Russell Rockne

Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach

Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the subgroups that may have responded to or may have been injured by treatment. Such statistics offer scant reassurance to individual patients who have suffered through these treatments. Furthermore, current imaging-based treatment response metrics in individual patients ignore patient-specific differences in tumor growth kinetics, which have been shown to vary widely across patients even within the same histological diagnosis and, unfortunately, these metrics have shown only minimal success in predicting patient outcome. We consider nine newly diagnosed GBM patients receiving diagnostic biopsy followed by standard-of-care external beam radiation therapy (XRT). We present and apply a patient-specific, biologically based mathematical model for glioma growth that quantifies response to XRT in individual patients in vivo. The mathematical model uses net rates of proliferation and migration of malignant tumor cells to characterize the tumors growth and invasion along with the linear-quadratic model for the response to radiation therapy. Using only routinely available pre-treatment MRIs to inform the patient-specific bio-mathematical model simulations, we find that radiation response in these patients, quantified by both clinical and model-generated measures, could have been predicted prior to treatment with high accuracy. Specifically, we find that the net proliferation rate is correlated with the radiation response parameter (r = 0.89, p = 0.0007), resulting in a predictive relationship that is tested with a leave-one-out cross-validation technique. This relationship predicts the tumor size post-therapy to within inter-observer tumor volume uncertainty. The results of this study suggest that a mathematical model can create a virtual in silico tumor with the same growth kinetics as a particular patient and can not only predict treatment response in individual patients in vivo but also provide a basis for evaluation of response in each patient to any given therapy.

A mathematical model for brain tumor response to radiation therapy

Gliomas are highly invasive primary brain tumors, accounting for nearly 50% of all brain tumors (Alvord and Shaw in The pathology of the aging human nervous system. Lea & Febiger, Philadelphia, pp 210–281, 1991). Their aggressive growth leads to short life expectancies, as well as a fairly algorithmic approach to treatment: diagnostic magnetic resonance image (MRI) followed by biopsy or surgical resection with accompanying second MRI, external beam radiation therapy concurrent with and followed by chemotherapy, with MRIs conducted at various times during treatment as prescribed by the physician. Swanson et al. (Harpold et al. in J Neuropathol Exp Neurol 66:1–9, 2007) have shown that the defining and essential characteristics of gliomas in terms of net rates of proliferation (ρ) and invasion (D) can be determined from serial MRIs of individual patients. We present an extension to Swanson’s reaction-diffusion model to include the effects of radiation therapy using the classic linear-quadratic radiobiological model (Hall in Radiobiology for the radiologist. Lippincott, Philadelphia, pp 478–480, 1994) for radiation efficacy, along with an investigation of response to various therapy schedules and dose distributions on a virtual tumor (Swanson et al. in AACR annual meeting, Los Angeles, 2007).

Complementary but Distinct Roles for MRI and 18F-Fluoromisonidazole PET in the Assessment of Human Glioblastomas

Glioblastoma multiforme is a primary brain tumor known for its rapid proliferation, diffuse invasion, and prominent neovasculature and necrosis. This study explores the in vivo link between these characteristics and hypoxia by comparing the relative spatial geometry of developing vasculature inferred from gadolinium-enhanced T1-weighted MRI (T1Gd), edematous tumor extent revealed on T2-weighted MRI (T2), and hypoxia assessed by 18F-fluoromisonidazole PET (18F-FMISO). Given the role of hypoxia in upregulating angiogenic factors, we hypothesized that the distribution of hypoxia seen on 18F-FMISO is correlated spatially and quantitatively with the amount of leaky neovasculature seen on T1Gd. Methods: A total of 24 patients with glioblastoma underwent T1Gd, T2, and 18F-FMISO—11 studies preceded surgical resection or biopsy, 7 followed surgery and preceded radiation therapy, and 11 followed radiation therapy. Abnormal regions seen on the MRI scan were segmented, including the necrotic center (T0), the region of abnormal blood–brain barrier associated with disrupted vasculature (T1Gd), and infiltrating tumor cells and edema (T2). The 18F-FMISO images were scaled to the blood 18F-FMISO activity to create tumor-to-blood ratio (T/B) images. The hypoxic volume (HV) was defined as the region with T/Bs greater than 1.2, and the maximum T/B (T/Bmax) was determined by the voxel with the greatest T/B value. Results: The HV generally occupied a region straddling the outer edge of the T1Gd abnormality and into the T2. A significant correlation between HV and the volume of the T1Gd abnormality that relied on the existence of a large outlier was observed. However, there was consistent correlation between surface areas of all MRI-defined regions and the surface area of the HV. The T/Bmax, typically located within the T1Gd region, was independent of the MRI-defined tumor size. Univariate survival analysis found the most significant predictors of survival to be HV, surface area of HV, surface area of T1Gd, and T/Bmax. Conclusion: Hypoxia may drive the peripheral growth of glioblastomas. This conclusion supports the spatial link between the volumes and surface areas of the hypoxic and MRI regions; the magnitude of hypoxia, T/Bmax, remains independent of size.

Toward Patient-Specific, Biologically Optimized Radiation Therapy Plans for the Treatment of Glioblastoma

Purpose To demonstrate a method of generating patient-specific, biologically-guided radiotherapy dose plans and compare them to the standard-of-care protocol. Methods and Materials We integrated a patient-specific biomathematical model of glioma proliferation, invasion and radiotherapy with a multiobjective evolutionary algorithm for intensity-modulated radiation therapy optimization to construct individualized, biologically-guided plans for 11 glioblastoma patients. Patient-individualized, spherically-symmetric simulations of the standard-of-care and optimized plans were compared in terms of several biological metrics. Results The integrated model generated spatially non-uniform doses that, when compared to the standard-of-care protocol, resulted in a 67% to 93% decrease in equivalent uniform dose to normal tissue, while the therapeutic ratio, the ratio of tumor equivalent uniform dose to that of normal tissue, increased between 50% to 265%. Applying a novel metric of treatment response (Days Gained) to the patient-individualized simulation results predicted that the optimized plans would have a significant impact on delaying tumor progression, with increases from 21% to 105% for 9 of 11 patients. Conclusions Patient-individualized simulations using the combination of a biomathematical model with an optimization algorithm for radiation therapy generated biologically-guided doses that decreased normal tissue EUD and increased therapeutic ratio with the potential to improve survival outcomes for treatment of glioblastoma.

Gene therapy enhances chemotherapy tolerance and efficacy in glioblastoma patients

BACKGROUND Temozolomide (TMZ) is one of the most potent chemotherapy agents for the treatment of glioblastoma. Unfortunately, almost half of glioblastoma tumors are TMZ resistant due to overexpression of methylguanine methyltransferase (MGMT(hi)). Coadministration of O6-benzylguanine (O6BG) can restore TMZ sensitivity, but causes off-target myelosuppression. Here, we conducted a prospective clinical trial to test whether gene therapy to confer O6BG resistance in hematopoietic stem cells (HSCs) improves chemotherapy tolerance and outcome. METHODS We enrolled 7 newly diagnosed glioblastoma patients with MGMT(hi) tumors. Patients received autologous gene-modified HSCs following single-agent carmustine administration. After hematopoietic recovery, patients underwent O6BG/TMZ chemotherapy in 28-day cycles. Serial blood samples and tumor images were collected throughout the study. Chemotherapy tolerance was determined by the observed myelosuppression and recovery following each cycle. Patient-specific biomathematical modeling of tumor growth was performed. Progression-free survival (PFS) and overall survival (OS) were also evaluated. RESULTS Gene therapy permitted a significant increase in the mean number of tolerated O6BG/TMZ cycles (4.4 cycles per patient, P < 0.05) compared with historical controls without gene therapy (n = 7 patients, 1.7 cycles per patient). One patient tolerated an unprecedented 9 cycles and demonstrated long-term PFS without additional therapy. Overall, we observed a median PFS of 9 (range 3.5-57+) months and OS of 20 (range 13-57+) months. Furthermore, biomathematical modeling revealed markedly delayed tumor growth at lower cumulative TMZ doses in study patients compared with patients that received standard TMZ regimens without O6BG. CONCLUSION These data support further development of chemoprotective gene therapy in combination with O6BG and TMZ for the treatment of glioblastoma and potentially other tumors with overexpression of MGMT. TRIAL REGISTRATION Clinicaltrials.gov NCT00669669. FUNDING R01CA114218, R01AI080326, R01HL098489, P30DK056465, K01DK076973, R01HL074162, R01CA164371, R01NS060752, U54CA143970.

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images.

Glioblastoma multiforme (GBM) is a class of primary brain tumours characterized by their ability to rapidly proliferate and diffusely infiltrate surrounding brain tissue. The aggressive growth of GBM leads to the development of regions of low oxygenation (hypoxia), which can be clinically assessed through [18F]-fluoromisonidazole (FMISO) positron emission tomography (PET) imaging. Building upon the success of our previous mathematical modelling efforts, we have expanded our model to include the tumour microenvironment, specifically incorporating hypoxia, necrosis and angiogenesis. A pharmacokinetic model for the FMISO-PET tracer is applied at each spatial location throughout the brain and an analytical simulator for the image acquisition and reconstruction methods is applied to the resultant tracer activity map. The combination of our anatomical model with one for FMISO tracer dynamics and PET image reconstruction is able to produce a patient-specific virtual PET image that reproduces the image characteristics of the clinical PET scan as well as shows no statistical difference in the distribution of hypoxia within the tumour. This work establishes proof of principle for a link between anatomical (magnetic resonance image [MRI]) and molecular (PET) imaging on a patient-specific basis as well as address otherwise untenable questions in molecular imaging, such as determining the effect on tracer activity from cellular density. Although further investigation is necessary to establish the predicitve value of this technique, this unique tool provides a better dynamic understanding of the biological connection between anatomical changes seen on MRI and biochemical activity seen on PET of GBM in vivo.

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 patients 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 [18F]-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.

Invasion and proliferation kinetics in enhancing gliomas predict IDH1 mutation status

BACKGROUND Glioblastomas with a specific mutation in the isocitrate dehydrogenase 1 (IDH1) gene have a better prognosis than gliomas with wild-type IDH1. METHODS Here we compare the IDH1 mutational status in 172 contrast-enhancing glioma patients with the invasion profile generated by a patient-specific mathematical model we developed based on MR imaging. RESULTS We show that IDH1-mutated contrast-enhancing gliomas were relatively more invasive than wild-type IDH1 for all 172 contrast-enhancing gliomas as well as the subset of 158 histologically confirmed glioblastomas. The appearance of this relatively increased, model-predicted invasive profile appears to be determined more by a lower model-predicted net proliferation rate rather than an increased model-predicted dispersal rate of the glioma cells. Receiver operator curve analysis of the model-predicted MRI-based invasion profile revealed an area under the curve of 0.91, indicative of a predictive relationship. The robustness of this relationship was tested by cross-validation analysis of the invasion profile as a predictive metric for IDH1 status. CONCLUSIONS The strong correlation between IDH1 mutation status and the MRI-based invasion profile suggests that use of our tumor growth model may lead to noninvasive clinical detection of IDH1 mutation status and thus lead to better treatment planning, particularly prior to surgical resection, for contrast-enhancing gliomas.

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.

Response Classification Based on a Minimal Model of Glioblastoma Growth Is Prognostic for Clinical Outcomes and Distinguishes Progression from Pseudoprogression

Glioblastoma multiforme is the most aggressive type of primary brain tumor. Glioblastoma growth dynamics vary widely across patients, making it difficult to accurately gauge their response to treatment. We developed a model-based metric of therapy response called Days Gained that accounts for this heterogeneity. Here, we show in 63 newly diagnosed patients with glioblastoma that Days Gained scores from a simple glioblastoma growth model computed at the time of the first postradiotherapy MRI scan are prognostic for time to tumor recurrence and overall patient survival. After radiation treatment, Days Gained also distinguished patients with pseudoprogression from those with true progression. Because Days Gained scores can be easily computed with routinely available clinical imaging devices, this model offers immediate potential to be used in ongoing prospective studies.