%) and specificity (90 vs. 80%) for predicting 6 month progression free survival and was a better predictor of time to progression during standard radiochemotherapy compared to the full CIMPLE solution (log-rank; no invasion estimation, P = 0.0134; full solution, P = 0.0555). Together, results suggest the "no invasion" approximation allows for quick estimation of proliferation rate using diffusion MRI data obtained from multiple scans obtained daily or biweekly for use in quantifying early treatment response.

Clinically relevant modeling of tumor growth and treatment response

Current mathematical models of tumor growth are limited in their clinical application because they require input data that are nearly impossible to obtain with sufficient spatial resolution in patients even at a single time point--for example, extent of vascularization, immune infiltrate, ratio of tumor-to-normal cells, or extracellular matrix status. Here we propose the use of emerging, quantitative tumor imaging methods to initialize a new generation of predictive models. In the near future, these models could be able to forecast clinical outputs, such as overall response to treatment and time to progression, which will provide opportunities for guided intervention and improved patient care.

A mechanically coupled reaction-diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy

There is currently a paucity of reliable techniques for predicting the response of breast tumors to neoadjuvant chemotherapy. The standard approach is to monitor gross changes in tumor size as measured by physical exam and/or conventional imaging, but these methods generally do not show whether a tumor is responding until the patient has received many treatment cycles. One promising approach to address this clinical need is to integrate quantitative in vivo imaging data into biomathematical models of tumor growth in order to predict eventual response based on early measurements during therapy. In this work, we illustrate a novel biomechanical mathematical modeling approach in which contrast enhanced and diffusion weighted magnetic resonance imaging data acquired before and after the first cycle of neoadjuvant therapy are used to calibrate a patient-specific response model which subsequently is used to predict patient outcome at the conclusion of therapy. We present a modification of the reaction-diffusion tumor growth model whereby mechanical coupling to the surrounding tissue stiffness is incorporated via restricted cell diffusion. We use simulations and experimental data to illustrate how incorporating tissue mechanical properties leads to qualitatively and quantitatively different tumor growth patterns than when such properties are ignored. We apply the approach to patient data in a preliminary dataset of eight patients exhibiting a varying degree of responsiveness to neoadjuvant therapy, and we show that the mechanically coupled reaction-diffusion tumor growth model, when projected forward, more accurately predicts residual tumor burden at the conclusion of therapy than the non-mechanically coupled model. The mechanically coupled model predictions exhibit a significant correlation with data observations (PCC = 0.84, p < 0.01), and show a statistically significant >4 fold reduction in model/data error (p = 0.02) as compared to the non-mechanically coupled model.

Parameterizing the Logistic Model of Tumor Growth by DW-MRI and DCE-MRI Data to Predict Treatment Response and Changes in Breast Cancer Cellularity during Neoadjuvant Chemotherapy

Diffusion-weighted and dynamic contrast-enhanced magnetic resonance imaging (MRI) data of 28 patients were obtained pretreatment, after one cycle, and after completion of all cycles of neoadjuvant chemotherapy (NAC). For each patient at each time point, the tumor cell number was estimated using the apparent diffusion coefficient and the extravascular extracellular (v e) and plasma volume (v p) fractions. The proliferation/death rate was obtained using the number of tumor cells from the first two time points in conjunction with the logistic model of tumor growth, which was then used to predict tumor cellularity at the conclusion of NAC. The Pearson correlation coefficient between the predicted and the experimental number of tumor cells measured at the end of NAC was 0.81 (P = .0043). The proliferation rate estimated after the first cycle of therapy was able to separate patients who went on to achieve pathologic complete response from those who did not (P = .021) with a sensitivity and specificity of 82.4% and 72.7%, respectively. These data provide preliminary results indicating that incorporating readily available quantitative MRI data into a simple model of tumor growth can lead to potentially clinically relevant information for predicting an individual patient's response to NAC.

From patient-specific mathematical neuro-oncology to precision medicine

Gliomas are notoriously aggressive, malignant brain tumors that have variable response to treatment. These patients often have poor prognosis, informed primarily by histopathology. Mathematical neuro-oncology (MNO) is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern “precision medicine” approaches to tailor therapy in a patient-specific manner. Patient-specific models (PSMs) can be used to overcome imaging limitations, improve prognostic predictions, stratify patients, and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This review focuses on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific MNO.

Serial diffusion MRI to monitor and model treatment response of the targeted nanotherapy CRLX101

PURPOSE

Targeted nanotherapies are being developed to improve tumor drug delivery and enhance therapeutic response. Techniques that can predict response will facilitate clinical translation and may help define optimal treatment strategies. We evaluated the efficacy of diffusion-weighted magnetic resonance imaging to monitor early response to CRLX101 (a cyclodextrin-based polymer particle containing the DNA topoisomerase I inhibitor camptothecin) nanotherapy (formerly IT-101), and explored its potential as a therapeutic response predictor using a mechanistic model of tumor cell proliferation.

EXPERIMENTAL DESIGN

Diffusion MRI was serially conducted following CRLX101 administration in a mouse lymphoma model. Apparent diffusion coefficients (ADCs) extracted from the data were used as treatment response biomarkers. Animals treated with irinotecan (CPT-11) and saline were imaged for comparison. ADC data were also input into a mathematical model of tumor growth. Histological analysis using cleaved-caspase 3, terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling, Ki-67, and hematoxylin and eosin (H&E) were conducted on tumor samples for correlation with imaging results.

RESULTS

CRLX101-treated tumors at day 2, 4, and 7 posttreatment exhibited changes in mean ADC = 16 ± 9%, 24 ± 10%, 49 ± 17%, and size (TV) = -5 ± 3%, -30 ± 4%, and -45 ± 13%, respectively. Both parameters were statistically greater than controls [p(ADC) ≤ 0.02, and p(TV) ≤ 0.01 at day 4 and 7], and noticeably greater than CPT-11-treated tumors (ADC = 5 ± 5%, 14 ± 7%, and 18 ± 6%; TV = -15 ± 5%, -22 ± 13%, and -26 ± 8%). Model-derived parameters for cell proliferation obtained using ADC data distinguished CRLX101-treated tumors from controls (P = 0.02).

CONCLUSIONS

Temporal changes in ADC specified early CRLX101 treatment response and could be used to model image-derived cell proliferation rates following treatment. Comparisons of targeted and nontargeted treatments highlight the utility of noninvasive imaging and modeling to evaluate, monitor, and predict responses to targeted nanotherapeutics.

Quantitative probabilistic functional diffusion mapping in newly diagnosed glioblastoma treated with radiochemotherapy

BACKGROUND

Functional diffusion mapping (fDM) is a cancer imaging technique that uses voxel-wise changes in apparent diffusion coefficients (ADC) to evaluate response to treatment. Despite promising initial results, uncertainty in image registration remains the largest barrier to widespread clinical application. The current study introduces a probabilistic approach to fDM quantification to overcome some of these limitations.

METHODS

A total of 143 patients with newly diagnosed glioblastoma who were undergoing standard radiochemotherapy were enrolled in this retrospective study. Traditional and probabilistic fDMs were calculated using ADC maps acquired before and after therapy. Probabilistic fDMs were calculated by applying random, finite translational, and rotational perturbations to both pre-and posttherapy ADC maps, then repeating calculation of fDMs reflecting changes after treatment, resulting in probabilistic fDMs showing the voxel-wise probability of fDM classification. Probabilistic fDMs were then compared with traditional fDMs in their ability to predict progression-free survival (PFS) and overall survival (OS).

RESULTS

Probabilistic fDMs applied to patients with newly diagnosed glioblastoma treated with radiochemotherapy demonstrated shortened PFS and OS among patients with a large volume of tumor with decreasing ADC evaluated at the posttreatment time with respect to the baseline scans. Alternatively, patients with a large volume of tumor with increasing ADC evaluated at the posttreatment time with respect to baseline scans were more likely to progress later and live longer. Probabilistic fDMs performed better than traditional fDMs at predicting 12-month PFS and 24-month OS with use of receiver-operator characteristic analysis. Univariate log-rank analysis on Kaplan-Meier data also revealed that probabilistic fDMs could better separate patients on the basis of PFS and OS, compared with traditional fDMs.

CONCLUSIONS

Results suggest that probabilistic fDMs are a more predictive biomarker in terms of 12-month PFS and 24-month OS in newly diagnosed glioblastoma, compared with traditional fDM analysis.

Magnetic Resonance Imaging of Glioma in the Era of Antiangiogenic Therapy

Since it supplanted computed tomography in the early 1990s, magnetic resonance (MR) imaging has remained the standard tool to evaluate disease status in patients with brain tumors. With the recent adoption of antiangiogenic therapy for gliomas, it has become increasingly clear that leakiness of the blood-brain barrier, the physiologic correlate of contrast enhancement, is affected by a multitude of pathophysiologic processes, not all of which correlate with tumor burden. To address this issue, physiologic imaging including diffusion and perfusion MR imaging has been investigated as an avenue to acquire predictive and prognostic biomarkers useful in the evaluation of high-grade gliomas.

An imaging-based stochastic model for simulation of tumour vasculature

A mathematical model which reconstructs the structure of existing vasculature using patient-specific anatomical, functional and molecular imaging as input was developed. The vessel structure is modelled according to empirical vascular parameters, such as the mean vessel branching angle. The model is calibrated such that the resultant oxygen map modelled from the simulated microvasculature stochastically matches the input oxygen map to a high degree of accuracy (R(2) ≈ 1). The calibrated model was successfully applied to preclinical imaging data. Starting from the anatomical vasculature image (obtained from contrast-enhanced computed tomography), a representative map of the complete vasculature was stochastically simulated as determined by the oxygen map (obtained from hypoxia [(64)Cu]Cu-ATSM positron emission tomography). The simulated microscopic vasculature and the calculated oxygenation map successfully represent the imaged hypoxia distribution (R(2) = 0.94). The model elicits the parameters required to simulate vasculature consistent with imaging and provides a key mathematical relationship relating the vessel volume to the tissue oxygen tension. Apart from providing an excellent framework for visualizing the imaging gap between the microscopic and macroscopic imagings, the model has the potential to be extended as a tool to study the dynamics between the tumour and the vasculature in a patient-specific manner and has an application in the simulation of anti-angiogenic therapies.

Functional diffusion maps (fDMs) evaluated before and after radiochemotherapy predict progression-free and overall survival in newly diagnosed glioblastoma

Functional diffusion mapping (fDM) has shown promise as a sensitive imaging biomarker for predicting survival in initial studies consisting of a small number of patients, mixed tumor grades, and before routine use of anti-angiogenic therapy. The current study tested whether fDM performed before and after radiochemotherapy could predict progression-free and overall survival in 143 patients with newly diagnosed glioblastoma from 2007 through 2010, many treated with anti-angiogenic therapy after recurrence. Diffusion and conventional MRI scans were obtained before and 4 weeks after completion of radiotherapy and concurrent temozolomide treatment. FDM was created by coregistering pre- and posttreatment apparent diffusion coefficient (ADC) maps and then performing voxel-wise subtraction. FDMs were categorized according to the degree of change in ADC in pre- and posttreatment fluid-attenuated inversion recovery (FLAIR) and contrast-enhancing regions. The volume fraction of fDM-classified increasing ADC(+), decreasing ADC(-), and change in ADC(+/-) were tested to determine whether they were predictive of survival. Both Bonferroni-corrected univariate log-rank analysis and Cox proportional hazards modeling demonstrated that patients with decreasing ADC in a large volume fraction of pretreatment FLAIR or contrast-enhancing regions were statistically more likely to progress earlier and expire sooner than in patients with a lower volume fraction. The current study supports the hypothesis that fDM is a sensitive imaging biomarker for predicting survival in glioblastoma.

Integrating Imaging Data into Predictive Biomathematical and Biophysical Models of Cancer

While there is a mature literature on biomathematical and biophysical modeling in cancer, many of the existing approaches are not of clinical utility, as they require input data that are extremely difficult to obtain in an intact organism, and/or require a large number of assumptions on the free parameters included in the models. Thus, there has only been very limited application of such models to solve problems of clinical import. More recently, however, there has been increased activity at the interface of quantitative, noninvasive imaging data, and tumor mathematical modeling. In addition to reporting on bulk tumor morphology and volume, emerging imaging techniques can quantitatively report on for example tumor vascularity, glucose metabolism, cell density and proliferation, and hypoxia. In this paper, we first motivate the problem of predicting therapy response by highlighting some (acknowledged) shortcomings in existing methods. We then provide introductions to a number of representative quantitative imaging methods and describe how they are currently (and potentially can be) used to initialize and constrain patient specific mathematical and biophysical models of tumor growth and treatment response, thereby increasing the clinical utility of such approaches. We conclude by highlighting some of the exciting research directions when one integrates quantitative imaging and tumor modeling.

Integration of diffusion-weighted MRI data and a simple mathematical model to predict breast tumor cellularity during neoadjuvant chemotherapy

Diffusion-weighted magnetic resonance imaging data obtained early in the course of therapy can be used to estimate tumor proliferation rates, and the estimated rates can be used to predict tumor cellularity at the conclusion of therapy. Six patients underwent diffusion-weighted magnetic resonance imaging immediately before, after one cycle, and after all cycles of neoadjuvant chemotherapy. Apparent diffusion coefficient values were calculated for each voxel and for a whole tumor region of interest. Proliferation rates were estimated using the apparent diffusion coefficient data from the first two time points and then used with the logistic model of tumor growth to predict cellularity after therapy. The predicted number of tumor cells was then correlated to the corresponding experimental data. Pearson's correlation coefficient for the region of interest analysis yielded 0.95 (P = 0.004), and, after applying a 3 × 3 mean filter to the apparent diffusion coefficient data, the voxel-by-voxel analysis yielded a Pearson correlation coefficient of 0.70 ± 0.10 (P < 0.05).

Nonlinear registration of diffusion-weighted images improves clinical sensitivity of functional diffusion maps in recurrent glioblastoma treated with bevacizumab

Diffusion-weighted imaging estimates of apparent diffusion coefficient (ADC) have shown sensitivity to brain tumor cellularity as well as response to therapy. Functional diffusion maps (fDMs) exploit these principles by examining voxelwise changes in ADC within the same patient over time. Currently, the fDM technique involves linear image registration of ADC maps from subsequent follow-up times to pretreatment ADC maps; however, misregistration of ADC maps due to geometric distortions as well as mass effect from growing tumor can confound fDM measurements. In this study, we compare the use of a nonlinear registration scheme to the current linear fDM technique in 70 patients with recurrent glioblastoma multiforme treated with bevacizumab. Results suggest that nonlinear registration of pretreatment ADC maps to post-treatment ADC maps improves the clinical predictability, sensitivity, and specificity of fDMs for both progression-free and overall survival.

Cell invasion, motility, and proliferation level estimate (CIMPLE) maps derived from serial diffusion MR images in recurrent glioblastoma treated with bevacizumab

Microscopic invasion of tumor cells and undetected tumor proliferation is the primary reason for a dismal prognosis in glioblastoma patients. Identification and quantification of spatially localized brain regions undergoing high rates of cell migration and proliferation is critical for improving patient survival; however, there are currently no non-invasive imaging biomarkers for estimating proliferation and migration rates of human gliomas in vivo. To accomplish this, we developed CIMPLE (cell invasion, motility, and proliferation level estimates) image maps using serial diffusion MRI scans and a solution to a glioma growth model equation. CIMPLE represent a novel method of quantifying the level of aggressive malignant behavior. In the current pilot study, we demonstrate the utility of CIMPLE maps to predict progression free survival (PFS) and overall survival (OS) in 26 recurrent glioblastoma patients treated with bevacizumab from our Neuro-Oncology database. Voxel-wise estimates of cell proliferation rate predicted spatial regions of contrast enhancement in 35% of patients. A linear correlation was found between the mean proliferation rate and progression-free survival (PFS; P < 0.0001) as well as overall survival (OS; P = 0.0093). Similarly, the mean proliferation rate was able to stratify patients with early and late PFS as well as OS.