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Department of Obstetrics and Gynecology (I.C., O.N.), Mount Sinai Hospital (I.C., N.S., O.N., F.I.), Toronto, Canada M5G 1X5; Department of Pediatrics (M.P., I.C.), The Hospital for Sick Children (M.P., N.S.), Toronto, Canada M5G 1X8; Departments of Physiology (M.P., N.S., I.C.) and Medical Biophysics and Computer Science (I.J.), Ontario Cancer Institute, Princess Margaret Hospital (I.J., X.Z.), Toronto, Ontario, Canada M5G 2M9; University of Toronto (I.C., M.P., N.S., I.J.), Toronto, Ontario, Canada M5S 1A1; and New Jersey Medical School (S.Z.)., Newark, New Jersey 07101-1709
Address all correspondence and requests for reprints to: Isabella Caniggia, M.D., Ph.D., Mount Sinai Hospital, Samuel Lunenfeld Research Institute, 600 University Avenue, Room 871, Toronto, Ontario, Canada M5G 1X5. E-mail: caniggia{at}mshri.on.ca.
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Abstract |
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Design: Using high-throughput functional genomics, we determined the global gene expression profiles of placentae from high altitude pregnancies, a natural in vivo model of chronic hypoxia, as well as that of first-trimester explants under 3 and 20% oxygen, an in vitro organ culture model. We next compared the genomic profile from these two models with that obtained from pregnancies complicated by preeclampsia. Microarray data were analyzed using the binary tree-structured vector quantization algorithm, which generates global gene expression maps.
Results: Our results highlight a striking global gene expression similarity between 3% O2-treated explants, high-altitude placentae, and importantly placentae from preeclamptic pregnancies. We demonstrate herein the utility of explant culture and high-altitude placenta as biologically relevant and powerful models for studying the oxygen-mediated events in preeclampsia.
Conclusion: Our results provide molecular evidence that aberrant global placental gene expression changes in preeclampsia may be due to reduced oxygenation and that these events can successfully be mimicked by in vivo and in vitro models of placental hypoxia.
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Introduction |
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TopAbstractIntroductionPatients and MethodsResultsDiscussionReferences |
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2% O2), when the intervillous space is separated from the maternal uterine circulation by endovascular trophoblastic plugs obstructing the opening of uteroplacental arteries (1). This low O2 environment is critical for early embryonic development. At 8–10 wk gestation, endovascular invasion ensues. Oxygen tension is known to regulate this process (2, 3, 4). Invasion coincides with progressive dislocation of endovascular plugs, giving rise to a dramatic increase in O2 tension within the intervillous space reaching 55–60 mm Hg (8% O2) at the initial stages of intervillous perfusion (5). This decreases to a mean of approximately 40 mm Hg toward the end of the third trimester as a result of increasing O2 extraction from the placenta and the fetus. Various locations within the same placenta are differentially perfused as central regions (proximal to the umbilical cord) are more oxygenated when compared with distal/peripheral organ sites (6). Hence, villous trophoblast cells can encounter fluctuations in O2 tension, depending on their spatial location and blood flow (6). These developmental and hemodynamic events, regulated by O2 throughout placental development, act synergistically to regulate placental development and ensure a healthy outcome. Failure of the oxygen-associated developmental events contributes to placental disease (7, 8, 9). Abnormal first-trimester trophoblast differentiation is associated with pregnancies complicated by preeclampsia and/or intrauterine growth restriction (IUGR). Preeclampsia, a disorder unique to humans, affects 5–10% of all pregnancies and remains a leading cause of fetal and maternal morbidity and mortality (10, 11). A key histopathologic correlation is shallow invasion and aberrant remodeling of maternal spiral arteries, which leads to decreased uteroplacental perfusion. Reduced perfusion in the preeclamptic placenta has been linked to inflammatory processes, oxidative stress, and even infarctions (12, 13). Experimental hypoxia is correlated with preeclampsia features, inducing trophoblast cell death, release of proinflammatory cytokines, and oxidative stress (7, 14, 15, 16). The putative effect of reduced oxygenation on global gene expression changes in placental tissues from preeclamptic patients remains unclear.
In vitro methods mimicking the effects of reduced oxygen in the human placenta are important if we are to understand the dysregulated molecular events characteristic of preeclampsia and IUGR. Several models are commonly used, including transformed cell lines, primary isolated cytotrophoblast cells, and organ culture. However, there is substantial disagreement as to the relevance and utility of these models. We therefore attempted a systematic comparison of global patterns of gene expression in in vitro first-trimester chorionic villous explants cultured under low and high O2 conditions; high-altitude (HA) placental tissue as an in vivo model of chronic hypoxia; and preeclampsia, a complex disorder widely believed to be associated with placental hypoxia. Using unbiased gene profiling, we found that aberrant gene expression in preeclampsia may be the result of reduced oxygenation and that placental explants under low-oxygen and HA placenta mimic this situation.
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Patients and Methods |
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TopAbstractIntroductionPatients and MethodsResultsDiscussionReferences |
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Tissue collections were performed in compliance with participating institutions’ ethics guidelines and in accordance with the guidelines in The Declaration of Helsinki. Each participant provided written informed consent. First-trimester human placental tissue (5–6 wk gestation, n = 10; 12–13 wk gestation, n = 12) was obtained from elective terminations by dilatation and curettage. Preeclamptic placentae [PE; n = 11 including two complicated by IUGR, and one complicated by hemolysis elevated liver enzymes and low platelets, 10 nonlabor, one labor] and preterm, normotensive, age-matched, control placentae (AMC; n = 9, four multiplets and five preterm labor, all in labor) were collected from deliveries at Mount Sinai Hospital. High-altitude (HA) and moderate-altitude (MA) placental samples (n = 8 each) were collected from normal, healthy pregnancies with spontaneous vaginal deliveries in women living at 3100 and 1600 m in Colorado. The Leadville group (3100 m) exhibited decreased overall birth weights relative to MA pregnancies (1600 m). Ten term placentae, obtained from cesarean deliveries without labor (C/S group) in healthy normotensive patients at sea level (Toronto, Canada), were also included as an additional control group. In addition, five term normal healthy placentae were used as a neutral internal reference control allowing for normalization of microarray data across various chips. The C/S group and the term reference group were normal and within healthy physiologic range for all maternal and fetal clinical parameters. Due to organ heterogeneity, multiple specimens were sampled from central and peripheral regions and both the maternal and fetal sides of term and age-matched control placentae. Areas with calcified, necrotic, or visually ischemic tissue were omitted from sampling. The preeclamptic group was selected to represent classic severe early-onset preeclampsia according to both clinical and pathological criteria based on the American College of Obstetrics and Gynecology criteria (17). All preterm and term control groups did not show clinical or pathological signs of preeclampsia, infection, or other maternal or placental disease. Clinical parameters for PE, AMC, MA, and HA participants are summarized in Table 1
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First-trimester explant culture was performed as described previously (3, 18). Explants were maintained at 37 C in either standard tissue culture condition (5% CO2-95% air) or maintained in an atmosphere of 3% O2-92% N2-5% CO2 for 48 h. Four sets of explants from four different placentae were used. A minimum of nine explants per experimental condition (3% O2 vs. 20% O2) was examined.
RNA isolation
Total RNA was isolated from individual placentae using an RNeasy kit (QIAGEN, Santa Clarita, CA). RNA quality and integrity was checked on denaturing 1.2% agarose gel. Only RNA samples demonstrating 28S to 18S rRNA ratio of 2:1 or more (as determined by densitometric analysis) were included in study. RNA was prepared to a final concentration of at least 1 µg/µl.
Microarray experiments and analyses
Figure 1 summarizes how microarray experiments were conducted. The labeling and hybridization procedures were according to University Health Network Microarray Centre’s indirect labeling protocol (http://www.microarrays.ca/support/proto.html). Tissue samples were pooled for the microarray experiments. The purpose of a pooling strategy was 2-fold. First, this strategy enabled thorough sampling, as multiple samples from the same experimental condition were combined. Second, pooling increases the signal to noise ratio within the expression data set, diminishing the false-positive discovery rate for clusters of differentially or similarly expressed genes across different experimental conditions (19). All cyanine-3-labeled experimental samples were compared with the same neutral pooled RNA sample, obtained from five term placentae acquired from vaginal deliveries of normotensive healthy women (reference RNA). The purpose of choosing a pooled reference sample was to introduce a basic normalization parameter, which improves the reliability of gene expression comparison across different experimental conditions as well as arrays (19). An equal amount of RNA (10 µg) of each individual test sample from each experimental condition was pooled. Fluorophore-labeled cDNA was hybridized to 1.7k version 4 human microarrays, containing 1700 double-spotted well-characterized human genes (http://www.microarray.ca; for a complete list of genes and related information spotted on 1.7k version 4 arrays refer to http://www.microarrays.ca/support/glists.html). Arrays were scanned using a GenePix 4000 microarray scanner and spot density was analyzed using the GenePix Pro 4.0 Acquisition and Analysis software (Axon Instruments, CA).
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Quantitative real-time PCR
To test whether pooled samples vs. individual samples would differ significantly when analyzed for gene expression, the vascular endothelial growth factor (VEGF) and the integrin 
6 Assay-on-Demand Taqman probes and primers (Applied Biosystems, Foster City, CA) were used in quantitative real-time PCR (qPCR) analyses to validate differential gene expression as predicted by the BTSVQ and statistical analyses. Analysis was done using the DNA Engine Opticon 2 system (MJ Research, Waltham, MA), and data were normalized against expression of 18S rRNA as previously described (22). Each individual sample that had been combined in the pooled experimental sample as well as the pooled sample used in the array experiment was assessed for differential gene expression. qPCR analyses were performed using three replicates of each condition at all times. Statistical significance was determined by Student’s t test, significance as defined as P < 0.05.
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Results |
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The raw data using full gene expression profiles (first- and third-trimester tissues) was subjected to an unsupervised analysis using BTSVQ software. BTSVQ combines a partitive k-means clustering and an SOM algorithm to achieve unsupervised clustering of both samples and genes. This type of unsupervised analysis divides the parent data set (data from all arrays using all gene expressions) into a binary cluster tree by iteratively using a k-means algorithm with k = 2 (Fig. 2A). SOM was then applied to clustered samples based on their quantified gene expression profiles. Partitive clustering results were cross-verified with the clusters generated by SOMs. Clustered genes, represented using SOMs, were then used to identify differentially expressed genes and visualize the global pattern of the two physiological hypoxia models (high altitude and explants cultured at 3% oxygen) and the pathological hypoxia (preeclampsia) samples. For each level of the binary tree, the genes are ranked both with respect to the likelihood of the gene being differentially expressed across all the samples in the same cluster and t statistics. This provides an accurate method of excluding genes with variable expression across samples as well as genes with low significance and thus enables selection of the most differentiating genes between clusters. The cluster structure in gene space is visualized using component planes of the already computed SOM.
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Data output: structure and reproducibility
Figure 2B
demonstrates the structure of each global expression profile obtained per microarray. Gene expression data are transformed into hexagonal map units in a component plane of a SOM. Each unit represents a group of genes with similar expression pattern selected by the SOM algorithm. This achieves data compression with minimal loss of information. The averaged gene expressions are then projected into a color space for visualization. Interpolating the color between individual map units in SOM creates the color gradient that represents a pseudoexpression value for a group of genes within a cluster (red corresponding to gene overexpression, blue representing gene underexpression relative to the reference sample). As such, a specific area within the component plane represents the same gene cluster across all arrays in the study. A similarity in color in the same area of two different component planes (e.g. 3% oxygen and high altitude) hence indicates a similar gene expression pattern. Conversely, difference in color in the same area across various component planes translates into differential gene expression. This visualization thus achieves data compression with minimal loss of information.
To help diminish the noise in microarray experiments (largely due to hybridization, washing, scanning, spot-density analysis, array spotting variability, etc.) and increase statistical power, we repeated arrays in duplicate or triplicate for each experimental condition. Figure 2B (right panel) demonstrates the reproducibility and consistency of multiple, replicate arrays derived from the same sample. We also tested whether pooling vs. examination of individual samples would bias the results. Global microarray expression profiling (BTSVQ and statistical analyses) demonstrated that VEGF transcript, a known hypoxia-induced gene (23), was differentially expressed between explants cultured under 3 and 20% O2 (3%: 1-fold increase, P = 0.0297), between high vs. moderate altitude placentae (HA: 1.7-fold increase, P = 0.0437) as well as in preeclamptic relative to age-matched control tissues (PE: 2.5-fold increase, P = 0.0463), increasing in conditions of hypoxia. Using qPCR, we demonstrated that VEGF expression was in fact significantly increased in preeclampsia and 3% explants relative to their respective controls demonstrating the validity of the expression profiling (Fig. 2C). Importantly, the data further demonstrates that there is no difference in the results obtained measuring the individual samples vs. the pooled samples, demonstrating the power and reliability of the pooling strategy (Fig. 2C). Additionally, global gene expression analyses also demonstrated the increased expression of integrin-6 between the various hypoxia conditions and their respective controls (for all conditions P < 0.05; PE vs. AMC: 1-fold increase, 3 vs. 20%: 2.5-fold increase and HA vs. MA: 0.5-fold increase). This gene, a well-known marker of immature trophoblast phenotype, was further validated using qPCR for its differential expression in the hypoxia conditions relative to their controls. Figure 2D demonstrates that integrin-6 expression is in fact significantly increased in 3% explant, PE and HA groups relative to 20% explant, AMC and MA samples, once again validating the accuracy of the expression profile analyses. Furthermore, global array analysis showed increased expression of a number of genes known to be regulated by hypoxia inducible factor (HIF) 1 in all three hypoxia experimental conditions tested (Table 2).
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Figure 3 demonstrates reproducibility of the gene expression profiles (duplicate arrays represented in Fig. 3, A–C). Figure 3A shows the gene expression profile obtained from first-trimester tissue samples (10–12 wk) and first-trimester villous explants exposed to 3 and 20% O2. Explants treated with 3 vs. 20% O2 differ considerably from one another. Whereas the 20% O2 concentration is well above the in vivo physiologic oxygen range for placental tissue, we did not observe substantive alterations in global gene expression between normal first-trimester tissues (in vivo, 10–12 wk) and 20% O2-treated explants in vitro (Fig. 3A). Figure 3B shows the gene expression pattern in moderate and high-altitude placentae, with noticeable differences in expression profile between the two and between those at sea level (Fig. 3C, term cesarean deliveries and vaginal deliveries). When PE and AMCs were compared, we also observed noticeable differences in their global gene expression profiles (Fig. 3C, center and right panels). It is important to emphasize that the AMC group is not a perfect control group because most patients within this group suffer from preterm labor. As well, it has been reported that placentae from preterm labor pregnancies exhibit a certain degree of histological similarity to those obtained from preeclamptic pregnancies (24). Moreover, the AMC group also includes four twin pregnancies. Multiple pregnancies are known to be associated with increased risk for developing preeclampsia (25). Thus, it is virtually impossible to compare gene expression obtained from the early severe onset PE group with that of a perfect (nonpathological) age-matched control group. Additionally, we also observed alterations in the global gene expression pattern between the term C/S and AMC groups (Fig. 3C, left and middle panels). The changes observed between these two control groups (C/S vs. AMC) may be attributed to differences in mean gestational age and presence of underlying pathology (leading to preterm labor) as well as absence vs. presence of spontaneous labor. Future studies are needed to address this issue.
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). These data collectively demonstrate that global gene expression in preeclampsia may be affected by reduced oxygenation and most importantly that this complex pathology can be mimicked by in vitro and in vivo models of placental hypoxia. Global gene expression analyses further demonstrated that the percentage of unchanged genes between HA vs. 3%, PE vs. HA, and 3% vs. PE was, respectively, 90.4, 94.4, and 90.8%. We also performed correlation studies to determine the degree of similarity among the three hypoxia conditions (3% explants, HA and PE) both graphically and numerically. Figure 3E depicts a graphical correlation matrix demonstrating a positive significant correlation coefficient between 3% explants and HA conditions (r = 0.43; P < 0.001). A stronger correlation was observed between HA and PE (r = 0.5; P < 0.001) and particularly between 3% explants and PE (r = 0.6; P < 0.001). These data further demonstrate that our in vitro and in vivo models of placental hypoxia can successfully mimic a global gene expression profile similar to that of PE. Of interest, HA conditions showed no correlation relative to its control MA, whereas low correlation between PE and AMC was noted. Furthermore, positive correlation between explants maintained at either 3 or 20% oxygen was observed. The latter was not surprising because the same tissues from the same placentae were used in explant cultures. Clusters of similarly and differentially expressed genes
In addition to performing global expression analyses, we also selected two highly conserved areas between the SOMs of 3% O2-treated explants, high altitude, and PE and examined the similarly and differentially expressed genes contained within these two regions (Fig. 4, areas A and B). Areas A and B were selected because they differ markedly from their respective controls (20% O2-treated explants, moderate altitude, and age-matched control placentae). The list of genes contained within areas A and B was subsequently retrieved and subjected to statistical analysis to yield commonly expressed genes among the three different hypoxic conditions. The table in Fig. 4 depicts the list of similarly expressed genes in areas A and B among the three conditions shown in Fig. 4. In addition, we included a list of differentially expressed genes (including fold changes and P value) in areas A and B, which are increasing in the three hypoxia conditions relative to their respective controls (Fig. 5).
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Discussion |
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TopAbstractIntroductionPatients and MethodsResultsDiscussionReferences |
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During in vivo placental development and before the opening of the intervillous space, placentation is known to occur in a low-oxygen environment, required for normal placental and embryonic development (26). In vitro, extravillous trophoblast cells in a low-oxygen environment maintain a noninvasive, proliferative phenotype, and low pO2 inhibits differentiation of extravillous trophoblast cells along the invasive pathway (2, 3, 8). Failure of differentiation to the invasive phenotype is thought to compromise remodeling of maternal myometrial spiral arteries and may predispose the developing placenta to a state of chronic or intermittent hypoxia and/or oxidative stress because it is the case in PE (14, 27, 28, 29). That hypoxia and/or oxidative stress are important in this pregnancy disorder is demonstrated on the organismic level by reduced uteroplacental perfusion (Doppler studies) at the organ level by markers of hypoxia and at the molecular level by an accumulating body of evidence suggesting dysregulations in HIF-1 expression in preeclampsia (4, 30, 31, 32). These findings underline the importance of investigating the global effects of reduced oxygenation on trophoblast biology using relevant experimental models.
The use of placental explant models has been previously subjected to debate (33, 34). In this study we have demonstrated the suitability, reliability, and power of an in vitro first-trimester human placental explant model as well as a naturally occurring high-altitude model of placental hypoxia for studying the global effects of reduced oxygenation in placental tissues. Using unbiased global gene expression profiling, we have shown that extrapolating findings from these models and applying them to an in vivo pathologic context is a reasonable and reproducible strategy for the study of oxygen effects on placental gene expression in two distinct but biologically relevant experimental models.
After the opening of the intervillous space, the oxygen level within the placenta is approximately 6–8% (5). However, our results support that using 20% O2 as a standard control condition in first-trimester explant studies is relevant to the in vivo situation at the end of the first trimester (after the opening of the intervillous space to maternal blood). In preeclampsia, placental perfusion can be decreased 50–70% (35), potentially resulting in an intervillous oxygen concentration of approximately 2–4% (36). It is not surprising, therefore, to observe the close similarity in global gene profiling between explants incubated under 3% oxygen and preeclamptic placental tissues. These data represent the first large-scale molecular evidence that global gene expression in preeclampsia is recapitulated by reduced oxygenation and that an immature trophoblast phenotype reminiscent of early first-trimester gestation (<8 wk gestation) is maintained (2, 3).
Placentation at high altitude has recently emerged as a natural in vivo model for studying the hypoxia-related aspect of placental pathologies such as preeclampsia and IUGR. Placentae from high altitude pregnancies (>3000 m) have decreased uterine arterial remodeling, less uteroplacental arterial invasion, increased proliferation of villous cytotrophoblast cells, decreased uteroplacental perfusion, and increased circulating levels of proinflammatory cytokines and catecholamines, similar to what is observed in preeclampsia (36, 37). In addition, the incidence of preeclampsia and IUGR is increased by 2- to 4-fold in pregnancies above 2700 m accompanied by maternal physiological changes of pregnancy that appear intermediate between normal pregnancy and preeclampsia (36). Gene profiling revealed a dramatic resemblance in the global gene expression profile between placentae from high altitude pregnancies and first-trimester villous explants kept at 3% oxygen. The striking similarity between these two conditions is likely due to both lowered PaO2 of the maternal blood entering the intervillous space and reduced uterine arterial blood flow (30%) in high-altitude pregnancies when compared with sea level (36). Our data demonstrate the first in vivo physiological effect of reduced oxygenation on global gene expression in high-altitude placentae. The resemblance between the 3% O2 first-trimester explants, preeclamptic, and high-altitude tissue supports the argument that hypoxia induces or maintains a relatively immature trophoblast phenotype.
The primary objective of our work was not to identify specific differential gene expression but rather to identify clusters of genes that may be similarly expressed in conditions of in vivo and in vitro placental hypoxia and relate these clusters to a pathologic state affected by aberrant placental oxygenation (preeclampsia). After global gene expression analyses of the entire set of arrays, we identified a number of genes commonly expressed among the three hypoxic conditions and substantially different from their respective controls. Some of these, which are known to be affected by hypoxia and/or in preeclampsia include VEGF; cytochrome P450; glutathione s-transferase 
; endothelin receptor type B; cadherin 3 (placental); coagulation factors II and VIII; E-selectin; colony stimulating factor 1; tumor protein p53; IGF binding protein 6; integrin-6; and others (38, 39, 40, 41, 42, 43). Additionally, we have reported the increased expression of seven known HIF-1 regulated genes in the three hypoxic conditions relative to their respective controls (Table 2). Array analyses showed significant differences in VEGF and integrin-6 (located outside areas A and B) and glutathione s-transferase (located inside areas A and B) between the hypoxia conditions and their respective controls. We validated using qPCR that VEGF, a well-characterized hypoxia-induced gene (23), as well as integrin-6 were differentially expressed in hypoxia conditions vs. control scenarios, increasing under reduced oxygenation. It is presently unknown whether integrin-6 is a hypoxia-regulated gene, as such future studies should address whether this gene is regulated by oxygen.
Studies have previously reported that VEGF expression is increased in placental tissue from preeclamptic and high-altitude pregnancies; in addition, in vitro studies have shown that VEGF is also augmented in primary isolated trophoblast cells cultured under reduced oxygenation (36, 44, 45, 46, 47). These findings corroborate our observation of increased VEGF expression in in vitro and in vivo models of placental hypoxia. The increased expression of VEGF in preeclampsia and high-altitude pregnancies could serve as a compensatory mechanism for reversal of impaired angiogenesis or as a direct physiologic adaptive response to reduced oxygenation (36, 46, 48). Studies have shown that trophoblast cells in preeclamptic and high-altitude placentae as well as explants cultured under low oxygen (3%) exhibit an undifferentiated proliferative phenotype (2, 3, 8, 36, 49). Interestingly, the expression of integrin-6, previously reported to be restricted to undifferentiated/proliferative cytotrophoblast cells (50), is increased in the current experimental models, a finding that support the idea that under hypoxia conditions trophoblast cells maintain an immature phenotype. Finally, we should point out that preeclampsia is also a condition characterized by oxidative stress (27). Interestingly, it has been reported that expression of glutathione s-transferases , a member of a family of enzymes with peroxidase activity, is increased in preeclamptic pregnancies as well as under hypoxic conditions in carcinogenic cell lines and rats exposed to hypoxia (51, 52, 53, 54). Our results agree with these observations and may highlight a role for this enzyme as a compensatory mechanism to prevent further oxidative damage under reduced oxygenation.
Transition from an in vivo environment to a more minimalist in vitro experimental model often results in loss of physiological parameters that may adversely affect the integrity and reliability of the experiment. In this study we have shown that mimicry of a complex biological scenario in vitro is in fact feasible. We have demonstrated herein that aberrant changes in global placental gene expression in preeclampsia may be due to reduced oxygenation and that in vivo and in vitro manipulations yield similar expression profiles relevant to oxygenation of the tissue of interest. Both the villous explant culture and the high-altitude model are supported here as biologically relevant models for studying placental pathologies characterized by aberrant oxygenation. The functional genomic approach devised in this study is both powerful and reproducible, meriting further exploration of the similarly and differentially expressed gene clusters examined here.
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Acknowledgments |
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Footnotes |
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First Published Online April 19, 2005
Abbreviations: AMC, Preterm, normotensive, age-matched, control placentae; BTSVQ, binary tree-structured vector quantization; C/S, term placentae, obtained from cesarean deliveries without labor; HA, high altitude; HIF, hypoxia inducible factor; IUGR, intrauterine growth restriction; MA, moderate altitude; PE, preeclamptic placentae; qPCR, quantitative real-time PCR; SOM, self-organizing map; VEGF, vascular endothelial growth factor.
Received January 13, 2005.
Accepted April 7, 2005.
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