Detrended fluctuation analysis of genome-wide copy number profiles of glioblastomas using array-based comparative genomic hybridization^,

Abstract

We examined whole genomic aberrations of biopsied samples from 19 independent glioblastomas by array-based comparative genomic hybridization analysis. The highest frequencies of copy number gains were observed on RFC2 (73.3%), EGFR (63.2%), and FGR, ELN, CDKN1C, FES, TOP2A, and ARSA (57.9% each). The highest frequencies of copy number losses were detected on TBR1 (52.6%), BMI1 (52.6%), EGR2 (47.4%), DMBT1 (47.4%), MTAP (42.1%), and FGFR2 (42.1%). The copy number gains of CDKN1C and INS and the copy number losses of TBR1 were significantly correlated with longer survival of patients. High-level amplifications were identified on EGFR, SAS/CDK4, PDGFRA, MDM2, and ARSA. These genes are assumed to be involved in tumorigenesis or progression of glioblastomas. The first attempts to apply detrended fluctuation analysis to copy number profiles by considering the reading direction as the time axis demonstrated that higher long-term fractal scaling exponents (α2) correlated well with longer survival of glioblastoma patients. The present study indicates that array-based comparative genomic hybridization analysis has great potential for assessment of copy number changes and altered chromosomal regions of brain tumors. Furthermore, we show that nonlinear analysis methods of whole genome copy number profiles may provide prognostic information about glioblastoma patients.

Despite great efforts in basic life science and clinical research, little progress has been made in improving the prognosis for patients with glioblastomas. Surgical cure of gliomas is impossible in practice because of their high infiltrating activity. The clinical course is dependent upon the biological behavior of the tumor cells.

There is increasing evidence that the accumulation of genetic and epigenetic alterations is essential for tumor initiation and progression (Cavenee et al., 2000). Recent success of PCV (procarbazine, lomustine, and vincristine) chemotherapy for anaplastic oligodendrogliomas with losses of chromosome 1p and 19q (Cairncross et al., 1998) has encouraged us to characterize the molecular biology of brain tumors.

Conventional comparative genomic hybridization (metaphase-CGH)⁴ has been widely used to screen for chromosomal gains and losses throughout the entire genome of a tumor (Kallioniemi et al., 1994). Microarray-based CGH (array-CGH) is a recently developed genomic analysis technology that enables high-throughput screening of gene aberrations with sensitivity to detect single gene copy changes (Pinkel et al., 1998; Snijders et al., 2001). In this study, we employed array CGH for mapping of copy number alterations in glioblastomas and analyzed the potential correlation between genomic changes and prognosis of patients.

Nonlinear and chaos theories have made clear that long-range power-law correlations exist in a remarkably wide variety of systems (Keshner, 1982; Pentland, 1984). In nonlinear analysis, detrended fluctuation analysis (DFA), which calculates the root-mean-square fluctuation of integrated and detrended sequential data series, permits the detection of intrinsic self-similarity and extraction of hidden information from physiological data (Peng et al., 1995). The long-term fractal scaling exponent determined by DFA is considered a predictor of prognosis for patients with heart disease (Makikallio et al., 1999, 2001). In the present study, we applied DFA to copy number profiles for quantifying the long-range correlation property.

Materials and Methods

Patients

A total of 19 de novo glioblastoma tissue samples were obtained at craniotomy in the Saga Medical School Hospital with approval from the Research Ethics Board of Saga University. After surgery, all glioblastoma patients were treated with IAR therapy — a combination of interferon-β; ACNU, an abbreviated form of 1-(4-amino-2-methyl-5-pyrimidinyl)methyl-3-(2-chloroethyl)-3-nitrosourea hydrochloride; and radiation therapy (Yoshida et al., 1994). Long-term survivors for this study were defined as patients who lived at least 12 months from the time of an initial surgical diagnosis of glioblastoma. Short-term survivors were patients with a survival of less than 12 months from initial diagnosis. All patients were diagnosed at first surgery as having glioblastoma by using WHO criteria (Kleihues and Sobin, 2000).

Samples

All specimens were snap-frozen in liquid nitrogen within 30 to 60 min of surgical excision and stored at – 80°C until use. An initial frozen section with H&E staining was examined to allow trimming of the block for exclusion of normal or necrotic tissue. Tumor tissues were hand-dissected from normal tissue. Tumor tissues were considered suitable for study and selected for DNA isolation when the proportion of tumor tissues to normal brain tissues was greater than 80% as determined by visual inspection of H&E-stained slides.

Genomic DNA Extraction

Ten-micrometer sections of glioblastoma tissues were cut for DNA extraction. High-molecular-weight DNA was extracted from each tumor specimen with a DNeasy Tissue Kit (Qiagen, Valencia, Calif., USA) according to the manufacturer’s instructions. In addition, normal DNA that was isolated from lymphocytes of healthy donors and of a patient who had glioblastoma was used for quality control studies.

DNA Labeling

Approximately 0.1 mg of DNA from tumor samples (test DNA) and normal reference DNA were labeled by random priming with Cy3-dCTP and Cy5-dCTP (Perkin Elmer, Foster City, Calif., USA), respectively, according to the protocols recommended by the manufacturer (Vysis, Inc., Downers Grove, Ill., USA). Briefly, an 85.6-μl reaction was set up containing 100 ng of DNA and a final concentration of 1× random primer solution. After the DNA was denatured at 100°C for 10 min, 10 μl of nucleotide mix, 2.4 μl of Cy3-dCTP or Cy5-dCTP, and 2 μl of the Klenow fragment supplied in the kit were added on ice to produce a final reaction volume of 100 μl. The reaction was incubated at 37°C for 2 h and stopped by adding 6 μl of stop buffer. Unincorporated fluorescent nucleotides were removed by ethanol precipitation.

Slides and Hybridization

Each aliquot of labeled DNA (2.5 μl) was mixed with 25 μl Cot-1 DNA (Vysis, Inc.), denatured at 80°C for 10 min, and incubated at 37°C for 1 h to allow blocking of repetitive sequences. We used commercially available genomic DNA microarray slides. The GenoSensor Array 300 (Vysis, Inc.) contained 287 targets and included telomeres, microdeletions, oncogenes, and tumor suppressor genes, which were cloned from P1, PAC, or BAC libraries. The complete list of clone names and their chromosomal locations is available (Supplementary Table 1).² The hybridization mixture was then introduced into the hybridization chamber of a microarray slide, and the slide was incubated 60 to 66 h at 37°C. After removal from the hybridization chamber, the microarray slide was washed 3 times with 50% formamide/2× standard saline citrate solution. The slide was then washed 4 times with 1× standard saline citrate solution for 5 min at room temperature. The microarray slides were counterstained with DAPI (4,6-diamidino-2-phenylindole) solution and covered with a cover slip.

Analysis of Fluorescence Imaging

Hybridized microarray slides were analyzed by using the GenoSensor Reader System (Vysis, Inc.). The system contained a large-field multicolor fluorescence imaging system that captured an image of the hybridized chip in three color planes: green, red, and blue. Signals from test DNA (Cy3-dCTP) and reference DNA (Cy5-dCTP) were quantitatively detected with exposure times of 0.5 to 20 s by the autoexposure system. Images were analyzed with the GenoSensor Reader software (Vysis, Inc.), which segmented the array targets according to the DAPI staining. After subtracting the background in the green and red fluorescence images, we calculated the total intensity and the intensity ratio of green (test) and red (reference) signals for each target (three replicate spots for each target gene). The normalized ratio of target indicated the degree of gain or loss of copy number when compared with the sample’s modal copy number.

Metaphase-CGH Analysis

CGH and digital image analyses were carried out according to protocols described previously (Harada et al., 2002). The gain and loss of DNA sequence copy number were judged by the green/red ratios >1.2 and <0.8, respectively. A ratio of >1.4 was referred to as amplification.

Statistical Analysis

Two-group comparisons of the parameters of the short-term survivors (less than 12 months) and those of the long-term survivors (more than 12 months) were performed with the Fisher’s exact test for categorical variables and with the 2-sample t-test for dependent continuous variables. Survival estimates were computed by Kaplan-Meier methods, and log-rank analysis was performed to compare the survival curves of the groups. Continuous measures are summarized as mean ± SD. A value of P < 0.05 was considered statistically significant. Data were analyzed with Statistica 2000 (StatSoft Japan, Inc., Tokyo, Japan).

Detrended Fluctuation Analysis

To detect the presence or absence of fractal-like scaling properties in the glioblastoma genome, we used DFA (Iyengar et al., 1996; Peng et al., 1993, 1995) to quantify the fractal scaling properties of copy number profiles.

The DFA computation involves the following steps. First, each of the time series is integrated as

where y(k) is the kth value of the integrated series; x(i) is a correlated signal, where i = 1, . . . , N_max, and N_max is the length of the signal; and M is the mean of the entire sequence. Next, the integrated signal y(k) is divided into boxes of equal length, n. In each box of length n, a least-squares line is fitted to the data, which represents the trend in that window. The y coordinates of the fitted line in each box are denoted by y_n(k).

Next, we detrended the integrated signal y(k) by subtracting the local trend y_n(k) in each box of length n. For a given box size n, the root-mean-square fluctuation of this integrated and detrended series is calculated as

The calculation of F(n) was repeated for a broad range of scales (box sizes n) to provide a relationship between F(n) and the box size n and plotted as a function of n on a log-log plot. A linear relationship on a log-log plot indicates the presence of scaling. The scaling exponent α represents the slope of this line, which relates the average root-mean-square fluctuation function F(n) (log) and the box size n (log).

In this study, both the short-term α1 and the long-term α2 scaling exponents were calculated. We used the Mono Multifractal Analysis Program (Computer Convenience, Inc., Fukuoka, Japan) to perform all of the nonlinear analyses. For the white Gaussian noise, where the value at one instant is not correlated with any previous value, α takes the value of 0.5 (Montroll and Shlesinger, 1984). The fractal-like signal (1/f signal spectrum) results in exponent value 1 (α = 1.0) (Bak et al., 1987). Furthermore, α = 1.5 corresponds to Brownian noise (1/f² signal spectrum), which is the integration of white noise (Buldyrev et al., 1994). When 0 < α < 0.5, power-law anticorrelations are present such that large values are more likely to be followed by small values and vice versa (Beran, 1994). If α is greater than 0.5 and less than or equal to 1.0, then there is a long-range power-law correlation that captures our interest (Peng et al., 1995).

Results

We first confirmed the quality of the hybridization results with GenoSensor Array 300 (Vysis, Inc.) by conducting three experiments. We hybridized each DNA extract from the same normal lymphocyte that was labeled by random priming with Cy3-dCTP and Cy5-dCTP. The intensities of the hybridization signal were between 0.80 and 1.19. There was no aberration of copy number in the normal lymphocyte (Supplementary Fig. 1).² On the basis of control experiments using test and reference DNA from four normal individuals, we determined gain or loss of DNA sequence copy numbers by a green/red ratio of >1.2 or <0.8, respectively. When the intensity of the hybridization signal was elevated more than 2-fold compared with normal DNA, the target DNA was considered to be displaying gene amplification. Next, we performed the hybridizations using tumor sample DNA and lymphocyte DNA from the same patient, who is still alive and not included in the 19 glioblastoma patients. In the tumor sample, aberrations of copy number were detected in several genes, whereas there was no genomic aberration in lymphocyte DNA from the same patient (Supplementary Figs. 2A and 2B),² which means the copy number aberrations are the result of the tumor and not simply the genome of the patient. Finally, we compared the results of array-CGH and metaphase-CGH in several cases. The aberrations of copy number in array-CGH corresponded well to the peaks in metaphase-CGH profiles (Supplementary Figs. 3A and 3B).²

Despite current therapeutic modalities, the median survival for patients with newly diagnosed glioblastoma has remained at approximately 12 months. At 2 years after initial surgical procedure, >90% of patients are deceased. It was decided a priori to compare long-term survivors (⩾12 months) with short-term survivors (<12 months), and patients were identified and classified according to these criteria. The median age of the 8 cases of the long-term survival group was 53.5 years (range, 30–68 years), which was similar to that of the 11 cases in the short-term survival group (median age, 53.6 years; range, 8 – 74 years; P = 0.9, t-test). The groups of patients were not statistically different with regard to Karnofsky performance status (⩽70 vs. >70) (Table 1).

Table 1.

Clinical characteristics of 19 glioblastoma patients

Characteristic	Long-term survival group 8 cases	Short-term survival group 11 cases	P-value	α1 < α26 cases	α1 ⩾ α2 13 cases	P-value
Patient age, years
Range	30–68	8–74		30–68	8–74
Mean ± SD	53.5 ± 15.6	53.6 ± 18.1	0.987	55.7 ± 15.36	52.6 ± 16.65	0.721
Sex			0.647			>0.9999
Male	2	7		3	6
Female	6	4		3	7
KPS score preop			0.069			0.349
KPS < 70	2	8		2	7
KPS ⩾ 70	6	3		4	6
Survival time, months
Range	12.0–25.8	4.2–11.8		11.8–25.8	4.2–18.0
Mean ± SD	16.4 ± 4.4	7.9 ± 2.9	<0.0001*	16.5 ± 5.17	9.13 ± 4.07	0.035*
No. of aberrations
Range	29–75	4–103		29–75	4–103
Mean ± SD	51.3 ± 15.0	54.6 ± 30.9	0.779	55.8 ± 15.8	52.0 ± 28.7	0.765
No. of gains
Range	25–53	4–58		26–53	4–58
Mean ± SD	36.4 ± 9.8	31.2 ± 16.8	0.447	36.7 ± 10.8	31.8 ± 15.7	0.507
No. of losses
Range	3–22	0–45		3–30	0–45
Mean ± SD	16.1 ± 6.3	23.5 ± 15.3	0.221	19.2 ± 3.6	20.9 ± 14.3	0.787

Abbreviations: α1, short-term scaling exponent; α2 long-term scaling exponent; KPS, Karnofsky performance status; SD, standard deviation.

^*P < 0.05.

The distribution of copy number aberrations on genomic DNA from these 19 glioblastoma tissue samples was detected by array-CGH (Supplementary Table 1 and Supplementary Fig. 4).² A large part of the genome is affected, and the distribution of copy number alterations is not uniform throughout the genome. The pattern of genomic aberrations consisted of 264 copy number aberrations (mean per tumor, 54.6; range, 4 – 72) and included 195 copy number gains (mean, 34.3; range, 4–58), 170 copy number losses (mean, 20.3; range, 0–45), and 18 amplifications.

In the present study, overall, copy number gain of RFC2 was identified in 14 cases (73.3%), EGFR in 12 cases (63.2%), and FGR, ELN, CDKN1C, FES, TOP2A, and ARSA in 11 cases (57.9% each) (Table 2). Copy number loss was detected on TBR1 and BMI1 in 10 cases (52.6%) each, EGR2 and DMBT1 in nine cases (47.4%) each, and MTAP and FGFR2 in eight cases (42.1%) each (Table 3).

Table 2.

Most frequently gained clones

Name	Cytogenetic location	Number of cases
RFC2, CYLN2	7q11.23	14
G31341	7p tel	12
EGFR	7p12.3-p12.1	12
CEB108/T7	1p tel	11
FGR (SRC2)	1p36.2-p36.1	11
ELN	7q11.23	11
CDKN1C (p57)	11p15.5	11
FES	15q26.1	11
TOP2A	17q21-q22	11
ARSA	22q tel	11
stSG48460	7q tel	10
INS	11p tel	10
SHGC-103396	17q tel	9
JUNB	19p13.2	9
HIRA (TUPLE1)	22q11.21	9
1PTEL06	1p tel	8
RASSF1	3p21.3	8
C84C11/T3	5p tel	8
SERPINE1	7q21.3-q22	8
H18962	9q tel	8

Table 3.

Most frequently lost clones

Name	Cytogenetic location	Number of cases
TBR1	2q23-q37	10
BMI1	10p13	10
10QTEL006	10p tel	9
EGR2	10q21.3	9
DMBT1	10q25.3-q26.1	9
3PTEL01, CHL1	3p tel	8
MTAP	9p21.3	8
D10S249, D10S533	10p15	8
D10S167	10p11-10q11	8
FGFR2	10q26	8
3PTEL25	3p tel	7
TERC	3q26	7
CDKN2A (p16)	9p21	7
IGH (SHGC-36156)	14q tel	7
ERBB4 (HER-4)	2q33.3-q34	6
PTEN	10q23.3	6
D6S434	6q16.3	5
ESR1	6q25.1	5
AFM137XA11	9p11.2	5
GATA3	10p15	5

As shown in Table 4, EGFR (4 cases), SAS/CDK4 (4 cases), PDGFRA (2 cases), MDM2 (2 cases), and ARSA (2 cases) showed gene amplification. There was no statistical difference in the overall number of aberrations, gains, and losses between the long-term survival group and short-term survival group (Table 1). However, the copy number aberrations of several genes or loci listed in Table 5 were significantly correlated with survival time.

Table 4.

Most frequently amplified clones.

Name	Cytogenetic location	Number of cases	Range of magnitude
EGFR	7p12.3-p12.1	4	4.24–59.9
SAS, CDK4	12q13-q14	4	2.05–5.99
PDGFRA	4q11-q13	2	2.13–2.46
MDM2	12q14.3-q15	2	4.01–5.11
ARSA	22q tel	2	2.03–2.2
PGRMC2	4q26	1	2.56
C84C11/T3	5p tel	1	4.27
D6S434	6q16.3	1	2.49
MET	7q31	1	3.33
11PTEL03	11p tel	1	2.75
CCND1	11q13	1	2.48
FGF4, FGF3	11q13	1	2.43
EMS1	11q13	1	2.32
CDK2, ERBB3	12q13	1	2.59
GLI	12q13.2-q13.3	1	6.02
D13S327	13q tel	1	2.12
SNRPN	15q12	1	2.18
NME1 (NME23)	17q21.3	1	2.13

Table 5.

Relationship of number of genomic aberrations to survival time and α values

		Number of aberrations			Number of aberrations
Name	Cytogenic location	Long-term survival group (n = 8)	Short-term survival group (n = 11)	P-value	α1 < α2 (n = 6)	α1 ⩾ α2 (n = 13)	P-value
CEB108/T7	1p tel	7	4	0.058	6	5	0.018*
TBR1	2q23-q37	7	3	0.019*	5	5	0.141
CSF1R	5q33-q35	5	3	0.181	5	3	0.003*
GATA3	10p15	3	2	0.603	4	1	0.017*
WI-2389, D10S1260	10p14-p13	3	2	0.603	4	1	0.017*
11PTEL03	11p tel	2	6	0.352	0	8	0.018*
INS	11p tel	7	3	0.019*	6	4	0.011*
CDKN1C (p57)	11p15.5	8	3	0.003*	5	6	0.177
AKT1	14q32.32	3	3	>0.9999	4	2	0.046*
LLGL1	17p12-17p11.2	3	2	0.603	3	0	0.021*
INSR	19p13.2	4	1	0.111	5	0	0.0005*
CCNE1	19q12	3	3	>0.9999	4	2	0.046*
AKT2	19q13.1-q13.2	4	3	0.377	5	2	0.009*

Abbreviations: α, scaling exponent; α1, short-term scaling exponent; α2 long-term scaling exponent.

^*P < 0.05

Table 6 presents a summary of fractal scale exponents for two groups determined by DFA. Comparison of measures of correlation properties in the short-term survival group and the long-term survival group reveals that long-term survivors have significantly higher values for α2 than short-term survivors, despite no significant difference in α1 for the two groups. The Kaplan-Meier survival curve (Fig. 1) demonstrates that the cases with α2 exponents that are higher than α1 exponents show significantly longer survival than cases with α2 exponents that are lower than α1 exponents (log-rank [Mantel-Cox] P = 0.027). These data show that the existence of fractal-like behavior in long-term fractal scaling properties is a good prognostic indicator.

Table 6.

Results of detrended fluctuation analysis^*

DFA	All patients	Long-term survival group	Short-term survival group	P-value
α	0.69 ± 0.14	0.71 ± 0.11	0.69 ± 0.16	0.71
α1	0.72 ± 0.14	0.69 ± 0.14	0.73 ± 0.14	0.569
α2	0.66 ± 0.14	0.74 ± 0.11	0.60 ± 0.14	0.038*

Abbreviations: α, scaling exponent; α1, short-term scaling exponent; α2 long-term scaling exponent; DFA, detrended fluctuation analysis; SD, standard deviation.

^*All data are presented as mean ± SD.

^#P < 0.05.

Fig. 1.

Kaplan-Meier survival curve demonstrating that cases with higher α2 than α1 exponents have significantly longer survivals than cases with lower α2 than a1 exponents.

Discussion

Array-CGH provides quantitative copy number measurements and detects small loci containing amplification and deletion that potentially harbor specific oncogenes and tumor suppressor genes. Overall, our study of array-CGH showed that genomic gains were detected at chromosomes 1, 7, 19, and 20 and genomic losses were observed on 10, 13, and 22. These genomic imbalances demonstrated concordance with the reported data of metaphase-CGH (del Mar Inda et al., 2003; Maruno et al., 1999). Our quality control study demonstrated that the aberrations of copy number in array-CGH corresponded well to the peaks in metaphase-CGH profiles. The good reproducibility, with more than 85% of the array loci giving identical results, showed aberrations that have been reported in metaphase-CGH (Arai et al., 2003; Takeo et al., 2001). Moreover, amplifications of some genes detected by array-CGH are not detected as amplifications in metaphase-CGH (Peng et al., 2003).

EGFR has been reported to be the most commonly amplified oncogene observed in glioblastomas (30%–40%) (Arslantas et al., 2004; Kraus et al., 2002), and EGFR gene amplification is one of the poor prognosis factors (Shinojima et al., 2003). In the present study, the copy number gain of EGFR was detected in 12 cases (63.2%), which included EGFR amplification in 4 cases. However, the copy number gains or amplifications of EGFR gene were not significantly correlated with survival time.

Loss of chromosome 10 and mutation of the PTEN gene have previously been shown to be independently associated with poor survival outcomes in patients with anaplastic astrocytoma, although a prognostic association in glioblastoma was not found (Balesaria et al., 1999; Smith et al., 2001). We also showed that loss of the PTEN gene, which was detected in three cases in both survival groups, was not associated with survival time.

Our study confirms reports from previous studies in which amplified genes were detected in glioblastoma, such as MYCN (2p24.1) (Jay et al., 1994), PDGFRA (4q11-q13) (Muleris et al., 1994; Smith et al., 2000), MET (7q31) (Fischer et al., 1995), MYC (8q24) (Trent et al., 1986), and GLI, SAS/CDK4, and MDM2 (12q13.2-q15) (Kinzler et al., 1988; Reifenberger et al., 1995, 1996). These genes were also detected in our array-CGH analysis. However, the gains of RFC2 (7q11.23) and CDKN1C (11p15.5) and losses of TBR1 (2q23-q37), BMI1 (10p13), and EGR2 (10q21.3) that were detected in this study have not been previously reported in glioblastomas.

The names of gene loci that showed significant correlation with either survival time or the value of α are listed in Table 5. Both INS (insulin) and INSR (insulin receptor), which play a major role in the insulin pathway, are suspected to be prognostic factors. Glick et al. (1989) have shown that insulin-binding activity of meningiomas was higher than that of glioblastomas. Recently, several studies reported that the polymorphism of INS may play a role in the etiology of prostate cancer (Ho et al., 2003), and INS inhibits TNF-α-dependent cell killing and induction of p53, p21, and apoptosis (Akca et al., 2002). Our present results and these previous reports suggest that the insulin pathway may be involved in the growth control of glioblastoma cells.

Interestingly, as shown in Table 5, glioblastoma DNA of patients with a long survival time showed a higher number of genomic aberrations than that of patients with a short survival time. To better understand the biological significance of these observations, in which we focused on an individual gene, we attempted to apply the nonlinear analysis in chaos theory to copy number profiles of glioblastoma obtained by array-CGH. Our rationale for attempting this analysis was based on recent work in nonlinear and fractal dynamic analysis, which has emphasized that long-range power-law correlations exist in many physiological time series.

We used DFA for our study because DFA has been used to uncover hidden abnormalities or alterations in time-series data in nonlinear analysis methods. Although DFA was originally established to analyze the context of time series or records, the DFA computation procedure can be readily applied to the analysis of ordered linear sequences, such as DNA, by considering the reading direction as the time axis (Bernaola-Galván et al., 1996; Peng et al., 1994). Peng et al. (1992) were the first to attempt to apply DFA to DNA sequences. They found that intron-containing DNA coding regions exhibit long-range power-law correlations extending across more than 10⁴ nucleotides, whereas intronless coding regions display only short-range correlations (Peng et al., 1992, 1994). A recent report by Yu et al. (2001) on three kinds of length sequences of a bacteria genome indicates that long-range correlations exist in most of these sequences.

To the best of our knowledge, this is the first study to analyze nonlinear dynamics of copy number profiles by array-CGH. We found that reduced long-term fractal scaling exponents (α2) correlated well with short survival times. Several clinical studies of patients with cardiovascular diseases have made clear that reduced fractal scaling properties of heartbeat variability are observed in patients with congestive heart disease (Peng et al., 1995), myocardial infarction (Bigger et al., 1996), and life-threatening arrhythmias (Makikallio et al., 1998).

The significance for existent data and prognostic information of long-range correlations in copy number profiles is not clear. Goldberger (1996) speculated that breakdown of long-term fractal dynamics, which are apparent in many diseases, may be associated with a reduced ability to adapt to physiological stress. It is possible that in the short-term survival range, genomic aberrations of the glioblastoma genome become uncontrolled and occur randomly. However, in long-term ranges, the genomic imbalances are still controlled in long-term survivors.

Array-CGH is a useful tool for the identification of genetic changes of glioblastomas. Nonlinear analysis of whole-genome copy number profiles provides prognostic information for patients with glioblastoma. Statistical analysis of our results might not yield a high degree of confidence because of the limited number of cases in our study. Our results should be confirmed by further prospective studies.