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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 tumor''s 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. [ABSTRACT FROM AUTHOR]

A reply by R. Rockne et al to a letter to the editor about their article "Predicting the Efficacy of Radiotherapy in Individual Glioblastoma Patients in Vivo: A Mathematical Modeling Approach" that was published in a 2010 issue.

We reported that an acquired miR-142 deficit transforms chronic phase (CP) chronic myeloid leukemia (CML) leukemic stem cells (LSCs) into blast crisis (BC) LSCs. Given the role of miR-142 in the development and activity of the immune system, we postulated that this deficit also promotes LSC immune escape. Herein, we report on IL-6-driven miR-142 deficit occurring in T cells during BC transformation. In CML murine models, miR-142 deficit impairs thymic differentiation of lymphoid-primed multipotent progenitors (LMPP) into T cells and prevents T cells' metabolic reprogramming, thereby leading to loss of T cells and leukemia immune escape. Correcting miR-142 deficit with a miR-142 mimic compound (M-miR-142), alone or in combination with immune checkpoint antibodies, restores T cell number and immune activity, leading to LSC elimination and prolonged survival of BC CML murine and patient-derived xenograft models. These observations may open new therapeutic opportunities for BC CML and other myeloid malignancies., Competing Interests: Competing interests: The authors declare no competing interests., (© 2025. The Author(s).)

Purpose: Perfusion modeling presents significant opportunities for imaging biomarker development in breast cancer but has historically been held back by the need for data beyond the clinical standard of care (SoC) and uncertainty in the interpretability of results. We aimed to design a perfusion model applicable to breast cancer SoC dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) series with results stable to low temporal resolution imaging, comparable with published results using full-resolution DCE-MRI, and correlative with orthogonal imaging modalities indicative of biophysical markers., Methods: Subsampled high-temporal-resolution DCE-MRI series were run through our perfusion model and resulting fits were compared for consistency. The fits were also compared against previously published results from institutions using the full resolution series. The model was then evaluated on a separate cohort for validity of biomarker indications. Finally, the model was used as a fundamental part of predicting response to neoadjuvant chemotherapy (NACT)., Results: Temporally subsampled DCE-MRI series yield perfusion fit variations on the scale of 1% of the tumor median value when input frames are varied. Fits generated from pseudoclinical series are within the variation range seen between imaging sites (ρ = 0.55), voxel-wise. The model also demonstrates significant correlations with orthogonal positron emission tomography imaging, indicating potential for use as a biomarker proxy. Specifically, using the perfusion fits as the grounding for a biophysical simulation of response, we correctly predict the pathologic complete response status after NACT in 15 of 18 patients, for an accuracy of 0.83, with a specificity and sensitivity of 0.83 as well., Conclusion: Clinical DCE-MRI data may be leveraged to provide stable perfusion fit results and indirectly interrogate the tumor microenvironment. These fits can then be used downstream for prediction of response to NACT with high accuracy.

Acute myeloid leukemia (AML) is prevalent in both adult and pediatric patients. Despite advances in patient categorization, the heterogeneity of AML remains a challenge. Recent studies have explored the use of gene expression data to enhance AML diagnosis and prognosis, however, alternative approaches rooted in physics and chemistry may provide another level of insight into AML transformation. Utilizing publicly available databases, we analyze 884 human and mouse blood and bone marrow samples. We employ a personalized medicine strategy, combining state-transition theory and surprisal analysis, to assess the RNA transcriptome of individual patients. The transcriptome is transformed into physical parameters that represent each sample's steady state and the free energy change (FEC) from that steady state, which is the state with the lowest free energy.We found the transcriptome steady state was invariant across normal and AML samples. FEC, representing active molecular processes, varied significantly between samples and was used to create patient-specific barcodes to characterize the biology of the disease. We discovered that AML samples that were in a transition state had the highest FEC. This disease state may be characterized as the most unstable and hence the most therapeutically targetable since a change in free energy is a thermodynamic requirement for disease progression. We also found that distinct sets of ongoing processes may be at the root of otherwise similar clinical phenotypes, implying that our integrated analysis of transcriptome profiles may facilitate a personalized medicine approach to cure AML and restore a steady state in each patient., (© 2024. The Author(s).)

The mechanisms underlying the transformation of chronic myeloid leukemia (CML) from chronic phase (CP) to blast crisis (BC) are not fully elucidated. Here, we show lower levels of miR-142 in CD34 + CD38 - blasts from BC CML patients than in those from CP CML patients, suggesting that miR-142 deficit is implicated in BC evolution. Thus, we create miR-142 knockout CML (i.e., miR-142 -/- BCR-ABL) mice, which develop BC and die sooner than miR-142 wt CML (i.e., miR-142 +/+ BCR-ABL) mice, which instead remain in CP CML. Leukemic stem cells (LSCs) from miR-142 -/- BCR-ABL mice recapitulate the BC phenotype in congenic recipients, supporting LSC transformation by miR-142 deficit. State-transition and mutual information analyses of "bulk" and single cell RNA-seq data, metabolomic profiling and functional metabolic assays identify enhanced fatty acid β-oxidation, oxidative phosphorylation and mitochondrial fusion in LSCs as key steps in miR-142-driven BC evolution. A synthetic CpG-miR-142 mimic oligodeoxynucleotide rescues the BC phenotype in miR-142 -/- BCR-ABL mice and patient-derived xenografts., (© 2023. Springer Nature Limited.)

Multiple myeloma (MM) is still an incurable disorder despite improved antibody and cellular therapies against different MM antigens. Single targeted antigens have so far been ineffective against MM with most patients relapsing after initial response. Hence, sequential immunotherapies directed at different targets are expected to perform better than monotherapy alone. Here, we optimized and established in preclinical studies the therapeutic rationale of using targeted alpha therapy (TAT) directed against CD38 antigen ( 225 Ac-DOTA-daratumumab) with CAR T cell therapy directed at CS1 antigen in a systemic MM model. The sequential therapies compared CAR T therapy followed by TAT to TAT followed by CAR T therapy. CAR T cell monotherapy increased median survival from 49 days (d) in untreated controls to 71d with a modest improvement to 89d for 3.7 kBq of TAT given 14d later. When CAR T was followed by 7.4 kBq of TAT 29d later, sequential therapy increased median survival from 47d in untreated controls to 106d, compared to 68d for CAR T monotherapy. When CAR T therapy was followed by untargeted alpha immunotherapy using 7.4 kBq of 225 Ac-DOTA-trastuzumab (anti-HER2) antibody 29d later, there was only a slight improvement in response over CAR T monotherapy demonstrating the role of tumor targeting. TAT (7.4 kBq) followed by CAR T therapy was also effective when CAR T therapy was delayed for 21d vs 14d or 28d post TAT, highlighting the importance of timing sequential therapies. Sequential targeted therapies using CS1 CAR T or 225 Ac-DOTA-CD38 TAT in either order shows promise over monotherapies alone., (© 2023. The Author(s).)

Heterogeneity of endothelial cell (EC) populations reflects their diverse functions in maintaining tissue's homeostasis. However, their phenotypic, molecular, and functional properties are not entirely mapped. We use the Tie2-CreERT2;Rosa26-tdTomato reporter mouse to trace, profile, and cultivate primary ECs from different organs. As paradigm platform, we use this strategy to study bone marrow endothelial cells (BMECs). Single-cell mRNA sequencing of primary BMECs reveals that their diversity and native molecular signatures is transitorily preserved in an ex vivo culture that conserves key cell-to-cell microenvironment interactions. Macrophages sustain BMEC cellular diversity and expansion and preserve sinusoidal-like BMECs ex vivo. Endomucin expression discriminates BMECs in populations exhibiting mutually exclusive properties and distinct sinusoidal/arterial and tip/stalk signatures. In contrast to arterial-like, sinusoidal-like BMECs are short-lived, form 2D-networks, contribute to in vivo angiogenesis, and support hematopoietic stem/progenitor cells in vitro. This platform can be extended to other organs' ECs to decode mechanistic information and explore therapeutics., (© 2022. The Author(s).)

MiR-126 and miR-155 are key microRNAs (miRNAs) that regulate, respectively, hematopoietic cell quiescence and proliferation. Herein we showed that in acute myeloid leukemia (AML), the biogenesis of these two miRNAs is interconnected through a network of regulatory loops driven by the FMS-like tyrosine kinase 3-internal tandem duplication (FLT3-ITD). In fact, FLT3-ITD induces the expression of miR-155 through a noncanonical mechanism of miRNA biogenesis that implicates cytoplasmic Drosha ribonuclease III (DROSHA). In turn, miR-155 down-regulates SH2-containing inositol phosphatase 1 (SHIP1), thereby increasing phosphor-protein kinase B (AKT) that in turn serine-phosphorylates, stabilizes, and activates Sprouty related EVH1 domain containing 1 (SPRED1). Activated SPRED1 inhibits the RAN/XPO5 complex and blocks the nucleus-to-cytoplasm transport of pre-miR-126, which cannot then complete the last steps of biogenesis. The net result is aberrantly low levels of mature miR-126 that allow quiescent leukemia blasts to be recruited into the cell cycle and proliferate. Thus, miR-126 down-regulation in proliferating AML blasts is downstream of FLT3-ITD–dependent miR-155 expression that initiates a complex circuit of concatenated regulatory feedback (i.e., miR-126/SPRED1, miR-155/human dead-box protein 3 [DDX3X]) and feed-forward (i.e., miR-155/SHIP1/AKT/miR-126) regulatory loops that eventually converge into an output signal for leukemic growth.

Targeted therapies for multiple myeloma (MM) include the anti-CD38 antibody daratumumab, which, in addition to its inherent cytotoxicity, can be radiolabeled with tracers for imaging and with β- and α-emitter radionuclides for radioimmunotherapy. Methods: We have compared the potential therapeutic efficacy of β- versus α-emitter radioimmunotherapy using radiolabeled DOTA-daratumumab in a preclinical model of disseminated multiple myeloma. Multiple dose levels were investigated to find the dose with the highest efficacy and lowest toxicity. Results: In a dose–response study with the β-emitter 177Lu-DOTA-daratumumab, the lowest tested dose, 1.85 MBq, extended survival from 37 to 47 d but did not delay tumor growth. Doses of 3.7 and 7.4 MBq extended survival to 55 and 58 d, respectively, causing a small equivalent delay in tumor growth, followed by regrowth. The higher dose, 11.1 MBq, eradicated the tumor but had no effect on survival compared with untreated controls, because of whole-body toxicity. In contrast, the α-emitter 225Ac-DOTA-daratumumab had a dose-dependent effect, in which 0.925, 1.85, and 3.7 kBq increased survival, compared with untreated controls (35 d), to 47, 52, and 73 d, respectively, with a significant delay in tumor growth for all 3 doses. Higher doses of 11.1 and 22.2 kBq resulted in equivalent survival to 82 d but with significant whole-body toxicity. Parallel studies with untargeted 225Ac-DOTA-trastuzumab conferred no improvement over untreated controls and resulted in whole-body toxicity. Conclusion: We conclude, and mathematic modeling confirms, that maximal biologic doses were achieved by targeted α-therapy and demonstrated 225Ac to be superior to 177Lu in delaying tumor growth and decreasing whole-body toxicity.

18F-Fluorodeoxyglucose (FDG) positron emission tomography/computed tomography (PET/CT) is one of the most widely used imaging techniques to detect multiple myeloma (MM). Intracellular FDG uptake depicts in vivo metabolic activity, which can be seen in both malignant and nonmalignant cells, resulting in limited sensitivity and specificity. Our group showed preclinically that tracing MM dissemination using a CD38-directed human antibody, daratumumab, that is radioconjugated with 64Cu via the chelator DOTA (64Cu-daratumumab), led to improved sensitivity and specificity over that of FDG. Here, we report the results of a phase 1 trial designed to (1) assess the safety and feasibility of 64Cu-daratumumab PET/CT and (2) preliminarily evaluate and characterize the ability of 64Cu-daratumumab to accurately detect or exclude MM lesions. A total of 12 daratumumab-naive patients were imaged. Prior to the injection of 15 mCi/5 mg of 64Cu-daratumumab, patients were treated with 0 (n = 3), 10 (n = 3), 45 (n = 3), or 95 mg (n = 3) of unlabeled daratumumab to assess its effect on image quality. No significant adverse events were observed from either unlabeled daratumumab or 64Cu-daratumumab. Of the dose levels tested, 45 mg unlabeled daratumumab was the most optimal in terms of removing background signal without saturating target sites. 64Cu-daratumumab PET/CT provided safe whole-body imaging of MM. A trial comparing the sensitivity and specificity of 64Cu-daratumumab PET/CT with that of FDG PET/CT is planned. This trial was registered at www.clinicaltrials.gov as #NCT03311828., (© 2020 by The American Society of Hematology.)

Circulating tumor DNA holds substantial promise as an early detection biomarker, particularly for cancers that do not have currently accepted screening methodologies, such as ovarian, pancreatic, and gastric cancers. Many features intrinsic to ctDNA analysis may be leveraged to enhance its use as an early cancer detection biomarker: including ctDNA fragment lengths, DNA copy number variations, and associated patient phenotypic information. Furthermore, ctDNA testing may be synergistically used with other multi-omic biomarkers to enhance early detection. For instance, assays may incorporate early detection proteins (i.e., CA-125), epigenetic markers, circulating tumor RNA, nucleosomes, exosomes, and associated immune markers. Many companies are currently competing to develop a marketable early cancer detection test that leverages ctDNA. Although some hurdles (like early stage disease assay accuracy, high implementation costs, confounding from clonal hematopoiesis, and lack of clinical utility studies) need to be addressed before integration into healthcare, ctDNA assays hold substantial potential as an early cancer screening test., Competing Interests: Declaration of Competing Interest MM is an inventor on patent applications covering technologies described herein. SWG is a consultant to Grail, Inc. Laura Goetz holds an equity position in Q Bio, Inc. All other authors declare no conflicts of interest., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Purpose: Response assessment with computed tomography after stereotactic body radiation therapy (SBRT) for non-small cell lung cancer (NSCLC) is challenging because myriad anatomic changes can occur after treatment. Diffusion-weighted magnetic resonance imaging (MRI) may provide additional data to guide therapy response. The primary objective was to evaluate the effect of SBRT on the mean apparent diffusion coefficient (ADC)., Methods and Materials: This is a prospective clinical study of patients with NSCLC who received SBRT to the primary lung lesion. Patients underwent MRI scans before and at 1 month after completion of SBRT. MRI consisted of T1- and T2-weighted sequences, along with postcontrast, dynamic-contrast, and diffusion-weighted sequences with construction of ADC maps. Two blinded radiologists generated the ADC. SBRT was given over 5 fractions., Results: A total of 13 patients were enrolled. Twelve patients were eligible for analysis. An average increase of 50% and 46% in mean single-plane ADC was observed after treatment by readers 1 and 2, respectively (P < .01, both reviewers). There was good interobserver agreement of single-plane ADC values between the 2 radiologists (Pearson correlation of 0.85 [baseline] and 0.89 [1-month post-SBRT], P < .001 for both). There was also a significant 18% increase in mean volumetric ADC on the 1-month scan (Wilcoxon P = .02). Two patients developed a local failure after SBRT, 1 at 6 months and the other at 34 months. Using a threshold of volumetric ADC increase of greater than 40%, 2 of 2 patients demonstrated local failure compared with 0 of 10 patients below this limit., Conclusions: A statistically significant increase in ADC was observed 1 month after treatment. An ADC increase of 40% at 1 month was associated with a higher rate of local failure. This pilot study provides impetus for studying ADC as a radiomic biomarker in patients receiving lung SBRT for NSCLC., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Purpose: Despite the intra- and intertumoral heterogeneity seen in glioblastoma multiforme (GBM), there is little definitive data on the underlying cause of the differences in patient survivals. Serial imaging assessment of tumor growth allows quantification of tumor growth kinetics (TGK) measured in terms of changes in the velocity of radial expansion seen on imaging. Because a systematic study of this entire TGK phenotype-growth before treatment and during each treatment to recurrence -has never been coordinately studied in GBMs, we sought to identify whether patients cluster into discrete groups on the basis of their TGK., Patients and Methods: From our multi-institutional database, we identified 48 patients who underwent maximally safe resection followed by radiotherapy with imaging follow-up through the time of recurrence. The patients were then clustered into two groups through a k-means algorithm taking as input only the TGK before and during treatment., Results: There was a significant survival difference between the clusters ( P = .003). Paradoxically, patients among the long-lived cluster had significantly larger tumors at diagnosis ( P = .027) and faster growth before treatment ( P = .003) but demonstrated a better response to adjuvant chemotherapy ( P = .048). A predictive model was built to identify which cluster patients would likely fall into on the basis of information that would be available to clinicians immediately after radiotherapy (accuracy, 90.3%)., Conclusion: Dichotomizing the heterogeneity of GBMs into two populations-one faster growing yet more responsive with increased survival and one slower growing yet less responsive with shorter survival-suggests that many patients who receive standard-of-care treatments may get better benefit from select alternative treatments.

Here we present a mathematical model of movement in an abstract space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single cell RNA sequencing data to characterize cellular states in a high-dimensional space, which is then mapped into ℝ 2 or ℝ 2 with dimension reduction techniques. We represent trajectories in the differentiation space as a graph, and model directed and random movement on the graph with partial differential equations. We hypothesize that flow in this space can be used to model normal and abnormal differentiation processes. We present a mathematical model of hematopoeisis parameterized with publicly available single cell RNA-Seq data and use it to simulate the pathogenesis of acute myeloid leukemia (AML). The model predicts the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of a mouse model of AML., Competing Interests: Disclosure statement No potential conflicts of interest are disclosed by the authors.

Recently, two phase III studies of bevacizumab, an anti-angiogenic, for newly diagnosed glioblastoma (GBM) patients were released. While they were unable to statistically significantly demonstrate that bevacizumab in combination with other therapies increases the overall survival of GBM patients, there remains a question of potential benefits for subpopulations of patients. We use a mathematical model of GBM growth to investigate differential benefits of combining surgical resection, radiation and bevacizumab across observed tumour growth kinetics. The differential hypoxic burden after gross total resection (GTR) was assessed along with the change in radiation cell kill from bevacizumab-induced tissue re-normalization when starting therapy for tumours at different diagnostic sizes. Depending on the tumour size at the time of treatment, our model predicted that GTR would remove a variable portion of the hypoxic burden ranging from 11% to 99.99%. Further, our model predicted that the combination of bevacizumab with radiation resulted in an additional cell kill ranging from 2.6×10(7) to 1.1×10(10) cells. By considering the outcomes given individual tumour kinetics, our results indicate that the subpopulation of patients who would receive the greatest benefit from bevacizumab and radiation combination therapy are those with large, aggressive tumours and who are not eligible for GTR.

Object: Malignant gliomas are incurable, primary brain neoplasms noted for their potential to extensively invade brain parenchyma. Current methods of clinical imaging do not elucidate the full extent of brain invasion, making it difficult to predict which, if any, patients are likely to benefit from gross total resection. Our goal was to apply a mathematical modeling approach to estimate the overall tumor invasiveness on a patient-by-patient basis and determine whether gross total resection would improve survival in patients with relatively less invasive gliomas., Methods: In 243 patients presenting with contrast-enhancing gliomas, estimates of the relative invasiveness of each patient's tumor, in terms of the ratio of net proliferation rate of the glioma cells to their net dispersal rate, were derived by applying a patient-specific mathematical model to routine pretreatment MR imaging. The effect of varying degrees of extent of resection on overall survival was assessed for cohorts of patients grouped by tumor invasiveness., Results: We demonstrate that patients with more diffuse tumors showed no survival benefit (P = 0.532) from gross total resection over subtotal/biopsy, while those with nodular (less diffuse) tumors showed a significant benefit (P = 0.00142) with a striking median survival benefit of over eight months compared to sub-totally resected tumors in the same cohort (an 80% improvement in survival time for GTR only seen for nodular tumors)., Conclusions: These results suggest that our patient-specific, model-based estimates of tumor invasiveness have clinical utility in surgical decision making. Quantification of relative invasiveness assessed from routinely obtained pre-operative imaging provides a practical predictor of the benefit of gross total resection.

We demonstrate a patient-specific method of adaptive IMRT treatment for glioblastoma using a multiobjective evolutionary algorithm (MOEA). The MOEA generates spatially optimized dose distributions using an iterative dialogue between the MOEA and a mathematical model of tumor cell proliferation, diffusion and response. Dose distributions optimized on a weekly basis using biological metrics have the potential to substantially improve and individualize treatment outcomes. Optimized dose distributions were generated using three different decision criteria for the tumor and compared with plans utilizing standard dose of 1.8 Gy/fraction to the CTV (T2-visible MRI region plus a 2.5 cm margin). The sets of optimal dose distributions generated using the MOEA approach the Pareto Front (the set of IMRT plans that delineate optimal tradeoffs amongst the clinical goals of tumor control and normal tissue sparing). MOEA optimized doses demonstrated superior performance as judged by three biological metrics according to simulated results. The predicted number of reproductively viable cells 12 weeks after treatment was found to be the best target objective for use in the MOEA.

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.

Recent advances in clinical medicine have elucidated two significantly different subtypes of glioblastoma which carry very different prognoses, both defined by mutations in isocitrate dehydrogenase-1 (IDH-1). The mechanistic consequences of this mutation have not yet been fully clarified, with conflicting opinions existing in the literature; however, IDH-1 mutation may be used as a surrogate marker to distinguish between primary and secondary glioblastoma multiforme (sGBM) from malignant progression of a lower grade glioma. We develop a mathematical model of IDH-1 mutated secondary glioblastoma using evolutionary game theory to investigate the interactions between four different phenotypic populations within the tumor: autonomous growth, invasive, glycolytic, and the hybrid invasive/glycolytic cells. Our model recapitulates glioblastoma behavior well and is able to reproduce two recent experimental findings, as well as make novel predictions concerning the rate of invasive growth as a function of vascularity, and fluctuations in the proportions of phenotypic populations that a glioblastoma will experience under different microenvironmental constraints.

Background: Identifying the origin of gliomas carries important implications for advancing the treatment of these recalcitrant tumors. Recent research promotes the hypothesis of a subventricular zone (SVZ) origin for the stemlike gliomagenic cells identified within human glioma specimens. However, conflicting evidence suggests that SVZ-like cells are not uniquely gliomagenic but this capacity may be shared by cycling progenitors distributed throughout the subcortical white matter (SCWM)., Objective: To review radiological evidence in glioblastoma multiforme (GBM) patients to provide insight into the question of glioma ontogeny., Methods: We explored whether GBMs at first diagnosis demonstrated a pattern of anatomic distribution consistent with origin at the SVZ through retrospective analysis of preoperative contrast-enhanced T1-weighted magnetic resonance images in 63 patients. We then examined the relationship of tumor volume, point of origin, and proximity to the ventricles using a computer model of glioma growth., Results: Fewer than half of the GBMs analyzed had contrast-enhancing portions that contacted the ventricle on preoperative imaging. A strong correlation was found between tumor volume and the distance between the contrast-enhancing edge of the tumor and the ventricle, demonstrating that tumors abutting the ventricle are significantly larger than those that do not. The lesions simulated by the computer model validated our assumption that tumors that are radiographically distant from the ventricles are unlikely to have originated in the SVZ and supported our hypothesis that as they grow, the edges of all tumors will near the ventricles, regardless of their point of origin., Conclusion: This work offers further support for the hypothesis that the origins of GBMs are at sites distributed throughout the white matter and are not limited to the region of the SVZ.

Glioblastomas are the most aggressive primary brain tumors, characterized by their rapid proliferation and diffuse infiltration of the brain tissue. Survival patterns in patients with glioblastoma have been associated with a number of clinicopathologic factors including age and neurologic status, yet a significant quantitative link to in vivo growth kinetics of each glioma has remained elusive. Exploiting a recently developed tool for quantifying glioma net proliferation and invasion rates in individual patients using routinely available magnetic resonance images (MRI), we propose to link these patient-specific kinetic rates of biological aggressiveness to prognostic significance. Using our biologically based mathematical model for glioma growth and invasion, examination of serial pretreatment MRIs of 32 glioblastoma patients allowed quantification of these rates for each patient's tumor. Survival analyses revealed that even when controlling for standard clinical parameters (e.g., age and Karnofsky performance status), these model-defined parameters quantifying biological aggressiveness (net proliferation and invasion rates) were significantly associated with prognosis. One hypothesis generated was that the ratio of the actual survival time after whatever therapies were used to the duration of survival predicted (by the model) without any therapy would provide a therapeutic response index (TRI) of the overall effectiveness of the therapies. The TRI may provide important information, not otherwise available, about the effectiveness of the treatments in individual patients. To our knowledge, this is the first report indicating that dynamic insight from routinely obtained pretreatment imaging may be quantitatively useful in characterizing the survival of individual patients with glioblastoma. Such a hybrid tool bridging mathematical modeling and clinical imaging may allow for stratifying patients for clinical studies relative to their pretreatment biological aggressiveness.

Gliomas, the most common of primary brain tumors, are known for their widespread invasion of tissue near the gross tumor mass. My research was based on my mentor's focus on developing mathematical models for the growth of gliomas within the central nervous system (CNS). The model focuses on two key parameters: D, the spread of glioma cells to tissues within the central nervous system, and ρ , the net proliferation rate of glioma cells. The model was created to account for the fact that even after gross total resection of portions of the tumor detectable on magnetic resonance imaging (MRI) scans, invasive glioma cells are found in tissues surrounding the area of resection. Additionally, this model considers the location of the tumor within the CNS because tumor cells are known to diffuse at a faster pace in white matter compared to grey matter. As a result a more accurate prediction of the patient's longevity and the time period of the tumor's inevitable recurrence can be made. This accuracy will allow physicians to make improved diagnosis and treatment of gliomas, thereby extending the patients' survival.

Glioblastoma multiforme (GBM) are aggressive and uniformly fatal primary brain tumors characterized by their diffuse invasion of the normal-appearing parenchyma peripheral to the clinical imaging abnormality. Hypoxia, a hallmark of aggressive tumor behavior often noted in GBMs, has been associated with resistance to therapy, poorer survival, and more malignant tumor phenotypes. Based on the existence of a set of novel imaging techniques and modeling tools, our objective was to assess a hypothesized quantitative link between tumor growth kinetics [assessed via mathematical models and routine magnetic resonance imaging (MRI)] and the hypoxic burden of the tumor [assessed via positron emission tomography (PET) imaging]. Our biomathematical model for glioma kinetics describes the spatial and temporal evolution of a glioma in terms of concentration of malignant tumor cells. This model has already been proven useful as a novel tool to dynamically quantify the net rates of proliferation (rho) and invasion (D) of the glioma cells in individual patients. Estimates of these kinetic rates can be calculated from routinely available pretreatment MRI in vivo. Eleven adults with GBM were imaged preoperatively with (18)F-fluoromisonidazole (FMISO)-PET and serial gadolinium-enhanced T1- and T2-weighted MRIs to allow the estimation of patient-specific net rates of proliferation (rho) and invasion (D). Hypoxic volumes were quantified from each FMISO-PET scan following standard techniques. To control for tumor size variability, two measures of hypoxic burden were considered: relative hypoxia (RH), defined as the ratio of the hypoxic volume to the T2-defined tumor volume, and the mean intensity on FMISO-PET scaled to the blood activity of the tracer (mean T/B). Pearson correlations between RH and the net rate of cell proliferation (rho) reached significance (P < 0.04). Moreover, highly significant positive correlations were found between biological aggressiveness ratio (rho/D) and both RH (P < 0.00003) and the mean T/B (P < 0.0007).

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 (rho) 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).

Unlabelled: 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.

Aims: The initial aims were to use recently available observations of glioblastomas (as part of a previous study) that had been imaged twice without intervening treatment before receiving radiotherapy in order to obtain quantitative measures of glioma growth and invasion according to a new bio-mathematical model. The results were so interesting as to raise the question whether the degree of radio-sensitivity of each tumour could be estimated by comparing the model-predicted and actual durations of survival and total numbers of glioma cells after radiotherapy., Materials and Methods: The gadolinium-enhanced T1-weighted and T2-weighted magnetic resonance imaging volumes were segmented and used to calculate the velocity of radial expansion (v) and the net rates of proliferation (rho) and invasion/dispersal (D) for each patient according to the bio-mathematical model., Results: The ranges of the values of v, D and rho show that glioblastomas, although clustering at the high end of rates, vary widely one from the other. The effects of X-ray therapy varied from patient to patient. About half survived as predicted without treatment, indicating radio-resistance of these tumours. The other half survived up to about twice as long as predicted without treatment and could have had a corresponding loss of glioma cells, indicating some degree of radio-sensitivity. These results approach the historical estimates that radiotherapy can double survival of the average patient with a glioblastoma., Conclusions: These cases are among the first for which values of v, D and rho have been calculated for glioblastomas. The results constitute a 'proof of principle' by combining our bio-mathematical model for glioma growth and invasion with pre-treatment imaging observations to provide a new tool showing that individual glioblastomas may be identified as having been radio-resistant or radio-sensitive.