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Heterogeneity of red blood cell perfusion in capillary networks supplied by a single arteriole in resting skeletal muscle.

Flow heterogeneity within capillary beds may have two sources: (1) unequal distribution of red blood cell (RBC) supply among arterioles and (2) unique properties of RBC flow in branching networks of capillaries. Our aim was to investigate the capillary network as a source of both spatial and temporal heterogeneity of RBC flow. Five networks, each supplied by a single arteriole, were studied in frog sartorius muscle (one network per frog) by intravital video microscopy. Simultaneous data on RBC velocity (millimeters per second), lineal density (RBCs per millimeter), and supply rate (RBCs per second) were measured continuously (10 samples per second) from video recordings in 5 to 10 capillary segments per network for 10 minutes by use of automated computer analysis. To quantify heterogeneity, mean values from successive 10-second intervals were tabulated for each flow parameter in each capillary segment (ie, portion of capillary between successive bifurcations), and percent coefficient of variation (SD/mean.100%) was calculated for (1) spatial heterogeneity among vessels (CVs) every 10 seconds and for the entire 10-minute sample and (2) temporal heterogeneity within vessels for every capillary segment and for the mean flow parameter. Analysis of these data indicates that (1) capillary networks are a significant source of both spatial and temporal flow heterogeneity, and (2) continuous redistributions of flow occur within networks, resulting in substantial temporal changes in CVs, although a persistent spatial heterogeneity of perfusion still exists on a 10-minute basis. In most networks, CVs decreased as supply rate within the network increased, thus indicating that rheology plays a significant role in determining the perfusion heterogeneity.

Animals↗

Assessing the sensitivity of decision-analytic results to unobserved markers of risk: defining the effects of heterogeneity bias.

An important assumption made when constructing a Markov model is that all persons residing in a health state are identical. Failure to adjust for population heterogeneity caused by unobserved variables can therefore cause bias in model results. The authors used a simple model to evaluate the potential impact of heterogeneity bias, defined as the percentage change in the life expectancy gain with an intervention predicted by a model that does not adjust for heterogeneity (unadjusted model) compared to one that does (adjusted model). The life expectancy gains were consistently greater in the unadjusted model compared to the adjusted model (positive bias). For an annual probability of developing disease of 1%, the heterogeneity bias exceeded 50% when the relative risk of disease with the heterogeneity factor versus without the factor was greater than 15 and the prevalence of the heterogeneity factor was between 5% and 25%. When constructing decision-analytic models, analysts need to be cognizant of unobserved factors that introduce heterogeneity into the cohort. This analysis provides a general framework to determine when issues of heterogeneity may be important.

Adult↗

Changes in the heterogeneity of cerebral glucose metabolism with healthy aging: quantitative assessment by fractal analysis.

BACKGROUND AND PURPOSE: It has been shown that heterogeneity of cerebral glucose metabolism is increased in neuropsychiatric degenerative diseases. However, proper assessment of older patients requires knowledge about the effect of aging on heterogeneity. This study characterized the effects of aging on the heterogeneity of the distribution of cerebral glucose metabolism in healthy volunteers. METHODS: Sixty-six healthy volunteers (age range, 19-75 years) underwent flurodeoxyglucose brain positron emission tomography (PET), and all the PET images were spatially normalized onto a previously segmented standard brain template to parcel the brain regions automatically. Fractal dimension was regarded as a quantitative measurement for the heterogeneity of cerebral glucose metabolism and obtained for 9 brain regions. Participants were subdivided into young/midlife and elderly groups, and the Student t test was applied to the comparison of fractal dimensions in those groups. Analysis of covariance was performed for each region to explore the effects of age, gender, age-by-gender interaction, and total counts in the brain on the observed metabolic heterogeneity. RESULTS: Fractal dimensions were higher for elderly volunteers in most brain regions. Differences between the 2 groups in fractal dimension emerged within the whole gray matter, temporal lobe, striatum, and cingulate. No significant gender differences, age-by-gender interactions, or total counts were observed. Significant age effects were observed in the whole gray matter, frontal lobe, temporal lobe, striatum, and cingulate gyrus. CONCLUSIONS: Heterogeneity in the cerebral glucose metabolism of healthy volunteers increased with age, and individual variations of heterogeneity were higher in older volunteers. However, there was no significant difference between male and female volunteers of the same age. The effect of age on heterogeneity was not regionally uniform.

Adult↗

Heterogeneity of narrowing in normal and asthmatic airways measured by HRCT.

Asthmatic airway narrowing is heterogeneous and contributes to airway hyperresponsiveness. The present study compared heterogeneity of narrowing during methacholine challenge in asthmatics and normal subjects using high-resolution computed tomography (HRCT). The current authors defined heterogeneity as variability in narrowing greater than the repeatability of measurement. Airways of <2 mm diameter were compared with larger airways from baseline and postmethacholine HRCT of the right lower lung in 13 normals (seven had repeat baseline scans) and seven asthmatics. The coefficient of repeatability was calculated from repeat scans (RepAi) and was compared with heterogeneity of narrowing measured by the variability in narrowing from pre versus postmethacholine scans (VardeltaAi). Forced expiratory volume in one second decreased 27+/-6% and 24+/-8% in normals and asthmatics, respectively. Airways >2 mm narrowed more heterogeneously in asthmatics (VardeltaAi=+/-0.85 mm) compared with normals (VardeltaAi=+/-0.67 mm), with both being greater than the measure of repeatability (RepAi=+/-0.16 mm). Small airway narrowing was not heterogeneous in asthmatics (VardeltaAi=+/-0.59 mm) or normals (VardeltaAi=+/-0.53 mm) compared with repeatability (RepAi=0.51 mm). It is possible to study heterogeneity of airway narrowing in small and large airways using high resolution computed tomography. Airway narrowing is heterogeneous in the large airways of asthmatics and normals, being greater in asthmatics.

Adult↗

In silico microdissection of microarray data from heterogeneous cell populations.

BACKGROUND: Very few analytical approaches have been reported to resolve the variability in microarray measurements stemming from sample heterogeneity. For example, tissue samples used in cancer studies are usually contaminated with the surrounding or infiltrating cell types. This heterogeneity in the sample preparation hinders further statistical analysis, significantly so if different samples contain different proportions of these cell types. Thus, sample heterogeneity can result in the identification of differentially expressed genes that may be unrelated to the biological question being studied. Similarly, irrelevant gene combinations can be discovered in the case of gene expression based classification. RESULTS: We propose a computational framework for removing the effects of sample heterogeneity by "microdissecting" microarray data in silico. The computational method provides estimates of the expression values of the pure (non-heterogeneous) cell samples. The inversion of the sample heterogeneity can be facilitated by providing accurate estimates of the mixing percentages of different cell types in each measurement. For those cases where no such information is available, we develop an optimization-based method for joint estimation of the mixing percentages and the expression values of the pure cell samples. We also consider the problem of selecting the correct number of cell types. CONCLUSION: The efficiency of the proposed methods is illustrated by applying them to a carefully controlled cDNA microarray data obtained from heterogeneous samples. The results demonstrate that the methods are capable of reconstructing both the sample and cell type specific expression values from heterogeneous mixtures and that the mixing percentages of different cell types can also be estimated. Furthermore, a general purpose model selection method can be used to select the correct number of cell types.

Algorithms↗

Heterogeneity in disease free survival between centers: lessons learned from an EORTC breast cancer trial.

BACKGROUND: Large phase III clinical trials convey a lot of important information besides the main analysis of the treatment effect. For example, the use of multicenter clinical trial data to identify prognostic indices is now common. In addition, the study of heterogeneity in patient outcome between centers has received considerable attention in recent years. In this paper, we explain and illustrate a method used to investigate such heterogeneity with data from an early breast cancer clinical trial. METHODS: The inclusion of a random effect for center in a Cox proportional hazards model allows us to study the heterogeneity in time-to-event outcomes between centers. Such a model has the major advantage that it provides a measure of the spread of outcomes over centers. This technique is illustrated using data from EORTC trial 10854, a randomized phase III trial comparing perioperative chemotherapy with no perioperative chemotherapy for early breast cancer; 2793 patients were entered by 14 centers. RESULTS: Substantial heterogeneity between centers was detected for disease-free survival. This can be explained by the geographical area in which the center is located, with better outcomes achieved in France as compared with southern Europe and South Africa. None of the prognostic factors considered could explain this heterogeneity. CONCLUSION: Although clinical trials are run with the objective of removing as much heterogeneity as possible, some heterogeneity in the outcome of patients between centers may remain, as was the case in our study. The use of a random effect for center within a Cox PH model is an excellent method to investigate this heterogeneity. Such types of analyses, although exploratory, provide further insight into possible factors which may have an impact on the patient's outcome.

Breast Neoplasms↗

Spatial heterogeneity in refractoriness as a proarrhythmic substrate: theoretical evaluation by numerical simulation.

Spatial heterogeneity in the refractoriness of the ventricular myocardium due to a regionally prolonged refractory period has often been observed in patients with cardiovascular disease as the substrate for functional reentrant tachyarrhythmias. The present study sought to determine how functional reentrant activity could occur due to the spatial heterogeneity, using numerical simulation. Spatial heterogeneity in the refractoriness was introduced into a two-dimensional array by the regionally prolonged refractory period expressed as a square cluster. Double stimulation, conducted from a single source, was introduced into 4 types of matrices, which differed in their level of spatial heterogeneity. A pseudoelectrocardiogram was calculated from these matrices. Spiral waves were initiated in all the matrices except for the lowest heterogeneous matrix. A vulnerable window of the coupling interval, which induced spiral waves, was observed and was wider in proportion to the level of the heterogeneity. A higher level of heterogeneity and more limited range of coupling intervals were required to sustain the spiral waves. Furthermore, in the pseudoelectrocardiogram, sustained spiral waves exhibited a waveform like that in torsades de pointes (TdP) and their transformation into ventricular fibrillation (VF). Spatial heterogeneity in refractoriness due to a regionally prolonged refractory period could be a substrate for functional reentrant tachyarrhythmias, possibly including TdP and VF.

Cardiovascular Diseases↗

Molecular diversity after a range expansion in heterogeneous environments.

Recent range expansions have probably occurred in many species, as they often happen after speciation events, after ice ages, or after the introduction of invasive species. While it has been shown that range expansions lead to patterns of molecular diversity distinct from those of a pure demographic expansion, the fact that many species do live in heterogeneous environments has not been taken into account. We develop here a model of range expansion with a spatial heterogeneity of the environment, which is modeled as a gamma distribution of the carrying capacities of the demes. By allowing temporal variation of these carrying capacities, our model becomes a new metapopulation model linking ecological parameters to molecular diversity. We show by extensive simulations that environmental heterogeneity induces a loss of genetic diversity within demes and increases the degree of population differentiation. We find that metapopulations with low average densities are much more affected by environmental heterogeneity than metapopulations with high average densities, which are relatively insensitive to spatial and temporal variations of the environment. Spatial heterogeneity is shown to have a larger impact on genetic diversity than temporal heterogeneity. Overall, temporal heterogeneity and local extinctions are not found to leave any specific signature on molecular diversity that cannot be produced by spatial heterogeneity.

Computer Simulation↗

Heterogeneity and clonal variation related to cell surface expression of a mouse lung tumor-associated antigen quantified using flow cytometry.

Previous reports have established that line 1, a spontaneous BALB/c lung carcinoma, expresses a Mr 180,000 tumor-associated surface antigen (TSP-180). In this study, using a monoclonal antibody and flow cytometry to quantify cell surface TSP-180 expression, we found that essentially all cells in a tissue culture-adapted line 1 population express TSP-180, but that the amount of TSP-180 expressed by cells is quite heterogeneous. Variation in amount of TSP-180 was found to be in part related to cell size heterogeneity, and to the expression of TSP-180 being cell cycle-dependent. The amount of surface-expressed TSP-180 correlated somewhat with cell size, and was greater on the average for cells in the G2 cell cycle compartment. However, cells of a defined size and specific cell cycle stage still showed marked heterogeneity of expression. Even though the average amount of TSP-180 expressed per cell decreased during in vitro propagation, little change in heterogeneity was observed. To explore whether any TSP-180-related heterogeneity resulted from heritable variation of expression, 263 limiting dilution-derived line 1 clones were analyzed. The majority displayed, shortly after cloning, heterogeneous TSP-180 profiles and mean TSP-180 levels similar to those observed for the parent tumor. Occasionally, however, clones were isolated that again appeared as heterogeneous as the parent, but differed by as much as 3-fold in mean TSP-180 expression. Extensive passage did not substantially increase the low probability of isolating clones which differed in expression of TSP-180. Differences in TSP-180 expression among clones were found to be relatively stable upon passage, typically maintained after recloning, and large enough to influence clonal susceptibility to TSP-180-directed antibody and complement-mediated lysis. Heritable variation in TSP-180 expression among some clones was also shown to be independent of differences related to cell size, cell cycle, or expression of another line 1 surface antigen (P-100). We concluded that although clones demonstrating large heritable differences in TSP-180 expression can occasionally be isolated, line 1 TSP-180 heterogeneity is predominantly nonheritable, being similar to that present in recently cloned lines, quite stable during in vitro passage, and not totally accounted for by cell cycle or cell size variation.

Animals↗

Assessing genetic markers of tumour progression in the context of intratumour heterogeneity.

This is a report from the Kananaskis working group on quantitative methods in tumour heterogeneity. Tumour progression is currently believed to result from genetic instability and consequent acquisition of new genetic properties in some of the tumour cells. Cross-sectional assessment of genetic markers for human tumours requires quantifiable measures of intratumour heterogeneity for each parameter or characteristic observed; the relevance of heterogeneity to tumour progression can best be ascertained by repeated assessment along a tumour progressional time line. This paper outlines experimental and analytic considerations that, with repeated use, should lead to a better understanding of tumour heterogeneity, and hence, to improvements in patient diagnosis and therapy. Four general principles were agreed upon at the Symposium: (1) the concept of heterogeneity requires a quantifiable definition so that it can be assessed repeatably; (2) the quantification of heterogeneity is necessary so that testable hypotheses may be formulated and checked to determine the degree of support from observed data; (3) it is necessary to consider (a) what is being measured, (b) what is currently measurable, and (c) what should be measured; and (4) the proposal of working models is a useful step that will assist our understanding of the origins and significance of heterogeneity in tumours. The properties of these models should then be studied so that hypotheses may be refined and validated.

Disease Progression↗

Subcloning the RBL-2H3 mucosal mast cell line reduces Ca2+ response heterogeneity at the single-cell level.

Ca2+ imaging experiments have revealed that for a wide variety of cell types, including RBL-2H3 mucosal mast cells, there are considerable cell-to-cell differences of the Ca2+ responses of individual cells. This heterogeneity is evident in both the shape and latency of the responses. Mast cells within a single microscopic field of view, which have experienced identical culture conditions and experimental preparation, display a wide variety of responses upon antigen stimulation. We have subcloned the RBL-2H3 mucosal mast cell line to test the hypothesis that genetic heterogeneity within the population is the cause of the Ca2+ response heterogeneity. We found that cell-to-cell variability was significantly reduced in four of five clonal lines. The response heterogeneity remaining within the clones was not an experimental artifact caused by differences in the amount of fura-2 loaded by individual cells. Factors other than genetic heterogeneity must partly account for Ca2+ response heterogeneity. It is possible that the complex shapes and variability of the Ca2+ responses are reflections of the fact that there are multiple factors underlying the Ca2-response to antigen stimulation. Small differences from cell to cell in one or more of these factors could be a cause of the remaining Ca2+ response heterogeneity.

Animals↗

Cytogenetic heterogeneity and histologic tumor growth patterns in prostatic cancer.

Twenty-five prostatic adenocarcinomas were studied for the presence of intratumoral cytogenetic heterogeneity by interphase in situ hybridization (ISH) to routinely processed tissue sections. ISH with a chromosome Y-specific repetitive DNA probe provided a model to investigate patterns of chromosomal heterogeneity within and between different pathological grades. The Gleason grading system was used, since it is based on a detailed classification of growth patterns. Heterogeneity with respect to ploidy of the tumor was examined by ISH with a repetitive DNA probe specific for chromosome 1. The ploidy status of these cancers was confirmed by DNA flow cytometry (P < 0.001). Cytogenetic heterogeneity at the (Y) chromosomal level was observed between Gleason areas, within one area, and even within single tumor glands. The different patterns of chromosomal heterogeneity were seen in all tumor grades and stages. Differences in ploidy status were also found following the aforementioned histological patterns, again, in all grades and stages. Intraglandular heterogeneity was most frequently seen. No correlation was found between cytogenetic heterogeneity and proliferative activity (Ki-67 immunostaining). In contrast to current views on clonality, suggesting regional separation of subclones with different DNA content, this study demonstrates that these subclones can be interspersed.

Adenocarcinoma↗

Tests for covariate-associated heterogeneity in IBD allele sharing of affected relatives.

Linkage studies that aim to map susceptibility genes for complex diseases commonly test for excess allele sharing among affected relatives. Conventional methods based on identical-by-descent IBD allele sharing do not allow for possible differences among families, such as arise in the case of locus heterogeneity, and thus have reduced ability to detect linkage in the presence of such heterogeneity. We investigated two approaches to test for heterogeneity in allele sharing, using a family-level covariate that may be associated with different disease mechanisms leading to differences in allele sharing. Likelihood ratio tests for heterogeneity were formulated based on an extension of the linear and exponential likelihood models developed by Kong and Cox. Alternatively, we examined the asymptotic and permutation distributions of T-tests for differences between mean allele-sharing linkage scores from two covariate-defined family subgroups, assuming exchangeability. The size and power of heterogeneity tests were evaluated for S(all) and S(pairs) allele-sharing scoring functions using data sets of families with affected sibling and cousin pairs, generated under a model of locus heterogeneity. In certain simulation scenarios, the likelihood ratio test statistics did not follow the expected asymptotic distributions. The type I error estimates for the T-statistics conformed to nominal 5 and 1% levels in all scenarios considered, and corresponding power was comparable to that of the likelihood ratio tests. Application of these tests for heterogeneity detected significant differences in allele sharing between subgroups of families with inflammatory bowel disease.

Algorithms↗

Triangle test statistic in discordant sib pairs: test of genetic heterogeneity of asthma and atopy in CSGA families.

The purpose of our study was to detect genetic heterogeneity (i.e., different genotype relative risks of genetic factor) between atopic and non-atopic asthma and between atopy associated or independent of asthma. Genetic heterogeneity was tested in the Caucasian Collaborative Study on the Genetics of Asthma families using the TTS (triangle test statistic) and the predivided sample test. The TTS was proposed to detect both linkage and intra-sib-pair genetic heterogeneity; such heterogeneity may exist if the sibs differ for a factor on which the penetrances of the putative linked gene depend. The TTS has been applied to asthmatic pairs discordant for atopy and atopic sib pairs discordant for asthma. To confirm genetic heterogeneity detected by the TTS, the predivided sample test was also applied among concordant and discordant sib pairs. The analyses detected a genetic factor on chromosome 8p that could be involved in atopy with different genotype relative risks according to whether asthma is present. This would suggest a pleiotropic effect of this genetic factor in asthma and atopy. Two other regions located on chromosomes 8q and 20p were detected for genetic heterogeneity with asthma and atopy, respectively, but the factor of heterogeneity could be independent from the presence of atopy or asthma, respectively. It could be a characteristic of the disease such as the severity or the presence of an environmental factor.

Adult↗

Multi-omic underpinnings of heterogeneous aging across multiple organ systems.

Aging is the main determinant of chronic diseases and mortality, yet organ-specific aging trajectories vary, and the molecular basis underlying this heterogeneity remains unclear. To elucidate this, we integrated genomic, epigenomic, transcriptomic, proteomic, and metabolomic data, employing post-genome-wide association study methodologies to systematically investigate the molecular mechanisms of nine organ-specific aging clocks and four blood-based epigenetic clocks. We uncovered genetic correlations and specific phenotypic clusters among these aging-related traits, identified prioritized genetic drug targets for heterogeneous aging, and elucidated downstream proteomic and metabolomic effects mediated by heterogeneous aging. We constructed a cross-layer molecular interaction network of heterogeneous aging across multiple organ systems and characterized detectable biomarkers of this heterogeneity. Integrating these findings, we developed an R/Shiny-based framework that provides a comprehensive multi-omic molecular landscape of heterogeneous aging, thereby advancing the understanding of aging heterogeneity and informing precision medicine strategies to delay organ-specific aging and prevent or treat its associated chronic diseases.

Aging↗

Apparent heterogeneity of recombinant interferon gamma receptors produced in prokaryotic and eukaryotic expression systems.

Recombinant proteins show several types of heterogeneity and post-translational modifications which are usually related to their production system. The apparent heterogeneity of recombinant interferon gamma receptors and interferon gamma receptor-immunoglobulin G fusion proteins expressed in Escherichia coli, baculovirus-infected insect cells and Chinese hamster ovary cells have been studied. In general, all proteins tested showed some type of heterogeneity which was detectable by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. The E. coli-derived receptor included non-native conformations involving mis-paired or non-formed disulfides. This type of heterogeneity affected the biological activity of the protein. In addition, the prokaryotic protein had trapped phosphoric acid during downstream processing. The phosphoric acid entrapment did not affect ligand binding capacity. The eukaryotic proteins showed heterogeneity because of the unequal cleavage of the signal peptide and because of differences in glycosylation. The latter types of heterogeneity did not affect activity. Glycosylation-related heterogeneity was partially derived from the unequal utilization of the potential N-glycosylation sites and differently affected the apparent molecular masses and migrations of the proteins on polyacrylamide gels. The results may be useful in characterization studies of recombinant proteins.

Amino Acid Sequence↗

Ovarian carcinoma heterogeneity as demonstrated by DNA ploidy.

BACKGROUND: In ovarian carcinoma, DNA ploidy measured by flow cytometric (FCM) analysis is an independent prognostic factor. However, limited sampling may underestimate the extent of ploidy variation (i.e., heterogeneity). Uncovering these hidden populations may explain poor outcomes in patients with ostensibly favorable ploidy patterns. The authors examined ploidy in a mean of 6.4 tumor samples per patient to better assess the occurrence of heterogeneity. METHODS: FCM analysis was performed on multiple samples from 19 cases of advanced, serous ovarian carcinoma. Tumors were considered as heterogeneous by two definitions: (1) the presence of more than one ploidy pattern (e.g., diploidy and tetraploidy); and (2) the existence of DNA indices of sufficient variation so as to characterize two distinct populations of neoplastic cells. RESULTS: With the first definition, 47% (9 of 19) of the tumors were heterogeneous, 37% (7 of 19) homogeneous-aneuploid, and 16% (3 of 19) homogeneous-diploid. These three groups showed no significant differences in histologic type, grade, patient age, stage, or survival. With the second definition, 27% (4 of 15) of the non-diploid cases were heterogeneous and 73% (11 of 15) were homogeneous. When these two groups were compared as to type, grade, patient age, and stage, no significant differences were demonstrated. However, the median survival of the patients with heterogeneous tumors was significantly longer (P < 0.05) than the survival of patients with homogeneous tumors. CONCLUSIONS: Ovarian carcinoma heterogeneity is high when multiple sites are assayed. This suggests conservative interpretation of ploidy when only a single sample is analyzed and examination of multiple samples when practicable.

Aneuploidy↗

Regional heterogeneity in the DNA content of human gliomas.

BACKGROUND: Regional heterogeneity causes significant errors in the histologic classification and grading of gliomas, but little is known about its implications for other modalities. Attempts to predict glioma behavior using flow cytometry (FCM) have yielded contradictory results, possibly due to regional heterogeneity in DNA content, a recognized phenomenon that has not been evaluated systematically. METHODS: The authors used FCM to analyze the DNA content of 353 regions from 18 resected human gliomas. Five to 60 regions were sampled from each tumor, and the topographic relationships of ploidy, proliferative activity (S-phase fraction [SPF]), and histologic features were established. RESULTS: Most tumors demonstrated heterogeneity among regions in the number and relative sizes of aneuploid populations and/or proliferative activity. The degree of heterogeneity increased with tumor grade. Heterogeneity in histologic features, ploidy, and proliferative activity appeared to vary independently, except for a significant association between the presence of mitotic figures and the SPF of individual regions (P < 0.0001). The clustering of regions with similar percentages of aneuploid cells supported the concept of local clonal expansion. CONCLUSIONS: Gliomas express significant regional heterogeneity in ploidy and proliferative activity and this will have an adverse effect on the usefulness of their analysis. However, the independent variation of ploidy, proliferative activity, and histologic features suggests that the use of multiple analyses may allow more accurate prediction of glioma patient survival. Regional heterogeneity appears be a fundamental property of malignant gliomas; systematic studies to determine its effects on the diagnostic usefulness of other new methods used to evaluate gliomas are indicated.

Aneuploidy↗