A quantitative model for differential motility of gliomas in grey and white matter

We have extended a mathematical model of gliomas based on proliferation and diffusion rates to incorporate the effects of augmented cell motility in white matter as compared to grey matter. Using a detailed mapping of the white and grey matter in the brain developed for a MRI simulator, we have been able to simulate model tumours on an anatomically accurate brain domain. Our simulations show good agreement with clinically observed tumour geometries and suggest paths of submicroscopic tumour invasion not detectable on CT or MRI images. We expect this model to give insight into microscopic and submicroscopic invasion of the human brain by glioma cells. This method gives insight in microscopic and submicroscopic invasion of the human brain by glioma cells. Additionally, the model can be useful in defining expected pathways of invasion by glioma cells and thereby identify regions of the brain on which to focus treatments.

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

Gliomas are brain tumours that differ from most other cancers by their diffuse invasion of the surrounding normal tissue and their notorious recurrence following all forms of therapy. We have developed a mathematical model to quantify the spatio-temporal growth and invasion of gliomas in three dimensions throughout a virtual human brain. The model quantifies the extent of tumorous invasion of individual gliomas in three-dimensions to a degree beyond the limits of present medical imaging, including even microscopy, and makes clear why current therapies based on existing imaging techniques are inadequate and cannot be otherwise without other methods for detecting tumour cells in the brain. The model's estimate of the extent of tumourous invasion beyond that defined by standard medical imaging can be useful in more accurately planning therapy regimes as well as predicting sites of potential recurrence without waiting for reemergence on follow-up imaging.

A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle

The prediction of the outcome of individual patients with glioblastoma would be of great significance for monitoring responses to therapy. We hypothesise that, although a large number of genetic-metabolic abnormalities occur upstream, there are two ‘final common pathways’ dominating glioblastoma growth – net rates of proliferation (ρ) and dispersal (D). These rates can be estimated from features of pretreatment MR images and can be applied in a mathematical model to predict tumour growth, impact of extent of tumour resection and patient survival. Only the pre-operative gadolinium-enhanced T1-weighted (T1-Gd) and T2-weighted (T2) volume data from 70 patients with previously untreated glioblastoma were used to derive a ratio D/ρ for each patient. We developed a ‘virtual control’ for each patient with the same size tumour at the time of diagnosis, the same ratio of net invasion to proliferation (D/ρ) and the same extent of resection. The median durations of survival and the shapes of the survival curves of actual and ‘virtual’ patients subjected to biopsy or subtotal resection (STR) superimpose exactly. For those actually receiving gross total resection (GTR), as shown by post-operative CT, the actual survival curve lies between the ‘virtual’ results predicted for 100 and 125% resection of the T1-Gd volume. The concordance between predicted (virtual) and actual survivals suggests that the mathematical model is realistic enough to allow precise definition of the effectiveness of individualised treatments and their site(s) of action on proliferation (ρ) and/or dispersal (D) of the tumour cells without knowledge of any other clinical or pathological information.

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 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.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: a proof of principle

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.

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.

An automated high performance capillary liquid chromatography-Fourier transform ion cyclotron resonance mass spectrometer for high-throughput proteomics

We describe a fully automated high performance liquid chromatography 9.4 tesla Fourier transform ion resonance cyclotron (FTICR) mass spectrometer system designed for proteomics research. A synergistic suite of ion introduction and manipulation technologies were developed and integrated as a high-performance front-end to a commercial Bruker Daltonics FTICR instrument. The developments incorporated included a dual-ESI-emitter ion source; a dual-channel electrodynamic ion funnel; tandem quadrupoles for collisional cooling and focusing, ion selection, and ion accumulation, and served to significantly improve the sensitivity, dynamic range, and mass measurement accuracy of the mass spectrometer. In addition, a novel technique for accumulating ions in the ICR cell was developed that improved both resolution and mass measurement accuracy. A new calibration methodology is also described where calibrant ions are introduced and controlled via a separate channel of the dual-channel ion funnel, allowing calibrant species to be introduced to sample spectra on a real-time basis, if needed. We also report on overall instrument automation developments that facilitate high-throughput and unattended operation. These included an automated version of the previously reported very high resolution, high pressure reversed phase gradient capillary liquid chromatography (LC) system as the separations component. A commercial autosampler was integrated to facilitate 24 h/day operation. Unattended operation of the instrument revealed exceptional overall performance: Reproducibility (1-5% deviation in uncorrected elution times), repeatability (<20% deviation in detected abundances for more abundant peptides from the same aliquot analyzed a few weeks apart), and robustness (high-throughput operation for 5 months without significant downtime). When combined with modulated-ion-energy gated trapping, the dynamic calibration of FTICR mass spectra provided decreased mass measurement errors for peptide identifications in conjunction with high resolution capillary LC separations over a dynamic range of peptide peak intensities for each spectrum of 10(3), and >10(5) for peptide abundances in the overall separation.

A quantitative model for the dynamics of serum prostate-specific antigen as a marker for cancerous growth: an explanation for a medical anomaly

Prostate-specific antigen (PSA) is an enzyme produced by both normal and cancerous prostate epithelial cells. Although PSA is the most widely used serum marker to detect and follow patients with prostatic adenocarcinoma, there are certain anomalies in the values of serum levels of PSA that are not understood. We developed a mathematical model for the dynamics of serum levels of PSA as a function of the tumor volume. Our model results show good agreement with experimental observations and provide an explanation for the existence of significant prostatic tumor mass despite a low-serum PSA. This result can be very useful in enhancing the use of serum PSA levels as a marker for cancer growth.

Correlation of in vitro infiltration with glioma histological type in organotypic brain slices

Diffuse invasion of the brain, an intrinsic property of gliomas, renders these tumours incurable, and is a principal determinant of their spatial and temporal growth. Knowledge of the invasive potential of gliomas is highly desired in order to understand their behaviour in vivo. Comprehensive ex vivo invasion studies including tumours of different histological types and grades are however lacking, mostly because reliable physiological invasion assays have been difficult to establish. Using an organotypic rodent brain slice assay, we evaluated the invasiveness of 42 grade II–IV glioma biopsy specimens, and correlated it with the histological phenotype, the absence or presence of deletions on chromosomes 1p and 19q assessed by fluorescent in situ hybridisation, and proliferation and apoptosis indices assessed by immunocytochemistry. Oligodendroglial tumours with 1p/19q loss were less invasive than astrocytic tumours of similar tumour grade. Correlation analysis of invasiveness cell proliferation and apoptosis further suggested that grade II–III oligodendroglial tumours with 1p/19q loss grow in situ as relatively circumscribed compact masses in contrast to the more infiltrative and more diffuse astrocytomas. Lower invasiveness may be an important characteristic of oligodendroglial tumours, adding to our understanding of their more indolent clinical evolution and responsiveness to therapy.

Adaptive IMRT using a multiobjective evolutionary algorithm integrated with a diffusion-invasion model of glioblastoma

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.

Performance of Standardized Relative CBV for Quantifying Regional Histologic Tumor Burden in Recurrent High-Grade Glioma: Comparison against Normalized Relative CBV Using Image-Localized Stereotactic Biopsies

BACKGROUND AND PURPOSE

Perfusion MR imaging measures of relative CBV can distinguish recurrent tumor from posttreatment radiation effects in high-grade gliomas. Currently, relative CBV measurement requires normalization based on user-defined reference tissues. A recently proposed method of relative CBV standardization eliminates the need for user input. This study compares the predictive performance of relative CBV standardization against relative CBV normalization for quantifying recurrent tumor burden in high-grade gliomas relative to posttreatment radiation effects.

MATERIALS AND METHODS

We recruited 38 previously treated patients with high-grade gliomas (World Health Organization grades III or IV) undergoing surgical re-resection for new contrast-enhancing lesions concerning for recurrent tumor versus posttreatment radiation effects. We recovered 112 image-localized biopsies and quantified the percentage of histologic tumor content versus posttreatment radiation effects for each sample. We measured spatially matched normalized and standardized relative CBV metrics (mean, median) and fractional tumor burden for each biopsy. We compared relative CBV performance to predict tumor content, including the Pearson correlation (r), against histologic tumor content (0%-100%) and the receiver operating characteristic area under the curve for predicting high-versus-low tumor content using binary histologic cutoffs (≥50%; ≥80% tumor).

RESULTS

Across relative CBV metrics, fractional tumor burden showed the highest correlations with tumor content (0%-100%) for normalized (r = 0.63, P < .001) and standardized (r = 0.66, P < .001) values. With binary cutoffs (ie, ≥50%; ≥80% tumor), predictive accuracies were similar for both standardized and normalized metrics and across relative CBV metrics. Median relative CBV achieved the highest area under the curve (normalized = 0.87, standardized = 0.86) for predicting ≥50% tumor, while fractional tumor burden achieved the highest area under the curve (normalized = 0.77, standardized = 0.80) for predicting ≥80% tumor.

CONCLUSIONS

Standardization of relative CBV achieves similar performance compared with normalized relative CBV and offers an important step toward workflow optimization and consensus methodology.

Accurate Patient-Specific Machine Learning Models of Glioblastoma Invasion Using Transfer Learning

BACKGROUND AND PURPOSE

MR imaging-based modeling of tumor cell density can substantially improve targeted treatment of glioblastoma. Unfortunately, interpatient variability limits the predictive ability of many modeling approaches. We present a transfer learning method that generates individualized patient models, grounded in the wealth of population data, while also detecting and adjusting for interpatient variabilities based on each patient's own histologic data.

MATERIALS AND METHODS

We recruited patients with primary glioblastoma undergoing image-guided biopsies and preoperative imaging, including contrast-enhanced MR imaging, dynamic susceptibility contrast MR imaging, and diffusion tensor imaging. We calculated relative cerebral blood volume from DSC-MR imaging and mean diffusivity and fractional anisotropy from DTI. Following image coregistration, we assessed tumor cell density for each biopsy and identified corresponding localized MR imaging measurements. We then explored a range of univariate and multivariate predictive models of tumor cell density based on MR imaging measurements in a generalized one-model-fits-all approach. We then implemented both univariate and multivariate individualized transfer learning predictive models, which harness the available population-level data but allow individual variability in their predictions. Finally, we compared Pearson correlation coefficients and mean absolute error between the individualized transfer learning and generalized one-model-fits-all models.

RESULTS

Tumor cell density significantly correlated with relative CBV (r = 0.33, P < .001), and T1-weighted postcontrast (r = 0.36, P < .001) on univariate analysis after correcting for multiple comparisons. With single-variable modeling (using relative CBV), transfer learning increased predictive performance (r = 0.53, mean absolute error = 15.19%) compared with one-model-fits-all (r = 0.27, mean absolute error = 17.79%). With multivariate modeling, transfer learning further improved performance (r = 0.88, mean absolute error = 5.66%) compared with one-model-fits-all (r = 0.39, mean absolute error = 16.55%).

CONCLUSIONS

Transfer learning significantly improves predictive modeling performance for quantifying tumor cell density in glioblastoma.

Treatment of unstable tibial shaft fractures by closed intramedullary nailing with flexible (Ender-type) pins

Eighty patients with unstable tibial diaphyseal fractures were treated by closed intramedullary nailing with Ender-type flexible pins. The majority of injuries occurred from falling while snow skiing. Sixty-six fractures were closed and 14 were open. Fifty-eight fractures involved the distal, 21 fractures the middle, and one fracture the proximal one third of the tibial shaft. The average time to roentgenographic union was 15.5 weeks (range, ten to 34 weeks) for closed and open Grade I and II fractures. The time to union in Grade III fractures was 50 weeks (range, 36-64 weeks). There were two nonunions and two delayed unions. Both nonunions occurred in Grade IIIA open shaft fractures. Intramedullary stabilization with flexible, Ender-type pins provides good control of unstable tibial shaft fractures. The use of pins with a smaller diameter (3.5 or 4 mm) allows the surgeon to place more pins across the fracture site. The use of multiple pins and packing the intramedullary canal may provide better rotational stability. The use of Ender-type pins for fixation of Type IIIA open tibial shaft fractures is contraindicated.

Training for Alpine skiing

Skiing requires aerobic fitness. For aerobic conditioning, there must be significant elevation in heart rate during training. Although anaerobic training benefits physical fitness in general, skiing requires more aerobic than anaerobic conditioning. Strength, power, and endurance can be maintained through the use of concentric and eccentric contractions, using a variety of equipment and sports. Care should be taken to avoid injury to the patellofemoral joint during training. It is important to use specificity in choosing sports, as well as the exercise patterns in preseason training. If these principles are recognized in ski conditioning, a successful and effective training program will result.