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.

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 (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).

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.

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 (rho) 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/rho 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/rho) 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 (rho) and/or dispersal (D) of the tumour cells without knowledge of any other clinical or pathological information.

NeuN expression correlates with reduced mitotic index of neoplastic cells in central neurocytomas.

In the developing brain, neuronal differentiation is associated with permanent exit from the mitotic cycle. This raises the possibility that neuronal differentiation may suppress proliferative activity, even in neoplastic cells. As a first step towards understanding the relation between neuronal differentiation and mitotic cycling in brain tumours, we studied the expression of NeuN (a neuronal marker) and Ki-67 (a mitotic marker) by double-labelling immuno-fluorescence in 16 brain tumours with neuronal differentiation. The tumours included a series of 11 central neurocytomas, and five single cases of other tumour types. In the central neurocytomas, NeuN(+) cells had a 15-fold lower Ki-67 labelling index, on average, than did NeuN(-) cells (P < 0.01). In the other tumours (one extraventricular neurocytoma, one desmoplastic medulloblastoma, one olfactory neuroblastoma, one ganglioglioma and one anaplastic ganglioglioma), the Ki-67 labelling index was always at least fourfold lower in NeuN(+) cells than in NeuN(-) cells. These results indicate that neuronal differentiation is associated with a substantial decrease of proliferative activity in neoplastic cells of central neurocytomas, and suggest that the same may be true across diverse types of brain tumours. However, tumours with extensive neuronal differentiation may nevertheless have a high overall Ki-67 labelling index, if the mitotic activity of NeuN(-) cells is high. The correlation between NeuN expression and reduced mitotic activity in neurocytoma cells is consistent with the hypothesis that neuronal differentiation suppresses proliferation, but further studies will be necessary to determine causality and investigate underlying mechanisms.

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 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.

Pleomorphic xanthoastrocytoma: DNA flow cytometry and outcome analysis of 12 patients.

BACKGROUND: Pleomorphic xanthoastrocytoma (PXA) is an astrocytic tumor occurring primarily in childhood and adolescence with some malignant histologic features but a relatively slow clinical course. However, some tumors progress more rapidly and can undergo malignant degeneration. The authors attempted to determine whether various histologic features or tumor cell proliferative indices might help identify lesions at risk for early progression and distinguish PXAs from malignant gliomas. METHODS: In a retrospective study of 12 patients with PXA, the tumor's histologic features and DNA flow cytometric parameters were compared with their clinical course. DNA flow cytometry values for the S- and G2-phase of the PXAs also were compared with control group samples of malignant and low grade astrocytomas. RESULTS: Of the 12 tumors at initial diagnosis, 5 were considered typical PXAs whereas 7 had some atypical features (4 with paucity of reticulin fibers, 1 with focal necrosis, and 2 with both atypical reticulin and focal necrosis). During the follow-up period (range, 3.75-11 years; mean, 6.8 years), 2 patients had recurrences; 1 atypical reticulin PXA progressed to glioblastoma after 6.5 years and the 1 tumor with focal necrosis recurred at 6 months and again at 2 years with typical histologic features. DNA flow cytometry parameters of the typical PXA group were similar to values for malignant astrocytoma and significantly higher than values for control specimens of low grade astrocytomas. There were no distinctive DNA flow cytometric features that could distinguish this last tumor from others with a more benign clinical course. CONCLUSIONS: Measurements of the S-phase and G2-phase obtained from DNA flow cytometry and atypical histologic features cannot reliably identify PXA patients at risk for early progression and overall are significantly higher than values obtained for low grade gliomas. Therefore, frequent (i.e., two to three times per year) postoperative clinical and radiologic examinations are necessary to judge the appropriateness of adjuvant therapy in patients with PXA. The paradox of slow growth but DNA flow cytometry consistent with aggressive malignant lesions may represent a cell-cycle arrest mechanism in these lesions that could be verified in subsequent studies.

Neuropathology: art and science.

So many examples of computer-designed (rather than human-designed) displays occurred at a recent meeting of the American Association of Neuropathologists that we were stimulated to develop simple guides to help improve presentation. Various color combinations provide examples of the best (and worst) contrast between the message and the medium (background).

Human mucopolysaccharidosis IIID: clinical, biochemical, morphological and immunohistochemical characteristics.

Mucopolysaccharidosis IIID (MPS IIID) is one of the rarest of the MPS-III syndromes. To date, the clinical manifestations of 10 patients have been reported, the deficient N-acetylglucosamine 6-sulfatase (G6S) enzyme has been purified, and the G6S gene has been cloned, sequenced and localized. However, morphological manifestations of this condition have not been reported and the pathogenesis of the severe neurological deficits remains an enigma. In this paper we describe and correlate the clinical, biochemical and pathological observations for 2 cases of MPS IIID. We used monoclonal antibodies against heparan sulfate (HS) and GM2-ganglioside, thin layer chromatography, mass spectrometry, and morphological techniques to demonstrate the nature and the distribution of the uncatabolized substrates. The majority of the cells in various tissues showed morphological changes expected with lysosomal storage of HS. The central nervous system (CNS) was most severely affected because of the secondary storage of GM2 and GM3 gangliosides in addition to the primary accumulation of HS. The extent as well as the distribution of the diverse storage materials varied within and among different neurons as observed in MPS-III A, B, and C syndromes. This study supports the hypothesis that the neurological dysfunction and neurodegeneration common to the Sanfilippo syndromes is, in part, due to the secondary metabolic perturbations induced by HS accumulation.

Fatal head injuries in ground-level falls.

We analyzed 75 cases of fatal ground-level falls that were investigated by the King County Medical Examiner over a 48-month period, with autopsies performed on 87% of the deaths: 69% of the cases were men and 61% occurred in ages > or = 70 years; only 12% were aged < 50 years, with the youngest aged 28 years. Most of the falls occurred in or about the residence, and many individuals were known to have fallen onto hard surfaces. In 77% of cases there was significant pre-existing natural disease, mostly cardiovascular disease. Liver disease was more frequently a contributing factor in those aged < 50 years. Ethanol was present in 48% of those cases tested, more frequently present in men than in women. Basal skull fractures were present in 37% of cases, and acute subdural hematomas, the most common intracranial lesion, were present in 85%. We concluded that fatal ground-level falls were much more common in elderly persons, owing to a greater predisposition to falling, as well as intrinsic age-related changes, including a greater susceptibility to acute subdural hematoma.

The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas.

This paper is a natural three-dimensional extension of a simple two-dimensional mathematical model of glioma growth and diffusion. The model was originally constructed to simulate a case of recurrent anaplastic astrocytoma treated with chemotherapy, and then modified to allow estimation of the effects of the extent of surgical resection and of variations in growth and diffusion to cover the whole range of glioma behavior. Growth is considered to be constant and exponential (analogous to continuously compounding interest) and is expressed as a decimal fraction per day; the diffusion coefficient is expressed as cm2 per day. Model predictions suggest that diffusion, practically ignored until the present, is a more important component of glioma growth than the growth rate. Even with very early diagnosis, only those tumors with a low diffusion coefficient and a rapid growth rate benefit from a wide resection. Surgical resections generally fail, just as dropping fire-fighters into the burned out center of a forest fire fails, the action being on the periphery as the tumor cells or fires spread out from the center.

Neuropathology of the limbic system.

The history and development of the fanciful terminology concerning the structures of the limbic system are discussed. The diseases involving the limbic system are divided into three groups; (1) diseases in which the limbic system is more or less selectively involved, such as limbic encephalitis, herpes simplex encephalitis, cerebral confusions by the falx and tentorium, and internal herniations through the falx and tentorium; (2) diseases in which the limbic system is predominantly involved, such as arhinencephalia, holoprosencephaly, cyst of cavum septi pellucidi, Pick's disease, Alzheimer's disease, hippocampal sclerosis, and vascular diseases of the hippocampal formation; and (3) diseases in which the limbic system is randomly involved, such as various types of neoplasms and vascular and inflammatory lesions. The relationship between destructive lesions of the hippocampus and memory also is emphasized.

Resolution of CNS lesions following treatment of experimental allergic encephalomyelitis in macaques with monoclonal antibody to the CD18 leukocyte integrin.

Experimental allergic encephalomyelitis (EAE) in macaques is an acute inflammatory and demyelinating disease of the central nervous system (CNS) which has been studied extensively as a model of the human demyelinating disease multiple sclerosis (MS). The in vivo administration of monoclonal antibodies against CD18, the common beta-chain of a leukocyte integrin, at the onset of clinical disease, significantly prolonged the survival of nine of 11 macaques (82%) and in some cases completely reversed the clinical appearance of disease. Treatment with anti-CD18 mAbs dramatically reduced the extent of inflammation in brain lesions as determined by magnetic resonance imaging (MRI). These improvements confirm that anti-CD18 mAbs are powerful anti-inflammatory agents in vivo and suggest that such mAbs may provide effective treatment of both demyelinating and inflammatory CNS diseases in man.

Global cerebral dysplasia due to dysplasia and hyperplasia of periventricular germinal cells.

Complete obliteration of the cerebral ventricular cavities has not been previously described as an entity among central nervous system malformations. Markedly disorganized maldevelopment of the deep cerebral nuclei and moderately disorganized maldevelopment of the cerebral cortex were observed in the brains of two cases, a 3-year-old female and a male newborn infant. One showed complete and the other partial obliteration of the lateral and third ventricles. Both showed severe maldevelopment of the basal ganglia, which were represented by a large central mass consisting of randomly distributed multiple nodules of gray matter without any discernible differentiation into lenticulostriate nuclei, thalamus, or hypothalamus. Minor malformations involved the cerebral cortex, cerebellum, and mesencephalon to varying degrees. Each of the above two cases was thought to be unique and different until the brain of a fetus of 155 days' gestation was studied. This fetal brain showed exuberant and disorganized periventricular proliferation and migration of germinal matrix cells, with obliteration of the lateral and third ventricles. It was concluded that hyperplasia and disorganized migration of the periventricular germinal matrix early in gestation of whatever cause itself can result in severe maldevelopment of the deep cerebral nuclei and obliteration of the ventricular cavities.

A mathematical model of glioma growth: the effect of extent of surgical resection.

We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.

Experimental allergic encephalomyelitis in non-human primates: diffusion imaging of acute and chronic brain lesions.

Diffusion imaging and T2-weighted magnetic resonance imaging were performed on 16 monkeys with experimental allergic encephalomyelitis (EAE), a model of the human demyelinating disease MS. The purpose of this study was to determine whether local changes in diffusion image intensity could be correlated with the formation of acute and chronic demyelinating lesions. Diffusion image analysis was restricted to the internal capsule of the brain because of its anatomic orientation of fiber pathways. Acute inflammatory EAE lesions were large and monophasic, as visualized by T2-weighted MRI, and were accompanied by a decrease in the diffusion MR image signal with the diffusion-sensitizing gradient in all three orthogonal directions (n = 27 brain regions, P < 0.005). Chronic demyelinating lesions were preceded by multiple inflammatory attacks, as visualized by MRI, and by a decrease in diffusion MR image signal with the diffusion-sensitizing gradient in the two orthogonal directions perpendicular to the fibers of the internal capsule (n = 18 brain regions, P < 0.005). However, for the chronic group, there was no significant change in the diffusion MR image signal with diffusion-sensitizing gradient parallel to the fibers of the internal capsule at the terminal scan, suggesting little change in the water diffusion within the nerve fibers. These results suggest that diffusion imaging holds promise for measuring subtle changes in water diffusion due to different types of brain damage.