BACKGROUND
genes are not randomly distributed and their coordinated expression is regulated by their position along chromosomes  <cit> .
new mathematical approaches are therefore needed for the analysis of expression microarrays in order to identify variations in expression of spatially related genes and map them along chromosomes.
the relationship between changes in dna copy number and variations of mrna expression has been previously investigated  but only a few studies have used microarrays to examine large chromosomal abnormalities  <cit> .
here we propose a novel mathematical model based on single value decomposition  and haar wavelets, named chromowave, that detect variations in expression of spatially related gene and visualise them on chromosomes.
wavelets are a recently introduced mathematical tool for the treatment of signals with "non-stationary behaviour"  <cit>  .
the counterpart of the wavelet transform is the fourier transform that achieves optimal encoding of periodic signals.
the use of wavelets for data encoding, transmission and compression is now pervasive in many fields including analysis of gene sequences and functional genomics data  <cit> .
application to microarrays has been proposed for the analysis of light signals of microarrays plates  <cit>  or to de-noise microarray time-series  <cit> .
only three studies applied wavelets to explore the variation in expression of gene clusters and identify their position on chromosomes  <cit> .
allen et al.
<cit>  first adopted the wavelet transform and used smooth wavelets to study periodical patterns of mrna expression elicited by different promoters in the e. coli genome.
using a supervised statistical approach, we introduced the haar wavelet analysis for the detection of chromosomal patterns of expression in neurodegenerative diseases  <cit> .
the same methodology was validated by hsu et al.
<cit>  to denoise array-based comparative genomic hybridization  data.
aggarwal et al  <cit>  combined wavelets with an empirical supervised approach to analyze chromosomal expression in a set of tumour cell-lines and matched the extracted clusters with abnormal karyotypes.
their technique was limited as it allowed the analysis of only one cell-line at a time.
these two studies demonstrated that wavelets have the ability to identify the areas on chromosomes where genes show similar and coherent levels of expression.
in chromowave, the haar wavelet model has been further refined relaxing the previous approximation of constant gene-gene distance by taking into account the variability of inter-probe distance throughout the genome.
here, we have applied chromowave to a sample of  <dig> low grade and anaplastic diffuse gliomas  and we have demonstrated its ability of extracting and visualizing large patterns of chromosomal expression that underpin meaningful biological variation and that are relevant to clinical outcome.
results were cross-validated by application of the technique to a matching data-set previously published by another laboratory  <cit> .
RESULTS
when applied to the data-set containing the  <dig> tumour cases, the first pattern generated by chromowave  consisted in a multi-chromosomal pattern of variation that revealed considerably reduced gene expression in large regions of chromosomes 1p, 9q, and 19q and of the whole chromosomes  <dig>   <dig>   <dig> and  <dig>  smaller clusters of differentially expressed genes were also observed on the other chromosomes, particularly  <dig>   <dig>   <dig>   <dig>   <dig> and negligible variations were present on chromosomes  <dig>   <dig>   <dig>  and xp.
this pattern is illustrated in figure  <dig> and relative data are contained in the additional file  <dig>  remaining patterns accounted for < 10% of the data variability and were not considered.
note the clean display of the profiles that are completely de-noised.
figure  <dig> illustrates the individual profile for case o <dig> extracted using the supervised technique previously developed  <cit> .
for this data-set, fish analysis demonstrated various combinations of monosomy on chromosomes 1p, 9q,  <dig>   <dig>   <dig>   <dig> and 19q, .
this table illustrates the combined variation of gene expression of chromosomes 1p,  <dig>  9p,  <dig>   <dig>   <dig>  19q detected by chromowave and the variations detected by fish analysis.
note that the case-loadings reflect the normalization to the average that is performed by the svd.
therefore, the more positive the case loading is the greater is the loss.
as a rule of thumb loadings close to or grater than zero indicate monosomy.
positive cases are highlighted in bold.
cases underlined are hyperploid and cases highlighted in italics showed a discrepancy between fish and chromowave  – o: oligodendroglioma – oa: oligoastrocytoma – a: astrocytoma – aa: anaplastic astrocytoma; ii grade ii, iii grade iii – na: not available.
we then compared fish measurements to the individual chromosomal expressions extracted by chromowave.
when applied to one chromosome at a time, the svd extracted as main components  chromosome wide diffuse signals on chromosomes  <dig>   <dig>   <dig>   <dig> and  <dig> and diffuse homogeneous expression on the chromosomal arms 1p and 19q.
case loadings for these patterns are displayed in table  <dig>  note that the case-loadings in table  <dig> reflect the normalization to the average that is performed by the svd.
therefore, the more positive the case loading is the more the pattern is expressed , the more negative the loading the less the pattern is expressed.
when we compared the fish measurements with these case-loadings we observed significant association for chromosome 1p  and 19q  indicating that loss of genetic material was the main cause of the reduction of expression seen by chromowave.
interestingly, one oligodendroglioma  clearly demonstrated low expression 1p/19q with chromowave but no structural loss could be detected by fish .
the reduced mrna expression detected by chromowave on chromosomes  <dig>  9q,  <dig>   <dig> and  <dig> was less commonly associated with chromosomal alterations seen by fish .
in particular, six tumours showed low expression of 9q without alteration detected by fish and among the seven lesions demonstrating low expression in chromosome  <dig>  only one showed monosomy.
the discrepancy between fish counts and expression data raises several hypotheses.
first, this may be inherent to the fish method where the probe targets only a short dna sequence on the chromosome and is not informative of possible large losses of genetic material in regions flanking the probe target.
the chromosomal areas targeted by the fish probes are shown on figure  <dig>  second, alternative genetic and epigenetic mechanisms can cause expression changes in adjacent genes in the absence of chromosomal loss such as translocation, uniparental disomy or methylation/acetylation silencing, all frequently reported in cancer.
third, hyperploidy which is frequently seen in malignant gliomas may also account for some of these observations.
conversely, in three cases, chromowave case loading was quite negative while fish demonstrated loss of genetic material .
however, inspection of individual cases  allowed the following observations.
in case  <dig>  chromowave did not display a chromosome wide reduction but in 9q.
<dig>  showed a region of  <dig> kb with selective loss of expression around the ass gene that is targeted by the fish probe .
for case o <dig>  chromowave showed loss of expression but restricted to small clusters including a telomeric region of  <dig>  mb in chromosome 13q <dig> before and around the rb gene where the fish target is located .
case o <dig> also had loss of expression on 1p but restricted to a telomeric segment of  <dig> mb that included the chr1p <dig>  locus targeted by the fish probe .
this finding suggests that in these cases fish recognized small alterations and not large structural anomalies that were instead identified by chromowave.
when we tested the case loadings identified by chromowave with outcome  using cox regression, we found that the pattern in figure  <dig> was significantly predictive of favourable outcome .
by testing each of the chromosomes and their various combinations we then observed that the covariation of chromosomes 1p,  <dig> and 18had the strongest correlation with survival .
in contrast, the major gene expression pattern obtained with the same svd analysis but without haar wavelet transformation did not correlate with survival  suggesting that the distribution of gene expression changes on chromosomes is more relevant to tumour behaviour than their raw variations of amplitude.
sensitivity to individual cases
in order to verify the stability of the pattern and its dependency upon single cases, we performed a jack-knife test to verify that association remained significant with the exclusion of single cases.
the genome-wide svd analysis was repeated after removal of one case , the chromosomal pattern was extracted and stored, and the correlation of the resulting case loadings with survival re-calculated using cox regression, this process generated  <dig> p-values.
the 95% confidence interval of the empirical p-value distribution obtained was calculated by normal approximation of the log-transformed p-values.
throughout the  <dig> permutations, the global patterns recovered were indistinguishable from that obtained with all cases, all the  <dig> patterns were significantly associated with outcome  and resulting p-values were tightly distributed .
sensitivity to chromosome biology: chromosome y and gender sensitivity
for validation purposes, chromowave was applied only to the probes of chromosome y only for the  <dig> tumour cases.
the main pattern of variation was extracted and the association between resulting case loadings and gender was tested by means of a student t-test.
the main component extracted by the algorithm, which accounted for 94% of the variability, was a uniform pattern on the chromosome .
the corresponding case loadings are shown in figure 4b and illustrate the perfect separation of arrays according to gender .
numerical values for the loadings are also contained in table  <dig>
sensitivity to denoising parameters
the settings used in this work , inter-probe distance penalization at eq.)
were chosen at the very conservative end of standard wavelet methodology with the deliberate aim to minimize false positives at the expense of sensitivity.
figure  <dig> illustrates the incremental effect of the applied methodology  to the analysis of chr.
<dig> for this data-set.
note the ability of the technique to render a clean profile for the chr1p anomaly that is common in the types of gliomas considered here.
importantly, the additional penalization for inter-probe distance  removes entirely the remaining spikes on chr1p rendering a clean and biologically sensible profile.
as independent validation of the pattern extracted by chromowave on chr.
<dig>  we calculated the power spectrum of the ordered probes on chr1p.
the spectrum of the raw data and the one of the de-noised pattern are illustrated in figure  <dig>  note that the de-noising procedure removes the noise in the high frequencies but preserves the large structure in the signal that is obviously present at frequencies of less than  <dig> hz.
the power spectrum calculation adopts the fft and is based on the assumption of equidistant probes.
this assumption is relaxed in chromowave.
sensitivity/specificity analysis
although the technique presented here is unsupervised, its sensitivity/specificity can be evaluated through simulation studies by assuming the signal distribution known.
the main problem with simulations in this context is the faithful generation of the noise covariance structure of chromosomal expression that is unknown.
to recover the noise covariance we have selected chr <dig> that has evident chr1p loss pattern in this data-set.
we have removed from the data-set this specific monosomy by zeroing the first singular component.
the remaining singular components had morgera's complexity ~ <dig>  <cit>  indicating that all that was left was noise.
we have therefore built a simulation by adding a telomeric pattern of various intensities  and of varying spatial dimensions  to  <dig> of the  <dig> arrays.
in the second simulation we maintained a chr1p loss pattern but varied the number of arrays to which the pattern was added.
the detection/specificity measure was obtained by generating, for each intensity,  <dig> permutations of the arrays and therefore adding the signal to a random sub-set.
at each iteration, chromowave extracted the first eigenvector of the wavelet transformed data and a student's t-test  was performed between the two groups of arrays .
the detection metric was calculated as the number the null-hypothesis rejected divided by the number of permutations.
results for the  <dig> simulations are shown in figure  <dig> in terms of detection versus intensity.
the latter is shown in log <dig> scale .
in general terms, any pattern change greater than ~ <dig>   is detected with probability  <dig> whatever the size or the sub-set of arrays it affects.
specificity was always below or equal the specified limit  in all conditions tested confirming that noise distribution adhered to the assumptions.
clinical reproducibility: application to freije et al.
dataset
final validation was performed by assessing the reproducibility of the association between chromosomes 1p,  <dig> and  <dig> and outcome in a published set of arrays of comparable tumour types.
the only comparable data-set that was publicly available at the time of writing was published by freije et al.
<cit> .
microarray files  and clinical data were downloaded from the authors' website  <cit> .
we excluded glioblastomas from the set and we examined the  <dig> arrays that included  <dig> anaplastic oligodendrogliomas,  <dig> anaplastic astrocytomas and  <dig> mixed anaplastic oligo-astrocytomas.
microarray files were pre-processed and normalized using the same procedure adopted for our data and then entered into chromowave.
chromosomal expressions were obtained by application of the svd to each chromosome independently.
as in our data-set, diffuse patterns of expression were found in chromosomes 1p,  <dig>   <dig>   <dig>   <dig> and 19q.
case loadings for chromosomes 1p,  <dig> and  <dig> were then entered into a cox regression model to test their association with survival that resulted being remarkably strong  and similar to what found in our data-set.
discussion
chromowave allows the unsupervised identification of clusters of adjacent genes with homogeneous changes of expression and their mapping on chromosomes, resulting in the display of multi-chromosomal gene expression patterns.
here we have demonstrated that these patterns are reliable, reproducible and statistically robust but that they are also clinically relevant.
in this application, the svd was the method of choice for statistical analysis in wavelet space: however this approach is amenable to treatment with any other unsupervised technique .
low grade and anaplastic diffuse gliomas represent an interesting model to explore the variation of expression of spatially related genes rather than their individual expression.
characteristic genetic and epigenetic alterations have been found that predict favourable outcome in some tumour histological subtypes while being non informative or even carrying a poor prognosis in others.
for instance, the extensively investigated allelic loss of chromosomes 1p/19q or the hypermethylation of the promoter of the drug-resistance gene o6-methylguanine-dna methyltranferase are associated with chemosensitivity and therefore longer survival in a subset of oligodendrogliomas  <cit>  but have unclear prognostic value or even correlate with more aggressive behaviour in astrocytomas and mixed oligoastrocytomas  <cit> .
moreover, no strong candidate tumour suppressor/promoter gene has been singled out yet on these frequently lost chromosomal segments  <cit> .
a few studies have used expression microarrays to investigate diffuse gliomas  <cit>  but none explored the expression change of gene clusters that could be relevant to tumour progression with regards to their distribution on chromosomes.
in our microarray dataset, derived for a group of  <dig> who grade ii and iii gliomas, chromowave generated a multi-chromosomal pattern of variation that correlated with outcome.
the pattern included diffuse losses on 1p and 19q but also on  <dig>  9q,  <dig> and  <dig>  among these, changes on 1p,  <dig> and  <dig> had the strongest correlation with survival.
this finding was replicated on a comparable set of microarray data previously published by another laboratory  <cit> .
notably, while the main pattern of chromosomal variation extracted by the svd correlated with survival, the main pattern of rna variation extracted by the svd from the raw data  did not.
this suggests a major role of chromosomal rna modulation in tumour behaviour as opposed to the variation of the bulk of gene expression.
fish studies suggested that, in our dataset, low expression on chromosomes 1p and 19q were most often the consequence of large allelic loss in these regions, an alteration commonly seen in oligodendrogliomas.
however, fish counts could not explain the diffusely reduced expression on  <dig>  9q,  <dig> and  <dig> raising several hypotheses: genetic loss occurring in regions flanking the fish probe targets, genetic changes that do not result in gene loss detectable by fish such as translocation and uniparental disomy, or epigenetic alterations such as methylation-based gene silencing.
clearly, extensive ancillary studies are needed to determine the various mechanisms underlying the chromowave gene expression patterns.
comparative genomic hybridisation , allelic polymorphism analysis and methylation studies are currently in progress in our laboratory.
whatever the causative mechanisms, the finding that large gene expression changes in chromosomes  <dig>  9q,  <dig> and  <dig> occur frequently in grade ii and iii diffuse gliomas and that they bear prognostic information is novel.
CONCLUSIONS
in conclusion, we propose a new mathematical model that has proved powerful in our dataset for detecting and mapping to chromosomes biologically meaningful gene expression changes.
the possibility of visualising changes of spatially related genes and their position on chromosomes make chromowave a valuable screening method to explore microarray datasets.
the mechanisms contributing to these expression patterns are probably multiple and complex.
additional studies combining fish, cgh/acgh, allelic polymorphism and methylation analysis are clearly needed and should target those chromosomal areas identified by chromowave as supporting clinically relevant gene expression changes.

 genes are not randomly distributed and their coordinated expression is regulated by their position along chromosomes. new mathematical approaches are therefore needed for the analysis of expression microarrays in order to identify variations in expression of spatially related genes and map them along chromosomes. the relationship between changes in dna copy number and variations of mrna expression has been previously investigated but only a few studies have used microarrays to examine large chromosomal abnormalities. here we propose a novel mathematical model based on single value decomposition and haar wavelets, named chromowave, that detect variations in expression of spatially related gene and visualise them on chromosomes. wavelets are a recently introduced mathematical tool for the treatment of signals with "non-stationary behaviour". the counterpart of the wavelet transform is the fourier transform that achieves optimal encoding of periodic signals. the use of wavelets for data encoding, transmission and compression is now pervasive in many fields including analysis of gene sequences and functional genomics data. application to microarrays has been proposed for the analysis of light signals of microarrays plates or to de-noise microarray time-series. only three studies applied wavelets to explore the variation in expression of gene clusters and identify their position on chromosomes. allen et al. first adopted the wavelet transform and used smooth wavelets to study periodical patterns of mrna expression elicited by different promoters in the e. coli genome. using a supervised statistical approach, we introduced the haar wavelet analysis for the detection of chromosomal patterns of expression in neurodegenerative diseases. the same methodology was validated by hsu et al. to denoise array-based comparative genomic hybridization data. aggarwal et al combined wavelets with an empirical supervised approach to analyze chromosomal expression in a set of tumour cell-lines and matched the extracted clusters with abnormal karyotypes. their technique was limited as it allowed the analysis of only one cell-line at a time. these two studies demonstrated that wavelets have the ability to identify the areas on chromosomes where genes show similar and coherent levels of expression. in chromowave, the haar wavelet model has been further refined relaxing the previous approximation of constant gene-gene distance by taking into account the variability of inter-probe distance throughout the genome. here, we have applied chromowave to a sample of low grade and anaplastic diffuse gliomas and we have demonstrated its ability of extracting and visualizing large patterns of chromosomal expression that underpin meaningful biological variation and that are relevant to clinical outcome. results were cross-validated by application of the technique to a matching data-set previously published by another laboratory.  when applied to the data-set containing the tumour cases, the first pattern generated by chromowave consisted in a multi-chromosomal pattern of variation that revealed considerably reduced gene expression in large regions of chromosomes 1p, 9q, and 19q and of the whole chromosomes and smaller clusters of differentially expressed genes were also observed on the other chromosomes, particularly and negligible variations were present on chromosomes and xp. this pattern is illustrated in figure and relative data are contained in the additional file remaining patterns accounted for < 10% of the data variability and were not considered. note the clean display of the profiles that are completely de-noised. figure illustrates the individual profile for case o extracted using the supervised technique previously developed. for this data-set, fish analysis demonstrated various combinations of monosomy on chromosomes 1p, 9q, and 19q,. this table illustrates the combined variation of gene expression of chromosomes 1p, 9p, 19q detected by chromowave and the variations detected by fish analysis. note that the case-loadings reflect the normalization to the average that is performed by the svd. therefore, the more positive the case loading is the greater is the loss. as a rule of thumb loadings close to or grater than zero indicate monosomy. positive cases are highlighted in bold. cases underlined are hyperploid and cases highlighted in italics showed a discrepancy between fish and chromowave – o: oligodendroglioma – oa: oligoastrocytoma – a: astrocytoma – aa: anaplastic astrocytoma; ii grade ii, iii grade iii – na: not available. we then compared fish measurements to the individual chromosomal expressions extracted by chromowave. when applied to one chromosome at a time, the svd extracted as main components chromosome wide diffuse signals on chromosomes and and diffuse homogeneous expression on the chromosomal arms 1p and 19q. case loadings for these patterns are displayed in table note that the case-loadings in table reflect the normalization to the average that is performed by the svd. therefore, the more positive the case loading is the more the pattern is expressed, the more negative the loading the less the pattern is expressed. when we compared the fish measurements with these case-loadings we observed significant association for chromosome 1p and 19q indicating that loss of genetic material was the main cause of the reduction of expression seen by chromowave. interestingly, one oligodendroglioma clearly demonstrated low expression 1p/19q with chromowave but no structural loss could be detected by fish. the reduced mrna expression detected by chromowave on chromosomes 9q, and was less commonly associated with chromosomal alterations seen by fish. in particular, six tumours showed low expression of 9q without alteration detected by fish and among the seven lesions demonstrating low expression in chromosome only one showed monosomy. the discrepancy between fish counts and expression data raises several hypotheses. first, this may be inherent to the fish method where the probe targets only a short dna sequence on the chromosome and is not informative of possible large losses of genetic material in regions flanking the probe target. the chromosomal areas targeted by the fish probes are shown on figure second, alternative genetic and epigenetic mechanisms can cause expression changes in adjacent genes in the absence of chromosomal loss such as translocation, uniparental disomy or methylation/acetylation silencing, all frequently reported in cancer. third, hyperploidy which is frequently seen in malignant gliomas may also account for some of these observations. conversely, in three cases, chromowave case loading was quite negative while fish demonstrated loss of genetic material. however, inspection of individual cases allowed the following observations. in case chromowave did not display a chromosome wide reduction but in 9q. showed a region of kb with selective loss of expression around the ass gene that is targeted by the fish probe. for case o chromowave showed loss of expression but restricted to small clusters including a telomeric region of mb in chromosome 13q before and around the rb gene where the fish target is located. case o also had loss of expression on 1p but restricted to a telomeric segment of mb that included the chr1p locus targeted by the fish probe. this finding suggests that in these cases fish recognized small alterations and not large structural anomalies that were instead identified by chromowave. when we tested the case loadings identified by chromowave with outcome using cox regression, we found that the pattern in figure was significantly predictive of favourable outcome. by testing each of the chromosomes and their various combinations we then observed that the covariation of chromosomes 1p, and 18had the strongest correlation with survival. in contrast, the major gene expression pattern obtained with the same svd analysis but without haar wavelet transformation did not correlate with survival suggesting that the distribution of gene expression changes on chromosomes is more relevant to tumour behaviour than their raw variations of amplitude. sensitivity to individual cases in order to verify the stability of the pattern and its dependency upon single cases, we performed a jack-knife test to verify that association remained significant with the exclusion of single cases. the genome-wide svd analysis was repeated after removal of one case, the chromosomal pattern was extracted and stored, and the correlation of the resulting case loadings with survival re-calculated using cox regression, this process generated p-values. the 95% confidence interval of the empirical p-value distribution obtained was calculated by normal approximation of the log-transformed p-values. throughout the permutations, the global patterns recovered were indistinguishable from that obtained with all cases, all the patterns were significantly associated with outcome and resulting p-values were tightly distributed. sensitivity to chromosome biology: chromosome y and gender sensitivity for validation purposes, chromowave was applied only to the probes of chromosome y only for the tumour cases. the main pattern of variation was extracted and the association between resulting case loadings and gender was tested by means of a student t-test. the main component extracted by the algorithm, which accounted for 94% of the variability, was a uniform pattern on the chromosome. the corresponding case loadings are shown in figure 4b and illustrate the perfect separation of arrays according to gender. numerical values for the loadings are also contained in table sensitivity to denoising parameters the settings used in this work, inter-probe distance penalization at eq.) were chosen at the very conservative end of standard wavelet methodology with the deliberate aim to minimize false positives at the expense of sensitivity. figure illustrates the incremental effect of the applied methodology to the analysis of chr. for this data-set. note the ability of the technique to render a clean profile for the chr1p anomaly that is common in the types of gliomas considered here. importantly, the additional penalization for inter-probe distance removes entirely the remaining spikes on chr1p rendering a clean and biologically sensible profile. as independent validation of the pattern extracted by chromowave on chr. we calculated the power spectrum of the ordered probes on chr1p. the spectrum of the raw data and the one of the de-noised pattern are illustrated in figure note that the de-noising procedure removes the noise in the high frequencies but preserves the large structure in the signal that is obviously present at frequencies of less than hz. the power spectrum calculation adopts the fft and is based on the assumption of equidistant probes. this assumption is relaxed in chromowave. sensitivity/specificity analysis although the technique presented here is unsupervised, its sensitivity/specificity can be evaluated through simulation studies by assuming the signal distribution known. the main problem with simulations in this context is the faithful generation of the noise covariance structure of chromosomal expression that is unknown. to recover the noise covariance we have selected chr that has evident chr1p loss pattern in this data-set. we have removed from the data-set this specific monosomy by zeroing the first singular component. the remaining singular components had morgera's complexity ~ indicating that all that was left was noise. we have therefore built a simulation by adding a telomeric pattern of various intensities and of varying spatial dimensions to of the arrays. in the second simulation we maintained a chr1p loss pattern but varied the number of arrays to which the pattern was added. the detection/specificity measure was obtained by generating, for each intensity, permutations of the arrays and therefore adding the signal to a random sub-set. at each iteration, chromowave extracted the first eigenvector of the wavelet transformed data and a student's t-test was performed between the two groups of arrays. the detection metric was calculated as the number the null-hypothesis rejected divided by the number of permutations. results for the simulations are shown in figure in terms of detection versus intensity. the latter is shown in log scale. in general terms, any pattern change greater than ~ is detected with probability whatever the size or the sub-set of arrays it affects. specificity was always below or equal the specified limit in all conditions tested confirming that noise distribution adhered to the assumptions. clinical reproducibility: application to freije et al. dataset final validation was performed by assessing the reproducibility of the association between chromosomes 1p, and and outcome in a published set of arrays of comparable tumour types. the only comparable data-set that was publicly available at the time of writing was published by freije et al.. microarray files and clinical data were downloaded from the authors' website. we excluded glioblastomas from the set and we examined the arrays that included anaplastic oligodendrogliomas, anaplastic astrocytomas and mixed anaplastic oligo-astrocytomas. microarray files were pre-processed and normalized using the same procedure adopted for our data and then entered into chromowave. chromosomal expressions were obtained by application of the svd to each chromosome independently. as in our data-set, diffuse patterns of expression were found in chromosomes 1p, and 19q. case loadings for chromosomes 1p, and were then entered into a cox regression model to test their association with survival that resulted being remarkably strong and similar to what found in our data-set. discussion chromowave allows the unsupervised identification of clusters of adjacent genes with homogeneous changes of expression and their mapping on chromosomes, resulting in the display of multi-chromosomal gene expression patterns. here we have demonstrated that these patterns are reliable, reproducible and statistically robust but that they are also clinically relevant. in this application, the svd was the method of choice for statistical analysis in wavelet space: however this approach is amenable to treatment with any other unsupervised technique. low grade and anaplastic diffuse gliomas represent an interesting model to explore the variation of expression of spatially related genes rather than their individual expression. characteristic genetic and epigenetic alterations have been found that predict favourable outcome in some tumour histological subtypes while being non informative or even carrying a poor prognosis in others. for instance, the extensively investigated allelic loss of chromosomes 1p/19q or the hypermethylation of the promoter of the drug-resistance gene o6-methylguanine-dna methyltranferase are associated with chemosensitivity and therefore longer survival in a subset of oligodendrogliomas but have unclear prognostic value or even correlate with more aggressive behaviour in astrocytomas and mixed oligoastrocytomas. moreover, no strong candidate tumour suppressor/promoter gene has been singled out yet on these frequently lost chromosomal segments. a few studies have used expression microarrays to investigate diffuse gliomas but none explored the expression change of gene clusters that could be relevant to tumour progression with regards to their distribution on chromosomes. in our microarray dataset, derived for a group of who grade ii and iii gliomas, chromowave generated a multi-chromosomal pattern of variation that correlated with outcome. the pattern included diffuse losses on 1p and 19q but also on 9q, and among these, changes on 1p, and had the strongest correlation with survival. this finding was replicated on a comparable set of microarray data previously published by another laboratory. notably, while the main pattern of chromosomal variation extracted by the svd correlated with survival, the main pattern of rna variation extracted by the svd from the raw data did not. this suggests a major role of chromosomal rna modulation in tumour behaviour as opposed to the variation of the bulk of gene expression. fish studies suggested that, in our dataset, low expression on chromosomes 1p and 19q were most often the consequence of large allelic loss in these regions, an alteration commonly seen in oligodendrogliomas. however, fish counts could not explain the diffusely reduced expression on 9q, and raising several hypotheses: genetic loss occurring in regions flanking the fish probe targets, genetic changes that do not result in gene loss detectable by fish such as translocation and uniparental disomy, or epigenetic alterations such as methylation-based gene silencing. clearly, extensive ancillary studies are needed to determine the various mechanisms underlying the chromowave gene expression patterns. comparative genomic hybridisation, allelic polymorphism analysis and methylation studies are currently in progress in our laboratory. whatever the causative mechanisms, the finding that large gene expression changes in chromosomes 9q, and occur frequently in grade ii and iii diffuse gliomas and that they bear prognostic information is novel.  in conclusion, we propose a new mathematical model that has proved powerful in our dataset for detecting and mapping to chromosomes biologically meaningful gene expression changes. the possibility of visualising changes of spatially related genes and their position on chromosomes make chromowave a valuable screening method to explore microarray datasets. the mechanisms contributing to these expression patterns are probably multiple and complex. additional studies combining fish, cgh/acgh, allelic polymorphism and methylation analysis are clearly needed and should target those chromosomal areas identified by chromowave as supporting clinically relevant gene expression changes. 
chromowave generated multi-chromosomal pattern featuring low expression in chromosomes 1p, 9q, and 19q. in this study, fish data showed that monosomy was frequently associated with diffuse low gene expression on chromosome 1p and 19q but not on chromosomes 9q, and comparative genomic hybridisation, allelic polymorphism analysis and methylation studies are in progress in order to identify the various mechanisms involved in this multi-chromosomal expression pattern. fish analysis indicated that monosomy 1p and 19q was a frequent feature of tumours displaying the chromowave pattern but that allelic loss on chromosomes 9q, and was much less common. expression microarrays represent a powerful technique for the simultaneous investigation of thousands of genes. this pattern was not only statistically robust but also clinically relevant as it was predictive of favourable outcome. the ability to detect expression changes of spatially related genes and to map their position on chromosomes makes chromowave a valuable screening method for the identification and display of regional gene expression changes of clinical relevance.
 expression microarrays represent a powerful technique for the simultaneous investigation of thousands of genes. the evidence that genes are not randomly distributed in the genome and that their coordinated expression depends on their position on chromosomes has highlighted the need for mathematical approaches to exploit this dependency for the analysis of expression data-sets.  we have devised a novel mathematical technique based on the haar wavelet transform and applied it to a dataset obtained with the affymetrix® hg-u133_plus_ array in gliomas. chromowave generated multi-chromosomal pattern featuring low expression in chromosomes 1p, 9q, and 19q. this pattern was not only statistically robust but also clinically relevant as it was predictive of favourable outcome. this finding was replicated on a data-set independently acquired by another laboratory. fish analysis indicated that monosomy 1p and 19q was a frequent feature of tumours displaying the chromowave pattern but that allelic loss on chromosomes 9q, and was much less common.  the ability to detect expression changes of spatially related genes and to map their position on chromosomes makes chromowave a valuable screening method for the identification and display of regional gene expression changes of clinical relevance. in this study, fish data showed that monosomy was frequently associated with diffuse low gene expression on chromosome 1p and 19q but not on chromosomes 9q, and comparative genomic hybridisation, allelic polymorphism analysis and methylation studies are in progress in order to identify the various mechanisms involved in this multi-chromosomal expression pattern. 