The median age of our patients at diagnosis was 56 years, which is considerably lower than that reported in studies on MM from North America, Europe or Asia 
. A younger age of the patients at diagnosis, when compared with other countries, has also been reported for other hematological neoplasias in Brazil, such as myelodysplastic syndromes and myeloid leukemias 
. Besides that, a recent epidemiological survey of patients with multiple myeloma in our country showed a similar mean age and also a high frequency of advanced ISS 
. No final conclusive explanation has been found for this phenomenon. But one might speculate that this could be due to a high exposure to carcinogenic agents in Brazil. It has been shown that herbicides and pesticides are risk factors for the genesis of multiple myeloma 
. But not only farm workers with direct contact to these toxins are at risk. The general population may be frequently exposed to residual toxins in food 
Our patients showed a high frequency of advanced disease according to the ISS and additional poor risk factors. This resulted in a median survival of 24.9 months for all patients, much shorter than that reported by other studies 
. There are several possible explanations for this phenomenon. Delayed diagnosis in patients who depend on a public health system, as in our case, is not rare. In addition, unawareness of symptoms or indolence might be common in patients from lower socio-economic classes. And finally, a more aggressive character of MM in our country cannot be totally excluded. The patients with additional poor prognostic factors had a median survival of about 12.1 months, which is close to that reported by Greipp at al 
. However, only 5% of the total population reported in that study had these criteria for additional high risk.
The International Staging System (ISS), based only on two laboratory variables, the β2-microglobulin and albumin serum concentrations, has replaced the Durie-Salmon staging system in 2005 and is currently considered standard for staging of myeloma 
. It was further validated in patients in North America, Europe, and Asia; in patients below and above 65 years of age; in patients with standard therapy or autologous bone marrow transplantation; and in comparison with the Durie/Salmon staging system. The prognostic importance of this staging system was confirmed in our study.
Regarding the great variability of myeloma pathophysiology, there are additional prognostic factors, such as age, hemoglobin concentration, serum creatinine and calcium levels. But, this could not be confirmed in our investigation. Since the number of patients was relatively small, the test power was limited and we may have missed to demonstrate them as significant risk factors. Special attention was drawn to prognostic factors, which could improve a risk-stratification model able to define high-risk patients who can benefit from novel therapeutic strategies.
Plasma cell cytogenetic abnormalities and labeling index have also shown to be of prognostic value, but, these techniques require fresh unfixed material, are sophisticated and expensive, and can be performed only in few laboratories. Therefore it would be interesting to look for additional prognostic factors, which are not cost-expensive, can be examined retrospectively and be assessed independently of a specialized laboratory.
Cell morphology, evaluated subjectively by a trained observer, has also been considered a prognostic variable in multiple myelomas 
but the drawback of this method is the considerable inter-observer variability. Goasguen et al. developed a protocol for morphologic analysis of myeloma cells based on more objective morphologic criteria in routinely stained slides 
. These criteria included the presence of a nucleolus, blast-like chromatin and a nuclear-cytoplasmatic ratio >0.6, thus creating 8 possible subtypes. This procedure was able to identify an intermediate prognostic subgroup of patients, but the method was still dependent on a trained human observer 
. Leleu et al 
described in detail the nuclear shape changes in myeloma cells and created the variable “percentage of plasma cells with irregular nuclear shape”. This variable was a prognostic factor in the univariate analysis and significantly associated with other prognostic parameters such as Ki67 labeling index, hemoglobin values and hypodiploidy, but not with beta-2-microglobulin. In both studies, however, morphologic variables were not independent risk factors in multivariate regressions.
Computerized analysis of microscopic images overcomes the necessity of morphologic expertise and expert opinion and has shown to be an objective and reproducible method for diagnostic and prognostic purposes 
. Image analysis is able to detect subtle morphologic changes which cannot be recognized even by a trained observer 
. Among these techniques, the examination of the fractal characteristics of nuclear chromatin has shown to be of increasing importance 
The use of the fractal concept for image analysis has several advantages. The fractal dimension has shown to be robust against the segmentation process 
. In routine cytological preparations fractal derived variables are much less dependent on staining variations than variables derived from the grey-level co-occurrence matrix 
. Form factors, which are classically used for the quantitative description of irregular outlines, depend highly on the magnification scale, whereas fractals are scale independent 
The fractal dimension represents a statistical description but, moreover, is also intimately related to the theoretical concepts of complexity and morphogenesis. Therefore it provides a deeper insight into the understanding of the biology of normal tissues and neoplasias 
. The fractal concept, developed by Mandelbrot 
in the sixties and seventies of the last century got popularity due to the famous images created by computer programs based on fractal geometry. It is however a ubiquitous theoretical framework for many processes or objects in our known universe. Fractality implies scale-independent self-similarity or self-affinity. The fractal concept may be applied to every kind of science. Fractal characteristics can be found when measurement values of a certain variable are scale independent so that in a log-log plot the measurement points can be well approximated by a regression line. Therefore the fractal property is always related to a measurement variable. An “object” or a “process” can reveal simultaneously fractal characteristics of many different variables or features.
Introducing the fractal concept in biology and medicine has improved our understanding of many physiological processes, such as allometric scaling growth, allosteric enzyme kinetics, intracellular bio-energetic dynamics, metabolic rate in mammals, population genetics, modeling of drug clearance, neo-angiogenesis, tumor growth, organization of nucleotides in DNA and RNA, and cardiovascular physiology 
. Fractals are very useful to characterize properly the complexity of macroscopic and microscopic anatomy, namely to describe the design principles underlying living organisms.
Fractal structures can be created by iterations 
. This happens for instance during condensation of a polymer such as DNA when it is repeatedly subjected to the self-similar process of crumpling. The result is a folded polymer with fractal properties. In this way, a long polymer can be packed in a small volume without entanglements. This facilitates unravelling when necessary, as for DNA transcription, and is therefore advantageous for cell physiology 
. Recent studies using different methods of analysis showed that DNA, nuclear chromatin and the surrounding nucleoplasmic space have a fractal organization 
Our study revealed that the staining pattern of nuclear chromatin of myeloma cells, (May-Grünwald –Giemsa method) has also fractal characteristics. An important challenge is to explain, why patients with a worse prognosis, revealed an increased FD of the chromatin staining pattern in May-Grünwald –Giemsa stained smears. Changes of the nuclear architecture, observed in histological or cytological preparations, reflect genomic and non-genomic alterations.
Multiple genetic aberrations have been described during the pathogenesis of multiple myelomas 
. Secondary translocations and gene mutations have been implicated in disease progression, such as complex abnormalities of MYC, activation of N-RAS, K-RAS, and FGFR3 mutations, mutations or deletions of TP53, RB1, and PTEN and inactivation of cyclin-dependent kinase inhibitors 
Furthermore, epigenetic changes causing altered gene and protein expression play a major role in the pathogenesis of multiple myelomas. Hypermethylation of the genes p15, p16, DAP-kinase, BAD, BAK, BAX, BIK, SOCS-1, and E-Cadherin, has been reported 
Hypermethylation of CpG islands within gene promoter regions accompanied by deacetylation of histone proteins provokes transcriptional silencing. In parallel, global hypomethylation of repetitive elements occurs in association with tumor progression and increase of chromosomal instability 
. Therefore, in advanced cases, which are genetically unstable and therefore more aggressive, we expect a more complex chromatin rearrangement with global hypomethylaton and an increased number of hypermethylated CPG islands.
The routinely MGG stained cytologic smears permit to estimate the topographic localization of methylated regions in the nucleus. Co-localization analysis has shown that the deeply Giemsa-stained compacted heterochromatin domains have the same geographic distribution as the methyl-rich regions within each nucleus 
. Therefore, aggressive myelomas should have a more complex chromatin structure with an increased number of darker and lighter areas, leading to a higher fractal dimension of the nuclear chromatin, as found in our study.
Indeed, the FD of MGG-stained nuclear chromatin showed to be an independent adverse prognostic factor for the overall survival of our patients. In a similar way, previous studies have demonstrated an association between a higher FD value of the nuclear chromatin and a worse outcome of patients with other neoplasias, such as malignant melanomas, squamous cell carcinomas of the oral cavity and larynx 
This implies that the complexity of chromatin distribution contains important prognostic information which is independent of clinical variables, ISS stage, or relevant cytogenetic aberrations. In the present study, the frequency of cytogenetic abnormalities was low when compared to other reports 
. Technical problems, however, could have precluded the finding of some abnormalities.
The goodness-of-fit of the fractal dimension was also of independent prognostic relevance, but as a favorable factor. Thus a chromatin architecture closer to the "ideal fractal" was associated with a prolonged survival of the patient, as it has been shown previously for blasts of B precursor acute lymphatic leukemia 
Explanations for this finding are speculative at the moment. But it might be possible that the large number of genetic and epigenetic modifications in aggressive tumors could disturb the process of auto-organization of the nucleus to such an extent that the scale-free auto-similarity of chromatin structures is not as perfect as in less aggressive cases.
Our study revealed that both the fractal dimension and its goodness-of-fit permit to quantify DNA remodeling and methylation status in MGG-stained bone marrow smears of myeloma patients and therefore may be new and biologically relevant prognostic factors for this disease. A more detailed scientific validation of the texture analyses is necessary, of course. Data from genome-wide methylation or chromatin analyses should be compared with fractal data derived from digitalized images of routinely stained tumor smears or sections, in order to define better the equivalence between changes of the image texture and genome-wide biochemical chromatin changes.
Since there is a vast heterogeneity of molecular profiles among myeloma patients, detailed individual genomic evaluations for targeted therapies seem not to be helpful at the moment, as has been emphasized recently 
In this situation, a global evaluation of the nucleus, as presented in this investigation, could be interesting. This technique is simple, reproducible and unexpensive and may be applied to routine slides from the files, thus permitting retrospective studies without any additional costs. Therefore, we think it could be useful in daily routine practice in future. But since our study was based on a relatively small number of patients, it should, of course, be followed by confirmatory investigations based on more and new patients in different centers