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Current Alzheimer Research, 2012, 9, 000-000 1
1567-2050/12 $58.00+.00 © 2012 Bentham Science Publishers
The Nun Study: Risk Factors for Pathology and Clinical-Pathologic
Correlations
James A. Mortimer*
Department of Epidemiology of Biostatistics, University of South Florida, Tampa, Florida, USA
Abstract: The Nun Study was the first cohort study to enroll and follow a large, well-defined population that included
demented and non-demented participants, all of whom agreed to donate their brains for research. The inclusion of system-
atic neuropathologic analysis in this study has resulted in a greater understanding of the role of Alzheimer and vascular
pathology in the expression of memory deficits and dementia and has provided data showing that biomarkers for the pa-
thology may be evident many decades earlier in adult life. Findings related to neuropathology in this study have included
the following: (1) Although clinical outcomes were strongly correlated with Alzheimer neuropathology, about one-third of
the participants fulfilling criteria for neuropathologic Alzheimer’s disease (AD) were not demented at the time of death.
(2) Brain infarcts by themselves had little effect on cognitive status, but played an important role in increasing the risk o f
dementia associated with Alzheimer pathology. (3) Hippocampal volume was strongly correlated with Braak neurofibril-
lary stage even in participants with normal cognitive function. (4) A linguistic characteristic of essays written in early
adult life, idea density, had a strong association with not only clinical outcomes in late life, but the severity of Alzheimer
neuropathology as well. (5) The effect of apolipoprotein E-e4 on dementia was mediated through Alzheimer, but not vas-
cular pathology.
Keywords: Alzheimer’s disease, brain infarcts, clinical-pathologic correlation, dementia, epidemiologic cohort study, risk fac-
tors.
THE NUN STUDY
The Nun Study began as a study of successful aging in
1986 with a pilot study of 100 Catholic School Sisters of
Notre Dame living at a single convent in Mankato, Minne-
sota [1]. Its initial publications dealt with the role of educa-
tion in longevity and independence in activities of daily liv-
ing [2, 3]. The focus on Alzheimer’s disease resulted from a
chance meeting between David Snowdon, the principal in-
vestigator of the initial study, and myself at his poster pres-
entation at the Gerontological Society of America meeting in
1988 [1]. My previous work had included an epidemiologic
case-control study of Alzheimer’s disease and clinical-
pathologic studies of selected patients with Alzheimer’s and
Parkinson’s diseases. I was intrigued by the possibility that
the origins of Alzheimer’s disease might be found in early
life and that increased brain reserve resulting from early edu-
cation and brain development might forestall presentation of
symptoms. Snowdon’s finding that more educated sisters
lived longer [2] and had better mental as well as physical
function at any age [3] led to the initial hypothesis behind
our NIH application for the Nun Study, that better-educated
sisters had greater brain reserve and therefore may have
higher resistance to the expression of Alzheimer symptoms.
The existence of archives at the convents containing high
school and college transcripts, photographs, detailed records
about the sister’s lifelong activities, and autobiographies
*Address correspondence to this author at the Department of Epidemiology
and Biostatistics, University of South Florida, 13201 Bruce B. Downs Blvd.,
MDC-56, Tampa, FL 33612-3805. USA; Tel: (813) 974-7046; Fax: (813)
974-4719; E-mail: jmortime @health.usf.edu.
written by the sisters in the early part of the twentieth cen-
tury, meant that we would have access to information about
the early lives of sisters who were now greater than 75 years
of age. The collaboration with Dr. Bill Markesbery, a neuro-
pathologist at the University of Kentucky, permitted system-
atic study of autopsied brains from those sisters who died
during the study.
The final piece of the puzzle was secured in 1990 when
we approached the sisters to ask them to participate in a lon-
gitudinal study of brain aging with brain donation as a re-
quirement. Despite reservations on our part in asking for this
donation, we were surprised to discover that almost two-
thirds of those approach ed agreed to particip ate in what was
to become a 15-year prospective study of a group of elderly
Catholic sisters.
The Nun Study remains as one of the few longitudinal
studies th at can link early life risk factors to declines in cog-
nitive and physical function, the incidence of dementia and
neuropathologic findings at autopsy. Confounding from a
wide variety of factors was minimized, as none of the par-
ticipants smoked, consumed alcohol heavily or had children,
and all lived in the same buildings, ate out of the same kitch-
ens, had comparable access to preventive, medical and nurs-
ing services, and had similar social networks, social supports
and religious backgrounds [4]. In addition, approximately
79% of the sisters had similar education and occupational
backgrounds, i.e., a bachelor’s degree and a teaching occupa-
tion [5].
2 Current Alzheimer Research, 2012, Vol. 9 , No. 6 James A. Mortimer
METHODS
Study Design
The source population (n=3,926) included all School
Sisters of Notre Dame who were born between 1890 and
1916 and took their vows in the United States [Fig. (1)]. Of
this population, 1,031 survived to be eligible for inclusion in
the study between 1991-1993. Sisters with a bachelor’s de-
gree were more likely to survive than those with a high
school education or less [2]. Of 1,031 eligible sisters, 678
(66%) living in communities in the midwestern, eastern and
southern United States agree to participate in all aspects of
the study. Eligibility required agreement to access of convent
archival records, annual assessment of physical and cogni-
tive function, and brain donation at death. Participants
(n=678) did not differ significantly from non-participants
(n= 353) by age, annual mortality rate, or country of birth. At
the time of their first assessment in 1991-1993, the sisters
were between 75 and 102 years of age (mean=83.3, standard
deviation = 5.5, median=82.3). Autopsied sisters were be-
tween 76 and 107 years of age at the time of their deaths
(mean=90.5, standard deviation=5.4, median=90.7). The
number of deaths in Fig. (1) includes those who withdrew
from the study before death. While the autopsy rate for all
who enrolled initially was 90.5%, for those who continued in
the study until death it was 96%.
Fig. (1). Flow chart of study showing participation and autopsy
rates.
Table 1 shows the distribution of age by educational at-
tainment in the sample of 678 Catholic sisters at the time of
enrollment in the study. Seventy-nine percent of the sisters
had received a bachelor’s degree, consistent with the main
occupation of teaching.
Cognitive and Physical Function Evaluations
Cognitive function was evaluated annually with the
CERAD neuropsychological battery [6]. This battery as-
sesses memory, concentration, language, visuospatial ability,
and orientation to time and place. Performance-based testing
was used to evaluate basic and instrumental activities of
daily living [7, 8]. In addition, participants provided self-
rated assessments of their global functional ability and health
[9]. Sisters were considered to be demented when all of the
following conditions were met: 1) impairment in memory
(defined by a score <4 on the Delayed Word Recall Test); 2)
impairment in one or more other areas of cognition (defined
by scores of <11 on Verbal Fluency, <13 on Boston Naming
or <8 on Constructional Praxis); 3) impairment in basic or
instrumental activities of daily living (defined by inability to
use a telephone, handle money, or dress oneself); and 4) evi-
dence of a decline in ability from a previous level attribut-
able to cognitive impairment. Participants were considered to
have Mild Cognitive Impairment (MCI) when they had 1)
impairment in memory or another area of cognitive function;
2) intact global cognitive function as assessed by the Mini-
Mental State Exam; 3) intact activities of daily living; and 4)
no dementia. For MCI, the cut points for impaired cognitive
test scores were set at 1.5 standard deviations below the age-
appropriate means.
Neuropathological Assessment
Gross and microscopic evaluations of the brains of par-
ticipants who died during the follow-up period of the study
were performed by a board-certified clinical neuropatholo-
gist who was blinded to diagnosis, cognitive test scores, and
functional assessments. Diffuse and neuritic plaques (NPs)
and neurofibrillary tangles (NFTs) were counted in the five
most severely affected fields of the middle frontal gyrus
(Brodmann area 9), inferior parietal lobule (areas 39/40),
middle temporal gyrus (area 21), and the CA1 and subiculum
of the hippocampus after staining with the modified
Bielschowsky method. The Gallyas stain, which is better for
detecting neuropil threads and argyrophilic grains and
slightly better for detecting NFT in medial temporal lobe
structures, was used to count the neurofibrillary pathology in
CA1 and subiculum of the hippocampus. All sections were
cut at 8-mm thickness.
To meet the study’s neuropathologic criteria for AD, par-
ticipants were required to have (1) abundant senile plaques in
the frontal, temporal, or parietal lobes, i.e., 16 or more senile
plaques per mm2; (2) NPs in at least 1 lobe; and (3) NFT in
at least 1 lobe and abundant NFT in the entorhinal cortex,
hippocampus, and amygdala. Participants meeting the
study’s neuropathologic criteria all satisfied CERAD criteria
for neuropathologic AD [10] and had a high or intermediate
likelihood of neuropathologic AD according to the National
Institute on Aging/Reagan Institute guidelines [11].
The Nun Study Current Alzheimer Research, 2012, Vol. 9, No. 6 3
Cortical and subcortical infarcts were identified at the
gross examination of the intact brain and of 1.5 cm thick
coronal sections of the cerebral hemispheres, brainstem, and
cerebellum. They were categorized as large (1.5 cm) or
lacunar (<1.5 cm). The degree of atherosclerosis in the circle
of Willis was rated in four grades from absent to severe (0-
3). Because there is no universally accepted staging of athe-
rosclerosis in the circle of Willis, the scale used reflects the
subjective impression of the study neuropathologist regard-
ing the overall average of involvement of the number of the
affected vessels at the base of the brain and the degree of
atherosclerotic depositions in these vessels. In the present
study, 13% of participants had absent to mild atherosclerosis
(plaques presen t in 0% to less than 25% of the vessel walls
of the circle of Willis), 33% moderate (25% to 50% inclu-
sive) and 54% severe (>50%).
Chronic microinfarcts were identified from slides of the
caudate nucleus, putamen, globus pallidus, thalamus, internal
capsule, frontal lobe (area 9), temporal lobe, parietal lobe,
occipital lobe (areas 18 and 19), and hippocampus. The se-
verity of amyloid angiopathy was rated from 1 (absent) to 4
(severe). The number of blood vessels containing -amyloid
by immunostaining was counted in six regions, including the
leptomeninges and the cortex of the frontal, parietal, tempo-
ral, and occipital lobes and hippocampus. When six or more
blood vessels contained amyloid in greater than 50% of the
wall in three or more brain regions and leptomeninges, it was
considered as severe. When two or more regions and lepto-
meninges had six or more affected vessels it was considered
as moderate, and when one region showed six or more af-
fected vessels it was considered as mild. If the severity was
less than this, amyloid angiopathy was considered to be ab-
sent. Amyloid angiopathy determined in this manner was
absent in 24%, mild in 43%, moderate in 5%, and severe in
28%.
Several quantitative measures were derived from the neu-
ropathologic data, including Braak neurofibrillary stage [12]
and mean numbers of cortical and regional NFT and NP.
Descriptive characteristics of the autopsied sample are
shown in (Table 2). Sixty-three percent met study criteria for
neuropathologic AD. The mean Braak neurofibrillary stage
was 3.3 (s.d.=1.8).
Table 2. Neuropathological Characteristics of the Autopsied
Sample
Neuropathological Characteristic Percent
Met Nun Study criteria for neuropathological AD 62.5
Lacunar infarcts present 32.6
Large infarcts present 17.8
Chronic microinfarcts present 24.1
Braak neurofibrillary stage 0 3.7
1 9.5
2 33.1
3 14.0
4 8.9
5 13.4
6 17.5
RESULTS
Neuropathologic data were used to address three issues:
(1) clinical-pathologic correlation, i.e., the association of
autopsy findings with clinical status at the time of death; (2)
MRI-pathologic correlation, and (3) risk factors for Alz-
heimer pathology.
Clinical-Pathologic Correlations
The Nun Study has produced several findings related to
clinical-pathologic correlations. One of the first observations
was that approximately one third of the participants meeting
neuropathologic criteria for AD at autopsy remained demen-
tia-free through their last annual cognitive assessment before
death [13]. This finding, which has been confirmed in other
studies [14, 15], suggests that while AD pathology might be
necessary for development of Alzheimer dementia, it is not
sufficient.
One of the explanations for this observation is provided
by data on the effects of brain infarcts on the risk of demen-
tia. In the Nun Study, the presence of a brain infarct, particu-
Table 1. Age and Education Distributions for Nun Study Participants at Enrollment
All Sisters Attained Bachelor’s Degree Did Not Attain Bachelor’s Degree
Age Gro up n (%) n (%) n (%)
75-79 230 (34) 195 (36) 35 (24)
80-84 220 (32) 170 (32) 50 (35)
85-89 137 (20) 105 (20) 32 (22)
90-94 68 (10) 49 (9) 19 (13)
95+ 23 (4) 15 (3) 8 (6)
All ages 678 (100) 534 (100) 144 (100)
4 Current Alzheimer Research, 2012, Vol. 9 , No. 6 James A. Mortimer
larly a subcortical lacunar infarct, greatly increased the odds
of being demented among those satisfying neuropathologic
criteria for AD [13]. In participants who did not meet neuro-
pathologic criteria for AD, those with and without brain in-
farcts differed little in their final Mini-Mental State Exami-
nation scores and scores on most other cognitive tests, sug-
gesting that the presence of infarcts alone has relatively little
effect on cognition. Also, in this group the prevalence of
dementia was almost the same in individuals with and with-
out infarcts (7% and 8%, respectively), providing little sup-
port for the concept of pure vascular dementia. Indeed, vas-
cular dementia was very rare among the Catholic sisters de-
spite a high rate of vascular lesions. In 118 participants with
dementia, only 3 (2.5%) had neuropathologic findings con-
sistent with this diagnosis [16]. Despite the poor association
between infarcts and cognitive test scores among those with
little Alzheimer pathology [13], additional studies revealed
that functional status is somewhat compromised in those
with infarcts alone, but not to the extent seen in those with
neuropathologic AD [17].
Another important observation is that AD neuropathol-
ogy occurred independently of vascular pathology. Analyses
of cognitive outcomes provided support for an additive inter-
action of these two types of pathology [13]. Similar findings
have been reported in other autopsy studies [18, 19].
The specificity of the association between Alzheimer
neuropathology and clinical state was explored in a group of
autopsied sisters who did not have vascular or other pathol-
ogy that could explain cognitive impairment [20]. Although
there was a strong relationship between Braak neurofibrillary
stage and cognitive state (normal, Mild Cognitive Impair-
ment, Global Cognitive Impairment, dementia), there was
considerable overlap in groups, with some of those with low
Braak stages showing substantial cognitive impairment while
others with high Braak stages showed only mild impairment.
The presence of memory impairment was associated with
higher Braak stage as well as with higher incidence of
conversion to dementia in groups classified as having mild or
global cognitive impairment. In addition to Braak neurofi-
brillary stage, atrophy of the neocortex was significantly
associated with the presence of dementia before death.
Finally, based on a study of brains from the Nun Study,
Iacono et al. [21] reported that increased neuronal size in the
CA1 region of the hippocampus might help to explain the
presence of participants fulfilling criteria for neuropathologic
AD who did not express dementia symptoms during life.
MRI-Pathologic Correlations
Using postmortem MRI, the Nun Study was the first
study to show a strong correlation between hippocampal
volume and Braak neurofibrillary stage (r=-0.71, p<.001,
controlling for age at death) [22]. Among cognitively intact
subjects, those in Braak stage II could be distinguished from
those in stage I or 0 on the basis of hippocampal volume,
suggesting that this MRI index may be useful in distinguish-
ing very early stages of preclinical Alzheimer’s disease [23].
Subsequent studies by other investigators [24-27], most
based on pathologic correlation with pre-mortem scans [24-
26], reported correlations ranging from 0.39 to 0.80 between
hippocampal volume and hippocampal NFT burden or Braak
stage. Additional analyses of data from the Nun Study
showed that hippocampal volume was strongly associated
with fulfillment of study criteria for neuropathologic AD
even among sisters with normal cognitive function (p=.003)
[23]. In individuals who remained nondemented, hippocam-
pal volume also was a better indicator of AD neuropathology
than a delayed memory measure. Among non-demented sis-
ters, Braak stages III and VI were distinguishable from
Braak stages II or lower (p <0.001). Among cognitively in-
tact individuals, those in Braak stage II could be distin-
guished from those in stage I or less (p < 0.025). Volumetric
measures of the hippocampus therefore may be useful in
identifying non-demented individuals who satisfy neuropa-
thologic criteria for AD or advanced pathologic stages of AD
that may be present long before clinical expression. Subse-
quent analyses showed that hippocampal volume mediates
the association between Alzheimer neuropathology and defi-
cits in delayed verbal recall [28].
Risk Factors for Pathology
We have proposed that there are two distinct set of risk
factors for dementia: (1) those for the underlying pathology
and (2) those for its clinical expression [29, 30]. The Nun
Study with its extensive archival data is ideally suited to
identification of early life risk factors for brain pathology,
and in particular Alzheimer neuropathology.
The first risk factor for Alzheimer pathology discovered
in the Nun Study was unique and suggested that the origins
of this pathology may date to early adulthood [4]. To deter-
mine whether initial brain or cognitive reserve delayed onset
of dementia, we examined characteristics of autobiographical
essays written by the sisters when they took their final vows
at any average age of 22. Our initial expectation was that
better linguistic function would be a marker for cognitive
ability, which could buffer the effects of underlying brain
pathology through increased reserve. Each sister was asked
to “write a short sketch of her own life. This account should
not contain more than two to three hundred words and
should be written on a single sheet of paper..” We investi-
gated two linguistic measures derived from 93 handwritten
essays written by sisters during the 1930’s, idea density and
grammatical complexity. Idea density was defined as the
average number of ideas expressed per 10 words and had
been shown in previous work to be associated with educa-
tional level, vocabulary and general knowledge. Grammati-
cal complexity reflected the structure of sentences, ranging
from simple one-clause sentences to complex sentences with
multiple forms of embedding and subordination. Previous
work showed that it was associated with working memory
and performance on speeded tasks. The essays were coded
by an expert in linguistic function at the University of Kan-
sas; cognitive data were collected by the study in the field;
and neuropathologic assessment was performed independ-
ently. In all cases, ratings of each type of data were done
blind to the other assessments.
In the initial publication on linguistic function, idea den-
sity and grammatical complexity were shown to be inde-
pendent predictors of changes in MMSE scores 60 years
later, controlling for age and educational attainment [4].
When performance in the bottom quartile of MMSE scores
The Nun Study Current Alzheimer Research, 2012, Vol. 9, No. 6 5
adjusted for age and education was used as the outcome,
sisters with idea density scores in the lowest tertile had over
30 times the odds of having poor MMSE performance in late
life compared to those in the upper two tertiles of this meas-
ure (OR=30.8, 95% CI: 2.6-362.7). Grammatical complexity
showed a somewhat weaker, though still very strong associa-
tion (OR=16.6, 95% CI: 2.0-130.9). The strength of these
associations were remarkab le, given the fact that the two
measures were obtained 60 years apart. Even more remark-
able, one of these measures, idea density had a very strong
association with the mean number of neurofibrillary tangles
per 0.586 mm2 in the hippocampus and neocortex adjusted
for age at death and years of education. In addition, sisters
who had low idea density were almost 60 times more likely
to have neuropathologic AD compared to those with high
idea density. Of substantial interest, despite its associatio n
with poor cognitive performance, grammatical complexity
was not related to the severity of Alzheimer neuropathology
later in life.
Subsequent publications from the Nun Study reported
findings based on a larger sample size [31] and examined the
association between the linguistic measures and vascular
function [31, 32]. Despite its association with Alzheimer
pathology, idea density was not related to the presence of
large or lacunar infarcts or to the degree of atherosclerosis in
the circle of Willis [31, 32]. The specificity of the associa-
tion of the severity of Alzheimer neuropathology with idea
density, but not with vascular pathology and the lack of as-
sociation of grammatical complexity with Alzheimer’s neu-
ropathology suggests that idea density could serve as a pre-
clinical marker of pathological Alzheimer’s disease in early
adulthood.
The 4 allele of apolipoprotein E (APOE) is an important
risk factor for dementia [33] and AD [33-36]. However, its
association with Alzheimer and vascular neuropathology is
controversial. Autopsy-based studies have demonstrated sig-
nificant correlations between the 4 allele and the density of
NPs [37-39], NFT [38, 40-42] and amyloid deposition [40-
45], but some studies did not find an association with
plaques [46-48] or NFT [37, 43, 46, 48, 49] Two studies [50,
51] reported that the frequency of cerebrovascular lesions
was not increased in APOE-4, whereas another group [52]
reported that APOE-4 significantly increased the odds of
both cortical and subcortical infarctions.
We examined the association of APOE-4 with both vas-
cular and Alzheimer neuropathology in the Nun Study [53].
Although those with one or more 4 alleles had higher mean
counts of neocortical NFT, higher mean counts of neocorti-
cal NPs and higher ratings of the severity of amyloid an-
giopathy, we did not find a statistically significant associa-
tion of APOE-4 with the presence of large infarcts or lacu-
nar infarcts, th e degree of atherosclerosis in the circle of
Willis or the presence of chronic microinfarcts. Addition of
Alzheimer neuropathology to a model predicting dementia
greatly reduced the effect of APOE-4, while addition of
vascular pathology had no effect on the association with
APOE-4, suggesting that the effect of 4 on dementia is
mediated by the severity of AD pathology. Although infarcts
and atherosclerosis contribute to the occurrence of dementia,
this contribution appears to be unrelated to APOE genotype.
Our findings are consistent with those from the Religious
Orders Study, which reported that a global index of Alz-
heimer pathology mediated the effect of APOE-4 on de-
mentia [54]. These investigators also did not find a signifi-
cant mediation of chronic infarcts in the association between
APOE-4 and global cognition [55].
Finally, dementia is characterized by global atrophy. The
Nun Study provided the first evidence that lower serum fo-
late can contribute to greater atrophy, especially in partici-
pants with substantial Alzheimer neuropathology [56]. The
presence of this association in the absence of significant
cerebrovascular pathology suggests that folate may be acting
as a growth factor providing compensation for brain damage.
Risk Factors for Clinical Expression are not Associated
with Neuropathology
In the Nun Study, we found that a combination of small
head circumference and lower attained education greatly
increased the risk of dementia, consistent with previous stud-
ies showing associations of these reserve measures with the
risk of dementia and cognitive decline [57]. However, nei-
ther of these risk factors was associated with the severity of
Alzheimer neuropathology.
Other Risk Factors are not Associated with Neuropa-
thology
A study of tooth loss in the Catholic sisters showed a
significant association between the degree of loss of non-
third molars and the incidence of dementia [58]. However,
there was no association with either Alzheimer disease neu-
ropathology or with the presence of brain infarcts, and the
non-third molar loss also lacked an association with APOE-
4. The association with tooth loss w ith incident demen tia in
this study remains unexplained, but could be associated with
early life brain growth related to socio-economic status [30].
CONCLUSION
The Nun Study was the first cohort study to enroll and
follow a large, well-defined population of participants, all of
whom agreed to donate their brains for research. The impor-
tance of studying a sample without significant selection bias
cannot be overstated. Although many autopsy studies have a
high response rate among those with dementia, participation
selection bias among those without dementia may lead to
omission of non-demented individuals with marked neuropa-
thology. The underrepresentation of these individuals would
tend to produce a stronger clinical-pathologic correlation by
focusing on those in the extremes, neglecting those in the
middle where more overlap is evident.
The inclusion of systematic neuropathologic analysis in
the Nun Study has resulted in a greater understanding of the
role of Alzheimer and vascular pathology in the expression
of memory deficits and dementia and has provided data
showing that biomarkers for the pathology may be evident
many decades earlier in adult life. The latter finding is par-
ticularly significant to our attempts to prevent AD, as it sug-
gests that we may be able to identify individuals at high risk
of this outcome not years, but rather decades before the first
6 Current Alzheimer Research, 2012, Vol. 9 , No. 6 James A. Mortimer
symptoms appear, at a time when intervention would likely
be more successful.
The findings from the Nun Study demonstrate the distinct
nature of risk factors for Alzheimer pathology as compared
with risk factors for its clinical expression. An understanding
of the roles played by Alzheimer, vascular and Lewy body
disease in the expression of dementia can only be obtained
through studies in which the neuropathologic substrate can
be studied carefully in individuals who are followed during
life. How the different pathologies interact with each other
and with cognitive and brain reserve, and which are most
important for prevention are central questions that underlie
our search for an effective way to prevent dementia.
ACKNO WLED GMEN TS
This study was supported by grants R01-AG09862 (Dr.
Snowdon), P50-AG025711 (Dr. Mortimer), and P30-
AG028383 (Dr. Markesbery) from the National Institute on
Aging, Bethesda, MD. It would not have been possible with-
out the spirited support of the members, leaders, and health
care providers of the School Sisters of Notre Dame religious
congregation, as well as the contributions of the many inves-
tigators and staff who participated in the Nun Study over its
20-year course.
CONFLICT OF INTEREST
None declared.
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Received: ????????????? Revised: ????????????? Accepted: ?????????????
